0.04/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.12/0.34 % Computer : n005.cluster.edu 0.12/0.34 % Model : x86_64 x86_64 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.34 % Memory : 8042.1875MB 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.34 % CPULimit : 960 0.12/0.34 % DateTime : Thu Jul 2 15:21:52 EDT 2020 0.12/0.34 % CPUTime : 1.22/1.58 ============================== Prover9 =============================== 1.22/1.58 Prover9 (32) version 2009-11A, November 2009. 1.22/1.58 Process 18629 was started by sandbox2 on n005.cluster.edu, 1.22/1.58 Thu Jul 2 15:21:53 2020 1.22/1.58 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_18459_n005.cluster.edu". 1.22/1.58 ============================== end of head =========================== 1.22/1.58 1.22/1.58 ============================== INPUT ================================= 1.22/1.58 1.22/1.58 % Reading from file /tmp/Prover9_18459_n005.cluster.edu 1.22/1.58 1.22/1.58 set(prolog_style_variables). 1.22/1.58 set(auto2). 1.22/1.58 % set(auto2) -> set(auto). 1.22/1.58 % set(auto) -> set(auto_inference). 1.22/1.58 % set(auto) -> set(auto_setup). 1.22/1.58 % set(auto_setup) -> set(predicate_elim). 1.22/1.58 % set(auto_setup) -> assign(eq_defs, unfold). 1.22/1.58 % set(auto) -> set(auto_limits). 1.22/1.58 % set(auto_limits) -> assign(max_weight, "100.000"). 1.22/1.58 % set(auto_limits) -> assign(sos_limit, 20000). 1.22/1.58 % set(auto) -> set(auto_denials). 1.22/1.58 % set(auto) -> set(auto_process). 1.22/1.58 % set(auto2) -> assign(new_constants, 1). 1.22/1.58 % set(auto2) -> assign(fold_denial_max, 3). 1.22/1.58 % set(auto2) -> assign(max_weight, "200.000"). 1.22/1.58 % set(auto2) -> assign(max_hours, 1). 1.22/1.58 % assign(max_hours, 1) -> assign(max_seconds, 3600). 1.22/1.58 % set(auto2) -> assign(max_seconds, 0). 1.22/1.58 % set(auto2) -> assign(max_minutes, 5). 1.22/1.58 % assign(max_minutes, 5) -> assign(max_seconds, 300). 1.22/1.58 % set(auto2) -> set(sort_initial_sos). 1.22/1.58 % set(auto2) -> assign(sos_limit, -1). 1.22/1.58 % set(auto2) -> assign(lrs_ticks, 3000). 1.22/1.58 % set(auto2) -> assign(max_megs, 400). 1.22/1.58 % set(auto2) -> assign(stats, some). 1.22/1.58 % set(auto2) -> clear(echo_input). 1.22/1.58 % set(auto2) -> set(quiet). 1.22/1.58 % set(auto2) -> clear(print_initial_clauses). 1.22/1.58 % set(auto2) -> clear(print_given). 1.22/1.58 assign(lrs_ticks,-1). 1.22/1.58 assign(sos_limit,10000). 1.22/1.58 assign(order,kbo). 1.22/1.58 set(lex_order_vars). 1.22/1.58 clear(print_given). 1.22/1.58 1.22/1.58 % formulas(sos). % not echoed (957 formulas) 1.22/1.58 1.22/1.58 ============================== end of input ========================== 1.22/1.58 1.22/1.58 % From the command line: assign(max_seconds, 960). 1.22/1.58 1.22/1.58 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 1.22/1.58 1.22/1.58 % Formulas that are not ordinary clauses: 1.22/1.58 1 (all X all Xa scratc821882501_ecect(X,Xa) = scratc1945325559d_e_in(aa_TPTP_ind_TPTP_ind(scratc1398137874_power,X),scratc1549854014d_anec(X,Xa))) # label(fact_def__ecect) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 2 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_ri,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_rj,Uu)))) # label(fact_ATP_Olambda__32) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 3 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1799471091d_outn(X),aa_TPTP_ind_TPTP_ind(scratc1883353206nd_inn(Xa),Xb)) = aa_TPTP_ind_TPTP_ind(scratc683642354eft1to(X,Xa),Xb)) # label(fact_def__left1to) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 4 (all X all Xa all Xb all Xc all Xd all Xe (pp(aa_fun171081125l_bool(scratc943234093l_some(X),aa_TPT43085870d_bool(scratc1931817854_prop1(X,Xa,Xb,Xc,Xd),Xe))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1527045308_prop2(X,Xa,Xb,Xc),Xd),Xe)))) # label(fact_def__prop2) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 5 (all X aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc804121290d_d_Pi,aa_TPTP_ind_TPTP_ind(scratc656271931_d_1to,scratc835753143nd_n_2)),aTP_Lamm_af(X)) = aa_TPTP_ind_TPTP_ind(scratc983082494r1type,X)) # label(fact_def__pair1type) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 6 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hl,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_hk(Uu),Uua))))) # label(fact_ATP_Olambda__310) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 7 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_ii(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ij,Uu),Uua)))) # label(fact_ATP_Olambda__303) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 8 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fb,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fa,Uu))))) # label(fact_ATP_Olambda__142) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 9 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_pd(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pe,Uu),Uua)))) # label(fact_ATP_Olambda__262) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 10 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kw(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__472) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 11 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_fun1235454963TP_ind(aTP_Lamm_bu(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc1747570160bnd_if(aa_TPTP_ind_bool(Uua,Uub),Uub),scratc1850438389nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bi(Uu),Uua)))) # label(fact_ATP_Olambda__344) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 12 (all X all Xa all Xb all Xc all Xd scratc319789690indeq2(X,Xa,Xb,Xc,Xd) = aa_TPT1424761345TP_ind(scratc1073566648_indeq(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc185334392d_11_i(X,Xa,Xb),Xc),Xd))) # label(fact_def__indeq2) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 13 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hq(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__381) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 14 