0.07/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.14/0.34 % Computer : n007.cluster.edu 0.14/0.34 % Model : x86_64 x86_64 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.34 % Memory : 8042.1875MB 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.34 % CPULimit : 1440 0.14/0.34 % WCLimit : 180 0.14/0.34 % DateTime : Mon Jul 3 11:54:13 EDT 2023 0.14/0.34 % CPUTime : 1.48/1.69 ============================== Prover9 =============================== 1.48/1.69 Prover9 (32) version 2009-11A, November 2009. 1.48/1.69 Process 30941 was started by sandbox2 on n007.cluster.edu, 1.48/1.69 Mon Jul 3 11:54:14 2023 1.48/1.69 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1440 -f /tmp/Prover9_30650_n007.cluster.edu". 1.48/1.69 ============================== end of head =========================== 1.48/1.69 1.48/1.69 ============================== INPUT ================================= 1.48/1.69 1.48/1.69 % Reading from file /tmp/Prover9_30650_n007.cluster.edu 1.48/1.69 1.48/1.69 set(prolog_style_variables). 1.48/1.69 set(auto2). 1.48/1.69 % set(auto2) -> set(auto). 1.48/1.69 % set(auto) -> set(auto_inference). 1.48/1.69 % set(auto) -> set(auto_setup). 1.48/1.69 % set(auto_setup) -> set(predicate_elim). 1.48/1.69 % set(auto_setup) -> assign(eq_defs, unfold). 1.48/1.69 % set(auto) -> set(auto_limits). 1.48/1.69 % set(auto_limits) -> assign(max_weight, "100.000"). 1.48/1.69 % set(auto_limits) -> assign(sos_limit, 20000). 1.48/1.69 % set(auto) -> set(auto_denials). 1.48/1.69 % set(auto) -> set(auto_process). 1.48/1.69 % set(auto2) -> assign(new_constants, 1). 1.48/1.69 % set(auto2) -> assign(fold_denial_max, 3). 1.48/1.69 % set(auto2) -> assign(max_weight, "200.000"). 1.48/1.69 % set(auto2) -> assign(max_hours, 1). 1.48/1.69 % assign(max_hours, 1) -> assign(max_seconds, 3600). 1.48/1.69 % set(auto2) -> assign(max_seconds, 0). 1.48/1.69 % set(auto2) -> assign(max_minutes, 5). 1.48/1.69 % assign(max_minutes, 5) -> assign(max_seconds, 300). 1.48/1.69 % set(auto2) -> set(sort_initial_sos). 1.48/1.69 % set(auto2) -> assign(sos_limit, -1). 1.48/1.69 % set(auto2) -> assign(lrs_ticks, 3000). 1.48/1.69 % set(auto2) -> assign(max_megs, 400). 1.48/1.69 % set(auto2) -> assign(stats, some). 1.48/1.69 % set(auto2) -> clear(echo_input). 1.48/1.69 % set(auto2) -> set(quiet). 1.48/1.69 % set(auto2) -> clear(print_initial_clauses). 1.48/1.69 % set(auto2) -> clear(print_given). 1.48/1.69 assign(lrs_ticks,-1). 1.48/1.69 assign(sos_limit,10000). 1.48/1.69 assign(order,kbo). 1.48/1.69 set(lex_order_vars). 1.48/1.69 clear(print_given). 1.48/1.69 1.48/1.69 % formulas(sos). % not echoed (1284 formulas) 1.48/1.69 1.48/1.69 ============================== end of input ========================== 1.48/1.69 1.48/1.69 % From the command line: assign(max_seconds, 1440). 1.48/1.69 1.48/1.69 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 1.48/1.69 1.48/1.69 % Formulas that are not ordinary clauses: 1.48/1.69 1 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_da(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uua),Uub)),Uu)))) # label(fact_ATP_Olambda__579) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 2 (all Uu all Uua (pp(scratc1115724827_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,Uua),scratc282061419nd_n_1)),Uu),aa_fun171081125l_bool(scratc540698651_n_all,aa_TPT43085870d_bool(aTP_Lamm_ao(Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sz,Uu),Uua)))) # label(fact_ATP_Olambda__268) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 3 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_ul(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_um,Uu),Uua)))) # label(fact_ATP_Olambda__377) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 4 (all X aa_TPTP_ind_TPTP_ind(scratc294253259_proj0,X) = aa_fun277296641TP_ind(scratc460841235eplSep(X,aTP_Lamm_bu),scratc1016586773_d_Unj)) # label(fact_def__proj0) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 5 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ds,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_dr,Uu))))) # label(fact_ATP_Olambda__226) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 6 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1133920905_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,aa_TPTP_ind_TPTP_ind(scratc294253260_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc294253259_proj0,X22)))) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,aa_TPTP_ind_TPTP_ind(scratc294253259_proj0,X22)),X0)) & aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1860414882d_pair,aa_TPTP_ind_TPTP_ind(scratc294253259_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc294253260_proj1,X22)) = X22))) # label(fact_k__Sigma__eta__proj0__proj1) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 7 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X22),X0)) -> aa_TPTP_ind_TPTP_ind(X12,X22) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1133920905_Sigma,X0),X12)),X22))) # label(fact_beta) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 8 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_te,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_td,Uu))))) # label(fact_ATP_Olambda__99) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 9 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_vo,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_vn,Uu))))) # label(fact_ATP_Olambda__80) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 10 (all X aa_TPTP_ind_TPTP_ind(scratc1952078626d_plus,X) = scratc1879612791nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1719206485d_d_Pi,scratc1920067545nd_nat),aTP_Lamm_al),aa_TPT43085870d_bool(scratc1087267889_prop2,X))) # label(fact_def__plus) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 11 (all Uu (gg_TPTP_ind(Uu) -> ((exists X2 (gg_TPTP_ind(X2) & Uu = aa_TPTP_ind_TPTP_ind(scratc488888935d_Inj0,X2))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))))) # label(fact_ATP_Olambda__249) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 12 (all X all Xa (pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1879547204nd_imp,X),scratc1223190007_d_not(Xa))) <-> pp(scratc99680130d_l_ec(X,Xa)))) # label(fact_def__l__ec) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 13 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uu)),scratc282061419nd_n_1)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ts,Uu)))) # label(fact_ATP_Olambda__15) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 14 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_abk,Uu)) <-> scratc2128269225_is_of(aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uu),aTP_Lamm_lc))) # label(fact_ATP_Olambda__14) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 15 (all Uu scratc1920067545nd_nat = aa_TPTP_ind_TPTP_ind(aTP_Lamm_al,Uu)) # label(fact_ATP_Olambda__740) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 16 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kr,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_kq(Uu),Uua))))) # label(fact_ATP_Olambda__426) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 17 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_mi,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_mh,Uu))))) # label(fact_ATP_Olambda__161) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 18 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zg,Uu),Uua)))) # label(fact_ATP_Olambda__292) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 19 (all X0 (gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(scratc2014913431_nat_p,X0)) -> (exists X13 (gg_TPTP_ind(X13) & pp(aa_TPTP_ind_bool(scratc2014913431_nat_p,X13)) & X0 = aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,X13))) | X0 = scratc1169782717ptyset))) # label(fact_nat__inv) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 20 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vg(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__500) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 21 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_yz,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_yy,Uu))))) # label(fact_ATP_Olambda__49) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 22 (all Uu all Uua all Uub all Uuc (gg_TPTP_ind(Uuc) & gg_TPTP_ind(Uub) & gg_TPTP_ind(Uua) -> (-pp(Uu) & Uub = Uuc | Uua = Uuc & pp(Uu) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ca(Uu),Uua),Uub),Uuc))))) # label(fact_ATP_Olambda__669) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 23 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_nn,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_nm,Uu))))) # label(fact_ATP_Olambda__148) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 24 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ez(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fa,Uu),Uua)))) # label(fact_ATP_Olambda__466) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 25 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_abs(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc712927111d_e_is(Uu),aa_TPTP_ind_TPTP_ind(scratc1226053384_first(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc759553526d_pair(Uu,Uua),Uub),Uuc))),Uub)))) # label(fact_ATP_Olambda__658) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 26 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bm(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,Uub),Uu)) & pp(aa_TPTP_ind_bool(Uua,Uub)))) # label(fact_ATP_Olambda__578) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 27 (all P all Q all R aa_bool_bool(aa_TPT2142672771l_bool(P,R),aa_TPTP_ind_bool(Q,R)) = aa_TPTP_ind_bool(cOMBS_2003118649l_bool(P,Q),R)) # label(help_COMBS_1_1_COMBS_001t__TPTP____Interpret__Oind_001t__HOL__Obool_001t__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 28 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_aau,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_aav,Uu)))) # label(fact_ATP_Olambda__29) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 29 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,X0) = aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,X12) -> X12 = X0))) # label(fact_ordsucc__inj) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 30 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X22),X0)) -> (pp(aa_TPTP_ind_bool(X12,X22)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X22),aa_fun1431113780TP_ind(scratc999473378_d_Sep(X0),X12)))))) # label(fact_k__SepI) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 31 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ui,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_uh(Uu),Uua))))) # label(fact_ATP_Olambda__378) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 32 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rd,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_rc(Uu),Uua))))) # label(fact_ATP_Olambda__392) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 33 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_aca(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1183411315_image(aa_fun1431113780TP_ind(scratc999473378_d_Sep(Uu),Uua),Uu),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1133920905_Sigma,aa_fun1431113780TP_ind(scratc999473378_d_Sep(Uu),Uua)),scratc712927106d_e_in(Uu,Uua))),Uub))))) # label(fact_ATP_Olambda__581) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 34 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kb(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__558) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 35 (all X all Xa scratc460841235eplSep(X,Xa) = aa_TPT494704832TP_ind(scratc1307610839d_repl,aa_fun1431113780TP_ind(scratc999473378_d_Sep(X),Xa))) # label(fact_def__d__ReplSep) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 36 (all X all Xa all Xb (pp(aa_bool_bool(scratc100336135d_l_or(X),aa_bool_bool(scratc100336135d_l_or(Xa),Xb))) <-> pp(scratc1929444168nd_or3(X,Xa,Xb)))) # label(fact_def__or3) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 37 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ay(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aa_TPT43085870d_bool(aTP_Lamm_au,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_ax(Uu),Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__732) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 38 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rq(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uub),Uua)))))) # label(fact_ATP_Olambda__562) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 39 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ye(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__545) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 40 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_un,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_um,Uu))))) # label(fact_ATP_Olambda__88) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 41 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_lb,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_la,Uu))))) # label(fact_ATP_Olambda__168) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 42 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fj(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uua),Uuc))))))) # label(fact_ATP_Olambda__714) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 43 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1920592336nd_nis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1920592336nd_nis,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aab(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__570) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 44 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_tt,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,Uu),scratc282061419nd_n_1)))) # label(fact_ATP_Olambda__23) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 45 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_pa(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uua),Uuc))))))) # label(fact_ATP_Olambda__676) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 46 (all X all Xa scratc22673458d_soft(aa_fun1431113780TP_ind(scratc999473378_d_Sep(X),Xa),X,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1133920905_Sigma,aa_fun1431113780TP_ind(scratc999473378_d_Sep(X),Xa)),scratc712927106d_e_in(X,Xa))) = scratc1929641030nd_out(X,Xa)) # label(fact_def__out) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 47 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_rw(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rx,Uu),Uua)))) # label(fact_ATP_Olambda__386) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 48 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_tn,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_to,Uu)))) # label(fact_ATP_Olambda__94) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 49 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_qa,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_qb,Uu)))) # label(fact_ATP_Olambda__125) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 50 (all X (pp(aa_TPTP_ind_bool(scratc215026647closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X1),X)) -> (all X2 ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X3),X1)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,aa_TPTP_ind_TPTP_ind(X2,X3)),X))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1307610839d_repl,X1),X2)),X))))))))) # label(fact_def__d__Repl__closed) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 51 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_uk(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ul(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__601) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 52 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1593616289lbprop(X),Xa),Xb)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1879547204nd_imp,aa_TPTP_ind_bool(X,Xb)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,Xa),Xb))))) # label(fact_def__lbprop) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 53 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(X),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Xa),Xb))),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(X),Xb)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc14224249_prop1(X),Xa),Xb)))) # label(fact_def__d__430__prop1) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 54 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> -pp(X0) & aa_TPTP_ind_TPTP_ind(scratc102755877bnd_if(X0,X12),X22) = X22 | X12 = aa_TPTP_ind_TPTP_ind(scratc102755877bnd_if(X0,X12),X22) & pp(X0))) # label(fact_if__i__correct) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 55 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,Uua),aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uu)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tn,Uu),Uua)))) # label(fact_ATP_Olambda__285) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 56 (all X all Xa (pp(aa_bool_bool(scratc100336135d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706324_moreq,X),Xa)))) # label(fact_def__moreq) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 57 (all X0 all X12 all X22 all X32 (pp(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc102755877bnd_if(X0,X22),X32))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X12),X22))))) # label(fact_k__If__In__then__E) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 58 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_dv,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_dw,Uu)))) # label(fact_ATP_Olambda__225) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 59 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_tk,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_tj,Uu))))) # label(fact_ATP_Olambda__96) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 60 (all X scratc100336135d_l_or(X) = aa_boo1142376798l_bool(scratc1879547204nd_imp,scratc1223190007_d_not(X))) # label(fact_def__l__or) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 61 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gn(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uu),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uua),Uub))),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uu),Uub)))))) # label(fact_ATP_Olambda__526) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 62 (all X (pp(aa_TPTP_ind_bool(scratc335317087closed,X)) & pp(aa_TPTP_ind_bool(scratc500050101closed,X)) & pp(aa_TPTP_ind_bool(scratc215026647closed,X)) <-> pp(aa_TPTP_ind_bool(scratc775647028closed,X)))) # label(fact_def__d__ZF__closed) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 63 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xz,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_xy(Uu),Uua))))) # label(fact_ATP_Olambda__351) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 64 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_xw,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_xx,Uu)))) # label(fact_ATP_Olambda__61) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 65 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mv(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_mu(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__620) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 66 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qd,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_qc(Uu),Uua))))) # label(fact_ATP_Olambda__400) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 67 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uuc),Uua))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_qx(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__707) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 68 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_pw,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_px,Uu)))) # label(fact_ATP_Olambda__126) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 69 (all X all Xa (pp(scratc1223190007_d_not(scratc99680130d_l_ec(X,Xa))) <-> pp(scratc1115724827_d_and(X,Xa)))) # label(fact_def__d__and) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 70 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ah(Uu),Uua),Uub),Uuc) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,Uub),aa_TPTP_ind_TPTP_ind(scratc1637978109eft1to(Uu,Uua),Uuc))) # label(fact_ATP_Olambda__729) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 71 (all Uu all Uua all Uub (scratc2128269225_is_of(aa_TPTP_ind_TPTP_ind(scratc712927106d_e_in(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_au,Uu)) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_acd(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__494) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 72 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_aam,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_aal,Uu))))) # label(fact_ATP_Olambda__32) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 73 (all X all Xa ((pp(X) -> pp(scratc1223190007_d_not(Xa))) <-> scratc494614920d_r_ec(X,Xa))) # label(fact_def__r__ec) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 74 (all B_1 all B_2 gg_bool(aa_bool_bool(B_1,B_2))) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 75 (all Uu all Uua all Uub (scratc2128269225_is_of(aa_TPTP_ind_TPTP_ind(scratc1738843356second(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_au,Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abw(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__492) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 76 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc1929181822nd_one(X0),X12)) -> pp(aa_TPTP_ind_bool(X12,scratc1879612791nd_ind(X0,X12))))) # label(fact_oneax) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 77 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_tm,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_tl,Uu))))) # label(fact_ATP_Olambda__95) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 78 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_nw,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_nx,Uu)))) # label(fact_ATP_Olambda__145) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 79 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_abq(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc712927111d_e_is(Uua),aa_TPTP_ind_TPTP_ind(scratc1738843356second(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc759553526d_pair(Uu,Uua),Uub),Uuc))),Uuc)))) # label(fact_ATP_Olambda__659) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 80 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,Uua),aa_TPTP_ind_TPTP_ind(scratc165739421_power,Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abl,Uu),Uua)))) # label(fact_ATP_Olambda__338) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 81 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1719206485d_d_Pi,X),Xa) = aa_fun1431113780TP_ind(scratc999473378_d_Sep(aa_TPTP_ind_TPTP_ind(scratc165739421_power,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1133920905_Sigma,X),aTP_Lamm_bp(Xa)))),aa_fun1913827119d_bool(aTP_Lamm_bq(X),Xa))) # label(fact_def__d__Pi) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 82 (all P all Q all R aa_TPT2142672771l_bool(cOMBB_658106424TP_ind(P,Q),R) = aa_boo1142376798l_bool(P,aa_TPTP_ind_bool(Q,R))) # label(help_COMBB_1_1_COMBB_001t__HOL__Obool_001t__fun_It__HOL__Obool_Mt__HOL__Obool_J_001t__TPTP____Interpret__Oind_U) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 83 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fj(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fk(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__639) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 84 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_rm,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_rl,Uu))))) # label(fact_ATP_Olambda__114) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 85 (all X all Xa all Xb all Xc all Xd scratc383083951indeq2(X,Xa,Xb,Xc,Xd) = aa_TPT1424761345TP_ind(scratc1988651843_indeq(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213220141d_11_i(X,Xa,Xb),Xc),Xd))) # label(fact_def__indeq2) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 86 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fr(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fs(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__637) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 87 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_op,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_oo,Uu))))) # label(fact_ATP_Olambda__133) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 88 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1880006386nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc712927111d_e_is(X),Xc),Xb),X,Xa),aa_TPTP_ind_TPTP_ind(scratc1984233995sel_wa(X,Xa,Xb),Xc)) = aa_TPTP_ind_TPTP_ind(scratc1984233996sel_wb(X,Xa,Xb),Xc)) # label(fact_def__wissel__wb) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 89 (all X all Xa all Xb (pp(scratc1115724827_d_and(scratc1929444168nd_or3(X,Xa,Xb),scratc1845845133nd_ec3(X,Xa,Xb))) <-> scratc1219098378_orec3(X,Xa,Xb))) # label(fact_def__orec3) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 90 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1920592336nd_nis,aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uu)),scratc282061419nd_n_1)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_abj,Uu)))) # label(fact_ATP_Olambda__16) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 91 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706324_moreq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ih(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__690) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 92 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_zz,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_aaa,Uu)))) # label(fact_ATP_Olambda__37) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 93 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abz(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aa_TPT43085870d_bool(aTP_Lamm_au,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aby(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__585) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 94 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_aah,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_aag,Uu))))) # label(fact_ATP_Olambda__34) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 95 (all Uu ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1920592336nd_nis,Uu),scratc282061419nd_n_1)) -> pp(aa_fun171081125l_bool(scratc493910842n_some,aa_TPT43085870d_bool(aTP_Lamm_ar,Uu)))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_aba,Uu)))) # label(fact_ATP_Olambda__1) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 96 (all Uu all Uua ((pp(scratc1223190007_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ym,Uu),Uua)))) # label(fact_ATP_Olambda__325) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 97 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_lz,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ly,Uu))))) # label(fact_ATP_Olambda__164) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 98 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_ua,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ub,Uu)))) # label(fact_ATP_Olambda__91) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 99 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abf,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587467d_n_in,Uua),Uu)))) # label(fact_ATP_Olambda__342) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 100 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_aaz,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1920592336nd_nis,Uu),scratc282061419nd_n_1)) -> pp(aa_fun171081125l_bool(scratc656490912_n_one,aa_TPT43085870d_bool(aTP_Lamm_ar,Uu)))))) # label(fact_ATP_Olambda__2) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 101 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sc(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uua),Uub)))))) # label(fact_ATP_Olambda__530) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 102 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_tq,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_tp,Uu))))) # label(fact_ATP_Olambda__93) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 103 (all X scratc1245779368d_outn(X) = scratc1929641030nd_out(scratc1920067545nd_nat,aa_TPT43085870d_bool(aTP_Lamm_ak,X))) # label(fact_def__outn) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 104 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_zv,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_zu,Uu))))) # label(fact_ATP_Olambda__39) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 105 (all X all Xa all Xb (pp(scratc1115724827_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc409976095ective(X),Xa),Xb),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1580609604ective(X),Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc593695325ective(X),Xa),Xb)))) # label(fact_def__bijective) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 106 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc231390674d_n_fr,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1921379518nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc1921379518nd_num,Xa))),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1837714885nd_den,X)),aa_TPTP_ind_TPTP_ind(scratc1837714885nd_den,Xa))) = aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(X),Xa)) # label(fact_def__n__tf) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 107 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xy(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__539) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 108 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_el,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_em,Uu)))) # label(fact_ATP_Olambda__221) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 109 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ix,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_iw(Uu),Uua))))) # label(fact_ATP_Olambda__440) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 110 (all X all Xa all Xb all Xc all Xd scratc1879612791nd_ind(Xb,aa_TPT43085870d_bool(scratc294646855_prop2(X,Xa,Xb,Xc),Xd)) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1988651843_indeq(X,Xa,Xb),Xc),Xd)) # label(fact_def__indeq) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 111 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ii(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ih(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__629) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 112 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tl,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uua),scratc282061419nd_n_1)),Uu))))) # label(fact_ATP_Olambda__279) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 113 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aai(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__522) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 114 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dq(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dp(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__646) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 115 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(scratc102755877bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,scratc1169782717ptyset),Uub),Uu),Uua) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_bz(Uu),Uua),Uub)) # label(fact_ATP_Olambda__487) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 116 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wx(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__564) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 117 (all B_1 gg_TPTP_ind(scratc1846697984nd_eps(B_1))) # label(gsy_c_Scratch__tptp__translate__63417__16348_ONUM788__thf__4__p_Obnd__eps) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 118 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1920592336nd_nis,Xa),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc704870765_prop1,X),Xa)))) # label(fact_def__d__27__prop1) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 119 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_pi(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uua),Uuc))))))) # label(fact_ATP_Olambda__680) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 120 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dd(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_de(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__649) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 121 (all P all X7 (-pp(aa_TPTP_ind_bool(P,X7)) | pp(fEx_TPTP_ind(P)))) # label(help_fEx_1_1_fEx_001t__TPTP____Interpret__Oind_U) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 122 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_rb(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__706) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 123 (all Uu all Uua (gg_TPTP_ind(Uu) -> aa_TPTP_ind_TPTP_ind(aTP_Lamm_aj(Uu),Uua) = Uu)) # label(fact_ATP_Olambda__738) # label(axiom) # label(non_clause). [assumption]. 