0.02/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.02/0.10 % Command : tptp2X_and_run_prover9 %d %s 0.09/0.30 % Computer : n015.cluster.edu 0.09/0.30 % Model : x86_64 x86_64 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.30 % Memory : 8042.1875MB 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64 0.09/0.30 % CPULimit : 960 0.09/0.30 % DateTime : Thu Jul 2 14:40:15 EDT 2020 0.09/0.30 % CPUTime : 2.10/2.46 ============================== Prover9 =============================== 2.10/2.46 Prover9 (32) version 2009-11A, November 2009. 2.10/2.46 Process 18619 was started by sandbox2 on n015.cluster.edu, 2.10/2.46 Thu Jul 2 14:40:17 2020 2.10/2.46 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_18446_n015.cluster.edu". 2.10/2.46 ============================== end of head =========================== 2.10/2.46 2.10/2.46 ============================== INPUT ================================= 2.10/2.46 2.10/2.46 % Reading from file /tmp/Prover9_18446_n015.cluster.edu 2.10/2.46 2.10/2.46 set(prolog_style_variables). 2.10/2.46 set(auto2). 2.10/2.46 % set(auto2) -> set(auto). 2.10/2.46 % set(auto) -> set(auto_inference). 2.10/2.46 % set(auto) -> set(auto_setup). 2.10/2.46 % set(auto_setup) -> set(predicate_elim). 2.10/2.46 % set(auto_setup) -> assign(eq_defs, unfold). 2.10/2.46 % set(auto) -> set(auto_limits). 2.10/2.46 % set(auto_limits) -> assign(max_weight, "100.000"). 2.10/2.46 % set(auto_limits) -> assign(sos_limit, 20000). 2.10/2.46 % set(auto) -> set(auto_denials). 2.10/2.46 % set(auto) -> set(auto_process). 2.10/2.46 % set(auto2) -> assign(new_constants, 1). 2.10/2.46 % set(auto2) -> assign(fold_denial_max, 3). 2.10/2.46 % set(auto2) -> assign(max_weight, "200.000"). 2.10/2.46 % set(auto2) -> assign(max_hours, 1). 2.10/2.46 % assign(max_hours, 1) -> assign(max_seconds, 3600). 2.10/2.46 % set(auto2) -> assign(max_seconds, 0). 2.10/2.46 % set(auto2) -> assign(max_minutes, 5). 2.10/2.46 % assign(max_minutes, 5) -> assign(max_seconds, 300). 2.10/2.46 % set(auto2) -> set(sort_initial_sos). 2.10/2.46 % set(auto2) -> assign(sos_limit, -1). 2.10/2.46 % set(auto2) -> assign(lrs_ticks, 3000). 2.10/2.46 % set(auto2) -> assign(max_megs, 400). 2.10/2.46 % set(auto2) -> assign(stats, some). 2.10/2.46 % set(auto2) -> clear(echo_input). 2.10/2.46 % set(auto2) -> set(quiet). 2.10/2.46 % set(auto2) -> clear(print_initial_clauses). 2.10/2.46 % set(auto2) -> clear(print_given). 2.10/2.46 assign(lrs_ticks,-1). 2.10/2.46 assign(sos_limit,10000). 2.10/2.46 assign(order,kbo). 2.10/2.46 set(lex_order_vars). 2.10/2.46 clear(print_given). 2.10/2.46 2.10/2.46 % formulas(sos). % not echoed (1240 formulas) 2.10/2.46 2.10/2.46 ============================== end of input ========================== 2.10/2.46 2.10/2.46 % From the command line: assign(max_seconds, 960). 2.10/2.46 2.10/2.46 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 2.10/2.46 2.10/2.46 % Formulas that are not ordinary clauses: 2.10/2.46 1 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sm,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513572130moreis,Uua),aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uu)))))) # label(fact_ATP_Olambda__271) # label(axiom) # label(non_clause). [assumption]. 2.10/2.46 2 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pb(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__495) # label(axiom) # label(non_clause). [assumption]. 2.10/2.46 3 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_xu,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_xt,Uu))))) # label(fact_ATP_Olambda__51) # label(axiom) # label(non_clause). [assumption]. 2.10/2.46 4 (all Uu all Uua ((pp(scratc683290802_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379326120lesseq,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mh,Uu),Uua)))) # label(fact_ATP_Olambda__308) # label(axiom) # label(non_clause). [assumption]. 2.10/2.46 5 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dm(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__484) # label(axiom) # label(non_clause). [assumption]. 2.10/2.46 6 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513572130moreis,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xz,Uu),Uua)))) # label(fact_ATP_Olambda__278) # label(axiom) # label(non_clause). [assumption]. 2.10/2.46 7 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_qm(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qn,Uu),Uua)))) # label(fact_ATP_Olambda__368) # label(axiom) # label(non_clause). [assumption]. 2.10/2.46 8 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_lt(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lu(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__597) # label(axiom) # label(non_clause). [assumption]. 2.10/2.46 9 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_je,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_jd(Uu),Uua))))) # label(fact_ATP_Olambda__409) # label(axiom) # label(non_clause). [assumption]. 2.10/2.46 10 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ry,Uu),Uua)) <-> pp(scratc575825622_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,Uua),scratc1882202790nd_n_1)),Uu),aa_fun171081125l_bool(scratc799446_n_all,aa_TPT43085870d_bool(aTP_Lamm_ak(Uu),Uua)))))) # label(fact_ATP_Olambda__254) # label(axiom) # label(non_clause). [assumption]. 2.10/2.46 11 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wg,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_wf(Uu),Uua))))) # label(fact_ATP_Olambda__334) # label(axiom) # label(non_clause). [assumption]. 2.10/2.46 12 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cc(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uua),Uub)),Uu)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uua),Uuc)),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uub),Uuc)))))) # label(fact_ATP_Olambda__639) # label(axiom) # label(non_clause). [assumption]. 2.10/2.46 13 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_vl(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vm(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__572) # label(axiom) # label(non_clause). [assumption]. 2.10/2.46 14 (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_au(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_at(Uu),Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__705) # label(axiom) # label(non_clause). [assumption]. 2.10/2.46 15 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qg,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_qf(Uu),Uua))))) # label(fact_ATP_Olambda__370) # label(axiom) # label(non_clause). [assumption]. 2.10/2.46 16 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rs,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),Uua)),Uua))))) # label(fact_ATP_Olambda__256) # label(axiom) # label(non_clause). [assumption]. 2.10/2.46 17 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379326120lesseq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379326120lesseq,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379326120lesseq,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gm(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__656) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 18 (all B_1 gg_bool(fEx_TPTP_ind(B_1))) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 19 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc661733832_indeq(X,Xa,Xb),Xc),Xd) = scratc1936696956nd_ind(Xb,aa_TPT43085870d_bool(scratc1115212492_prop2(X,Xa,Xb,Xc),Xd))) # label(fact_def__indeq) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 20 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ot(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uua),Uuc))))))) # label(fact_ATP_Olambda__695) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 21 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zh(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__500) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 22 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gd,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uua),aa_TPTP_ind_TPTP_ind(scratc13795140_367_w(Uu),Uua))),Uu))))) # label(fact_ATP_Olambda__264) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 23 (all P all Q (-pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)) | pp(P))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 24 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_od(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_oe(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__592) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 25 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kt(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379326120lesseq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379326120lesseq,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379326120lesseq,Uu),Uub)))))) # label(fact_ATP_Olambda__524) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 26 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gf(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uua),Uub)),Uu)))) # label(fact_ATP_Olambda__557) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 27 (all P (gg_bool(P) -> fFalse = P | P = fTrue)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 28 (all X all Xa scratc2046619021_first(X,Xa) = scratc1114818896_proj0) # label(fact_def__first) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 29 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uu)),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zk,Uu),Uua)))) # label(fact_ATP_Olambda__301) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 30 (all X0 all X12 pp(aa_fun171081125l_bool(scratc91799413all_of(aa_TPT43085870d_bool(aTP_Lamm_aat(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_aaw(X0),X12)))) # label(fact_first__p) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 31 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lq(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_lp(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__598) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 32 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_rx,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),scratc1882202790nd_n_1)),Uu)))) # label(fact_ATP_Olambda__4) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 33 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_db(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_da(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__620) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 34 (all Uu all Uua all Uub (pp(scratc575825622_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uu),Uub),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uub),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_km(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__554) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 35 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_fh,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fi,Uu)))) # label(fact_ATP_Olambda__206) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 36 (all X aa_fun1431113780TP_ind(scratc459574173_d_Sep(scratc1977151710nd_nat),aa_TPT43085870d_bool(aTP_Lamm_ag,X)) = aa_TPTP_ind_TPTP_ind(scratc179666987_d_1to,X)) # label(fact_def__d__1to) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 37 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1533492748d_e_is(Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,Uua),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,Uub),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_abe(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__633) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 38 (all X0 all X12 pp(aa_fun171081125l_bool(scratc91799413all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,X0)),aa_fun1584354236d_bool(aTP_Lamm_abi(X0),X12)))) # label(fact_e__isp) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 39 (all Uu all Uua (pp(scratc1593517495_amone(scratc1977151710nd_nat,aa_TPT43085870d_bool(aTP_Lamm_yr(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yv,Uu),Uua)))) # label(fact_ATP_Olambda__460) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 40 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fj(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uua),Uub)))))) # label(fact_ATP_Olambda__527) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 41 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1361989810d_Subq,X12),X0)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc986305058_power,X0))))) # label(fact_k__PowerEq) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 42 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_eq(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__683) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 43 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_abi(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_abh(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__560) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 44 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hg(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271961_moreq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uua),Uuc))))))) # label(fact_ATP_Olambda__663) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 45 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_il(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_im,Uu),Uua)))) # label(fact_ATP_Olambda__414) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 46 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_tj(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513572130moreis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__646) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 47 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc448820014d_anec(X,Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1349943869l_some(X),aa_TPT43085870d_bool(scratc1902929359nd_ecp(X,Xa),Xb))))) # label(fact_def__anec) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 48 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_rk,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_rl,Uu)))) # label(fact_ATP_Olambda__105) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 49 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wd,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_wc(Uu),Uua))))) # label(fact_ATP_Olambda__335) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 50 (all X aa_TPTP_ind_TPTP_ind(scratc936929700d_24_g,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc523788228_Sigma,scratc1977151710nd_nat),aTP_Lamm_al(X))) # label(fact_def__d__24__g) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 51 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X22),aa_fun1431113780TP_ind(scratc459574173_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(X12,X22)))) # label(fact_k__SepE2) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 52 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc1986265987nd_one(X0),X12)) -> pp(aa_TPTP_ind_bool(X12,scratc1936696956nd_ind(X0,X12))))) # label(fact_oneax) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 53 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ww,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_wv,Uu))))) # label(fact_ATP_Olambda__61) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 54 (all X all Xa (pp(aa_bool_bool(scratc920901772d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379326120lesseq,X),Xa)))) # label(fact_def__lesseq) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 55 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_hp(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hq,Uu),Uua)))) # label(fact_ATP_Olambda__421) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 56 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_uj,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_ui(Uu),Uua))))) # label(fact_ATP_Olambda__349) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 57 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nl,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1051956311d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1978463683nd_num,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1894799050nd_den,Uu)),Uua))),Uu)))) # label(fact_ATP_Olambda__249) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 58 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_zj,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_zi,Uu))))) # label(fact_ATP_Olambda__33) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 59 (all X all Xa aa_fun1431113780TP_ind(scratc459574173_d_Sep(aa_TPTP_ind_TPTP_ind(scratc986305058_power,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc523788228_Sigma,X),aTP_Lamm_bl(Xa)))),aa_fun1913827119d_bool(aTP_Lamm_bm(X),Xa)) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc392288474d_d_Pi,X),Xa)) # label(fact_def__d__Pi) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 60 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc91799413all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bj(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bk(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__561) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 61 (all Uu all Uua aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,Uu),Uua)) = aa_TPTP_ind_TPTP_ind(aTP_Lamm_al(Uu),Uua)) # label(fact_ATP_Olambda__461) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 62 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_sg,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_sh,Uu)))) # label(fact_ATP_Olambda__97) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 63 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jb,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_ja(Uu),Uua))))) # label(fact_ATP_Olambda__410) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 64 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_si,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_sj,Uu)))) # label(fact_ATP_Olambda__96) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 65 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aag,Uu),Uua)))) # label(fact_ATP_Olambda__255) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 66 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_po,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_pn(Uu),Uua))))) # label(fact_ATP_Olambda__375) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 67 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_oj,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ok,Uu)))) # label(fact_ATP_Olambda__129) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 68 (all X all Xa (pp(scratc683290802_d_not(aa_fun171081125l_bool(scratc91799413all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,X)),scratc1978070090nd_non(X,Xa)))) <-> pp(aa_fun171081125l_bool(scratc1349943869l_some(X),Xa)))) # label(fact_def__l__some) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 69 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aaw(Uu),Uua),Uub)) <-> scratc1588370020_is_of(aa_TPTP_ind_TPTP_ind(scratc2046619021_first(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aq,Uu)))) # label(fact_ATP_Olambda__471) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 70 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nj,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_ni(Uu),Uua))))) # label(fact_ATP_Olambda__388) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 71 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc888417639_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1977676501nd_nis,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(X),Xb))))) # label(fact_def__d__28__prop1) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 72 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),scratc1882202790nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_zv,Uu)))) # label(fact_ATP_Olambda__3) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 73 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ds(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uu),Uua))))) # label(fact_ATP_Olambda__480) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 74 (all X aa_TPTP_ind_TPTP_ind(scratc903099694_428_g,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc523788228_Sigma,scratc1977151710nd_nat),aTP_Lamm_ai(X))) # label(fact_def__d__428__g) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 75 (all X0 all X12 pp(aa_fun171081125l_bool(scratc91799413all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,X0)),aa_TPT43085870d_bool(aTP_Lamm_aay(X0),X12)))) # label(fact_e__pair__p) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 76 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cn,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_cm,Uu))))) # label(fact_ATP_Olambda__227) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 77 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_qi(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uua),Uuc))))))) # label(fact_ATP_Olambda__675) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 78 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_ef(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eg,Uu),Uua)))) # label(fact_ATP_Olambda__443) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 79 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cw(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cx(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__621) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 80 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc2093768511n_some,aa_TPT43085870d_bool(scratc1841546987ffprop(X),Xa))))) # label(fact_def__d__29__ii) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 81 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_zc,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_zb,Uu))))) # label(fact_ATP_Olambda__36) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 82 (all X0 all X12 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1116728996ective(aa_fun1431113780TP_ind(scratc459574173_d_Sep(X0),X12)),X0),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc523788228_Sigma,aa_fun1431113780TP_ind(scratc459574173_d_Sep(X0),X12)),scratc1533492743d_e_in(X0,X12))))) # label(fact_otax1) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 83 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_er(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_eq(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__614) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 84 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_be(Uu),Uua),Uub),Uuc) = aa_TPTP_ind_TPTP_ind(scratc1405965280bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2003976952_image(Uu,Uua),Uub),Uuc),aa_TPTP_ind_TPTP_ind(scratc1622814829d_soft(Uu,Uua,Uub),Uuc)),scratc559650040ptyset)) # label(fact_ATP_Olambda__630) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 85 (all X0 all X12 pp(aa_fun171081125l_bool(scratc91799413all_of(aa_fun1584354236d_bool(aTP_Lamm_aba(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_abb(X0),X12)))) # label(fact_e__inp) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 86 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fx,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_fw,Uu))))) # label(fact_ATP_Olambda__201) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 87 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hu,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_ht,Uu))))) # label(fact_ATP_Olambda__187) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 88 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_on,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_om(Uu),Uua))))) # label(fact_ATP_Olambda__383) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 89 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_mv,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_mw,Uu)))) # label(fact_ATP_Olambda__145) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 90 (all X all Xa all Xb all Xc all Xd aa_TPT1424761345TP_ind(scratc661733832_indeq(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1750571112d_11_i(X,Xa,Xb),Xc),Xd)) = scratc1990668394indeq2(X,Xa,Xb,Xc,Xd)) # label(fact_def__indeq2) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 91 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_vd(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uuc),Uua))))))) # label(fact_ATP_Olambda__682) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 92 (all Uu all Uua all Uub all Uuc (scratc1588370020_is_of(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc211927547d_pair(Uu,Uua),Uub),Uuc),aa_TPT43085870d_bool(aTP_Lamm_aat(Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aax(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__636) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 93 (all Uu aa_TPT494704832TP_ind(scratc760268562d_repl,aa_TPTP_ind_TPTP_ind(scratc1835233233tminus(Uu),aa_TPTP_ind_TPTP_ind(scratc1263638928d_Sing,scratc559650040ptyset))) = aa_TPT494704832TP_ind(aTP_Lamm_br,Uu)) # label(fact_ATP_Olambda__235) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 94 (all X all Xa all Xb (pp(scratc575825622_d_and(scratc1986528333nd_or3(X,Xa,Xb),scratc1902929298nd_ec3(X,Xa,Xb))) <-> scratc2039664015_orec3(X,Xa,Xb))) # label(fact_def__orec3) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 95 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_rw,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_rv,Uu))))) # label(fact_ATP_Olambda__101) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 96 (all Uu all Uua (pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1936631369nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153104d_n_in,Uua),Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153104d_n_in,aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uua)),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ao,Uu),Uua)))) # label(fact_ATP_Olambda__267) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 97 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rv,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),Uua)),Uu))))) # label(fact_ATP_Olambda__260) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 98 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zw,Uu),Uua)) <-> pp(scratc575825622_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,Uua),scratc1882202790nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uu)),aa_fun171081125l_bool(scratc799446_n_all,aa_TPT43085870d_bool(aTP_Lamm_am,Uua)))))) # label(fact_ATP_Olambda__252) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 99 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cu,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_ct(Uu),Uua))))) # label(fact_ATP_Olambda__454) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 100 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_wz,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_wy,Uu))))) # label(fact_ATP_Olambda__60) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 101 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ft,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_fs,Uu))))) # label(fact_ATP_Olambda__202) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 102 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc392288474d_d_Pi,X0),X12))) -> (all X32 (gg_TPTP_ind(X32) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X32),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc392288474d_d_Pi,X0),X12))) -> ((all X42 (gg_TPTP_ind(X42) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X42),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,X32),X42) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,X22),X42)))) -> X32 = X22))))))) # label(fact_k__Pi__ext) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 103 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ma,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_lz,Uu))))) # label(fact_ATP_Olambda__154) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 104 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_gw,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_gx,Uu)))) # label(fact_ATP_Olambda__193) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 105 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uu),Uua)) -> pp(scratc683290802_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xp,Uu),Uua)))) # label(fact_ATP_Olambda__288) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 106 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_ii,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ij,Uu)))) # label(fact_ATP_Olambda__182) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 107 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_vn,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_vo,Uu)))) # label(fact_ATP_Olambda__72) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 108 (all X (pp(scratc683290802_d_not(X)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1936631369nd_imp,X),fFalse)))) # label(fact_def__d__not) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 109 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ih(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uu),Uua))))) # label(fact_ATP_Olambda__481) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 110 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1115212493_prop3(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,X),Xb)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,Xa),Xb))))) # label(fact_def__prop3) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 111 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_rt,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_rs,Uu))))) # label(fact_ATP_Olambda__102) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 112 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fa(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uub),Uua)))))) # label(fact_ATP_Olambda__528) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 113 (all X0 all X12 pp(aa_fun171081125l_bool(scratc91799413all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,X0)),aa_TPT43085870d_bool(aTP_Lamm_aaq(X0),X12)))) # label(fact_secondis1) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 114 (all X0 all X12 pp(aa_fun171081125l_bool(scratc91799413all_of(aa_TPT43085870d_bool(aTP_Lamm_aat(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_aau(X0),X12)))) # label(fact_pairis1) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 115 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_tn(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_to(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__577) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 116 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_aac,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_aab,Uu))))) # label(fact_ATP_Olambda__28) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 117 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc682452588_prop2,X),Xa)) <-> pp(scratc575825622_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,Xa),scratc1882202790nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,X)),aa_TPTP_ind_bool(scratc682452587_prop1,Xa))))) # label(fact_def__d__24__prop2) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 118 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_yh,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_yi,Uu)))) # label(fact_ATP_Olambda__44) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 119 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zn,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uua)))))) # label(fact_ATP_Olambda__302) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 120 (all X all Xa all Xb all Xc scratc1936696956nd_ind(X,aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bf(Xa),Xb),Xc)) = aa_TPTP_ind_TPTP_ind(scratc1622814829d_soft(X,Xa,Xb),Xc)) # label(fact_def__soft) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 121 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_gv(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gw,Uu),Uua)))) # label(fact_ATP_Olambda__426) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 122 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_un,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_um,Uu))))) # label(fact_ATP_Olambda__80) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 123 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_xv,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_xw,Uu)))) # label(fact_ATP_Olambda__50) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 124 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xe,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_xd(Uu),Uua))))) # label(fact_ATP_Olambda__328) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 125 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_na,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_mz,Uu))))) # label(fact_ATP_Olambda__143) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 126 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_dc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_dd,Uu)))) # label(fact_ATP_Olambda__223) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 127 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_wq,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_wp,Uu))))) # label(fact_ATP_Olambda__63) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 128 (all X7 all Y (gg_TPTP_ind(Y) & gg_TPTP_ind(X7) -> -pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) | Y = X7)) # label(help_fequal_1_1_fequal_001t__TPTP____Interpret__Oind_T) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 129 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_qo,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_qn,Uu))))) # label(fact_ATP_Olambda__113) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 130 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc91799413all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aax(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aay(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__562) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 131 (all X (pp(aa_TPTP_ind_bool(scratc1483302904_prop4,X)) <-> pp(aa_fun171081125l_bool(scratc1349943869l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc392288474d_d_Pi,scratc1977151710nd_nat),aTP_Lamm_ah)),aa_TPT43085870d_bool(scratc1483302902_prop2,X))))) # label(fact_def__d__428__prop4) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 132 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_rf,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_rg,Uu)))) # label(fact_ATP_Olambda__107) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 133 (all X scratc1533492743d_e_in(scratc1977151710nd_nat,aa_TPT43085870d_bool(aTP_Lamm_ag,X)) = scratc1936696966nd_inn(X)) # label(fact_def__inn) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 134 (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]. 