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dm,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_dn,Uu)))) # label(fact_ATP_Olambda__158) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 15 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1106035156_Sigma,X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1507337520munion,X),aTP_Lamm_bo(Xa))) # label(fact_def__d__Sigma) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 16 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hd,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_hc,Uu))))) # label(fact_ATP_Olambda__123) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 17 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_ps,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_pt,Uu)))) # label(fact_ATP_Olambda__51) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 18 (all X all Xa all Xb all Xc all Xd aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1106035156_Sigma,X),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_bc(X),Xb),Xc),Xd)) = aa_TPTP_ind_TPTP_ind(scratc327405859hangef(X,Xa,Xb,Xc),Xd)) # label(fact_def__changef) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 19 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_na(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__379) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 20 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dq,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_dr,Uu)))) # label(fact_ATP_Olambda__156) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 21 (all X aa_TPTP_ind_TPTP_ind(scratc1682036828d_Inj0,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1861302562d_repl,X),scratc1682036829d_Inj1)) # label(fact_def__d__Inj0) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 22 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_rv,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(scratc835753142nd_n_1),Uu)),aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uu))))) # label(fact_ATP_Olambda__5) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 23 (all X all Xa (pp(scratc1052430566_d_and(aa_bool_bool(scratc1332734588d_l_or(X),Xa),scratc1332078583d_l_ec(X,Xa))) <-> scratc1773702580d_orec(X,Xa))) # label(fact_def__orec) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 24 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_pq,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_pr,Uu)))) # label(fact_ATP_Olambda__52) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 25 (all X all Xa all Xb scratc1472090682d_left(X,Xb,Xa) = scratc1726949701eft_f1(X,Xa,Xb)) # label(fact_def__left__f1) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 26 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jx,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(scratc835753142nd_n_1),Uu)),Uu)))) # label(fact_ATP_Olambda__6) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 27 (all X all Xa scratc1849585603nd_ect(X,Xa) = aa_fun1431113780TP_ind(scratc936179117_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1398137874_power,X)),scratc1549854014d_anec(X,Xa))) # label(fact_def__ect) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 28 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_la(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lb(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__430) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 29 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_fun171081125l_bool(scratc1832573285all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_av(Uua),Uub),Uuc),Uud))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_aw(Uu),Uua),Uub),Uuc),Uud)))) # label(fact_ATP_Olambda__501) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 30 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ee,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ef,Uu)))) # label(fact_ATP_Olambda__151) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 31 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_am,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,Uu),aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,Uu),Uua)))))) # label(fact_ATP_Olambda__201) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 32 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_rr,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_rq,Uu))))) # label(fact_ATP_Olambda__29) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 33 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,Uu),Uua)) -> pp(scratc1159895746_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qa,Uu),Uua)))) # label(fact_ATP_Olambda__222) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 34 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc359684433_fixfu(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_aw(X),Xa),Xb),Xc))))) # label(fact_def__fixfu) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 35 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_df(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dg,Uu),Uua)))) # label(fact_ATP_Olambda__332) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 36 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_jc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_jd,Uu)))) # label(fact_ATP_Olambda__107) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 37 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,Uu),Uua)) -> pp(scratc1159895746_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_py,Uu),Uua)))) # label(fact_ATP_Olambda__223) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 38 (all X0 (pp(aa_fun171081125l_bool(scratc1687058735n_some,X0)) -> pp(aa_fun171081125l_bool(scratc1687058735n_some,scratc1916071231nd_min(X0))))) # label(fact_satz27) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 39 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uuc),Uua))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ih(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__480) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 40 