1.48/1.69 124 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aby(Uu),Uua),Uub),Uuc)) <-> scratc2128269225_is_of(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc759553526d_pair(Uu,Uua),Uub),Uuc),aa_TPT43085870d_bool(aTP_Lamm_abu(Uu),Uua)))) # label(fact_ATP_Olambda__663) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 125 (all Q all P (pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) | -pp(Q))) # label(help_fimplies_2_1_U) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 126 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706324_moreq,Uu),Uua)) -> pp(scratc1223190007_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nm,Uu),Uua)))) # label(fact_ATP_Olambda__311) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 127 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_gt,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_gu,Uu)))) # label(fact_ATP_Olambda__202) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 128 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ko,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_kn(Uu),Uua))))) # label(fact_ATP_Olambda__427) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 129 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_rv,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_ru,Uu))))) # label(fact_ATP_Olambda__111) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 130 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_a,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,Uu),scratc1953113565nd_rat)))) # label(fact_ATP_Olambda__25) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 131 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_jz,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ka,Uu)))) # label(fact_ATP_Olambda__178) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 132 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc599574102fixfu2(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aa_TPT43085870d_bool(aTP_Lamm_au,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ay(X),Xa),Xb),Xc))))) # label(fact_def__fixfu2) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 133 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ww,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_wv,Uu))))) # label(fact_ATP_Olambda__70) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 134 (all X (pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1879547204nd_imp,X),fFalse)) <-> pp(scratc1223190007_d_not(X)))) # label(fact_def__d__not) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 135 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uu),Uu)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ov,Uu)))) # label(fact_ATP_Olambda__22) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 136 (all X0 (pp(aa_TPTP_ind_bool(scratc2014913431_nat_p,X0)) -> pp(aa_TPTP_ind_bool(scratc2014913431_nat_p,aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,X0))))) # label(fact_nat__ordsucc) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 137 (all X0 all X12 pp(aa_fun171081125l_bool(scratc639425392all_of(aa_TPT43085870d_bool(aTP_Lamm_abu(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_abw(X0),X12)))) # label(fact_second__p) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 138 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_en(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uu),Uua))))) # label(fact_ATP_Olambda__506) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 139 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jl(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jm(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__626) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 140 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fo(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fn(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__638) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 141 (all X all Xa (pp(aa_fun171081125l_bool(scratc540698651_n_all,aa_TPT43085870d_bool(aTP_Lamm_ao(X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1179442032_prop1,X),Xa)))) # label(fact_def__d__428__prop1) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 142 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_vg(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vh,Uu),Uua)))) # label(fact_ATP_Olambda__371) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 143 (all X all Xa all Xb all Xc scratc1879612791nd_ind(X,aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bj(Xa),Xb),Xc)) = aa_TPTP_ind_TPTP_ind(scratc22673458d_soft(X,Xa,Xb),Xc)) # label(fact_def__soft) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 144 (all X scratc2013318955d_esti(X) = scratc102755885bnd_in) # label(fact_def__esti) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 145 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_sf(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sg,Uu),Uua)))) # label(fact_ATP_Olambda__383) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 146 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_df,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_de(Uu),Uua))))) # label(fact_ATP_Olambda__479) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 147 (all X0 all X12 (gg_TPTP_ind(X12) -> X12 = aa_TPTP_ind_TPTP_ind(scratc294253260_proj1,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1860414882d_pair,X0),X12)))) # label(fact_proj1__pair__eq) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 148 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hk(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hj(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__635) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 149 (all Uu all Uua aa_TPTP_ind_TPTP_ind(scratc381596720nunion(aa_TPTP_ind_TPTP_ind(scratc1811264907d_Sing,scratc1169782717ptyset)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1307610839d_repl,Uu),Uua)) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(aTP_Lamm_bw,Uu),Uua)) # label(fact_ATP_Olambda__332) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 150 (all X all Xa aa_fun1431113780TP_ind(scratc999473378_d_Sep(aa_TPTP_ind_TPTP_ind(scratc165739421_power,X)),scratc996162291d_anec(X,Xa)) = scratc1845845198nd_ect(X,Xa)) # label(fact_def__ect) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 151 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hp,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ho(Uu),Uua))))) # label(fact_ATP_Olambda__449) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 152 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uuc),Uua))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fn(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__711) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 153 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xj(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__532) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 154 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gp,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_go,Uu))))) # label(fact_ATP_Olambda__204) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 155 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fc(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__501) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 156 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_nr,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_nq,Uu))))) # label(fact_ATP_Olambda__147) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 157 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_zc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_zd,Uu)))) # label(fact_ATP_Olambda__47) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 158 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1719206485d_d_Pi,X0),X12))) -> (all X32 (gg_TPTP_ind(X32) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X32),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1719206485d_d_Pi,X0),X12))) -> ((all X42 (gg_TPTP_ind(X42) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X42),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,X32),X42) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,X22),X42)))) -> X22 = X32))))))) # label(fact_k__Pi__ext) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 159 (all X0 all X12 pp(aa_fun171081125l_bool(scratc639425392all_of(aa_TPT43085870d_bool(aTP_Lamm_au,X0)),aa_fun1584354236d_bool(aTP_Lamm_aca(X0),X12)))) # label(fact_otax2) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 160 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_vd(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ve,Uu),Uua)))) # label(fact_ATP_Olambda__372) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 161 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fp,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_fo(Uu),Uua))))) # label(fact_ATP_Olambda__462) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 162 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_up(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_uo(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__600) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 163 (all X all Xa (scratc2009866277_l_iff(X,Xa) <-> pp(scratc1115724827_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1879547204nd_imp,X),Xa),aa_bool_bool(aa_boo1142376798l_bool(scratc1879547204nd_imp,Xa),X))))) # label(fact_def__l__iff) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 164 (all X0 all X12 pp(aa_fun171081125l_bool(scratc639425392all_of(aa_TPT43085870d_bool(aTP_Lamm_au,X0)),aa_TPT43085870d_bool(aTP_Lamm_abt(X0),X12)))) # label(fact_firstis1) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 165 (all X all Xa all Xb (pp(scratc1115724827_d_and(X,scratc1115724827_d_and(Xa,Xb))) <-> scratc996096644d_and3(X,Xa,Xb))) # label(fact_def__and3) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 166 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abu(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,Uub),aa_TPTP_ind_TPTP_ind(scratc1503458065etprod(Uu),Uua))))) # label(fact_ATP_Olambda__591) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 167 (all X scratc232309061d_n_ts(X) = aa_TPT1424761345TP_ind(scratc102231095bnd_ap,aa_TPTP_ind_TPTP_ind(scratc2105341982_times,X))) # label(fact_def__n__ts) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 168 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_gq(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gr,Uu),Uua)))) # label(fact_ATP_Olambda__453) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 169 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_wo,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_wp,Uu)))) # label(fact_ATP_Olambda__72) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 170 (all X0 all X12 all X22 (gg_TPTP_ind(X22) & gg_TPTP_ind(X12) -> X12 = aa_TPTP_ind_TPTP_ind(scratc102755877bnd_if(X0,X12),X22) | aa_TPTP_ind_TPTP_ind(scratc102755877bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__or) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 171 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yq,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uu),Uua)) -> pp(scratc1223190007_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,Uu),Uua)))))) # label(fact_ATP_Olambda__307) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 172 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),scratc282061419nd_n_1)),Uu)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_sy,Uu)))) # label(fact_ATP_Olambda__4) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 173 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706324_moreq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_eb(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__689) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 174 (all P all Q (pp(P) | -pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 175 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ew(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__505) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 176 (all X all Xa all Xb all Xc (scratc996096644d_and3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879612793nd_inf,Xb),aa_TPTP_ind_TPTP_ind(scratc8676528_class,X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879612793nd_inf,Xc),aa_TPTP_ind_TPTP_ind(scratc8676528_class,Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Xb),Xc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc294646914_propm(X,Xa),Xb),Xc)))) # label(fact_def__propm) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 177 (all X0 all X12 ((exists X2 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X2),X0)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X12),X2)) & gg_TPTP_ind(X2))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc673001287_union,X0))))) # label(fact_k__UnionEq) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 178 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ks,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_kr,Uu))))) # label(fact_ATP_Olambda__172) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 179 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_of,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_oe,Uu))))) # label(fact_ATP_Olambda__141) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 180 (all X all Xa all Xb (gg_TPTP_ind(Xb) -> Xb = aa_TPTP_ind_TPTP_ind(scratc712927106d_e_in(X,Xa),Xb))) # label(fact_def__e__in) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 181 (all X0 pp(aa_fun171081125l_bool(scratc639425392all_of(aa_TPT43085870d_bool(aTP_Lamm_au,X0)),aa_TPT43085870d_bool(aTP_Lamm_ack,X0)))) # label(fact_refis) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 182 (all Uu all Uua all Uub all Uuc all Uud all Uue (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_ax(Uu),Uua),Uub),Uuc),Uud),Uue)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aa_TPT43085870d_bool(aTP_Lamm_au,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_aw(Uu),Uua),Uub),Uuc),Uud),Uue))))) # label(fact_ATP_Olambda__735) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 183 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc231390674d_n_fr,aa_TPTP_ind_TPTP_ind(scratc597631537367_vo(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1837714885nd_den,X)),aa_TPTP_ind_TPTP_ind(scratc1837714885nd_den,Xa))) = aa_TPTP_ind_TPTP_ind(scratc1454525887_367_w(X),Xa)) # label(fact_def__d__367__w) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 184 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc758693855t_more,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1897569848l_some(scratc636914614d_frac),aa_TPT43085870d_bool(aTP_Lamm_af(X),Xa))))) # label(fact_def__rt__more) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 185 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uua)),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tb,Uu),Uua)))) # label(fact_ATP_Olambda__271) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 186 (all X (pp(aa_TPTP_ind_bool(scratc500050101closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,aa_TPTP_ind_TPTP_ind(scratc165739421_power,X1)),X))))))) # label(fact_def__d__Power__closed) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 187 (all P (gg_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 188 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_ld(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_le,Uu),Uua)))) # label(fact_ATP_Olambda__412) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 189 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc712927111d_e_is(Uu),Uub),Uuc)) -> pp(aa_TPTP_ind_bool(Uua,Uuc)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_aci(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__724) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 190 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1909615789d_Subq,X0),X12)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1909615789d_Subq,X12),X0)) -> X12 = X0)))) # label(fact_set__ext) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 191 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_tv(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tw,Uu),Uua)))) # label(fact_ATP_Olambda__381) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 192 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_ps,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_pt,Uu)))) # label(fact_ATP_Olambda__127) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 193 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_yp,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_yo,Uu))))) # label(fact_ATP_Olambda__54) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 194 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_xi,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_xh,Uu))))) # label(fact_ATP_Olambda__66) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 195 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_tr,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,scratc282061419nd_n_1),aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uu))))) # label(fact_ATP_Olambda__245) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 196 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_xb,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_xc,Uu)))) # label(fact_ATP_Olambda__68) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 197 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jp(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__716) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 198 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ot,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uua),Uu))))) # label(fact_ATP_Olambda__300) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 199 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_oq(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__569) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 200 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2043040867t_less,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc758693855t_more,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cj,Uu),Uua)))) # label(fact_ATP_Olambda__291) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 201 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_abe,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,Uu),aa_TPTP_ind_TPTP_ind(scratc165739421_power,scratc1920067545nd_nat))))) # label(fact_ATP_Olambda__20) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 202 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1217717974unmore(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc999473378_d_Sep(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bc(X),Xa),Xb))) # label(fact_def__unmore) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 203 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pg,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_pf(Uu),Uua))))) # label(fact_ATP_Olambda__406) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 204 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_vl,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_vk,Uu))))) # label(fact_ATP_Olambda__81) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 205 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919225325lesseq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919225325lesseq,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919225325lesseq,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hn(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__683) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 206 (all X0 (pp(aa_fun171081125l_bool(scratc493910842n_some,X0)) -> pp(aa_fun171081125l_bool(scratc656490912_n_one,scratc1912330826nd_min(X0))))) # label(fact_satz27a) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 207 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ei,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_eh,Uu))))) # label(fact_ATP_Olambda__222) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 208 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_dn,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_do,Uu)))) # label(fact_ATP_Olambda__227) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 209 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hr(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hs(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__633) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 210 (all X (pp(aa_TPTP_ind_bool(scratc2014913431_nat_p,X)) <-> (all X1 (pp(aa_TPTP_ind_bool(X1,scratc1169782717ptyset)) -> ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(X1,X2)) -> pp(aa_TPTP_ind_bool(X1,aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,X2)))))) -> pp(aa_TPTP_ind_bool(X1,X))))))) # label(fact_def__nat__p) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 211 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_ro,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_rp,Uu)))) # label(fact_ATP_Olambda__113) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 212 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_hw(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hx,Uu),Uua)))) # label(fact_ATP_Olambda__447) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 213 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fx,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_fw,Uu))))) # label(fact_ATP_Olambda__210) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 214 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_kd,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_kc,Uu))))) # label(fact_ATP_Olambda__177) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 215 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_vi,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_vh,Uu))))) # label(fact_ATP_Olambda__82) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 216 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,Uua),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),scratc282061419nd_n_1)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tp,Uu),Uua)))) # label(fact_ATP_Olambda__284) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 217 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_et(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eu,Uu),Uua)))) # label(fact_ATP_Olambda__468) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 218 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ce,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cd,Uu))))) # label(fact_ATP_Olambda__240) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 219 (all X all Xa all Xb all Xc all Xd (pp(scratc1115724827_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1879547204nd_imp,X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc712927111d_e_is(Xa),Xd),Xb)),aa_bool_bool(aa_boo1142376798l_bool(scratc1879547204nd_imp,scratc1223190007_d_not(X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc712927111d_e_is(Xa),Xd),Xc)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc294646854_prop1(X,Xa,Xb),Xc),Xd)))) # label(fact_def__prop1) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 220 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_xo,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_xp,Uu)))) # label(fact_ATP_Olambda__64) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 221 (all Uu ((pp(aa_TPTP_ind_bool(scratc309369991_cond1,Uu)) -> (pp(aa_TPTP_ind_bool(scratc309369992_cond2,Uu)) -> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_abf,Uu))))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_abg,Uu)))) # label(fact_ATP_Olambda__9) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 222 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rc(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_rb(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__608) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 223 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_jg,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_jh,Uu)))) # label(fact_ATP_Olambda__183) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 224 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abx(Uu),Uua),Uub)) <-> scratc2128269225_is_of(aa_TPTP_ind_TPTP_ind(scratc1226053384_first(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_au,Uu)))) # label(fact_ATP_Olambda__493) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 225 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abh,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__269) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 226 (all X (pp(aa_TPTP_ind_bool(scratc309369992_cond2,X)) <-> pp(aa_fun171081125l_bool(scratc540698651_n_all,aa_TPT43085870d_bool(aTP_Lamm_as,X))))) # label(fact_def__cond2) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 227 (all X0 pp(aa_TPTP_ind_bool(scratc775647028closed,aa_TPTP_ind_TPTP_ind(scratc300486565univof,X0)))) # label(fact_k__UnivOf__ZF__closed) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 228 (all Uu all Uua all Uub all Uuc (pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1879547204nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013318955d_esti(Uu),Uuc),Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013318955d_esti(Uu),Uuc),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_be(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__665) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 229 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X33),X0)) -> aa_TPTP_ind_TPTP_ind(X12,X33) = aa_TPTP_ind_TPTP_ind(X22,X33)))) -> aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1133920905_Sigma,X0),X22) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1133920905_Sigma,X0),X12))) # label(fact_xi__ext) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 230 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_si(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sj,Uu),Uua)))) # label(fact_ATP_Olambda__382) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 231 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ta,Uu)) <-> pp(aa_fun171081125l_bool(scratc1929181822nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1719206485d_d_Pi,scratc1920067545nd_nat),aTP_Lamm_al)),aa_TPT43085870d_bool(aTP_Lamm_sz,Uu))))) # label(fact_ATP_Olambda__8) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 232 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_js,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_jr,Uu))))) # label(fact_ATP_Olambda__180) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 233 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1897569848l_some(scratc636914614d_frac),aa_TPT43085870d_bool(aTP_Lamm_da(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_db,Uu),Uua)))) # label(fact_ATP_Olambda__481) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 234 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_no(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_np(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__619) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 235 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uu),Uua)) -> pp(scratc1223190007_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yo,Uu),Uua)))) # label(fact_ATP_Olambda__314) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 236 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ek(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_el,Uu),Uua)))) # label(fact_ATP_Olambda__471) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 237 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_rf(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rg(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__607) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 238 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_qx(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qy(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__609) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 239 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_iy,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ix,Uu))))) # label(fact_ATP_Olambda__186) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 240 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ht,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_hs(Uu),Uua))))) # label(fact_ATP_Olambda__448) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 241 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hg(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uua),Uub)),Uu)))) # label(fact_ATP_Olambda__580) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 242 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_th,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uua),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),scratc282061419nd_n_1))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,Uua),Uu))))) # label(fact_ATP_Olambda__273) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 243 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vk,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_vj(Uu),Uua))))) # label(fact_ATP_Olambda__370) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 244 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ip(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iq(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__627) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 245 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vs(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__543) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 246 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_abo(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013318955d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc999473378_d_Sep(Uu),Uua))) -> pp(aa_TPTP_ind_bool(Uua,Uub))))) # label(fact_ATP_Olambda__490) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 247 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ry,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_rx,Uu))))) # label(fact_ATP_Olambda__110) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 248 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ac(Uu),Uua),Uub),Uuc)) <-> scratc996096644d_and3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879612793nd_inf,Uub),aa_TPTP_ind_TPTP_ind(scratc8676528_class,Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879612793nd_inf,Uuc),aa_TPTP_ind_TPTP_ind(scratc8676528_class,Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uub),Uuc)))) # label(fact_ATP_Olambda__657) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 249 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_zf,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_ze,Uu))))) # label(fact_ATP_Olambda__46) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 250 (all Uu all Uua all Uub all Uuc all Uud all Uue all Uuf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_av(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uue),Uuf)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc712927111d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,Uub),Uuc)),Uue)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,Uub),Uud)),Uuf))))))) # label(fact_ATP_Olambda__736) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 251 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uua),scratc282061419nd_n_1)),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_td,Uu),Uua)))) # label(fact_ATP_Olambda__267) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 252 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vm(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__511) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 253 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc996162291d_anec(X,Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1897569848l_some(X),aa_TPT43085870d_bool(scratc1845845194nd_ecp(X,Xa),Xb))))) # label(fact_def__anec) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 254 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_qe,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_qd,Uu))))) # label(fact_ATP_Olambda__124) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 255 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xw,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_xv(Uu),Uua))))) # label(fact_ATP_Olambda__352) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 256 (all X all Xa (pp(aa_fun171081125l_bool(scratc493910842n_some,aa_TPT43085870d_bool(scratc304196016ffprop(X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,X),Xa)))) # label(fact_def__d__29__ii) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 257 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uu),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kt,Uu),Uua)))) # label(fact_ATP_Olambda__334) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 258 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yk,Uu),Uua)) <-> (pp(scratc1223190007_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__326) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 259 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wr(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_wq(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__594) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 260 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kh(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uub),Uua)))))) # label(fact_ATP_Olambda__553) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 261 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ai(Uu),Uua),Uub),Uuc) = aa_TPTP_ind_TPTP_ind(scratc1880006386nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc712927111d_e_is(aa_TPTP_ind_TPTP_ind(scratc719566192_d_1to,scratc282061420nd_n_2)),Uuc),scratc227913929d_n_1t),Uu,Uua),Uub)) # label(fact_ATP_Olambda__654) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 262 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fv(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uub),Uua)))))) # label(fact_ATP_Olambda__556) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 263 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xb,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_xa(Uu),Uua))))) # label(fact_ATP_Olambda__357) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 264 (all Uu (pp(aa_fun171081125l_bool(scratc1897569848l_some(scratc636914614d_frac),aa_TPT43085870d_bool(aTP_Lamm_ls,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_lt,Uu)))) # label(fact_ATP_Olambda__243) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 265 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qu(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uua),Uub)))))) # label(fact_ATP_Olambda__535) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 266 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gb(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__551) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 267 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rw(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uua),Uub)))))) # label(fact_ATP_Olambda__571) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 268 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc231390674d_n_fr,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1921379518nd_num,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1837714885nd_den,Uu)),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_oo,Uu),Uua)))) # label(fact_ATP_Olambda__333) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 269 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aa_TPT43085870d_bool(aTP_Lamm_au,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_aci(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_acj(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__583) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 270 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ji(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jj,Uu),Uua)))) # label(fact_ATP_Olambda__436) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 271 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jo,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_jn,Uu))))) # label(fact_ATP_Olambda__181) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 272 (all B_1 all B_2 gg_TPTP_ind(aa_fun277296641TP_ind(B_1,B_2))) # label(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__TPTP____Interpret__Oind_J_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 273 (all X all Xa (pp(aa_fun171081125l_bool(scratc639425392all_of(X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (scratc2128269225_is_of(X2,X) -> pp(aa_TPTP_ind_bool(Xa,X2))))))) # label(fact_def__all__of) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 274 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ec(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ed,Uu),Uua)))) # label(fact_ATP_Olambda__473) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 275 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lo,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uu),Uua)) -> pp(aa_fun171081125l_bool(scratc1897569848l_some(scratc636914614d_frac),aa_TPT43085870d_bool(aTP_Lamm_ln(Uu),Uua)))))) # label(fact_ATP_Olambda__303) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 276 (all Uu all Uua ((pp(scratc1223190007_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919225325lesseq,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ni,Uu),Uua)))) # label(fact_ATP_Olambda__329) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 277 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zs(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__589) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 278 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xk,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_xj(Uu),Uua))))) # label(fact_ATP_Olambda__354) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 279 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jx(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jy(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__623) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 280 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_ym,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_yn,Uu)))) # label(fact_ATP_Olambda__55) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 281 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rh,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_rg(Uu),Uua))))) # label(fact_ATP_Olambda__391) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 282 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_py(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pz(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__610) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 283 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_gl,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_gm,Uu)))) # label(fact_ATP_Olambda__205) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 284 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uu),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kx(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__524) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 285 (all X all Xa (pp(aa_TPTP_ind_bool(Xa,X)) <-> scratc2128269225_is_of(X,Xa))) # label(fact_def__is__of) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 286 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_ve,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_vf,Uu)))) # label(fact_ATP_Olambda__83) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 287 (all Uu (pp(aa_fun171081125l_bool(scratc1897569848l_some(scratc636914614d_frac),aa_TPT43085870d_bool(aTP_Lamm_lq,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_lr,Uu)))) # label(fact_ATP_Olambda__244) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 288 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc712927111d_e_is(aa_TPTP_ind_TPTP_ind(scratc1503458065etprod(Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc759553526d_pair(Uu,Uua),aa_TPTP_ind_TPTP_ind(scratc1226053384_first(Uu,Uua),Uub)),aa_TPTP_ind_TPTP_ind(scratc1738843356second(Uu,Uua),Uub))),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abv(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__486) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 289 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_nv,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_nu,Uu))))) # label(fact_ATP_Olambda__146) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 290 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_gf,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_gg,Uu)))) # label(fact_ATP_Olambda__207) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 291 (all X all Xa (pp(scratc1929444168nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1881595115_prop1,X),Xa)))) # label(fact_def__d__29__prop1) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 292 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X22),aa_fun1431113780TP_ind(scratc999473378_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(X12,X22)))) # label(fact_k__SepE2) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 293 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_or,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_oq(Uu),Uua))))) # label(fact_ATP_Olambda__413) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 294 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ey,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ex,Uu))))) # label(fact_ATP_Olambda__217) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 295 (all X all Xa (pp(aa_fun171081125l_bool(scratc1897569848l_some(X),Xa)) <-> pp(scratc1223190007_d_not(aa_fun171081125l_bool(scratc639425392all_of(aa_TPT43085870d_bool(aTP_Lamm_au,X)),scratc1920985925nd_non(X,Xa)))))) # label(fact_def__l__some) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 296 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1984233995sel_wa(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc1880006386nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc712927111d_e_is(X),Xc),Xa),X,Xb),Xc)) # label(fact_def__wissel__wa) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 297 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vy(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__538) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 298 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wf(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_we(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__597) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 299 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ud(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_uc(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__603) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 300 (all X0 ((all X13 (gg_TPTP_ind(X13) -> ((all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X22),X13)) -> pp(aa_TPTP_ind_bool(X0,X22)))) -> pp(aa_TPTP_ind_bool(X0,X13))))) -> (all X14 pp(aa_TPTP_ind_bool(X0,X14))))) # label(fact_k__In__ind) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 301 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_po,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_pn(Uu),Uua))))) # label(fact_ATP_Olambda__404) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 302 (all Uu aa_TPT494704832TP_ind(scratc1307610839d_repl,aa_TPTP_ind_TPTP_ind(scratc297882262tminus(Uu),aa_TPTP_ind_TPTP_ind(scratc1811264907d_Sing,scratc1169782717ptyset))) = aa_TPT494704832TP_ind(aTP_Lamm_bv,Uu)) # label(fact_ATP_Olambda__246) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 303 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cs,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cr,Uu))))) # label(fact_ATP_Olambda__233) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 304 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_eg(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eh,Uu),Uua)))) # label(fact_ATP_Olambda__472) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 305 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_nh,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ng,Uu))))) # label(fact_ATP_Olambda__151) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 306 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ty(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__677) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 307 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_sc(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sd,Uu),Uua)))) # label(fact_ATP_Olambda__384) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 308 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ie(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_if,Uu),Uua)))) # label(fact_ATP_Olambda__445) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 309 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_tw,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_tx,Uu)))) # label(fact_ATP_Olambda__92) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 310 (all B_1 gg_bool(scratc1223190007_d_not(B_1))) # label(gsy_c_Scratch__tptp__translate__63417__16348_ONUM788__thf__4__p_Obnd__d__not) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 311 (all X (pp(aa_fun171081125l_bool(scratc1897569848l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1719206485d_d_Pi,scratc1920067545nd_nat),aTP_Lamm_al)),aa_TPT43085870d_bool(scratc1179442033_prop2,X))) <-> pp(aa_TPTP_ind_bool(scratc1179442035_prop4,X)))) # label(fact_def__d__428__prop4) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 312 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_aai(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aaj,Uu),Uua)))) # label(fact_ATP_Olambda__345) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 313 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zz,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_zy(Uu),Uua))))) # label(fact_ATP_Olambda__347) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 314 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_im(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_in,Uu),Uua)))) # label(fact_ATP_Olambda__443) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 315 (all X aa_TPTP_ind_TPTP_ind(scratc294253260_proj1,X) = aa_fun277296641TP_ind(scratc460841235eplSep(X,aTP_Lamm_bt),scratc1016586773_d_Unj)) # label(fact_def__proj1) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 316 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aal,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uu)),Uua))))) # label(fact_ATP_Olambda__320) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 317 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kn(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uua),Uub)))))) # label(fact_ATP_Olambda__567) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 318 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_xn,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__12) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 319 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1921379518nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc1837714885nd_den,Xa))),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1921379518nd_num,Xa)),aa_TPTP_ind_TPTP_ind(scratc1837714885nd_den,X)))))) # label(fact_def__lessf) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 320 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),scratc282061419nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_aaw,Uu)))) # label(fact_ATP_Olambda__3) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 321 (all Uu all Uua all Uub all Uuc all Uud aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_bg(Uu),Uua),Uub),Uuc),Uud) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,aa_TPTP_ind_TPTP_ind(scratc979627425wissel(Uu,Uub),Uuc)),Uud))) # label(fact_ATP_Olambda__734) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 322 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc218225321moreis,Uu),Uua)) -> pp(scratc1223190007_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2043040867t_less,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ch,Uu),Uua)))) # label(fact_ATP_Olambda__304) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 323 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xo,Uu),Uua)))) # label(fact_ATP_Olambda__336) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 324 (all X (gg_TPTP_ind(X) -> (aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1860414882d_pair,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,X),scratc1169782717ptyset)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,X),aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,scratc1169782717ptyset))) = X <-> pp(aa_TPTP_ind_bool(scratc1726284942pair_p,X))))) # label(fact_def__pair__p) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 325 (all X (scratc1994683478nd_wel(X) <-> pp(scratc1223190007_d_not(scratc1223190007_d_not(X))))) # label(fact_def__wel) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 326 (all X aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1133920905_Sigma,scratc1920067545nd_nat),aTP_Lamm_ap(X)) = aa_TPTP_ind_TPTP_ind(scratc1547062377d_24_g,X)) # label(fact_def__d__24__g) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 327 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706324_moreq,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_id(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__693) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 328 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_aab(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aac,Uu),Uua)))) # label(fact_ATP_Olambda__346) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 329 (all Uu all Uua (scratc1219098378_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc173054068_rt_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc758693855t_more,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2043040867t_less,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cr,Uu),Uua)))) # label(fact_ATP_Olambda__250) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 330 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_qm,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_qn,Uu)))) # label(fact_ATP_Olambda__121) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 331 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uua),Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lq,Uu),Uua)))) # label(fact_ATP_Olambda__341) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 332 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yh(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__576) # label(axiom) # label(non_clause). [assumption]. 1.48/1.70 333 (all X all Xa scratc1736967696_ecect(X,Xa) = scratc712927106d_e_in(aa_TPTP_ind_TPTP_ind(scratc165739421_power,X),scratc996162291d_anec(X,Xa))) # label(fact_def__ecect) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 334 (all X0 all X12 pp(aa_fun171081125l_bool(scratc639425392all_of(aa_TPT43085870d_bool(aTP_Lamm_au,X0)),aa_fun1584354236d_bool(aTP_Lamm_abo(X0),X12)))) # label(fact_estie) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 335 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bj(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc712927111d_e_is(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__662) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 336 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ag(Uu),Uua),Uub),Uuc) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,Uub),aa_TPTP_ind_TPTP_ind(scratc893179352ght1to(Uu,Uua),Uuc))) # label(fact_ATP_Olambda__728) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 337 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_sg,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_sh,Uu)))) # label(fact_ATP_Olambda__107) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 338 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rn(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uub),Uua)))))) # label(fact_ATP_Olambda__572) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 339 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_fun171081125l_bool(scratc639425392all_of(aa_TPT43085870d_bool(aTP_Lamm_au,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_az(Uua),Uub),Uuc),Uud))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ba(Uu),Uua),Uub),Uuc),Uud)))) # label(fact_ATP_Olambda__733) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 340 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2044864309etprop(X,Xa),Xb),Xc)) <-> pp(scratc1115724827_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013318955d_esti(X),Xc),Xa),scratc1223190007_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013318955d_esti(X),Xc),Xb)))))) # label(fact_def__nissetprop) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 341 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dj,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_di(Uu),Uua))))) # label(fact_ATP_Olambda__478) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 342 (all X0 (scratc1994683478nd_wel(X0) -> pp(X0))) # label(fact_l__et) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 343 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc300486565univof,X0)))) # label(fact_k__UnivOf__In) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 344 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dl(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dm(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__647) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 345 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_kt,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ku,Uu)))) # label(fact_ATP_Olambda__171) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 346 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ld(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc231390674d_n_fr,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc231390674d_n_fr,Uu),Uub)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc231390674d_n_fr,Uua),Uub)))))) # label(fact_ATP_Olambda__520) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 347 (all Uu all Uua aa_TPTP_ind_TPTP_ind(scratc673001287_union,aa_TPTP_ind_TPTP_ind(Uu,Uua)) = aa_TPTP_ind_TPTP_ind(aTP_Lamm_bp(Uu),Uua)) # label(fact_ATP_Olambda__484) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 348 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_qz,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ra,Uu)))) # label(fact_ATP_Olambda__117) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 349 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_zk,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_zl,Uu)))) # label(fact_ATP_Olambda__43) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 350 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ut(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_us(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__599) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 351 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nw,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uua),Uu))))) # label(fact_ATP_Olambda__299) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 352 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_zn,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_zm,Uu))))) # label(fact_ATP_Olambda__42) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 353 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ij,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ik,Uu)))) # label(fact_ATP_Olambda__190) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 354 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc304196016ffprop(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,X),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Xa),Xb))))) # label(fact_def__diffprop) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 355 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919225325lesseq,X),Xa)) <-> pp(aa_bool_bool(scratc100336135d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,X),Xa))))) # label(fact_def__lesseq) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 356 (all P all Q (pp(P) | pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)))) # label(help_fimplies_1_1_U) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 357 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_qs,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_qt,Uu)))) # label(fact_ATP_Olambda__119) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 358 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_acg(Uu),Uua),Uub),Uuc)) <-> (pp(aa_fun171081125l_bool(scratc639425392all_of(aa_TPT43085870d_bool(aTP_Lamm_au,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_acf(Uua),Uub),Uuc))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc712927111d_e_is(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1719206485d_d_Pi,Uu),aTP_Lamm_aj(Uua))),Uub),Uuc))))) # label(fact_ATP_Olambda__668) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 359 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aae,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1920592336nd_nis,Uua),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__335) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 360 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mo,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706324_moreq,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919225325lesseq,Uua),Uu))))) # label(fact_ATP_Olambda__297) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 361 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uu),Uua)) -> pp(aa_fun171081125l_bool(scratc1897569848l_some(scratc636914614d_frac),aa_TPT43085870d_bool(aTP_Lamm_hg(Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hh,Uu),Uua)))) # label(fact_ATP_Olambda__302) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 362 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013318955d_esti(Uu),Uub),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bf(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__489) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 363 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yi,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_yh(Uu),Uua))))) # label(fact_ATP_Olambda__348) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 364 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_jd,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_je,Uu)))) # label(fact_ATP_Olambda__184) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 365 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qc(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__517) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 366 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),Uua)),Uu)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sq,Uu),Uua)))) # label(fact_ATP_Olambda__265) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 367 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc381596720nunion(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc673001287_union,aa_TPTP_ind_TPTP_ind(scratc1028407283_UPair(X),Xa))) # label(fact_def__binunion) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 368 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_vq,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_vr,Uu)))) # label(fact_ATP_Olambda__79) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 369 (all X (pp(aa_TPTP_ind_bool(scratc2058027186_prop1,X)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1920592336nd_nis,aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,X)),X)))) # label(fact_def__d__22__prop1) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 370 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_wy,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_wz,Uu)))) # label(fact_ATP_Olambda__69) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 371 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1920592336nd_nis,aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uu)),Uu)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_abb,Uu)))) # label(fact_ATP_Olambda__13) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 372 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_mf,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_me,Uu))))) # label(fact_ATP_Olambda__162) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 373 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vb,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_va(Uu),Uua))))) # label(fact_ATP_Olambda__373) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 374 (all X all Xa (pp(scratc1223190007_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc173054068_rt_is,X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc615895054rt_nis,X),Xa)))) # label(fact_def__rt__nis) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 375 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1924324820_right(X,Xa,Xb),Xc) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1133920905_Sigma,aa_TPTP_ind_TPTP_ind(scratc719566192_d_1to,Xb)),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ag(Xa),Xb),Xc))) # label(fact_def__right) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 376 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ll,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_lm,Uu)))) # label(fact_ATP_Olambda__167) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 377 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_hl,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_hm,Uu)))) # label(fact_ATP_Olambda__196) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 378 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc979627425wissel(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1133920905_Sigma,X),scratc1984233996sel_wb(X,Xa,Xb))) # label(fact_def__wissel) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 379 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ck,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cj,Uu))))) # label(fact_ATP_Olambda__237) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 380 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706324_moreq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706324_moreq,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706324_moreq,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hr(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__688) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 381 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uuc),Uua))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_we(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__709) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 382 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hv(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hw(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__632) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 383 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wb(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__537) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 384 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_xf,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_xe,Uu))))) # label(fact_ATP_Olambda__67) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 385 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706324_moreq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uu),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uua),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706324_moreq,Uub),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_mu(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__691) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 386 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ff(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uuc),Uua))))))) # label(fact_ATP_Olambda__715) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 387 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_la,Uu),Uua)))) # label(fact_ATP_Olambda__289) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 388 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sw,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),Uua)),Uu))))) # label(fact_ATP_Olambda__274) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 389 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nc,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uu),Uua)) -> pp(scratc1223190007_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706324_moreq,Uu),Uua)))))) # label(fact_ATP_Olambda__313) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 390 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_bi(Uu),Uua),Uub),Uuc) = aa_TPTP_ind_TPTP_ind(scratc102755877bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1183411315_image(Uu,Uua),Uub),Uuc),aa_TPTP_ind_TPTP_ind(scratc22673458d_soft(Uu,Uua,Uub),Uuc)),scratc1169782717ptyset)) # label(fact_ATP_Olambda__655) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 391 