2.10/2.47 135 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dy(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__491) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 136 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gb,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uu),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uua),aa_TPTP_ind_TPTP_ind(scratc13795140_367_w(Uu),Uua))))))) # label(fact_ATP_Olambda__269) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 137 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513572130moreis,Uu),Uua)) -> pp(scratc683290802_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xx,Uu),Uua)))) # label(fact_ATP_Olambda__289) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 138 (all B_1 all B_2 all B_3 gg_bool(scratc1986528333nd_or3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__62002__14561_ONUM781__thf__4__p_Obnd__or3) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 139 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_zl,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_zk,Uu))))) # label(fact_ATP_Olambda__32) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 140 (all X0 (pp(aa_TPTP_ind_bool(X0,scratc559650040ptyset)) -> ((all X13 (gg_TPTP_ind(X13) -> (pp(aa_TPTP_ind_bool(scratc1475014226_nat_p,X13)) -> (pp(aa_TPTP_ind_bool(X0,X13)) -> pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,X13))))))) -> (all X12 (pp(aa_TPTP_ind_bool(scratc1475014226_nat_p,X12)) -> pp(aa_TPTP_ind_bool(X0,X12))))))) # label(fact_nat__ind) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 141 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_us,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ut,Uu)))) # label(fact_ATP_Olambda__78) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 142 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X22),aa_fun1431113780TP_ind(scratc459574173_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X22),X0)))) # label(fact_k__SepE1) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 143 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_mk,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_mj,Uu))))) # label(fact_ATP_Olambda__149) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 144 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hp(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ho(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__604) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 145 (all X all Xa all Xb aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc523788228_Sigma,Xa),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_be(X),Xa),Xb)) = aa_TPTP_ind_TPTP_ind(scratc720156685nverse(X,Xa),Xb)) # label(fact_def__inverse) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 146 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1977676501nd_nis,aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uu)),scratc1882202790nd_n_1)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_aai,Uu)))) # label(fact_ATP_Olambda__16) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 147 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_kw(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kx,Uu),Uua)))) # label(fact_ATP_Olambda__401) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 148 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),Uua)),Uua)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uu)),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rm,Uu),Uua)))) # label(fact_ATP_Olambda__250) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 149 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1977676501nd_nis,Xa),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc300055464_prop1,X),Xa)))) # label(fact_def__d__27__prop1) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 150 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ab,Uu)))) # label(fact_ATP_Olambda__231) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 151 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qy(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__538) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 152 (all X all Xa scratc1313072605d_pair = scratc211927547d_pair(X,Xa)) # label(fact_def__d__pair) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 153 (all X0 pp(aa_fun171081125l_bool(scratc91799413all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,X0)),aa_TPT43085870d_bool(aTP_Lamm_abj,X0)))) # label(fact_refis) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 154 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271961_moreq,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hc(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__666) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 155 (all X all Xa scratc1622814829d_soft(aa_fun1431113780TP_ind(scratc459574173_d_Sep(X),Xa),X,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc523788228_Sigma,aa_fun1431113780TP_ind(scratc459574173_d_Sep(X),Xa)),scratc1533492743d_e_in(X,Xa))) = scratc1986725195nd_out(X,Xa)) # label(fact_def__out) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 156 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1918947691nunion(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1493566924_union,aa_TPTP_ind_TPTP_ind(scratc418274606_UPair(X),Xa))) # label(fact_def__binunion) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 157 (all X all Xa all Xb (pp(scratc575825622_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1116728996ective(X),Xa),Xb),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1839685631ective(X),Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1300448226ective(X),Xa),Xb)))) # label(fact_def__bijective) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 158 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_fq,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fr,Uu)))) # label(fact_ATP_Olambda__203) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 159 (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]. 2.10/2.47 160 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kp,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uua),Uu)))) # label(fact_ATP_Olambda__320) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 161 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_dn,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_do,Uu)))) # label(fact_ATP_Olambda__220) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 162 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ja(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__535) # label(axiom) # label(non_clause). [assumption]. 2.10/2.47 163 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_ld,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_le,Uu)))) # label(fact_ATP_Olambda__162) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 164 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1975577328nd_nIn,Uua),Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bt,Uu),Uua)))) # label(fact_ATP_Olambda__322) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 165 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rf,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_re(Uu),Uua))))) # label(fact_ATP_Olambda__362) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 166 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc371056682d_left(X,Xa,Xb),Xc) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc523788228_Sigma,aa_TPTP_ind_TPTP_ind(scratc179666987_d_1to,Xb)),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ad(Xa),Xb),Xc))) # label(fact_def__left) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 167 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jm(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__544) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 168 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc906447293_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(X),Xa)),Xb)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(X),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Xa),Xb)))))) # label(fact_def__d__431__prop1) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 169 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1533492748d_e_is(aa_TPTP_ind_TPTP_ind(scratc955832086etprod(Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc211927547d_pair(Uu,Uua),aa_TPTP_ind_TPTP_ind(scratc2046619021_first(Uu,Uua),Uub)),aa_TPTP_ind_TPTP_ind(scratc1198944151second(Uu,Uua),Uub))),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aau(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__464) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 170 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_wh,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_wg,Uu))))) # label(fact_ATP_Olambda__66) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 171 (all X0 ((all X13 (gg_TPTP_ind(X13) -> ((all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_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]. 2.10/2.48 172 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vt(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__551) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 173 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yr(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__566) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 174 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jg(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__530) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 175 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_tf(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__654) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 176 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),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__428) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 177 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hv(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__494) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 178 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_oj,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_oi(Uu),Uua))))) # label(fact_ATP_Olambda__384) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 179 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ez,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_ey,Uu))))) # label(fact_ATP_Olambda__209) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 180 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qt,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_qs(Uu),Uua))))) # label(fact_ATP_Olambda__366) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 181 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ei(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ej(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__616) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 182 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1051956311d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1978463683nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc1978463683nd_num,Xa))),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1894799050nd_den,X)),aa_TPTP_ind_TPTP_ind(scratc1894799050nd_den,Xa))) = aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(X),Xa)) # label(fact_def__n__tf) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 183 (all X all Xa (pp(scratc575825622_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1936631369nd_imp,X),Xa),aa_bool_bool(aa_boo1142376798l_bool(scratc1936631369nd_imp,Xa),X))) <-> scratc1469967072_l_iff(X,Xa))) # label(fact_def__l__iff) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 184 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mt,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_ms(Uu),Uua))))) # label(fact_ATP_Olambda__393) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 185 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_az(Uu),Uua),Uub),Uuc)) <-> pp(scratc920245767d_l_ec(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1465976678d_esti(Uu),Uuc),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1465976678d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__637) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 186 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_pc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_pd,Uu)))) # label(fact_ATP_Olambda__124) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 187 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_kq,Uu)) <-> pp(aa_fun171081125l_bool(scratc1349943869l_some(scratc89572337d_frac),aa_TPT43085870d_bool(aTP_Lamm_kp,Uu))))) # label(fact_ATP_Olambda__233) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 188 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_lm,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_ll,Uu))))) # label(fact_ATP_Olambda__159) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 189 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wf(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__540) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 190 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_lr,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ls,Uu)))) # label(fact_ATP_Olambda__157) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 191 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xn,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uu),Uua)) -> pp(scratc683290802_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513572130moreis,Uu),Uua)))))) # label(fact_ATP_Olambda__295) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 192 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_du,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_dt,Uu))))) # label(fact_ATP_Olambda__218) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 193 (all X (pp(scratc683290802_d_not(scratc683290802_d_not(X))) <-> scratc2051767643nd_wel(X))) # label(fact_def__wel) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 194 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ic,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_ib(Uu),Uua))))) # label(fact_ATP_Olambda__417) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 195 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ei(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__687) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 196 (all X aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc392288474d_d_Pi,aa_TPTP_ind_TPTP_ind(scratc179666987_d_1to,scratc1882202791nd_n_2)),aTP_Lamm_af(X)) = aa_TPTP_ind_TPTP_ind(scratc1311015950r1type,X)) # label(fact_def__pair1type) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 197 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc456499546ectelt(X,Xa),Xb) = aa_TPTP_ind_TPTP_ind(scratc571701423ectset(X,Xa),aa_TPTP_ind_TPTP_ind(scratc410640076_ecelt(X,Xa),Xb))) # label(fact_def__ectelt) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 198 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eu(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__533) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 199 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_no,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_nn,Uu))))) # label(fact_ATP_Olambda__133) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 200 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_wu(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wv,Uu),Uua)))) # label(fact_ATP_Olambda__331) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 201 (all X scratc698437091d_outn(X) = scratc1986725195nd_out(scratc1977151710nd_nat,aa_TPT43085870d_bool(aTP_Lamm_ag,X))) # label(fact_def__outn) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 202 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uua),Uub)),Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bz(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__556) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 203 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ln,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271961_moreq,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379326120lesseq,Uua),Uu))))) # label(fact_ATP_Olambda__281) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 204 (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]. 2.10/2.48 205 (all X aa_TPTP_ind_TPTP_ind(scratc1263638928d_Sing,X) = aa_TPTP_ind_TPTP_ind(scratc418274606_UPair(X),X)) # label(fact_def__d__Sing) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 206 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jd(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__545) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 207 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_vh(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__681) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 208 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_mr(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uu),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uua),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uub),Uuc))))))) # label(fact_ATP_Olambda__669) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 209 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_vr,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_vs,Uu)))) # label(fact_ATP_Olambda__71) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 210 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_mi,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_mh,Uu))))) # label(fact_ATP_Olambda__150) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 211 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_rh(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ri,Uu),Uua)))) # label(fact_ATP_Olambda__361) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 212 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_tl,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_tm,Uu)))) # label(fact_ATP_Olambda__88) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 213 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_tw(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tx,Uu),Uua)))) # label(fact_ATP_Olambda__353) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 214 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),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__430) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 215 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uu),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jw(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__502) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 216 (all X all Xa all Xb (scratc448754367d_and3(X,Xa,Xb) <-> pp(scratc575825622_d_and(X,scratc575825622_d_and(Xa,Xb))))) # label(fact_def__and3) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 217 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_zu,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_zt,Uu))))) # label(fact_ATP_Olambda__29) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 218 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1476779814_prop1,X),Xa)) <-> pp(scratc1986528333nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,X),Xa))))) # label(fact_def__d__29__prop1) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 219 (all X all Xa all 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(scratc1405965288bnd_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)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc780983997_rec_G(X),Xa),Xb)))) # label(fact_def__d__In__rec__G) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 220 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hk(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hl(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__605) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 221 (all X all Xa scratc1936696956nd_ind(scratc1977151710nd_nat,aa_TPT43085870d_bool(scratc1841546987ffprop(X),Xa)) = aa_TPTP_ind_TPTP_ind(scratc1052415500d_n_mn(X),Xa)) # label(fact_def__n__mn) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 222 (all X all Xa aa_TPT494704832TP_ind(scratc760268562d_repl,aa_fun1431113780TP_ind(scratc459574173_d_Sep(X),Xa)) = scratc719917262eplSep(X,Xa)) # label(fact_def__d__ReplSep) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 223 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2003976952_image(aa_fun1431113780TP_ind(scratc459574173_d_Sep(Uu),Uua),Uu),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc523788228_Sigma,aa_fun1431113780TP_ind(scratc459574173_d_Sep(Uu),Uua)),scratc1533492743d_e_in(Uu,Uua))),Uub))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_aaz(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__558) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 224 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1978463683nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc1894799050nd_den,Xa))),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1978463683nd_num,Xa)),aa_TPTP_ind_TPTP_ind(scratc1894799050nd_den,X)))))) # label(fact_def__moref) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 225 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_fun171081125l_bool(scratc91799413all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_av(Uua),Uub),Uuc),Uud))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_aw(Uu),Uua),Uub),Uuc),Uud)))) # label(fact_ATP_Olambda__706) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 226 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_xr,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_xs,Uu)))) # label(fact_ATP_Olambda__52) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 227 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X33),X0)) -> aa_TPTP_ind_TPTP_ind(X12,X33) = aa_TPTP_ind_TPTP_ind(X22,X33)))) -> aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc523788228_Sigma,X0),X12) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc523788228_Sigma,X0),X22))) # label(fact_xi__ext) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 228 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_dp(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dq,Uu),Uua)))) # label(fact_ATP_Olambda__448) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 229 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_zn,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_zo,Uu)))) # label(fact_ATP_Olambda__31) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 230 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uua),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),scratc1882202790nd_n_1))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sg,Uu),Uua)))) # label(fact_ATP_Olambda__259) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 231 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_uz,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_uy,Uu))))) # label(fact_ATP_Olambda__76) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 232 (all X aa_TPTP_ind_TPTP_ind(scratc698437091d_outn(X),scratc1882202790nd_n_1) = aa_TPTP_ind_TPTP_ind(scratc543506174d_1out,X)) # label(fact_def__d__1out) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 233 (all X0 all X12 all X22 (gg_TPTP_ind(X22) & gg_TPTP_ind(X12) -> X22 = aa_TPTP_ind_TPTP_ind(scratc1405965280bnd_if(X0,X12),X22) & -pp(X0) | pp(X0) & X12 = aa_TPTP_ind_TPTP_ind(scratc1405965280bnd_if(X0,X12),X22))) # label(fact_if__i__correct) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 234 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wj,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_wi(Uu),Uua))))) # label(fact_ATP_Olambda__333) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 235 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tl,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_tk(Uu),Uua))))) # label(fact_ATP_Olambda__356) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 236 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ox(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uua),Uuc))))))) # label(fact_ATP_Olambda__643) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 237 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vq(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_vp(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__571) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 238 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gi(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uua),Uub)),Uu)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uua),Uuc)),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uub),Uuc)))))) # label(fact_ATP_Olambda__640) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 239 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eb(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uu),Uua))))) # label(fact_ATP_Olambda__479) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 240 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_de(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_df(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__619) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 241 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_pk(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pl,Uu),Uua)))) # label(fact_ATP_Olambda__376) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 242 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ha,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_gz(Uu),Uua))))) # label(fact_ATP_Olambda__425) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 243 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_wt,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_ws,Uu))))) # label(fact_ATP_Olambda__62) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 244 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc719917262eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bn,Xa)),scratc1114818897_proj1)) # label(fact_def__ap) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 245 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ev,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_eu(Uu),Uua))))) # label(fact_ATP_Olambda__439) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 246 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uua),scratc1882202790nd_n_1)),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513572130moreis,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sc,Uu),Uua)))) # label(fact_ATP_Olambda__253) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 247 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_uu(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_uv,Uu),Uua)))) # label(fact_ATP_Olambda__345) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 248 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_en(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eo,Uu),Uua)))) # label(fact_ATP_Olambda__441) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 249 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ee(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ef(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__617) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 250 (all X all Xa all Xb all Xc scratc1936696956nd_ind(Xa,aa_TPT43085870d_bool(scratc1115212491_prop1(X,Xa,Xb),Xc)) = aa_TPTP_ind_TPTP_ind(scratc1937090551nd_ite(X,Xa,Xb),Xc)) # label(fact_def__ite) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 251 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_yk,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_yj,Uu))))) # label(fact_ATP_Olambda__43) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 252 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_kv,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_ku,Uu))))) # label(fact_ATP_Olambda__165) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 253 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379326120lesseq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uu),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uua),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379326120lesseq,Uub),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_lp(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__659) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 254 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jx,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_jw(Uu),Uua))))) # label(fact_ATP_Olambda__404) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 255 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ji,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_jh,Uu))))) # label(fact_ATP_Olambda__175) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 256 