0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.12/0.33 % Computer : n018.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 180 0.12/0.33 % DateTime : Thu Aug 29 17:17:52 EDT 2019 0.12/0.33 % CPUTime : 1.46/1.76 ============================== Prover9 =============================== 1.46/1.76 Prover9 (32) version 2009-11A, November 2009. 1.46/1.76 Process 7034 was started by sandbox on n018.cluster.edu, 1.46/1.76 Thu Aug 29 17:17:53 2019 1.46/1.76 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 180 -f /tmp/Prover9_6881_n018.cluster.edu". 1.46/1.76 ============================== end of head =========================== 1.46/1.76 1.46/1.76 ============================== INPUT ================================= 1.46/1.76 1.46/1.76 % Reading from file /tmp/Prover9_6881_n018.cluster.edu 1.46/1.76 1.46/1.76 set(prolog_style_variables). 1.46/1.76 set(auto2). 1.46/1.76 % set(auto2) -> set(auto). 1.46/1.76 % set(auto) -> set(auto_inference). 1.46/1.76 % set(auto) -> set(auto_setup). 1.46/1.76 % set(auto_setup) -> set(predicate_elim). 1.46/1.76 % set(auto_setup) -> assign(eq_defs, unfold). 1.46/1.76 % set(auto) -> set(auto_limits). 1.46/1.76 % set(auto_limits) -> assign(max_weight, "100.000"). 1.46/1.76 % set(auto_limits) -> assign(sos_limit, 20000). 1.46/1.76 % set(auto) -> set(auto_denials). 1.46/1.76 % set(auto) -> set(auto_process). 1.46/1.76 % set(auto2) -> assign(new_constants, 1). 1.46/1.76 % set(auto2) -> assign(fold_denial_max, 3). 1.46/1.76 % set(auto2) -> assign(max_weight, "200.000"). 1.46/1.76 % set(auto2) -> assign(max_hours, 1). 1.46/1.76 % assign(max_hours, 1) -> assign(max_seconds, 3600). 1.46/1.76 % set(auto2) -> assign(max_seconds, 0). 1.46/1.76 % set(auto2) -> assign(max_minutes, 5). 1.46/1.76 % assign(max_minutes, 5) -> assign(max_seconds, 300). 1.46/1.76 % set(auto2) -> set(sort_initial_sos). 1.46/1.76 % set(auto2) -> assign(sos_limit, -1). 1.46/1.76 % set(auto2) -> assign(lrs_ticks, 3000). 1.46/1.76 % set(auto2) -> assign(max_megs, 400). 1.46/1.76 % set(auto2) -> assign(stats, some). 1.46/1.76 % set(auto2) -> clear(echo_input). 1.46/1.76 % set(auto2) -> set(quiet). 1.46/1.76 % set(auto2) -> clear(print_initial_clauses). 1.46/1.76 % set(auto2) -> clear(print_given). 1.46/1.76 assign(lrs_ticks,-1). 1.46/1.76 assign(sos_limit,10000). 1.46/1.76 assign(order,kbo). 1.46/1.76 set(lex_order_vars). 1.46/1.76 clear(print_given). 1.46/1.76 1.46/1.76 % formulas(sos). % not echoed (1290 formulas) 1.46/1.76 1.46/1.76 ============================== end of input ========================== 1.46/1.76 1.46/1.76 % From the command line: assign(max_seconds, 180). 1.46/1.76 1.46/1.76 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 1.46/1.76 1.46/1.76 % Formulas that are not ordinary clauses: 1.46/1.76 1 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mh(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174643062lesseq,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uu),Uub)))))) # label(fact_ATP_Olambda__563) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 2 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_xq,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uu))))) # label(fact_ATP_Olambda__19) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 3 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fr(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fs(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__642) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 4 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_po,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_pn(Uu),Uua))))) # label(fact_ATP_Olambda__409) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 5 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gc(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__570) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 6 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jo,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_jn,Uu))))) # label(fact_ATP_Olambda__182) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 7 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ts,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_tr,Uu))))) # label(fact_ATP_Olambda__94) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 8 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fr(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uuc),Uua))))))) # label(fact_ATP_Olambda__715) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 9 (all X0 all X12 all X22 all X32 (pp(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc628861614bnd_if(X0,X22),X32))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X12),X22))))) # label(fact_k__If__In__then__E) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 10 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ev,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ew,Uu)))) # label(fact_ATP_Olambda__219) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 11 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gi(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__559) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 12 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wy(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__578) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 13 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_qe,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_qf,Uu)))) # label(fact_ATP_Olambda__125) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 14 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uuc),Uua))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_wi(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__713) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 15 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_aai,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_aaj,Uu)))) # label(fact_ATP_Olambda__35) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 16 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_uz,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_uy,Uu))))) # label(fact_ATP_Olambda__86) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 17 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ne,Uu),Uua)) <-> (pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039435_moreq,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uu),Uua))))) # label(fact_ATP_Olambda__332) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 18 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ec(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_eb(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__648) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 19 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174643062lesseq,X),Xa)) <-> pp(aa_bool_bool(scratc1112669246d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,X),Xa))))) # label(fact_def__lesseq) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 20 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc59543998etprop(X,Xa),Xb),Xc)) <-> pp(scratc371142564_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1890899764d_esti(X),Xc),Xa),scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1890899764d_esti(X),Xc),Xb)))))) # label(fact_def__nissetprop) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 21 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ob,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_oa,Uu))))) # label(fact_ATP_Olambda__145) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 22 (all X all Xa (pp(aa_fun171081125l_bool(scratc413789423l_some(X),Xa)) <-> pp(scratc478607744_d_not(aa_fun171081125l_bool(scratc1303128615all_of(aa_TPT43085870d_bool(aTP_Lamm_au,X)),scratc1721520380nd_non(X,Xa)))))) # label(fact_def__l__some) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 23 -(exists X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X0),scratc1354028742ptyset))) # label(fact_k__EmptyAx) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 24 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ci,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ch,Uu))))) # label(fact_ATP_Olambda__240) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 25 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1303128615all_of(aa_TPT43085870d_bool(aTP_Lamm_au,X0)),aa_TPT43085870d_bool(aTP_Lamm_abx(X0),X12)))) # label(fact_firstis1) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 26 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_aav,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_aaw,Uu)))) # label(fact_ATP_Olambda__30) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 27 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jh,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_jg(Uu),Uua))))) # label(fact_ATP_Olambda__442) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 28 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_yw,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_yx,Uu)))) # label(fact_ATP_Olambda__52) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 29 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ka,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_jz,Uu))))) # label(fact_ATP_Olambda__179) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 30 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ox,Uu),Uua)))) # label(fact_ATP_Olambda__302) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 31 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ja(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uu),Uua))))) # label(fact_ATP_Olambda__520) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 32 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hp,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ho(Uu),Uua))))) # label(fact_ATP_Olambda__454) # label(axiom) # label(non_clause). [assumption]. 1.46/1.76 33 (all X all Xa (pp(scratc371142564_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,Xa),scratc159642228nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,X)),aa_TPTP_ind_bool(scratc190454329_prop1,Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc190454330_prop2,X),Xa)))) # label(fact_def__d__24__prop2) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 34 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_nw(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nx(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__622) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 35 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_jk,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_jl,Uu)))) # label(fact_ATP_Olambda__183) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 36 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sj(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uua),Uub)))))) # label(fact_ATP_Olambda__525) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 37 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hc,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_hb,Uu))))) # label(fact_ATP_Olambda__201) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 38 (all X aa_TPTP_ind_TPTP_ind(scratc1656690599d_xout,X) = aa_TPTP_ind_TPTP_ind(scratc1123360177d_outn(X),X)) # label(fact_def__xout) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 39 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_nc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_nd,Uu)))) # label(fact_ATP_Olambda__155) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 40 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_acg(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(Uua,aa_TPTP_ind_TPTP_ind(scratc1725260217d_e_in(Uu,Uua),Uub))))) # label(fact_ATP_Olambda__656) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 41 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_kp,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_kq,Uu)))) # label(fact_ATP_Olambda__174) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 42 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kx,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uu),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uu),Uua))))) # label(fact_ATP_Olambda__338) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 43 (all X all Xa all Xb (pp(aa_bool_bool(scratc1112669246d_l_or(X),aa_bool_bool(scratc1112669246d_l_or(Xa),Xb))) <-> pp(scratc1729978623nd_or3(X,Xa,Xb)))) # label(fact_def__or3) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 44 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_uu,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_ut(Uu),Uua))))) # label(fact_ATP_Olambda__380) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 45 (all X all Xa all Xb (pp(aa_fun171081125l_bool(scratc1613924016nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bd(X),Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc898964782t_disj(X),Xa),Xb)))) # label(fact_def__st__disj) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 46 (all X0 (pp(aa_TPTP_ind_bool(scratc1270331168_nat_p,X0)) -> pp(aa_TPTP_ind_bool(scratc1270331168_nat_p,aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,X0))))) # label(fact_nat__ordsucc) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 47 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc942939880t_more,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cp,Uu),Uua)))) # label(fact_ATP_Olambda__292) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 48 (all X all Xa (pp(scratc371142564_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,Xa),scratc159642228nd_n_1)),X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1421322151_prop1,X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1421322152_prop2,X),Xa)))) # label(fact_def__d__428__prop2) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 49 (all X all Xa all Xb all Xc all Xd all Xe all Xf (pp(scratc371142564_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1890899764d_esti(X),Xf),aa_TPTP_ind_TPTP_ind(scratc601817159_ecect(X,Xa),Xd)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725260222d_e_is(Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,Xc),Xf)),Xe))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc737776956_prop1(X,Xa,Xb,Xc,Xd),Xe),Xf)))) # label(fact_def__d__10__prop1) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 50 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_abn,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1721126791nd_nis,aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uu)),scratc159642228nd_n_1)))) # label(fact_ATP_Olambda__16) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 51 (all X scratc628861622bnd_in = scratc1890899764d_esti(X)) # label(fact_def__esti) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 52 (all B_1 all B_2 gg_bool(scratc1785284969_amone(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__63821__3484_ONUM790__thf__4__p_Obnd__amone) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 53 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_pc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_pd,Uu)))) # label(fact_ATP_Olambda__132) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 54 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vz(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__546) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 55 (all X all Xa all Xb scratc1647232439nd_eps(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ca(X),Xa),Xb)) = aa_TPTP_ind_TPTP_ind(scratc628861614bnd_if(X,Xa),Xb)) # label(fact_def__if) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 56 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_aay,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_aaz,Uu)))) # label(fact_ATP_Olambda__29) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 57 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xs,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__340) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 58 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_es,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_et,Uu)))) # label(fact_ATP_Olambda__220) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 59 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hr(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174643062lesseq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174643062lesseq,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174643062lesseq,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uua),Uuc))))))) # label(fact_ATP_Olambda__687) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 60 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc565842745nunion(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1685334398_union,aa_TPTP_ind_TPTP_ind(scratc1212653308_UPair(X),Xa))) # label(fact_def__binunion) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 61 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_if,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ie(Uu),Uua))))) # label(fact_ATP_Olambda__450) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 62 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_mv(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mw,Uu),Uua)))) # label(fact_ATP_Olambda__421) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 63 (all X7 all Y (gg_TPTP_ind(X7) & gg_TPTP_ind(Y) -> -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]. 1.46/1.77 64 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_lk(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ll,Uu),Uua)))) # label(fact_ATP_Olambda__415) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 65 (all Uu all Uua ((pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yo,Uu),Uua)))) # label(fact_ATP_Olambda__330) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 66 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vb(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_va(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__602) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 67 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ms,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039435_moreq,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174643062lesseq,Uua),Uu))))) # label(fact_ATP_Olambda__299) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 68 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc308889072moreis,Uua),aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uu)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tr,Uu),Uua)))) # label(fact_ATP_Olambda__287) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 69 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ir,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_iq(Uu),Uua))))) # label(fact_ATP_Olambda__447) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 70 (all Uu (pp(aa_fun171081125l_bool(scratc1729716277nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc584055948d_d_Pi,scratc1720602000nd_nat),aTP_Lamm_al)),aa_TPT43085870d_bool(aTP_Lamm_td,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_te,Uu)))) # label(fact_ATP_Olambda__8) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 71 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_my(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039435_moreq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uu),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uua),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039435_moreq,Uub),Uuc))))))) # label(fact_ATP_Olambda__695) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 72 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pr(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_pq(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__617) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 73 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_rh,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ri,Uu)))) # label(fact_ATP_Olambda__116) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 74 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc677104934d_invf(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1318166930_Sigma,Xa),scratc2047737915d_soft(X,Xa,Xb))) # label(fact_def__invf) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 75 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_vp,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_vo,Uu))))) # label(fact_ATP_Olambda__81) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 76 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jx(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jy(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__628) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 77 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lw,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uua),Uu)))) # label(fact_ATP_Olambda__344) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 78 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_ws,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_wt,Uu)))) # label(fact_ATP_Olambda__72) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 79 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_fx,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fy,Uu)))) # label(fact_ATP_Olambda__211) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 80 (all B_1 all B_2 all B_3 gg_bool(scratc1646379588nd_ec3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__63821__3484_ONUM790__thf__4__p_Obnd__ec3) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 81 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ty(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tz(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__609) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 82 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_gp,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_gq,Uu)))) # label(fact_ATP_Olambda__205) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 83 (all X all Xa (pp(aa_fun171081125l_bool(scratc1729716277nd_one(X),Xa)) <-> pp(scratc371142564_d_and(scratc1785284969_amone(X,Xa),aa_fun171081125l_bool(scratc413789423l_some(X),Xa))))) # label(fact_def__one) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 84 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_kj,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_kk,Uu)))) # label(fact_ATP_Olambda__176) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 85 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ez,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ey,Uu))))) # label(fact_ATP_Olambda__218) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 86 (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]. 1.46/1.77 87 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc873743100d_anec(X,Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc413789423l_some(X),aa_TPT43085870d_bool(scratc1646379649nd_ecp(X,Xa),Xb))))) # label(fact_def__anec) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 88 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_og,Uu),Uua)) <-> pp(scratc1729978623nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uu),Uua))))) # label(fact_ATP_Olambda__257) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 89 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ki(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__572) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 90 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_mr,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_mq,Uu))))) # label(fact_ATP_Olambda__159) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 91 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ov,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ou(Uu),Uua))))) # label(fact_ATP_Olambda__417) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 92 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X22),aa_fun1431113780TP_ind(scratc254891115_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X22),X0)))) # label(fact_k__SepE1) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 93 (all B_1 gg_bool(fEx_TPTP_ind(B_1))) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 94 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vf,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_ve(Uu),Uua))))) # label(fact_ATP_Olambda__377) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 95 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_du(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dv,Uu),Uua)))) # label(fact_ATP_Olambda__480) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 96 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xw(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,Uu),Uub)))))) # label(fact_ATP_Olambda__548) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 97 (all Uu all Uua ((pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039435_moreq,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nk,Uu),Uua)))) # label(fact_ATP_Olambda__334) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 98 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_hp,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_hq,Uu)))) # label(fact_ATP_Olambda__196) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 99 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_abf,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1721126791nd_nis,aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__13) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 100 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fi,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_fh,Uu))))) # label(fact_ATP_Olambda__215) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 101 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_gl(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gm,Uu),Uua)))) # label(fact_ATP_Olambda__460) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 102 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_op,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_oo,Uu))))) # label(fact_ATP_Olambda__135) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 103 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_tm,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_tl,Uu))))) # label(fact_ATP_Olambda__97) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 104 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_vs,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_vr,Uu))))) # label(fact_ATP_Olambda__80) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 105 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X33),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,aa_TPTP_ind_TPTP_ind(X22,X33)),aa_TPTP_ind_TPTP_ind(X12,X33)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1318166930_Sigma,X0),X22)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc584055948d_d_Pi,X0),X12))))) # label(fact_lam__Pi) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 106 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_mb(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mc,Uu),Uua)))) # label(fact_ATP_Olambda__426) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 107 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cg,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cf,Uu))))) # label(fact_ATP_Olambda__241) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 108 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(X),Xa)),Xb)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(X),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Xa),Xb)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc778816504_prop1(X),Xa),Xb)))) # label(fact_def__d__25__prop1) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 109 (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(scratc1725260222d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,Uub),Uud)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_az(Uu),Uua),Uub),Uuc),Uud)))) # label(fact_ATP_Olambda__735) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 110 (all X all Xa all Xb (scratc873677453d_and3(scratc1112013241d_l_ec(X,Xa),scratc1112013241d_l_ec(Xa,Xb),scratc1112013241d_l_ec(Xb,X)) <-> pp(scratc1646379588nd_ec3(X,Xa,Xb)))) # label(fact_def__ec3) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 111 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sd(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__565) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 112 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_zk,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_zl,Uu)))) # label(fact_ATP_Olambda__45) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 113 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_zb,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_za,Uu))))) # label(fact_ATP_Olambda__50) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 114 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_as,Uu),Uua)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1680081659nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920578d_n_in,Uua),Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920578d_n_in,aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uua)),Uu))))) # label(fact_ATP_Olambda__283) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 115 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_md,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_mc,Uu))))) # label(fact_ATP_Olambda__164) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 116 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ft,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_fs(Uu),Uua))))) # label(fact_ATP_Olambda__466) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 117 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ix(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uu),Uua))))) # label(fact_ATP_Olambda__512) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 118 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jt(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uua),Uuc))))))) # label(fact_ATP_Olambda__720) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 119 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc154197684eft1to(X,Xa),Xb) = aa_TPTP_ind_TPTP_ind(scratc1123360177d_outn(X),aa_TPTP_ind_TPTP_ind(scratc1680147256nd_inn(Xa),Xb))) # label(fact_def__left1to) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 120 (all X all Xa (pp(aa_fun171081125l_bool(scratc413789423l_some(scratc514495423d_frac),aa_TPT43085870d_bool(aTP_Lamm_ad(X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,X),Xa)))) # label(fact_def__rt__less) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 121 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_pm(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pn(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__618) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 122 (all X all Xa all Xb (pp(scratc371142564_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc726999126ective(X),Xa),Xb),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1742772941ective(X),Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc910718356ective(X),Xa),Xb)))) # label(fact_def__bijective) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 123 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_yh,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_yg,Uu))))) # label(fact_ATP_Olambda__59) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 124 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_tw,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uu)),scratc159642228nd_n_1)))) # label(fact_ATP_Olambda__15) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 125 (all B_1 all B_2 all B_3 gg_bool(scratc1729978623nd_or3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__63821__3484_ONUM790__thf__4__p_Obnd__or3) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 126 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_sh,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_si,Uu)))) # label(fact_ATP_Olambda__108) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 127 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qn,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_qm(Uu),Uua))))) # label(fact_ATP_Olambda__402) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 128 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_xi,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_xj,Uu)))) # label(fact_ATP_Olambda__67) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 129 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_pa(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pb(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__621) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 130 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_or,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_oq,Uu))))) # label(fact_ATP_Olambda__134) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 131 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc795979768d_left(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(scratc1939081475eft_f1(X,Xa,Xb),Xc)) = aa_TPTP_ind_TPTP_ind(scratc1939081476eft_f2(X,Xa,Xb),Xc)) # label(fact_def__left__f2) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 132 (all X