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1307610839d_repl,aa_TPTP_ind_TPTP_ind(scratc165739421_power,aa_TPTP_ind_TPTP_ind(scratc165739421_power,scratc1169782717ptyset))),aa_TPT1424761345TP_ind(aTP_Lamm_bz(X),Xa)) = aa_TPTP_ind_TPTP_ind(scratc1028407283_UPair(X),Xa)) # label(fact_def__d__UPair) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 392 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_qk,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_qj,Uu))))) # label(fact_ATP_Olambda__122) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 393 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_mz,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_my,Uu))))) # label(fact_ATP_Olambda__155) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 394 (all X0 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X0),scratc1611392121_omega)) -> pp(aa_TPTP_ind_bool(scratc2014913431_nat_p,X0)))) # label(fact_omega__nat__p) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 395 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_za,Uu),Uua)))) # label(fact_ATP_Olambda__294) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 396 (all X aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc381596720nunion(X),aa_TPTP_ind_TPTP_ind(scratc1811264907d_Sing,X))) # label(fact_def__ordsucc) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 397 (all X0 all X12 all X22 ((pp(X0) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X12),X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,aa_TPTP_ind_TPTP_ind(scratc102755877bnd_if(X0,X12),scratc1169782717ptyset)),aa_TPTP_ind_TPTP_ind(scratc102755877bnd_if(X0,X22),aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,scratc1169782717ptyset)))))) # label(fact_k__If__In__01) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 398 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_eb(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ec(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__643) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 399 (all X all Xa all Xb (pp(aa_fun171081125l_bool(scratc1813389561nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bd(X),Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc714718757t_disj(X),Xa),Xb)))) # label(fact_def__st__disj) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 400 (all X all Xa all Xb (pp(aa_fun171081125l_bool(scratc1813389561nd_all(Xa),aa_TPT43085870d_bool(scratc1183411315_image(X,Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1580609604ective(X),Xa),Xb)))) # label(fact_def__surjective) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 401 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vt,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_vs(Uu),Uua))))) # label(fact_ATP_Olambda__367) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 402 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_qr(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qs,Uu),Uua)))) # label(fact_ATP_Olambda__395) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 403 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gf,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ge(Uu),Uua))))) # label(fact_ATP_Olambda__457) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 404 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_lo,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_lp,Uu)))) # label(fact_ATP_Olambda__166) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 405 (all X all Xa all Xb all Xc all Xd all Xe all Xf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1634590515_prop1(X,Xa,Xb,Xc,Xd),Xe),Xf)) <-> pp(scratc1115724827_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013318955d_esti(X),Xf),aa_TPTP_ind_TPTP_ind(scratc1736967696_ecect(X,Xa),Xd)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc712927111d_e_is(Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,Xc),Xf)),Xe))))) # label(fact_def__d__10__prop1) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 406 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hu,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ht,Uu))))) # label(fact_ATP_Olambda__194) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 407 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,X),Xa)) <-> pp(aa_bool_bool(scratc100336135d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,X),Xa))))) # label(fact_def__moreis) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 408 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1133920905_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,aa_TPTP_ind_TPTP_ind(scratc294253259_proj0,X22)),X0)))) # label(fact_proj0__Sigma) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 409 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),scratc282061419nd_n_1))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ss,Uu)))) # label(fact_ATP_Olambda__17) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 410 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ch,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ci,Uu)))) # label(fact_ATP_Olambda__238) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 411 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,Uu),scratc1920067545nd_nat)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_lc,Uu)))) # label(fact_ATP_Olambda__26) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 412 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pk,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_pj(Uu),Uua))))) # label(fact_ATP_Olambda__405) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 413 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_zj,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_zi,Uu))))) # label(fact_ATP_Olambda__44) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 414 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ws,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_wr(Uu),Uua))))) # label(fact_ATP_Olambda__360) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 415 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc918398959d_left(X,Xa,Xb),Xc) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1133920905_Sigma,aa_TPTP_ind_TPTP_ind(scratc719566192_d_1to,Xb)),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ah(Xa),Xb),Xc))) # label(fact_def__left) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 416 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cl,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc758693855t_more,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2043040867t_less,Uua),Uu))))) # label(fact_ATP_Olambda__290) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 417 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,Uub),aa_fun1431113780TP_ind(scratc999473378_d_Sep(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_acb(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__592) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 418 (all X all Xa scratc1879612791nd_ind(X,Xa) = scratc1846697984nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bm(X),Xa))) # label(fact_def__ind) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 419 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_sx,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_sw,Uu))))) # label(fact_ATP_Olambda__101) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 420 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_uy,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_ux(Uu),Uua))))) # label(fact_ATP_Olambda__374) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 421 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kk(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uua),Uub)))))) # label(fact_ATP_Olambda__557) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 422 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_vx,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_vw,Uu))))) # label(fact_ATP_Olambda__77) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 423 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_rj(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rk(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__606) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 424 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_abi,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_abh,Uu))))) # label(fact_ATP_Olambda__27) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 425 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_hk(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hl,Uu),Uua)))) # label(fact_ATP_Olambda__450) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 426 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_wd,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_wc,Uu))))) # label(fact_ATP_Olambda__75) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 427 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_nc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_nd,Uu)))) # label(fact_ATP_Olambda__153) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 428 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_no(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uu),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uua),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uub),Uuc))))))) # label(fact_ATP_Olambda__701) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 429 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hq,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_hp,Uu))))) # label(fact_ATP_Olambda__195) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 430 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_th,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ti,Uu)))) # label(fact_ATP_Olambda__97) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 431 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fd,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_fc(Uu),Uua))))) # label(fact_ATP_Olambda__465) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 432 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1918493163nd_nIn,Uua),Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bx,Uu),Uua)))) # label(fact_ATP_Olambda__343) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 433 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xe,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_xd(Uu),Uua))))) # label(fact_ATP_Olambda__356) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 434 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_kl,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_km,Uu)))) # label(fact_ATP_Olambda__174) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 435 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iu,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_it(Uu),Uua))))) # label(fact_ATP_Olambda__441) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 436 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jf(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uu),Uua))))) # label(fact_ATP_Olambda__515) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 437 (all X all Xa (pp(scratc1115724827_d_and(scratc772951858_amone(X,Xa),aa_fun171081125l_bool(scratc1897569848l_some(X),Xa))) <-> pp(aa_fun171081125l_bool(scratc1929181822nd_one(X),Xa)))) # label(fact_def__one) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 438 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_abp(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013318955d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc999473378_d_Sep(Uu),Uua)))))) # label(fact_ATP_Olambda__582) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 439 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_om,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc231390674d_n_fr,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1921379518nd_num,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1837714885nd_den,Uu)),Uua))),Uu)))) # label(fact_ATP_Olambda__263) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 440 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1458249569air_q0(X),Xa) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2007612175_pair1(X),aa_TPTP_ind_TPTP_ind(scratc318352169first1(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc643863125econd1(X),Xa))) # label(fact_def__pair__q0) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 441 (all X0 (pp(aa_fun171081125l_bool(scratc493910842n_some,X0)) -> pp(aa_fun171081125l_bool(scratc493910842n_some,scratc1912330826nd_min(X0))))) # label(fact_satz27) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 442 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_sb,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_sa,Uu))))) # label(fact_ATP_Olambda__109) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 443 (all Uu all Uua (pp(scratc1929444168nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc493910842n_some,aa_TPT43085870d_bool(scratc304196016ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc493910842n_some,aa_TPT43085870d_bool(scratc304196016ffprop(Uua),Uu)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zq,Uu),Uua)))) # label(fact_ATP_Olambda__260) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 444 (all X0 all X12 (gg_TPTP_ind(X0) -> aa_TPTP_ind_TPTP_ind(scratc294253259_proj0,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1860414882d_pair,X0),X12)) = X0)) # label(fact_proj0__pair__eq) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 445 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rt(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uub),Uua)))))) # label(fact_ATP_Olambda__531) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 446 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc409976095ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1813389561nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bl(X),Xa),Xb))))) # label(fact_def__injective) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 447 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc712927111d_e_is(Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,Uua),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,Uub),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_acf(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__660) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 448 (all X0 pp(aa_fun171081125l_bool(scratc639425392all_of(aa_TPT43085870d_bool(aTP_Lamm_abl,X0)),aa_TPT43085870d_bool(aTP_Lamm_abn,X0)))) # label(fact_isseti) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 449 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_vz,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_wa,Uu)))) # label(fact_ATP_Olambda__76) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 450 (all X7 all Y (gg_TPTP_ind(X7) & gg_TPTP_ind(Y) -> X7 = Y | -pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)))) # label(help_fequal_1_1_fequal_001t__TPTP____Interpret__Oind_T) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 451 (all X0 all X12 pp(aa_fun171081125l_bool(scratc639425392all_of(aa_TPT43085870d_bool(aTP_Lamm_au,X0)),aa_TPT43085870d_bool(aTP_Lamm_abr(X0),X12)))) # label(fact_secondis1) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 452 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_fd,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fe,Uu)))) # label(fact_ATP_Olambda__215) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 453 (all X all Xa (pp(aa_fun171081125l_bool(scratc639425392all_of(aa_TPT43085870d_bool(aTP_Lamm_au,X)),aa_fun1584354236d_bool(aTP_Lamm_bo(X),Xa))) <-> pp(scratc772951858_amone(X,Xa)))) # label(fact_def__amone) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 454 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_xm,Uu)))) # label(fact_ATP_Olambda__19) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 455 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sn,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),Uua)),Uua)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uu)),Uua))))) # label(fact_ATP_Olambda__264) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 456 (all Uu all Uua (scratc1219098378_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_oe,Uu),Uua)))) # label(fact_ATP_Olambda__252) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 457 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nq,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_np(Uu),Uua))))) # label(fact_ATP_Olambda__415) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 458 (all X aa_TPTP_ind_TPTP_ind(scratc719566192_d_1to,X) = aa_fun1431113780TP_ind(scratc999473378_d_Sep(scratc1920067545nd_nat),aa_TPT43085870d_bool(aTP_Lamm_ak,X))) # label(fact_def__d__1to) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 459 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bs(Uu),Uua) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1307610839d_repl,aa_TPTP_ind_TPTP_ind(Uu,Uua)),aa_TPT1424761345TP_ind(scratc1860414882d_pair,Uua))) # label(fact_ATP_Olambda__318) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 460 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_jj,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_jk,Uu)))) # label(fact_ATP_Olambda__182) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 461 (all Uu all Uua all Uub ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X3),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,Uub),X3)),aa_TPTP_ind_TPTP_ind(Uua,X3)))))) <-> pp(aa_TPTP_ind_bool(aa_fun1913827119d_bool(aTP_Lamm_bq(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__653) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 462 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1909615789d_Subq,X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X2),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X2),Xa))))))) # label(fact_def__d__Subq) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 463 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mj(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uu),Uub)))))) # label(fact_ATP_Olambda__560) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 464 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cp,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cq,Uu)))) # label(fact_ATP_Olambda__234) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 465 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,Uub),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1719206485d_d_Pi,Uu),aTP_Lamm_aj(Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ace(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__588) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 466 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_et(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uu),Uua))))) # label(fact_ATP_Olambda__502) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 467 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dc,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_db,Uu))))) # label(fact_ATP_Olambda__230) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 468 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_aan,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(scratc282061419nd_n_1),Uu))))) # label(fact_ATP_Olambda__11) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 469 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ju(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jt(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__624) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 470 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_jq(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jr,Uu),Uua)))) # label(fact_ATP_Olambda__434) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 471 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_aae,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_aaf,Uu)))) # label(fact_ATP_Olambda__35) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 472 (all X0 all X12 pp(aa_fun171081125l_bool(scratc639425392all_of(aa_TPT43085870d_bool(aTP_Lamm_abu(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_abv(X0),X12)))) # label(fact_pairis1) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 473 (all X0 all X12 pp(aa_fun171081125l_bool(scratc639425392all_of(aa_TPT43085870d_bool(aTP_Lamm_ace(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_ach(X0),X12)))) # label(fact_e__fisi) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 474 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_lj(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__719) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 475 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_pe(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pf(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__615) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 476 scratc2132865311bvious <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1879547204nd_imp,fFalse),fFalse)) # label(fact_def__obvious) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 477 (all Uu all Uua all Uub all Uuc all Uud all Uue all Uuf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_aw(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aa_TPT43085870d_bool(aTP_Lamm_au,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_av(Uua),Uub),Uuc),Uud),Uue),Uuf))))) # label(fact_ATP_Olambda__737) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 478 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zk,Uu),Uua)) <-> pp(scratc1929444168nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__254) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 479 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc489433998indrat(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc383083951indeq2(scratc636914614d_frac,scratc231325074d_n_eq,Xb,Xc,X),Xa)) # label(fact_def__indrat) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 480 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fg(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ff(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__640) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 481 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_vm(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vn,Uu),Uua)))) # label(fact_ATP_Olambda__369) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 482 (all X all Xa all Xb (pp(scratc1845845133nd_ec3(X,Xa,Xb)) <-> scratc996096644d_and3(scratc99680130d_l_ec(X,Xa),scratc99680130d_l_ec(Xa,Xb),scratc99680130d_l_ec(Xb,X)))) # label(fact_def__ec3) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 483 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rl,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_rk(Uu),Uua))))) # label(fact_ATP_Olambda__390) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 484 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ie(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_id(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__630) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 485 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919225325lesseq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mg(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__547) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 486 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_jv,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_jw,Uu)))) # label(fact_ATP_Olambda__179) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 487 (all X all Xa all Xb aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1133920905_Sigma,Xa),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_bi(X),Xa),Xb)) = aa_TPTP_ind_TPTP_ind(scratc1267782664nverse(X,Xa),Xb)) # label(fact_def__inverse) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 488 (all X all Xa scratc1929641030nd_out(aa_TPTP_ind_TPTP_ind(scratc165739421_power,X),scratc996162291d_anec(X,Xa)) = scratc1111600628ectset(X,Xa)) # label(fact_def__ectset) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 489 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aag,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uua),Uu))))) # label(fact_ATP_Olambda__287) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 490 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ky,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_kz,Uu)))) # label(fact_ATP_Olambda__169) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 491 (all X fequal_TPTP_ind = scratc712927111d_e_is(X)) # label(fact_def__e__is) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 492 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_rt(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ru,Uu),Uua)))) # label(fact_ATP_Olambda__387) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 493 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc818613758_477_v(X),Xa) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc231390674d_n_fr,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1921379518nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc1837714885nd_den,Xa))),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1837714885nd_den,X)),aa_TPTP_ind_TPTP_ind(scratc1921379518nd_num,Xa)))) # label(fact_def__d__477__v) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 494 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_ye(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yf,Uu),Uua)))) # label(fact_ATP_Olambda__349) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 495 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aa_TPT43085870d_bool(aTP_Lamm_abl,Uu)),aa_TPT43085870d_bool(aTP_Lamm_abm(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abn,Uu),Uua)))) # label(fact_ATP_Olambda__319) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 496 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ak,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,Uua),Uu)))) # label(fact_ATP_Olambda__339) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 497 (all Uu (gg_TPTP_ind(Uu) -> Uu = aa_TPTP_ind_TPTP_ind(aTP_Lamm_an,Uu))) # label(fact_ATP_Olambda__739) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 498 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qo(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__540) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 499 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qp,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_qo(Uu),Uua))))) # label(fact_ATP_Olambda__396) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 500 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_sr,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_sq,Uu))))) # label(fact_ATP_Olambda__103) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 501 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lh,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_lg(Uu),Uua))))) # label(fact_ATP_Olambda__411) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 502 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc294646913_propl(X,Xa),Xb),Xc)) <-> scratc996096644d_and3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879612793nd_inf,Xb),aa_TPTP_ind_TPTP_ind(scratc8676528_class,X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879612793nd_inf,Xc),aa_TPTP_ind_TPTP_ind(scratc8676528_class,Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Xb),Xc)))) # label(fact_def__propl) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 503 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vd(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__512) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 504 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cx,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cw,Uu))))) # label(fact_ATP_Olambda__231) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 505 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_us(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__723) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 506 (all B_1 all B_2 gg_TPTP_ind(scratc1845845198nd_ect(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__63417__16348_ONUM788__thf__4__p_Obnd__ect) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 507 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xs(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__544) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 508 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ij,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ii(Uu),Uua))))) # label(fact_ATP_Olambda__444) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 509 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qf(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__509) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 510 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hn(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ho(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__634) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 511 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2043040867t_less,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1897569848l_some(scratc636914614d_frac),aa_TPT43085870d_bool(aTP_Lamm_ad(X),Xa))))) # label(fact_def__rt__less) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 512 -(exists X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X0),scratc1169782717ptyset))) # label(fact_k__EmptyAx) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 513 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_nz,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ny,Uu))))) # label(fact_ATP_Olambda__144) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 514 (all X ((all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,aa_TPTP_ind_TPTP_ind(scratc673001287_union,X1)),X))))) <-> pp(aa_TPTP_ind_bool(scratc335317087closed,X)))) # label(fact_def__d__Union__closed) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 515 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_wi(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__708) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 516 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_ap(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,Uu),Uua))) # label(fact_ATP_Olambda__483) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 517 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706324_moreq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ma(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__549) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 518 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cf,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc84241709lessis,Uu),Uua)) -> pp(scratc1223190007_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc758693855t_more,Uu),Uua)))))) # label(fact_ATP_Olambda__305) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 519 (all X all Xa (pp(scratc1115724827_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,Xa),scratc282061419nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,X)),aa_TPTP_ind_bool(scratc1087267888_prop1,Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1087267889_prop2,X),Xa)))) # label(fact_def__d__24__prop2) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 520 (all X aa_TPTP_ind_TPTP_ind(scratc1779109790d_xout,X) = aa_TPTP_ind_TPTP_ind(scratc1245779368d_outn(X),X)) # label(fact_def__xout) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 521 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mk,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_mj(Uu),Uua))))) # label(fact_ATP_Olambda__418) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 522 (all X all Xa all Xb aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1133920905_Sigma,Xa),scratc22673458d_soft(X,Xa,Xb)) = aa_TPTP_ind_TPTP_ind(scratc799524125d_invf(X,Xa),Xb)) # label(fact_def__invf) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 523 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lg(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc231390674d_n_fr,Uu),Uub)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc231390674d_n_fr,Uua),Uub))),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc231390674d_n_fr,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uua)),Uub))))) # label(fact_ATP_Olambda__496) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 524 (all X scratc1879612791nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1719206485d_d_Pi,scratc1920067545nd_nat),aTP_Lamm_al),aa_TPT43085870d_bool(scratc1179442033_prop2,X)) = aa_TPTP_ind_TPTP_ind(scratc2105341982_times,X)) # label(fact_def__times) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 525 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dt(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_du(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__645) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 526 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_gx,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_gy,Uu)))) # label(fact_ATP_Olambda__201) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 527 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xh,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_xg(Uu),Uua))))) # label(fact_ATP_Olambda__355) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 528 (all B_1 all B_2 gg_bool(scratc772951858_amone(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__63417__16348_ONUM788__thf__4__p_Obnd__amone) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 529 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gt,Uu),Uua)))) # label(fact_ATP_Olambda__288) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 530 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ir,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_iq(Uu),Uua))))) # label(fact_ATP_Olambda__442) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 531 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_sp,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(scratc282061419nd_n_1),Uu))))) # label(fact_ATP_Olambda__18) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 532 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ke(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uub),Uua)))))) # label(fact_ATP_Olambda__568) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 533 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_gb(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gc,Uu),Uua)))) # label(fact_ATP_Olambda__458) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 534 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_lx(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ly,Uu),Uua)))) # label(fact_ATP_Olambda__422) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 535 (all B_1 all B_2 gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2))) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 536 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fi,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_fh,Uu))))) # label(fact_ATP_Olambda__214) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 537 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ne,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_nf,Uu)))) # label(fact_ATP_Olambda__152) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 538 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_sd,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_se,Uu)))) # label(fact_ATP_Olambda__108) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 539 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1503458065etprod(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1133920905_Sigma,X),aTP_Lamm_aj(Xa))) # label(fact_def__setprod) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 540 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ge(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__555) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 541 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_fs(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ft,Uu),Uua)))) # label(fact_ATP_Olambda__461) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 542 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_ox(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_oy,Uu),Uua)))) # label(fact_ATP_Olambda__408) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 543 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ma(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mb,Uu),Uua)))) # label(fact_ATP_Olambda__421) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 544 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aa_TPT43085870d_bool(aTP_Lamm_au,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_abq(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abr(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__587) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 545 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vj(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__518) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 546 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fy(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uub),Uua)))))) # label(fact_ATP_Olambda__566) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 547 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_hx,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_hy,Uu)))) # label(fact_ATP_Olambda__193) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 548 (all B_1 all B_2 gg_bool(aa_fun171081125l_bool(B_1,B_2))) # label(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__HOL__Obool) # label(hypothesis) # label(non_clause). [assumption]. 