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X33),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,aa_TPTP_ind_TPTP_ind(X22,X33)),aa_TPTP_ind_TPTP_ind(X12,X33)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc523788228_Sigma,X0),X22)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc392288474d_d_Pi,X0),X12))))) # label(fact_lam__Pi) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 257 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ib(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uu),Uua))))) # label(fact_ATP_Olambda__485) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 258 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(X),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Xa),Xb))),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(X),Xb)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc318085118_prop1(X),Xa),Xb)))) # label(fact_def__d__430__prop1) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 259 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tt,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_ts(Uu),Uua))))) # label(fact_ATP_Olambda__354) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 260 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vi(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_vh(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__573) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 261 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_gk,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_gl,Uu)))) # label(fact_ATP_Olambda__196) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 262 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X22),X0)) -> (pp(aa_TPTP_ind_bool(X12,X22)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X22),aa_fun1431113780TP_ind(scratc459574173_d_Sep(X0),X12)))))) # label(fact_k__SepI) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 263 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc925090592munion,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1493566924_union,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc760268562d_repl,X),Xa))) # label(fact_def__famunion) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 264 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uub))),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,Uua),Uub)),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ak(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__505) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 265 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aar(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1533492748d_e_is(Uu),aa_TPTP_ind_TPTP_ind(scratc2046619021_first(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc211927547d_pair(Uu,Uua),Uub),Uuc))),Uub)))) # label(fact_ATP_Olambda__631) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 266 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_js,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_jt,Uu)))) # label(fact_ATP_Olambda__171) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 267 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ac(Uu),Uua),Uub),Uuc) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,Uub),aa_TPTP_ind_TPTP_ind(scratc283046675ght1to(Uu,Uua),Uuc))) # label(fact_ATP_Olambda__701) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 268 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_pt(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pu,Uu),Uua)))) # label(fact_ATP_Olambda__373) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 269 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_js,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uu),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uu),Uua))))) # label(fact_ATP_Olambda__313) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 270 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_qg,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_qh,Uu)))) # label(fact_ATP_Olambda__115) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 271 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_uu(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__520) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 272 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ix(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_iw(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__600) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 273 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_rp,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_rq,Uu)))) # label(fact_ATP_Olambda__103) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 274 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mj,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379326120lesseq,Uu),Uua)) -> pp(scratc683290802_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uu),Uua)))))) # label(fact_ATP_Olambda__291) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 275 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_fun1235454963TP_ind(aTP_Lamm_bu(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc1405965280bnd_if(aa_TPTP_ind_bool(Uua,Uub),Uub),scratc1903782149nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bi(Uu),Uua)))) # label(fact_ATP_Olambda__466) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 276 (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(scratc1533492748d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,Uub),Uud)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_av(Uu),Uua),Uub),Uuc),Uud)))) # label(fact_ATP_Olambda__704) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 277 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ld,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_lc(Uu),Uua))))) # label(fact_ATP_Olambda__399) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 278 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_tv(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__644) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 279 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uua)),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513572130moreis,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sa,Uu),Uua)))) # label(fact_ATP_Olambda__257) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 280 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271961_moreq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kz(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__526) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 281 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uua),Uub)),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uub),aa_TPTP_ind_TPTP_ind(scratc13795140_367_w(Uu),Uua))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fy(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__506) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 282 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,Uua),aa_TPTP_ind_TPTP_ind(scratc986305058_power,Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aak,Uu),Uua)))) # label(fact_ATP_Olambda__317) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 283 (all Uu all Uua all Uub all Uuc all Uud all Uue all 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(scratc1533492748d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,Uub),Uuc)),Uue)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,Uub),Uud)),Uuf))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_ar(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)))) # label(fact_ATP_Olambda__709) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 284 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271961_moreq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_da(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__662) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 285 (all B_1 all B_2 gg_TPTP_ind(scratc1902929363nd_ect(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__62002__14561_ONUM781__thf__4__p_Obnd__ect) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 286 (all X all Xa all Xb aa_fun1431113780TP_ind(scratc459574173_d_Sep(X),aa_TPT43085870d_bool(Xa,Xb)) = aa_TPTP_ind_TPTP_ind(scratc410640076_ecelt(X,Xa),Xb)) # label(fact_def__ecelt) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 287 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dv(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uu),Uua))))) # label(fact_ATP_Olambda__483) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 288 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1533492748d_e_is(Uu),Uua),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abj,Uu),Uua)))) # label(fact_ATP_Olambda__248) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 289 (all Uu all Uua aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc760268562d_repl,aa_TPTP_ind_TPTP_ind(Uu,Uua)),aa_TPT1424761345TP_ind(scratc1313072605d_pair,Uua)) = aa_TPTP_ind_TPTP_ind(aTP_Lamm_bo(Uu),Uua)) # label(fact_ATP_Olambda__299) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 290 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_pm,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_pl,Uu))))) # label(fact_ATP_Olambda__121) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 291 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vr,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_vq(Uu),Uua))))) # label(fact_ATP_Olambda__339) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 292 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sk,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uua),scratc1882202790nd_n_1)),Uu))))) # label(fact_ATP_Olambda__265) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 293 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tw(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_tv(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__575) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 294 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1533492748d_e_is(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,Uua),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bf(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__635) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 295 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_eo,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ep,Uu)))) # label(fact_ATP_Olambda__212) # label(axiom) # label(non_clause). [assumption]. 2.10/2.48 296 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_my,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_mx,Uu))))) # label(fact_ATP_Olambda__144) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 297 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_am,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,Uu),aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,Uu),Uua)))))) # label(fact_ATP_Olambda__263) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 298 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uuc),Uua))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_vl(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__678) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 299 (all X all Xa (pp(aa_fun171081125l_bool(scratc1986265987nd_one(X),Xa)) <-> pp(scratc575825622_d_and(scratc1593517495_amone(X,Xa),aa_fun171081125l_bool(scratc1349943869l_some(X),Xa))))) # label(fact_def__one) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 300 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_aad,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,Uu),aa_TPTP_ind_TPTP_ind(scratc986305058_power,scratc1977151710nd_nat))))) # label(fact_ATP_Olambda__20) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 301 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dw,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_dv(Uu),Uua))))) # label(fact_ATP_Olambda__446) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 302 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wy,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_wx(Uu),Uua))))) # label(fact_ATP_Olambda__330) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 303 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_vd(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ve(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__574) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 304 (all X0 all X12 pp(aa_fun171081125l_bool(scratc91799413all_of(aa_TPT43085870d_bool(aTP_Lamm_abd(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_abg(X0),X12)))) # label(fact_e__fisi) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 305 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_pw(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uuc),Uua))))))) # label(fact_ATP_Olambda__680) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 306 (all X0 (pp(aa_fun171081125l_bool(scratc2093768511n_some,X0)) -> pp(aa_fun171081125l_bool(scratc116591707_n_one,scratc1969414991nd_min(X0))))) # label(fact_satz27a) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 307 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hf,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_he,Uu))))) # label(fact_ATP_Olambda__191) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 308 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_fz,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ga,Uu)))) # label(fact_ATP_Olambda__200) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 309 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_uf(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ug,Uu),Uua)))) # label(fact_ATP_Olambda__350) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 310 (all Uu all Uua all Uub all Uuc (gg_TPTP_ind(Uua) & gg_TPTP_ind(Uuc) & gg_TPTP_ind(Uub) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bw(Uu),Uua),Uub),Uuc)) <-> -pp(Uu) & Uuc = Uub | Uuc = Uua & pp(Uu)))) # label(fact_ATP_Olambda__642) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 311 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1483302902_prop2,X),Xa)) <-> pp(scratc575825622_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,Xa),scratc1882202790nd_n_1)),X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1483302901_prop1,X),Xa))))) # label(fact_def__d__428__prop2) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 312 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> ((exists X3 (X22 = aa_TPTP_ind_TPTP_ind(X12,X3) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X3),X0)) & gg_TPTP_ind(X3))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc760268562d_repl,X0),X12)))))) # label(fact_k__ReplEq) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 313 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_aan(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1465976678d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc459574173_d_Sep(Uu),Uua))) -> pp(aa_TPTP_ind_bool(Uua,Uub))))) # label(fact_ATP_Olambda__468) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 314 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_uq,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_up,Uu))))) # label(fact_ATP_Olambda__79) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 315 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_cq,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cr,Uu)))) # label(fact_ATP_Olambda__226) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 316 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1918947691nunion(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc760268562d_repl,X),scratc2088746604d_Inj0)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc760268562d_repl,Xa),scratc2088746605d_Inj1)) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1313072605d_pair,X),Xa)) # label(fact_def__pair) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 317 (all X all Xa (pp(aa_fun171081125l_bool(scratc91799413all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,X)),scratc1978070090nd_non(X,aa_TPT43085870d_bool(aTP_Lamm_bb(X),Xa)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1865462474_empty,X),Xa)))) # label(fact_def__empty) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 318 (all X0 (pp(aa_fun171081125l_bool(scratc2093768511n_some,X0)) -> pp(aa_fun171081125l_bool(scratc2093768511n_some,scratc1969414991nd_min(X0))))) # label(fact_satz27) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 319 (all B_1 all B_2 gg_bool(scratc920245767d_l_ec(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__62002__14561_ONUM781__thf__4__p_Obnd__l__ec) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 320 (all Uu (pp(aa_fun171081125l_bool(scratc1349943869l_some(scratc89572337d_frac),aa_TPT43085870d_bool(aTP_Lamm_kr,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ks,Uu)))) # label(fact_ATP_Olambda__232) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 321 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tk(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_tj(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__578) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 322 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ym,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_yl,Uu))))) # label(fact_ATP_Olambda__42) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 323 (all X all Xa (pp(scratc683290802_d_not(scratc920245767d_l_ec(X,Xa))) <-> pp(scratc575825622_d_and(X,Xa)))) # label(fact_def__d__and) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 324 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_re(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uua),Uub)))))) # label(fact_ATP_Olambda__499) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 325 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aap(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1533492748d_e_is(Uua),aa_TPTP_ind_TPTP_ind(scratc1198944151second(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc211927547d_pair(Uu,Uua),Uub),Uuc))),Uuc)))) # label(fact_ATP_Olambda__632) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 326 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ci,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_ch(Uu),Uua))))) # label(fact_ATP_Olambda__457) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 327 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wa,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_vz(Uu),Uua))))) # label(fact_ATP_Olambda__336) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 328 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dl,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_dk,Uu))))) # label(fact_ATP_Olambda__221) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 329 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ne,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_nd,Uu))))) # label(fact_ATP_Olambda__141) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 330 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_sn,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_sm,Uu))))) # label(fact_ATP_Olambda__94) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 331 (all X all Xa scratc1902929363nd_ect(X,Xa) = aa_fun1431113780TP_ind(scratc459574173_d_Sep(aa_TPTP_ind_TPTP_ind(scratc986305058_power,X)),scratc448820014d_anec(X,Xa))) # label(fact_def__ect) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 332 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qf(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_qe(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__584) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 333 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_uo(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__477) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 334 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dh,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_dg,Uu))))) # label(fact_ATP_Olambda__222) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 335 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_nc,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_nb,Uu))))) # label(fact_ATP_Olambda__142) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 336 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_zg,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_zf,Uu))))) # label(fact_ATP_Olambda__34) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 337 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fn,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_fm(Uu),Uua))))) # label(fact_ATP_Olambda__433) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 338 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1405965280bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1405965288bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc760268562d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bu(X),Xa))),scratc559650040ptyset) = aa_fun1431113780TP_ind(scratc459574173_d_Sep(X),Xa)) # label(fact_def__d__Sep) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 339 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271961_moreq,Uu),Uua)) -> pp(scratc683290802_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ml,Uu),Uua)))) # label(fact_ATP_Olambda__292) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 340 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ws,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_wr(Uu),Uua))))) # label(fact_ATP_Olambda__332) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 341 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_an,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uua))))) # label(fact_ATP_Olambda__316) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 342 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_il(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ik(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__603) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 343 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_cp(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cq,Uu),Uua)))) # label(fact_ATP_Olambda__455) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 344 (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_as(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_ar(Uua),Uub),Uuc),Uud),Uue),Uuf))))) # label(fact_ATP_Olambda__710) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 345 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iu,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_it(Uu),Uua))))) # label(fact_ATP_Olambda__412) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 346 (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]. 2.10/2.49 347 (all X all Xa scratc571701423ectset(X,Xa) = scratc1986725195nd_out(aa_TPTP_ind_TPTP_ind(scratc986305058_power,X),scratc448820014d_anec(X,Xa))) # label(fact_def__ectset) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 348 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cz,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_cy,Uu))))) # label(fact_ATP_Olambda__224) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 349 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rh(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uua),Uub))),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),Uub)))))) # label(fact_ATP_Olambda__503) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 350 (all X all Xa all Xb aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc523788228_Sigma,X),scratc95826375sel_wb(X,Xa,Xb)) = aa_TPTP_ind_TPTP_ind(scratc439728220wissel(X,Xa),Xb)) # label(fact_def__wissel) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 351 (all X all Xa all Xb (scratc448754367d_and3(scratc920245767d_l_ec(X,Xa),scratc920245767d_l_ec(Xa,Xb),scratc920245767d_l_ec(Xb,X)) <-> pp(scratc1902929298nd_ec3(X,Xa,Xb)))) # label(fact_def__ec3) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 352 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ki(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__692) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 353 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_im,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_in,Uu)))) # label(fact_ATP_Olambda__181) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 354 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_io(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uua),Uuc))))))) # label(fact_ATP_Olambda__689) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 355 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc371056682d_left(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(scratc1144702773eft_f1(X,Xa,Xb),Xc)) = aa_TPTP_ind_TPTP_ind(scratc1144702774eft_f2(X,Xa,Xb),Xc)) # label(fact_def__left__f2) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 356 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ms(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_mr(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__595) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 357 (all P all Q (pp(Q) | -pp(P) | -pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 358 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_fg(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fh,Uu),Uua)))) # label(fact_ATP_Olambda__435) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 359 (all X all Xa (pp(scratc683290802_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1977676501nd_nis,X),Xa)))) # label(fact_def__nis) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 360 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1361989810d_Subq,X12),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc986305058_power,X0))))) # label(fact_k__PowerI) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 361 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_uc(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__490) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 362 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_aag,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_aah,Uu)))) # label(fact_ATP_Olambda__27) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 363 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wr(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,Uu),Uub)))))) # label(fact_ATP_Olambda__522) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 364 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271961_moreq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uu),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uua),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271961_moreq,Uub),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_lt(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__664) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 365 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1925936612first1(X),Xa) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,Xa),scratc1048479566d_n_1t)) # label(fact_def__first1) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 366 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gi(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gj(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__612) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 367 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fo,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_fn,Uu))))) # label(fact_ATP_Olambda__204) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 368 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_hh(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hi,Uu),Uua)))) # label(fact_ATP_Olambda__423) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 369 (all Uu all Uua (gg_TPTP_ind(Uu) -> aa_TPTP_ind_TPTP_ind(aTP_Lamm_af(Uu),Uua) = Uu)) # label(fact_ATP_Olambda__711) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 370 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_zr,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_zq,Uu))))) # label(fact_ATP_Olambda__30) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 371 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aq,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,Uua),Uu)))) # label(fact_ATP_Olambda__323) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 372 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uu),Uua)) -> pp(scratc683290802_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379326120lesseq,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_md,Uu),Uua)))) # label(fact_ATP_Olambda__293) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 373 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_fa(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fb,Uu),Uua)))) # label(fact_ATP_Olambda__437) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 374 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ex(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__543) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 375 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ho(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uua),Uuc))))))) # label(fact_ATP_Olambda__668) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 376 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_es,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_et,Uu)))) # label(fact_ATP_Olambda__211) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 377 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qk,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_qj(Uu),Uua))))) # label(fact_ATP_Olambda__369) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 378 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ps,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_pr,Uu))))) # label(fact_ATP_Olambda__119) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 379 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc986305058_power,X0))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1361989810d_Subq,X12),X0)))) # label(fact_k__PowerE) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 380 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_dy(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dz,Uu),Uua)))) # label(fact_ATP_Olambda__445) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 381 (all X0 pp(aa_TPTP_ind_bool(scratc1079507897closed,aa_TPTP_ind_TPTP_ind(scratc1908071008univof,X0)))) # label(fact_k__UnivOf__ZF__closed) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 382 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_pu,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_pv,Uu)))) # label(fact_ATP_Olambda__118) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 383 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1051956311d_n_fr,Uu),Uub)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1051956311d_n_fr,Uua),Uub))),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1051956311d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uua)),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kf(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__474) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 384 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pq(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513572130moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513572130moreis,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uub),Uua)))))) # label(fact_ATP_Olambda__514) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 385 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mo(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_mn(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__596) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 386 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cp(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_co(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__623) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 387 