aa_TPT1424761345TP_ind(scratc628336832bnd_ap,aa_TPTP_ind_TPTP_ind(scratc970191445_times,X)) = scratc1244642172d_n_ts(X)) # label(fact_def__n__ts) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 133 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uua),Uu))))) # label(fact_ATP_Olambda__290) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 134 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc853501306_indeq(X,Xa,Xb),Xc),Xd) = scratc1680147246nd_ind(Xb,aa_TPT43085870d_bool(scratc1306979966_prop2(X,Xa,Xb,Xc),Xd))) # label(fact_def__indeq) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 135 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_el,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_em,Uu)))) # label(fact_ATP_Olambda__222) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 136 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bc(Uu),Uua),Uub),Uuc)) <-> pp(aa_fun171081125l_bool(scratc413789423l_some(Uua),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bb(Uu),Uub),Uuc))))) # label(fact_ATP_Olambda__731) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 137 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aav,Uu),Uua)))) # label(fact_ATP_Olambda__274) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 138 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039435_moreq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_me(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__553) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 139 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_tg,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_tf,Uu))))) # label(fact_ATP_Olambda__100) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 140 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc2146397332sel_wa(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc1680540841nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725260222d_e_is(X),Xc),Xa),X,Xb),Xc)) # label(fact_def__wissel__wa) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 141 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ace(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc48260778_image(aa_fun1431113780TP_ind(scratc254891115_d_Sep(Uu),Uua),Uu),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1318166930_Sigma,aa_fun1431113780TP_ind(scratc254891115_d_Sep(Uu),Uua)),scratc1725260217d_e_in(Uu,Uua))),Uub))))) # label(fact_ATP_Olambda__585) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 142 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc308889072moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc308889072moreis,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wf(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__541) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 143 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc308889072moreis,X),Xa)) <-> pp(aa_bool_bool(scratc1112669246d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,X),Xa))))) # label(fact_def__moreis) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 144 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tl,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uua),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),scratc159642228nd_n_1))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,Uua),Uu))))) # label(fact_ATP_Olambda__275) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 145 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,Uu),aa_TPTP_ind_TPTP_ind(scratc1178072532_power,scratc1720602000nd_nat))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_abi,Uu)))) # label(fact_ATP_Olambda__20) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 146 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_aau,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),scratc159642228nd_n_1))))) # label(fact_ATP_Olambda__10) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 147 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xb(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__568) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 148 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jt(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ju(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__629) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 149 (all Uu all Uua ((pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc308889072moreis,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yq,Uu),Uua)))) # label(fact_ATP_Olambda__329) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 150 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc849034026lbprop(X),Xa),Xb)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1680081659nd_imp,aa_TPTP_ind_bool(X,Xb)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,Xa),Xb))))) # label(fact_def__lbprop) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 151 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cr,Uu),Uua)) <-> pp(scratc1646379588nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1575955453_rt_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc942939880t_more,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,Uu),Uua))))) # label(fact_ATP_Olambda__258) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 152 (all X all Xa scratc601817159_ecect(X,Xa) = scratc1725260217d_e_in(aa_TPTP_ind_TPTP_ind(scratc1178072532_power,X),scratc873743100d_anec(X,Xa))) # label(fact_def__ecect) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 153 (all X0 (pp(aa_fun171081125l_bool(scratc1157614065n_some,X0)) -> pp(aa_fun171081125l_bool(scratc1157614065n_some,scratc1712865281nd_min(X0))))) # label(fact_satz27) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 154 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_qc(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uua),Uuc))))))) # label(fact_ATP_Olambda__674) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 155 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_fz(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ga,Uu),Uua)))) # label(fact_ATP_Olambda__464) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 156 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_aat,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_aas,Uu))))) # label(fact_ATP_Olambda__31) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 157 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ig,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_if,Uu))))) # label(fact_ATP_Olambda__192) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 158 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qj(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__513) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 159 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xc,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_xb(Uu),Uua))))) # label(fact_ATP_Olambda__362) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 160 (all X all Xa all Xb (pp(scratc371142564_d_and(scratc1729978623nd_or3(X,Xa,Xb),scratc1646379588nd_ec3(X,Xa,Xb))) <-> scratc83947841_orec3(X,Xa,Xb))) # label(fact_def__orec3) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 161 (all Uu all Uua all Uub all Uuc all Uud all Uue all Uuf (pp(aa_fun171081125l_bool(scratc1303128615all_of(aa_TPT43085870d_bool(aTP_Lamm_au,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_av(Uua),Uub),Uuc),Uud),Uue),Uuf))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_aw(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)))) # label(fact_ATP_Olambda__741) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 162 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_rw,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_rv,Uu))))) # label(fact_ATP_Olambda__112) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 163 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jg(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uu),Uua))))) # label(fact_ATP_Olambda__511) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 164 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rc(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_rb(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__613) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 165 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_yn,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_ym,Uu))))) # label(fact_ATP_Olambda__57) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 166 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ks,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_kr(Uu),Uua))))) # label(fact_ATP_Olambda__431) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 167 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kf(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uub),Uua)))))) # label(fact_ATP_Olambda__562) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 168 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_km,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_kn,Uu)))) # label(fact_ATP_Olambda__175) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 169 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_aax,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(scratc159642228nd_n_1),Uu)),aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uu))))) # label(fact_ATP_Olambda__5) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 170 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_jq(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jr,Uu),Uua)))) # label(fact_ATP_Olambda__439) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 171 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1721126791nd_nis,X),Xa)) <-> pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,X),Xa))))) # label(fact_def__nis) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 172 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174643062lesseq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174643062lesseq,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174643062lesseq,aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dl(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__686) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 173 (all X all Xa all Xb scratc1939081475eft_f1(X,Xa,Xb) = scratc795979768d_left(X,Xb,Xa)) # label(fact_def__left__f1) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 174 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_qd(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qe,Uu),Uua)))) # label(fact_ATP_Olambda__405) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 175 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_aak,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_aal,Uu)))) # label(fact_ATP_Olambda__34) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 176 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_iw,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_iv,Uu))))) # label(fact_ATP_Olambda__188) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 177 (all X aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc584055948d_d_Pi,aa_TPTP_ind_TPTP_ind(scratc2122467577_d_1to,scratc159642229nd_n_2)),aTP_Lamm_aj(X)) = aa_TPTP_ind_TPTP_ind(scratc921286080r1type,X)) # label(fact_def__pair1type) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 178 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1303128615all_of(aa_TPT43085870d_bool(aTP_Lamm_au,X0)),aa_fun1584354236d_bool(aTP_Lamm_ace(X0),X12)))) # label(fact_otax2) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 179 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eu(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__518) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 180 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_er(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__510) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 181 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zg,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc308889072moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,Uua),Uu))))) # label(fact_ATP_Olambda__295) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 182 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cb,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cc,Uu)))) # label(fact_ATP_Olambda__243) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 183 (all X all Xa scratc994261093second(X,Xa) = scratc1306586371_proj1) # label(fact_def__second) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 184 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_uk(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__685) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 185 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_xd,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_xc,Uu))))) # label(fact_ATP_Olambda__69) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 186 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_mf,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_mg,Uu)))) # label(fact_ATP_Olambda__163) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 187 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jb,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ja(Uu),Uua))))) # label(fact_ATP_Olambda__444) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 188 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1243723785d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1721913973nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc1721913973nd_num,Xa))),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1638249340nd_den,X)),aa_TPTP_ind_TPTP_ind(scratc1638249340nd_den,Xa))) = aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(X),Xa)) # label(fact_def__n__tf) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 189 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_fl,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fm,Uu)))) # label(fact_ATP_Olambda__214) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 190 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_lx,Uu)) <-> pp(aa_fun171081125l_bool(scratc413789423l_some(scratc514495423d_frac),aa_TPT43085870d_bool(aTP_Lamm_lw,Uu))))) # label(fact_ATP_Olambda__245) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 191 (all Uu all Uua (pp(scratc1729978623nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1157614065n_some,aa_TPT43085870d_bool(scratc488442041ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc1157614065n_some,aa_TPT43085870d_bool(scratc488442041ffprop(Uua),Uu)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zu,Uu),Uua)))) # label(fact_ATP_Olambda__262) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 192 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_sj(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sk,Uu),Uua)))) # label(fact_ATP_Olambda__387) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 193 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_mj,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_mi,Uu))))) # label(fact_ATP_Olambda__162) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 194 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_yu,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_yv,Uu)))) # label(fact_ATP_Olambda__53) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 195 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_xa,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_wz,Uu))))) # label(fact_ATP_Olambda__70) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 196 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_pz(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qa,Uu),Uua)))) # label(fact_ATP_Olambda__406) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 197 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_uo(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_up(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__605) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 198 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_le,Uu),Uua)))) # label(fact_ATP_Olambda__291) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 199 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hd(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uua),Uub)),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uub),aa_TPTP_ind_TPTP_ind(scratc1771548918_367_w(Uu),Uua))))))) # label(fact_ATP_Olambda__532) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 200 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_di(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dh(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__653) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 201 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1890899764d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc254891115_d_Sep(Uu),Uua))) -> pp(aa_TPTP_ind_bool(Uua,Uub))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_abs(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__494) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 202 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_jv,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_jw,Uu)))) # label(fact_ATP_Olambda__180) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 203 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ne,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_nf,Uu)))) # label(fact_ATP_Olambda__154) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 204 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_ud(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ue,Uu),Uua)))) # label(fact_ATP_Olambda__384) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 205 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abv(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aa_TPT43085870d_bool(aTP_Lamm_au,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_abu(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__591) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 206 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_sm(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sn,Uu),Uua)))) # label(fact_ATP_Olambda__386) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 207 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uua),Uub)),Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_de(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__583) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 208 (all B_1 all B_2 gg_bool(aa_TPTP_ind_bool(B_1,B_2))) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 209 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kb(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__716) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 210 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uu),Uua)),Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kz,Uu),Uua)))) # label(fact_ATP_Olambda__319) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 211 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ms,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_mt,Uu)))) # label(fact_ATP_Olambda__158) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 212 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_hx,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_hy,Uu)))) # label(fact_ATP_Olambda__194) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 213 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hg,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uu),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uua),aa_TPTP_ind_TPTP_ind(scratc1771548918_367_w(Uu),Uua))))))) # label(fact_ATP_Olambda__285) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 214 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kr(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uua),Uub)))))) # label(fact_ATP_Olambda__571) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 215 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lu,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uua),Uu)))) # label(fact_ATP_Olambda__345) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 216 (all X ((all X1 (pp(aa_TPTP_ind_bool(X1,scratc1354028742ptyset)) -> ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(X1,X2)) -> pp(aa_TPTP_ind_bool(X1,aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,X2)))))) -> pp(aa_TPTP_ind_bool(X1,X))))) <-> pp(aa_TPTP_ind_bool(scratc1270331168_nat_p,X)))) # label(fact_def__nat__p) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 217 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ek(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_el,Uu),Uua)))) # label(fact_ATP_Olambda__476) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 218 (all X scratc1680147256nd_inn(X) = scratc1725260217d_e_in(scratc1720602000nd_nat,aa_TPT43085870d_bool(aTP_Lamm_ak,X))) # label(fact_def__inn) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 219 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ye,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_yd,Uu))))) # label(fact_ATP_Olambda__60) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 220 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dp(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dq(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__651) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 221 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ov,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ow,Uu)))) # label(fact_ATP_Olambda__140) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 222 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc2047737915d_soft(X,Xa,Xb),Xc) = scratc1680147246nd_ind(X,aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bj(Xa),Xb),Xc))) # label(fact_def__soft) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 223 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ns(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uu),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uua),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uub),Uuc))))))) # label(fact_ATP_Olambda__705) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 224 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hm,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_hl,Uu))))) # label(fact_ATP_Olambda__197) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 225 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_it(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iu(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__631) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 226 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ma,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_lz,Uu))))) # label(fact_ATP_Olambda__165) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 227 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc1729716277nd_one(X0),X12)) -> scratc1383686962_is_of(scratc1680147246nd_ind(X0,X12),aa_TPT43085870d_bool(aTP_Lamm_au,X0)))) # label(fact_ind__p) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 228 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ua,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_tz(Uu),Uua))))) # label(fact_ATP_Olambda__385) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 229 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_db,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_da,Uu))))) # label(fact_ATP_Olambda__231) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 230 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ki(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kj,Uu),Uua)))) # label(fact_ATP_Olambda__434) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 231 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ra,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_qz,Uu))))) # label(fact_ATP_Olambda__118) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 232 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_hi,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_hj,Uu)))) # label(fact_ATP_Olambda__198) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 233 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_uu,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_uv,Uu)))) # label(fact_ATP_Olambda__87) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 234 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_mk(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ml,Uu),Uua)))) # label(fact_ATP_Olambda__423) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 235 (all Uu ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1721126791nd_nis,Uu),scratc159642228nd_n_1)) -> pp(aa_fun171081125l_bool(scratc1157614065n_some,aa_TPT43085870d_bool(aTP_Lamm_ar,Uu)))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_abe,Uu)))) # label(fact_ATP_Olambda__1) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 236 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vr,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_vq(Uu),Uua))))) # label(fact_ATP_Olambda__373) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 237 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_aap,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_aaq,Uu)))) # label(fact_ATP_Olambda__32) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 238 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_aaf(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aag,Uu),Uua)))) # label(fact_ATP_Olambda__350) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 239 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X22),X0)) -> (all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X32),aa_TPTP_ind_TPTP_ind(X12,X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1737995691d_pair,X22),X32)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1318166930_Sigma,X0),X12))))))) # label(fact_pair__Sigma) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 240 (all Uu ((pp(aa_TPTP_ind_bool(scratc1321703102_cond1,Uu)) -> (pp(aa_TPTP_ind_bool(scratc1321703103_cond2,Uu)) -> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_abj,Uu))))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_abk,Uu)))) # label(fact_ATP_Olambda__9) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 241 (all Uu all Uua (gg_TPTP_ind(Uu) -> aa_TPTP_ind_TPTP_ind(aTP_Lamm_aj(Uu),Uua) = Uu)) # label(fact_ATP_Olambda__742) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 242 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc565842745nunion(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1185191648d_repl,X),scratc1152592158d_Inj0)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1185191648d_repl,Xa),scratc1152592159d_Inj1)) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1737995691d_pair,X),Xa)) # label(fact_def__pair) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 243 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,Uu),Uub)) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_bh(Uu),Uua),Uub)) # label(fact_ATP_Olambda__597) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 244 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dz,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_dy(Uu),Uua))))) # label(fact_ATP_Olambda__479) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 245 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ng,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_nh,Uu)))) # label(fact_ATP_Olambda__153) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 246 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_uq,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_up(Uu),Uua))))) # label(fact_ATP_Olambda__381) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 247 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_kt,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ks,Uu))))) # label(fact_ATP_Olambda__173) # label(axiom) # label(non_clause). [assumption]. 1.46/1.77 248 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,X),Xb)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1306979967_prop3(X),Xa),Xb)))) # label(fact_def__prop3) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 249 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mf,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_me(Uu),Uua))))) # label(fact_ATP_Olambda__425) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 250 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tn,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uua)),Uu))))) # label(fact_ATP_Olambda__284) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 251 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1742772941ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1613924016nd_all(Xa),aa_TPT43085870d_bool(scratc48260778_image(X,Xa),Xb))))) # label(fact_def__surjective) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 252 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jn,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_jm(Uu),Uua))))) # label(fact_ATP_Olambda__440) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 253 (all B_1 gg_TPTP_ind(scratc1647232439nd_eps(B_1))) # label(gsy_c_Scratch__tptp__translate__63821__3484_ONUM790__thf__4__p_Obnd__eps) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 254 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wo,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_wn(Uu),Uua))))) # label(fact_ATP_Olambda__366) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 255 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hw(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hv(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__637) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 256 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc308889072moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_us(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__679) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 257 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc488442041ffprop(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,X),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Xa),Xb))))) # label(fact_def__diffprop) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 258 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ls,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uu),Uua)) -> pp(aa_fun171081125l_bool(scratc413789423l_some(scratc514495423d_frac),aa_TPT43085870d_bool(aTP_Lamm_lr(Uu),Uua)))))) # label(fact_ATP_Olambda__305) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 259 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cz,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cy,Uu))))) # label(fact_ATP_Olambda__232) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 260 (all X7 all Y (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) | Y != X7)) # label(help_fequal_2_1_fequal_001t__TPTP____Interpret__Oind_T) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 261 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_gx,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_gy,Uu)))) # label(fact_ATP_Olambda__202) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 262 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_py(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uua),Uuc))))))) # label(fact_ATP_Olambda__726) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 263 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abp,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,Uua),aa_TPTP_ind_TPTP_ind(scratc1178072532_power,Uu))))) # label(fact_ATP_Olambda__342) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 264 (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(scratc1725260222d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,Uub),Uuc)),Uue)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_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_av(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)))) # label(fact_ATP_Olambda__740) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 265 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc413789423l_some(scratc514495423d_frac),aa_TPT43085870d_bool(aTP_Lamm_de(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_df,Uu),Uua)))) # label(fact_ATP_Olambda__485) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 266 (all B_1 all B_2 gg_TPTP_ind(aa_fun1431113780TP_ind(B_1,B_2))) # label(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 267 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_gu(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gv,Uu),Uua)))) # label(fact_ATP_Olambda__457) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 268 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),Uua)),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sx,Uu),Uua)))) # label(fact_ATP_Olambda__272) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 269 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_wm(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__712) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 270 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hk(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uua),Uub)),Uu)))) # label(fact_ATP_Olambda__584) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 271 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X22),X0)) -> (pp(aa_TPTP_ind_bool(X12,X22)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X22),aa_fun1431113780TP_ind(scratc254891115_d_Sep(X0),X12)))))) # label(fact_k__SepI) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 