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_ph,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_pi,Uu)))) # label(fact_ATP_Olambda__56) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 41 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_mh,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_mg,Uu))))) # label(fact_ATP_Olambda__81) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 42 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ln(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_lm(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__427) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 43 (all X all Xa all Xb aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1106035156_Sigma,Xa),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_be(X),Xa),Xb)) = aa_TPTP_ind_TPTP_ind(scratc313446909nverse(X,Xa),Xb)) # label(fact_def__inverse) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 44 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_kl,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_km,Uu)))) # label(fact_ATP_Olambda__94) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 45 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_kq,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_kp,Uu))))) # label(fact_ATP_Olambda__92) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 46 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ss(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1945325564d_e_is(Uua),aa_TPTP_ind_TPTP_ind(scratc1675549095second(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1952701419d_pair(Uu,Uua),Uub),Uuc))),Uuc)))) # label(fact_ATP_Olambda__454) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 47 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kd,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uua)),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,Uua),Uu))))) # label(fact_ATP_Olambda__195) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 48 (all P all Q all R aa_TPTP_ind_bool(aa_TPT43085870d_bool(P,R),Q) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(cOMBC_1555011498d_bool(P),Q),R)) # label(help_COMBC_1_1_COMBC_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind_001t__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 49 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bi(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(Uua,Uub)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,Uub),Uu)))) # label(fact_ATP_Olambda__406) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 50 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_lv(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lw,Uu),Uua)))) # label(fact_ATP_Olambda__287) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 51 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_lo,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_lp,Uu)))) # label(fact_ATP_Olambda__86) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 52 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc955280034d_Subq,X12),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1398137874_power,X0))))) # label(fact_k__PowerI) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 53 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc237192304univof,X0)))) # label(fact_k__UnivOf__In) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 54 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_df(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1886782970_lessf,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc855931064lesseq,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1886782970_lessf,Uu),Uub)))))) # label(fact_ATP_Olambda__391) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 55 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qq,Uu),Uua)) <-> pp(scratc1849585538nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1687058735n_some,aa_TPT43085870d_bool(scratc276310267ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc1687058735n_some,aa_TPT43085870d_bool(scratc276310267ffprop(Uua),Uu)))))) # label(fact_ATP_Olambda__185) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 56 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fq,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463723527d_n_eq,Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1463789127d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1925119923nd_num,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1841455290nd_den,Uu)),Uua)))))) # label(fact_ATP_Olambda__245) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 57 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,Uua),Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ag,Uu),Uua)))) # label(fact_ATP_Olambda__251) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 58 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cw(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc855931064lesseq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc855931064lesseq,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc855931064lesseq,Uu),Uub)))))) # label(fact_ATP_Olambda__387) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 59 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_el,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ek,Uu))))) # label(fact_ATP_Olambda__148) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 60 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,Uu),scratc1190606337d_frac)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_a,Uu)))) # label(fact_ATP_Olambda__23) # label(axiom) # label(non_clause). [assumption]. 