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc856707564367_vo(X),Xa) = scratc1936696956nd_ind(scratc1977151710nd_nat,aa_TPT43085870d_bool(scratc1841546987ffprop(aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1978463683nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc1894799050nd_den,Xa))),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1978463683nd_num,Xa)),aa_TPTP_ind_TPTP_ind(scratc1894799050nd_den,X))))) # label(fact_def__d__367__vo) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 388 (all X all Xa (pp(aa_fun171081125l_bool(scratc91799413all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,X)),aa_fun1584354236d_bool(aTP_Lamm_bk(X),Xa))) <-> pp(scratc1593517495_amone(X,Xa)))) # label(fact_def__amone) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 389 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_fe,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ff,Uu)))) # label(fact_ATP_Olambda__207) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 390 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gy(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gz(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__608) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 391 (all X all Xa all Xb (gg_TPTP_ind(Xb) -> Xb = aa_TPTP_ind_TPTP_ind(scratc1533492743d_e_in(X,Xa),Xb))) # label(fact_def__e__in) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 392 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gq(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gr(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__610) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 393 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jh,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_jg(Uu),Uua))))) # label(fact_ATP_Olambda__408) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 394 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_gr(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gs,Uu),Uua)))) # label(fact_ATP_Olambda__427) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 395 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cy,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_cx(Uu),Uua))))) # label(fact_ATP_Olambda__453) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 396 (all Uu all Uua ((pp(scratc683290802_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513572130moreis,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xl,Uu),Uua)))) # label(fact_ATP_Olambda__304) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 397 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ur(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__521) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 398 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yx(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,Uua),Uub))))) # label(fact_ATP_Olambda__488) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 399 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_yy,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_yz,Uu)))) # label(fact_ATP_Olambda__37) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 400 (all X (pp(aa_TPTP_ind_bool(scratc1129935629_cond2,X)) <-> pp(aa_fun171081125l_bool(scratc799446_n_all,aa_TPT43085870d_bool(aTP_Lamm_ao,X))))) # label(fact_def__cond2) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 401 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_md,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_me,Uu)))) # label(fact_ATP_Olambda__152) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 402 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc1908071008univof,X0)))) # label(fact_k__UnivOf__In) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 403 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_va(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vb,Uu),Uua)))) # label(fact_ATP_Olambda__343) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 404 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uu),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uua),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uub),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_mn(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__674) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 405 (all X all Xa all Xb all Xc all Xd all Xe (pp(aa_fun171081125l_bool(scratc1349943869l_some(X),aa_TPT43085870d_bool(scratc1229775214_prop1(X,Xa,Xb,Xc,Xd),Xe))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1115212492_prop2(X,Xa,Xb,Xc),Xd),Xe)))) # label(fact_def__prop2) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 406 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ki(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kj(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__599) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 407 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_ek,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_el,Uu)))) # label(fact_ATP_Olambda__213) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 408 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vz(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__511) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 409 (all Uu all Uua aa_fun277296641TP_ind(aa_TPT494704832TP_ind(aTP_Lamm_bs,Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1918947691nunion(aa_TPTP_ind_TPTP_ind(scratc1263638928d_Sing,scratc559650040ptyset)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc760268562d_repl,Uu),Uua))) # label(fact_ATP_Olambda__311) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 410 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379326120lesseq,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gu(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__671) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 411 (all Uu all Uua (gg_TPTP_ind(Uua) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bn,Uu),Uua)) <-> (exists X3 (aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1313072605d_pair,Uu),X3) = Uua & gg_TPTP_ind(X3)))))) # label(fact_ATP_Olambda__463) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 412 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_ai(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,Uu),Uua)),Uua)) # label(fact_ATP_Olambda__298) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 413 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(scratc1882202790nd_n_1),Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_zm,Uu)))) # label(fact_ATP_Olambda__11) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 414 (all X all Xa (pp(scratc575825622_d_and(aa_TPTP_ind_bool(scratc1052349889d_n_lb(X),Xa),aa_TPTP_ind_bool(X,Xa))) <-> pp(aa_TPTP_ind_bool(scratc1969414991nd_min(X),Xa)))) # label(fact_def__min) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 415 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_ap,Uu)) <-> Uu != scratc559650040ptyset))) # label(fact_ATP_Olambda__236) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 416 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_qa(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__679) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 417 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uua)),Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wp,Uu),Uua)))) # label(fact_ATP_Olambda__296) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 418 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_wj,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_wk,Uu)))) # label(fact_ATP_Olambda__65) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 419 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_vt(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vu,Uu),Uua)))) # label(fact_ATP_Olambda__338) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 420 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ov,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_ou(Uu),Uua))))) # label(fact_ATP_Olambda__381) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 421 (all Uu (pp(aa_fun171081125l_bool(scratc1986265987nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc392288474d_d_Pi,scratc1977151710nd_nat),aTP_Lamm_ah)),aa_TPT43085870d_bool(aTP_Lamm_zw,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_zx,Uu)))) # label(fact_ATP_Olambda__7) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 422 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_la,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_lb,Uu)))) # label(fact_ATP_Olambda__163) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 423 (all B_1 all B_2 gg_bool(scratc1593517495_amone(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__62002__14561_ONUM781__thf__4__p_Obnd__amone) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 424 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_um,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_ul(Uu),Uua))))) # label(fact_ATP_Olambda__348) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 425 (all X all Xa (pp(aa_fun171081125l_bool(scratc799446_n_all,aa_TPT43085870d_bool(aTP_Lamm_ak(X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1483302901_prop1,X),Xa)))) # label(fact_def__d__428__prop1) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 426 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kg,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_kf(Uu),Uua))))) # label(fact_ATP_Olambda__390) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 427 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153104d_n_in,Uua),Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aae,Uu),Uua)))) # label(fact_ATP_Olambda__321) # label(axiom) # label(non_clause). [assumption]. 2.10/2.49 428 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bi(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(Uua,Uub)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,Uub),Uu)))) # label(fact_ATP_Olambda__555) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 429 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_nh,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_ng,Uu))))) # label(fact_ATP_Olambda__136) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 430 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_sw,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_sv,Uu))))) # label(fact_ATP_Olambda__92) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 431 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fs,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uua),Uu))))) # label(fact_ATP_Olambda__274) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 432 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271961_moreq,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kw(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__531) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 433 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_eb(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ec,Uu),Uua)))) # label(fact_ATP_Olambda__444) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 434 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_tq,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_tp,Uu))))) # label(fact_ATP_Olambda__87) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 435 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_oz,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_oy(Uu),Uua))))) # label(fact_ATP_Olambda__380) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 436 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_mg,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_mf,Uu))))) # label(fact_ATP_Olambda__151) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 437 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc1978070090nd_non(X,Xa),Xb)) <-> pp(scratc683290802_d_not(aa_TPTP_ind_bool(Xa,Xb))))) # label(fact_def__non) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 438 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_di(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uua),Uuc))))))) # label(fact_ATP_Olambda__667) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 439 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_aba(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,Uub),aa_fun1431113780TP_ind(scratc459574173_d_Sep(Uu),Uua))))) # label(fact_ATP_Olambda__569) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 440 (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]. 2.10/2.50 441 (all X all Xa all Xb scratc371056682d_left(X,Xb,Xa) = scratc1144702773eft_f1(X,Xa,Xb)) # label(fact_def__left__f1) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 442 (all Uu all Uua aa_TPTP_ind_TPTP_ind(scratc1493566924_union,aa_TPTP_ind_TPTP_ind(Uu,Uua)) = aa_TPTP_ind_TPTP_ind(aTP_Lamm_bl(Uu),Uua)) # label(fact_ATP_Olambda__462) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 443 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc252181848d_invf(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc523788228_Sigma,Xa),scratc1622814829d_soft(X,Xa,Xb))) # label(fact_def__invf) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 444 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379326120lesseq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cs(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__657) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 445 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc523788228_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1313072605d_pair,aa_TPTP_ind_TPTP_ind(scratc1114818896_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1114818897_proj1,X22)) = X22 & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,aa_TPTP_ind_TPTP_ind(scratc1114818896_proj0,X22)),X0)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,aa_TPTP_ind_TPTP_ind(scratc1114818897_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1114818896_proj0,X22))))))) # label(fact_k__Sigma__eta__proj0__proj1) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 446 (all X0 all X12 scratc1588370020_is_of(aa_fun1431113780TP_ind(scratc459574173_d_Sep(X0),X12),aa_TPT43085870d_bool(aTP_Lamm_aak,X0))) # label(fact_setof__p) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 447 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_sq,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,scratc1882202790nd_n_1),aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uu))))) # label(fact_ATP_Olambda__234) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 448 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(Uua,aa_TPTP_ind_TPTP_ind(scratc1533492743d_e_in(Uu,Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_abb(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__627) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 449 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ra,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_qz,Uu))))) # label(fact_ATP_Olambda__109) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 450 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_qx,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_qw,Uu))))) # label(fact_ATP_Olambda__110) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 451 (all X scratc1936696956nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc392288474d_d_Pi,scratc1977151710nd_nat),aTP_Lamm_ah),aa_TPT43085870d_bool(scratc682452588_prop2,X)) = aa_TPTP_ind_TPTP_ind(scratc1404736349d_plus,X)) # label(fact_def__plus) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 452 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_lo,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_ln,Uu))))) # label(fact_ATP_Olambda__158) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 453 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_td,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_tc(Uu),Uua))))) # label(fact_ATP_Olambda__358) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 454 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_bp,Uu)) <-> (exists X2 (aa_TPTP_ind_TPTP_ind(scratc2088746605d_Inj1,X2) = Uu & gg_TPTP_ind(X2)))))) # label(fact_ATP_Olambda__237) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 455 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_rr,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),scratc1882202790nd_n_1))))) # label(fact_ATP_Olambda__17) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 456 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_io(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ip(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__602) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 457 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qw,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_qv(Uu),Uua))))) # label(fact_ATP_Olambda__365) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 458 (all X0 all X12 pp(aa_fun171081125l_bool(scratc91799413all_of(aa_fun1584354236d_bool(aTP_Lamm_aba(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_abc(X0),X12)))) # label(fact_e__in__p) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 459 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1841546987ffprop(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,X),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Xa),Xb))))) # label(fact_def__diffprop) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 460 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zt,Uu),Uua)))) # label(fact_ATP_Olambda__262) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 461 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mv,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uua),Uu))))) # label(fact_ATP_Olambda__283) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 462 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_yn,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_yo,Uu)))) # label(fact_ATP_Olambda__41) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 463 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ue,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_ud,Uu))))) # label(fact_ATP_Olambda__83) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 464 (all X ((all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,aa_TPTP_ind_TPTP_ind(scratc986305058_power,X1)),X))))) <-> pp(aa_TPTP_ind_bool(scratc1189416944closed,X)))) # label(fact_def__d__Power__closed) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 465 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ya,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_xz,Uu))))) # label(fact_ATP_Olambda__48) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 466 (all X all Xa scratc1903782149nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bi(X),Xa)) = scratc1936696956nd_ind(X,Xa)) # label(fact_def__ind) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 467 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),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__340) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 468 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tg(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_tf(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__579) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 469 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_wm,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__12) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 470 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ng,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_nf(Uu),Uua))))) # label(fact_ATP_Olambda__389) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 471 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_uy,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_ux(Uu),Uua))))) # label(fact_ATP_Olambda__344) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 472 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_ca,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cb,Uu)))) # label(fact_ATP_Olambda__230) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 473 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ul(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__489) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 474 (all X0 all X12 pp(aa_fun171081125l_bool(scratc91799413all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,X0)),aa_fun1584354236d_bool(aTP_Lamm_aaz(X0),X12)))) # label(fact_otax2) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 475 (all X (gg_TPTP_ind(X) -> (X = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1313072605d_pair,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,X),scratc559650040ptyset)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,X),aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,scratc559650040ptyset))) <-> pp(aa_TPTP_ind_bool(scratc1178658963pair_p,X))))) # label(fact_def__pair__p) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 476 (all X0 scratc559650040ptyset != aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,X0)) # label(fact_neq__ordsucc__0) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 477 (all P all Q all R aa_boo1142376798l_bool(P,aa_TPTP_ind_bool(Q,R)) = aa_TPT2142672771l_bool(cOMBB_658106424TP_ind(P,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]. 2.10/2.50 478 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bh(Uu),Uua),Uub),Uuc)) <-> pp(aa_fun171081125l_bool(scratc1870473726nd_all(Uu),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_bg(Uu),Uua),Uub),Uuc))))) # label(fact_ATP_Olambda__699) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 479 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_nw(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nx,Uu),Uua)))) # label(fact_ATP_Olambda__387) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 480 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iy,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_ix(Uu),Uua))))) # label(fact_ATP_Olambda__411) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 481 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc180990886_inj_h(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc523788228_Sigma,X),aa_TPT1424761345TP_ind(aTP_Lamm_bd(Xc),Xd))) # label(fact_def__inj__h) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 482 (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]. 2.10/2.50 483 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_hy(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hz,Uu),Uua)))) # label(fact_ATP_Olambda__418) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 484 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ck(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271961_moreq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271961_moreq,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271961_moreq,aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uua),Uuc))))))) # label(fact_ATP_Olambda__660) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 485 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,Uua),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ys(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__567) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 486 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1975577328nd_nIn,X),Xa)) <-> -pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X),Xa)))) # label(fact_def__nIn) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 487 (all Uu ((pp(aa_TPTP_ind_bool(scratc1129935628_cond1,Uu)) -> (pp(aa_TPTP_ind_bool(scratc1129935629_cond2,Uu)) -> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_aae,Uu))))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_aaf,Uu)))) # label(fact_ATP_Olambda__9) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 488 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ed,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_ec,Uu))))) # label(fact_ATP_Olambda__215) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 489 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271961_moreq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271961_moreq,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271961_moreq,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gq(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__661) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 490 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_su(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sv,Uu),Uua)))) # label(fact_ATP_Olambda__360) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 491 (all Uu all Uua ((pp(scratc683290802_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xt,Uu),Uua)))) # label(fact_ATP_Olambda__303) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 492 (all Uu all Uua all Uub ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X3),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,Uub),X3)),aa_TPTP_ind_TPTP_ind(Uua,X3)))))) <-> pp(aa_TPTP_ind_bool(aa_fun1913827119d_bool(aTP_Lamm_bm(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__628) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 493 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(Uu),Uua),Uub),Uuc)) <-> pp(aa_fun171081125l_bool(scratc1349943869l_some(Uua),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ax(Uu),Uub),Uuc))))) # label(fact_ATP_Olambda__700) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 494 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (-pp(X0) -> X22 = aa_TPTP_ind_TPTP_ind(scratc1405965280bnd_if(X0,X12),X22)))) # label(fact_if__i__0) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 495 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X22),X0)) -> (all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X32),aa_TPTP_ind_TPTP_ind(X12,X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1313072605d_pair,X22),X32)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc523788228_Sigma,X0),X12))))))) # label(fact_pair__Sigma) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 496 (all Uu (gg_TPTP_ind(Uu) -> aa_TPTP_ind_TPTP_ind(aTP_Lamm_aj,Uu) = Uu)) # label(fact_ATP_Olambda__712) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 497 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),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__406) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 498 (all X ((all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X1),X)) -> (all X2 ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X3),X1)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,aa_TPTP_ind_TPTP_ind(X2,X3)),X))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc760268562d_repl,X1),X2)),X))))))) <-> pp(aa_TPTP_ind_bool(scratc48604636closed,X)))) # label(fact_def__d__Repl__closed) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 499 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hh(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hg(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__606) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 500 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_aao(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1465976678d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc459574173_d_Sep(Uu),Uua)))))) # label(fact_ATP_Olambda__559) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 501 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uu),aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fp(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__501) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 502 (all X all Xa (scratc1315180557d_r_ec(X,Xa) <-> (pp(X) -> pp(scratc683290802_d_not(Xa))))) # label(fact_def__r__ec) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 503 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X22),X0)) -> aa_TPTP_ind_TPTP_ind(X12,X22) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc523788228_Sigma,X0),X12)),X22))) # label(fact_beta) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 504 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uu)),scratc1882202790nd_n_1)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_sr,Uu)))) # label(fact_ATP_Olambda__15) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 505 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uu),Uua)) -> pp(aa_fun171081125l_bool(scratc1349943869l_some(scratc89572337d_frac),aa_TPT43085870d_bool(aTP_Lamm_gf(Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gg,Uu),Uua)))) # label(fact_ATP_Olambda__286) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 506 (all X0 (pp(aa_TPTP_ind_bool(scratc1475014226_nat_p,X0)) -> pp(aa_TPTP_ind_bool(scratc1475014226_nat_p,aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,X0))))) # label(fact_nat__ordsucc) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 507 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_abf(Uu),Uua),Uub),Uuc)) <-> (pp(aa_fun171081125l_bool(scratc91799413all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_abe(Uua),Uub),Uuc))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1533492748d_e_is(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc392288474d_d_Pi,Uu),aTP_Lamm_af(Uua))),Uub),Uuc))))) # label(fact_ATP_Olambda__641) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 508 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_wl,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uu))))) # label(fact_ATP_Olambda__19) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 509 (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(scratc379588518lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__523) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 510 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc698437091d_outn(X),aa_TPTP_ind_TPTP_ind(scratc1936696966nd_inn(Xa),Xb)) = aa_TPTP_ind_TPTP_ind(scratc1090352130eft1to(X,Xa),Xb)) # label(fact_def__left1to) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 511 (all X all Xa all Xb aa_fun1431113780TP_ind(scratc459574173_d_Sep(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(X),Xa),Xb)) = aa_TPTP_ind_TPTP_ind(scratc677818769unmore(X,Xa),Xb)) # label(fact_def__unmore) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 512 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cc(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cd(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__626) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 513 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lz,Uu),Uua)) <-> (pp(scratc683290802_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271961_moreq,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uu),Uua))))) # label(fact_ATP_Olambda__307) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 514 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_abc(Uu),Uua),Uub)) <-> scratc1588370020_is_of(aa_TPTP_ind_TPTP_ind(scratc1533492743d_e_in(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aq,Uu)))) # label(fact_ATP_Olambda__472) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 515 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ud,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_uc(Uu),Uua))))) # label(fact_ATP_Olambda__351) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 516 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513572130moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513572130moreis,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ux(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__516) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 517 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_ha,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_hb,Uu)))) # label(fact_ATP_Olambda__192) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 518 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_gg,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_gh,Uu)))) # label(fact_ATP_Olambda__197) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 519 (all Uu (gg_TPTP_ind(Uu) -> ((exists X2 (Uu = aa_TPTP_ind_TPTP_ind(scratc2088746604d_Inj0,X2) & gg_TPTP_ind(X2))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))))) # label(fact_ATP_Olambda__238) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 520 (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]. 