272 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jq(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jp(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__630) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 273 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zk,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uua),Uu))))) # label(fact_ATP_Olambda__294) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 274 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_mu(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mv(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__625) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 275 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ab,Uu)))) # label(fact_ATP_Olambda__244) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 276 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_dm(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dn,Uu),Uua)))) # label(fact_ATP_Olambda__482) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 277 (all X (pp(aa_TPTP_ind_bool(scratc1421322154_prop4,X)) <-> pp(aa_fun171081125l_bool(scratc413789423l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc584055948d_d_Pi,scratc1720602000nd_nat),aTP_Lamm_al)),aa_TPT43085870d_bool(scratc1421322152_prop2,X))))) # label(fact_def__d__428__prop4) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 278 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ao(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uub))),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,Uua),Uub)),Uu))))) # label(fact_ATP_Olambda__531) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 279 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zi,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uua),Uu))))) # label(fact_ATP_Olambda__303) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 280 (all Uu all Uua all Uub all Uuc (pp(aa_fun171081125l_bool(scratc1613924016nd_all(Uu),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_bk(Uu),Uua),Uub),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bl(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__730) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 281 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cb,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,Uu),Uua)) -> pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc380388658moreis,Uu),Uua)))))) # label(fact_ATP_Olambda__309) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 282 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_li,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_lj,Uu)))) # label(fact_ATP_Olambda__138) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 283 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_il(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039435_moreq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uua),Uuc))))))) # label(fact_ATP_Olambda__694) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 284 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iq(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ip(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__632) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 285 (all Uu all Uua all Uub all Uuc (scratc873677453d_and3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1680147248nd_inf,Uub),aa_TPTP_ind_TPTP_ind(scratc1021009639_class,Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1680147248nd_inf,Uuc),aa_TPTP_ind_TPTP_ind(scratc1021009639_class,Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ae(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__660) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 286 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_pq(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc308889072moreis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uua),Uuc))))))) # label(fact_ATP_Olambda__676) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 287 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ip(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__704) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 288 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725260222d_e_is(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,Uua),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bj(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__666) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 289 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jj(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__519) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 290 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1303128615all_of(aa_TPT43085870d_bool(aTP_Lamm_aby(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_acb(X0),X12)))) # label(fact_first__p) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 291 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tf,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uua)),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc308889072moreis,Uua),Uu))))) # label(fact_ATP_Olambda__273) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 292 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_iy,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_iz,Uu)))) # label(fact_ATP_Olambda__187) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 293 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rv,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_ru(Uu),Uua))))) # label(fact_ATP_Olambda__392) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 294 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_yc(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yd,Uu),Uua)))) # label(fact_ATP_Olambda__355) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 295 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc473135711unmore(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc254891115_d_Sep(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bc(X),Xa),Xb))) # label(fact_def__unmore) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 296 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_aab,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_aaa,Uu))))) # label(fact_ATP_Olambda__38) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 297 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1318166930_Sigma,X0),X12))) -> X22 = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1737995691d_pair,aa_TPTP_ind_TPTP_ind(scratc1306586370_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1306586371_proj1,X22))))) # label(fact_proj__Sigma__eta) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 298 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ty(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__683) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 299 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ep,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_eo(Uu),Uua))))) # label(fact_ATP_Olambda__475) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 300 (all X (pp(aa_TPTP_ind_bool(scratc1017527147closed,X)) <-> pp(aa_TPTP_ind_bool(scratc1650562408closed,X)) & pp(aa_TPTP_ind_bool(scratc1815295422closed,X)) & pp(aa_TPTP_ind_bool(scratc363539598closed,X)))) # label(fact_def__d__ZF__closed) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 301 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1642495594air_q0(X),Xa) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc872461638_pair1(X),aa_TPTP_ind_TPTP_ind(scratc1721253554first1(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1307566348econd1(X),Xa))) # label(fact_def__pair__q0) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 302 (all B_1 all B_2 gg_bool(scratc1112013241d_l_ec(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__63821__3484_ONUM790__thf__4__p_Obnd__l__ec) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 303 (all Uu scratc1720602000nd_nat = aa_TPTP_ind_TPTP_ind(aTP_Lamm_al,Uu)) # label(fact_ATP_Olambda__744) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 304 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc2123791476_inj_h(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1318166930_Sigma,X),aa_TPT1424761345TP_ind(aTP_Lamm_bh(Xc),Xd))) # label(fact_def__inj__h) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 305 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,Xa),scratc1240312639d_n_2t) = aa_TPTP_ind_TPTP_ind(scratc1307566348econd1(X),Xa)) # label(fact_def__second1) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 306 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ql,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_qk,Uu))))) # label(fact_ATP_Olambda__123) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 307 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725260222d_e_is(Uu),Uub),Uuc)) -> pp(aa_TPTP_ind_bool(Uua,Uuc)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_acm(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__728) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 308 (all Uu all Uua all Uub all Uuc (gg_TPTP_ind(Uub) & gg_TPTP_ind(Uuc) & gg_TPTP_ind(Uua) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ca(Uu),Uua),Uub),Uuc)) <-> Uuc = Uub & -pp(Uu) | Uuc = Uua & pp(Uu)))) # label(fact_ATP_Olambda__673) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 309 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_tk,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_tj,Uu))))) # label(fact_ATP_Olambda__98) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 310 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_lc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ld,Uu)))) # label(fact_ATP_Olambda__169) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 311 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dk,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_dj,Uu))))) # label(fact_ATP_Olambda__229) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 312 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_wc(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wd,Uu),Uua)))) # label(fact_ATP_Olambda__369) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 313 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1212653308_UPair(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1185191648d_repl,aa_TPTP_ind_TPTP_ind(scratc1178072532_power,aa_TPTP_ind_TPTP_ind(scratc1178072532_power,scratc1354028742ptyset))),aa_TPT1424761345TP_ind(aTP_Lamm_bz(X),Xa))) # label(fact_def__d__UPair) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 314 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yy,Uu),Uua)) <-> (pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,Uu),Uua))))) # label(fact_ATP_Olambda__328) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 315 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc308889072moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc308889072moreis,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qv(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__540) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 316 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iv,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_iu(Uu),Uua))))) # label(fact_ATP_Olambda__446) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 317 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1318166930_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,aa_TPTP_ind_TPTP_ind(scratc1306586371_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1306586370_proj0,X22)))))) # label(fact_proj1__Sigma) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 318 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc942939880t_more,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc413789423l_some(scratc514495423d_frac),aa_TPT43085870d_bool(aTP_Lamm_af(X),Xa))))) # label(fact_def__rt__more) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 319 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ib,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ia(Uu),Uua))))) # label(fact_ATP_Olambda__451) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 320 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1771548918_367_w(X),Xa) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1243723785d_n_fr,aa_TPTP_ind_TPTP_ind(scratc759794874367_vo(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1638249340nd_den,X)),aa_TPTP_ind_TPTP_ind(scratc1638249340nd_den,Xa)))) # label(fact_def__d__367__w) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 321 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),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__453) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 322 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc942939880t_more,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cn,Uu),Uua)))) # label(fact_ATP_Olambda__293) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 323 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_qw,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_qx,Uu)))) # label(fact_ATP_Olambda__119) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 324 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hz(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174643062lesseq,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uua),Uuc))))))) # label(fact_ATP_Olambda__702) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 325 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jd(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uu),Uua))))) # label(fact_ATP_Olambda__508) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 326 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ls,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_lt,Uu)))) # label(fact_ATP_Olambda__166) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 327 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ih(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039435_moreq,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uua),Uuc))))))) # label(fact_ATP_Olambda__697) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 328 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ws,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_wr(Uu),Uua))))) # label(fact_ATP_Olambda__365) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 329 (all X0 all X12 (gg_TPTP_ind(X12) -> X12 = aa_TPTP_ind_TPTP_ind(scratc1306586371_proj1,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1737995691d_pair,X0),X12)))) # label(fact_proj1__pair__eq) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 330 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_pi(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uua),Uuc))))))) # label(fact_ATP_Olambda__724) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 331 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gk,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_gj,Uu))))) # label(fact_ATP_Olambda__207) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 332 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dg,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_df,Uu))))) # label(fact_ATP_Olambda__230) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 333 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_vv,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_vu,Uu))))) # label(fact_ATP_Olambda__79) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 334 (all X0 all X12 all X22 ((pp(X0) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X12),X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,aa_TPTP_ind_TPTP_ind(scratc628861614bnd_if(X0,X12),scratc1354028742ptyset)),aa_TPTP_ind_TPTP_ind(scratc628861614bnd_if(X0,X22),aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,scratc1354028742ptyset)))))) # label(fact_k__If__In__01) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 335 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wv(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_wu(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__598) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 336 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc367018365ectset(X,Xa),aa_TPTP_ind_TPTP_ind(scratc602407550_ecelt(X,Xa),Xb)) = aa_TPTP_ind_TPTP_ind(scratc251816488ectelt(X,Xa),Xb)) # label(fact_def__ectelt) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 337 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_la,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_kz,Uu))))) # label(fact_ATP_Olambda__170) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 338 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sr,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),Uua)),Uua)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uu)),Uua))))) # label(fact_ATP_Olambda__266) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 339 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_og,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_oh,Uu)))) # label(fact_ATP_Olambda__142) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 340 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_rb(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uuc),Uua))))))) # label(fact_ATP_Olambda__711) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 341 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nm,Uu),Uua)) <-> (pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174643062lesseq,Uu),Uua))))) # label(fact_ATP_Olambda__333) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 342 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jp(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uuc),Uua))))))) # label(fact_ATP_Olambda__721) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 343 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_fun1235454963TP_ind(aTP_Lamm_by(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc628861614bnd_if(aa_TPTP_ind_bool(Uua,Uub),Uub),scratc1647232439nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bm(Uu),Uua)))) # label(fact_ATP_Olambda__492) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 344 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1575955453_rt_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1575955453_rt_is,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1575955453_rt_is,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cx(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__552) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 345 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mb(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039435_moreq,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uu),Uub)))))) # label(fact_ATP_Olambda__558) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 346 (all X0 (pp(aa_TPTP_ind_bool(scratc1270331168_nat_p,X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X0),scratc476241584_omega)))) # label(fact_nat__p__omega) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 347 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ux(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_uw(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__603) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 348 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ns(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nt(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__623) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 349 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xh(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__577) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 350 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cx(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cy,Uu),Uua)))) # label(fact_ATP_Olambda__484) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 351 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_dz,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ea,Uu)))) # label(fact_ATP_Olambda__225) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 352 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc308889072moreis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xz(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__538) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 353 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,Uub),aa_TPTP_ind_TPTP_ind(scratc154197684eft1to(Uu,Uua),Uuc)) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ah(Uu),Uua),Uub),Uuc)) # label(fact_ATP_Olambda__733) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 354 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1303128615all_of(aa_TPT43085870d_bool(aTP_Lamm_aby(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_abz(X0),X12)))) # label(fact_pairis1) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 355 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zw(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__593) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 356 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_xk(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xl,Uu),Uua)))) # label(fact_ATP_Olambda__359) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 357 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1243723785d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1721913973nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc1638249340nd_den,Xa))),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1638249340nd_den,X)),aa_TPTP_ind_TPTP_ind(scratc1721913973nd_num,Xa))) = aa_TPTP_ind_TPTP_ind(scratc1135636789_477_v(X),Xa)) # label(fact_def__d__477__v) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 358 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ur,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_uq,Uu))))) # label(fact_ATP_Olambda__88) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 359 (all X0 all X12 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc726999126ective(aa_fun1431113780TP_ind(scratc254891115_d_Sep(X0),X12)),X0),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1318166930_Sigma,aa_fun1431113780TP_ind(scratc254891115_d_Sep(X0),X12)),scratc1725260217d_e_in(X0,X12))))) # label(fact_otax1) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 360 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_yk,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_yj,Uu))))) # label(fact_ATP_Olambda__58) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 361 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1303128615all_of(aa_TPT43085870d_bool(aTP_Lamm_au,X0)),aa_fun1584354236d_bool(aTP_Lamm_acn(X0),X12)))) # label(fact_e__isp) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 362 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ij,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ik,Uu)))) # label(fact_ATP_Olambda__191) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 363 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_pv(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pw,Uu),Uua)))) # label(fact_ATP_Olambda__407) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 364 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_rk(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rl,Uu),Uua)))) # label(fact_ATP_Olambda__395) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 365 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qp(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uub),Uua)))))) # label(fact_ATP_Olambda__545) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 366 (all Uu all Uua ((pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc942939880t_more,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc246405046lessis,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ch,Uu),Uua)))) # label(fact_ATP_Olambda__326) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 367 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_pa(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__682) # label(axiom) # label(non_clause). [assumption]. 1.46/1.78 368 (all Uu all Uua all Uub all Uuc (pp(scratc1112013241d_l_ec(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1890899764d_esti(Uu),Uuc),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1890899764d_esti(Uu),Uuc),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bd(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__668) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 369 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gz(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__722) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 370 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),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__455) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 371 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aaf(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1721126791nd_nis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1721126791nd_nis,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uub)))))) # label(fact_ATP_Olambda__574) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 372 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_zf,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_ze,Uu))))) # label(fact_ATP_Olambda__48) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 373 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_je,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_jf,Uu)))) # label(fact_ATP_Olambda__185) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 374 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_ol,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_om,Uu)))) # label(fact_ATP_Olambda__136) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 375 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc844466543_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(X),Xa)),Xb)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(X),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Xa),Xb)))))) # label(fact_def__d__431__prop1) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 376 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fj(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fk(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__644) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 377 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1955540854_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1721126791nd_nis,Xa),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(X),Xa))))) # label(fact_def__d__27__prop1) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 378 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_ww,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_wx,Uu)))) # label(fact_ATP_Olambda__71) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 379 (all X all Xa (scratc1265284014_l_iff(X,Xa) <-> pp(scratc371142564_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1680081659nd_imp,X),Xa),aa_bool_bool(aa_boo1142376798l_bool(scratc1680081659nd_imp,Xa),X))))) # label(fact_def__l__iff) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 380 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_td,Uu),Uua)) <-> pp(scratc371142564_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,Uua),scratc159642228nd_n_1)),Uu),aa_fun171081125l_bool(scratc1943600036_n_all,aa_TPT43085870d_bool(aTP_Lamm_ao(Uu),Uua)))))) # label(fact_ATP_Olambda__270) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 381 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ij,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ii(Uu),Uua))))) # label(fact_ATP_Olambda__449) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 382 (all Q all P (pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) | -pp(Q))) # label(help_fimplies_2_1_U) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 383 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_abu(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725260222d_e_is(Uua),aa_TPTP_ind_TPTP_ind(scratc994261093second(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1423256749d_pair(Uu,Uua),Uub),Uuc))),Uuc)))) # label(fact_ATP_Olambda__663) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 384 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),scratc159642228nd_n_1))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_sw,Uu)))) # label(fact_ATP_Olambda__17) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 385 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aap,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uu)),Uua))))) # label(fact_ATP_Olambda__323) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 386 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_qj(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qk,Uu),Uua)))) # label(fact_ATP_Olambda__403) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 387 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_vb(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vc,Uu),Uua)))) # label(fact_ATP_Olambda__378) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 388 (all Uu all Uua (scratc83947841_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1157614065n_some,aa_TPT43085870d_bool(aTP_Lamm_zw(Uu),Uua)),aa_fun171081125l_bool(scratc1157614065n_some,aa_TPT43085870d_bool(aTP_Lamm_zx(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zy,Uu),Uua)))) # label(fact_ATP_Olambda__261) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 389 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_abg,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_abh,Uu)))) # label(fact_ATP_Olambda__28) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 390 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_in,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_io,Uu)))) # label(fact_ATP_Olambda__190) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 391 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_vm,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_vl,Uu))))) # label(fact_ATP_Olambda__82) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 392 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rx(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__535) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 393 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_nx(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ny,Uu),Uua)))) # label(fact_ATP_Olambda__418) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 394 (all X all Xa all Xb all Xc all Xd (pp(scratc371142564_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1680081659nd_imp,X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725260222d_e_is(Xa),Xd),Xb)),aa_bool_bool(aa_boo1142376798l_bool(scratc1680081659nd_imp,scratc478607744_d_not(X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725260222d_e_is(Xa),Xd),Xc)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1306979965_prop1(X,Xa,Xb),Xc),Xd)))) # label(fact_def__prop1) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 395 (all X0 ((all X13 (gg_TPTP_ind(X13) -> ((all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X22),X13)) -> pp(aa_TPTP_ind_bool(X0,X22)))) -> pp(aa_TPTP_ind_bool(X0,X13))))) -> (all X14 pp(aa_TPTP_ind_bool(X0,X14))))) # label(fact_k__In__ind) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 396 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_fun171081125l_bool(scratc1303128615all_of(aa_TPT43085870d_bool(aTP_Lamm_au,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_ax(Uu),Uua),Uub),Uuc),Uud))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ay(Uu),Uua),Uub),Uuc),Uud)))) # label(fact_ATP_Olambda__736) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 397 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),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__469) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 398 (all X0 all X12 scratc1383686962_is_of(aa_fun1431113780TP_ind(scratc254891115_d_Sep(X0),X12),aa_TPT43085870d_bool(aTP_Lamm_abp,X0))) # label(fact_setof__p) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 399 (all X0 all X12 all X22 (gg_TPTP_ind(X22) & gg_TPTP_ind(X12) -> aa_TPTP_ind_TPTP_ind(scratc628861614bnd_if(X0,X12),X22) = X22 | X12 = aa_TPTP_ind_TPTP_ind(scratc628861614bnd_if(X0,X12),X22))) # label(fact_if__i__or) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 400 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hr(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hs(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__638) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 401 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vw(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__547) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 402 (all Uu all Uua aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,Uu),Uua)),Uua) = aa_TPTP_ind_TPTP_ind(aTP_Lamm_am(Uu),Uua)) # label(fact_ATP_Olambda__320) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 403 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yj,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_yi(Uu),Uua))))) # label(fact_ATP_Olambda__353) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 404 