1.22/1.58 61 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1530322028lbprop(X),Xa),Xb)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1883287609nd_imp,aa_TPTP_ind_bool(X,Xb)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,Xa),Xb))))) # label(fact_def__lbprop) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 62 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_na(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nb,Uu),Uua)))) # label(fact_ATP_Olambda__277) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 63 (all X all Xa aa_fun1431113780TP_ind(scratc936179117_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1398137874_power,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1106035156_Sigma,X),aTP_Lamm_bl(Xa)))),aa_fun1913827119d_bool(aTP_Lamm_bm(X),Xa)) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc804121290d_d_Pi,X),Xa)) # label(fact_def__d__Pi) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 64 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1832573285all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,X0)),aa_fun1584354236d_bool(aTP_Lamm_sq(X0),X12)))) # label(fact_estie) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 65 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ig,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_if,Uu))))) # label(fact_ATP_Olambda__114) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 66 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ep,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eo,Uu))))) # label(fact_ATP_Olambda__146) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 67 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_en,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_em,Uu))))) # label(fact_ATP_Olambda__147) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 68 (all X all Xa all Xb (pp(scratc1159895746_d_not(aa_TPTP_ind_bool(Xa,Xb))) <-> pp(aa_TPTP_ind_bool(scratc1924726330nd_non(X,Xa),Xb)))) # label(fact_def__non) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 69 (all Q all P (-pp(Q) | pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)))) # label(help_fimplies_2_1_U) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 70 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),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__320) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 71 (all P (gg_bool(P) -> fFalse = P | P = fTrue)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 72 (all X all Xa all Xb (pp(aa_fun171081125l_bool(scratc1817129966nd_all(Xa),aa_TPT43085870d_bool(scratc268326120_image(X,Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1076607503ective(X),Xa),Xb)))) # label(fact_def__surjective) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 73 (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]. 1.22/1.59 74 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X33),X0)) -> aa_TPTP_ind_TPTP_ind(X22,X33) = aa_TPTP_ind_TPTP_ind(X12,X33)))) -> aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1106035156_Sigma,X0),X22) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1106035156_Sigma,X0),X12))) # label(fact_xi__ext) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 75 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aa_TPT43085870d_bool(aTP_Lamm_sn,Uu)),aa_TPT43085870d_bool(aTP_Lamm_so(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sp,Uu),Uua)))) # label(fact_ATP_Olambda__233) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 76 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iv(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__372) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 77 (all X all Xa (pp(aa_fun171081125l_bool(scratc943234093l_some(X),Xa)) <-> pp(scratc1159895746_d_not(aa_fun171081125l_bool(scratc1832573285all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,X)),scratc1924726330nd_non(X,Xa)))))) # label(fact_def__l__some) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 78 (all X ((all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,aa_TPTP_ind_TPTP_ind(scratc1398137874_power,X1)),X))))) <-> pp(aa_TPTP_ind_bool(scratc233918976closed,X)))) # label(fact_def__d__Power__closed) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 79 (all P all Q (pp(Q) | -pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 80 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_lt,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_ls,Uu))))) # label(fact_ATP_Olambda__85) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 81 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fz(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fy(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__443) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 82 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1924332741nd_nis,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(X),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1590460279_prop1(X),Xa),Xb)))) # label(fact_def__d__28__prop1) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 83 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1886782970_lessf,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc85621118_moref,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ey,Uu),Uua)))) # label(fact_ATP_Olambda__217) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 84 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_mm,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_mn,Uu)))) # label(fact_ATP_Olambda__79) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 85 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lg,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_lf(Uu),Uua))))) # label(fact_ATP_Olambda__291) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 86 (all X0 all X12 all X22 all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc804121290d_d_Pi,X0),X12))) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X32),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,X22),X32)),aa_TPTP_ind_TPTP_ind(X12,X32)))))) # label(fact_ap__Pi) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 87 (all X (pp(aa_fun171081125l_bool(scratc477404390_n_all,aa_TPT43085870d_bool(aTP_Lamm_am,X))) <-> pp(aa_TPTP_ind_bool(scratc1384495227_prop1,X)))) # label(fact_def__d__24__prop1) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 88 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_iy(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iz,Uu),Uua)))) # label(fact_ATP_Olambda__298) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 