2.10/2.50 521 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1349943869l_some(scratc89572337d_frac),aa_TPT43085870d_bool(aTP_Lamm_bz(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ca,Uu),Uua)))) # label(fact_ATP_Olambda__459) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 522 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qs(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uub),Uua)))))) # label(fact_ATP_Olambda__509) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 523 pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1936631369nd_imp,fFalse),fFalse)) <-> scratc1585239332bvious # label(fact_def__obvious) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 524 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hj,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_hi,Uu))))) # label(fact_ATP_Olambda__190) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 525 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uuc),Uua))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ee(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__688) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 526 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_ic,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_id,Uu)))) # label(fact_ATP_Olambda__184) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 527 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_cd(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ce,Uu),Uua)))) # label(fact_ATP_Olambda__458) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 528 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uua)),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_si,Uu),Uua)))) # label(fact_ATP_Olambda__268) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 529 (all X all Xa all Xb aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc523788228_Sigma,aa_TPTP_ind_TPTP_ind(scratc179666987_d_1to,scratc1882202791nd_n_2)),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ae(X),Xa),Xb)) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc680694164_pair1(X),Xa),Xb)) # label(fact_def__pair1) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 530 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ot(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ou(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__588) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 531 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dp(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__492) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 532 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lj,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_li(Uu),Uua))))) # label(fact_ATP_Olambda__397) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 533 (all X aa_TPTP_ind_TPTP_ind(scratc1918947691nunion(X),aa_TPTP_ind_TPTP_ind(scratc1263638928d_Sing,X)) = aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,X)) # label(fact_def__ordsucc) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 534 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1780638511_rt_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1780638511_rt_is,Uua),Uu))))) # label(fact_ATP_Olambda__280) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 535 (all Uu all Uua ((pp(scratc683290802_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271961_moreq,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mf,Uu),Uua)))) # label(fact_ATP_Olambda__309) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 536 (all X all Xa all Xb (pp(aa_fun171081125l_bool(scratc1870473726nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ba(X),Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc250935473d_incl(X),Xa),Xb)))) # label(fact_def__incl) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 537 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1051956311d_n_fr,aa_TPTP_ind_TPTP_ind(scratc856707564367_vo(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1894799050nd_den,X)),aa_TPTP_ind_TPTP_ind(scratc1894799050nd_den,Xa))) = aa_TPTP_ind_TPTP_ind(scratc13795140_367_w(X),Xa)) # label(fact_def__d__367__w) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 538 (all X fequal_TPTP_ind = scratc1533492748d_e_is(X)) # label(fact_def__e__is) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 539 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jf,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_je,Uu))))) # label(fact_ATP_Olambda__176) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 540 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2095335265_fixfu(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_aw(X),Xa),Xb),Xc))))) # label(fact_def__fixfu) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 541 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_yw,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_yv,Uu))))) # label(fact_ATP_Olambda__38) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 542 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_pj,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_pi,Uu))))) # label(fact_ATP_Olambda__122) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 543 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_gb,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_gc,Uu)))) # label(fact_ATP_Olambda__199) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 544 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_vw(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vx,Uu),Uua)))) # label(fact_ATP_Olambda__337) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 545 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_lf(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lg,Uu),Uua)))) # label(fact_ATP_Olambda__398) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 546 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yf,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uua),Uu))))) # label(fact_ATP_Olambda__276) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 547 (all X all Xa scratc1903782149nd_eps(aa_TPT43085870d_bool(scratc780983997_rec_G(X),Xa)) = aa_TPTP_ind_TPTP_ind(scratc447680842In_rec(X),Xa)) # label(fact_def__d__In__rec) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 548 (all X0 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X0),scratc284474110_omega)) -> pp(aa_TPTP_ind_bool(scratc1475014226_nat_p,X0)))) # label(fact_omega__nat__p) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 549 (all X all Xa all Xb all Xc all Xd all Xe all Xf (pp(scratc575825622_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1465976678d_esti(X),Xf),aa_TPTP_ind_TPTP_ind(scratc410049685_ecect(X,Xa),Xd)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1533492748d_e_is(Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,Xc),Xf)),Xe))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1229775214_prop1(X,Xa,Xb,Xc,Xd),Xe),Xf)))) # label(fact_def__d__10__prop1) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 550 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bj(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(Uua,Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1533492748d_e_is(Uu),Uub),Uuc)))))) # label(fact_ATP_Olambda__698) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 551 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_ob,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_oc,Uu)))) # label(fact_ATP_Olambda__131) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 552 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc986305058_power,X0)))) # label(fact_k__Self__In__Power) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 553 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_ml,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_mm,Uu)))) # label(fact_ATP_Olambda__148) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 554 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jq,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_jp(Uu),Uua))))) # label(fact_ATP_Olambda__405) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 555 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rp,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),Uua)),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uua)))))) # label(fact_ATP_Olambda__251) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 556 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_op(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513572130moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uua),Uuc))))))) # label(fact_ATP_Olambda__647) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 557 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ea,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_dz,Uu))))) # label(fact_ATP_Olambda__216) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 558 (all X scratc920901772d_l_or(X) = aa_boo1142376798l_bool(scratc1936631369nd_imp,scratc683290802_d_not(X))) # label(fact_def__l__or) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 559 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hw,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_hv(Uu),Uua))))) # label(fact_ATP_Olambda__419) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 560 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_nr,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_nq,Uu))))) # label(fact_ATP_Olambda__140) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 561 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_hs(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ht,Uu),Uua)))) # label(fact_ATP_Olambda__420) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 562 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_by,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,Uu),scratc89572337d_frac)))) # label(fact_ATP_Olambda__24) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 563 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hk(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uua),Uuc))))))) # label(fact_ATP_Olambda__673) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 564 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gy(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379326120lesseq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uua),Uuc))))))) # label(fact_ATP_Olambda__658) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 565 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1978463683nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc1894799050nd_den,Xa))),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1978463683nd_num,Xa)),aa_TPTP_ind_TPTP_ind(scratc1894799050nd_den,X)))))) # label(fact_def__lessf) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 566 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ba(Uu),Uua),Uub),Uuc)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1936631369nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1465976678d_esti(Uu),Uuc),Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1465976678d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__638) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 567 (all B_1 all B_2 all B_3 gg_bool(scratc1902929298nd_ec3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__62002__14561_ONUM781__thf__4__p_Obnd__ec3) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 568 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_lj,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_lk,Uu)))) # label(fact_ATP_Olambda__160) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 569 (all X aa_TPTP_ind_TPTP_ind(scratc698437091d_outn(X),X) = aa_TPTP_ind_TPTP_ind(scratc1231767513d_xout,X)) # label(fact_def__xout) # label(axiom) # label(non_clause). [assumption]. 2.10/2.50 570 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_sc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_sd,Uu)))) # label(fact_ATP_Olambda__99) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 571 (all B_1 gg_bool(scratc683290802_d_not(B_1))) # label(gsy_c_Scratch__tptp__translate__62002__14561_ONUM781__thf__4__p_Obnd__d__not) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 572 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_hw,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_hx,Uu)))) # label(fact_ATP_Olambda__186) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 573 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,X),Xa)) <-> pp(aa_bool_bool(scratc920901772d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,X),Xa))))) # label(fact_def__lessis) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 574 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rc,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_rb(Uu),Uua))))) # label(fact_ATP_Olambda__363) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 575 (all Uu all Uua all Uub (scratc1588370020_is_of(aa_TPTP_ind_TPTP_ind(scratc1198944151second(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aq,Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aav(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__470) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 576 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nf(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1051956311d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uua),Uub))),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1051956311d_n_fr,Uu),Uua))))) # label(fact_ATP_Olambda__475) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 577 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_su(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_st(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__582) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 578 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_yf,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_yg,Uu)))) # label(fact_ATP_Olambda__45) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 579 (all X0 pp(aa_fun171081125l_bool(scratc91799413all_of(aa_TPT43085870d_bool(aTP_Lamm_aak,X0)),aa_TPT43085870d_bool(aTP_Lamm_aam,X0)))) # label(fact_isseti) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 580 (all Uu all Uua (pp(scratc1902929298nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mz,Uu),Uua)))) # label(fact_ATP_Olambda__244) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 581 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tp,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_to(Uu),Uua))))) # label(fact_ATP_Olambda__355) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 582 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_ev,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ew,Uu)))) # label(fact_ATP_Olambda__210) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 583 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qq,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_qp(Uu),Uua))))) # label(fact_ATP_Olambda__367) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 584 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vj,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_vi(Uu),Uua))))) # label(fact_ATP_Olambda__341) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 585 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc734115635hangef(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc523788228_Sigma,X),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_bc(X),Xb),Xc),Xd))) # label(fact_def__changef) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 586 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ll,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379326120lesseq,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271961_moreq,Uua),Uu))))) # label(fact_ATP_Olambda__279) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 587 (all X aa_TPTP_ind_TPTP_ind(scratc1114818896_proj0,X) = aa_fun277296641TP_ind(scratc719917262eplSep(X,aTP_Lamm_bq),scratc476687568_d_Unj)) # label(fact_def__proj0) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 588 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ui(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__496) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 589 (all Uu all Uua all Uub all Uuc all Uud aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,aa_TPTP_ind_TPTP_ind(scratc439728220wissel(Uu,Uub),Uuc)),Uud)) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_bc(Uu),Uua),Uub),Uuc),Uud)) # label(fact_ATP_Olambda__707) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 590 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_ej(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ek,Uu),Uua)))) # label(fact_ATP_Olambda__442) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 591 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_if,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ig,Uu)))) # label(fact_ATP_Olambda__183) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 592 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ss,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513572130moreis,Uu),scratc1882202790nd_n_1)))) # label(fact_ATP_Olambda__23) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 593 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mb,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uu),Uua)) -> pp(scratc683290802_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271961_moreq,Uu),Uua)))))) # label(fact_ATP_Olambda__294) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 594 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_vf,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_vg,Uu)))) # label(fact_ATP_Olambda__74) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 595 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aaq(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aap(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__564) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 596 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mx,Uu),Uua)))) # label(fact_ATP_Olambda__282) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 597 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_qb(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qc,Uu),Uua)))) # label(fact_ATP_Olambda__371) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 598 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1051956311d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1978463683nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc1894799050nd_den,Xa))),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1894799050nd_den,X)),aa_TPTP_ind_TPTP_ind(scratc1978463683nd_num,Xa))) = aa_TPTP_ind_TPTP_ind(scratc1525366659_477_v(X),Xa)) # label(fact_def__d__477__v) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 599 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uuc),Uua))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_qe(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__676) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 600 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1902929359nd_ecp(X,Xa),Xb),Xc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1533492748d_e_is(aa_TPTP_ind_TPTP_ind(scratc986305058_power,X)),Xb),aa_TPTP_ind_TPTP_ind(scratc410640076_ecelt(X,Xa),Xc))))) # label(fact_def__ecp) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 601 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_rz,Uu)) <-> pp(aa_fun171081125l_bool(scratc1986265987nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc392288474d_d_Pi,scratc1977151710nd_nat),aTP_Lamm_ah)),aa_TPT43085870d_bool(aTP_Lamm_ry,Uu))))) # label(fact_ATP_Olambda__8) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 602 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gu(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gv(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__609) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 603 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qp(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__539) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 604 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_xf,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_xe,Uu))))) # label(fact_ATP_Olambda__58) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 605 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ke,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_kd,Uu))))) # label(fact_ATP_Olambda__138) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 606 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_pp,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_po,Uu))))) # label(fact_ATP_Olambda__120) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 607 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_px(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_py,Uu),Uua)))) # label(fact_ATP_Olambda__372) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 608 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_rd,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_rc,Uu))))) # label(fact_ATP_Olambda__108) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 609 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cg(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379326120lesseq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379326120lesseq,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379326120lesseq,aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uua),Uuc))))))) # label(fact_ATP_Olambda__655) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 610 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ju,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uu),Uua)),Uu)))) # label(fact_ATP_Olambda__297) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 611 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dr,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_dq,Uu))))) # label(fact_ATP_Olambda__219) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 612 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_we,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_wd,Uu))))) # label(fact_ATP_Olambda__67) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 613 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_iu,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_iv,Uu)))) # label(fact_ATP_Olambda__179) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 614 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc523788228_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1313072605d_pair,aa_TPTP_ind_TPTP_ind(scratc1114818896_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1114818897_proj1,X22)) = X22))) # label(fact_proj__Sigma__eta) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 615 (all X scratc1052612295d_n_pl(X) = aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1404736349d_plus,X))) # label(fact_def__n__pl) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 616 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc1986265987nd_one(X0),X12)) -> scratc1588370020_is_of(scratc1936696956nd_ind(X0,X12),aa_TPT43085870d_bool(aTP_Lamm_aq,X0)))) # label(fact_ind__p) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 617 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_bv(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc1405965280bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,scratc559650040ptyset),Uub),Uu),Uua)) # label(fact_ATP_Olambda__465) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 618 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_nx,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ny,Uu)))) # label(fact_ATP_Olambda__132) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 619 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_is(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uuc),Uua))))))) # label(fact_ATP_Olambda__686) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 620 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_hq,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_hr,Uu)))) # label(fact_ATP_Olambda__188) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 621 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ns,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uua),Uu))))) # label(fact_ATP_Olambda__284) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 622 (all B_1 all B_2 gg_TPTP_ind(scratc1936696956nd_ind(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__62002__14561_ONUM781__thf__4__p_Obnd__ind) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 623 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fd(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uua),Uub)))))) # label(fact_ATP_Olambda__532) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 624 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,Uua),Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ag,Uu),Uua)))) # label(fact_ATP_Olambda__318) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 625 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dx,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_dw,Uu))))) # label(fact_ATP_Olambda__217) # label(axiom) # label(non_clause). [assumption]. 2.10/2.51 626 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yb,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513572130moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,Uua),Uu))))) # label(fact_ATP_Olambda__277) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 627 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ni(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1051956311d_n_fr,Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1051956311d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uua),Uub)))))) # label(fact_ATP_Olambda__507) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 628 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fw,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_fv(Uu),Uua))))) # label(fact_ATP_Olambda__431) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 629 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_th,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_tg(Uu),Uua))))) # label(fact_ATP_Olambda__357) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 630 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_dj(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dk,Uu),Uua)))) # label(fact_ATP_Olambda__450) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 631 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jk,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_jj(Uu),Uua))))) # label(fact_ATP_Olambda__407) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 632 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_hz,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ia,Uu)))) # label(fact_ATP_Olambda__185) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 633 (all X all Xa (pp(aa_fun171081125l_bool(scratc2093768511n_some,aa_TPT43085870d_bool(scratc1841546987ffprop(Xa),X))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,X),Xa)))) # label(fact_def__iii) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 634 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zf,Uu),Uua)))) # label(fact_ATP_Olambda__273) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 635 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,Uub),aa_TPTP_ind_TPTP_ind(scratc1090352130eft1to(Uu,Uua),Uuc)) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ad(Uu),Uua),Uub),Uuc)) # label(fact_ATP_Olambda__702) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 636 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nw(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_nv(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__594) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 637 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_od(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uua),Uuc))))))) # label(fact_ATP_Olambda__693) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 638 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_oa(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ob,Uu),Uua)))) # label(fact_ATP_Olambda__386) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 639 (all X0 (scratc2051767643nd_wel(X0) -> pp(X0))) # label(fact_l__et) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 640 (all X all Xa ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X2),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X2),Xa))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1361989810d_Subq,X),Xa)))) # label(fact_def__d__Subq) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 641 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_se,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_sf,Uu)))) # label(fact_ATP_Olambda__98) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 642 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_qr,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_qq,Uu))))) # label(fact_ATP_Olambda__112) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 643 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),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__416) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 644 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_jn,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_jo,Uu)))) # label(fact_ATP_Olambda__173) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 645 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kk,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_kj(Uu),Uua))))) # label(fact_ATP_Olambda__403) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 646 (all X (pp(aa_TPTP_ind_bool(scratc1024683930closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,aa_TPTP_ind_TPTP_ind(scratc1493566924_union,X1)),X))))))) # label(fact_def__d__Union__closed) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 647 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(X),Xa)),Xb)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(X),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Xa),Xb)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1270814762_prop1(X),Xa),Xb)))) # label(fact_def__d__25__prop1) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 648 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_up,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_uo(Uu),Uua))))) # label(fact_ATP_Olambda__347) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 649 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_ug,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_uh,Uu)))) # label(fact_ATP_Olambda__82) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 650 (all X all Xa (pp(aa_fun171081125l_bool(scratc799446_n_all,aa_TPT43085870d_bool(scratc1053717084lbprop(X),Xa))) <-> pp(aa_TPTP_ind_bool(scratc1052349889d_n_lb(X),Xa)))) # label(fact_def__n__lb) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 651 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc104586080t_disj(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1870473726nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_az(X),Xa),Xb))))) # label(fact_def__st__disj) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 652 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cj,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_ci,Uu))))) # label(fact_ATP_Olambda__228) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 653 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),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__352) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 654 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ze,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_zd,Uu))))) # label(fact_ATP_Olambda__35) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 655 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513572130moreis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wu(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__512) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 656 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_hl(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hm,Uu),Uua)))) # label(fact_ATP_Olambda__422) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 657 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gn(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gm(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__611) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 658 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_og,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_of,Uu))))) # label(fact_ATP_Olambda__130) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 659 (all Uu (scratc1588370020_is_of(aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uu),aTP_Lamm_kb) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_aaj,Uu)))) # label(fact_ATP_Olambda__14) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 660 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yp,Uu),Uua)) <-> pp(scratc1986528333nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc2093768511n_some,aa_TPT43085870d_bool(scratc1841546987ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc2093768511n_some,aa_TPT43085870d_bool(scratc1841546987ffprop(Uua),Uu)))))) # label(fact_ATP_Olambda__246) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 661 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_kk,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_kl,Uu)))) # label(fact_ATP_Olambda__167) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 662 (all X aa_TPTP_ind_TPTP_ind(scratc1114818897_proj1,X) = aa_fun277296641TP_ind(scratc719917262eplSep(X,aTP_Lamm_bp),scratc476687568_d_Unj)) # label(fact_def__proj1) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 663 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_cu,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cv,Uu)))) # label(fact_ATP_Olambda__225) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 664 (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]. 