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pj(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_pi(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__619) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 405 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dl(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dm(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__652) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 406 (all X aa_TPTP_ind_TPTP_ind(scratc1754835376d_1out,X) = aa_TPTP_ind_TPTP_ind(scratc1123360177d_outn(X),scratc159642228nd_n_1)) # label(fact_def__d__1out) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 407 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vl,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_vk(Uu),Uua))))) # label(fact_ATP_Olambda__375) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 408 (all X all Xa ((all X2 (gg_TPTP_ind(X2) -> (scratc1383686962_is_of(X2,X) -> pp(aa_TPTP_ind_bool(Xa,X2))))) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(X),Xa)))) # label(fact_def__all__of) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 409 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Xa),X))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2009684326_prop1,X),Xa)))) # label(fact_def__d__429__prop1) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 410 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_zt,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_zs,Uu))))) # label(fact_ATP_Olambda__41) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 411 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_le,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_lf,Uu)))) # label(fact_ATP_Olambda__168) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 412 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_fe,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ff,Uu)))) # label(fact_ATP_Olambda__216) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 413 (all X all Xa (pp(aa_fun171081125l_bool(scratc1303128615all_of(aa_TPT43085870d_bool(aTP_Lamm_au,X)),scratc1721520380nd_non(X,aa_TPT43085870d_bool(aTP_Lamm_bf(X),Xa)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2057229948_empty,X),Xa)))) # label(fact_def__empty) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 414 (all Uu aa_TPT494704832TP_ind(scratc1185191648d_repl,aa_TPTP_ind_TPTP_ind(scratc482128287tminus(Uu),aa_TPTP_ind_TPTP_ind(scratc327484482d_Sing,scratc1354028742ptyset))) = aa_TPT494704832TP_ind(aTP_Lamm_bv,Uu)) # label(fact_ATP_Olambda__248) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 415 (all X all Xa scratc1646379653nd_ect(X,Xa) = aa_fun1431113780TP_ind(scratc254891115_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1178072532_power,X)),scratc873743100d_anec(X,Xa))) # label(fact_def__ect) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 416 (all X all Xa (pp(scratc371142564_d_and(X,Xa)) <-> pp(scratc478607744_d_not(scratc1112013241d_l_ec(X,Xa))))) # label(fact_def__d__and) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 417 (all Uu all Uua (pp(scratc371142564_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,Uua),scratc159642228nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uu)),aa_fun171081125l_bool(scratc1943600036_n_all,aa_TPT43085870d_bool(aTP_Lamm_aq,Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abb,Uu),Uua)))) # label(fact_ATP_Olambda__268) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 418 (all X all Xa all Xb all Xc (pp(aa_fun171081125l_bool(scratc1303128615all_of(aa_TPT43085870d_bool(aTP_Lamm_au,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ba(X),Xa),Xb),Xc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc139619091_fixfu(X,Xa),Xb),Xc)))) # label(fact_def__fixfu) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 419 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dh(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uua),Uub)),Uu)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uua),Uuc)),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uub),Uuc)))))) # label(fact_ATP_Olambda__670) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 420 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_sf,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_se,Uu))))) # label(fact_ATP_Olambda__109) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 421 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ih(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ii(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__634) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 422 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_sb,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_sc,Uu)))) # label(fact_ATP_Olambda__110) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 423 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kv,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ku(Uu),Uua))))) # label(fact_ATP_Olambda__430) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 424 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ej(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ek(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__646) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 425 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc308889072moreis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_uo(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__677) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 426 (all X aa_TPTP_ind_TPTP_ind(scratc1152592158d_Inj0,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1185191648d_repl,X),scratc1152592159d_Inj1)) # label(fact_def__d__Inj0) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 427 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_rj(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uuc),Uua))))))) # label(fact_ATP_Olambda__707) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 428 (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(scratc308889072moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc308889072moreis,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__542) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 429 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fe,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_fd(Uu),Uua))))) # label(fact_ATP_Olambda__470) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 430 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc308889072moreis,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ze,Uu),Uua)))) # label(fact_ATP_Olambda__296) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 431 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yw,Uu),Uua)) <-> (pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc308889072moreis,Uu),Uua))))) # label(fact_ATP_Olambda__335) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 432 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_im(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_in,Uu),Uua)))) # label(fact_ATP_Olambda__448) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 433 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cr,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cs,Uu)))) # label(fact_ATP_Olambda__235) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 434 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_xn(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xo,Uu),Uua)))) # label(fact_ATP_Olambda__358) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 435 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rg(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_rf(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__612) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 436 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039435_moreq,X),Xa)) <-> pp(aa_bool_bool(scratc1112669246d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,X),Xa))))) # label(fact_def__moreq) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 437 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ct,Uu),Uua)) <-> pp(scratc1729978623nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1575955453_rt_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc942939880t_more,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,Uu),Uua))))) # label(fact_ATP_Olambda__255) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 438 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aa_TPT43085870d_bool(aTP_Lamm_aci(Uu),Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ack(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_acl(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__499) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 439 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uu),aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gu(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__527) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 440 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ku(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uua),Uub)))))) # label(fact_ATP_Olambda__556) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 441 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_yf(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yg,Uu),Uua)))) # label(fact_ATP_Olambda__354) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 442 (all X0 scratc1354028742ptyset != aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,X0)) # label(fact_neq__ordsucc__0) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 443 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_va(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__675) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 444 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pf(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_pe(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__620) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 445 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_nb,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_na,Uu))))) # label(fact_ATP_Olambda__156) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 446 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_vh(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vi,Uu),Uua)))) # label(fact_ATP_Olambda__376) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 447 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_aao,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_aan,Uu))))) # label(fact_ATP_Olambda__33) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 448 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yf(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__579) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 449 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ln(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lo(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__626) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 450 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uu),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uua),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uub),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_nw(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__700) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 451 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_th,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ti,Uu)))) # label(fact_ATP_Olambda__99) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 452 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vu,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_vt(Uu),Uua))))) # label(fact_ATP_Olambda__372) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 453 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_wh,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_wg,Uu))))) # label(fact_ATP_Olambda__75) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 454 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gz(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ha(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__640) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 455 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qm(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__502) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 456 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fw(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fv(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__641) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 457 (all X aa_TPTP_ind_TPTP_ind(scratc1306586371_proj1,X) = aa_fun277296641TP_ind(scratc623004572eplSep(X,aTP_Lamm_bt),scratc272004510_d_Unj)) # label(fact_def__proj1) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 458 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_ta,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_tb,Uu)))) # label(fact_ATP_Olambda__101) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 459 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zo,Uu),Uua)) <-> pp(scratc1729978623nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__256) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 460 (all X all Xa all Xb all Xc scratc1680147246nd_ind(Xa,aa_TPT43085870d_bool(scratc1306979965_prop1(X,Xa,Xb),Xc)) = aa_TPTP_ind_TPTP_ind(scratc1680540841nd_ite(X,Xa,Xb),Xc)) # label(fact_def__ite) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 461 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1185191648d_repl,X0),X12))) <-> (exists X3 (aa_TPTP_ind_TPTP_ind(X12,X3) = X22 & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X3),X0)) & gg_TPTP_ind(X3)))))) # label(fact_k__ReplEq) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 462 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,scratc159642228nd_n_1),aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_tv,Uu)))) # label(fact_ATP_Olambda__247) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 463 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_qs(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qt,Uu),Uua)))) # label(fact_ATP_Olambda__400) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 464 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1077425377ght1to(X,Xa),Xb) = aa_TPTP_ind_TPTP_ind(scratc1123360177d_outn(aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(X),aa_TPTP_ind_TPTP_ind(scratc1680147256nd_inn(Xa),Xb)))) # label(fact_def__right1to) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 465 (all B_1 gg_bool(scratc478607744_d_not(B_1))) # label(gsy_c_Scratch__tptp__translate__63821__3484_ONUM790__thf__4__p_Obnd__d__not) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 466 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_vf,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_vg,Uu)))) # label(fact_ATP_Olambda__84) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 467 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kl(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uub),Uua)))))) # label(fact_ATP_Olambda__557) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 468 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_mn(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mo,Uu),Uua)))) # label(fact_ATP_Olambda__422) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 469 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_aam(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aan,Uu),Uua)))) # label(fact_ATP_Olambda__349) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 470 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_od,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_oc,Uu))))) # label(fact_ATP_Olambda__144) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 471 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tp,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uua),scratc159642228nd_n_1)),Uu))))) # label(fact_ATP_Olambda__281) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 472 (all X (pp(aa_TPTP_ind_bool(scratc1650562408closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,aa_TPTP_ind_TPTP_ind(scratc1685334398_union,X1)),X))))))) # label(fact_def__d__Union__closed) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 473 (all X all Xa scratc2047737915d_soft(aa_fun1431113780TP_ind(scratc254891115_d_Sep(X),Xa),X,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1318166930_Sigma,aa_fun1431113780TP_ind(scratc254891115_d_Sep(X),Xa)),scratc1725260217d_e_in(X,Xa))) = scratc1730175485nd_out(X,Xa)) # label(fact_def__out) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 474 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ft,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fu,Uu)))) # label(fact_ATP_Olambda__212) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 475 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1719469294munion,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1685334398_union,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1185191648d_repl,X),Xa))) # label(fact_def__famunion) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 476 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,X),Xa)) <-> pp(aa_bool_bool(scratc1112669246d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,X),Xa))))) # label(fact_def__lessis) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 477 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_km,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_kl(Uu),Uua))))) # label(fact_ATP_Olambda__433) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 478 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_oc,Uu),Uua)))) # label(fact_ATP_Olambda__300) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 479 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_eu(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ev,Uu),Uua)))) # label(fact_ATP_Olambda__473) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 480 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dd,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,Uu),scratc514495423d_frac)))) # label(fact_ATP_Olambda__24) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 481 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_vx,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_vy,Uu)))) # label(fact_ATP_Olambda__78) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 482 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174643062lesseq,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039435_moreq,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mq,Uu),Uua)))) # label(fact_ATP_Olambda__297) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 483 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_tu,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_tt,Uu))))) # label(fact_ATP_Olambda__93) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 484 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725260222d_e_is(aa_TPTP_ind_TPTP_ind(scratc19677640etprod(Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1423256749d_pair(Uu,Uua),aa_TPTP_ind_TPTP_ind(scratc90902847_first(Uu,Uua),Uub)),aa_TPTP_ind_TPTP_ind(scratc994261093second(Uu,Uua),Uub))),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abz(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__490) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 485 (all P all Q all R aa_TPT2142672771l_bool(cOMBB_658106424TP_ind(P,Q),R) = aa_boo1142376798l_bool(P,aa_TPTP_ind_bool(Q,R))) # label(help_COMBB_1_1_COMBB_001t__HOL__Obool_001t__fun_It__HOL__Obool_Mt__HOL__Obool_J_001t__TPTP____Interpret__Oind_U) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 486 (all X all Xa scratc623004572eplSep(X,Xa) = aa_TPT494704832TP_ind(scratc1185191648d_repl,aa_fun1431113780TP_ind(scratc254891115_d_Sep(X),Xa))) # label(fact_def__d__ReplSep) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 487 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uua)),Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xu,Uu),Uua)))) # label(fact_ATP_Olambda__318) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 488 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_qn,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_qo,Uu)))) # label(fact_ATP_Olambda__122) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 489 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc246405046lessis,X),Xa)) <-> pp(aa_bool_bool(scratc1112669246d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1575955453_rt_is,X),Xa))))) # label(fact_def__rt__lessis) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 490 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ph,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_pg,Uu))))) # label(fact_ATP_Olambda__131) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 491 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174643062lesseq,Uu),Uua)) -> pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_no,Uu),Uua)))) # label(fact_ATP_Olambda__313) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 492 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_zh,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_zg,Uu))))) # label(fact_ATP_Olambda__47) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 493 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wa,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_vz(Uu),Uua))))) # label(fact_ATP_Olambda__370) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 494 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hl,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uu),Uua)) -> pp(aa_fun171081125l_bool(scratc413789423l_some(scratc514495423d_frac),aa_TPT43085870d_bool(aTP_Lamm_hk(Uu),Uua)))))) # label(fact_ATP_Olambda__304) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 495 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jm(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__507) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 496 (all Uu all Uua (gg_TPTP_ind(Uua) -> ((exists X3 (gg_TPTP_ind(X3) & Uua = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1737995691d_pair,Uu),X3))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_br,Uu),Uua))))) # label(fact_ATP_Olambda__489) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 497 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ad(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc413789423l_some(scratc514495423d_frac),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ac(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__655) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 498 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sg(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uua),Uub)))))) # label(fact_ATP_Olambda__534) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 499 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_zz,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_zy,Uu))))) # label(fact_ATP_Olambda__39) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 500 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1721913973nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc1638249340nd_den,Xa))),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1721913973nd_num,Xa)),aa_TPTP_ind_TPTP_ind(scratc1638249340nd_den,X)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,X),Xa)))) # label(fact_def__moref) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 501 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1721913973nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc1638249340nd_den,Xa))),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1721913973nd_num,Xa)),aa_TPTP_ind_TPTP_ind(scratc1638249340nd_den,X)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,X),Xa)))) # label(fact_def__lessf) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 502 (all X all Xa scratc1647232439nd_eps(aa_TPT43085870d_bool(scratc719003247_rec_G(X),Xa)) = aa_TPTP_ind_TPTP_ind(scratc350768152In_rec(X),Xa)) # label(fact_def__d__In__rec) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 503 (all X all Xa scratc628336832bnd_ap = scratc680841465d_tofs(X,Xa)) # label(fact_def__tofs) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 504 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ss,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_sr,Uu))))) # label(fact_ATP_Olambda__104) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 505 (all X all Xa all Xb all Xc (pp(aa_fun171081125l_bool(scratc1303128615all_of(aa_TPT43085870d_bool(aTP_Lamm_au,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ay(X),Xa),Xb),Xc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2002475487fixfu2(X,Xa),Xb),Xc)))) # label(fact_def__fixfu2) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 506 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc380388658moreis,X),Xa)) <-> pp(aa_bool_bool(scratc1112669246d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc942939880t_more,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1575955453_rt_is,X),Xa))))) # label(fact_def__rt__moreis) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 507 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gw,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_gv,Uu))))) # label(fact_ATP_Olambda__203) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 508 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vk(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__504) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 509 (all Uu (pp(aa_fun171081125l_bool(scratc413789423l_some(scratc514495423d_frac),aa_TPT43085870d_bool(aTP_Lamm_lu,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_lv,Uu)))) # label(fact_ATP_Olambda__246) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 510 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(X),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Xa),Xb))),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(X),Xb)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc256104368_prop1(X),Xa),Xb)))) # label(fact_def__d__430__prop1) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 511 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rr(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__576) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 512 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_vn(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vo,Uu),Uua)))) # label(fact_ATP_Olambda__374) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 513 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_abt(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1890899764d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc254891115_d_Sep(Uu),Uua)))))) # label(fact_ATP_Olambda__586) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 514 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cj,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc246405046lessis,Uu),Uua)) -> pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc942939880t_more,Uu),Uua)))))) # label(fact_ATP_Olambda__307) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 515 (all X aa_TPTP_ind_TPTP_ind(scratc1212653308_UPair(X),X) = aa_TPTP_ind_TPTP_ind(scratc327484482d_Sing,X)) # label(fact_def__d__Sing) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 516 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_xw(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xx,Uu),Uua)))) # label(fact_ATP_Olambda__357) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 517 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1279598277rt_nis,X),Xa)) <-> pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1575955453_rt_is,X),Xa))))) # label(fact_def__rt__nis) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 518 (all X (pp(aa_TPTP_ind_bool(scratc1161213627_prop1,X)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1721126791nd_nis,aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,X)),X)))) # label(fact_def__d__22__prop1) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 519 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039435_moreq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ef(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__693) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 520 (all X all Xa all Xb all Xc all Xd scratc1785985336indeq2(X,Xa,Xb,Xc,Xd) = aa_TPT1424761345TP_ind(scratc853501306_indeq(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc397466166d_11_i(X,Xa,Xb),Xc),Xd))) # label(fact_def__indeq2) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 521 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cm,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cl,Uu))))) # label(fact_ATP_Olambda__238) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 522 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gb,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ga,Uu))))) # label(fact_ATP_Olambda__210) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 523 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ug(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__725) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 524 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_yq,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_yr,Uu)))) # label(fact_ATP_Olambda__55) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 525 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc623004572eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_br,Xa)),scratc1306586371_proj1)) # label(fact_def__ap) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 526 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_xf,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_xg,Uu)))) # label(fact_ATP_Olambda__68) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 527 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc872461638_pair1(X),Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1318166930_Sigma,aa_TPTP_ind_TPTP_ind(scratc2122467577_d_1to,scratc159642229nd_n_2)),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ai(X),Xa),Xb))) # label(fact_def__pair1) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 528 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_rg(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rh,Uu),Uua)))) # label(fact_ATP_Olambda__396) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 529 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_xp,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_xo,Uu))))) # label(fact_ATP_Olambda__65) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 530 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cv,Uu),Uua)) <-> scratc83947841_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1575955453_rt_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc942939880t_more,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,Uu),Uua)))) # label(fact_ATP_Olambda__252) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 531 (all Uu (gg_TPTP_ind(Uu) -> Uu = aa_TPTP_ind_TPTP_ind(aTP_Lamm_an,Uu))) # label(fact_ATP_Olambda__743) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 532 (all X all Xa aa_fun1431113780TP_ind(scratc254891115_d_Sep(X),aa_TPT43085870d_bool(aTP_Lamm_bx,Xa)) = aa_TPTP_ind_TPTP_ind(scratc482128287tminus(X),Xa)) # label(fact_def__setminus) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 533 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hn(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uua),Uub)),Uu)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uua),Uuc)),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uub),Uuc)))))) # label(fact_ATP_Olambda__671) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 534 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_oy,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ox,Uu))))) # label(fact_ATP_Olambda__139) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 535 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aaa,Uu),Uua)) <-> pp(scratc1785284969_amone(scratc1720602000nd_nat,aa_TPT43085870d_bool(aTP_Lamm_zw(Uu),Uua))))) # label(fact_ATP_Olambda__486) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 536 (all Uu all Uua all Uub all Uuc (scratc873677453d_and3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1680147248nd_inf,Uub),aa_TPTP_ind_TPTP_ind(scratc1021009639_class,Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1680147248nd_inf,Uuc),aa_TPTP_ind_TPTP_ind(scratc1021009639_class,Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ac(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__661) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 537 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_xv,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_xu,Uu))))) # label(fact_ATP_Olambda__63) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 538 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_be(Uu),Uua),Uub),Uuc)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1680081659nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1890899764d_esti(Uu),Uuc),Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1890899764d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__669) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 539 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abj,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920578d_n_in,Uua),Uu)))) # label(fact_ATP_Olambda__346) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 540 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_dr,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ds,Uu)))) # label(fact_ATP_Olambda__227) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 541 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_yt,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_ys,Uu))))) # label(fact_ATP_Olambda__54) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 542 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uu),Uua)) -> pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039435_moreq,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ng,Uu),Uua)))) # label(fact_ATP_Olambda__316) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 543 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gl(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__569) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 544 (all X0 pp(aa_TPTP_ind_bool(scratc1017527147closed,aa_TPTP_ind_TPTP_ind(scratc1703387950univof,X0)))) # label(fact_k__UnivOf__ZF__closed) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 545 (all X all Xa all Xb all Xc all Xd all Xe (pp(aa_fun171081125l_bool(scratc413789423l_some(X),aa_TPT43085870d_bool(scratc737776956_prop1(X,Xa,Xb,Xc,Xd),Xe))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1306979966_prop2(X,Xa,Xb,Xc),Xd),Xe)))) # label(fact_def__prop2) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 546 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,Uua),Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ak,Uu),Uua)))) # label(fact_ATP_Olambda__343) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 547 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dp(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039435_moreq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039435_moreq,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039435_moreq,aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uua),Uuc))))))) # label(fact_ATP_Olambda__691) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 548 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vt(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__503) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 549 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_aba,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),scratc159642228nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uu))))) # label(fact_ATP_Olambda__3) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 550 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_qc(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qd(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__614) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 551 (all B_1 all B_2 gg_bool(aa_fun171081125l_bool(B_1,B_2))) # label(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__HOL__Obool) # label(hypothesis) # label(non_clause). [assumption]. 