1.48/1.71 549 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_am(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,Uu),Uua)),Uua)) # label(fact_ATP_Olambda__317) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 550 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lv,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_lu(Uu),Uua))))) # label(fact_ATP_Olambda__423) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 551 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_aas,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_aar,Uu))))) # label(fact_ATP_Olambda__30) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 552 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_re,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_rd,Uu))))) # label(fact_ATP_Olambda__116) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 553 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_sm,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_sl,Uu))))) # label(fact_ATP_Olambda__105) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 554 (all X scratc639425392all_of(aa_TPT43085870d_bool(aTP_Lamm_au,X)) = scratc1813389561nd_all(X)) # label(fact_def__all) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 555 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rz(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__561) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 556 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_tz(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ua,Uu),Uua)))) # label(fact_ATP_Olambda__380) # label(axiom) # label(non_clause). [assumption]. 1.48/1.71 557 (all X all Xa scratc1879612791nd_ind(scratc1920067545nd_nat,aa_TPT43085870d_bool(scratc304196016ffprop(aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1921379518nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc1837714885nd_den,Xa))),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1921379518nd_num,Xa)),aa_TPTP_ind_TPTP_ind(scratc1837714885nd_den,X)))) = aa_TPTP_ind_TPTP_ind(scratc597631537367_vo(X),Xa)) # label(fact_def__d__367__vo) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 558 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ow(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ox(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__617) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 559 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ns(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nt(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__618) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 560 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_zq,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_zr,Uu)))) # label(fact_ATP_Olambda__40) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 561 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ao(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uub))),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,Uua),Uub)),Uu))))) # label(fact_ATP_Olambda__527) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 562 (all X aa_TPTP_ind_TPTP_ind(scratc196346793_428_g,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1133920905_Sigma,scratc1920067545nd_nat),aTP_Lamm_am(X))) # label(fact_def__d__428__g) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 563 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ne,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uu),Uua)) -> pp(scratc1223190007_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919225325lesseq,Uu),Uua)))))) # label(fact_ATP_Olambda__312) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 564 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ja,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_iz(Uu),Uua))))) # label(fact_ATP_Olambda__439) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 565 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_so,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_sn,Uu))))) # label(fact_ATP_Olambda__104) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 566 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yc,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_yb(Uu),Uua))))) # label(fact_ATP_Olambda__350) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 567 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_yq,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_yr,Uu)))) # label(fact_ATP_Olambda__53) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 568 (all B_1 all B_2 gg_bool(aa_TPTP_ind_bool(B_1,B_2))) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 569 (all X all Xa scratc1860414882d_pair = scratc759553526d_pair(X,Xa)) # label(fact_def__d__pair) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 570 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yw,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,Uu),Uua)) -> pp(scratc1223190007_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uu),Uua)))))) # label(fact_ATP_Olambda__309) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 571 (all X all Xa (pp(aa_TPTP_ind_bool(scratc1912330826nd_min(X),Xa)) <-> pp(scratc1115724827_d_and(aa_TPTP_ind_bool(scratc231784252d_n_lb(X),Xa),aa_TPTP_ind_bool(X,Xa))))) # label(fact_def__min) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 572 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X22),aa_fun1431113780TP_ind(scratc999473378_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X22),X0)))) # label(fact_k__SepE1) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 573 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_rf(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uuc),Uua))))))) # label(fact_ATP_Olambda__703) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 574 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_wi(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wj(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__596) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 575 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xq,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uua)),Uu)))) # label(fact_ATP_Olambda__315) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 576 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_mp,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_mo,Uu))))) # label(fact_ATP_Olambda__158) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 577 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_il(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_im(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__628) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 578 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ze,Uu),Uua)))) # label(fact_ATP_Olambda__301) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 579 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1860414882d_pair,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc381596720nunion(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1307610839d_repl,X),scratc488888935d_Inj0)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1307610839d_repl,Xa),scratc488888936d_Inj1))) # label(fact_def__pair) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 580 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dr,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_dq(Uu),Uua))))) # label(fact_ATP_Olambda__476) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 581 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_uz,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_uy,Uu))))) # label(fact_ATP_Olambda__85) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 582 (all X all Xa all Xb all Xc all Xd aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1133920905_Sigma,X),aa_TPT1424761345TP_ind(aTP_Lamm_bh(Xc),Xd)) = aa_TPTP_ind_TPTP_ind(scratc720890091_inj_h(X,Xa,Xb,Xc),Xd)) # label(fact_def__inj__h) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 583 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xv(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__534) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 584 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fw,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_fv(Uu),Uua))))) # label(fact_ATP_Olambda__460) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 585 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fm,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_fl,Uu))))) # label(fact_ATP_Olambda__213) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 586 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uu),Uua)),Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kv,Uu),Uua)))) # label(fact_ATP_Olambda__316) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 587 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_aaj,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_aak,Uu)))) # label(fact_ATP_Olambda__33) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 588 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc165739421_power,X0))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1909615789d_Subq,X12),X0)))) # label(fact_k__PowerE) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 589 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1133920905_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,aa_TPTP_ind_TPTP_ind(scratc294253260_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc294253259_proj0,X22)))))) # label(fact_proj1__Sigma) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 590 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_rq(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rr,Uu),Uua)))) # label(fact_ATP_Olambda__388) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 591 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zc,Uu),Uua)))) # label(fact_ATP_Olambda__293) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 592 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_aay,Uu)) <-> pp(aa_fun171081125l_bool(scratc1929181822nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1719206485d_d_Pi,scratc1920067545nd_nat),aTP_Lamm_al)),aa_TPT43085870d_bool(aTP_Lamm_aax,Uu))))) # label(fact_ATP_Olambda__7) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 593 (all Uu all Uua all Uub all Uuc all Uud ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc712927111d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,Uub),Uud)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_az(Uu),Uua),Uub),Uuc),Uud)))) # label(fact_ATP_Olambda__731) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 594 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_st,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),Uua)),Uua))))) # label(fact_ATP_Olambda__270) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 595 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tj,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uua)),Uu))))) # label(fact_ATP_Olambda__282) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 596 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bb(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013318955d_esti(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__661) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 597 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_pk,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_pl,Uu)))) # label(fact_ATP_Olambda__129) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 598 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919225325lesseq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uu),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uua),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919225325lesseq,Uub),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_mq(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__686) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 599 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_yd,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_yc,Uu))))) # label(fact_ATP_Olambda__59) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 600 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eo,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_en(Uu),Uua))))) # label(fact_ATP_Olambda__470) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 601 (all P all Q all R aa_TPTP_ind_bool(aa_TPT43085870d_bool(cOMBC_1555011498d_bool(P),Q),R) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind_001t__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 602 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_vc,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_vb,Uu))))) # label(fact_ATP_Olambda__84) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 603 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,X),Xa)) <-> pp(aa_bool_bool(scratc100336135d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,X),Xa))))) # label(fact_def__lessis) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 604 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc165739421_power,X0))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1909615789d_Subq,X12),X0)))) # label(fact_k__PowerEq) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 605 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ns(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uu),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uua),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uub),Uuc))))))) # label(fact_ATP_Olambda__696) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 606 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ez(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uu),Uua))))) # label(fact_ATP_Olambda__513) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 607 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sa,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_rz(Uu),Uua))))) # label(fact_ATP_Olambda__385) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 608 (all X aa_TPT1424761345TP_ind(scratc102231095bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1952078626d_plus,X)) = scratc232046658d_n_pl(X)) # label(fact_def__n__pl) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 609 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_ql(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qm,Uu),Uua)))) # label(fact_ATP_Olambda__397) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 610 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vp(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__499) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 611 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_lv,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_lw,Uu)))) # label(fact_ATP_Olambda__165) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 612 (all X all Xa (pp(aa_bool_bool(scratc100336135d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc758693855t_more,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc173054068_rt_is,X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc218225321moreis,X),Xa)))) # label(fact_def__rt__moreis) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 613 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dh(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919225325lesseq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919225325lesseq,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919225325lesseq,aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uua),Uuc))))))) # label(fact_ATP_Olambda__682) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 614 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_yv,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_yu,Uu))))) # label(fact_ATP_Olambda__51) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 615 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gv(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uua),Uuc))))))) # label(fact_ATP_Olambda__718) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 616 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_mb,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_mc,Uu)))) # label(fact_ATP_Olambda__163) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 617 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1909615789d_Subq,X12),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc165739421_power,X0))))) # label(fact_k__PowerI) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 618 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_zo,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_zp,Uu)))) # label(fact_ATP_Olambda__41) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 619 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_uw(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ux(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__598) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 620 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jd,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_jc(Uu),Uua))))) # label(fact_ATP_Olambda__438) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 621 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qr(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__536) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 622 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ug(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__681) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 623 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mm,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919225325lesseq,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706324_moreq,Uua),Uu))))) # label(fact_ATP_Olambda__295) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 624 (all X0 all X12 pp(aa_fun171081125l_bool(scratc639425392all_of(aa_TPT43085870d_bool(aTP_Lamm_au,X0)),aa_fun1584354236d_bool(aTP_Lamm_acj(X0),X12)))) # label(fact_e__isp) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 625 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jc(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__507) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 626 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ct(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cu,Uu),Uua)))) # label(fact_ATP_Olambda__480) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 627 (all X all Xa scratc1846697984nd_eps(aa_TPT43085870d_bool(scratc477123128_rec_G(X),Xa)) = aa_TPTP_ind_TPTP_ind(scratc188604815In_rec(X),Xa)) # label(fact_def__d__In__rec) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 628 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_fa,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fb,Uu)))) # label(fact_ATP_Olambda__216) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 629 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_pm(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pn(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__613) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 630 (all X all Xa all Xb all Xc all Xd all Xe (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc294646855_prop2(X,Xa,Xb,Xc),Xd),Xe)) <-> pp(aa_fun171081125l_bool(scratc1897569848l_some(X),aa_TPT43085870d_bool(scratc1634590515_prop1(X,Xa,Xb,Xc,Xd),Xe))))) # label(fact_def__prop2) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 631 (all Uu all Uua all Uub (pp(scratc1115724827_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uu),Uub),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uub),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ln(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__577) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 632 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zw,Uu),Uua)) <-> pp(scratc772951858_amone(scratc1920067545nd_nat,aa_TPT43085870d_bool(aTP_Lamm_zs(Uu),Uua))))) # label(fact_ATP_Olambda__482) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 633 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cd,Uu),Uua)) <-> (pp(scratc1223190007_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc758693855t_more,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc84241709lessis,Uu),Uua))))) # label(fact_ATP_Olambda__322) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 634 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_md(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919225325lesseq,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uu),Uub)))))) # label(fact_ATP_Olambda__559) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 635 (all X7 all Y (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) | Y != X7)) # label(help_fequal_2_1_fequal_001t__TPTP____Interpret__Oind_T) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 636 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wc,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_wb(Uu),Uua))))) # label(fact_ATP_Olambda__364) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 637 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_bh(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,Uu),Uub))) # label(fact_ATP_Olambda__593) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 638 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_gz(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ha,Uu),Uua)))) # label(fact_ATP_Olambda__451) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 639 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919225325lesseq,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hv(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__698) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 640 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_aap,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_aao,Uu))))) # label(fact_ATP_Olambda__31) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 641 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc231390674d_n_fr,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1921379518nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc1837714885nd_den,Xa))),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1921379518nd_num,Xa)),aa_TPTP_ind_TPTP_ind(scratc1837714885nd_den,X)))),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1837714885nd_den,X)),aa_TPTP_ind_TPTP_ind(scratc1837714885nd_den,Xa))) = aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(X),Xa)) # label(fact_def__n__pf) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 642 (all X all Xa scratc1738843356second(X,Xa) = scratc294253260_proj1) # label(fact_def__second) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 643 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(scratc282061419nd_n_1),Uu)),Uu)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_sv,Uu)))) # label(fact_ATP_Olambda__6) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 644 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cg,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cf,Uu))))) # label(fact_ATP_Olambda__239) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 645 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pw,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_pv(Uu),Uua))))) # label(fact_ATP_Olambda__402) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 646 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919225325lesseq,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dp(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__697) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 647 (all X (pp(aa_fun171081125l_bool(scratc1897569848l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1719206485d_d_Pi,scratc1920067545nd_nat),aTP_Lamm_al)),aa_TPT43085870d_bool(scratc1087267889_prop2,X))) <-> pp(aa_TPTP_ind_bool(scratc294646857_prop4,X)))) # label(fact_def__prop4) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 648 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc477123128_rec_G(X),Xa),Xb)) <-> (all X3 ((all X4 all X5 (gg_TPTP_ind(X4) -> ((all X6 (gg_TPTP_ind(X6) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X6),X4)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(X3,X6),aa_TPTP_ind_TPTP_ind(X5,X6)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(X3,X4),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(X,X4),X5)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(X3,Xa),Xb)))))) # label(fact_def__d__In__rec__G) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 649 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_gw(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,Uu),Uua)))) # label(fact_ATP_Olambda__452) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 650 (all X all Xa all Xb scratc213220141d_11_i(X,Xa,Xb) = scratc1988651843_indeq(X,Xa,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1719206485d_d_Pi,X),aTP_Lamm_aj(Xb)))) # label(fact_def__d__11__i) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 651 (all Uu (gg_TPTP_ind(Uu) -> (scratc1169782717ptyset != Uu <-> pp(aa_TPTP_ind_bool(aTP_Lamm_at,Uu))))) # label(fact_ATP_Olambda__247) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 652 (all X all Xa all Xb scratc1754835450eft_f1(X,Xa,Xb) = scratc918398959d_left(X,Xb,Xa)) # label(fact_def__left__f1) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 653 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gk(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__550) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 654 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uu),aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gq(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__523) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 655 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc1920985925nd_non(X,Xa),Xb)) <-> pp(scratc1223190007_d_not(aa_TPTP_ind_bool(Xa,Xb))))) # label(fact_def__non) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 656 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_if,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ig,Uu)))) # label(fact_ATP_Olambda__191) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 657 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(scratc282061419nd_n_1),Uu)),aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_aat,Uu)))) # label(fact_ATP_Olambda__5) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 658 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fu,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ft,Uu))))) # label(fact_ATP_Olambda__211) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 659 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_xl,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_xk,Uu))))) # label(fact_ATP_Olambda__65) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 660 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wo,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_wn(Uu),Uua))))) # label(fact_ATP_Olambda__361) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 661 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ej(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uua),Uuc))))))) # label(fact_ATP_Olambda__694) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 662 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_pu(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__722) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 663 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_wq(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__704) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 664 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aa_TPT43085870d_bool(aTP_Lamm_ace(Uu),Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_acg(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ach(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__495) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 665 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ic,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ib,Uu))))) # label(fact_ATP_Olambda__192) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 666 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_mn,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_mm,Uu))))) # label(fact_ATP_Olambda__159) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 667 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_abc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_abd,Uu)))) # label(fact_ATP_Olambda__28) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 