2.10/2.52 665 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_sk,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_sl,Uu)))) # label(fact_ATP_Olambda__95) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 666 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc2097018441indrat(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc1990668394indeq2(scratc89572337d_frac,scratc1051890711d_n_eq,Xb,Xc,X),Xa)) # label(fact_def__indrat) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 667 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abd(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,Uub),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc392288474d_d_Pi,Uu),aTP_Lamm_af(Uua)))))) # label(fact_ATP_Olambda__565) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 668 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mp,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_mo(Uu),Uua))))) # label(fact_ATP_Olambda__394) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 669 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_qi(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qj(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__583) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 670 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_so,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513572130moreis,Uua),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),scratc1882202790nd_n_1)))))) # label(fact_ATP_Olambda__270) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 671 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yl,Uu),Uua)) <-> scratc2039664015_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uu),Uua)))) # label(fact_ATP_Olambda__239) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 672 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nd,Uu),Uua)) <-> scratc2039664015_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uu),Uua)))) # label(fact_ATP_Olambda__240) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 673 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_oh(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uua),Uuc))))))) # label(fact_ATP_Olambda__653) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 674 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_nz(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513572130moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513572130moreis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513572130moreis,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uua),Uuc))))))) # label(fact_ATP_Olambda__649) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 675 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_st(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__652) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 676 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_xx,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_xy,Uu)))) # label(fact_ATP_Olambda__49) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 677 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_co(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379326120lesseq,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uua),Uuc))))))) # label(fact_ATP_Olambda__670) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 678 (all X all Xa all Xb all Xc all Xd (pp(scratc575825622_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1936631369nd_imp,X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1533492748d_e_is(Xa),Xd),Xb)),aa_bool_bool(aa_boo1142376798l_bool(scratc1936631369nd_imp,scratc683290802_d_not(X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1533492748d_e_is(Xa),Xd),Xc)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1115212491_prop1(X,Xa,Xb),Xc),Xd)))) # label(fact_def__prop1) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 679 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc955832086etprod(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc523788228_Sigma,X),aTP_Lamm_af(Xa))) # label(fact_def__setprod) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 680 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1051956311d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1978463683nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc1894799050nd_den,Xa))),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1978463683nd_num,Xa)),aa_TPTP_ind_TPTP_ind(scratc1894799050nd_den,X)))),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1894799050nd_den,X)),aa_TPTP_ind_TPTP_ind(scratc1894799050nd_den,Xa))) = aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(X),Xa)) # label(fact_def__n__pf) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 681 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_en(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_em(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__615) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 682 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_px(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_pw(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__586) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 683 -(exists X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X0),scratc559650040ptyset))) # label(fact_k__EmptyAx) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 684 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271961_moreq,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cw(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__665) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 685 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_iz,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_iy,Uu))))) # label(fact_ATP_Olambda__178) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 686 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_on,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_oo,Uu)))) # label(fact_ATP_Olambda__128) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 687 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_yt,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_yu,Uu)))) # label(fact_ATP_Olambda__39) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 688 (all X7 all Y (Y != X7 | pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)))) # label(help_fequal_2_1_fequal_001t__TPTP____Interpret__Oind_T) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 689 (all X0 (pp(aa_TPTP_ind_bool(scratc1475014226_nat_p,X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X0),scratc284474110_omega)))) # label(fact_nat__p__omega) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 690 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_qt,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_qu,Uu)))) # label(fact_ATP_Olambda__111) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 691 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tz(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__497) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 692 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_xb,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_xc,Uu)))) # label(fact_ATP_Olambda__59) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 693 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_of,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_oe(Uu),Uua))))) # label(fact_ATP_Olambda__385) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 694 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_de(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uua),Uuc))))))) # label(fact_ATP_Olambda__672) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 695 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_hd(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_he,Uu),Uua)))) # label(fact_ATP_Olambda__424) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 696 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_mt,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_mu,Uu)))) # label(fact_ATP_Olambda__146) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 697 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513572130moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513572130moreis,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pt(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__513) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 698 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_pe(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pf,Uu),Uua)))) # label(fact_ATP_Olambda__378) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 699 (all X0 all X12 pp(aa_fun171081125l_bool(scratc91799413all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,X0)),aa_fun1584354236d_bool(aTP_Lamm_aao(X0),X12)))) # label(fact_estii) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 700 (all P all Q all R aa_TPTP_ind_bool(cOMBS_2003118649l_bool(P,Q),R) = aa_bool_bool(aa_TPT2142672771l_bool(P,R),aa_TPTP_ind_bool(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]. 2.10/2.52 701 (all Uu aa_TPTP_ind_TPTP_ind(aTP_Lamm_ah,Uu) = scratc1977151710nd_nat) # label(fact_ATP_Olambda__713) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 702 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_ua,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ub,Uu)))) # label(fact_ATP_Olambda__84) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 703 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc96237146econd1(X),Xa) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,Xa),scratc1048545165d_n_2t)) # label(fact_def__second1) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 704 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dj(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_di(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__618) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 705 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc418274606_UPair(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc760268562d_repl,aa_TPTP_ind_TPTP_ind(scratc986305058_power,aa_TPTP_ind_TPTP_ind(scratc986305058_power,scratc559650040ptyset))),aa_TPT1424761345TP_ind(aTP_Lamm_bv(X),Xa))) # label(fact_def__d__UPair) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 706 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ly,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_lx,Uu))))) # label(fact_ATP_Olambda__155) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 707 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_zy,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1977676501nd_nis,Uu),scratc1882202790nd_n_1)) -> pp(aa_fun171081125l_bool(scratc116591707_n_one,aa_TPT43085870d_bool(aTP_Lamm_an,Uu)))))) # label(fact_ATP_Olambda__2) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 708 (all X0 all X12 all X22 ((pp(X0) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X12),X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,aa_TPTP_ind_TPTP_ind(scratc1405965280bnd_if(X0,X12),scratc559650040ptyset)),aa_TPTP_ind_TPTP_ind(scratc1405965280bnd_if(X0,X22),aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,scratc559650040ptyset)))))) # label(fact_k__If__In__01) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 709 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rk,Uu),Uua)))) # label(fact_ATP_Olambda__272) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 710 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1859176937_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Xa),X))))) # label(fact_def__d__26__prop1) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 711 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ka,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_jz,Uu))))) # label(fact_ATP_Olambda__168) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 712 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_tr(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ts(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__576) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 713 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_td,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_te,Uu)))) # label(fact_ATP_Olambda__90) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 714 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qm(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uub),Uua)))))) # label(fact_ATP_Olambda__549) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 715 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_vv,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_vu,Uu))))) # label(fact_ATP_Olambda__70) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 716 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uu),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uua),Uub))),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fm(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__504) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 717 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513572130moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513572130moreis,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_va(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__515) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 718 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uu),Uu)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_nu,Uu)))) # label(fact_ATP_Olambda__22) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 719 (all Uu all Uua all Uub all Uuc all Uud all Uue (pp(aa_fun171081125l_bool(scratc91799413all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_as(Uu),Uua),Uub),Uuc),Uud),Uue))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_at(Uu),Uua),Uub),Uuc),Uud),Uue)))) # label(fact_ATP_Olambda__708) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 720 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_xq,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_xp,Uu))))) # label(fact_ATP_Olambda__53) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 721 (all X aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc760268562d_repl,X),scratc2088746605d_Inj1) = aa_TPTP_ind_TPTP_ind(scratc2088746604d_Inj0,X)) # label(fact_def__d__Inj0) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 722 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379326120lesseq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lf(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__525) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 723 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pe(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__487) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 724 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc698437091d_outn(aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(X),aa_TPTP_ind_TPTP_ind(scratc1936696966nd_inn(Xa),Xb))) = aa_TPTP_ind_TPTP_ind(scratc283046675ght1to(X,Xa),Xb)) # label(fact_def__right1to) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 725 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ie(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uu),Uua))))) # label(fact_ATP_Olambda__493) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 726 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xj,Uu),Uua)) <-> (pp(scratc683290802_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__305) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 727 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_xm,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_xl,Uu))))) # label(fact_ATP_Olambda__55) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 728 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ct(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cs(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__622) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 729 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ru,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(scratc1882202790nd_n_1),Uu)),Uu)))) # label(fact_ATP_Olambda__6) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 730 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gk,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_gj(Uu),Uua))))) # label(fact_ATP_Olambda__429) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 731 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dt,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_ds(Uu),Uua))))) # label(fact_ATP_Olambda__447) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 732 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_us,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_ur(Uu),Uua))))) # label(fact_ATP_Olambda__346) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 733 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_os,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_or,Uu))))) # label(fact_ATP_Olambda__127) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 734 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ox(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_oy(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__587) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 735 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc523788228_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,aa_TPTP_ind_TPTP_ind(scratc1114818896_proj0,X22)),X0)))) # label(fact_proj0__Sigma) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 736 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_kt(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ku,Uu),Uua)))) # label(fact_ATP_Olambda__402) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 737 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_uk,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_uj,Uu))))) # label(fact_ATP_Olambda__81) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 738 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_gs,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_gt,Uu)))) # label(fact_ATP_Olambda__194) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 739 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abg(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aa_TPT43085870d_bool(aTP_Lamm_abd(Uu),Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_abf(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__473) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 740 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_qa(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qb(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__585) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 741 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_yq,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_yp,Uu))))) # label(fact_ATP_Olambda__40) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 742 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_jx,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_jy,Uu)))) # label(fact_ATP_Olambda__169) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 743 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_eh,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_eg,Uu))))) # label(fact_ATP_Olambda__214) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 744 (all X all Xa all Xb (pp(aa_fun171081125l_bool(scratc1870473726nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bh(X),Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1116728996ective(X),Xa),Xb)))) # label(fact_def__injective) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 745 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_tr(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__696) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 746 (all X0 all X12 pp(aa_fun171081125l_bool(scratc91799413all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,X0)),aa_fun1584354236d_bool(aTP_Lamm_aan(X0),X12)))) # label(fact_estie) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 747 (all Uu all Uua ((pp(scratc683290802_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379326120lesseq,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lx,Uu),Uua)))) # label(fact_ATP_Olambda__306) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 748 (all X0 all X12 pp(aa_fun171081125l_bool(scratc91799413all_of(aa_TPT43085870d_bool(aTP_Lamm_aat(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_aav(X0),X12)))) # label(fact_second__p) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 749 (all X all Xa (pp(aa_TPTP_ind_bool(Xa,X)) <-> scratc1588370020_is_of(X,Xa))) # label(fact_def__is__of) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 750 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_wb,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_wa,Uu))))) # label(fact_ATP_Olambda__68) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 751 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_np(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__546) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 752 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc250935473d_incl(Uu),Uua),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc250935473d_incl(Uu),Uub),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1533492748d_e_is(aa_TPTP_ind_TPTP_ind(scratc986305058_power,Uu)),Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aal(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__469) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 753 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fc,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_fb,Uu))))) # label(fact_ATP_Olambda__208) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 754 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_pf,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_pg,Uu)))) # label(fact_ATP_Olambda__123) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 755 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kr,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uua),Uu)))) # label(fact_ATP_Olambda__319) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 756 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vw(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__541) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 757 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_uf(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__478) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 758 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1937090551nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1533492748d_e_is(X),Xc),Xb),X,Xa),aa_TPTP_ind_TPTP_ind(scratc95826374sel_wa(X,Xa,Xb),Xc)) = aa_TPTP_ind_TPTP_ind(scratc95826375sel_wb(X,Xa,Xb),Xc)) # label(fact_def__wissel__wb) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 759 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1977676501nd_nis,aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uu)),Uu)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_aaa,Uu)))) # label(fact_ATP_Olambda__13) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 760 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pk(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__519) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 761 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_kh,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_kg,Uu))))) # label(fact_ATP_Olambda__137) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 762 (all P all Q (-pp(P) | -pp(Q) | pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 763 (all X all Xa (pp(scratc920245767d_l_ec(X,Xa)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1936631369nd_imp,X),scratc683290802_d_not(Xa))))) # label(fact_def__l__ec) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 764 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_pq(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pr,Uu),Uua)))) # label(fact_ATP_Olambda__374) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 765 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uuc),Uua))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ik(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__690) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 766 (all Uu ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1977676501nd_nis,Uu),scratc1882202790nd_n_1)) -> pp(aa_fun171081125l_bool(scratc2093768511n_some,aa_TPT43085870d_bool(aTP_Lamm_an,Uu)))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_zz,Uu)))) # label(fact_ATP_Olambda__1) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 767 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_yd,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ye,Uu)))) # label(fact_ATP_Olambda__46) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 768 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1405965280bnd_if(X,Xa),Xb) = scratc1903782149nd_eps(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bw(X),Xa),Xb))) # label(fact_def__if) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 769 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_oa(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_nz(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__593) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 770 (all X0 all X12 all X22 all X32 (pp(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1405965280bnd_if(X0,X22),X32))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X12),X22))))) # label(fact_k__If__In__then__E) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 771 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1835233233tminus(X),Xa) = aa_fun1431113780TP_ind(scratc459574173_d_Sep(X),aa_TPT43085870d_bool(aTP_Lamm_bt,Xa))) # label(fact_def__setminus) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 772 (all X all Xa all Xb (pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1936631369nd_imp,aa_TPTP_ind_bool(X,Xb)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053717084lbprop(X),Xa),Xb)))) # label(fact_def__lbprop) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 773 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_iw(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__685) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 774 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_rm,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_rn,Uu)))) # label(fact_ATP_Olambda__104) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 775 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yj,Uu),Uua)) <-> pp(scratc1986528333nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__241) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 776 (all X (pp(aa_TPTP_ind_bool(scratc682452587_prop1,X)) <-> pp(aa_fun171081125l_bool(scratc799446_n_all,aa_TPT43085870d_bool(aTP_Lamm_am,X))))) # label(fact_def__d__24__prop1) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 777 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_lu(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lv,Uu),Uua)))) # label(fact_ATP_Olambda__395) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 778 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ge,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_gd,Uu))))) # label(fact_ATP_Olambda__198) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 779 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_la,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_kz(Uu),Uua))))) # label(fact_ATP_Olambda__400) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 780 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_hm,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_hn,Uu)))) # label(fact_ATP_Olambda__189) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 781 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_er(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_es,Uu),Uua)))) # label(fact_ATP_Olambda__440) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 782 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xb,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_xa(Uu),Uua))))) # label(fact_ATP_Olambda__329) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 783 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yd,Uu),Uua)))) # label(fact_ATP_Olambda__285) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 784 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cl(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ck(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__624) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 785 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_ov,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ow,Uu)))) # label(fact_ATP_Olambda__126) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 786 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,Uu),scratc2010197730nd_rat)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_a,Uu)))) # label(fact_ATP_Olambda__25) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 787 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aam,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aa_TPT43085870d_bool(aTP_Lamm_aak,Uu)),aa_TPT43085870d_bool(aTP_Lamm_aal(Uu),Uua))))) # label(fact_ATP_Olambda__300) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 788 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vf,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_ve(Uu),Uua))))) # label(fact_ATP_Olambda__342) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 789 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uu),Uua)) -> pp(aa_fun171081125l_bool(scratc1349943869l_some(scratc89572337d_frac),aa_TPT43085870d_bool(aTP_Lamm_km(Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kn,Uu),Uua)))) # label(fact_ATP_Olambda__287) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 790 