1.54/1.79 552 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ht,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_hu,Uu)))) # label(fact_ATP_Olambda__195) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 553 (all Uu all Uua (pp(scratc1646379588nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zm,Uu),Uua)))) # label(fact_ATP_Olambda__259) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 554 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_pf(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pg,Uu),Uua)))) # label(fact_ATP_Olambda__411) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 555 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cd,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ce,Uu)))) # label(fact_ATP_Olambda__242) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 556 (all B_1 all B_2 gg_bool(aa_bool_bool(B_1,B_2))) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 557 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_wd,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_we,Uu)))) # label(fact_ATP_Olambda__76) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 558 (all X0 pp(aa_fun171081125l_bool(scratc1303128615all_of(aa_TPT43085870d_bool(aTP_Lamm_abp,X0)),aa_TPT43085870d_bool(aTP_Lamm_abr,X0)))) # label(fact_isseti) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 559 (all X all Xa (pp(aa_fun171081125l_bool(scratc1943600036_n_all,aa_TPT43085870d_bool(scratc849034026lbprop(X),Xa))) <-> pp(aa_TPTP_ind_bool(scratc1244117363d_n_lb(X),Xa)))) # label(fact_def__n__lb) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 560 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc380388658moreis,Uu),Uua)) -> pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cl,Uu),Uua)))) # label(fact_ATP_Olambda__306) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 561 (all Uu all Uua (pp(scratc1646379588nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_oe,Uu),Uua)))) # label(fact_ATP_Olambda__260) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 562 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ec(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ed,Uu),Uua)))) # label(fact_ATP_Olambda__478) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 563 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_no,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_np,Uu)))) # label(fact_ATP_Olambda__149) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 564 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ej(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__703) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 565 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vh(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__516) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 566 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_xl,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_xm,Uu)))) # label(fact_ATP_Olambda__66) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 567 (all X (pp(aa_TPTP_ind_bool(scratc1749575802_prop1,X)) <-> pp(aa_bool_bool(scratc1112669246d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,X),scratc159642228nd_n_1)),aa_fun171081125l_bool(scratc1157614065n_some,aa_TPT43085870d_bool(aTP_Lamm_ar,X)))))) # label(fact_def__d__23__prop1) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 568 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc308889072moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_pu(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__678) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 569 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_mw,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_mx,Uu)))) # label(fact_ATP_Olambda__157) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 570 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_mo,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_mp,Uu)))) # label(fact_ATP_Olambda__160) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 571 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1243723785d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1721913973nd_num,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1638249340nd_den,Uu)),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_os,Uu),Uua)))) # label(fact_ATP_Olambda__337) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 572 (all P all Q all R aa_bool_bool(aa_TPT2142672771l_bool(P,R),aa_TPTP_ind_bool(Q,R)) = aa_TPTP_ind_bool(cOMBS_2003118649l_bool(P,Q),R)) # label(help_COMBS_1_1_COMBS_001t__TPTP____Interpret__Oind_001t__HOL__Obool_001t__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 573 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(scratc159642228nd_n_1),Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_st,Uu)))) # label(fact_ATP_Olambda__18) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 574 (all P all Q (-pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) | -pp(P) | pp(Q))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 575 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fn(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__718) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 576 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1680081659nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725260222d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,Uub),Uud))),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725260222d_e_is(Uu),Uuc),Uud))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_bk(Uu),Uua),Uub),Uuc),Uud)))) # label(fact_ATP_Olambda__734) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 577 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc1703387950univof,X0)))) # label(fact_k__UnivOf__In) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 578 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1306980025_propm(X,Xa),Xb),Xc)) <-> scratc873677453d_and3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1680147248nd_inf,Xb),aa_TPTP_ind_TPTP_ind(scratc1021009639_class,X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1680147248nd_inf,Xc),aa_TPTP_ind_TPTP_ind(scratc1021009639_class,Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Xb),Xc)))) # label(fact_def__propm) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 579 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_xr,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__12) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 580 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_rs,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_rt,Uu)))) # label(fact_ATP_Olambda__113) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 581 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_uw(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__727) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 582 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_mh(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mi,Uu),Uua)))) # label(fact_ATP_Olambda__424) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 583 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xk(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__567) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 584 (all X0 (pp(aa_fun171081125l_bool(scratc1157614065n_some,X0)) -> pp(aa_fun171081125l_bool(scratc2059392297_n_one,scratc1712865281nd_min(X0))))) # label(fact_satz27a) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 585 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ef(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eg(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__647) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 586 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1890899764d_esti(Uu),Uub),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bf(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__493) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 587 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_lq,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_lp,Uu))))) # label(fact_ATP_Olambda__167) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 588 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gn,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_gm,Uu))))) # label(fact_ATP_Olambda__206) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 589 (all X (pp(scratc478607744_d_not(X)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1680081659nd_imp,X),fFalse)))) # label(fact_def__d__not) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 590 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_lm,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_ll,Uu))))) # label(fact_ATP_Olambda__137) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 591 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ud(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_uc(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__608) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 592 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_on(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1243723785d_n_fr,Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1243723785d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uua),Uub)))))) # label(fact_ATP_Olambda__533) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 593 (all Uu (gg_TPTP_ind(Uu) -> (Uu != scratc1354028742ptyset <-> pp(aa_TPTP_ind_bool(aTP_Lamm_at,Uu))))) # label(fact_ATP_Olambda__249) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 594 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_pu(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pv(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__616) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 595 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fp,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_fo(Uu),Uua))))) # label(fact_ATP_Olambda__467) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 596 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bx,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1719027618nd_nIn,Uua),Uu)))) # label(fact_ATP_Olambda__347) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 597 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mn(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__564) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 598 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),scratc159642228nd_n_1)),Uu)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_tc,Uu)))) # label(fact_ATP_Olambda__4) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 599 (all Uu all Uua all Uub (pp(scratc371142564_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uu),Uub),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uub),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lr(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__581) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 600 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1318166930_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,aa_TPTP_ind_TPTP_ind(scratc1306586370_proj0,X22)),X0)))) # label(fact_proj0__Sigma) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 601 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_ps,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_pt,Uu)))) # label(fact_ATP_Olambda__128) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 602 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_abd,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1721126791nd_nis,Uu),scratc159642228nd_n_1)) -> pp(aa_fun171081125l_bool(scratc2059392297_n_one,aa_TPT43085870d_bool(aTP_Lamm_ar,Uu)))))) # label(fact_ATP_Olambda__2) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 603 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1303128615all_of(aa_TPT43085870d_bool(aTP_Lamm_aby(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_aca(X0),X12)))) # label(fact_second__p) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 604 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),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__471) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 605 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1890899764d_esti(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,Uua),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bb(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__665) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 606 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uua),aa_TPTP_ind_TPTP_ind(scratc1771548918_367_w(Uu),Uua))),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hi,Uu),Uua)))) # label(fact_ATP_Olambda__280) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 607 (all P all Q (pp(P) | pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)))) # label(help_fimplies_1_1_U) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 608 (all X all Xa scratc1680147246nd_ind(X,Xa) = scratc1647232439nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bm(X),Xa))) # label(fact_def__ind) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 609 (all Uu all Uua all Uub all Uuc all Uud all Uue (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_ax(Uu),Uua),Uub),Uuc),Uud),Uue)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aa_TPT43085870d_bool(aTP_Lamm_au,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_aw(Uu),Uua),Uub),Uuc),Uud),Uue))))) # label(fact_ATP_Olambda__739) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 610 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc795979768d_left(X,Xa,Xb),Xc) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1318166930_Sigma,aa_TPTP_ind_TPTP_ind(scratc2122467577_d_1to,Xb)),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ah(Xa),Xb),Xc))) # label(fact_def__left) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 611 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yl(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__580) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 612 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_tp,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_tq,Uu)))) # label(fact_ATP_Olambda__95) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 613 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_co,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cn,Uu))))) # label(fact_ATP_Olambda__237) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 614 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_nr,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_nq,Uu))))) # label(fact_ATP_Olambda__148) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 615 (all X all Xa scratc1306586370_proj0 = scratc90902847_first(X,Xa)) # label(fact_def__first) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 616 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zx(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,Uua),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uub))))) # label(fact_ATP_Olambda__594) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 617 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fa(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__509) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 618 (all B_1 all B_2 gg_TPTP_ind(scratc1680147246nd_ind(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__63821__3484_ONUM790__thf__4__p_Obnd__ind) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 619 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,Xa),scratc1240247040d_n_1t) = aa_TPTP_ind_TPTP_ind(scratc1721253554first1(X),Xa)) # label(fact_def__first1) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 620 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_qg(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qh,Uu),Uua)))) # label(fact_ATP_Olambda__404) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 621 (all X all Xa all Xb aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1318166930_Sigma,X),scratc2146397333sel_wb(X,Xa,Xb)) = aa_TPTP_ind_TPTP_ind(scratc235045162wissel(X,Xa),Xb)) # label(fact_def__wissel) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 622 (all X0 all X12 (gg_TPTP_ind(X12) & gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc425835364d_Subq,X0),X12)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc425835364d_Subq,X12),X0)) -> X0 = X12)))) # label(fact_set__ext) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 623 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_oo,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_on(Uu),Uua))))) # label(fact_ATP_Olambda__413) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 624 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ha(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hb,Uu),Uua)))) # label(fact_ATP_Olambda__456) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 625 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1575955453_rt_is,Uu),Uu)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_dc,Uu)))) # label(fact_ATP_Olambda__21) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 626 (all Uu all Uua aa_fun277296641TP_ind(aa_TPT494704832TP_ind(aTP_Lamm_bw,Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc565842745nunion(aa_TPTP_ind_TPTP_ind(scratc327484482d_Sing,scratc1354028742ptyset)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1185191648d_repl,Uu),Uua))) # label(fact_ATP_Olambda__336) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 627 (all P all Q (pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)) | -pp(Q) | -pp(P))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 628 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xe(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__537) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 629 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_pe(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc308889072moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc308889072moreis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc308889072moreis,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uua),Uuc))))))) # label(fact_ATP_Olambda__680) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 630 (all B_1 all B_2 gg_TPTP_ind(scratc1646379653nd_ect(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__63821__3484_ONUM790__thf__4__p_Obnd__ect) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 631 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_fb,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fc,Uu)))) # label(fact_ATP_Olambda__217) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 632 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cf,Uu),Uua)) <-> (pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc380388658moreis,Uu),Uua))))) # label(fact_ATP_Olambda__327) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 633 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_wo,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_wp,Uu)))) # label(fact_ATP_Olambda__73) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 634 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nu,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_nt(Uu),Uua))))) # label(fact_ATP_Olambda__419) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 635 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uu),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lb(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__528) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 636 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_un,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_um,Uu))))) # label(fact_ATP_Olambda__89) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 637 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dr,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_dq(Uu),Uua))))) # label(fact_ATP_Olambda__481) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 638 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_jy(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jz,Uu),Uua)))) # label(fact_ATP_Olambda__437) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 639 (all Uu all Uua all Uub all Uuc ((pp(aa_fun171081125l_bool(scratc1303128615all_of(aa_TPT43085870d_bool(aTP_Lamm_au,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_acj(Uua),Uub),Uuc))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725260222d_e_is(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc584055948d_d_Pi,Uu),aTP_Lamm_aj(Uua))),Uub),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ack(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__672) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 640 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ml,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_mm,Uu)))) # label(fact_ATP_Olambda__161) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 641 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aak,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uua),Uu))))) # label(fact_ATP_Olambda__289) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 642 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_rn(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__706) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 643 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sb,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_sa(Uu),Uua))))) # label(fact_ATP_Olambda__390) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 644 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_uc(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc308889072moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc308889072moreis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc308889072moreis,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__681) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 645 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fz(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uub),Uua)))))) # label(fact_ATP_Olambda__560) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 646 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(Uua,Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725260222d_e_is(Uu),Uub),Uuc)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bn(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__729) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 647 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1646379649nd_ecp(X,Xa),Xb),Xc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725260222d_e_is(aa_TPTP_ind_TPTP_ind(scratc1178072532_power,X)),Xb),aa_TPTP_ind_TPTP_ind(scratc602407550_ecelt(X,Xa),Xc))))) # label(fact_def__ecp) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 648 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vq(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__515) # label(axiom) # label(non_clause). [assumption]. 1.54/1.79 649 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ps,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_pr(Uu),Uua))))) # label(fact_ATP_Olambda__408) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 650 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kg,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_kf(Uu),Uua))))) # label(fact_ATP_Olambda__435) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 651 (all X fequal_TPTP_ind = scratc1725260222d_e_is(X)) # label(fact_def__e__is) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 652 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_wj(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wk,Uu),Uua)))) # label(fact_ATP_Olambda__367) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 653 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nq,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039435_moreq,Uu),Uua)) -> pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uu),Uua)))))) # label(fact_ATP_Olambda__314) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 654 (all X all Xa all Xb all Xc (scratc873677453d_and3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1680147248nd_inf,Xb),aa_TPTP_ind_TPTP_ind(scratc1021009639_class,X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1680147248nd_inf,Xc),aa_TPTP_ind_TPTP_ind(scratc1021009639_class,Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Xb),Xc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1306980024_propl(X,Xa),Xb),Xc)))) # label(fact_def__propl) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 655 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_aae,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_aad,Uu))))) # label(fact_ATP_Olambda__37) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 656 (all X all Xa all Xb aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1318166930_Sigma,Xa),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_bi(X),Xa),Xb)) = aa_TPTP_ind_TPTP_ind(scratc1931485887nverse(X,Xa),Xb)) # label(fact_def__inverse) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 657 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_qh,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_qi,Uu)))) # label(fact_ATP_Olambda__124) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 658 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ar,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uua))))) # label(fact_ATP_Olambda__341) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 659 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_oq,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1243723785d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1721913973nd_num,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1638249340nd_den,Uu)),Uua))),Uu)))) # label(fact_ATP_Olambda__265) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 660 (all X (pp(aa_TPTP_ind_bool(scratc363539598closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X1),X)) -> (all X2 ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X3),X1)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,aa_TPTP_ind_TPTP_ind(X2,X3)),X))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1185191648d_repl,X1),X2)),X))))))))) # label(fact_def__d__Repl__closed) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 661 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ui,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_uh(Uu),Uua))))) # label(fact_ATP_Olambda__383) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 662 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1243723785d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1721913973nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc1638249340nd_den,Xa))),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1721913973nd_num,Xa)),aa_TPTP_ind_TPTP_ind(scratc1638249340nd_den,X)))),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1638249340nd_den,X)),aa_TPTP_ind_TPTP_ind(scratc1638249340nd_den,Xa))) = aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(X),Xa)) # label(fact_def__n__pf) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 663 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dt(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_du(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__650) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 664 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gf(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__555) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 665 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc675858559d_incl(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1613924016nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_be(X),Xa),Xb))))) # label(fact_def__incl) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 666 (all P (gg_bool(P) -> P = fFalse | fTrue = P)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 667 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(scratc628861614bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc48260778_image(Uu,Uua),Uub),Uuc),aa_TPTP_ind_TPTP_ind(scratc2047737915d_soft(Uu,Uua,Uub),Uuc)),scratc1354028742ptyset) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_bi(Uu),Uua),Uub),Uuc)) # label(fact_ATP_Olambda__659) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 668 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1303128615all_of(aa_fun1584354236d_bool(aTP_Lamm_acf(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_acg(X0),X12)))) # label(fact_e__inp) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 669 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_lo(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lp,Uu),Uua)))) # label(fact_ATP_Olambda__428) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 670 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_pl,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_pk,Uu))))) # label(fact_ATP_Olambda__130) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 671 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ya,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_xz(Uu),Uua))))) # label(fact_ATP_Olambda__356) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 672 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc942939880t_more,Uu),Uua)) -> pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc246405046lessis,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cd,Uu),Uua)))) # label(fact_ATP_Olambda__308) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 673 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174643062lesseq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uu),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uua),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174643062lesseq,Uub),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_mu(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__690) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 674 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(scratc1680540841nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725260222d_e_is(aa_TPTP_ind_TPTP_ind(scratc2122467577_d_1to,scratc159642229nd_n_2)),Uuc),scratc1240247040d_n_1t),Uu,Uua),Uub) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ai(Uu),Uua),Uub),Uuc)) # label(fact_ATP_Olambda__658) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 675 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1303128615all_of(aa_TPT43085870d_bool(aTP_Lamm_au,X0)),aa_fun1584354236d_bool(aTP_Lamm_abs(X0),X12)))) # label(fact_estie) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 676 (all X0 all X12 (gg_TPTP_ind(X12) & gg_TPTP_ind(X0) -> (aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,X0) = aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,X12) -> X12 = X0))) # label(fact_ordsucc__inj) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 677 (all P all Q (-pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)) | pp(Q))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 678 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qq,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_qp(Uu),Uua))))) # label(fact_ATP_Olambda__401) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 679 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abq(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc675858559d_incl(Uu),Uua),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc675858559d_incl(Uu),Uub),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725260222d_e_is(aa_TPTP_ind_TPTP_ind(scratc1178072532_power,Uu)),Uua),Uub)))))) # label(fact_ATP_Olambda__495) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 680 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(scratc628861614bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,scratc1354028742ptyset),Uub),Uu),Uua) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_bz(Uu),Uua),Uub)) # label(fact_ATP_Olambda__491) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 681 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_js,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_jr,Uu))))) # label(fact_ATP_Olambda__181) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 682 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ot,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_os,Uu))))) # label(fact_ATP_Olambda__133) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 683 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_um,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_ul(Uu),Uua))))) # label(fact_ATP_Olambda__382) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 684 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ko(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__561) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 685 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gt,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_gs,Uu))))) # label(fact_ATP_Olambda__204) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 686 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_tx,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc308889072moreis,Uu),scratc159642228nd_n_1)))) # label(fact_ATP_Olambda__23) # label(axiom) # label(non_clause). [assumption]. 