668 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wn(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_wm(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__595) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 669 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zy(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__510) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 670 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_gi,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_gj,Uu)))) # label(fact_ATP_Olambda__206) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 671 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cl,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cm,Uu)))) # label(fact_ATP_Olambda__236) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 672 (all X aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1307610839d_repl,X),scratc488888936d_Inj1) = aa_TPTP_ind_TPTP_ind(scratc488888935d_Inj0,X)) # label(fact_def__d__Inj0) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 673 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dg,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_df,Uu))))) # label(fact_ATP_Olambda__229) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 674 (all Uu all Uua ((pp(scratc1223190007_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yu,Uu),Uua)))) # label(fact_ATP_Olambda__324) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 675 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dk,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_dj,Uu))))) # label(fact_ATP_Olambda__228) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 676 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_uv,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_uu,Uu))))) # label(fact_ATP_Olambda__86) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 677 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_dz,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ea,Uu)))) # label(fact_ATP_Olambda__224) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 678 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ct(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc173054068_rt_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc173054068_rt_is,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc173054068_rt_is,Uu),Uub)))))) # label(fact_ATP_Olambda__548) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 679 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_fp,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fq,Uu)))) # label(fact_ATP_Olambda__212) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 680 (all X0 all X12 pp(aa_fun171081125l_bool(scratc639425392all_of(aa_fun1584354236d_bool(aTP_Lamm_acb(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_acc(X0),X12)))) # label(fact_e__inp) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 681 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cc,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cb,Uu))))) # label(fact_ATP_Olambda__241) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 682 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tv(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_tu(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__605) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 683 (all X all Xa all Xb all Xc (pp(aa_fun171081125l_bool(scratc639425392all_of(aa_TPT43085870d_bool(aTP_Lamm_au,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ba(X),Xa),Xb),Xc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1274769628_fixfu(X,Xa),Xb),Xc)))) # label(fact_def__fixfu) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 684 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ev,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_eu,Uu))))) # label(fact_ATP_Olambda__218) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 685 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc1281741614hangef(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1133920905_Sigma,X),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_bg(X),Xb),Xc),Xd))) # label(fact_def__changef) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 686 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_na,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_nb,Uu)))) # label(fact_ATP_Olambda__154) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 687 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1183411315_image(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1897569848l_some(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bj(Xa),Xb),Xc))))) # label(fact_def__image) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 688 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iw(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__516) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 689 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_zg,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_zh,Uu)))) # label(fact_ATP_Olambda__45) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 690 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,Xa),scratc227979528d_n_2t) = aa_TPTP_ind_TPTP_ind(scratc643863125econd1(X),Xa)) # label(fact_def__second1) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 691 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_es,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_er,Uu))))) # label(fact_ATP_Olambda__219) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 692 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(X),Xa)),Xb)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(X),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Xa),Xb)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1675630063_prop1(X),Xa),Xb)))) # label(fact_def__d__25__prop1) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 693 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_yk,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_yl,Uu)))) # label(fact_ATP_Olambda__56) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 694 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_om,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_on,Uu)))) # label(fact_ATP_Olambda__134) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 695 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_he,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_hf,Uu)))) # label(fact_ATP_Olambda__198) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 696 (all X0 scratc1169782717ptyset != aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,X0)) # label(fact_neq__ordsucc__0) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 697 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yy,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,Uu),Uua)) -> pp(scratc1223190007_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uu),Uua)))))) # label(fact_ATP_Olambda__308) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 698 (all B_1 gg_bool(fEx_TPTP_ind(B_1))) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 699 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gi,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_gh(Uu),Uua))))) # label(fact_ATP_Olambda__456) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 700 (all Uu (gg_TPTP_ind(Uu) -> ((exists X2 (aa_TPTP_ind_TPTP_ind(scratc488888936d_Inj1,X2) = Uu & gg_TPTP_ind(X2))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_bt,Uu))))) # label(fact_ATP_Olambda__248) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 701 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jt(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uuc),Uua))))))) # label(fact_ATP_Olambda__713) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 702 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qv,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_qu(Uu),Uua))))) # label(fact_ATP_Olambda__394) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 703 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ip(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__695) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 704 (all X0 all X12 pp(aa_fun171081125l_bool(scratc639425392all_of(aa_TPT43085870d_bool(aTP_Lamm_abu(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_abx(X0),X12)))) # label(fact_first__p) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 705 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ja,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_jb,Uu)))) # label(fact_ATP_Olambda__185) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 706 (all P all Q (-pp(P) | pp(Q) | -pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 707 (all Uu all Uua ((pp(scratc1223190007_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ys,Uu),Uua)))) # label(fact_ATP_Olambda__331) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 708 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lu(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919225325lesseq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919225325lesseq,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919225325lesseq,Uu),Uub)))))) # label(fact_ATP_Olambda__546) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 709 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yb(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__575) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 710 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uuc),Uua))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jl(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__717) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 711 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_oi,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_oh,Uu))))) # label(fact_ATP_Olambda__136) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 712 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1245779368d_outn(X),aa_TPTP_ind_TPTP_ind(scratc1879612801nd_inn(Xa),Xb)) = aa_TPTP_ind_TPTP_ind(scratc1637978109eft1to(X,Xa),Xb)) # label(fact_def__left1to) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 713 (all X aa_TPTP_ind_TPTP_ind(scratc1811264907d_Sing,X) = aa_TPTP_ind_TPTP_ind(scratc1028407283_UPair(X),X)) # label(fact_def__d__Sing) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 714 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc102755877bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc102755885bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1307610839d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_by(X),Xa))),scratc1169782717ptyset) = aa_fun1431113780TP_ind(scratc999473378_d_Sep(X),Xa)) # label(fact_def__d__Sep) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 715 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X33),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,aa_TPTP_ind_TPTP_ind(X22,X33)),aa_TPTP_ind_TPTP_ind(X12,X33)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1133920905_Sigma,X0),X22)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1719206485d_d_Pi,X0),X12))))) # label(fact_lam__Pi) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 716 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_kb(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kc,Uu),Uua)))) # label(fact_ATP_Olambda__431) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 717 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ph,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_pg,Uu))))) # label(fact_ATP_Olambda__130) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 718 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zt(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,Uua),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uub))))) # label(fact_ATP_Olambda__590) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 719 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cp,Uu),Uua)) <-> pp(scratc1929444168nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc173054068_rt_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc758693855t_more,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2043040867t_less,Uu),Uua))))) # label(fact_ATP_Olambda__253) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 720 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_py(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__670) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 721 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc231390674d_n_fr,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uua),Uub))),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc231390674d_n_fr,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_og(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__497) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 722 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fr(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uua),Uuc))))))) # label(fact_ATP_Olambda__710) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 723 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xg(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__563) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 724 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_oa,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ob,Uu)))) # label(fact_ATP_Olambda__143) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 725 (all X0 (pp(aa_TPTP_ind_bool(scratc2014913431_nat_p,X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X0),scratc1611392121_omega)))) # label(fact_nat__p__omega) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 726 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_yx,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_yw,Uu))))) # label(fact_ATP_Olambda__50) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 727 (all X0 all X12 pp(aa_fun171081125l_bool(scratc639425392all_of(aa_TPT43085870d_bool(aTP_Lamm_au,X0)),aa_TPT43085870d_bool(aTP_Lamm_abz(X0),X12)))) # label(fact_e__pair__p) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 728 (all X all Xa all Xb aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1133920905_Sigma,aa_TPTP_ind_TPTP_ind(scratc719566192_d_1to,scratc282061420nd_n_2)),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ai(X),Xa),Xb)) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2007612175_pair1(X),Xa),Xb)) # label(fact_def__pair1) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 729 (all B_1 all B_2 gg_TPTP_ind(scratc1879612791nd_ind(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__63417__16348_ONUM788__thf__4__p_Obnd__ind) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 730 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706324_moreq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706324_moreq,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706324_moreq,aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dl(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__687) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 731 (all X (pp(aa_TPTP_ind_bool(scratc1087267888_prop1,X)) <-> pp(aa_fun171081125l_bool(scratc540698651_n_all,aa_TPT43085870d_bool(aTP_Lamm_aq,X))))) # label(fact_def__d__24__prop1) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 732 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc165739421_power,X0)))) # label(fact_k__Self__In__Power) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 733 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_mt,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ms,Uu))))) # label(fact_ATP_Olambda__157) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 734 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uua),Uub))),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_si(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__525) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 735 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xd(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__573) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 736 (all B_1 all B_2 gg_bool(scratc99680130d_l_ec(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__63417__16348_ONUM788__thf__4__p_Obnd__l__ec) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 737 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kq(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__552) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 738 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abm(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc798277750d_incl(Uu),Uua),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc798277750d_incl(Uu),Uub),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc712927111d_e_is(aa_TPTP_ind_TPTP_ind(scratc165739421_power,Uu)),Uua),Uub)))))) # label(fact_ATP_Olambda__491) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 739 (all X0 all X12 all X22 all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1719206485d_d_Pi,X0),X12))) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X32),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,X22),X32)),aa_TPTP_ind_TPTP_ind(X12,X32)))))) # label(fact_ap__Pi) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 740 (all Uu all Uua all Uub all Uuc (pp(aa_fun171081125l_bool(scratc1897569848l_some(Uua),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bb(Uu),Uub),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bc(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__727) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 741 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1133920905_Sigma,X0),X12))) -> X22 = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1860414882d_pair,aa_TPTP_ind_TPTP_ind(scratc294253259_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc294253260_proj1,X22))))) # label(fact_proj__Sigma__eta) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 742 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_oh,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_og(Uu),Uua))))) # label(fact_ATP_Olambda__410) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 743 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1880006386nd_ite(X,Xa,Xb),Xc) = scratc1879612791nd_ind(Xa,aa_TPT43085870d_bool(scratc294646854_prop1(X,Xa,Xb),Xc))) # label(fact_def__ite) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 744 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,Uu),aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aq,Uu),Uua)))) # label(fact_ATP_Olambda__277) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 745 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_in,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_io,Uu)))) # label(fact_ATP_Olambda__189) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 746 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hz(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919225325lesseq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uua),Uuc))))))) # label(fact_ATP_Olambda__685) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 747 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ju(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jv,Uu),Uua)))) # label(fact_ATP_Olambda__433) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 748 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_uj,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_ui,Uu))))) # label(fact_ATP_Olambda__89) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 749 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_iv,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_iu,Uu))))) # label(fact_ATP_Olambda__187) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 750 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_nt(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nu,Uu),Uua)))) # label(fact_ATP_Olambda__414) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 751 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_uk(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__673) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 752 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_sj,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_sk,Uu)))) # label(fact_ATP_Olambda__106) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 753 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ej(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ek(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__641) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 754 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pc,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_pb(Uu),Uua))))) # label(fact_ATP_Olambda__407) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 755 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_rs,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_rr,Uu))))) # label(fact_ATP_Olambda__112) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 756 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_qg,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_qh,Uu)))) # label(fact_ATP_Olambda__123) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 757 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_tg,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_tf,Uu))))) # label(fact_ATP_Olambda__98) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 758 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tz(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ty(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__604) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 759 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_ws,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_wt,Uu)))) # label(fact_ATP_Olambda__71) # label(axiom) # label(non_clause). [assumption]. 1.48/1.72 760 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mr(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_mq(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__621) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 761 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc116508590_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Xa),X))))) # label(fact_def__d__26__prop1) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 762 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_mv(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mw,Uu),Uua)))) # label(fact_ATP_Olambda__416) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 763 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_kx(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ky,Uu),Uua)))) # label(fact_ATP_Olambda__425) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 764 (all Uu all Uua (gg_TPTP_ind(Uua) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_br,Uu),Uua)) <-> (exists X3 (gg_TPTP_ind(X3) & aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1860414882d_pair,Uu),X3) = Uua))))) # label(fact_ATP_Olambda__485) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 765 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eq(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__514) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 766 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sf(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uua),Uub)))))) # label(fact_ATP_Olambda__521) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 767 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_uh(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ug(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__602) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 768 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ur,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_uq,Uu))))) # label(fact_ATP_Olambda__87) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 769 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kl,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_kk(Uu),Uua))))) # label(fact_ATP_Olambda__428) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 770 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aau,Uu),Uua)))) # label(fact_ATP_Olambda__276) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 771 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_yt,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_ys,Uu))))) # label(fact_ATP_Olambda__52) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 772 (all B_1 all B_2 all B_3 gg_bool(scratc1929444168nd_or3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__63417__16348_ONUM788__thf__4__p_Obnd__or3) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 773 (all X all Xa (pp(scratc1115724827_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,Xa),scratc282061419nd_n_1)),X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1179442032_prop1,X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1179442033_prop2,X),Xa)))) # label(fact_def__d__428__prop2) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 774 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ack,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc712927111d_e_is(Uu),Uua),Uua)))) # label(fact_ATP_Olambda__262) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 775 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_pz(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qa,Uu),Uua)))) # label(fact_ATP_Olambda__401) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 776 (all X0 all X12 pp(aa_fun171081125l_bool(scratc639425392all_of(aa_TPT43085870d_bool(aTP_Lamm_au,X0)),aa_fun1584354236d_bool(aTP_Lamm_abp(X0),X12)))) # label(fact_estii) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 777 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aar,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__272) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 778 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ex,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ew(Uu),Uua))))) # label(fact_ATP_Olambda__467) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 779 (all X all Xa (pp(aa_fun171081125l_bool(scratc540698651_n_all,aa_TPT43085870d_bool(scratc1593616289lbprop(X),Xa))) <-> pp(aa_TPTP_ind_bool(scratc231784252d_n_lb(X),Xa)))) # label(fact_def__n__lb) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 780 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_er,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_eq(Uu),Uua))))) # label(fact_ATP_Olambda__469) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 781 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_kf,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_kg,Uu)))) # label(fact_ATP_Olambda__176) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 782 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iz(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uu),Uua))))) # label(fact_ATP_Olambda__504) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 783 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hb,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ha,Uu))))) # label(fact_ATP_Olambda__200) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 784 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cv,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cu,Uu))))) # label(fact_ATP_Olambda__232) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 785 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ou,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ot,Uu))))) # label(fact_ATP_Olambda__139) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 786 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ab,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,Uu))))) # label(fact_ATP_Olambda__242) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 787 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ni,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_nj,Uu)))) # label(fact_ATP_Olambda__150) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 788 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ok,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_oj(Uu),Uua))))) # label(fact_ATP_Olambda__409) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 789 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tf,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uua),aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uu))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,Uua),Uu))))) # label(fact_ATP_Olambda__275) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 790 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_xq,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_xr,Uu)))) # label(fact_ATP_Olambda__63) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 791 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_me,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_md(Uu),Uua))))) # label(fact_ATP_Olambda__420) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 792 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_pm(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uua),Uuc))))))) # label(fact_ATP_Olambda__672) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 793 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_st,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_su,Uu)))) # label(fact_ATP_Olambda__102) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 794 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_mx,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_mw,Uu))))) # label(fact_ATP_Olambda__156) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 795 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xa(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__533) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 796 (all X0 all X12 all X22 (gg_TPTP_ind(X12) -> (pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc102755877bnd_if(X0,X12),X22) = X12))) # label(fact_if__i__1) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 797 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_mk,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ml,Uu)))) # label(fact_ATP_Olambda__160) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 798 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_pq(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uua),Uuc))))))) # label(fact_ATP_Olambda__674) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 799 (all X0 all X12 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc409976095ective(aa_fun1431113780TP_ind(scratc999473378_d_Sep(X0),X12)),X0),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1133920905_Sigma,aa_fun1431113780TP_ind(scratc999473378_d_Sep(X0),X12)),scratc712927106d_e_in(X0,X12))))) # label(fact_otax1) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 800 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1921379518nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc1837714885nd_den,Xa))),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1921379518nd_num,Xa)),aa_TPTP_ind_TPTP_ind(scratc1837714885nd_den,X)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,X),Xa)))) # label(fact_def__n__eq) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 801 (all Uu all Uua ((pp(scratc1223190007_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2043040867t_less,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc218225321moreis,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cb,Uu),Uua)))) # label(fact_ATP_Olambda__323) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 802 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_dm(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dn,Uu),Uua)))) # label(fact_ATP_Olambda__477) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 803 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ue,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_ud(Uu),Uua))))) # label(fact_ATP_Olambda__379) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 804 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_oc,Uu),Uua)) <-> pp(scratc1929444168nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uu),Uua))))) # label(fact_ATP_Olambda__255) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 805 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,Xa),scratc227913929d_n_1t) = aa_TPTP_ind_TPTP_ind(scratc318352169first1(X),Xa)) # label(fact_def__first1) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 806 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vw,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_vv(Uu),Uua))))) # label(fact_ATP_Olambda__366) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 807 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vz,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_vy(Uu),Uua))))) # label(fact_ATP_Olambda__365) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 808 (all Uu all Uua (pp(scratc1845845133nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zi,Uu),Uua)))) # label(fact_ATP_Olambda__257) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 