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_xn,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_xo,Uu)))) # label(fact_ATP_Olambda__54) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 791 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_zh(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zi,Uu),Uua)))) # label(fact_ATP_Olambda__324) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 792 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fv(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fu(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__613) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 793 (all X all Xa (pp(aa_fun171081125l_bool(scratc1349943869l_some(X),aa_TPT43085870d_bool(aTP_Lamm_bb(X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc845245027nempty,X),Xa)))) # label(fact_def__nonempty) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 794 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_db(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dc,Uu),Uua)))) # label(fact_ATP_Olambda__452) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 795 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pn(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__518) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 796 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_is(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_it(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__601) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 797 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gp,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_go,Uu))))) # label(fact_ATP_Olambda__195) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 798 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_qd,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_qc,Uu))))) # label(fact_ATP_Olambda__116) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 799 (all X all Xa all Xb all Xc (pp(aa_fun171081125l_bool(scratc1349943869l_some(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bf(Xa),Xb),Xc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2003976952_image(X,Xa),Xb),Xc)))) # label(fact_def__image) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 800 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_sp,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_so,Uu))))) # label(fact_ATP_Olambda__93) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 801 (all X0 all X12 all X22 (gg_TPTP_ind(X12) -> (pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc1405965280bnd_if(X0,X12),X22) = X12))) # label(fact_if__i__1) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 802 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_zs,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(scratc1882202790nd_n_1),Uu)),aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uu))))) # label(fact_ATP_Olambda__5) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 803 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc156456688etprop(X,Xa),Xb),Xc)) <-> pp(scratc575825622_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1465976678d_esti(X),Xc),Xa),scratc683290802_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1465976678d_esti(X),Xc),Xb)))))) # label(fact_def__nissetprop) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 804 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513572130moreis,X),Xa)) <-> pp(aa_bool_bool(scratc920901772d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,X),Xa))))) # label(fact_def__moreis) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 805 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2071665076_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Xa),X))))) # label(fact_def__d__429__prop1) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 806 (all X (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1977676501nd_nis,aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,X)),X)) <-> pp(aa_TPTP_ind_bool(scratc1653211885_prop1,X)))) # label(fact_def__d__22__prop1) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 807 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_kc(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kd,Uu),Uua)))) # label(fact_ATP_Olambda__391) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 808 (all X (pp(aa_fun171081125l_bool(scratc1349943869l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc392288474d_d_Pi,scratc1977151710nd_nat),aTP_Lamm_ah)),aa_TPT43085870d_bool(scratc682452588_prop2,X))) <-> pp(aa_TPTP_ind_bool(scratc1115212494_prop4,X)))) # label(fact_def__prop4) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 809 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sz,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_sy(Uu),Uua))))) # label(fact_ATP_Olambda__359) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 810 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dg,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_df(Uu),Uua))))) # label(fact_ATP_Olambda__451) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 811 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_qk,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ql,Uu)))) # label(fact_ATP_Olambda__114) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 812 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_oz,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_pa,Uu)))) # label(fact_ATP_Olambda__125) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 813 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aas(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aar(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__563) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 814 (all X (pp(aa_bool_bool(scratc920901772d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,X),scratc1882202790nd_n_1)),aa_fun171081125l_bool(scratc2093768511n_some,aa_TPT43085870d_bool(aTP_Lamm_an,X)))) <-> pp(aa_TPTP_ind_bool(scratc94090412_prop1,X)))) # label(fact_def__d__23__prop1) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 815 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_ce,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cf,Uu)))) # label(fact_ATP_Olambda__229) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 816 (all X all Xa (pp(aa_bool_bool(scratc920901772d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271961_moreq,X),Xa)))) # label(fact_def__moreq) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 817 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uuc),Uua))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_em(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__684) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 818 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(scratc1882202790nd_n_1),Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ro,Uu)))) # label(fact_ATP_Olambda__18) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 819 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,Uu),Uua)) -> pp(scratc683290802_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xv,Uu),Uua)))) # label(fact_ATP_Olambda__290) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 820 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_wo,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_wn,Uu))))) # label(fact_ATP_Olambda__64) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 821 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_nj,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_nk,Uu)))) # label(fact_ATP_Olambda__135) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 822 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hc(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hd(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__607) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 823 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ax(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1465976678d_esti(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__634) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 824 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1978463683nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc1894799050nd_den,Xa))),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1978463683nd_num,Xa)),aa_TPTP_ind_TPTP_ind(scratc1894799050nd_den,X)))))) # label(fact_def__n__eq) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 825 (all X0 all X12 pp(aa_fun171081125l_bool(scratc91799413all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,X0)),aa_TPT43085870d_bool(aTP_Lamm_aas(X0),X12)))) # label(fact_firstis1) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 826 (all X all Xa all Xb (pp(aa_bool_bool(scratc920901772d_l_or(X),aa_bool_bool(scratc920901772d_l_or(Xa),Xb))) <-> pp(scratc1986528333nd_or3(X,Xa,Xb)))) # label(fact_def__or3) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 827 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,Uu),Uub)) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_bd(Uu),Uua),Uub)) # label(fact_ATP_Olambda__570) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 828 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(scratc1937090551nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1533492748d_e_is(aa_TPTP_ind_TPTP_ind(scratc179666987_d_1to,scratc1882202791nd_n_2)),Uuc),scratc1048479566d_n_1t),Uu,Uua),Uub) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ae(Uu),Uua),Uub),Uuc)) # label(fact_ATP_Olambda__629) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 829 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fq,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_fp(Uu),Uua))))) # label(fact_ATP_Olambda__432) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 830 (all B_1 all B_2 gg_bool(scratc575825622_d_and(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__62002__14561_ONUM781__thf__4__p_Obnd__d__and) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 831 (all X scratc1936696956nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc392288474d_d_Pi,scratc1977151710nd_nat),aTP_Lamm_ah),aa_TPT43085870d_bool(scratc1483302902_prop2,X)) = aa_TPTP_ind_TPTP_ind(scratc778423971_times,X)) # label(fact_def__times) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 832 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fg(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__542) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 833 (all X all Xa scratc1405440498bnd_ap = scratc255918379d_tofs(X,Xa)) # label(fact_def__tofs) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 834 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1780638511_rt_is,Uu),Uu)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu)))) # label(fact_ATP_Olambda__21) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 835 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1937090551nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1533492748d_e_is(X),Xc),Xa),X,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc95826374sel_wa(X,Xa,Xb),Xc)) # label(fact_def__wissel__wa) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 836 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_vk,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_vj,Uu))))) # label(fact_ATP_Olambda__73) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 837 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc523788228_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,aa_TPTP_ind_TPTP_ind(scratc1114818897_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1114818896_proj0,X22)))))) # label(fact_proj1__Sigma) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 838 (all X0 all X12 (gg_TPTP_ind(X0) -> X0 = aa_TPTP_ind_TPTP_ind(scratc1114818896_proj0,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1313072605d_pair,X0),X12)))) # label(fact_proj0__pair__eq) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 839 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_op(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_oq(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__589) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 840 (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_bg(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1936631369nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1533492748d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,Uub),Uud))),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1533492748d_e_is(Uu),Uuc),Uud))))) # label(fact_ATP_Olambda__703) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 841 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1051956311d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1051956311d_n_fr,Uu),Uub)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1051956311d_n_fr,Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kc(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__498) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 842 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_xj,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_xk,Uu)))) # label(fact_ATP_Olambda__56) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 843 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wi(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__510) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 844 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_jq,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_jr,Uu)))) # label(fact_ATP_Olambda__172) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 845 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_nl,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_nm,Uu)))) # label(fact_ATP_Olambda__134) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 846 (all Uu all Uua (pp(scratc1902929298nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yh,Uu),Uua)))) # label(fact_ATP_Olambda__243) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 847 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zq,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__258) # label(axiom) # label(non_clause). [assumption]. 2.10/2.52 848 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jj(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uua),Uub)))))) # label(fact_ATP_Olambda__534) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 849 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_vx,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_vy,Uu)))) # label(fact_ATP_Olambda__69) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 850 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dn,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_dm(Uu),Uua))))) # label(fact_ATP_Olambda__449) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 851 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_oi(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_oh(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__591) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 852 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jp(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uua),Uub)))))) # label(fact_ATP_Olambda__529) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 853 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513572130moreis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ol(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__645) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 854 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_tn(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513572130moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__648) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 855 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1977676501nd_nis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1977676501nd_nis,aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aab,Uu),Uua)))) # label(fact_ATP_Olambda__266) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 856 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jc,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_jb,Uu))))) # label(fact_ATP_Olambda__177) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 857 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rb(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uua),Uub)))))) # label(fact_ATP_Olambda__508) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 858 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_sx(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sy(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__581) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 859 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_za(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zb,Uu),Uua)))) # label(fact_ATP_Olambda__325) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 860 (all X all Xa all Xb (pp(aa_fun171081125l_bool(scratc1870473726nd_all(Xa),aa_TPT43085870d_bool(scratc2003976952_image(X,Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1839685631ective(X),Xa),Xb)))) # label(fact_def__surjective) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 861 (all X scratc1870473726nd_all(X) = scratc91799413all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,X))) # label(fact_def__all) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 862 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xg(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__553) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 863 (all X0 all X12 (gg_TPTP_ind(X12) & gg_TPTP_ind(X0) -> (aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,X0) = aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,X12) -> X12 = X0))) # label(fact_ordsucc__inj) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 864 (all X all Xa all Xb all Xc (pp(aa_fun171081125l_bool(scratc91799413all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_au(X),Xa),Xb),Xc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc59674897fixfu2(X,Xa),Xb),Xc)))) # label(fact_def__fixfu2) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 865 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_kb,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,Uu),scratc1977151710nd_nat)))) # label(fact_ATP_Olambda__26) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 866 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_or,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_oq(Uu),Uua))))) # label(fact_ATP_Olambda__382) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 867 (all X0 (gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(scratc1475014226_nat_p,X0)) -> (exists X13 (gg_TPTP_ind(X13) & pp(aa_TPTP_ind_bool(scratc1475014226_nat_p,X13)) & aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,X13) = X0)) | scratc559650040ptyset = X0))) # label(fact_nat__inv) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 868 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_abh(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1533492748d_e_is(Uu),Uub),Uuc)) -> pp(aa_TPTP_ind_bool(Uua,Uuc)))))) # label(fact_ATP_Olambda__697) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 869 (all X0 all X12 all X22 all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc392288474d_d_Pi,X0),X12))) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X32),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,X22),X32)),aa_TPTP_ind_TPTP_ind(X12,X32)))))) # label(fact_ap__Pi) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 870 (all X scratc1405965288bnd_in = scratc1465976678d_esti(X)) # label(fact_def__esti) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 871 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_sa,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_sb,Uu)))) # label(fact_ATP_Olambda__100) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 872 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_mq,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_mp,Uu))))) # label(fact_ATP_Olambda__147) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 873 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_ph(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pi,Uu),Uua)))) # label(fact_ATP_Olambda__377) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 874 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qz,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_qy(Uu),Uua))))) # label(fact_ATP_Olambda__364) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 875 (all X all Xa all Xb scratc1750571112d_11_i(X,Xa,Xb) = scratc661733832_indeq(X,Xa,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc392288474d_d_Pi,X),aTP_Lamm_af(Xb)))) # label(fact_def__d__11__i) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 876 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_np(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nq,Uu),Uua)))) # label(fact_ATP_Olambda__392) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 877 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_yc,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_yb,Uu))))) # label(fact_ATP_Olambda__47) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 878 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xr,Uu),Uua)) <-> (pp(scratc683290802_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513572130moreis,Uu),Uua))))) # label(fact_ATP_Olambda__310) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 879 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_zp,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),scratc1882202790nd_n_1))))) # label(fact_ATP_Olambda__10) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 880 (all X all Xa (scratc672668580d_orec(X,Xa) <-> pp(scratc575825622_d_and(aa_bool_bool(scratc920901772d_l_or(X),Xa),scratc920245767d_l_ec(X,Xa))))) # label(fact_def__orec) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 881 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> X22 = aa_TPTP_ind_TPTP_ind(scratc1405965280bnd_if(X0,X12),X22) | aa_TPTP_ind_TPTP_ind(scratc1405965280bnd_if(X0,X12),X22) = X12)) # label(fact_if__i__or) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 882 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc925090592munion,X),aTP_Lamm_bo(Xa)) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc523788228_Sigma,X),Xa)) # label(fact_def__d__Sigma) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 883 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_sz,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ta,Uu)))) # label(fact_ATP_Olambda__91) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 884 (all Q all P (-pp(Q) | pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)))) # label(help_fimplies_2_1_U) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 885 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_ju,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_jv,Uu)))) # label(fact_ATP_Olambda__170) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 886 (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(scratc513572130moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uu),Uub)))))) # label(fact_ATP_Olambda__517) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 887 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_py,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_pz,Uu)))) # label(fact_ATP_Olambda__117) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 888 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_tb(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__694) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 889 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pc,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_pb(Uu),Uua))))) # label(fact_ATP_Olambda__379) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 890 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hs(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uu),Uua))))) # label(fact_ATP_Olambda__486) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 891 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_lq(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lr,Uu),Uua)))) # label(fact_ATP_Olambda__396) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 892 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cg(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ch(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__625) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 893 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_tx,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ty,Uu)))) # label(fact_ATP_Olambda__85) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 894 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ph(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__476) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 895 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_uv,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_uw,Uu)))) # label(fact_ATP_Olambda__77) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 896 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nb,Uu),Uua)) <-> pp(scratc1986528333nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uu),Uua))))) # label(fact_ATP_Olambda__242) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 897 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ey,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_ex(Uu),Uua))))) # label(fact_ATP_Olambda__438) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 898 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc848116892air_q0(X),Xa) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc680694164_pair1(X),aa_TPTP_ind_TPTP_ind(scratc1925936612first1(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc96237146econd1(X),Xa))) # label(fact_def__pair__q0) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 899 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ky,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_kx,Uu))))) # label(fact_ATP_Olambda__164) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 900 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_fj(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fk,Uu),Uua)))) # label(fact_ATP_Olambda__434) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 901 (all B_1 gg_TPTP_ind(scratc1903782149nd_eps(B_1))) # label(gsy_c_Scratch__tptp__translate__62002__14561_ONUM781__thf__4__p_Obnd__eps) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 902 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_lh,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_lg,Uu))))) # label(fact_ATP_Olambda__161) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 903 (all X all Xa scratc410049685_ecect(X,Xa) = scratc1533492743d_e_in(aa_TPTP_ind_TPTP_ind(scratc986305058_power,X),scratc448820014d_anec(X,Xa))) # label(fact_def__ecect) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 904 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_vb,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_vc,Uu)))) # label(fact_ATP_Olambda__75) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 905 (all Uu all Uua (scratc2039664015_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc2093768511n_some,aa_TPT43085870d_bool(aTP_Lamm_yr(Uu),Uua)),aa_fun171081125l_bool(scratc2093768511n_some,aa_TPT43085870d_bool(aTP_Lamm_ys(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yt,Uu),Uua)))) # label(fact_ATP_Olambda__245) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 906 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ko,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_kn,Uu))))) # label(fact_ATP_Olambda__166) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 907 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874685d_n_tf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fu(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__691) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 908 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cm,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_cl(Uu),Uua))))) # label(fact_ATP_Olambda__456) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 909 (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]. 