1.54/1.80 687 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cp,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cq,Uu)))) # label(fact_ATP_Olambda__236) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 688 (all X all Xa all Xb (gg_TPTP_ind(Xb) -> aa_TPTP_ind_TPTP_ind(scratc1725260217d_e_in(X,Xa),Xb) = Xb)) # label(fact_def__e__in) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 689 (all X0 all X12 all X22 (gg_TPTP_ind(X22) & gg_TPTP_ind(X12) -> aa_TPTP_ind_TPTP_ind(scratc628861614bnd_if(X0,X12),X22) = X12 & pp(X0) | X22 = aa_TPTP_ind_TPTP_ind(scratc628861614bnd_if(X0,X12),X22) & -pp(X0))) # label(fact_if__i__correct) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 690 (all X all Xa ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X2),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X2),Xa))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc425835364d_Subq,X),Xa)))) # label(fact_def__d__Subq) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 691 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1318166930_Sigma,X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1719469294munion,X),aTP_Lamm_bs(Xa))) # label(fact_def__d__Sigma) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 692 (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(scratc1243658185d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uu),Uua))))) # label(fact_ATP_Olambda__517) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 693 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_nu,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_nv,Uu)))) # label(fact_ATP_Olambda__147) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 694 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),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__371) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 695 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_sy,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_sx,Uu))))) # label(fact_ATP_Olambda__102) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 696 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_di(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dj,Uu),Uua)))) # label(fact_ATP_Olambda__483) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 697 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jc,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_jb,Uu))))) # label(fact_ATP_Olambda__186) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 698 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_gi(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gj,Uu),Uua)))) # label(fact_ATP_Olambda__461) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 699 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_zo,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_zp,Uu)))) # label(fact_ATP_Olambda__43) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 700 (all P all X7 (pp(fEx_TPTP_ind(P)) | -pp(aa_TPTP_ind_bool(P,X7)))) # label(help_fEx_1_1_fEx_001t__TPTP____Interpret__Oind_U) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 701 (all X (pp(aa_TPTP_ind_bool(scratc1306979968_prop4,X)) <-> pp(aa_fun171081125l_bool(scratc413789423l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc584055948d_d_Pi,scratc1720602000nd_nat),aTP_Lamm_al)),aa_TPT43085870d_bool(scratc190454330_prop2,X))))) # label(fact_def__prop4) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 702 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_pw,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_px,Uu)))) # label(fact_ATP_Olambda__127) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 703 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abg,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1721126791nd_nis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1721126791nd_nis,aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uua)))))) # label(fact_ATP_Olambda__282) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 704 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_id(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174643062lesseq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uua),Uuc))))))) # label(fact_ATP_Olambda__689) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 705 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_en(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__698) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 706 (all Uu (gg_TPTP_ind(Uu) -> ((exists X2 (gg_TPTP_ind(X2) & Uu = aa_TPTP_ind_TPTP_ind(scratc1152592159d_Inj1,X2))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_bt,Uu))))) # label(fact_ATP_Olambda__250) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 707 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aas,Uu),Uua)))) # label(fact_ATP_Olambda__324) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 708 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc584055948d_d_Pi,X0),X12))) -> (all X32 (gg_TPTP_ind(X32) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X32),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc584055948d_d_Pi,X0),X12))) -> ((all X42 (gg_TPTP_ind(X42) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X42),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,X32),X42) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,X22),X42)))) -> X22 = X32))))))) # label(fact_k__Pi__ext) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 709 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,Uub),aa_fun1431113780TP_ind(scratc254891115_d_Sep(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_acf(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__596) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 710 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_my(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mz(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__624) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 711 (all X aa_boo1142376798l_bool(scratc1680081659nd_imp,scratc478607744_d_not(X)) = scratc1112669246d_l_or(X)) # label(fact_def__l__or) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 712 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_ry,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_rz,Uu)))) # label(fact_ATP_Olambda__111) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 713 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bs(Uu),Uua) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1185191648d_repl,aa_TPTP_ind_TPTP_ind(Uu,Uua)),aa_TPT1424761345TP_ind(scratc1737995691d_pair,Uua))) # label(fact_ATP_Olambda__321) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 714 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ou(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__573) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 715 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lh(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1243723785d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1243723785d_n_fr,Uu),Uub)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1243723785d_n_fr,Uua),Uub)))))) # label(fact_ATP_Olambda__524) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 716 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc628861614bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc628861622bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1185191648d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_by(X),Xa))),scratc1354028742ptyset) = aa_fun1431113780TP_ind(scratc254891115_d_Sep(X),Xa)) # label(fact_def__d__Sep) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 717 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_zq,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_zr,Uu)))) # label(fact_ATP_Olambda__42) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 718 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ym,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_yl(Uu),Uua))))) # label(fact_ATP_Olambda__352) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 719 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc1178072532_power,X0)))) # label(fact_k__Self__In__Power) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 720 (all B_1 all B_2 gg_TPTP_ind(aa_fun277296641TP_ind(B_1,B_2))) # label(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__TPTP____Interpret__Oind_J_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 721 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ve(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__523) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 722 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eh,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_eg(Uu),Uua))))) # label(fact_ATP_Olambda__477) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 723 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_go(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__554) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 724 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_acj(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725260222d_e_is(Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,Uua),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,Uub),Uuc))))) # label(fact_ATP_Olambda__664) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 725 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_kw,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_kv,Uu))))) # label(fact_ATP_Olambda__172) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 726 (all X (pp(aa_fun171081125l_bool(scratc1943600036_n_all,aa_TPT43085870d_bool(aTP_Lamm_aq,X))) <-> pp(aa_TPTP_ind_bool(scratc190454329_prop1,X)))) # label(fact_def__d__24__prop1) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 727 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_pp,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_po,Uu))))) # label(fact_ATP_Olambda__129) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 728 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_dv,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_dw,Uu)))) # label(fact_ATP_Olambda__226) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 729 (all X all Xa all Xb (pp(scratc371142564_d_and(X,scratc371142564_d_and(Xa,Xb))) <-> scratc873677453d_and3(X,Xa,Xb))) # label(fact_def__and3) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 730 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kd,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_kc(Uu),Uua))))) # label(fact_ATP_Olambda__436) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 731 (all B_1 all B_2 gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2))) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 732 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cu,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ct,Uu))))) # label(fact_ATP_Olambda__234) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 733 (all Uu all Uua all Uub all Uuc all Uud aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_bg(Uu),Uua),Uub),Uuc),Uud) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,aa_TPTP_ind_TPTP_ind(scratc235045162wissel(Uu,Uub),Uuc)),Uud))) # label(fact_ATP_Olambda__738) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 734 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ex(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uu),Uua))))) # label(fact_ATP_Olambda__506) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 735 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,Uu),Uua)) -> pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_za,Uu),Uua)))) # label(fact_ATP_Olambda__312) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 736 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1721913973nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc1638249340nd_den,Xa))),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1721913973nd_num,Xa)),aa_TPTP_ind_TPTP_ind(scratc1638249340nd_den,X)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,X),Xa)))) # label(fact_def__n__eq) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 737 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1680540841nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725260222d_e_is(X),Xc),Xb),X,Xa),aa_TPTP_ind_TPTP_ind(scratc2146397332sel_wa(X,Xa,Xb),Xc)) = aa_TPTP_ind_TPTP_ind(scratc2146397333sel_wb(X,Xa,Xb),Xc)) # label(fact_def__wissel__wb) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 738 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ol,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_ok(Uu),Uua))))) # label(fact_ATP_Olambda__414) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 739 (all X (gg_TPTP_ind(X) -> (pp(aa_TPTP_ind_bool(scratc242504517pair_p,X)) <-> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1737995691d_pair,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,X),scratc1354028742ptyset)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,X),aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,scratc1354028742ptyset))) = X))) # label(fact_def__pair__p) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 740 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_wq(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wr(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__599) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 741 (all X (pp(aa_fun171081125l_bool(scratc1943600036_n_all,aa_TPT43085870d_bool(aTP_Lamm_as,X))) <-> pp(aa_TPTP_ind_bool(scratc1321703103_cond2,X)))) # label(fact_def__cond2) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 742 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1318166930_Sigma,X0),X12))) -> X22 = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1737995691d_pair,aa_TPTP_ind_TPTP_ind(scratc1306586370_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1306586371_proj1,X22)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,aa_TPTP_ind_TPTP_ind(scratc1306586370_proj0,X22)),X0)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,aa_TPTP_ind_TPTP_ind(scratc1306586371_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1306586370_proj0,X22))))))) # label(fact_k__Sigma__eta__proj0__proj1) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 743 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039435_moreq,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_eb(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__696) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 744 (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(scratc628861622bnd_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(scratc719003247_rec_G(X),Xa),Xb)))) # label(fact_def__d__In__rec__G) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 745 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1244182974d_n_mn(X),Xa) = scratc1680147246nd_ind(scratc1720602000nd_nat,aa_TPT43085870d_bool(scratc488442041ffprop(X),Xa))) # label(fact_def__n__mn) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 746 (all X all Xa (pp(aa_TPTP_ind_bool(scratc1712865281nd_min(X),Xa)) <-> pp(scratc371142564_d_and(aa_TPTP_ind_bool(scratc1244117363d_n_lb(X),Xa),aa_TPTP_ind_bool(X,Xa))))) # label(fact_def__min) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 747 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gh,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_gg,Uu))))) # label(fact_ATP_Olambda__208) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 748 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hh,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_hg,Uu))))) # label(fact_ATP_Olambda__199) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 749 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_gd,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ge,Uu)))) # label(fact_ATP_Olambda__209) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 750 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),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__474) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 751 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jk,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_jj(Uu),Uua))))) # label(fact_ATP_Olambda__441) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 752 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zs,Uu),Uua)) <-> pp(scratc1646379588nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1157614065n_some,aa_TPT43085870d_bool(scratc488442041ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc1157614065n_some,aa_TPT43085870d_bool(scratc488442041ffprop(Uua),Uu)))))) # label(fact_ATP_Olambda__263) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 753 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_mz(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_na,Uu),Uua)))) # label(fact_ATP_Olambda__420) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 754 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_xs,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_xt,Uu)))) # label(fact_ATP_Olambda__64) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 755 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(scratc159642228nd_n_1),Uu)),Uu)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_sz,Uu)))) # label(fact_ATP_Olambda__6) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 756 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_yy,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_yz,Uu)))) # label(fact_ATP_Olambda__51) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 757 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc425835364d_Subq,X12),X0)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1178072532_power,X0))))) # label(fact_k__PowerEq) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 758 (all X0 pp(aa_fun171081125l_bool(scratc1303128615all_of(aa_TPT43085870d_bool(aTP_Lamm_au,X0)),aa_TPT43085870d_bool(aTP_Lamm_aco,X0)))) # label(fact_refis) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 759 (all X aa_TPTP_ind_TPTP_ind(scratc1306586370_proj0,X) = aa_fun277296641TP_ind(scratc623004572eplSep(X,aTP_Lamm_bu),scratc272004510_d_Unj)) # label(fact_def__proj0) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 760 (all Uu (gg_TPTP_ind(Uu) -> ((exists X2 (gg_TPTP_ind(X2) & Uu = aa_TPTP_ind_TPTP_ind(scratc1152592158d_Inj0,X2))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu))))) # label(fact_ATP_Olambda__251) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 761 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_wa,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_wb,Uu)))) # label(fact_ATP_Olambda__77) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 762 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jv,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ju(Uu),Uua))))) # label(fact_ATP_Olambda__438) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 763 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc308889072moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yc(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__543) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 764 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_abw(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725260222d_e_is(Uu),aa_TPTP_ind_TPTP_ind(scratc90902847_first(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1423256749d_pair(Uu,Uua),Uub),Uuc))),Uub)))) # label(fact_ATP_Olambda__662) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 765 (all X all Xa (pp(aa_TPTP_ind_bool(Xa,X)) <-> scratc1383686962_is_of(X,Xa))) # label(fact_def__is__of) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 766 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_vn(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__522) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 767 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ee,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ed,Uu))))) # label(fact_ATP_Olambda__224) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 768 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,Uub),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc584055948d_d_Pi,Uu),aTP_Lamm_aj(Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aci(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__592) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 769 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_zu,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_zv,Uu)))) # label(fact_ATP_Olambda__40) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 770 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aam(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__526) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 771 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1178072532_power,X0))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc425835364d_Subq,X12),X0)))) # label(fact_k__PowerE) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 772 (all X all Xa (-pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1719027618nd_nIn,X),Xa)))) # label(fact_def__nIn) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 773 (all X (scratc1795217933nd_wel(X) <-> pp(scratc478607744_d_not(scratc478607744_d_not(X))))) # label(fact_def__wel) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 774 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_rc(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rd,Uu),Uua)))) # label(fact_ATP_Olambda__397) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 775 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_rl,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_rm,Uu)))) # label(fact_ATP_Olambda__115) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 776 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_abm,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_abl,Uu))))) # label(fact_ATP_Olambda__27) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 777 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_fun171081125l_bool(scratc1303128615all_of(aa_TPT43085870d_bool(aTP_Lamm_au,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_az(Uua),Uub),Uuc),Uud))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ba(Uu),Uua),Uub),Uuc),Uud)))) # label(fact_ATP_Olambda__737) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 778 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hf,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_he,Uu))))) # label(fact_ATP_Olambda__200) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 779 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xn(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__536) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 780 (all Uu (pp(aa_fun171081125l_bool(scratc1729716277nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc584055948d_d_Pi,scratc1720602000nd_nat),aTP_Lamm_al)),aa_TPT43085870d_bool(aTP_Lamm_abb,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_abc,Uu)))) # label(fact_ATP_Olambda__7) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 781 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wz,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_wy(Uu),Uua))))) # label(fact_ATP_Olambda__363) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 782 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rp,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_ro(Uu),Uua))))) # label(fact_ATP_Olambda__394) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 783 (all X all Xa all Xb aa_fun1431113780TP_ind(scratc254891115_d_Sep(X),aa_TPT43085870d_bool(Xa,Xb)) = aa_TPTP_ind_TPTP_ind(scratc602407550_ecelt(X,Xa),Xb)) # label(fact_def__ecelt) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 784 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1303128615all_of(aa_TPT43085870d_bool(aTP_Lamm_au,X0)),aa_TPT43085870d_bool(aTP_Lamm_abv(X0),X12)))) # label(fact_secondis1) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 785 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_zi,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_zj,Uu)))) # label(fact_ATP_Olambda__46) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 786 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_lb(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lc,Uu),Uua)))) # label(fact_ATP_Olambda__429) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 787 (all X aa_TPT1424761345TP_ind(scratc628336832bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1829659435d_plus,X)) = scratc1244379769d_n_pl(X)) # label(fact_def__n__pl) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 788 (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(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,Uu),aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,Uu),Uua)))))) # label(fact_ATP_Olambda__279) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 789 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ta,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),Uua)),Uu))))) # label(fact_ATP_Olambda__276) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 790 (all Uu all Uua all Uub ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X3),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,Uub),X3)),aa_TPTP_ind_TPTP_ind(Uua,X3)))))) <-> pp(aa_TPTP_ind_bool(aa_fun1913827119d_bool(aTP_Lamm_bq(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__657) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 791 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_sl,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_sk,Uu))))) # label(fact_ATP_Olambda__107) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 792 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aay,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__278) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 793 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_rr(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rs,Uu),Uua)))) # label(fact_ATP_Olambda__393) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 794 (all X all Xa (pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1680081659nd_imp,X),scratc478607744_d_not(Xa))) <-> pp(scratc1112013241d_l_ec(X,Xa)))) # label(fact_def__l__ec) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 795 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_so,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_sn,Uu))))) # label(fact_ATP_Olambda__106) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 796 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_go(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gp,Uu),Uua)))) # label(fact_ATP_Olambda__459) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 797 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ok(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1243723785d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uua),Uub))),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1243723785d_n_fr,Uu),Uua))))) # label(fact_ATP_Olambda__501) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 798 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_of,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_oe,Uu))))) # label(fact_ATP_Olambda__143) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 799 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tt,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc308889072moreis,Uua),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),scratc159642228nd_n_1)))))) # label(fact_ATP_Olambda__286) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 800 (all X all Xa scratc1730175485nd_out(aa_TPTP_ind_TPTP_ind(scratc1178072532_power,X),scratc873743100d_anec(X,Xa)) = scratc367018365ectset(X,Xa)) # label(fact_def__ectset) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 801 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_aac(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aad,Uu),Uua)))) # label(fact_ATP_Olambda__351) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 802 (all Uu all Uua all Uub (scratc1383686962_is_of(aa_TPTP_ind_TPTP_ind(scratc90902847_first(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_au,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_acb(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__497) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 803 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fv(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__714) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 804 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc1945444837hangef(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1318166930_Sigma,X),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_bg(X),Xb),Xc),Xd))) # label(fact_def__changef) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 805 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc984781556_prop1,X),Xa)) <-> pp(scratc1729978623nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,X),Xa))))) # label(fact_def__d__29__prop1) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 806 (all X all Xa (scratc1506948031d_r_ec(X,Xa) <-> (pp(X) -> pp(scratc478607744_d_not(Xa))))) # label(fact_def__r__ec) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 807 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174643062lesseq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dx(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__688) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 808 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ei,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_eh,Uu))))) # label(fact_ATP_Olambda__223) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 809 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_rx(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ry,Uu),Uua)))) # label(fact_ATP_Olambda__391) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 810 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nc,Uu),Uua)) <-> (pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174643062lesseq,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uu),Uua))))) # label(fact_ATP_Olambda__331) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 811 (all X all Xa (pp(aa_fun171081125l_bool(scratc1157614065n_some,aa_TPT43085870d_bool(scratc488442041ffprop(Xa),X))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,X),Xa)))) # label(fact_def__iii) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 812 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yi(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__549) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 