809 (all P all Q (-pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)) | pp(Q))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 810 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Xa),X))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1767804207_prop1,X),Xa)))) # label(fact_def__d__429__prop1) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 811 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_hc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_hd,Uu)))) # label(fact_ATP_Olambda__199) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 812 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_qp,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_qq,Uu)))) # label(fact_ATP_Olambda__120) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 813 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vv(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__542) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 814 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ko,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_kp,Uu)))) # label(fact_ATP_Olambda__173) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 815 (all X aa_TPTP_ind_TPTP_ind(scratc604263049r1type,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1719206485d_d_Pi,aa_TPTP_ind_TPTP_ind(scratc719566192_d_1to,scratc282061420nd_n_2)),aTP_Lamm_aj(X))) # label(fact_def__pair1type) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 816 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mh,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_mg(Uu),Uua))))) # label(fact_ATP_Olambda__419) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 817 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X22),X0)) -> (all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X32),aa_TPTP_ind_TPTP_ind(X12,X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1860414882d_pair,X22),X32)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1133920905_Sigma,X0),X12))))))) # label(fact_pair__Sigma) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 818 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_uu,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_ut(Uu),Uua))))) # label(fact_ATP_Olambda__375) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 819 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_jf(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jg,Uu),Uua)))) # label(fact_ATP_Olambda__437) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 820 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_aac,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_aad,Uu)))) # label(fact_ATP_Olambda__36) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 821 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cy,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc173054068_rt_is,Uu),Uu)))) # label(fact_ATP_Olambda__21) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 822 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1535223269munion,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc673001287_union,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1307610839d_repl,X),Xa))) # label(fact_def__famunion) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 823 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_bk(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1879547204nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc712927111d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,Uub),Uud))),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc712927111d_e_is(Uu),Uuc),Uud))))) # label(fact_ATP_Olambda__730) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 824 (all Uu all Uua (pp(scratc1115724827_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,Uua),scratc282061419nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uu)),aa_fun171081125l_bool(scratc540698651_n_all,aa_TPT43085870d_bool(aTP_Lamm_aq,Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aax,Uu),Uua)))) # label(fact_ATP_Olambda__266) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 825 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nk,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919225325lesseq,Uu),Uua)) -> pp(scratc1223190007_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uu),Uua)))))) # label(fact_ATP_Olambda__310) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 826 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ls,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uua),Uu)))) # label(fact_ATP_Olambda__340) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 827 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abt(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aa_TPT43085870d_bool(aTP_Lamm_au,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_abs(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__586) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 828 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_fk(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fl,Uu),Uua)))) # label(fact_ATP_Olambda__463) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 829 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_zb,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_za,Uu))))) # label(fact_ATP_Olambda__48) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 830 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_pu(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pv(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__611) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 831 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aao,Uu),Uua)))) # label(fact_ATP_Olambda__321) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 832 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_pr(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ps,Uu),Uua)))) # label(fact_ATP_Olambda__403) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 833 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_wf(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wg,Uu),Uua)))) # label(fact_ATP_Olambda__363) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 834 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cw,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc173054068_rt_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc173054068_rt_is,Uua),Uu))))) # label(fact_ATP_Olambda__296) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 835 (all X0 (pp(aa_TPTP_ind_bool(X0,scratc1169782717ptyset)) -> ((all X13 (gg_TPTP_ind(X13) -> (pp(aa_TPTP_ind_bool(scratc2014913431_nat_p,X13)) -> (pp(aa_TPTP_ind_bool(X0,X13)) -> pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,X13))))))) -> (all X12 (pp(aa_TPTP_ind_bool(scratc2014913431_nat_p,X12)) -> pp(aa_TPTP_ind_bool(X0,X12))))))) # label(fact_nat__ind) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 836 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_zx,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_zw,Uu))))) # label(fact_ATP_Olambda__38) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 837 (all Uu all Uua (pp(scratc1845845133nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc493910842n_some,aa_TPT43085870d_bool(scratc304196016ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc493910842n_some,aa_TPT43085870d_bool(scratc304196016ffprop(Uua),Uu)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zo,Uu),Uua)))) # label(fact_ATP_Olambda__261) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 838 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1920592336nd_nis,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(X),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1293232940_prop1(X),Xa),Xb)))) # label(fact_def__d__28__prop1) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 839 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_au,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,Uua),Uu)))) # label(fact_ATP_Olambda__344) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 840 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_mr(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ms,Uu),Uua)))) # label(fact_ATP_Olambda__417) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 841 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_is,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ir,Uu))))) # label(fact_ATP_Olambda__188) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 842 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ee,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ed,Uu))))) # label(fact_ATP_Olambda__223) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 843 (all X aa_TPTP_ind_TPTP_ind(scratc1091132153d_1out,X) = aa_TPTP_ind_TPTP_ind(scratc1245779368d_outn(X),scratc282061419nd_n_1)) # label(fact_def__d__1out) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 844 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_qw,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_qv,Uu))))) # label(fact_ATP_Olambda__118) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 845 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc893179352ght1to(X,Xa),Xb) = aa_TPTP_ind_TPTP_ind(scratc1245779368d_outn(aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(X),aa_TPTP_ind_TPTP_ind(scratc1879612801nd_inn(Xa),Xb)))) # label(fact_def__right1to) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 846 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_oa,Uu),Uua)) <-> pp(scratc1845845133nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uu),Uua))))) # label(fact_ATP_Olambda__258) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 847 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_uo(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053471335moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__675) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 848 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_vt,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_vu,Uu)))) # label(fact_ATP_Olambda__78) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 849 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_my,Uu),Uua)) <-> (pp(scratc1223190007_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919225325lesseq,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uu),Uua))))) # label(fact_ATP_Olambda__327) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 850 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_rj(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__702) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 851 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_wj(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wk,Uu),Uua)))) # label(fact_ATP_Olambda__362) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 852 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ki,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_kj,Uu)))) # label(fact_ATP_Olambda__175) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 853 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_gr,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_gs,Uu)))) # label(fact_ATP_Olambda__203) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 854 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cz,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,Uu),scratc636914614d_frac)))) # label(fact_ATP_Olambda__24) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 855 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_wx(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wy,Uu),Uua)))) # label(fact_ATP_Olambda__358) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 856 (all X (pp(aa_bool_bool(scratc100336135d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,X),scratc282061419nd_n_1)),aa_fun171081125l_bool(scratc493910842n_some,aa_TPT43085870d_bool(aTP_Lamm_ar,X)))) <-> pp(aa_TPTP_ind_bool(scratc498905713_prop1,X)))) # label(fact_def__d__23__prop1) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 857 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_uc(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__721) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 858 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_nl,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_nk,Uu))))) # label(fact_ATP_Olambda__149) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 859 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (-pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc102755877bnd_if(X0,X12),X22) = X22))) # label(fact_if__i__0) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 860 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hi,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_hh,Uu))))) # label(fact_ATP_Olambda__197) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 861 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_wk,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_wl,Uu)))) # label(fact_ATP_Olambda__73) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 862 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc1929181822nd_one(X0),X12)) -> scratc2128269225_is_of(scratc1879612791nd_ind(X0,X12),aa_TPT43085870d_bool(aTP_Lamm_au,X0)))) # label(fact_ind__p) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 863 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ib,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ia(Uu),Uua))))) # label(fact_ATP_Olambda__446) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 864 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_pq(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pr(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__612) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 865 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_le,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_lf,Uu)))) # label(fact_ATP_Olambda__138) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 866 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(Uua,Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc712927111d_e_is(Uu),Uub),Uuc)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bn(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__725) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 867 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_or,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_os,Uu)))) # label(fact_ATP_Olambda__140) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 868 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vq,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_vp(Uu),Uua))))) # label(fact_ATP_Olambda__368) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 869 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uua),Uub)),Uu)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uua),Uuc)),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uub),Uuc)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hj(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__667) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 870 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_jy(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jz,Uu),Uua)))) # label(fact_ATP_Olambda__432) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 871 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_pe(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uua),Uuc))))))) # label(fact_ATP_Olambda__720) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 872 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1737558087_ecelt(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc999473378_d_Sep(X),aa_TPT43085870d_bool(Xa,Xb))) # label(fact_def__ecelt) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 873 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kf,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_ke(Uu),Uua))))) # label(fact_ATP_Olambda__430) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 874 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_it(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__508) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 875 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_fy(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fz,Uu),Uua)))) # label(fact_ATP_Olambda__459) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 876 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc758693855t_more,Uu),Uua)) -> pp(scratc1223190007_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc84241709lessis,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,Uu),Uua)))) # label(fact_ATP_Olambda__306) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 877 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_co,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cn,Uu))))) # label(fact_ATP_Olambda__235) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 878 (all X all Xa (-pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1918493163nd_nIn,X),Xa)))) # label(fact_def__nIn) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 879 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ow(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uua),Uuc))))))) # label(fact_ATP_Olambda__678) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 880 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_lk(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ll,Uu),Uua)))) # label(fact_ATP_Olambda__424) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 881 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gz(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uua),Uub)),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uub),aa_TPTP_ind_TPTP_ind(scratc1454525887_367_w(Uu),Uua))))))) # label(fact_ATP_Olambda__528) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 882 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1535223269munion,X),aTP_Lamm_bs(Xa)) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1133920905_Sigma,X),Xa)) # label(fact_def__d__Sigma) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 883 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(scratc102755877bnd_if(aa_TPTP_ind_bool(Uua,Uub),Uub),scratc1846697984nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bm(Uu),Uua))) = aa_TPTP_ind_TPTP_ind(aa_fun1235454963TP_ind(aTP_Lamm_by(Uu),Uua),Uub)) # label(fact_ATP_Olambda__488) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 884 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abc,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1920592336nd_nis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1920592336nd_nis,aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uua)))))) # label(fact_ATP_Olambda__280) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 885 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eg(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ef(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__642) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 886 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ng,Uu),Uua)) <-> (pp(scratc1223190007_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706324_moreq,Uu),Uua))))) # label(fact_ATP_Olambda__330) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 887 (all X0 all X12 pp(aa_fun171081125l_bool(scratc639425392all_of(aa_fun1584354236d_bool(aTP_Lamm_acb(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_acd(X0),X12)))) # label(fact_e__in__p) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 888 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1845845194nd_ecp(X,Xa),Xb),Xc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc712927111d_e_is(aa_TPTP_ind_TPTP_ind(scratc165739421_power,X)),Xb),aa_TPTP_ind_TPTP_ind(scratc1737558087_ecelt(X,Xa),Xc))))) # label(fact_def__ecp) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 889 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_gn(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_go,Uu),Uua)))) # label(fact_ATP_Olambda__454) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 890 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1921379518nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc1837714885nd_den,Xa))),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1921379518nd_num,Xa)),aa_TPTP_ind_TPTP_ind(scratc1837714885nd_den,X)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,X),Xa)))) # label(fact_def__moref) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 891 (all X all Xa scratc102231095bnd_ap = scratc803260656d_tofs(X,Xa)) # label(fact_def__tofs) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 892 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gd,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_gc,Uu))))) # label(fact_ATP_Olambda__208) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 893 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ol,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_ok,Uu))))) # label(fact_ATP_Olambda__135) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 894 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1754835451eft_f2(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc918398959d_left(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(scratc1754835450eft_f1(X,Xa,Xb),Xc))) # label(fact_def__left__f2) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 895 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dt(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919225325lesseq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uua),Uuc))))))) # label(fact_ATP_Olambda__684) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 896 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_xs(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xt,Uu),Uua)))) # label(fact_ATP_Olambda__353) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 897 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_oj(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc231390674d_n_fr,Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc231390674d_n_fr,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uua),Uub)))))) # label(fact_ATP_Olambda__529) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 898 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_pa(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pb(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__616) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 899 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_uq,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_up(Uu),Uua))))) # label(fact_ATP_Olambda__376) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 900 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_fz,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ga,Uu)))) # label(fact_ATP_Olambda__209) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 901 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qz,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_qy(Uu),Uua))))) # label(fact_ATP_Olambda__393) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 902 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uua),aa_TPTP_ind_TPTP_ind(scratc1454525887_367_w(Uu),Uua))),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_he,Uu),Uua)))) # label(fact_ATP_Olambda__278) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 903 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ro,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_rn(Uu),Uua))))) # label(fact_ATP_Olambda__389) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 904 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_jm(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jn,Uu),Uua)))) # label(fact_ATP_Olambda__435) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 905 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_od,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_oc,Uu))))) # label(fact_ATP_Olambda__142) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 906 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_oz,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_oy,Uu))))) # label(fact_ATP_Olambda__132) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 907 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(X),Xa)),Xb)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(X),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Xa),Xb)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc602586424_prop1(X),Xa),Xb)))) # label(fact_def__d__431__prop1) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 908 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_xt,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_xu,Uu)))) # label(fact_ATP_Olambda__62) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 909 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_lj(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lk(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__622) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 910 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dz,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_dy(Uu),Uua))))) # label(fact_ATP_Olambda__474) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 911 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qg,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_qf(Uu),Uua))))) # label(fact_ATP_Olambda__399) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 912 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_wg,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_wh,Uu)))) # label(fact_ATP_Olambda__74) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 913 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc297882262tminus(X),Xa) = aa_fun1431113780TP_ind(scratc999473378_d_Sep(X),aa_TPT43085870d_bool(aTP_Lamm_bx,Xa))) # label(fact_def__setminus) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 914 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_uf,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_ue,Uu))))) # label(fact_ATP_Olambda__90) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 915 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_qi(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qj,Uu),Uua)))) # label(fact_ATP_Olambda__398) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 916 (all Uu all Uua ((pp(scratc1223190007_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706324_moreq,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_na,Uu),Uua)))) # label(fact_ATP_Olambda__328) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 917 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_yi,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_yj,Uu)))) # label(fact_ATP_Olambda__57) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 918 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cn,Uu),Uua)) <-> pp(scratc1845845133nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc173054068_rt_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc758693855t_more,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2043040867t_less,Uu),Uua))))) # label(fact_ATP_Olambda__256) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 919 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_uw(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__671) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 920 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jx(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uua),Uuc))))))) # label(fact_ATP_Olambda__712) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 921 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_as,Uu),Uua)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1879547204nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587467d_n_in,Uua),Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587467d_n_in,aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uua)),Uu))))) # label(fact_ATP_Olambda__281) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 922 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_gk(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gl,Uu),Uua)))) # label(fact_ATP_Olambda__455) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 923 (all X all Xa all Xb scratc1846697984nd_eps(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ca(X),Xa),Xb)) = aa_TPTP_ind_TPTP_ind(scratc102755877bnd_if(X,Xa),Xb)) # label(fact_def__if) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 924 (all X all Xa all Xb (pp(aa_fun171081125l_bool(scratc1813389561nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_be(X),Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc798277750d_incl(X),Xa),Xb)))) # label(fact_def__incl) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 925 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hc,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uu),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uua),aa_TPTP_ind_TPTP_ind(scratc1454525887_367_w(Uu),Uua))))))) # label(fact_ATP_Olambda__283) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 926 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gv(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gw(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__636) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 927 (all X scratc1879612801nd_inn(X) = scratc712927106d_e_in(scratc1920067545nd_nat,aa_TPT43085870d_bool(aTP_Lamm_ak,X))) # label(fact_def__inn) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 928 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_il(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uua),Uuc))))))) # label(fact_ATP_Olambda__700) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 929 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_acc(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(Uua,aa_TPTP_ind_TPTP_ind(scratc712927106d_e_in(Uu,Uua),Uub))))) # label(fact_ATP_Olambda__652) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 930 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wv,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_wu(Uu),Uua))))) # label(fact_ATP_Olambda__359) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 931 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1111600628ectset(X,Xa),aa_TPTP_ind_TPTP_ind(scratc1737558087_ecelt(X,Xa),Xb)) = aa_TPTP_ind_TPTP_ind(scratc996398751ectelt(X,Xa),Xb)) # label(fact_def__ectelt) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 932 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ql(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__541) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 933 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jp(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jq(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__625) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 934 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sl,Uu),Uua)))) # label(fact_ATP_Olambda__286) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 935 (all X all Xa scratc294253259_proj0 = scratc1226053384_first(X,Xa)) # label(fact_def__first) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 936 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1897569848l_some(scratc636914614d_frac),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ac(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ad(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__651) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 937 (all X all Xa (pp(scratc1115724827_d_and(aa_bool_bool(scratc100336135d_l_or(X),Xa),scratc99680130d_l_ec(X,Xa))) <-> scratc1220010857d_orec(X,Xa))) # label(fact_def__orec) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 938 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046652d_n_pf(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ji(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__503) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 939 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dy(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dx(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__644) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 940 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1455377704nempty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1897569848l_some(X),aa_TPT43085870d_bool(aTP_Lamm_bf(X),Xa))))) # label(fact_def__nonempty) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 941 (all X all Xa (pp(aa_bool_bool(scratc100336135d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2043040867t_less,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc173054068_rt_is,X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc84241709lessis,X),Xa)))) # label(fact_def__rt__lessis) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 942 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706324_moreq,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lx(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__554) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 943 