2.10/2.53 910 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lc(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379326120lesseq,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uu),Uub)))))) # label(fact_ATP_Olambda__536) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 911 (all X (pp(aa_TPTP_ind_bool(scratc1079507897closed,X)) <-> pp(aa_TPTP_ind_bool(scratc1024683930closed,X)) & pp(aa_TPTP_ind_bool(scratc1189416944closed,X)) & pp(aa_TPTP_ind_bool(scratc48604636closed,X)))) # label(fact_def__d__ZF__closed) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 912 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xh,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_xg(Uu),Uua))))) # label(fact_ATP_Olambda__327) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 913 (all X (pp(aa_TPTP_ind_bool(scratc1475014226_nat_p,X)) <-> (all X1 (pp(aa_TPTP_ind_bool(X1,scratc559650040ptyset)) -> ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(X1,X2)) -> pp(aa_TPTP_ind_bool(X1,aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,X2)))))) -> pp(aa_TPTP_ind_bool(X1,X))))))) # label(fact_def__nat__p) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 914 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tc(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_tb(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__580) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 915 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_rj,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_ri,Uu))))) # label(fact_ATP_Olambda__106) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 916 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2072369992_29_ii,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_vp(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__677) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 917 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_yx(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yy,Uu),Uua)))) # label(fact_ATP_Olambda__326) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 918 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_lv,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_lw,Uu)))) # label(fact_ATP_Olambda__156) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 919 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_jk,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_jl,Uu)))) # label(fact_ATP_Olambda__174) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 920 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_fk,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fl,Uu)))) # label(fact_ATP_Olambda__205) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 921 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xa(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__552) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 922 (all Uu all Uua (pp(scratc1902929298nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1052153109d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc2093768511n_some,aa_TPT43085870d_bool(scratc1841546987ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc2093768511n_some,aa_TPT43085870d_bool(scratc1841546987ffprop(Uua),Uu)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yn,Uu),Uua)))) # label(fact_ATP_Olambda__247) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 923 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zd,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1977676501nd_nis,Uua),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__314) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 924 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iq,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_ip(Uu),Uua))))) # label(fact_ATP_Olambda__413) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 925 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uua),aa_TPTP_ind_TPTP_ind(scratc1321908992rdsucc,Uu))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_se,Uu),Uua)))) # label(fact_ATP_Olambda__261) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 926 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wc(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__550) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 927 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_za(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1977676501nd_nis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1977676501nd_nis,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uub)))))) # label(fact_ATP_Olambda__547) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 928 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc68269075rt_nis,X),Xa)) <-> pp(scratc683290802_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1780638511_rt_is,X),Xa))))) # label(fact_def__rt__nis) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 929 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_li(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1474950154_lessf,Uu),Uub)))))) # label(fact_ATP_Olambda__537) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 930 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_mc,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_mb,Uu))))) # label(fact_ATP_Olambda__153) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 931 (all X scratc1052874698d_n_ts(X) = aa_TPT1424761345TP_ind(scratc1405440498bnd_ap,aa_TPTP_ind_TPTP_ind(scratc778423971_times,X))) # label(fact_def__n__ts) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 932 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_th,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ti,Uu)))) # label(fact_ATP_Olambda__89) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 933 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jz,Uu),Uua)))) # label(fact_ATP_Olambda__275) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 934 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1361989810d_Subq,X0),X12)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1361989810d_Subq,X12),X0)) -> X12 = X0)))) # label(fact_set__ext) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 935 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513572130moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513572130moreis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513572130moreis,aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_sx(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__650) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 936 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,Uub),aa_TPTP_ind_TPTP_ind(scratc955832086etprod(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aat(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__568) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 937 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1493566924_union,X0))) <-> (exists X2 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X2),X0)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405965288bnd_in,X12),X2)) & gg_TPTP_ind(X2))))) # label(fact_k__UnionEq) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 938 (all X all Xa scratc1114818897_proj1 = scratc1198944151second(X,Xa)) # label(fact_def__second) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 939 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1051890711d_n_eq,Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1051956311d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1978463683nd_num,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1894799050nd_den,Uu)),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nn,Uu),Uua)))) # label(fact_ATP_Olambda__312) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 940 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1052612289d_n_pf(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1821271950_moref,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hy(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__482) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 941 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_nt,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_ns,Uu))))) # label(fact_ATP_Olambda__139) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 942 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_iq,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ir,Uu)))) # label(fact_ATP_Olambda__180) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 943 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ii,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_ih(Uu),Uua))))) # label(fact_ATP_Olambda__415) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 944 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc379588518lessis,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_nv(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__651) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 945 (all X all Xa all Xb all Xc aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc523788228_Sigma,aa_TPTP_ind_TPTP_ind(scratc179666987_d_1to,Xb)),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ac(Xa),Xb),Xc)) = aa_TPTP_ind_TPTP_ind(scratc597406809_right(X,Xa,Xb),Xc)) # label(fact_def__right) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 946 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1052874698d_n_ts(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qv(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__548) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 947 (all X0 all X12 (gg_TPTP_ind(X12) -> aa_TPTP_ind_TPTP_ind(scratc1114818897_proj1,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1313072605d_pair,X0),X12)) = X12)) # label(fact_proj1__pair__eq) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 948 (all Uu (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_tt,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_tu,Uu)))) # label(fact_ATP_Olambda__86) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 949 (all X all Xa (pp(aa_fun171081125l_bool(scratc91799413all_of(X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (scratc1588370020_is_of(X2,X) -> pp(aa_TPTP_ind_bool(Xa,X2))))))) # label(fact_def__all__of) # label(axiom) # label(non_clause). [assumption]. 2.10/2.53 950 (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]. 2.10/2.53 951 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_xi,Uu)) <-> pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aTP_Lamm_xh,Uu))))) # label(fact_ATP_Olambda__57) # label(axiom) # label(non_clause). [assumption]. 2.10/2.61 952 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1465976678d_esti(Uu),Uub),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bb(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__467) # label(axiom) # label(non_clause). [assumption]. 2.10/2.61 953 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wn,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1936368966nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc1052612295d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__315) # label(axiom) # label(non_clause). [assumption]. 2.10/2.61 954 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_by),aa_TPT43085870d_bool(aTP_Lamm_fd(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fe,Uu),Uua)))) # label(fact_ATP_Olambda__436) # label(axiom) # label(non_clause). [assumption]. 2.10/2.61 955 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc91799413all_of(aTP_Lamm_kb),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ol(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_om(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__590) # label(axiom) # label(non_clause). [assumption]. 2.10/2.61 2.10/2.61 ============================== end of process non-clausal formulas === 2.10/2.61 2.10/2.61 ============================== PROCESS INITIAL CLAUSES =============== 2.10/2.61 2.10/2.61 ============================== PREDICATE ELIMINATION ================= 2.10/2.61 956 -gg_bool(A) | fFalse = A | fTrue = A # label(help_fFalse_1_1_T) # label(axiom). [clausify(27)]. 2.10/2.61 957 gg_bool(fEx_TPTP_ind(A)) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom). [clausify(18)]. 2.10/2.61 Derived: fFalse = fEx_TPTP_ind(A) | fTrue = fEx_TPTP_ind(A). [resolve(956,a,957,a)]. 2.10/2.61 958 gg_bool(fFalse) # label(gsy_c_fFalse) # label(axiom). [assumption]. 2.10/2.61 Derived: fFalse = fFalse | fTrue = fFalse. [resolve(958,a,956,a)]. 2.10/2.61 959 gg_bool(aa_TPTP_ind_bool(A,B)) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom). [clausify(134)]. 2.10/2.61 Derived: fFalse = aa_TPTP_ind_bool(A,B) | fTrue = aa_TPTP_ind_bool(A,B). [resolve(959,a,956,a)]. 2.10/2.61 960 gg_bool(scratc1986528333nd_or3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__62002__14561_ONUM781__thf__4__p_Obnd__or3) # label(axiom). [clausify(138)]. 2.10/2.61 Derived: fFalse = scratc1986528333nd_or3(A,B,C) | fTrue = scratc1986528333nd_or3(A,B,C). [resolve(960,a,956,a)]. 2.10/2.61 961 gg_bool(undefined_bool(bool)) # label(gsy_c_HOL_Oundefined_001t__HOL__Obool) # label(axiom). [assumption]. 2.10/2.61 Derived: fFalse = undefined_bool(bool) | fTrue = undefined_bool(bool). [resolve(961,a,956,a)]. 2.10/2.61 962 gg_bool(scratc920245767d_l_ec(A,B)) # label(gsy_c_Scratch__tptp__translate__62002__14561_ONUM781__thf__4__p_Obnd__l__ec) # label(axiom). [clausify(319)]. 2.10/2.61 Derived: fFalse = scratc920245767d_l_ec(A,B) | fTrue = scratc920245767d_l_ec(A,B). [resolve(962,a,956,a)]. 2.10/2.61 963 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(346)]. 2.10/2.61 Derived: fFalse = aa_fun171081125l_bool(A,B) | fTrue = aa_fun171081125l_bool(A,B). [resolve(963,a,956,a)]. 2.10/2.61 964 gg_bool(fTrue) # label(gsy_c_fTrue) # label(axiom). [assumption]. 2.10/2.61 Derived: fFalse = fTrue | fTrue = fTrue. [resolve(964,a,956,a)]. 2.10/2.61 965 gg_bool(scratc1593517495_amone(A,B)) # label(gsy_c_Scratch__tptp__translate__62002__14561_ONUM781__thf__4__p_Obnd__amone) # label(axiom). [clausify(423)]. 2.10/2.61 Derived: fFalse = scratc1593517495_amone(A,B) | fTrue = scratc1593517495_amone(A,B). [resolve(965,a,956,a)]. 2.10/2.61 966 gg_bool(scratc1902929298nd_ec3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__62002__14561_ONUM781__thf__4__p_Obnd__ec3) # label(axiom). [clausify(567)]. 2.10/2.61 Derived: fFalse = scratc1902929298nd_ec3(A,B,C) | fTrue = scratc1902929298nd_ec3(A,B,C). [resolve(966,a,956,a)]. 2.10/2.61 967 gg_bool(scratc683290802_d_not(A)) # label(gsy_c_Scratch__tptp__translate__62002__14561_ONUM781__thf__4__p_Obnd__d__not) # label(axiom). [clausify(571)]. 2.10/2.61 Derived: fFalse = scratc683290802_d_not(A) | fTrue = scratc683290802_d_not(A). [resolve(967,a,956,a)]. 7.82/8.06 968 gg_bool(aa_bool_bool(A,B)) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom). [clausify(664)]. 7.82/8.06 Derived: fFalse = aa_bool_bool(A,B) | fTrue = aa_bool_bool(A,B). [resolve(968,a,956,a)]. 7.82/8.06 969 gg_bool(scratc575825622_d_and(A,B)) # label(gsy_c_Scratch__tptp__translate__62002__14561_ONUM781__thf__4__p_Obnd__d__and) # label(axiom). [clausify(830)]. 7.82/8.06 Derived: fFalse = scratc575825622_d_and(A,B) | fTrue = scratc575825622_d_and(A,B). [resolve(969,a,956,a)]. 7.82/8.06 970 pp(scratc575825622_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1936631369nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc1936631369nd_imp,B),A))) | -scratc1469967072_l_iff(A,B) # label(fact_def__l__iff) # label(axiom). [clausify(183)]. 7.82/8.06 971 -pp(scratc575825622_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1936631369nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc1936631369nd_imp,B),A))) | scratc1469967072_l_iff(A,B) # label(fact_def__l__iff) # label(axiom). [clausify(183)]. 7.82/8.06 972 pp(scratc683290802_d_not(scratc683290802_d_not(A))) | -scratc2051767643nd_wel(A) # label(fact_def__wel) # label(axiom). [clausify(193)]. 7.82/8.06 973 -pp(scratc683290802_d_not(scratc683290802_d_not(A))) | scratc2051767643nd_wel(A) # label(fact_def__wel) # label(axiom). [clausify(193)]. 7.82/8.06 974 -scratc2051767643nd_wel(A) | pp(A) # label(fact_l__et) # label(axiom). [clausify(639)]. 7.82/8.06 Derived: pp(A) | -pp(scratc683290802_d_not(scratc683290802_d_not(A))). [resolve(974,a,973,b)]. 7.82/8.06 975 scratc1315180557d_r_ec(A,B) | pp(A) # label(fact_def__r__ec) # label(axiom). [clausify(502)]. 7.82/8.06 976 -scratc1315180557d_r_ec(A,B) | -pp(A) | pp(scratc683290802_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(502)]. 7.82/8.06 977 scratc1315180557d_r_ec(A,B) | -pp(scratc683290802_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(502)]. 7.82/8.06 978 scratc672668580d_orec(A,B) | -pp(scratc575825622_d_and(aa_bool_bool(scratc920901772d_l_or(A),B),scratc920245767d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(880)]. 7.82/8.06 979 -scratc672668580d_orec(A,B) | pp(scratc575825622_d_and(aa_bool_bool(scratc920901772d_l_or(A),B),scratc920245767d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(880)]. 7.82/8.06 7.82/8.06 ============================== end predicate elimination ============= 7.82/8.06 7.82/8.06 Auto_denials: (non-Horn, no changes). 7.82/8.06 7.82/8.06 Term ordering decisions: 7.82/8.06 Function symbol KB weights: aTP_Lamm_kb=1. aTP_Lamm_by=1. scratc1051890711d_n_eq=1. scratc1052153109d_n_is=1. scratc1474950154_lessf=1. scratc1936368966nd_iii=1. scratc1821271950_moref=1. scratc2072369992_29_ii=1. scratc1405965288bnd_in=1. scratc1321908992rdsucc=1. scratc379588518lessis=1. scratc1405440498bnd_ap=1. scratc513572130moreis=1. scratc1882202790nd_n_1=1. aTP_Lamm_aq=1. scratc379326120lesseq=1. scratc1821271961_moreq=1. scratc1977151710nd_nat=1. scratc523788228_Sigma=1. scratc559650040ptyset=1. scratc1051956311d_n_fr=1. scratc1894799050nd_den=1. scratc392288474d_d_Pi=1. scratc1977676501nd_nis=1. scratc1978463683nd_num=1. scratc2093768511n_some=1. fFalse=1. scratc1475014226_nat_p=1. scratc986305058_power=1. scratc1936631369nd_imp=1. scratc89572337d_frac=1. scratc760268562d_repl=1. fTrue=1. scratc799446_n_all=1. scratc1313072605d_pair=1. aTP_Lamm_ah=1. scratc1361989810d_Subq=1. scratc1114818896_proj0=1. scratc1493566924_union=1. scratc1780638511_rt_is=1. scratc1882202791nd_n_2=1. scratc2010197730nd_rat=1. scratc48604636closed=1. aTP_Lamm_an=1. scratc1052153104d_n_in=1. scratc1114818897_proj1=1. aTP_Lamm_aak=1. aTP_Lamm_am=1. scratc1024683930closed=1. scratc1189416944closed=1. scratc179666987_d_1to=1. aTP_Lamm_a=1. aTP_Lamm_aa=1. aTP_Lamm_aab=1. aTP_Lamm_aaf=1. aTP_Lamm_aag=1. aTP_Lamm_ag=1. aTP_Lamm_gb=1. aTP_Lamm_gd=1. aTP_Lamm_gg=1. aTP_Lamm_kn=1. aTP_Lamm_ll=1. aTP_Lamm_ln=1. aTP_Lamm_lx=1. aTP_Lamm_lz=1. aTP_Lamm_mb=1. aTP_Lamm_md=1. aTP_Lamm_mf=1. aTP_Lamm_mh=1. aTP_Lamm_mj=1. aTP_Lamm_ml=1. aTP_Lamm_mv=1. aTP_Lamm_mx=1. aTP_Lamm_ns=1. aTP_Lamm_sa=1. aTP_Lamm_sc=1. aTP_Lamm_se=1. aTP_Lamm_sg=1. aTP_Lamm_si=1. aTP_Lamm_sk=1. aTP_Lamm_sm=1. aTP_Lamm_so=1. aTP_Lamm_xj=1. aTP_Lamm_xl=1. aTP_Lamm_xn=1. aTP_Lamm_xp=1. aTP_Lamm_xr=1. aTP_Lamm_xt=1. aTP_Lamm_xv=1. aTP_Lamm_xx=1. aTP_Lamm_xz=1. aTP_Lamm_yb=1. aTP_Lamm_yd=1. aTP_Lamm_yf=1. scratc1079507897closed=1. scratc1483302902_prop2=1. scratc2088746605d_Inj1=1. scratc284474110_omega=1. scratc682452588_prop2=1. aTP_Lamm_aae=1. aTP_Lamm_ao=1. aTP_Lamm_bn=1. aTP_Lamm_bp=1. aTP_Lamm_bq=1. aTP_Lamm_ca=1. aTP_Lamm_ce=1. aTP_Lamm_ci=1. aTP_Lamm_cm=1. aTP_Lamm_cq=1. aTP_Lamm_cu=1. aTP_Lamm_cy=1. aTP_Lamm_dc=1. aTP_Lamm_dg=1. aTP_Lamm_dk=1. aTP_Lamm_dn=1. aTP_Lamm_dq=1. aTP_Lamm_dt=1. aTP_Lamm_dw=1. aTP_Lamm_dz=1. aTP_Lamm_ec=1. aTP_Lamm_eg=1. aTP_Lamm_ek=1. aTP_Lamm_eo=1. aTP_Lamm_es=1. aTP_Lamm_ev=1. aTP_Lamm_ey=1. aTP_Lamm_fb=1. aTP_Lamm_fe=1. aTP_Lamm_fh=1. aTP_Lamm_fk=1. aTP_Lamm_fn=1. aTP_Lamm_fq=1. aTP_Lamm_fs=1. aTP_Lamm_fw=1. aTP_Lamm_fz=1. aTP_Lamm_gk=1. aTP_Lamm_go=1. aTP_Lamm_gs=1. aTP_Lamm_gw=1. aTP_Lamm_ha=1. aTP_Lamm_he=1. aTP_Lamm_hi=1. aTP_Lamm_hm=1. aTP_Lamm_hq=1. aTP_Lamm_ht=1. aTP_Lamm_hw=1. aTP_Lamm_hz=1. aTP_Lamm_ic=1. aTP_Lamm_if=1. aTP_Lamm_ii=1. aTP_Lamm_im=1. aTP_Lamm_iq=1. aTP_Lamm_iu=1. aTP_Lamm_iy=1. aTP_Lamm_jb=1. aTP_Lamm_je=1. aTP_Lamm_jh=1. aTP_Lamm_jk=1. aTP_Lamm_jn=1. aTP_Lamm_jq=1. aTP_Lamm_js=1. aTP_Lamm_ju=1. aTP_Lamm_jx=1. aTP_Lamm_jz=1. aTP_Lamm_kd=1. aTP_Lamm_kg=1. aTP_Lamm_kk=1. aTP_Lamm_kp=1. aTP_Lamm_kr=1. aTP_Lamm_ku=1. aTP_Lamm_kx=1. aTP_Lamm_la=1. aTP_Lamm_ld=1. aTP_Lamm_lg=1. aTP_Lamm_lj=1. aTP_Lamm_lr=1. aTP_Lamm_lv=1. aTP_Lamm_mp=1. aTP_Lamm_mt=1. aTP_Lamm_mz=1. aTP_Lamm_nb=1. aTP_Lamm_nd=1. aTP_Lamm_ng=1. aTP_Lamm_nj=1. aTP_Lamm_nl=1. aTP_Lamm_nn=1. aTP_Lamm_nq=1. aTP_Lamm_nx=1. aTP_Lamm_ob=1. aTP_Lamm_of=1. aTP_Lamm_oj=1. aTP_Lamm_on=1. aTP_Lamm_or=1. aTP_Lamm_ov=1. aTP_Lamm_oz=1. aTP_Lamm_pc=1. aTP_Lamm_pf=1. aTP_Lamm_pi=1. aTP_Lamm_pl=1. aTP_Lamm_po=1. aTP_Lamm_pr=1. aTP_Lamm_pu=1. aTP_Lamm_py=1. aTP_Lamm_qc=1. aTP_Lamm_qg=1. aTP_Lamm_qk=1. aTP_Lamm_qn=1. aTP_Lamm_qq=1. aTP_Lamm_qt=1. aTP_Lamm_qw=1. aTP_Lamm_qz=1. aTP_Lamm_rc=1. aTP_Lamm_rf=1. aTP_Lamm_ri=1. aTP_Lamm_rk=1. aTP_Lamm_rm=1. aTP_Lamm_rp=1. aTP_Lamm_rs=1. aTP_Lamm_rv=1. aTP_Lamm_ry=1. aTP_Lamm_sv=1. aTP_Lamm_sz=1. aTP_Lamm_td=1. aTP_Lamm_th=1. aTP_Lamm_tl=1. aTP_Lamm_tp=1. aTP_Lamm_tt=1. aTP_Lamm_tx=1. aTP_Lamm_ua=1. aTP_Lamm_ud=1. aTP_Lamm_ug=1. aTP_Lamm_uj=1. aTP_Lamm_um=1. aTP_Lamm_up=1. aTP_Lamm_us=1. aTP_Lamm_uv=1. aTP_Lamm_uy=1. aTP_Lamm_vb=1. aTP_Lamm_vf=1. aTP_Lamm_vj=1. aTP_Lamm_vn=1. aTP_Lamm_vr=1. aTP_Lamm_vu=1. aTP_Lamm_vx=1. aTP_Lamm_wa=1. aTP_Lamm_wd=1. aTP_Lamm_wg=1. aTP_Lamm_wj=1. aTP_Lamm_wn=1. aTP_Lamm_wp=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_yh=1. aTP_Lamm_yj=1. aTP_Lamm_yl=1. aTP_Lamm_yn=1. aTP_Lamm_yp=1. aTP_Lamm_yt=1. aTP_Lamm_yv=1. aTP_Lamm_yy=1. aTP_Lamm_zb=1. aTP_Lamm_zd=1. aTP_Lamm_zf=1. aTP_Lamm_zi=1. aTP_Lamm_zk=1. aTP_Lamm_zn=1. aTP_Lamm_zq=1. aTP_Lamm_zt=1. aTP_Lamm_zw=1. aTP_Lamm_zy=1. aTP_Lamm_zz=1. fconj=1. fimplies=1. scratc1048479566d_n_1t=1. scratc1129935629_cond2=1. scratc116591707_n_one=1. scratc1263638928d_Sing=1. scratc1483302901_prop1=1. scratc2088746604d_Inj0=1. scratc682452587_prop1=1. aTP_Lamm_aaa=1. aTP_Lamm_aac=1. aTP_Lamm_aad=1. aTP_Lamm_aah=1. aTP_Lamm_aai=1. aTP_Lamm_aaj=1. aTP_Lamm_aam=1. aTP_Lamm_abj=1. aTP_Lamm_bt=1. aTP_Lamm_bx=1. aTP_Lamm_cb=1. aTP_Lamm_cf=1. aTP_Lamm_cj=1. aTP_Lamm_cn=1. aTP_Lamm_cr=1. aTP_Lamm_cv=1. aTP_Lamm_cz=1. aTP_Lamm_dd=1. aTP_Lamm_dh=1. aTP_Lamm_dl=1. aTP_Lamm_do=1. aTP_Lamm_dr=1. aTP_Lamm_du=1. aTP_Lamm_dx=1. aTP_Lamm_ea=1. aTP_Lamm_ed=1. aTP_Lamm_eh=1. aTP_Lamm_el=1. aTP_Lamm_ep=1. aTP_Lamm_et=1. aTP_Lamm_ew=1. aTP_Lamm_ez=1. aTP_Lamm_fc=1. aTP_Lamm_ff=1. aTP_Lamm_fi=1. aTP_Lamm_fl=1. aTP_Lamm_fo=1. aTP_Lamm_fr=1. aTP_Lamm_ft=1. aTP_Lamm_fx=1. aTP_Lamm_ga=1. aTP_Lamm_gc=1. aTP_Lamm_ge=1. aTP_Lamm_gh=1. aTP_Lamm_gl=1. aTP_Lamm_gp=1. aTP_Lamm_gt=1. aTP_Lamm_gx=1. aTP_Lamm_hb=1. aTP_Lamm_hf=1. aTP_Lamm_hj=1. aTP_Lamm_hn=1. aTP_Lamm_hr=1. aTP_Lamm_hu=1. aTP_Lamm_hx=1. aTP_Lamm_ia=1. aTP_Lamm_id=1. aTP_Lamm_ig=1. aTP_Lamm_ij=1. aTP_Lamm_in=1. aTP_Lamm_ir=1. aTP_Lamm_iv=1. aTP_Lamm_iz=1. aTP_Lamm_jc=1. aTP_Lamm_jf=1. aTP_Lamm_ji=1. aTP_Lamm_jl=1. aTP_Lamm_jo=1. aTP_Lamm_jr=1. aTP_Lamm_jt=1. aTP_Lamm_jv=1. aTP_Lamm_jy=1. aTP_Lamm_ka=1. aTP_Lamm_ke=1. aTP_Lamm_kh=1. aTP_Lamm_kl=1. aTP_Lamm_ko=1. aTP_Lamm_kq=1. aTP_Lamm_ks=1. aTP_Lamm_kv=1. aTP_Lamm_ky=1. aTP_Lamm_lb=1. aTP_Lamm_le=1. aTP_Lamm_lh=1. aTP_Lamm_lk=1. aTP_Lamm_lm=1. aTP_Lamm_lo=1. aTP_Lamm_ls=1. aTP_Lamm_lw=1. aTP_Lamm_ly=1. aTP_Lamm_ma=1. aTP_Lamm_mc=1. aTP_Lamm_me=1. aTP_Lamm_mg=1. aTP_Lamm_mi=1. aTP_Lamm_mk=1. aTP_Lamm_mm=1. aTP_Lamm_mq=1. aTP_Lamm_mu=1. aTP_Lamm_mw=1. aTP_Lamm_my=1. aTP_Lamm_na=1. aTP_Lamm_nc=1. aTP_Lamm_ne=1. aTP_Lamm_nh=1. aTP_Lamm_nk=1. aTP_Lamm_nm=1. aTP_Lamm_no=1. aTP_Lamm_nr=1. aTP_Lamm_nt=1. aTP_Lamm_nu=1. aTP_Lamm_ny=1. aTP_Lamm_oc=1. aTP_Lamm_og=1. aTP_Lamm_ok=1. aTP_Lamm_oo=1. aTP_Lamm_os=1. aTP_Lamm_ow=1. aTP_Lamm_pa=1. aTP_Lamm_pd=1. aTP_Lamm_pg=1. aTP_Lamm_pj=1. aTP_Lamm_pm=1. aTP_Lamm_pp=1. aTP_Lamm_ps=1. aTP_Lamm_pv=1. aTP_Lamm_pz=1. aTP_Lamm_qd=1. aTP_Lamm_qh=1. aTP_Lamm_ql=1. aTP_Lamm_qo=1. aTP_Lamm_qr=1. aTP_Lamm_qu=1. aTP_Lamm_qx=1. aTP_Lamm_ra=1. aTP_Lamm_rd=1. aTP_Lamm_rg=1. aTP_Lamm_rj=1. aTP_Lamm_rl=1. aTP_Lamm_rn=1. aTP_Lamm_ro=1. aTP_Lamm_rq=1. aTP_Lamm_rr=1. aTP_Lamm_rt=1. aTP_Lamm_ru=1. aTP_Lamm_rw=1. aTP_Lamm_rx=1. aTP_Lamm_rz=1. aTP_Lamm_sb=1. aTP_Lamm_sd=1. aTP_Lamm_sf=1. aTP_Lamm_sh=1. aTP_Lamm_sj=1. aTP_Lamm_sl=1. aTP_Lamm_sn=1. aTP_Lamm_sp=1. aTP_Lamm_sq=1. aTP_Lamm_sr=1. aTP_Lamm_ss=1. aTP_Lamm_sw=1. aTP_Lamm_ta=1. aTP_Lamm_te=1. aTP_Lamm_ti=1. aTP_Lamm_tm=1. aTP_Lamm_tq=1. aTP_Lamm_tu=1. aTP_Lamm_ty=1. aTP_Lamm_ub=1. aTP_Lamm_ue=1. aTP_Lamm_uh=1. aTP_Lamm_uk=1. aTP_Lamm_un=1. aTP_Lamm_uq=1. aTP_Lamm_ut=1. aTP_Lamm_uw=1. aTP_Lamm_uz=1. aTP_Lamm_vc=1. aTP_Lamm_vg=1. aTP_Lamm_vk=1. aTP_Lamm_vo=1. aTP_Lamm_vs=1. aTP_Lamm_vv=1. aTP_Lamm_vy=1. aTP_Lamm_wb=1. aTP_Lamm_we=1. aTP_Lamm_wh=1. aTP_Lamm_wk=1. aTP_Lamm_wl=1. aTP_Lamm_wm=1. aTP_Lamm_wo=1. aTP_Lamm_wq=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_xk=1. aTP_Lamm_xm=1. aTP_Lamm_xo=1. aTP_Lamm_xq=1. aTP_Lamm_xs=1. aTP_Lamm_xu=1. aTP_Lamm_xw=1. aTP_Lamm_xy=1. aTP_Lamm_ya=1. aTP_Lamm_yc=1. aTP_Lamm_ye=1. aTP_Lamm_yg=1. aTP_Lamm_yi=1. aTP_Lamm_yk=1. aTP_Lamm_ym=1. aTP_Lamm_yo=1. aTP_Lamm_yq=1. aTP_Lamm_yu=1. aTP_Lamm_yw=1. aTP_Lamm_yz=1. aTP_Lamm_zc=1. aTP_Lamm_ze=1. aTP_Lamm_zg=1. aTP_Lamm_zj=1. aTP_Lamm_zl=1. aTP_Lamm_zm=1. aTP_Lamm_zo=1. aTP_Lamm_zp=1. aTP_Lamm_zr=1. aTP_Lamm_zs=1. aTP_Lamm_zu=1. aTP_Lamm_zv=1. aTP_Lamm_zx=1. fequal_TPTP_ind=1. scratc1048545165d_n_2t=1. scratc1129935628_cond1=1. scratc1908071008univof=1. scratc1975577328nd_nIn=1. scratc476687568_d_Unj=1. aTP_Lamm_ab=1. aTP_Lamm_aj=1. aTP_Lamm_ap=1. aTP_Lamm_br=1. aTP_Lamm_bs=1. bool=1. scratc1048479561d_n_1o=1. scratc1115212494_prop4=1. scratc1178658963pair_p=1. scratc1311015950r1type=1. scratc1404736349d_plus=1. scratc1476779814_prop1=1. scratc1483302904_prop4=1. scratc1653211885_prop1=1. scratc1859176937_prop1=1. scratc1865462474_empty=1. scratc1953044276428_id=1. scratc2071665076_prop1=1. scratc300055464_prop1=1. scratc68269075rt_nis=1. scratc778423971_times=1. scratc845245027nempty=1. scratc925090592munion=1. scratc94090412_prop1=1. scratc1231767513d_xout=1. scratc16727572d_fixf=1. scratc1780638506_rt_in=1. scratc1936696958nd_inf=1. scratc2108549948rt_all=1. scratc248853832d_i1_s=1. scratc25180068let_u0=1. scratc536789081t_some=1. scratc543506174d_1out=1. scratc76858561rt_one=1. scratc829242165_class=1. scratc848379288air_u0=1. scratc903018905_ratof=1. scratc903099694_428_g=1. scratc936929700d_24_g=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. scratc575825622_d_and=1. aa_fun1431113780TP_ind=1. aa_boo1142376798l_bool=1. aa_TPT1123896796d_bool=1. scratc1405965280bnd_if=1. scratc920245767d_l_ec=1. aa_fun1212484691d_bool=1. scratc1533492743d_e_in=1. scratc1936696956nd_ind=1. aa_TPT1791839040TP_ind=1. aa_TPT985247859d_bool=1. scratc211927547d_pair=1. aa_fun987228051d_bool=1. scratc1593517495_amone=1. scratc1198944151second=1. scratc2003976952_image=1. scratc2046619021_first=1. aa_TPT125613450d_bool=1. scratc1978070090nd_non=1. aa_fun1913827119d_bool=1. scratc448820014d_anec=1. aa_fun1107270209d_bool=1. aa_fun845057962d_bool=1. scratc1902929359nd_ecp=1. scratc410049685_ecect=1. scratc410640076_ecelt=1. scratc719917262eplSep=1. scratc1902929363nd_ect=1. scratc1986725195nd_out=1. scratc59674897fixfu2=1. aa_TPT1781712639TP_ind=1. aa_TPT2142672771l_bool=1. aa_fun1235454963TP_ind=1. cOMBB_658106424TP_ind=1. cOMBS_2003118649l_bool=1. scratc1090352130eft1to=1. scratc156456688etprop=1. scratc2095335265_fixfu=1. scratc283046675ght1to=1. scratc439728220wissel=1. scratc456499546ectelt=1. scratc571701423ectset=1. scratc252181848d_invf=1. scratc255918379d_tofs=1. scratc677818769unmore=1. scratc720156685nverse=1. f11=1. f19=1. f22=1. f24=1. f25=1. scratc91799413all_of=1. scratc1052612295d_n_pl=1. scratc1052874698d_n_ts=1. scratc1052612289d_n_pf=1. scratc1052874685d_n_tf=1. scratc683290802_d_not=1. scratc1533492748d_e_is=1. scratc1349943869l_some=1. scratc459574173_d_Sep=1. scratc1465976678d_esti=1. scratc1841546987ffprop=1. scratc920901772d_l_or=1. scratc1870473726nd_all=1. scratc1986265987nd_one=1. aTP_Lamm_af=1. scratc698437091d_outn=1. scratc780983997_rec_G=1. aTP_Lamm_aat=1. aTP_Lamm_lp=1. aTP_Lamm_lt=1. aTP_Lamm_mn=1. aTP_Lamm_mr=1. scratc13795140_367_w=1. aTP_Lamm_aal=1. aTP_Lamm_abh=1. aTP_Lamm_ak=1. aTP_Lamm_ar=1. aTP_Lamm_bb=1. aTP_Lamm_bj=1. aTP_Lamm_bw=1. aTP_Lamm_cc=1. aTP_Lamm_cg=1. aTP_Lamm_ck=1. aTP_Lamm_co=1. aTP_Lamm_cs=1. aTP_Lamm_cw=1. aTP_Lamm_da=1. aTP_Lamm_de=1. aTP_Lamm_di=1. aTP_Lamm_ee=1. aTP_Lamm_ei=1. aTP_Lamm_em=1. aTP_Lamm_eq=1. aTP_Lamm_fu=1. aTP_Lamm_fy=1. aTP_Lamm_gi=1. aTP_Lamm_gm=1. aTP_Lamm_gq=1. aTP_Lamm_gu=1. aTP_Lamm_gy=1. aTP_Lamm_hc=1. aTP_Lamm_hg=1. aTP_Lamm_hk=1. aTP_Lamm_ho=1. aTP_Lamm_ik=1. aTP_Lamm_io=1. aTP_Lamm_is=1. aTP_Lamm_iw=1. aTP_Lamm_ki=1. aTP_Lamm_kt=1. aTP_Lamm_kw=1. aTP_Lamm_kz=1. aTP_Lamm_lc=1. aTP_Lamm_lf=1. aTP_Lamm_li=1. aTP_Lamm_np=1. aTP_Lamm_nv=1. aTP_Lamm_nz=1. aTP_Lamm_od=1. aTP_Lamm_oh=1. aTP_Lamm_ol=1. aTP_Lamm_op=1. aTP_Lamm_ot=1. aTP_Lamm_ox=1. aTP_Lamm_pw=1. aTP_Lamm_qa=1. aTP_Lamm_qe=1. aTP_Lamm_qi=1. aTP_Lamm_st=1. aTP_Lamm_sx=1. aTP_Lamm_tb=1. aTP_Lamm_tf=1. aTP_Lamm_tj=1. aTP_Lamm_tn=1. aTP_Lamm_tr=1. aTP_Lamm_tv=1. aTP_Lamm_vd=1. aTP_Lamm_vh=1. aTP_Lamm_vl=1. aTP_Lamm_vp=1. aTP_Lamm_wr=1. aTP_Lamm_wu=1. aTP_Lamm_wx=1. aTP_Lamm_xa=1. aTP_Lamm_xd=1. aTP_Lamm_xg=1. aTP_Lamm_yr=1. scratc250935473d_incl=1. aTP_Lamm_abd=1. aTP_Lamm_abf=1. aTP_Lamm_av=1. aTP_Lamm_bf=1. aTP_Lamm_bi=1. aTP_Lamm_bm=1. aTP_Lamm_dm=1. aTP_Lamm_dp=1. aTP_Lamm_ds=1. aTP_Lamm_dv=1. aTP_Lamm_dy=1. aTP_Lamm_eb=1. aTP_Lamm_eu=1. aTP_Lamm_ex=1. aTP_Lamm_fa=1. aTP_Lamm_fd=1. aTP_Lamm_fg=1. aTP_Lamm_fj=1. aTP_Lamm_hs=1. aTP_Lamm_hv=1. aTP_Lamm_hy=1. aTP_Lamm_ib=1. aTP_Lamm_ie=1. aTP_Lamm_ih=1. aTP_Lamm_ja=1. aTP_Lamm_jd=1. aTP_Lamm_jg=1. aTP_Lamm_jj=1. aTP_Lamm_jm=1. aTP_Lamm_jp=1. aTP_Lamm_pb=1. aTP_Lamm_pe=1. aTP_Lamm_ph=1. aTP_Lamm_pk=1. aTP_Lamm_pn=1. aTP_Lamm_pq=1. aTP_Lamm_pt=1. aTP_Lamm_qm=1. aTP_Lamm_qp=1. aTP_Lamm_qs=1. aTP_Lamm_qv=1. aTP_Lamm_qy=1. aTP_Lamm_rb=1. aTP_Lamm_tz=1. aTP_Lamm_uc=1. aTP_Lamm_uf=1. aTP_Lamm_ui=1. aTP_Lamm_ul=1. aTP_Lamm_uo=1. aTP_Lamm_ur=1. aTP_Lamm_uu=1. aTP_Lamm_ux=1. aTP_Lamm_va=1. aTP_Lamm_vt=1. aTP_Lamm_vw=1. aTP_Lamm_vz=1. aTP_Lamm_wc=1. aTP_Lamm_wf=1. aTP_Lamm_wi=1. aTP_Lamm_yx=1. aTP_Lamm_za=1. scratc1116728996ective=1. scratc1903782149nd_eps=1. scratc1936696966nd_inn=1. scratc955832086etprod=1. aTP_Lamm_aan=1. aTP_Lamm_aao=1. aTP_Lamm_aap=1. aTP_Lamm_aar=1. aTP_Lamm_aax=1. aTP_Lamm_aaz=1. aTP_Lamm_aba=1. aTP_Lamm_abe=1. aTP_Lamm_as=1. aTP_Lamm_at=1. aTP_Lamm_au=1. aTP_Lamm_aw=1. aTP_Lamm_ax=1. aTP_Lamm_az=1. aTP_Lamm_ba=1. aTP_Lamm_bg=1. aTP_Lamm_bh=1. aTP_Lamm_bk=1. aTP_Lamm_bz=1. aTP_Lamm_cd=1. aTP_Lamm_ch=1. aTP_Lamm_cl=1. aTP_Lamm_cp=1. aTP_Lamm_ct=1. aTP_Lamm_cx=1. aTP_Lamm_db=1. aTP_Lamm_df=1. aTP_Lamm_dj=1. aTP_Lamm_ef=1. aTP_Lamm_ej=1. aTP_Lamm_en=1. aTP_Lamm_er=1. aTP_Lamm_fm=1. aTP_Lamm_fp=1. aTP_Lamm_fv=1. aTP_Lamm_gf=1. aTP_Lamm_gj=1. aTP_Lamm_gn=1. aTP_Lamm_gr=1. aTP_Lamm_gv=1. aTP_Lamm_gz=1. aTP_Lamm_hd=1. aTP_Lamm_hh=1. aTP_Lamm_hl=1. aTP_Lamm_hp=1. aTP_Lamm_il=1. aTP_Lamm_ip=1. aTP_Lamm_it=1. aTP_Lamm_ix=1. aTP_Lamm_jw=1. aTP_Lamm_kc=1. aTP_Lamm_kf=1. aTP_Lamm_kj=1. aTP_Lamm_km=1. aTP_Lamm_lq=1. aTP_Lamm_lu=1. aTP_Lamm_mo=1. aTP_Lamm_ms=1. aTP_Lamm_nf=1. aTP_Lamm_ni=1. aTP_Lamm_nw=1. aTP_Lamm_oa=1. aTP_Lamm_oe=1. aTP_Lamm_oi=1. aTP_Lamm_om=1. aTP_Lamm_oq=1. aTP_Lamm_ou=1. aTP_Lamm_oy=1. aTP_Lamm_px=1. aTP_Lamm_qb=1. aTP_Lamm_qf=1. aTP_Lamm_qj=1. aTP_Lamm_re=1. aTP_Lamm_rh=1. aTP_Lamm_su=1. aTP_Lamm_sy=1. aTP_Lamm_tc=1. aTP_Lamm_tg=1. aTP_Lamm_tk=1. aTP_Lamm_to=1. aTP_Lamm_ts=1. aTP_Lamm_tw=1. aTP_Lamm_ve=1. aTP_Lamm_vi=1. aTP_Lamm_vm=1. aTP_Lamm_vq=1. aTP_Lamm_ys=1. aTP_Lamm_zh=1. fEx_TPTP_ind=1. scratc1052349889d_n_lb=1. scratc1053717084lbprop=1. scratc1839685631ective=1. scratc1918947691nunion=1. scratc1969414991nd_min=1. aTP_Lamm_aaq=1. aTP_Lamm_aas=1. aTP_Lamm_aau=1. aTP_Lamm_aav=1. aTP_Lamm_aaw=1. aTP_Lamm_aay=1. aTP_Lamm_abb=1. aTP_Lamm_abc=1. aTP_Lamm_abg=1. aTP_Lamm_abi=1. aTP_Lamm_ay=1. scratc1925936612first1=1. scratc418274606_UPair=1. scratc447680842In_rec=1. scratc680694164_pair1=1. scratc96237146econd1=1. aTP_Lamm_ac=1. aTP_Lamm_ad=1. aTP_Lamm_ae=1. aTP_Lamm_ai=1. aTP_Lamm_al=1. aTP_Lamm_bc=1. aTP_Lamm_bd=1. aTP_Lamm_be=1. aTP_Lamm_bl=1. aTP_Lamm_bo=1. aTP_Lamm_bu=1. aTP_Lamm_bv=1. cOMBC_1555011498d_bool=1. scratc104586080t_disj=1. scratc1115212493_prop3=1. scratc1270814762_prop1=1. scratc1300448226ective=1. scratc1835233233tminus=1. scratc318085118_prop1=1. scratc856707564367_vo=1. scratc888417639_prop1=1. scratc906447293_prop1=1. undefined_bool=1. scratc1052415500d_n_mn=1. scratc1525366659_477_v=1. scratc848116892air_q0=1. undefined_TPTP_ind=1. f2=1. f3=1. f12=1. f13=1. f15=1. f16=1. f18=1. f20=1. f21=1. f23=1. scratc1986528333nd_or3=1. scratc1902929298nd_ec3=1. scratc1622814829d_soft=1. scratc1937090551nd_ite=1. scratc1115212491_prop1=1. scratc371056682d_left=1. scratc661733832_indeq=1. scratc1144702773eft_f1=1. scratc1750571112d_11_i=1. scratc95826374sel_wa=1. scratc95826375sel_wb=1. scratc1144702774eft_f2=1. scratc2097018441indrat=1. scratc597406809_right=1. f4=1. f8=1. f9=1. f10=1. f14=1. f17=1. scratc1115212492_prop2=1. scratc180990886_inj_h=1. scratc734115635hangef=1. f1=1. f6=1. f7=1. scratc1229775214_prop1=1. scratc1990668394indeq2=1. f5=1. 31.12/31.42 31.12/31.42 ============================== end of process initial clauses ======== 31.12/31.42 31.12/31.42 ============================== CLAUSES FOR SEARCH ==================== 31.12/31.42 31.12/31.42 ============================== end of clauses for search ============= 31.12/31.42 31.12/31.42 ============================== SEARCH ================================ 31.12/31.42 31.12/31.42 % Starting search at 5.69 seconds. 31.12/31.42 31.12/31.42 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 379 (0.00 of 6.35 sec). 31.12/31.42 31.12/31.42 Low Water (keep): wt=47.000, iters=3672 31.12/31.42 31.12/31.42 Low Water (keep): wt=36.000, iters=3409 31.12/31.42 31.12/31.42 Low Water (keep): wt=35.000, iters=3341 31.12/31.42 31.12/31.42 Low Water (keep): wt=34.000, iters=3397 31.12/31.42 31.12/31.42 Low Water (keep): wt=33.000, iters=3433 31.12/31.42 31.12/31.42 Low Water (keep): wt=32.000, iters=3402 31.12/31.42 31.12/31.42 Low Water (keep): wt=31.000, iters=3341 31.12/31.42 31.12/31.42 Low Water (keep): wt=30.000, iters=3358 31.12/31.42 31.12/31.42 Low Water (keep): wt=29.000, iters=3393 31.12/31.42 31.12/31.42 Low Water (keep): wt=28.000, iters=3430 31.12/31.42 31.12/31.42 Low Water (keep): wt=27.000, iters=3363 31.12/31.42 31.12/31.42 Low Water (keep): wt=25.000, iters=3344 31.12/31.42 31.12/31.42 Low Water (keep): wt=24.000, iters=3334 31.12/31.42 31.12/31.42 Low Water (keep): wt=23.000, iters=3400 31.12/31.42 31.12/31.42 Low Water (keep): wt=21.000, iters=3822 31.12/31.42 31.12/31.42 Low Water (keep): wt=20.000, iters=3395 31.12/31.42 31.12/31.42 Low Water (keep): wt=19.000, iters=3348 31.12/31.42 31.12/31.42 Low Water (keep): wt=18.000, iters=3536 31.12/31.42 31.12/31.42 Low Water (keep): wt=17.000, iters=3456 31.12/31.42 31.12/31.42 Low Water (keep): wt=16.000, iters=3712 31.12/31.42 31.12/31.42 Low Water (keep): wt=15.000, iters=3542 31.12/31.42 31.12/31.42 Low Water (keep): wt=14.000, iters=3478 31.12/31.42 31.12/31.42 Low Water (displace): id=14833, wt=12.000 31.12/31.42 31.12/31.42 Low Water (displace): id=14837, wt=10.000 31.12/31.42 31.12/31.42 Low Water (keep): wt=13.000, iters=3335 31.12/31.42 31.12/31.42 Low Water (displace): id=14880, wt=8.000 31.12/31.42 31.12/31.42 Low Water (keep): wt=12.000, iters=3333 31.12/31.42 31.12/31.42 Low Water (keep): wt=11.000, iters=4591 31.12/31.42 31.12/31.42 Low Water (keep): wt=10.000, iters=3525 31.12/31.42 31.12/31.42 Low Water (displace): id=24697, wt=7.0Alarm clock 119.82/120.09 Prover9 interrupted 119.82/120.09 EOF