89 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ec,Uu),Uua)) <-> (pp(scratc1159895746_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc85621129_moreq,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1886782970_lessf,Uu),Uua))))) # label(fact_ATP_Olambda__240) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 90 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_he(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hf,Uu),Uua)))) # label(fact_ATP_Olambda__312) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 91 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_eq(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_er(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__445) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 92 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463723527d_n_eq,Uu),Uu)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fx,Uu)))) # label(fact_ATP_Olambda__21) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 93 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bf(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1945325564d_e_is(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__457) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 94 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1991612901_prop1,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc477404390_n_all,aa_TPT43085870d_bool(aTP_Lamm_ak(X),Xa))))) # label(fact_def__d__428__prop1) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 95 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ky,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_kx(Uu),Uua))))) # label(fact_ATP_Olambda__293) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 96 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mx(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__383) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 97 (all Uu all Uua all Uub (scratc2064974964_is_of(aa_TPTP_ind_TPTP_ind(scratc310968189_first(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aq,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sz(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__349) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 98 (all X all Xa (pp(scratc2005350311_amone(X,Xa)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,X)),aa_fun1584354236d_bool(aTP_Lamm_bk(X),Xa))))) # label(fact_def__amone) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 99 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ri,Uu),Uua)))) # label(fact_ATP_Olambda__209) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 100 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fv,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463723527d_n_eq,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463723527d_n_eq,Uua),Uu))))) # label(fact_ATP_Olambda__218) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 101 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(scratc835753142nd_n_1),Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_rp,Uu)))) # label(fact_ATP_Olambda__11) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 102 (all X all Xa all Xb all Xc all Xd (pp(scratc1052430566_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1883287609nd_imp,X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1945325564d_e_is(Xa),Xd),Xb)),aa_bool_bool(aa_boo1142376798l_bool(scratc1883287609nd_imp,scratc1159895746_d_not(X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1945325564d_e_is(Xa),Xd),Xc)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1527045307_prop1(X,Xa,Xb),Xc),Xd)))) # label(fact_def__prop1) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 103 (all X all Xa (pp(scratc1052430566_d_and(scratc2005350311_amone(X,Xa),aa_fun171081125l_bool(scratc943234093l_some(X),Xa))) <-> pp(aa_fun171081125l_bool(scratc1932922227nd_one(X),Xa)))) # label(fact_def__one) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 104 (all X0 all X12 (gg_TPTP_ind(X0) -> aa_TPTP_ind_TPTP_ind(scratc1526651712_proj0,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc266622957d_pair,X0),X12)) = X0)) # label(fact_proj0__pair__eq) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 105 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc85621118_moref,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc85621129_moreq,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc85621118_moref,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cz(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__390) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 106 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_in,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_io,Uu)))) # label(fact_ATP_Olambda__112) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 107 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_oa,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_nz(Uu),Uua))))) # label(fact_ATP_Olambda__270) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 108 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ea,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_eb,Uu)))) # label(fact_ATP_Olambda__153) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 109 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X22),aa_fun1431113780TP_ind(scratc936179117_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(X12,X22)))) # label(fact_k__SepE2) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 110 (all X all Xa all Xb all Xc aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1106035156_Sigma,aa_TPTP_ind_TPTP_ind(scratc656271931_d_1to,Xb)),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ad(Xa),Xb),Xc)) = aa_TPTP_ind_TPTP_ind(scratc1472090682d_left(X,Xa,Xb),Xc)) # label(fact_def__left) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 111 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc549122310etprod(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1106035156_Sigma,X),aTP_Lamm_af(Xa))) # label(fact_def__setprod) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 112 (all X