813 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_to,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_tn,Uu))))) # label(fact_ATP_Olambda__96) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 814 (all X all Xa (pp(scratc371142564_d_and(aa_bool_bool(scratc1112669246d_l_or(X),Xa),scratc1112013241d_l_ec(X,Xa))) <-> scratc1097591666d_orec(X,Xa))) # label(fact_def__orec) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 815 (all Uu all Uua ((pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc380388658moreis,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,Uu),Uua)))) # label(fact_ATP_Olambda__325) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 816 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_qt,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_qu,Uu)))) # label(fact_ATP_Olambda__120) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 817 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ko(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kp,Uu),Uua)))) # label(fact_ATP_Olambda__432) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 818 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X22),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1318166930_Sigma,X0),X12)),X22) = aa_TPTP_ind_TPTP_ind(X12,X22))) # label(fact_beta) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 819 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qw,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_qv(Uu),Uua))))) # label(fact_ATP_Olambda__399) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 820 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sh,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_sg(Uu),Uua))))) # label(fact_ATP_Olambda__388) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 821 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ug(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_uh(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__607) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 822 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aa_TPT43085870d_bool(aTP_Lamm_au,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_abw(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abx(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__590) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 823 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1367178679_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Xa),X))))) # label(fact_def__d__26__prop1) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 824 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc425835364d_Subq,X12),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1178072532_power,X0))))) # label(fact_k__PowerI) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 825 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fq,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_fp,Uu))))) # label(fact_ATP_Olambda__213) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 826 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_py(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pz(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__615) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 827 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qs(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__544) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 828 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_th,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uua),scratc159642228nd_n_1)),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc308889072moreis,Uua),Uu))))) # label(fact_ATP_Olambda__269) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 829 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_fk(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fl,Uu),Uua)))) # label(fact_ATP_Olambda__468) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 830 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ly(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lz,Uu),Uua)))) # label(fact_ATP_Olambda__427) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 831 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc1729716277nd_one(X0),X12)) -> pp(aa_TPTP_ind_bool(X12,scratc1680147246nd_ind(X0,X12))))) # label(fact_oneax) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 832 (all X ((all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,aa_TPTP_ind_TPTP_ind(scratc1178072532_power,X1)),X))))) <-> pp(aa_TPTP_ind_bool(scratc1815295422closed,X)))) # label(fact_def__d__Power__closed) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 833 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1303128615all_of(aa_TPT43085870d_bool(aTP_Lamm_au,X0)),aa_fun1584354236d_bool(aTP_Lamm_abt(X0),X12)))) # label(fact_estii) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 834 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_im(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_il(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__633) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 835 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ut(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_us(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__604) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 836 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_uk(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ul(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__606) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 837 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_rn(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ro(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__610) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 838 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc396419381_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1721126791nd_nis,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(X),Xb))))) # label(fact_def__d__28__prop1) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 839 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_xy,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_xx,Uu))))) # label(fact_ATP_Olambda__62) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 840 (all X scratc1730175485nd_out(scratc1720602000nd_nat,aa_TPT43085870d_bool(aTP_Lamm_ak,X)) = scratc1123360177d_outn(X)) # label(fact_def__outn) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 841 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wg,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_wf(Uu),Uua))))) # label(fact_ATP_Olambda__368) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 842 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_oz,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uu),Uu)))) # label(fact_ATP_Olambda__22) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 843 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_acd(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aa_TPT43085870d_bool(aTP_Lamm_au,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_acc(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__589) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 844 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uu),Uua)) -> pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174643062lesseq,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ni,Uu),Uua)))) # label(fact_ATP_Olambda__315) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 845 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_rq,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_rp,Uu))))) # label(fact_ATP_Olambda__114) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 846 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1303128615all_of(aa_TPT43085870d_bool(aTP_Lamm_aci(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_acl(X0),X12)))) # label(fact_e__fisi) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 847 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sa(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uua),Uub)))))) # label(fact_ATP_Olambda__575) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 848 (all X all Xa all Xb scratc853501306_indeq(X,Xa,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc584055948d_d_Pi,X),aTP_Lamm_aj(Xb))) = scratc397466166d_11_i(X,Xa,Xb)) # label(fact_def__d__11__i) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 849 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1639623729nempty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc413789423l_some(X),aa_TPT43085870d_bool(aTP_Lamm_bf(X),Xa))))) # label(fact_def__nonempty) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 850 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ie(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_id(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__635) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 851 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),Uua)),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_su,Uu),Uua)))) # label(fact_ATP_Olambda__267) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 852 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gr(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uu),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uua),Uub))),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uu),Uub)))))) # label(fact_ATP_Olambda__530) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 853 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_ya,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_yb,Uu)))) # label(fact_ATP_Olambda__61) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 854 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1892335383indrat(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc1785985336indeq2(scratc514495423d_frac,scratc1243658185d_n_eq,Xb,Xc,X),Xa)) # label(fact_def__indrat) # label(axiom) # label(non_clause). [assumption]. 1.56/1.80 855 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc726999126ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1613924016nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bl(X),Xa),Xb))))) # label(fact_def__injective) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 856 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gd,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_gc(Uu),Uua))))) # label(fact_ATP_Olambda__463) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 857 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_rf(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__710) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 858 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_xe(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xf,Uu),Uua)))) # label(fact_ATP_Olambda__361) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 859 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174643062lesseq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174643062lesseq,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174643062lesseq,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ly(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__550) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 860 (all X0 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X0),scratc476241584_omega)) -> pp(aa_TPTP_ind_bool(scratc1270331168_nat_p,X0)))) # label(fact_omega__nat__p) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 861 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_pj(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pk,Uu),Uua)))) # label(fact_ATP_Olambda__410) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 862 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ia(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hz(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__636) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 863 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_lh(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_li,Uu),Uua)))) # label(fact_ATP_Olambda__416) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 864 (all X aa_TPTP_ind_TPTP_ind(scratc1731308402d_24_g,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1318166930_Sigma,scratc1720602000nd_nat),aTP_Lamm_ap(X))) # label(fact_def__d__24__g) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 865 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cj,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ck,Uu)))) # label(fact_ATP_Olambda__239) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 866 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sp,Uu),Uua)))) # label(fact_ATP_Olambda__288) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 867 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_uy,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_ux(Uu),Uua))))) # label(fact_ATP_Olambda__379) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 868 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kb(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kc(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__627) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 869 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_sd(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_se,Uu),Uua)))) # label(fact_ATP_Olambda__389) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 870 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ho(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hn(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__639) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 871 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_kx,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ky,Uu)))) # label(fact_ATP_Olambda__171) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 872 (all X all Xa scratc1680147246nd_ind(scratc1720602000nd_nat,aa_TPT43085870d_bool(scratc488442041ffprop(aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1721913973nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc1638249340nd_den,Xa))),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1721913973nd_num,Xa)),aa_TPTP_ind_TPTP_ind(scratc1638249340nd_den,X)))) = aa_TPTP_ind_TPTP_ind(scratc759794874367_vo(X),Xa)) # label(fact_def__d__367__vo) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 873 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_fw(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fx,Uu),Uua)))) # label(fact_ATP_Olambda__465) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 874 (all X aa_fun1431113780TP_ind(scratc254891115_d_Sep(scratc1720602000nd_nat),aa_TPT43085870d_bool(aTP_Lamm_ak,X)) = aa_TPTP_ind_TPTP_ind(scratc2122467577_d_1to,X)) # label(fact_def__d__1to) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 875 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wj(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_wi(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__601) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 876 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc1721520380nd_non(X,Xa),Xb)) <-> pp(scratc478607744_d_not(aa_TPTP_ind_bool(Xa,Xb))))) # label(fact_def__non) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 877 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_vi,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_vj,Uu)))) # label(fact_ATP_Olambda__83) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 878 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aac(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__514) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 879 (all X all Xa all Xb all Xc aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1318166930_Sigma,aa_TPTP_ind_TPTP_ind(scratc2122467577_d_1to,Xb)),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ag(Xa),Xb),Xc)) = aa_TPTP_ind_TPTP_ind(scratc789174283_right(X,Xa,Xb),Xc)) # label(fact_def__right) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 880 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hx,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_hw(Uu),Uua))))) # label(fact_ATP_Olambda__452) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 881 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc308889072moreis,Uu),Uua)) -> pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zc,Uu),Uua)))) # label(fact_ATP_Olambda__311) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 882 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X22),aa_fun1431113780TP_ind(scratc254891115_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(X12,X22)))) # label(fact_k__SepE2) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 883 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc584055948d_d_Pi,X),Xa) = aa_fun1431113780TP_ind(scratc254891115_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1178072532_power,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1318166930_Sigma,X),aTP_Lamm_bp(Xa)))),aa_fun1913827119d_bool(aTP_Lamm_bq(X),Xa))) # label(fact_def__d__Pi) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 884 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ru(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uub),Uua)))))) # label(fact_ATP_Olambda__566) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 885 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ny,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_nz,Uu)))) # label(fact_ATP_Olambda__146) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 886 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qy(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc308889072moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc308889072moreis,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uua),Uub)))))) # label(fact_ATP_Olambda__539) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 887 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_zq,Uu),Uua)) <-> scratc83947841_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uu),Uua)))) # label(fact_ATP_Olambda__253) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 888 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_wu(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__708) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 889 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eo(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_en(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__645) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 890 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gs,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_gr(Uu),Uua))))) # label(fact_ATP_Olambda__458) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 891 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uuc),Uua))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_wq(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__709) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 892 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gg,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_gf(Uu),Uua))))) # label(fact_ATP_Olambda__462) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 893 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_pm(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__684) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 894 (all P all Q all R aa_TPTP_ind_bool(aa_TPT43085870d_bool(cOMBC_1555011498d_bool(P),Q),R) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind_001t__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 895 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174643062lesseq,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dt(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__701) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 896 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_ue,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_uf,Uu)))) # label(fact_ATP_Olambda__91) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 897 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_wm(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_wn(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__600) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 898 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_nk,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_nl,Uu)))) # label(fact_ATP_Olambda__151) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 899 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_rj(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rk(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__611) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 900 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cw,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cv,Uu))))) # label(fact_ATP_Olambda__233) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 901 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_oa,Uu),Uua)))) # label(fact_ATP_Olambda__301) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 902 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc19677640etprod(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1318166930_Sigma,X),aTP_Lamm_aj(Xa))) # label(fact_def__setprod) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 903 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_acc(Uu),Uua),Uub),Uuc)) <-> scratc1383686962_is_of(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1423256749d_pair(Uu,Uua),Uub),Uuc),aa_TPT43085870d_bool(aTP_Lamm_aby(Uu),Uua)))) # label(fact_ATP_Olambda__667) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 904 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,Uua),Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_au,Uu),Uua)))) # label(fact_ATP_Olambda__348) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 905 (all Uu all Uua aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,Uu),Uua)) = aa_TPTP_ind_TPTP_ind(aTP_Lamm_ap(Uu),Uua)) # label(fact_ATP_Olambda__487) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 906 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bo(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aa_TPT43085870d_bool(aTP_Lamm_au,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bn(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__588) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 907 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_af(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc413789423l_some(scratc514495423d_frac),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ae(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__654) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 908 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lk(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1243723785d_n_fr,Uu),Uub)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1243723785d_n_fr,Uua),Uub))),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1243723785d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uua)),Uub))))) # label(fact_ATP_Olambda__500) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 909 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1157614065n_some,aa_TPT43085870d_bool(scratc488442041ffprop(X),Xa))))) # label(fact_def__d__29__ii) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 910 (all X0 all X12 all X22 (gg_TPTP_ind(X12) -> (pp(X0) -> X12 = aa_TPTP_ind_TPTP_ind(scratc628861614bnd_if(X0,X12),X22)))) # label(fact_if__i__1) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 911 (all X scratc1680147246nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc584055948d_d_Pi,scratc1720602000nd_nat),aTP_Lamm_al),aa_TPT43085870d_bool(scratc190454330_prop2,X)) = aa_TPTP_ind_TPTP_ind(scratc1829659435d_plus,X)) # label(fact_def__plus) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 912 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (-pp(X0) -> X22 = aa_TPTP_ind_TPTP_ind(scratc628861614bnd_if(X0,X12),X22)))) # label(fact_if__i__0) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 913 (all X0 all X12 (gg_TPTP_ind(X0) -> aa_TPTP_ind_TPTP_ind(scratc1306586370_proj0,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1737995691d_pair,X0),X12)) = X0)) # label(fact_proj0__pair__eq) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 914 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1685334398_union,X0))) <-> (exists X2 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X12),X2)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X2),X0)) & gg_TPTP_ind(X2))))) # label(fact_k__UnionEq) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 915 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fg(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uu),Uua))))) # label(fact_ATP_Olambda__505) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 916 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ys,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uu),Uua)) -> pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc308889072moreis,Uu),Uua)))))) # label(fact_ATP_Olambda__317) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 917 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_it(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__699) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 918 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_aah,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_aag,Uu))))) # label(fact_ATP_Olambda__36) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 919 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_dn,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_do,Uu)))) # label(fact_ATP_Olambda__228) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 920 (all X all Xa (pp(aa_fun171081125l_bool(scratc1303128615all_of(aa_TPT43085870d_bool(aTP_Lamm_au,X)),aa_fun1584354236d_bool(aTP_Lamm_bo(X),Xa))) <-> pp(scratc1785284969_amone(X,Xa)))) # label(fact_def__amone) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 921 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ln(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__723) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 922 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hv(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039435_moreq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039435_moreq,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039435_moreq,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uua),Uuc))))))) # label(fact_ATP_Olambda__692) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 923 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fn(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fo(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__643) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 924 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_nm,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_nn,Uu)))) # label(fact_ATP_Olambda__150) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 925 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ic,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ib,Uu))))) # label(fact_ATP_Olambda__193) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 926 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ji,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_jh,Uu))))) # label(fact_ATP_Olambda__184) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 927 (all X aa_TPTP_ind_TPTP_ind(scratc513369824_428_g,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1318166930_Sigma,scratc1720602000nd_nat),aTP_Lamm_am(X))) # label(fact_def__d__428__g) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 928 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,Uub),aa_TPTP_ind_TPTP_ind(scratc19677640etprod(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aby(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__595) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 929 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uua),Uub))),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sm(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__529) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 930 pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1680081659nd_imp,fFalse),fFalse)) <-> scratc649084886bvious # label(fact_def__obvious) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 931 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_sp,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_sq,Uu)))) # label(fact_ATP_Olambda__105) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 932 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dx(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dy(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__649) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 933 (all Uu all Uua all Uub (scratc1383686962_is_of(aa_TPTP_ind_TPTP_ind(scratc1725260217d_e_in(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_au,Uu)) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ach(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__498) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 934 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_yp,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_yo,Uu))))) # label(fact_ATP_Olambda__56) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 935 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aca(Uu),Uua),Uub)) <-> scratc1383686962_is_of(aa_TPTP_ind_TPTP_ind(scratc994261093second(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_au,Uua)))) # label(fact_ATP_Olambda__496) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 936 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_wl,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_wk,Uu))))) # label(fact_ATP_Olambda__74) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 937 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qz,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_qy(Uu),Uua))))) # label(fact_ATP_Olambda__398) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 938 (all X0 (gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(scratc1270331168_nat_p,X0)) -> (exists X13 (pp(aa_TPTP_ind_bool(scratc1270331168_nat_p,X13)) & aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,X13) = X0 & gg_TPTP_ind(X13))) | X0 = scratc1354028742ptyset))) # label(fact_nat__inv) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 939 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_aar,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(scratc159642228nd_n_1),Uu))))) # label(fact_ATP_Olambda__11) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 940 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ag(Uu),Uua),Uub),Uuc) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,Uub),aa_TPTP_ind_TPTP_ind(scratc1077425377ght1to(Uu,Uua),Uuc))) # label(fact_ATP_Olambda__732) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 941 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_jd(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_je,Uu),Uua)))) # label(fact_ATP_Olambda__443) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 942 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fj(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244642159d_n_tf(Uuc),Uua))))))) # label(fact_ATP_Olambda__719) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 943 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_wv(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ww,Uu),Uua)))) # label(fact_ATP_Olambda__364) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 944 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jx(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1244379763d_n_pf(Uuc),Uua))))))) # label(fact_ATP_Olambda__717) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 945 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_uj,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_ui,Uu))))) # label(fact_ATP_Olambda__90) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 946 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aai,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1721126791nd_nis,Uua),aa_TPTP_ind_TPTP_ind(scratc1244379769d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__339) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 947 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_acn(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aa_TPT43085870d_bool(aTP_Lamm_au,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_acm(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__587) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 948 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ni,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_nj,Uu)))) # label(fact_ATP_Olambda__152) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 949 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ix(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iy,Uu),Uua)))) # label(fact_ATP_Olambda__445) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 950 (all X aa_TPTP_ind_TPTP_ind(scratc565842745nunion(X),aa_TPTP_ind_TPTP_ind(scratc327484482d_Sing,X)) = aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,X)) # label(fact_def__ordsucc) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 951 (all X0 (scratc1795217933nd_wel(X0) -> pp(X0))) # label(fact_l__et) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 952 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X33),X0)) -> aa_TPTP_ind_TPTP_ind(X22,X33) = aa_TPTP_ind_TPTP_ind(X12,X33)))) -> aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1318166930_Sigma,X0),X22) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1318166930_Sigma,X0),X12))) # label(fact_xi__ext) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 953 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pc,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_pb(Uu),Uua))))) # label(fact_ATP_Olambda__412) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 954 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_xh(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_xi,Uu),Uua)))) # label(fact_ATP_Olambda__360) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 955 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,Uu),scratc1720602000nd_nat)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_lg,Uu)))) # label(fact_ATP_Olambda__26) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 956 (all X aa_TPTP_ind_TPTP_ind(scratc970191445_times,X) = scratc1680147246nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc584055948d_d_Pi,scratc1720602000nd_nat),aTP_Lamm_al),aa_TPT43085870d_bool(scratc1421322152_prop2,X))) # label(fact_def__times) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 957 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bp(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1685334398_union,aa_TPTP_ind_TPTP_ind(Uu,Uua))) # label(fact_ATP_Olambda__488) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 958 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_vc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_vd,Uu)))) # label(fact_ATP_Olambda__85) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 959 (all X all Xa scratc1737995691d_pair = scratc1423256749d_pair(X,Xa)) # label(fact_def__d__pair) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 960 (all X scratc1303128615all_of(aa_TPT43085870d_bool(aTP_Lamm_au,X)) = scratc1613924016nd_all(X)) # label(fact_def__all) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 961 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_oj,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_oi,Uu))))) # label(fact_ATP_Olambda__141) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 962 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abl,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243920583d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__271) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 963 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_rd,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_re,Uu)))) # label(fact_ATP_Olambda__117) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 964 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_qq,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_qr,Uu)))) # label(fact_ATP_Olambda__121) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 965 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_oi,Uu),Uua)) <-> scratc83947841_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243658185d_n_eq,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013039424_moref,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uu),Uua)))) # label(fact_ATP_Olambda__254) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 966 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aa_TPT43085870d_bool(aTP_Lamm_abp,Uu)),aa_TPT43085870d_bool(aTP_Lamm_abq(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_abr,Uu),Uua)))) # label(fact_ATP_Olambda__322) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 967 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tj,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uua),aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uu))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,Uua),Uu))))) # label(fact_ATP_Olambda__277) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 968 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mk(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174643062lesseq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1666717628_lessf,Uu),Uub)))))) # label(fact_ATP_Olambda__551) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 969 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ub,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_ua,Uu))))) # label(fact_ATP_Olambda__92) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 970 (all B_1 all B_2 gg_bool(scratc371142564_d_and(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__63821__3484_ONUM790__thf__4__p_Obnd__d__and) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 971 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_zn,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_zm,Uu))))) # label(fact_ATP_Olambda__44) # label(axiom) # label(non_clause). [assumption]. 