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_wm(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uuc),Uua))))))) # label(fact_ATP_Olambda__705) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 944 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc460841235eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_br,Xa)),scratc294253260_proj1)) # label(fact_def__ap) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 945 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_du(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dv,Uu),Uua)))) # label(fact_ATP_Olambda__475) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 946 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309061d_n_ts(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qi(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__498) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 947 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_xz,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ya,Uu)))) # label(fact_ATP_Olambda__60) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 948 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_tu(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc919487723lessis,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__679) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 949 (all B_1 all B_2 gg_bool(scratc1115724827_d_and(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__63417__16348_ONUM788__thf__4__p_Obnd__d__and) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 950 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_aaq,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uu),scratc282061419nd_n_1))))) # label(fact_ATP_Olambda__10) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 951 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_pp,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_po,Uu))))) # label(fact_ATP_Olambda__128) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 952 (all B_1 all B_2 gg_TPTP_ind(aa_fun1431113780TP_ind(B_1,B_2))) # label(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 953 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1920592336nd_nis,X),Xa)) <-> pp(scratc1223190007_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,X),Xa))))) # label(fact_def__nis) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 954 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ia(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hz(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__631) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 955 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bo(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aa_TPT43085870d_bool(aTP_Lamm_au,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bn(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__584) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 956 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_rh,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ri,Uu)))) # label(fact_ATP_Olambda__115) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 957 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1897569848l_some(scratc636914614d_frac),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ae(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_af(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__650) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 958 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_lh,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_li,Uu)))) # label(fact_ATP_Olambda__137) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 959 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wu(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__574) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 960 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ep,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_eo,Uu))))) # label(fact_ATP_Olambda__220) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 961 (all X0 all X12 scratc2128269225_is_of(aa_fun1431113780TP_ind(scratc999473378_d_Sep(X0),X12),aa_TPT43085870d_bool(aTP_Lamm_abl,X0))) # label(fact_setof__p) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 962 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_kw,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_kv,Uu))))) # label(fact_ATP_Olambda__170) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 963 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> ((exists X3 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X3),X0)) & X22 = aa_TPTP_ind_TPTP_ind(X12,X3) & gg_TPTP_ind(X3))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc102755885bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1307610839d_repl,X0),X12)))))) # label(fact_k__ReplEq) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 964 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ki,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_kh(Uu),Uua))))) # label(fact_ATP_Olambda__429) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 965 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dd(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uua),Uub)),Uu)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uua),Uuc)),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uub),Uuc)))))) # label(fact_ATP_Olambda__666) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 966 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ny,Uu),Uua)))) # label(fact_ATP_Olambda__298) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 967 (all B_1 all B_2 all B_3 gg_bool(scratc1845845133nd_ec3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__63417__16348_ONUM788__thf__4__p_Obnd__ec3) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 968 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ae(Uu),Uua),Uub),Uuc)) <-> scratc996096644d_and3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879612793nd_inf,Uub),aa_TPTP_ind_TPTP_ind(scratc8676528_class,Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879612793nd_inf,Uuc),aa_TPTP_ind_TPTP_ind(scratc8676528_class,Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uub),Uuc)))) # label(fact_ATP_Olambda__656) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 969 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc654384517_lessf,aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ef(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__699) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 970 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ar,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1869534971rdsucc,Uua))))) # label(fact_ATP_Olambda__337) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 971 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_pd,Uu)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_pc,Uu))))) # label(fact_ATP_Olambda__131) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 972 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_yf,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_yg,Uu)))) # label(fact_ATP_Olambda__58) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 973 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,X),Xb)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc102231095bnd_ap,Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc294646856_prop3(X),Xa),Xb)))) # label(fact_def__prop3) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 974 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1044896837_empty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aa_TPT43085870d_bool(aTP_Lamm_au,X)),scratc1920985925nd_non(X,aa_TPT43085870d_bool(aTP_Lamm_bf(X),Xa)))))) # label(fact_def__empty) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 975 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_pi(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pj(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__614) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 976 (all Uu all Uua (scratc1219098378_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1365617091_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zm,Uu),Uua)))) # label(fact_ATP_Olambda__251) # label(axiom) # label(non_clause). [assumption]. 1.48/1.73 977 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zu,Uu),Uua)) <-> scratc1219098378_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231587472d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc493910842n_some,aa_TPT43085870d_bool(aTP_Lamm_zs(Uu),Uua)),aa_fun171081125l_bool(scratc493910842n_some,aa_TPT43085870d_bool(aTP_Lamm_zt(Uu),Uua))))) # label(fact_ATP_Olambda__259) # label(axiom) # label(non_clause). [assumption]. 1.48/1.76 978 (all X all Xa scratc1879612791nd_ind(scratc1920067545nd_nat,aa_TPT43085870d_bool(scratc304196016ffprop(X),Xa)) = aa_TPTP_ind_TPTP_ind(scratc231849863d_n_mn(X),Xa)) # label(fact_def__n__mn) # label(axiom) # label(non_clause). [assumption]. 1.48/1.76 979 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc493910842n_some,aa_TPT43085870d_bool(scratc304196016ffprop(Xa),X))))) # label(fact_def__iii) # label(axiom) # label(non_clause). [assumption]. 1.48/1.76 980 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gh(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231325074d_n_eq,aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uua),Uub)))))) # label(fact_ATP_Olambda__565) # label(axiom) # label(non_clause). [assumption]. 1.48/1.76 981 (all Uu all Uua all Uub all Uuc (pp(scratc99680130d_l_ec(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013318955d_esti(Uu),Uuc),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013318955d_esti(Uu),Uuc),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bd(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__664) # label(axiom) # label(non_clause). [assumption]. 1.48/1.76 982 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fh,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aTP_Lamm_fg(Uu),Uua))))) # label(fact_ATP_Olambda__464) # label(axiom) # label(non_clause). [assumption]. 1.48/1.76 983 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bl(Uu),Uua),Uub),Uuc)) <-> pp(aa_fun171081125l_bool(scratc1813389561nd_all(Uu),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_bk(Uu),Uua),Uub),Uuc))))) # label(fact_ATP_Olambda__726) # label(axiom) # label(non_clause). [assumption]. 1.48/1.76 984 (all P all Q (-pp(P) | pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)) | -pp(Q))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption]. 1.48/1.76 985 (all Uu (pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_lc),aa_TPT43085870d_bool(aTP_Lamm_tb,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_tc,Uu)))) # label(fact_ATP_Olambda__100) # label(axiom) # label(non_clause). [assumption]. 1.48/1.76 986 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dx(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706324_moreq,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1000706313_moref,aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc232309048d_n_tf(Uua),Uuc))))))) # label(fact_ATP_Olambda__692) # label(axiom) # label(non_clause). [assumption]. 1.48/1.76 987 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_di(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc639425392all_of(aTP_Lamm_cz),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dh(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__648) # label(axiom) # label(non_clause). [assumption]. 1.48/1.76 988 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc232046658d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1879284801nd_iii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_va(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__519) # label(axiom) # label(non_clause). [assumption]. 1.48/1.76 1.48/1.76 ============================== end of process non-clausal formulas === 1.48/1.76 1.48/1.76 ============================== PROCESS INITIAL CLAUSES =============== 1.48/1.76 1.48/1.76 ============================== PREDICATE ELIMINATION ================= 1.48/1.76 989 -gg_bool(A) | fTrue = A | A = fFalse # label(help_fFalse_1_1_T) # label(axiom). [clausify(187)]. 1.91/2.18 990 gg_bool(fFalse) # label(gsy_c_fFalse) # label(axiom). [assumption]. 1.91/2.18 991 gg_bool(aa_bool_bool(A,B)) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom). [clausify(74)]. 1.91/2.18 Derived: fTrue = fFalse | fFalse = fFalse. [resolve(989,a,990,a)]. 1.91/2.18 Derived: fTrue = aa_bool_bool(A,B) | aa_bool_bool(A,B) = fFalse. [resolve(989,a,991,a)]. 1.91/2.18 992 gg_bool(scratc1223190007_d_not(A)) # label(gsy_c_Scratch__tptp__translate__63417__16348_ONUM788__thf__4__p_Obnd__d__not) # label(axiom). [clausify(310)]. 1.91/2.18 Derived: fTrue = scratc1223190007_d_not(A) | scratc1223190007_d_not(A) = fFalse. [resolve(992,a,989,a)]. 1.91/2.18 993 gg_bool(fTrue) # label(gsy_c_fTrue) # label(axiom). [assumption]. 1.91/2.18 Derived: fTrue = fTrue | fTrue = fFalse. [resolve(993,a,989,a)]. 1.91/2.18 994 gg_bool(scratc772951858_amone(A,B)) # label(gsy_c_Scratch__tptp__translate__63417__16348_ONUM788__thf__4__p_Obnd__amone) # label(axiom). [clausify(528)]. 1.91/2.18 Derived: fTrue = scratc772951858_amone(A,B) | scratc772951858_amone(A,B) = fFalse. [resolve(994,a,989,a)]. 1.91/2.18 995 gg_bool(aa_fun171081125l_bool(A,B)) # label(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__HOL__Obool) # label(hypothesis). [clausify(548)]. 1.91/2.18 Derived: fTrue = aa_fun171081125l_bool(A,B) | aa_fun171081125l_bool(A,B) = fFalse. [resolve(995,a,989,a)]. 1.91/2.18 996 gg_bool(aa_TPTP_ind_bool(A,B)) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom). [clausify(568)]. 1.91/2.18 Derived: fTrue = aa_TPTP_ind_bool(A,B) | aa_TPTP_ind_bool(A,B) = fFalse. [resolve(996,a,989,a)]. 1.91/2.18 997 gg_bool(undefined_bool(bool)) # label(gsy_c_HOL_Oundefined_001t__HOL__Obool) # label(axiom). [assumption]. 1.91/2.18 Derived: fTrue = undefined_bool(bool) | undefined_bool(bool) = fFalse. [resolve(997,a,989,a)]. 1.91/2.18 998 gg_bool(fEx_TPTP_ind(A)) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom). [clausify(698)]. 1.91/2.18 Derived: fTrue = fEx_TPTP_ind(A) | fEx_TPTP_ind(A) = fFalse. [resolve(998,a,989,a)]. 1.91/2.18 999 gg_bool(scratc99680130d_l_ec(A,B)) # label(gsy_c_Scratch__tptp__translate__63417__16348_ONUM788__thf__4__p_Obnd__l__ec) # label(axiom). [clausify(736)]. 1.91/2.18 Derived: fTrue = scratc99680130d_l_ec(A,B) | scratc99680130d_l_ec(A,B) = fFalse. [resolve(999,a,989,a)]. 1.91/2.18 1000 gg_bool(scratc1929444168nd_or3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__63417__16348_ONUM788__thf__4__p_Obnd__or3) # label(axiom). [clausify(772)]. 1.91/2.18 Derived: fTrue = scratc1929444168nd_or3(A,B,C) | scratc1929444168nd_or3(A,B,C) = fFalse. [resolve(1000,a,989,a)]. 1.91/2.18 1001 gg_bool(scratc1115724827_d_and(A,B)) # label(gsy_c_Scratch__tptp__translate__63417__16348_ONUM788__thf__4__p_Obnd__d__and) # label(axiom). [clausify(949)]. 1.91/2.18 Derived: fTrue = scratc1115724827_d_and(A,B) | scratc1115724827_d_and(A,B) = fFalse. [resolve(1001,a,989,a)]. 1.91/2.18 1002 gg_bool(scratc1845845133nd_ec3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__63417__16348_ONUM788__thf__4__p_Obnd__ec3) # label(axiom). [clausify(967)]. 1.91/2.18 Derived: fTrue = scratc1845845133nd_ec3(A,B,C) | scratc1845845133nd_ec3(A,B,C) = fFalse. [resolve(1002,a,989,a)]. 1.91/2.18 1003 -pp(A) | pp(scratc1223190007_d_not(B)) | -scratc494614920d_r_ec(A,B) # label(fact_def__r__ec) # label(axiom). [clausify(73)]. 1.91/2.18 1004 pp(A) | scratc494614920d_r_ec(A,B) # label(fact_def__r__ec) # label(axiom). [clausify(73)]. 1.91/2.18 1005 -pp(scratc1223190007_d_not(A)) | scratc494614920d_r_ec(B,A) # label(fact_def__r__ec) # label(axiom). [clausify(73)]. 1.91/2.18 1006 scratc2009866277_l_iff(A,B) | -pp(scratc1115724827_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1879547204nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc1879547204nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(163)]. 1.91/2.18 1007 -scratc2009866277_l_iff(A,B) | pp(scratc1115724827_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1879547204nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc1879547204nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(163)]. 1.91/2.18 1008 scratc1994683478nd_wel(A) | -pp(scratc1223190007_d_not(scratc1223190007_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(325)]. 1.91/2.18 1009 -scratc1994683478nd_wel(A) | pp(scratc1223190007_d_not(scratc1223190007_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(325)]. 4.60/4.82 1010 -scratc1994683478nd_wel(A) | pp(A) # label(fact_l__et) # label(axiom). [clausify(342)]. 4.60/4.82 Derived: pp(A) | -pp(scratc1223190007_d_not(scratc1223190007_d_not(A))). [resolve(1010,a,1008,a)]. 4.60/4.82 1011 pp(scratc1115724827_d_and(aa_bool_bool(scratc100336135d_l_or(A),B),scratc99680130d_l_ec(A,B))) | -scratc1220010857d_orec(A,B) # label(fact_def__orec) # label(axiom). [clausify(937)]. 4.60/4.82 1012 -pp(scratc1115724827_d_and(aa_bool_bool(scratc100336135d_l_or(A),B),scratc99680130d_l_ec(A,B))) | scratc1220010857d_orec(A,B) # label(fact_def__orec) # label(axiom). [clausify(937)]. 4.60/4.82 4.60/4.82 ============================== end predicate elimination ============= 4.60/4.82 4.60/4.82 Auto_denials: (non-Horn, no changes). 4.60/4.82 4.60/4.82 Term ordering decisions: 4.60/4.82 Function symbol KB weights: aTP_Lamm_lc=1. aTP_Lamm_cz=1. scratc231325074d_n_eq=1. scratc231587472d_n_is=1. scratc654384517_lessf=1. scratc1000706313_moref=1. scratc1879284801nd_iii=1. scratc1365617091_29_ii=1. scratc102755885bnd_in=1. scratc1869534971rdsucc=1. scratc919487723lessis=1. scratc102231095bnd_ap=1. scratc1053471335moreis=1. scratc282061419nd_n_1=1. aTP_Lamm_au=1. scratc919225325lesseq=1. scratc1000706324_moreq=1. aTP_Lamm_a=1. scratc1920067545nd_nat=1. scratc1133920905_Sigma=1. scratc1169782717ptyset=1. scratc1837714885nd_den=1. scratc231390674d_n_fr=1. scratc636914614d_frac=1. scratc1719206485d_d_Pi=1. scratc1920592336nd_nis=1. scratc173054068_rt_is=1. scratc1921379518nd_num=1. scratc493910842n_some=1. fFalse=1. scratc165739421_power=1. scratc2014913431_nat_p=1. scratc1879547204nd_imp=1. scratc758693855t_more=1. scratc1307610839d_repl=1. scratc2043040867t_less=1. scratc1879612793nd_inf=1. scratc8676528_class=1. fTrue=1. scratc540698651_n_all=1. scratc1860414882d_pair=1. aTP_Lamm_al=1. scratc1909615789d_Subq=1. scratc1953113565nd_rat=1. scratc215026647closed=1. scratc282061420nd_n_2=1. scratc294253259_proj0=1. scratc673001287_union=1. aTP_Lamm_ar=1. scratc231587467d_n_in=1. scratc294253260_proj1=1. scratc84241709lessis=1. aTP_Lamm_abl=1. aTP_Lamm_aq=1. scratc218225321moreis=1. scratc335317087closed=1. scratc500050101closed=1. scratc719566192_d_1to=1. aTP_Lamm_aa=1. aTP_Lamm_abc=1. aTP_Lamm_abg=1. aTP_Lamm_abh=1. aTP_Lamm_ak=1. aTP_Lamm_cb=1. aTP_Lamm_cd=1. aTP_Lamm_cf=1. aTP_Lamm_ch=1. aTP_Lamm_cj=1. aTP_Lamm_cl=1. aTP_Lamm_cw=1. aTP_Lamm_hc=1. aTP_Lamm_he=1. aTP_Lamm_hh=1. aTP_Lamm_lo=1. aTP_Lamm_mm=1. aTP_Lamm_mo=1. aTP_Lamm_my=1. aTP_Lamm_na=1. aTP_Lamm_nc=1. aTP_Lamm_ne=1. aTP_Lamm_ng=1. aTP_Lamm_ni=1. aTP_Lamm_nk=1. aTP_Lamm_nm=1. aTP_Lamm_nw=1. aTP_Lamm_ny=1. aTP_Lamm_ot=1. aTP_Lamm_tb=1. aTP_Lamm_td=1. aTP_Lamm_tf=1. aTP_Lamm_th=1. aTP_Lamm_tj=1. aTP_Lamm_tl=1. aTP_Lamm_tn=1. aTP_Lamm_tp=1. aTP_Lamm_yk=1. aTP_Lamm_ym=1. aTP_Lamm_yo=1. aTP_Lamm_yq=1. aTP_Lamm_ys=1. aTP_Lamm_yu=1. aTP_Lamm_yw=1. aTP_Lamm_yy=1. aTP_Lamm_za=1. aTP_Lamm_zc=1. aTP_Lamm_ze=1. aTP_Lamm_zg=1. scratc1087267889_prop2=1. scratc1179442033_prop2=1. scratc1611392121_omega=1. scratc488888936d_Inj1=1. scratc775647028closed=1. aTP_Lamm_aac=1. aTP_Lamm_aae=1. aTP_Lamm_aag=1. aTP_Lamm_aaj=1. aTP_Lamm_aal=1. aTP_Lamm_aao=1. aTP_Lamm_aar=1. aTP_Lamm_aau=1. aTP_Lamm_aax=1. aTP_Lamm_aaz=1. aTP_Lamm_aba=1. aTP_Lamm_abf=1. aTP_Lamm_as=1. aTP_Lamm_br=1. aTP_Lamm_bt=1. aTP_Lamm_bu=1. aTP_Lamm_cn=1. aTP_Lamm_cp=1. aTP_Lamm_cr=1. aTP_Lamm_cu=1. aTP_Lamm_db=1. aTP_Lamm_df=1. aTP_Lamm_dj=1. aTP_Lamm_dn=1. aTP_Lamm_dr=1. aTP_Lamm_dv=1. aTP_Lamm_dz=1. aTP_Lamm_ed=1. aTP_Lamm_eh=1. aTP_Lamm_el=1. aTP_Lamm_eo=1. aTP_Lamm_er=1. aTP_Lamm_eu=1. aTP_Lamm_ex=1. aTP_Lamm_fa=1. aTP_Lamm_fd=1. aTP_Lamm_fh=1. aTP_Lamm_fl=1. aTP_Lamm_fp=1. aTP_Lamm_ft=1. aTP_Lamm_fw=1. aTP_Lamm_fz=1. aTP_Lamm_gc=1. aTP_Lamm_gf=1. aTP_Lamm_gi=1. aTP_Lamm_gl=1. aTP_Lamm_go=1. aTP_Lamm_gr=1. aTP_Lamm_gt=1. aTP_Lamm_gx=1. aTP_Lamm_ha=1. aTP_Lamm_hl=1. aTP_Lamm_hp=1. aTP_Lamm_ht=1. aTP_Lamm_hx=1. aTP_Lamm_ib=1. aTP_Lamm_if=1. aTP_Lamm_ij=1. aTP_Lamm_in=1. aTP_Lamm_ir=1. aTP_Lamm_iu=1. aTP_Lamm_ix=1. aTP_Lamm_ja=1. aTP_Lamm_jd=1. aTP_Lamm_jg=1. aTP_Lamm_jj=1. aTP_Lamm_jn=1. aTP_Lamm_jr=1. aTP_Lamm_jv=1. aTP_Lamm_jz=1. aTP_Lamm_kc=1. aTP_Lamm_kf=1. aTP_Lamm_ki=1. aTP_Lamm_kl=1. aTP_Lamm_ko=1. aTP_Lamm_kr=1. aTP_Lamm_kt=1. aTP_Lamm_kv=1. aTP_Lamm_ky=1. aTP_Lamm_la=1. aTP_Lamm_le=1. aTP_Lamm_lh=1. aTP_Lamm_ll=1. aTP_Lamm_lq=1. aTP_Lamm_ls=1. aTP_Lamm_lv=1. aTP_Lamm_ly=1. aTP_Lamm_mb=1. aTP_Lamm_me=1. aTP_Lamm_mh=1. aTP_Lamm_mk=1. aTP_Lamm_ms=1. aTP_Lamm_mw=1. aTP_Lamm_nq=1. aTP_Lamm_nu=1. aTP_Lamm_oa=1. aTP_Lamm_oc=1. aTP_Lamm_oe=1. aTP_Lamm_oh=1. aTP_Lamm_ok=1. aTP_Lamm_om=1. aTP_Lamm_oo=1. aTP_Lamm_or=1. aTP_Lamm_oy=1. aTP_Lamm_pc=1. aTP_Lamm_pg=1. aTP_Lamm_pk=1. aTP_Lamm_po=1. aTP_Lamm_ps=1. aTP_Lamm_pw=1. aTP_Lamm_qa=1. aTP_Lamm_qd=1. aTP_Lamm_qg=1. aTP_Lamm_qj=1. aTP_Lamm_qm=1. aTP_Lamm_qp=1. aTP_Lamm_qs=1. aTP_Lamm_qv=1. aTP_Lamm_qz=1. aTP_Lamm_rd=1. aTP_Lamm_rh=1. aTP_Lamm_rl=1. aTP_Lamm_ro=1. aTP_Lamm_rr=1. aTP_Lamm_ru=1. aTP_Lamm_rx=1. aTP_Lamm_sa=1. aTP_Lamm_sd=1. aTP_Lamm_sg=1. aTP_Lamm_sj=1. aTP_Lamm_sl=1. aTP_Lamm_sn=1. aTP_Lamm_sq=1. aTP_Lamm_st=1. aTP_Lamm_sw=1. aTP_Lamm_sz=1. aTP_Lamm_tw=1. aTP_Lamm_ua=1. aTP_Lamm_ue=1. aTP_Lamm_ui=1. aTP_Lamm_um=1. aTP_Lamm_uq=1. aTP_Lamm_uu=1. aTP_Lamm_uy=1. aTP_Lamm_vb=1. aTP_Lamm_ve=1. aTP_Lamm_vh=1. aTP_Lamm_vk=1. aTP_Lamm_vn=1. aTP_Lamm_vq=1. aTP_Lamm_vt=1. aTP_Lamm_vw=1. aTP_Lamm_vz=1. aTP_Lamm_wc=1. aTP_Lamm_wg=1. aTP_Lamm_wk=1. aTP_Lamm_wo=1. aTP_Lamm_ws=1. aTP_Lamm_wv=1. aTP_Lamm_wy=1. aTP_Lamm_xb=1. aTP_Lamm_xe=1. aTP_Lamm_xh=1. aTP_Lamm_xk=1. aTP_Lamm_xo=1. aTP_Lamm_xq=1. aTP_Lamm_xt=1. aTP_Lamm_xw=1. aTP_Lamm_xz=1. aTP_Lamm_yc=1. aTP_Lamm_yf=1. aTP_Lamm_yi=1. aTP_Lamm_zi=1. aTP_Lamm_zk=1. aTP_Lamm_zm=1. aTP_Lamm_zo=1. aTP_Lamm_zq=1. aTP_Lamm_zu=1. aTP_Lamm_zw=1. aTP_Lamm_zz=1. fconj=1. fimplies=1. scratc1087267888_prop1=1. scratc1179442032_prop1=1. scratc1811264907d_Sing=1. scratc227913929d_n_1t=1. scratc309369992_cond2=1. scratc488888935d_Inj0=1. scratc656490912_n_one=1. aTP_Lamm_aaa=1. aTP_Lamm_aad=1. aTP_Lamm_aaf=1. aTP_Lamm_aah=1. aTP_Lamm_aak=1. aTP_Lamm_aam=1. aTP_Lamm_aan=1. aTP_Lamm_aap=1. aTP_Lamm_aaq=1. aTP_Lamm_aas=1. aTP_Lamm_aat=1. aTP_Lamm_aav=1. aTP_Lamm_aaw=1. aTP_Lamm_aay=1. aTP_Lamm_abb=1. aTP_Lamm_abd=1. aTP_Lamm_abe=1. aTP_Lamm_abi=1. aTP_Lamm_abj=1. aTP_Lamm_abk=1. aTP_Lamm_abn=1. aTP_Lamm_ack=1. aTP_Lamm_bx=1. aTP_Lamm_cc=1. aTP_Lamm_ce=1. aTP_Lamm_cg=1. aTP_Lamm_ci=1. aTP_Lamm_ck=1. aTP_Lamm_cm=1. aTP_Lamm_co=1. aTP_Lamm_cq=1. aTP_Lamm_cs=1. aTP_Lamm_cv=1. aTP_Lamm_cx=1. aTP_Lamm_cy=1. aTP_Lamm_dc=1. aTP_Lamm_dg=1. aTP_Lamm_dk=1. aTP_Lamm_do=1. aTP_Lamm_ds=1. aTP_Lamm_dw=1. aTP_Lamm_ea=1. aTP_Lamm_ee=1. aTP_Lamm_ei=1. aTP_Lamm_em=1. aTP_Lamm_ep=1. aTP_Lamm_es=1. aTP_Lamm_ev=1. aTP_Lamm_ey=1. aTP_Lamm_fb=1. aTP_Lamm_fe=1. aTP_Lamm_fi=1. aTP_Lamm_fm=1. aTP_Lamm_fq=1. aTP_Lamm_fu=1. aTP_Lamm_fx=1. aTP_Lamm_ga=1. aTP_Lamm_gd=1. aTP_Lamm_gg=1. aTP_Lamm_gj=1. aTP_Lamm_gm=1. aTP_Lamm_gp=1. aTP_Lamm_gs=1. aTP_Lamm_gu=1. aTP_Lamm_gy=1. aTP_Lamm_hb=1. aTP_Lamm_hd=1. aTP_Lamm_hf=1. aTP_Lamm_hi=1. aTP_Lamm_hm=1. aTP_Lamm_hq=1. aTP_Lamm_hu=1. aTP_Lamm_hy=1. aTP_Lamm_ic=1. aTP_Lamm_ig=1. aTP_Lamm_ik=1. aTP_Lamm_io=1. aTP_Lamm_is=1. aTP_Lamm_iv=1. aTP_Lamm_iy=1. aTP_Lamm_jb=1. aTP_Lamm_je=1. aTP_Lamm_jh=1. aTP_Lamm_jk=1. aTP_Lamm_jo=1. aTP_Lamm_js=1. aTP_Lamm_jw=1. aTP_Lamm_ka=1. aTP_Lamm_kd=1. aTP_Lamm_kg=1. aTP_Lamm_kj=1. aTP_Lamm_km=1. aTP_Lamm_kp=1. aTP_Lamm_ks=1. aTP_Lamm_ku=1. aTP_Lamm_kw=1. aTP_Lamm_kz=1. aTP_Lamm_lb=1. aTP_Lamm_lf=1. aTP_Lamm_li=1. aTP_Lamm_lm=1. aTP_Lamm_lp=1. aTP_Lamm_lr=1. aTP_Lamm_lt=1. aTP_Lamm_lw=1. aTP_Lamm_lz=1. aTP_Lamm_mc=1. aTP_Lamm_mf=1. aTP_Lamm_mi=1. aTP_Lamm_ml=1. aTP_Lamm_mn=1. aTP_Lamm_mp=1. aTP_Lamm_mt=1. aTP_Lamm_mx=1. aTP_Lamm_mz=1. aTP_Lamm_nb=1. aTP_Lamm_nd=1. aTP_Lamm_nf=1. aTP_Lamm_nh=1. aTP_Lamm_nj=1. aTP_Lamm_nl=1. aTP_Lamm_nn=1. aTP_Lamm_nr=1. aTP_Lamm_nv=1. aTP_Lamm_nx=1. aTP_Lamm_nz=1. aTP_Lamm_ob=1. aTP_Lamm_od=1. aTP_Lamm_of=1. aTP_Lamm_oi=1. aTP_Lamm_ol=1. aTP_Lamm_on=1. aTP_Lamm_op=1. aTP_Lamm_os=1. aTP_Lamm_ou=1. aTP_Lamm_ov=1. aTP_Lamm_oz=1. aTP_Lamm_pd=1. aTP_Lamm_ph=1. aTP_Lamm_pl=1. aTP_Lamm_pp=1. aTP_Lamm_pt=1. aTP_Lamm_px=1. aTP_Lamm_qb=1. aTP_Lamm_qe=1. aTP_Lamm_qh=1. aTP_Lamm_qk=1. aTP_Lamm_qn=1. aTP_Lamm_qq=1. aTP_Lamm_qt=1. aTP_Lamm_qw=1. aTP_Lamm_ra=1. aTP_Lamm_re=1. aTP_Lamm_ri=1. aTP_Lamm_rm=1. aTP_Lamm_rp=1. aTP_Lamm_rs=1. aTP_Lamm_rv=1. aTP_Lamm_ry=1. aTP_Lamm_sb=1. aTP_Lamm_se=1. aTP_Lamm_sh=1. aTP_Lamm_sk=1. aTP_Lamm_sm=1. aTP_Lamm_so=1. aTP_Lamm_sp=1. aTP_Lamm_sr=1. aTP_Lamm_ss=1. aTP_Lamm_su=1. aTP_Lamm_sv=1. aTP_Lamm_sx=1. aTP_Lamm_sy=1. aTP_Lamm_ta=1. aTP_Lamm_tc=1. aTP_Lamm_te=1. aTP_Lamm_tg=1. aTP_Lamm_ti=1. aTP_Lamm_tk=1. aTP_Lamm_tm=1. aTP_Lamm_to=1. aTP_Lamm_tq=1. aTP_Lamm_tr=1. aTP_Lamm_ts=1. aTP_Lamm_tt=1. aTP_Lamm_tx=1. aTP_Lamm_ub=1. aTP_Lamm_uf=1. aTP_Lamm_uj=1. aTP_Lamm_un=1. aTP_Lamm_ur=1. aTP_Lamm_uv=1. aTP_Lamm_uz=1. aTP_Lamm_vc=1. aTP_Lamm_vf=1. aTP_Lamm_vi=1. aTP_Lamm_vl=1. aTP_Lamm_vo=1. aTP_Lamm_vr=1. aTP_Lamm_vu=1. aTP_Lamm_vx=1. aTP_Lamm_wa=1. aTP_Lamm_wd=1. aTP_Lamm_wh=1. aTP_Lamm_wl=1. aTP_Lamm_wp=1. aTP_Lamm_wt=1. aTP_Lamm_ww=1. aTP_Lamm_wz=1. aTP_Lamm_xc=1. aTP_Lamm_xf=1. aTP_Lamm_xi=1. aTP_Lamm_xl=1. aTP_Lamm_xm=1. aTP_Lamm_xn=1. aTP_Lamm_xp=1. aTP_Lamm_xr=1. aTP_Lamm_xu=1. aTP_Lamm_xx=1. aTP_Lamm_ya=1. aTP_Lamm_yd=1. aTP_Lamm_yg=1. aTP_Lamm_yj=1. aTP_Lamm_yl=1. aTP_Lamm_yn=1. aTP_Lamm_yp=1. aTP_Lamm_yr=1. aTP_Lamm_yt=1. aTP_Lamm_yv=1. aTP_Lamm_yx=1. aTP_Lamm_yz=1. aTP_Lamm_zb=1. aTP_Lamm_zd=1. aTP_Lamm_zf=1. aTP_Lamm_zh=1. aTP_Lamm_zj=1. aTP_Lamm_zl=1. aTP_Lamm_zn=1. aTP_Lamm_zp=1. aTP_Lamm_zr=1. aTP_Lamm_zv=1. aTP_Lamm_zx=1. fequal_TPTP_ind=1. scratc1016586773_d_Unj=1. scratc1918493163nd_nIn=1. scratc227979528d_n_2t=1. scratc300486565univof=1. scratc309369991_cond1=1. aTP_Lamm_ab=1. aTP_Lamm_an=1. aTP_Lamm_at=1. aTP_Lamm_bv=1. aTP_Lamm_bw=1. bool=1. scratc1044896837_empty=1. scratc116508590_prop1=1. scratc1179442035_prop4=1. scratc1455377704nempty=1. scratc1535223269munion=1. scratc1693968249428_id=1. scratc1726284942pair_p=1. scratc1767804207_prop1=1. scratc1881595115_prop1=1. scratc1952078626d_plus=1. scratc2058027186_prop1=1. scratc2105341982_times=1. scratc227913924d_n_1o=1. scratc294646857_prop4=1. scratc498905713_prop1=1. scratc604263049r1type=1. scratc615895054rt_nis=1. scratc704870765_prop1=1. scratc1091132153d_1out=1. scratc1146921758t_some=1. scratc1458511965air_u0=1. scratc1547062377d_24_g=1. scratc1575771843d_i1_s=1. scratc173054063_rt_in=1. scratc1779109790d_xout=1. scratc196346793_428_g=1. scratc508692279rt_all=1. scratc564069849d_fixf=1. scratc624484540rt_one=1. scratc82453268_ratof=1. scratc82475167let_u0=1. tPTP_ind=1. aa_TPT43085870d_bool=1. aa_TPTP_ind_bool=1. aa_fun171081125l_bool=1. aa_TPTP_ind_TPTP_ind=1. aa_TPT60673477d_bool=1. aa_TPT1424761345TP_ind=1. aa_fun277296641TP_ind=1. aa_TPT494704832TP_ind=1. aa_bool_bool=1. aa_fun1584354236d_bool=1. scratc1115724827_d_and=1. aa_fun1431113780TP_ind=1. aa_boo1142376798l_bool=1. aa_TPT1123896796d_bool=1. scratc102755877bnd_if=1. scratc99680130d_l_ec=1. aa_fun1212484691d_bool=1. scratc1879612791nd_ind=1. scratc712927106d_e_in=1. aa_TPT1791839040TP_ind=1. aa_TPT985247859d_bool=1. scratc759553526d_pair=1. aa_fun987228051d_bool=1. scratc772951858_amone=1. scratc1183411315_image=1. scratc1226053384_first=1. scratc1738843356second=1. aa_TPT125613450d_bool=1. scratc1920985925nd_non=1. aa_fun1913827119d_bool=1. scratc996162291d_anec=1. aa_fun1107270209d_bool=1. aa_fun845057962d_bool=1. scratc1736967696_ecect=1. scratc1737558087_ecelt=1. scratc1845845194nd_ecp=1. scratc460841235eplSep=1. scratc1845845198nd_ect=1. scratc1929641030nd_out=1. scratc599574102fixfu2=1. aa_TPT1781712639TP_ind=1. aa_TPT2142672771l_bool=1. aa_fun1235454963TP_ind=1. cOMBB_658106424TP_ind=1. cOMBS_2003118649l_bool=1. scratc1111600628ectset=1. scratc1274769628_fixfu=1. scratc1637978109eft1to=1. scratc2044864309etprop=1. scratc294646913_propl=1. scratc294646914_propm=1. scratc893179352ght1to=1. scratc979627425wissel=1. scratc996398751ectelt=1. scratc1217717974unmore=1. scratc1267782664nverse=1. scratc799524125d_invf=1. scratc803260656d_tofs=1. f7=1. f9=1. f12=1. f15=1. f23=1. scratc639425392all_of=1. scratc232046658d_n_pl=1. scratc232309061d_n_ts=1. scratc232046652d_n_pf=1. scratc232309048d_n_tf=1. scratc1223190007_d_not=1. scratc712927111d_e_is=1. scratc1897569848l_some=1. scratc999473378_d_Sep=1. scratc2013318955d_esti=1. scratc100336135d_l_or=1. scratc304196016ffprop=1. scratc1813389561nd_all=1. scratc1929181822nd_one=1. aTP_Lamm_aj=1. scratc1245779368d_outn=1. scratc477123128_rec_G=1. aTP_Lamm_abu=1. aTP_Lamm_mq=1. aTP_Lamm_mu=1. aTP_Lamm_no=1. aTP_Lamm_ns=1. scratc1454525887_367_w=1. aTP_Lamm_abm=1. aTP_Lamm_aci=1. aTP_Lamm_ao=1. aTP_Lamm_av=1. aTP_Lamm_bf=1. aTP_Lamm_bn=1. aTP_Lamm_ca=1. aTP_Lamm_ct=1. aTP_Lamm_dd=1. aTP_Lamm_dh=1. aTP_Lamm_dl=1. aTP_Lamm_dp=1. aTP_Lamm_dt=1. aTP_Lamm_dx=1. aTP_Lamm_eb=1. aTP_Lamm_ef=1. aTP_Lamm_ej=1. aTP_Lamm_ff=1. aTP_Lamm_fj=1. aTP_Lamm_fn=1. aTP_Lamm_fr=1. aTP_Lamm_gv=1. aTP_Lamm_gz=1. aTP_Lamm_hj=1. aTP_Lamm_hn=1. aTP_Lamm_hr=1. aTP_Lamm_hv=1. aTP_Lamm_hz=1. aTP_Lamm_id=1. aTP_Lamm_ih=1. aTP_Lamm_il=1. aTP_Lamm_ip=1. aTP_Lamm_jl=1. aTP_Lamm_jp=1. aTP_Lamm_jt=1. aTP_Lamm_jx=1. aTP_Lamm_lj=1. aTP_Lamm_lu=1. aTP_Lamm_lx=1. aTP_Lamm_ma=1. aTP_Lamm_md=1. aTP_Lamm_mg=1. aTP_Lamm_mj=1. aTP_Lamm_oq=1. aTP_Lamm_ow=1. aTP_Lamm_pa=1. aTP_Lamm_pe=1. aTP_Lamm_pi=1. aTP_Lamm_pm=1. aTP_Lamm_pq=1. aTP_Lamm_pu=1. aTP_Lamm_py=1. aTP_Lamm_qx=1. aTP_Lamm_rb=1. aTP_Lamm_rf=1. aTP_Lamm_rj=1. aTP_Lamm_tu=1. aTP_Lamm_ty=1. aTP_Lamm_uc=1. aTP_Lamm_ug=1. aTP_Lamm_uk=1. aTP_Lamm_uo=1. aTP_Lamm_us=1. aTP_Lamm_uw=1. aTP_Lamm_we=1. aTP_Lamm_wi=1. aTP_Lamm_wm=1. aTP_Lamm_wq=1. aTP_Lamm_xs=1. aTP_Lamm_xv=1. aTP_Lamm_xy=1. aTP_Lamm_yb=1. aTP_Lamm_ye=1. aTP_Lamm_yh=1. aTP_Lamm_zs=1. scratc798277750d_incl=1. aTP_Lamm_aab=1. aTP_Lamm_ace=1. aTP_Lamm_acg=1. aTP_Lamm_az=1. aTP_Lamm_bj=1. aTP_Lamm_bm=1. aTP_Lamm_bq=1. aTP_Lamm_en=1. aTP_Lamm_eq=1. aTP_Lamm_et=1. aTP_Lamm_ew=1. aTP_Lamm_ez=1. aTP_Lamm_fc=1. aTP_Lamm_fv=1. aTP_Lamm_fy=1. aTP_Lamm_gb=1. aTP_Lamm_ge=1. aTP_Lamm_gh=1. aTP_Lamm_gk=1. aTP_Lamm_it=1. aTP_Lamm_iw=1. aTP_Lamm_iz=1. aTP_Lamm_jc=1. aTP_Lamm_jf=1. aTP_Lamm_ji=1. aTP_Lamm_kb=1. aTP_Lamm_ke=1. aTP_Lamm_kh=1. aTP_Lamm_kk=1. aTP_Lamm_kn=1. aTP_Lamm_kq=1. aTP_Lamm_qc=1. aTP_Lamm_qf=1. aTP_Lamm_qi=1. aTP_Lamm_ql=1. aTP_Lamm_qo=1. aTP_Lamm_qr=1. aTP_Lamm_qu=1. aTP_Lamm_rn=1. aTP_Lamm_rq=1. aTP_Lamm_rt=1. aTP_Lamm_rw=1. aTP_Lamm_rz=1. aTP_Lamm_sc=1. aTP_Lamm_va=1. aTP_Lamm_vd=1. aTP_Lamm_vg=1. aTP_Lamm_vj=1. aTP_Lamm_vm=1. aTP_Lamm_vp=1. aTP_Lamm_vs=1. aTP_Lamm_vv=1. aTP_Lamm_vy=1. aTP_Lamm_wb=1. aTP_Lamm_wu=1. aTP_Lamm_wx=1. aTP_Lamm_xa=1. aTP_Lamm_xd=1. aTP_Lamm_xg=1. aTP_Lamm_xj=1. aTP_Lamm_zy=1. scratc1503458065etprod=1. scratc1846697984nd_eps=1. scratc1879612801nd_inn=1. scratc409976095ective=1. aTP_Lamm_aai=1. aTP_Lamm_abo=1. aTP_Lamm_abp=1. aTP_Lamm_abq=1. aTP_Lamm_abs=1. aTP_Lamm_aby=1. aTP_Lamm_ac=1. aTP_Lamm_aca=1. aTP_Lamm_acb=1. aTP_Lamm_acf=1. aTP_Lamm_ad=1. aTP_Lamm_ae=1. aTP_Lamm_af=1. aTP_Lamm_aw=1. aTP_Lamm_ax=1. aTP_Lamm_ay=1. aTP_Lamm_ba=1. aTP_Lamm_bb=1. aTP_Lamm_bd=1. aTP_Lamm_be=1. aTP_Lamm_bk=1. aTP_Lamm_bl=1. aTP_Lamm_bo=1. aTP_Lamm_da=1. aTP_Lamm_de=1. aTP_Lamm_di=1. aTP_Lamm_dm=1. aTP_Lamm_dq=1. aTP_Lamm_du=1. aTP_Lamm_dy=1. aTP_Lamm_ec=1. aTP_Lamm_eg=1. aTP_Lamm_ek=1. aTP_Lamm_fg=1. aTP_Lamm_fk=1. aTP_Lamm_fo=1. aTP_Lamm_fs=1. aTP_Lamm_gn=1. aTP_Lamm_gq=1. aTP_Lamm_gw=1. aTP_Lamm_hg=1. aTP_Lamm_hk=1. aTP_Lamm_ho=1. aTP_Lamm_hs=1. aTP_Lamm_hw=1. aTP_Lamm_ia=1. aTP_Lamm_ie=1. aTP_Lamm_ii=1. aTP_Lamm_im=1. aTP_Lamm_iq=1. aTP_Lamm_jm=1. aTP_Lamm_jq=1. aTP_Lamm_ju=1. aTP_Lamm_jy=1. aTP_Lamm_kx=1. aTP_Lamm_ld=1. aTP_Lamm_lg=1. aTP_Lamm_lk=1. aTP_Lamm_ln=1. aTP_Lamm_mr=1. aTP_Lamm_mv=1. aTP_Lamm_np=1. aTP_Lamm_nt=1. aTP_Lamm_og=1. aTP_Lamm_oj=1. aTP_Lamm_ox=1. aTP_Lamm_pb=1. aTP_Lamm_pf=1. aTP_Lamm_pj=1. aTP_Lamm_pn=1. aTP_Lamm_pr=1. aTP_Lamm_pv=1. aTP_Lamm_pz=1. aTP_Lamm_qy=1. aTP_Lamm_rc=1. aTP_Lamm_rg=1. aTP_Lamm_rk=1. aTP_Lamm_sf=1. aTP_Lamm_si=1. aTP_Lamm_tv=1. aTP_Lamm_tz=1. aTP_Lamm_ud=1. aTP_Lamm_uh=1. aTP_Lamm_ul=1. aTP_Lamm_up=1. aTP_Lamm_ut=1. aTP_Lamm_ux=1. aTP_Lamm_wf=1. aTP_Lamm_wj=1. aTP_Lamm_wn=1. aTP_Lamm_wr=1. aTP_Lamm_zt=1. fEx_TPTP_ind=1. scratc1580609604ective=1. scratc1593616289lbprop=1. scratc1912330826nd_min=1. scratc231784252d_n_lb=1. sAlarm clock 179.64/180.12 Prover9 interrupted 179.64/180.13 EOF