1.56/1.81 972 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_sv,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_su,Uu))))) # label(fact_ATP_Olambda__103) # label(axiom) # label(non_clause). [assumption]. 1.57/1.81 973 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_qa,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_qb,Uu)))) # label(fact_ATP_Olambda__126) # label(axiom) # label(non_clause). [assumption]. 1.57/1.81 974 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ir,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_is,Uu)))) # label(fact_ATP_Olambda__189) # label(axiom) # label(non_clause). [assumption]. 1.57/1.81 975 (all X0 (pp(aa_TPTP_ind_bool(X0,scratc1354028742ptyset)) -> ((all X13 (gg_TPTP_ind(X13) -> (pp(aa_TPTP_ind_bool(scratc1270331168_nat_p,X13)) -> (pp(aa_TPTP_ind_bool(X0,X13)) -> pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,X13))))))) -> (all X12 (pp(aa_TPTP_ind_bool(scratc1270331168_nat_p,X12)) -> pp(aa_TPTP_ind_bool(X0,X12))))))) # label(fact_nat__ind) # label(axiom) # label(non_clause). [assumption]. 1.57/1.81 976 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_kh,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_kg,Uu))))) # label(fact_ATP_Olambda__177) # label(axiom) # label(non_clause). [assumption]. 1.57/1.81 977 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_eq,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ep,Uu))))) # label(fact_ATP_Olambda__221) # label(axiom) # label(non_clause). [assumption]. 1.57/1.81 978 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1303128615all_of(aa_TPT43085870d_bool(aTP_Lamm_au,X0)),aa_TPT43085870d_bool(aTP_Lamm_acd(X0),X12)))) # label(fact_e__pair__p) # label(axiom) # label(non_clause). [assumption]. 1.57/1.81 979 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aco,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1725260222d_e_is(Uu),Uua),Uua)))) # label(fact_ATP_Olambda__264) # label(axiom) # label(non_clause). [assumption]. 1.57/1.81 980 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qg(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1244642172d_n_ts(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1679819256nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__521) # label(axiom) # label(non_clause). [assumption]. 1.57/1.81 981 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1303128615all_of(aa_fun1584354236d_bool(aTP_Lamm_acf(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_ach(X0),X12)))) # label(fact_e__in__p) # label(axiom) # label(non_clause). [assumption]. 1.57/1.81 982 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_ex(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ey,Uu),Uua)))) # label(fact_ATP_Olambda__472) # label(axiom) # label(non_clause). [assumption]. 1.57/1.81 983 (all X0 all X12 all X22 all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc584055948d_d_Pi,X0),X12))) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,X32),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc628336832bnd_ap,X22),X32)),aa_TPTP_ind_TPTP_ind(X12,X32)))))) # label(fact_ap__Pi) # label(axiom) # label(non_clause). [assumption]. 1.57/1.81 984 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,Uu),scratc1753648020nd_rat)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_a,Uu)))) # label(fact_ATP_Olambda__25) # label(axiom) # label(non_clause). [assumption]. 1.57/1.81 985 (all X all Xa all Xb all Xc (pp(aa_fun171081125l_bool(scratc413789423l_some(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bj(Xa),Xb),Xc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc48260778_image(X,Xa),Xb),Xc)))) # label(fact_def__image) # label(axiom) # label(non_clause). [assumption]. 1.57/1.81 986 (all X all Xa (pp(aa_fun171081125l_bool(scratc1943600036_n_all,aa_TPT43085870d_bool(aTP_Lamm_ao(X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1421322151_prop1,X),Xa)))) # label(fact_def__d__428__prop1) # label(axiom) # label(non_clause). [assumption]. 1.57/1.89 987 (all Uu (pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_lg),aa_TPT43085870d_bool(aTP_Lamm_zc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_zd,Uu)))) # label(fact_ATP_Olambda__49) # label(axiom) # label(non_clause). [assumption]. 1.57/1.89 988 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682640122_29_ii,Uu),Uua)) -> pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc174905460lessis,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_yu,Uu),Uua)))) # label(fact_ATP_Olambda__310) # label(axiom) # label(non_clause). [assumption]. 1.57/1.89 989 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_da,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1575955453_rt_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1575955453_rt_is,Uua),Uu))))) # label(fact_ATP_Olambda__298) # label(axiom) # label(non_clause). [assumption]. 1.57/1.89 990 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_abo,Uu)) <-> scratc1383686962_is_of(aa_TPTP_ind_TPTP_ind(scratc385754546rdsucc,Uu),aTP_Lamm_lg))) # label(fact_ATP_Olambda__14) # label(axiom) # label(non_clause). [assumption]. 1.57/1.89 991 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc628861622bnd_in,Uub),Uu)) & pp(aa_TPTP_ind_bool(Uua,Uub)) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bm(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__582) # label(axiom) # label(non_clause). [assumption]. 1.57/1.89 992 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ke,Uu)) <-> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_dd),aa_TPT43085870d_bool(aTP_Lamm_kd,Uu))))) # label(fact_ATP_Olambda__178) # label(axiom) # label(non_clause). [assumption]. 1.57/1.89 1.57/1.89 ============================== end of process non-clausal formulas === 1.57/1.89 1.57/1.89 ============================== PROCESS INITIAL CLAUSES =============== 1.57/1.89 1.57/1.89 ============================== PREDICATE ELIMINATION ================= 1.57/1.89 993 -gg_bool(A) | fFalse = A | A = fTrue # label(help_fFalse_1_1_T) # label(axiom). [clausify(666)]. 1.57/1.89 994 gg_bool(scratc1785284969_amone(A,B)) # label(gsy_c_Scratch__tptp__translate__63821__3484_ONUM790__thf__4__p_Obnd__amone) # label(axiom). [clausify(52)]. 1.57/1.89 995 gg_bool(scratc1646379588nd_ec3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__63821__3484_ONUM790__thf__4__p_Obnd__ec3) # label(axiom). [clausify(80)]. 1.57/1.89 996 gg_bool(fEx_TPTP_ind(A)) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom). [clausify(93)]. 1.57/1.89 997 gg_bool(scratc1729978623nd_or3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__63821__3484_ONUM790__thf__4__p_Obnd__or3) # label(axiom). [clausify(125)]. 1.57/1.89 998 gg_bool(fFalse) # label(gsy_c_fFalse) # label(axiom). [assumption]. 1.57/1.89 999 gg_bool(aa_TPTP_ind_bool(A,B)) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom). [clausify(208)]. 1.57/1.89 1000 gg_bool(scratc1112013241d_l_ec(A,B)) # label(gsy_c_Scratch__tptp__translate__63821__3484_ONUM790__thf__4__p_Obnd__l__ec) # label(axiom). [clausify(302)]. 1.57/1.89 1001 gg_bool(scratc478607744_d_not(A)) # label(gsy_c_Scratch__tptp__translate__63821__3484_ONUM790__thf__4__p_Obnd__d__not) # label(axiom). [clausify(465)]. 1.57/1.89 1002 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(551)]. 1.57/1.89 1003 gg_bool(aa_bool_bool(A,B)) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom). [clausify(556)]. 1.57/1.89 Derived: fFalse = scratc1785284969_amone(A,B) | scratc1785284969_amone(A,B) = fTrue. [resolve(993,a,994,a)]. 1.57/1.89 Derived: fFalse = scratc1646379588nd_ec3(A,B,C) | scratc1646379588nd_ec3(A,B,C) = fTrue. [resolve(993,a,995,a)]. 1.57/1.89 Derived: fFalse = fEx_TPTP_ind(A) | fEx_TPTP_ind(A) = fTrue. [resolve(993,a,996,a)]. 1.57/1.89 Derived: fFalse = scratc1729978623nd_or3(A,B,C) | scratc1729978623nd_or3(A,B,C) = fTrue. [resolve(993,a,997,a)]. 1.57/1.89 Derived: fFalse = fFalse | fFalse = fTrue. [resolve(993,a,998,a)]. 5.08/5.33 Derived: fFalse = aa_TPTP_ind_bool(A,B) | aa_TPTP_ind_bool(A,B) = fTrue. [resolve(993,a,999,a)]. 5.08/5.33 Derived: fFalse = scratc1112013241d_l_ec(A,B) | scratc1112013241d_l_ec(A,B) = fTrue. [resolve(993,a,1000,a)]. 5.08/5.33 Derived: fFalse = scratc478607744_d_not(A) | scratc478607744_d_not(A) = fTrue. [resolve(993,a,1001,a)]. 5.08/5.33 Derived: fFalse = aa_fun171081125l_bool(A,B) | aa_fun171081125l_bool(A,B) = fTrue. [resolve(993,a,1002,a)]. 5.08/5.33 Derived: fFalse = aa_bool_bool(A,B) | aa_bool_bool(A,B) = fTrue. [resolve(993,a,1003,a)]. 5.08/5.33 1004 gg_bool(undefined_bool(bool)) # label(gsy_c_HOL_Oundefined_001t__HOL__Obool) # label(axiom). [assumption]. 5.08/5.33 Derived: fFalse = undefined_bool(bool) | undefined_bool(bool) = fTrue. [resolve(1004,a,993,a)]. 5.08/5.33 1005 gg_bool(fTrue) # label(gsy_c_fTrue) # label(axiom). [assumption]. 5.08/5.33 Derived: fFalse = fTrue | fTrue = fTrue. [resolve(1005,a,993,a)]. 5.08/5.33 1006 gg_bool(scratc371142564_d_and(A,B)) # label(gsy_c_Scratch__tptp__translate__63821__3484_ONUM790__thf__4__p_Obnd__d__and) # label(axiom). [clausify(970)]. 5.08/5.33 Derived: fFalse = scratc371142564_d_and(A,B) | scratc371142564_d_and(A,B) = fTrue. [resolve(1006,a,993,a)]. 5.08/5.33 1007 scratc1265284014_l_iff(A,B) | -pp(scratc371142564_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1680081659nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc1680081659nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(379)]. 5.08/5.33 1008 -scratc1265284014_l_iff(A,B) | pp(scratc371142564_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1680081659nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc1680081659nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(379)]. 5.08/5.33 1009 scratc1795217933nd_wel(A) | -pp(scratc478607744_d_not(scratc478607744_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(773)]. 5.08/5.33 1010 -scratc1795217933nd_wel(A) | pp(scratc478607744_d_not(scratc478607744_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(773)]. 5.08/5.33 1011 -scratc1795217933nd_wel(A) | pp(A) # label(fact_l__et) # label(axiom). [clausify(951)]. 5.08/5.33 Derived: pp(A) | -pp(scratc478607744_d_not(scratc478607744_d_not(A))). [resolve(1011,a,1009,a)]. 5.08/5.33 1012 scratc1506948031d_r_ec(A,B) | pp(A) # label(fact_def__r__ec) # label(axiom). [clausify(806)]. 5.08/5.33 1013 -scratc1506948031d_r_ec(A,B) | -pp(A) | pp(scratc478607744_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(806)]. 5.08/5.33 1014 scratc1506948031d_r_ec(A,B) | -pp(scratc478607744_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(806)]. 5.08/5.33 1015 pp(scratc371142564_d_and(aa_bool_bool(scratc1112669246d_l_or(A),B),scratc1112013241d_l_ec(A,B))) | -scratc1097591666d_orec(A,B) # label(fact_def__orec) # label(axiom). [clausify(814)]. 5.08/5.33 1016 -pp(scratc371142564_d_and(aa_bool_bool(scratc1112669246d_l_or(A),B),scratc1112013241d_l_ec(A,B))) | scratc1097591666d_orec(A,B) # label(fact_def__orec) # label(axiom). [clausify(814)]. 5.08/5.33 5.08/5.33 ============================== end predicate elimination ============= 5.08/5.33 5.08/5.33 Auto_denials: (non-Horn, no changes). 5.08/5.33 5.08/5.33 Term ordering decisions: 5.08/5.33 Function symbol KB weights: aTP_Lamm_lg=1. aTP_Lamm_dd=1. scratc1243658185d_n_eq=1. scratc1243920583d_n_is=1. scratc1666717628_lessf=1. scratc1679819256nd_iii=1. scratc2013039424_moref=1. scratc1682640122_29_ii=1. scratc628861622bnd_in=1. scratc385754546rdsucc=1. scratc174905460lessis=1. scratc628336832bnd_ap=1. scratc308889072moreis=1. scratc159642228nd_n_1=1. aTP_Lamm_au=1. scratc174643062lesseq=1. aTP_Lamm_a=1. scratc2013039435_moreq=1. scratc1720602000nd_nat=1. scratc1318166930_Sigma=1. scratc1354028742ptyset=1. scratc1243723785d_n_fr=1. scratc1638249340nd_den=1. scratc514495423d_frac=1. scratc584055948d_d_Pi=1. scratc1721126791nd_nis=1. scratc1575955453_rt_is=1. scratc1721913973nd_num=1. scratc1157614065n_some=1. scratc79803244t_less=1. fFalse=1. scratc1178072532_power=1. scratc1270331168_nat_p=1. scratc1680081659nd_imp=1. scratc942939880t_more=1. scratc1185191648d_repl=1. scratc1021009639_class=1. scratc1680147248nd_inf=1. fTrue=1. scratc1943600036_n_all=1. scratc1737995691d_pair=1. aTP_Lamm_al=1. scratc380388658moreis=1. scratc425835364d_Subq=1. scratc1306586370_proj0=1. scratc159642229nd_n_2=1. scratc1685334398_union=1. scratc1753648020nd_rat=1. scratc363539598closed=1. aTP_Lamm_ar=1. scratc1243920578d_n_in=1. scratc1306586371_proj1=1. scratc246405046lessis=1. aTP_Lamm_abp=1. aTP_Lamm_aq=1. scratc1650562408closed=1. scratc1815295422closed=1. scratc2122467577_d_1to=1. aTP_Lamm_aa=1. aTP_Lamm_abg=1. aTP_Lamm_abk=1. aTP_Lamm_abl=1. aTP_Lamm_ak=1. aTP_Lamm_cb=1. aTP_Lamm_cd=1. aTP_Lamm_cf=1. aTP_Lamm_ch=1. aTP_Lamm_cj=1. aTP_Lamm_cl=1. aTP_Lamm_cn=1. aTP_Lamm_cp=1. aTP_Lamm_da=1. aTP_Lamm_hg=1. aTP_Lamm_hi=1. aTP_Lamm_hl=1. aTP_Lamm_ls=1. aTP_Lamm_mq=1. aTP_Lamm_ms=1. aTP_Lamm_nc=1. aTP_Lamm_ne=1. aTP_Lamm_ng=1. aTP_Lamm_ni=1. aTP_Lamm_nk=1. aTP_Lamm_nm=1. aTP_Lamm_no=1. aTP_Lamm_nq=1. aTP_Lamm_oa=1. aTP_Lamm_oc=1. aTP_Lamm_ox=1. aTP_Lamm_tf=1. aTP_Lamm_th=1. aTP_Lamm_tj=1. aTP_Lamm_tl=1. aTP_Lamm_tn=1. aTP_Lamm_tp=1. aTP_Lamm_tr=1. aTP_Lamm_tt=1. aTP_Lamm_yo=1. aTP_Lamm_yq=1. aTP_Lamm_ys=1. aTP_Lamm_yu=1. aTP_Lamm_yw=1. aTP_Lamm_yy=1. aTP_Lamm_za=1. aTP_Lamm_zc=1. aTP_Lamm_ze=1. aTP_Lamm_zg=1. aTP_Lamm_zi=1. aTP_Lamm_zk=1. scratc1017527147closed=1. scratc1152592159d_Inj1=1. scratc1421322152_prop2=1. scratc190454330_prop2=1. scratc476241584_omega=1. aTP_Lamm_aaa=1. aTP_Lamm_aad=1. aTP_Lamm_aag=1. aTP_Lamm_aai=1. aTP_Lamm_aak=1. aTP_Lamm_aan=1. aTP_Lamm_aap=1. aTP_Lamm_aas=1. aTP_Lamm_aav=1. aTP_Lamm_aay=1. aTP_Lamm_abb=1. aTP_Lamm_abd=1. aTP_Lamm_abe=1. aTP_Lamm_abj=1. aTP_Lamm_as=1. aTP_Lamm_br=1. aTP_Lamm_bt=1. aTP_Lamm_bu=1. aTP_Lamm_cr=1. aTP_Lamm_ct=1. aTP_Lamm_cv=1. aTP_Lamm_cy=1. aTP_Lamm_df=1. aTP_Lamm_dj=1. aTP_Lamm_dn=1. aTP_Lamm_dr=1. aTP_Lamm_dv=1. aTP_Lamm_dz=1. aTP_Lamm_ed=1. aTP_Lamm_eh=1. aTP_Lamm_el=1. aTP_Lamm_ep=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_fl=1. aTP_Lamm_fp=1. aTP_Lamm_ft=1. aTP_Lamm_fx=1. aTP_Lamm_ga=1. aTP_Lamm_gd=1. aTP_Lamm_gg=1. aTP_Lamm_gj=1. aTP_Lamm_gm=1. aTP_Lamm_gp=1. aTP_Lamm_gs=1. aTP_Lamm_gv=1. aTP_Lamm_gx=1. aTP_Lamm_hb=1. aTP_Lamm_he=1. aTP_Lamm_hp=1. aTP_Lamm_ht=1. aTP_Lamm_hx=1. aTP_Lamm_ib=1. aTP_Lamm_if=1. aTP_Lamm_ij=1. aTP_Lamm_in=1. aTP_Lamm_ir=1. aTP_Lamm_iv=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_jr=1. aTP_Lamm_jv=1. aTP_Lamm_jz=1. aTP_Lamm_kd=1. aTP_Lamm_kg=1. aTP_Lamm_kj=1. aTP_Lamm_km=1. aTP_Lamm_kp=1. aTP_Lamm_ks=1. aTP_Lamm_kv=1. aTP_Lamm_kx=1. aTP_Lamm_kz=1. aTP_Lamm_lc=1. aTP_Lamm_le=1. aTP_Lamm_li=1. aTP_Lamm_ll=1. aTP_Lamm_lp=1. aTP_Lamm_lu=1. aTP_Lamm_lw=1. aTP_Lamm_lz=1. aTP_Lamm_mc=1. aTP_Lamm_mf=1. aTP_Lamm_mi=1. aTP_Lamm_ml=1. aTP_Lamm_mo=1. aTP_Lamm_mw=1. aTP_Lamm_na=1. aTP_Lamm_nu=1. aTP_Lamm_ny=1. aTP_Lamm_oe=1. aTP_Lamm_og=1. aTP_Lamm_oi=1. aTP_Lamm_ol=1. aTP_Lamm_oo=1. aTP_Lamm_oq=1. aTP_Lamm_os=1. aTP_Lamm_ov=1. aTP_Lamm_pc=1. aTP_Lamm_pg=1. aTP_Lamm_pk=1. aTP_Lamm_po=1. aTP_Lamm_ps=1. aTP_Lamm_pw=1. aTP_Lamm_qa=1. aTP_Lamm_qe=1. aTP_Lamm_qh=1. aTP_Lamm_qk=1. aTP_Lamm_qn=1. aTP_Lamm_qq=1. aTP_Lamm_qt=1. aTP_Lamm_qw=1. aTP_Lamm_qz=1. aTP_Lamm_rd=1. aTP_Lamm_rh=1. aTP_Lamm_rl=1. aTP_Lamm_rp=1. aTP_Lamm_rs=1. aTP_Lamm_rv=1. aTP_Lamm_ry=1. aTP_Lamm_sb=1. aTP_Lamm_se=1. aTP_Lamm_sh=1. aTP_Lamm_sk=1. aTP_Lamm_sn=1. aTP_Lamm_sp=1. aTP_Lamm_sr=1. aTP_Lamm_su=1. aTP_Lamm_sx=1. aTP_Lamm_ta=1. aTP_Lamm_td=1. aTP_Lamm_ua=1. aTP_Lamm_ue=1. aTP_Lamm_ui=1. aTP_Lamm_um=1. aTP_Lamm_uq=1. aTP_Lamm_uu=1. aTP_Lamm_uy=1. aTP_Lamm_vc=1. aTP_Lamm_vf=1. aTP_Lamm_vi=1. aTP_Lamm_vl=1. aTP_Lamm_vo=1. aTP_Lamm_vr=1. aTP_Lamm_vu=1. aTP_Lamm_vx=1. aTP_Lamm_wa=1. aTP_Lamm_wd=1. aTP_Lamm_wg=1. aTP_Lamm_wk=1. aTP_Lamm_wo=1. aTP_Lamm_ws=1. aTP_Lamm_ww=1. aTP_Lamm_wz=1. aTP_Lamm_xc=1. aTP_Lamm_xf=1. aTP_Lamm_xi=1. aTP_Lamm_xl=1. aTP_Lamm_xo=1. aTP_Lamm_xs=1. aTP_Lamm_xu=1. aTP_Lamm_xx=1. aTP_Lamm_ya=1. aTP_Lamm_yd=1. aTP_Lamm_yg=1. aTP_Lamm_yj=1. aTP_Lamm_ym=1. aTP_Lamm_zm=1. aTP_Lamm_zo=1. aTP_Lamm_zq=1. aTP_Lamm_zs=1. aTP_Lamm_zu=1. aTP_Lamm_zy=1. fconj=1. fimplies=1. scratc1152592158d_Inj0=1. scratc1240247040d_n_1t=1. scratc1321703103_cond2=1. scratc1421322151_prop1=1. scratc190454329_prop1=1. scratc2059392297_n_one=1. scratc327484482d_Sing=1. aTP_Lamm_aab=1. aTP_Lamm_aae=1. aTP_Lamm_aah=1. aTP_Lamm_aaj=1. aTP_Lamm_aal=1. aTP_Lamm_aao=1. aTP_Lamm_aaq=1. aTP_Lamm_aar=1. aTP_Lamm_aat=1. aTP_Lamm_aau=1. aTP_Lamm_aaw=1. aTP_Lamm_aax=1. aTP_Lamm_aaz=1. aTP_Lamm_aba=1. aTP_Lamm_abc=1. aTP_Lamm_abf=1. aTP_Lamm_abh=1. aTP_Lamm_abi=1. aTP_Lamm_abm=1. aTP_Lamm_abn=1. aTP_Lamm_abo=1. aTP_Lamm_abr=1. aTP_Lamm_aco=1. aTP_Lamm_bx=1. aTP_Lamm_cc=1. aTP_Lamm_ce=1. aTP_Lamm_cg=1. aTP_Lamm_ci=1. aTP_Lamm_ck=1. aTP_Lamm_cm=1. aTP_Lamm_co=1. aTP_Lamm_cq=1. aTP_Lamm_cs=1. aTP_Lamm_cu=1. aTP_Lamm_cw=1. aTP_Lamm_cz=1. aTP_Lamm_db=1. aTP_Lamm_dc=1. aTP_Lamm_dg=1. aTP_Lamm_dk=1. aTP_Lamm_do=1. aTP_Lamm_ds=1. aTP_Lamm_dw=1. aTP_Lamm_ea=1. aTP_Lamm_ee=1. aTP_Lamm_ei=1. aTP_Lamm_em=1. aTP_Lamm_eq=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_fm=1. aTP_Lamm_fq=1. aTP_Lamm_fu=1. aTP_Lamm_fy=1. aTP_Lamm_gb=1. aTP_Lamm_ge=1. aTP_Lamm_gh=1. aTP_Lamm_gk=1. aTP_Lamm_gn=1. aTP_Lamm_gq=1. aTP_Lamm_gt=1. aTP_Lamm_gw=1. aTP_Lamm_gy=1. aTP_Lamm_hc=1. aTP_Lamm_hf=1. aTP_Lamm_hh=1. aTP_Lamm_hj=1. aTP_Lamm_hm=1. aTP_Lamm_hq=1. aTP_Lamm_hu=1. aTP_Lamm_hy=1. aTP_Lamm_ic=1. aTP_Lamm_ig=1. aTP_Lamm_ik=1. aTP_Lamm_io=1. aTP_Lamm_is=1. aTP_Lamm_iw=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_js=1. aTP_Lamm_jw=1. aTP_Lamm_ka=1. aTP_Lamm_ke=1. aTP_Lamm_kh=1. aTP_Lamm_kk=1. aTP_Lamm_kn=1. aTP_Lamm_kq=1. aTP_Lamm_kt=1. aTP_Lamm_kw=1. aTP_Lamm_ky=1. aTP_Lamm_la=1. aTP_Lamm_ld=1. aTP_Lamm_lf=1. aTP_Lamm_lj=1. aTP_Lamm_lm=1. aTP_Lamm_lq=1. aTP_Lamm_lt=1. aTP_Lamm_lv=1. aTP_Lamm_lx=1. aTP_Lamm_ma=1. aTP_Lamm_md=1. aTP_Lamm_mg=1. aTP_Lamm_mj=1. aTP_Lamm_mm=1. aTP_Lamm_mp=1. aTP_Lamm_mr=1. aTP_Lamm_mt=1. aTP_Lamm_mx=1. aTP_Lamm_nb=1. aTP_Lamm_nd=1. aTP_Lamm_nf=1. aTP_Lamm_nh=1. aTP_Lamm_nj=1. aTP_Lamm_nl=1. aTP_Lamm_nn=1. aTP_Lamm_np=1. aTP_Lamm_nr=1. aTP_Lamm_nv=1. aTP_Lamm_nz=1. aTP_Lamm_ob=1. aTP_Lamm_od=1. aTP_Lamm_of=1. aTP_Lamm_oh=1. aTP_Lamm_oj=1. aTP_Lamm_om=1. aTP_Lamm_op=1. aTP_Lamm_or=1. aTP_Lamm_ot=1. aTP_Lamm_ow=1. aTP_Lamm_oy=1. aTP_Lamm_oz=1. aTP_Lamm_pd=1. aTP_Lamm_ph=1. aTP_Lamm_pl=1. aTP_Lamm_pp=1. aTP_Lamm_pt=1. aTP_Lamm_px=1. aTP_Lamm_qb=1. aTP_Lamm_qf=1. aTP_Lamm_qi=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_re=1. aTP_Lamm_ri=1. aTP_Lamm_rm=1. aTP_Lamm_rq=1. aTP_Lamm_rt=1. aTP_Lamm_rw=1. aTP_Lamm_rz=1. aTP_Lamm_sc=1. aTP_Lamm_sf=1. aTP_Lamm_si=1. aTP_Lamm_sl=1. aTP_Lamm_so=1. aTP_Lamm_sq=1. aTP_Lamm_ss=1. aTP_Lamm_st=1. aTP_Lamm_sv=1. aTP_Lamm_sw=1. aTP_Lamm_sy=1. aTP_Lamm_sz=1. aTP_Lamm_tb=1. aTP_Lamm_tc=1. aTP_Lamm_te=1. aTP_Lamm_tg=1. aTP_Lamm_ti=1. aTP_Lamm_tk=1. aTP_Lamm_tm=1. aTP_Lamm_to=1. aTP_Lamm_tq=1. aTP_Lamm_ts=1. aTP_Lamm_tu=1. aTP_Lamm_tv=1. aTP_Lamm_tw=1. aTP_Lamm_tx=1. aTP_Lamm_ub=1. aTP_Lamm_uf=1. aTP_Lamm_uj=1. aTP_Lamm_un=1. aTP_Lamm_ur=1. aTP_Lamm_uv=1. aTP_Lamm_uz=1. aTP_Lamm_vd=1. aTP_Lamm_vg=1. aTP_Lamm_vj=1. aTP_Lamm_vm=1. aTP_Lamm_vp=1. aTP_Lamm_vs=1. aTP_Lamm_vv=1. aTP_Lamm_vy=1. aTP_Lamm_wb=1. aTP_Lamm_we=1. aTP_Lamm_wh=1. aTP_Lamm_wl=1. aTP_Lamm_wp=1. aTP_Lamm_wt=1. aTP_Lamm_wx=1. aTP_Lamm_xa=1. aTP_Lamm_xd=1. aTP_Lamm_xg=1. aTP_Lamm_xj=1. aTP_Lamm_xm=1. aTP_Lamm_xp=1. aTP_Lamm_xq=1. aTP_Lamm_xr=1. aTP_Lamm_xt=1. aTP_Lamm_xv=1. aTP_Lamm_xy=1. aTP_Lamm_yb=1. aTP_Lamm_ye=1. aTP_Lamm_yh=1. aTP_Lamm_yk=1. aTP_Lamm_yn=1. aTP_Lamm_yp=1. aTP_Lamm_yr=1. aTP_Lamm_yt=1. aTP_Lamm_yv=1. aTP_Lamm_yx=1. aTP_Lamm_yz=1. aTP_Lamm_zb=1. aTP_Lamm_zd=1. aTP_Lamm_zf=1. aTP_Lamm_zh=1. aTP_Lamm_zj=1. aTP_Lamm_zl=1. aTP_Lamm_zn=1. aTP_Lamm_zp=1. aTP_Lamm_zr=1. aTP_Lamm_zt=1. aTP_Lamm_zv=1. aTP_Lamm_zz=1. fequal_TPTP_ind=1. scratc1240312639d_n_2t=1. scratc1321703102_cond1=1. scratc1703387950univof=1. scratc1719027618nd_nIn=1. scratc272004510_d_Unj=1. aTP_Lamm_ab=1. aTP_Lamm_an=1. aTP_Lamm_at=1. aTP_Lamm_bv=1. aTP_Lamm_bw=1. bool=1. scratc1161213627_prop1=1. scratc1240247035d_n_1o=1. scratc1279598277rt_nis=1. scratc1306979968_prop4=1. scratc1367178679_prop1=1. scratc1421322154_prop4=1. scratc1639623729nempty=1. scratc1719469294munion=1. scratc1749575802_prop1=1. scratc1829659435d_plus=1. scratc1856131586428_id=1. scratc1955540854_prop1=1. scratc2009684326_prop1=1. scratc2057229948_empty=1. scratc242504517pair_p=1. scratc921286080r1type=1. scratc970191445_times=1. scratc984781556_prop1=1. scratc1094786379_ratof=1. scratc1172395502rt_all=1. scratc1288187763rt_one=1. scratc1331167783t_some=1. scratc1348710486let_u0=1. scratc1575955448_rt_in=1. scratc1642757990air_u0=1. scratc1656690599d_xout=1. scratc1731308402d_24_g=1. scratc1754835376d_1out=1. scratc440621306d_i1_s=1. scratc441650658d_fixf=1. scratc513369824_428_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. scratc371142564_d_and=1. aa_fun1431113780TP_ind=1. aa_boo1142376798l_bool=1. aa_TPT1123896796d_bool=1. scratc628861614bnd_if=1. scratc1112013241d_l_ec=1. aa_fun1212484691d_bool=1. scratc1680147246nd_ind=1. scratc1725260217d_e_in=1. aa_TPT1791839040TP_ind=1. aa_TPT985247859d_bool=1. scratc1423256749d_pair=1. aa_fun987228051d_bool=1. scratc1785284969_amone=1. scratc48260778_image=1. scratc90902847_first=1. scratc994261093second=1. aa_TPT125613450d_bool=1. scratc1721520380nd_non=1. aa_fun1913827119d_bool=1. scratc873743100d_anec=1. aa_fun1107270209d_bool=1. aa_fun845057962d_bool=1. scratc1646379649nd_ecp=1. scratc601817159_ecect=1. scratc602407550_ecelt=1. scratc623004572eplSep=1. scratc1646379653nd_ect=1. scratc1730175485nd_out=1. scratc2002475487fixfu2=1. aa_TPT1781712639TP_ind=1. aa_TPT2142672771l_bool=1. aa_fun1235454963TP_ind=1. cOMBB_658106424TP_ind=1. cOMBS_2003118649l_bool=1. scratc1077425377ght1to=1. scratc1306980024_propl=1. scratc1306980025_propm=1. scratc139619091_fixfu=1. scratc154197684eft1to=1. scratc235045162wissel=1. scratc251816488ectelt=1. scratc367018365ectset=1. scratc59543998etprop=1. scratc1931485887nverse=1. scratc473135711unmore=1. scratc677104934d_invf=1. scratc680841465d_tofs=1. f3=1. f5=1. f8=1. f12=1. f22=1. scratc1303128615all_of=1. scratc1244379769d_n_pl=1. scratc1244642172d_n_ts=1. scratc1244379763d_n_pf=1. scratc1244642159d_n_tf=1. scratc478607744_d_not=1. scratc1725260222d_e_is=1. scratc413789423l_some=1. scratc254891115_d_Sep=1. scratc1890899764d_esti=1. scratc1112669246d_l_or=1. scratc488442041ffprop=1. scratc1613924016nd_all=1. scratc1729716277nd_one=1. aTP_Lamm_aj=1. scratc1123360177d_outn=1. scratc719003247_rec_G=1. aTP_Lamm_aby=1. aTP_Lamm_mu=1. aTP_Lamm_my=1. aTP_Lamm_ns=1. aTP_Lamm_nw=1. scratc1771548918_367_w=1. aTP_Lamm_abq=1. aTP_Lamm_acm=1. aTP_Lamm_ao=1. aTP_Lamm_av=1. aTP_Lamm_bf=1. aTP_Lamm_bn=1. aTP_Lamm_ca=1. aTP_Lamm_cx=1. aTP_Lamm_dh=1. aTP_Lamm_dl=1. aTP_Lamm_dp=1. aTP_Lamm_dt=1. aTP_Lamm_dx=1. aTP_Lamm_eb=1. aTP_Lamm_ef=1. aTP_Lamm_ej=1. aTP_Lamm_en=1. aTP_Lamm_fj=1. aTP_Lamm_fn=1. aTP_Lamm_fr=1. aTP_Lamm_fv=1. aTP_Lamm_gz=1. aTP_Lamm_hd=1. aTP_Lamm_hn=1. aTP_Lamm_hr=1. aTP_Lamm_hv=1. aTP_Lamm_hz=1. aTP_Lamm_id=1. aTP_Lamm_ih=1. aTP_Lamm_il=1. aTP_Lamm_ip=1. aTP_Lamm_it=1. aTP_Lamm_jp=1. aTP_Lamm_jt=1. aTP_Lamm_jx=1. aTP_Lamm_kb=1. aTP_Lamm_ln=1. aTP_Lamm_ly=1. aTP_Lamm_mb=1. aTP_Lamm_me=1. aTP_Lamm_mh=1. aTP_Lamm_mk=1. aTP_Lamm_mn=1. aTP_Lamm_ou=1. aTP_Lamm_pa=1. aTP_Lamm_pe=1. aTP_Lamm_pi=1. aTP_Lamm_pm=1. aTP_Lamm_pq=1. aTP_Lamm_pu=1. aTP_Lamm_py=1. aTP_Lamm_qc=1. aTP_Lamm_rb=1. aTP_Lamm_rf=1. aTP_Lamm_rj=1. aTP_Lamm_rn=1. aTP_Lamm_ty=1. aTP_Lamm_uc=1. aTP_Lamm_ug=1. aTP_Lamm_uk=1. aTP_Lamm_uo=1. aTP_Lamm_us=1. aTP_Lamm_uw=1. aTP_Lamm_va=1. aTP_Lamm_wi=1. aTP_Lamm_wm=1. aTP_Lamm_wq=1. aTP_Lamm_wu=1. aTP_Lamm_xw=1. aTP_Lamm_xz=1. aTP_Lamm_yc=1. aTP_Lamm_yf=1. aTP_Lamm_yi=1. aTP_Lamm_yl=1. aTP_Lamm_zw=1. scratc675858559d_incl=1. aTP_Lamm_aac=1. aTP_Lamm_aaf=1. aTP_Lamm_aci=1. aTP_Lamm_ack=1. aTP_Lamm_az=1. aTP_Lamm_bj=1. aTP_Lamm_bm=1. aTP_Lamm_bq=1. aTP_Lamm_er=1. aTP_Lamm_eu=1. aTP_Lamm_ex=1. aTP_Lamm_fa=1. aTP_Lamm_fd=1. aTP_Lamm_fg=1. aTP_Lamm_fz=1. aTP_Lamm_gc=1. aTP_Lamm_gf=1. aTP_Lamm_gi=1. aTP_Lamm_gl=1. aTP_Lamm_go=1. aTP_Lamm_ix=1. aTP_Lamm_ja=1. aTP_Lamm_jd=1. aTP_Lamm_jg=1. aTP_Lamm_jj=1. aTP_Lamm_jm=1. aTP_Lamm_kf=1. aTP_Lamm_ki=1. aTP_Lamm_kl=1. aTP_Lamm_ko=1. aTP_Lamm_kr=1. aTP_Lamm_ku=1. aTP_Lamm_qg=1. aTP_Lamm_qj=1. aTP_Lamm_qm=1. aTP_Lamm_qp=1. aTP_Lamm_qs=1. aTP_Lamm_qv=1. aTP_Lamm_qy=1. aTP_Lamm_rr=1. aTP_Lamm_ru=1. aTP_Lamm_rx=1. aTP_Lamm_sa=1. aTP_Lamm_sd=1. aTP_Lamm_sg=1. aTP_Lamm_ve=1. aTP_Lamm_vh=1. aTP_Lamm_vk=1. aTP_Lamm_vn=1. aTP_Lamm_vq=1. aTP_Lamm_vt=1. aTP_Lamm_vw=1. aTP_Lamm_vz=1. aTP_Lamm_wc=1. aTP_Lamm_wf=1. aTP_Lamm_wy=1. aTP_Lamm_xb=1. aTP_Lamm_xe=1. aTP_Lamm_xh=1. aTP_Lamm_xk=1. aTP_Lamm_xn=1. scratc1647232439nd_eps=1. scratc1680147256nd_inn=1. scratc19677640etprod=1. scratc726999126ective=1. aTP_Lamm_aam=1. aTP_Lamm_abs=1. aTP_Lamm_abt=1. aTP_Lamm_abu=1. aTP_Lamm_abw=1. aTP_Lamm_ac=1. aTP_Lamm_acc=1. aTP_Lamm_ace=1. aTP_Lamm_acf=1. aTP_Lamm_acj=1. aTP_Lamm_ad=1. aTP_Lamm_ae=1. aTP_Lamm_af=1. aTP_Lamm_aw=1. aTP_Lamm_ax=1. aTP_Lamm_ay=1. aTP_Lamm_ba=1. aTP_Lamm_bb=1. aTP_Lamm_bd=1. aTP_Lamm_be=1. aTP_Lamm_bk=1. aTP_Lamm_bl=1. aTP_Lamm_bo=1. aTP_Lamm_de=1. aTP_Lamm_di=1. aTP_Lamm_dm=1. aTP_Lamm_dq=1. aTP_Lamm_du=1. aTP_Lamm_dy=1. aTP_Lamm_ec=1. aTP_Lamm_eg=1. aTP_Lamm_ek=1. aTP_Lamm_eo=1. aTP_Lamm_fk=1. aTP_Lamm_fo=1. aTP_Lamm_fs=1. aTP_Lamm_fw=1. aTP_Lamm_gr=1. aTP_Lamm_gu=1. aTP_Lamm_ha=1. aTP_Lamm_hk=1. aTP_Lamm_ho=1. aTP_Lamm_hs=1. aTP_Lamm_hw=1. aTP_Lamm_ia=1. aTP_Lamm_ie=1. aTP_Lamm_ii=1. aTP_Lamm_im=1. aTP_Lamm_iq=1. aTP_Lamm_iu=1. aTP_Lamm_jq=1. aTP_Lamm_ju=1. aTP_Lamm_jy=1. aTP_Lamm_kc=1. aTP_Lamm_lb=1. aTP_Lamm_lh=1. aTP_Lamm_lk=1. aTP_Lamm_lo=1. aTP_Lamm_lr=1. aTP_Lamm_mv=1. aTP_Lamm_mz=1. aTP_Lamm_nt=1. aTP_Lamm_nx=1. aTP_Lamm_ok=1. aTP_Lamm_on=1. aTP_Lamm_pb=1. aTP_Lamm_pf=1. aTP_Lamm_pj=1. aTP_Lamm_pn=1. aTP_Lamm_pr=1. aTP_Lamm_pv=1. aTP_Lamm_pz=1. aTP_Lamm_qd=1. aTP_Lamm_rc=1. aTP_Lamm_rg=1. aTP_Lamm_rk=1. aTP_Lamm_ro=1. aTP_Lamm_sj=1. aTP_Lamm_sm=1. aTP_Lamm_tz=1. aTP_Lamm_ud=1. aTP_Lamm_uh=1. aTP_Lamm_ul=1. aTP_Lamm_up=1. aTP_Lamm_ut=1. aTP_Lamm_ux=1. aTP_Lamm_vb=1. aTP_Lamm_wj=1. aTP_Lamm_wn=1. aTP_Lamm_wr=1. aTP_Lamm_wv=1. aTP_Lamm_zx=1. fEx_TPTP_ind=1. scratc1244117363d_n_lb=1. scratc1712865281nd_min=1. scratc1742772941ective=1. scratc565842745nunion=1. scratc849034026lbprop=1. aTP_Lamm_abv=1. aTP_Lamm_abx=1. aTP_Lamm_abz=1. aTP_Lamm_aca=1. aTP_Lamm_acb=1. aTP_Lamm_acd=1. aTP_Lamm_acg=1. aTP_Lamm_ach=1. aTP_Lamm_acl=1. aTP_Lamm_acn=1. aTP_Lamm_bc=1. scratc1212653308_UPair=1. scratc1307566348econd1=1. scratc1721253554first1=1. scratc350768152In_rec=1. scratc872461638_pair1=1. aTP_Lamm_ag=1. aTP_Lamm_ah=1. aTP_Lamm_ai=1. aTP_Lamm_am=1. aTP_Lamm_ap=1. aTP_Lamm_bg=1. aTP_Lamm_bh=1. aTP_Lamm_bi=1. aTP_Lamm_bp=1. aTP_Lamm_bs=1. aTP_Lamm_by=1. aTP_Lamm_bz=1. cOMBC_1555011498d_bool=1. scratc1306979967_prop3=1. scratc256104368_prop1=1. scratc396419381_prop1=1. scratc482128287tminus=1. scratc759794874367_vo=1. scratc778816504_prop1=1. scratc844466543_prop1=1. scratc898964782t_disj=1. scratc910718356ective=1. undefined_bool=1. scratc1135636789_477_v=1. scratc1244182974d_n_mn=1. scratc1642495594air_q0=1. undefined_TPTP_ind=1. f2=1. f4=1. f7=1. f10=1. f11=1. f13=1. f19=1. f21=1. f23=1. f25=1. scratc1729978623nd_or3=1. scratc1646379588nd_ec3=1. scratc1680540841nd_ite=1. scratc2047737915d_soft=1. scratc1306979965_prop1=1. scratc795979768d_left=1. scratc853501306_indeq=1. scratc1939081475eft_f1=1. scratc2146397332sel_wa=1. scratc2146397333sel_wb=1. scratc397466166d_11_i=1. scratc1892335383indrat=1. scratc1939081476eft_f2=1. scratc789174283_right=1. f1=1. f6=1. f9=1. f15=1. f20=1. f24=1. scratc1306979966_prop2=1. scratc1945444837hangef=1. scratc2123791476_inj_h=1. f14=1. f17=1. f18=1. scratc737776956_prop1=1. scratc1785985336indeq2=1. f16=1. 5.26/5.56 5.26/5.56 ============================== end of process initial clauses ======== 5.26/5.56 5.26/5.56 ============================== CLAUSES FOR SEARCH ==================== 5.26/5.56 5.26/5.56 ============================== end of clauses for search ============= 5.26/5.56 5.26/5.56 ============================== SEARCH ================================ 5.26/5.56 5.26/5.56 % Starting search at 3.69 seconds. 5.26/5.56 5.26/5.56 NOTE: Back_subsumption disabled, ratio of keCputime limit exceeded (core dumped) 180.02/180.29 EOF