scratc1464707514d_n_ts(X) = aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1190256787_times,X))) # label(fact_def__n__ts) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 113 (all X0 pp(aa_TPTP_ind_bool(scratc1587817897closed,aa_TPTP_ind_TPTP_ind(scratc237192304univof,X0)))) # label(fact_k__UnivOf__ZF__closed) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 114 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_gm,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_gn,Uu)))) # label(fact_ATP_Olambda__127) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 115 (all X0 all X12 all X22 (gg_TPTP_ind(X22) & gg_TPTP_ind(X12) -> X22 = aa_TPTP_ind_TPTP_ind(scratc1747570160bnd_if(X0,X12),X22) | X12 = aa_TPTP_ind_TPTP_ind(scratc1747570160bnd_if(X0,X12),X22))) # label(fact_if__i__or) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 116 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mf(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__360) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 117 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cx,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cw(Uu),Uua))))) # label(fact_ATP_Olambda__335) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 118 (all P all Q (-pp(P) | pp(Q) | -pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 119 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_mz,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_my,Uu))))) # label(fact_ATP_Olambda__75) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 120 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_cj,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ck,Uu)))) # label(fact_ATP_Olambda__135) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 121 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_qd,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_qc,Uu))))) # label(fact_ATP_Olambda__46) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 122 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_je(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uua),Uub)))))) # label(fact_ATP_Olambda__371) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 123 (all X (pp(aa_TPTP_ind_bool(scratc1381490636closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X1),X)) -> (all X2 ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X3),X1)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,aa_TPTP_ind_TPTP_ind(X2,X3)),X))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1861302562d_repl,X1),X2)),X))))))))) # label(fact_def__d__Repl__closed) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 124 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1832573285all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,X0)),aa_TPT43085870d_bool(aTP_Lamm_st(X0),X12)))) # label(fact_secondis1) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 125 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_qn,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_qm,Uu))))) # label(fact_ATP_Olambda__41) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 126 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fd,Uu)))) # label(fact_ATP_Olambda__141) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 127 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pg(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__386) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 128 (all X0 all X12 (gg_TPTP_ind(X12) & gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc955280034d_Subq,X0),X12)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc955280034d_Subq,X12),X0)) -> X0 = X12)))) # label(fact_set__ext) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 129 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_sl,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1924332741nd_nis,aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uu)),scratc835753142nd_n_1)))) # label(fact_ATP_Olambda__16) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 130 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fa,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc85621118_moref,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1886782970_lessf,Uua),Uu))))) # label(fact_ATP_Olambda__216) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 131 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ro,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_rn,Uu))))) # label(fact_ATP_Olambda__30) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 132 (all X0 all X12 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788795540ective(aa_fun1431113780TP_ind(scratc936179117_d_Sep(X0),X12)),X0),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1106035156_Sigma,aa_fun1431113780TP_ind(scratc936179117_d_Sep(X0),X12)),scratc1945325559d_e_in(X0,X12))))) # label(fact_otax1) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 133 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1000521534_UPair(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1861302562d_repl,aa_TPTP_ind_TPTP_ind(scratc1398137874_power,aa_TPTP_ind_TPTP_ind(scratc1398137874_power,scratc1141896968ptyset))),aa_TPT1424761345TP_ind(aTP_Lamm_bv(X),Xa))) # label(fact_def__d__UPair) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 134 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_po,Uu),Uua)) <-> (pp(scratc1159895746_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__237) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 135 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cg,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_cf(Uu),Uua))))) # label(fact_ATP_Olambda__324) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 136 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc916333164wissel(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1106035156_Sigma,X),scratc1480231895sel_wb(X,Xa,Xb))) # label(fact_def__wissel) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 137 (all X aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1106035156_Sigma,scratc1923807950nd_nat),aTP_Lamm_ai(X)) = aa_TPTP_ind_TPTP_ind(scratc575166238_428_g,X)) # label(fact_def__d__428__g) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 138 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hh(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__357) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 139 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qk,Uu),Uua)) <-> pp(scratc1849585538nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__181) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 140 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cf(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463723527d_n_eq,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1463789127d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464445105d_n_pf(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1463789127d_n_fr,Uu),Uub)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1463789127d_n_fr,Uua),Uub)))))) # label(fact_ATP_Olambda__364) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 141 (all X all Xa aa_fun1431113780TP_ind(scratc936179117_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1747570160bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1747570168bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1861302562d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bu(X),Xa))),scratc1141896968ptyset)) # label(fact_def__d__Sep) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 142 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc269996513tminus(X),Xa) = aa_fun1431113780TP_ind(scratc936179117_d_Sep(X),aa_TPT43085870d_bool(aTP_Lamm_bt,Xa))) # label(fact_def__setminus) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 143 (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(scratc1463985925d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uua),Uuc))))))) # label(fact_ATP_Olambda__483) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 144 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1832573285all_of(aa_fun1584354236d_bool(aTP_Lamm_td(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_te(X0),X12)))) # label(fact_e__inp) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 145 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dd,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dc(Uu),Uua))))) # label(fact_ATP_Olambda__333) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 146 (all Uu all Uua (gg_TPTP_ind(Uu) -> Uu = aa_TPTP_ind_TPTP_ind(aTP_Lamm_af(Uu),Uua))) # label(fact_ATP_Olambda__506) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 147 (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]. 1.22/1.59 148 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(X),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Xa),Xb))),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(X),Xb)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc826395118_prop1(X),Xa),Xb)))) # label(fact_def__d__430__prop1) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 149 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_av(Uu),Uua),Uub),Uuc),Uud)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1945325564d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,Uub),Uud)))))) # label(fact_ATP_Olambda__499) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 150 (all X aa_TPTP_ind_TPTP_ind(scratc1526651713_proj1,X) = aa_fun277296641TP_ind(scratc2104322782eplSep(X,aTP_Lamm_bp),scratc953292512_d_Unj)) # label(fact_def__proj1) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 151 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kj,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uua),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),scratc835753142nd_n_1))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,Uua),Uu))))) # label(fact_ATP_Olambda__197) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 152 (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(scratc1463985925d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__481) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 153 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,Uu),scratc835753142nd_n_1)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_kv,Uu)))) # label(fact_ATP_Olambda__22) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 154 (all X all Xa scratc1675549095second(X,Xa) = scratc1526651713_proj1) # label(fact_def__second) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 155 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_mb,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_ma,Uu))))) # label(fact_ATP_Olambda__83) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 156 (all X0 pp(aa_fun171081125l_bool(scratc1832573285all_of(aa_TPT43085870d_bool(aTP_Lamm_sn,X0)),aa_TPT43085870d_bool(aTP_Lamm_sp,X0)))) # label(fact_isseti) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 157 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1799471091d_outn(aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(X),aa_TPTP_ind_TPTP_ind(scratc1883353206nd_inn(Xa),Xb))) = aa_TPTP_ind_TPTP_ind(scratc865293603ght1to(X,Xa),Xb)) # label(fact_def__right1to) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 158 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_nx,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ny,Uu)))) # label(fact_ATP_Olambda__68) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 159 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ab,Uu)))) # label(fact_ATP_Olambda__169) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 160 (all X all Xa all Xb (pp(scratc1052430566_d_and(scratc1933184573nd_or3(X,Xa,Xb),scratc1849585538nd_ec3(X,Xa,Xb))) <-> scratc304013183_orec3(X,Xa,Xb))) # label(fact_def__orec3) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 161 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qc,Uu),Uua)))) # label(fact_ATP_Olambda__213) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 162 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_lz(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ma,Uu),Uua)))) # label(fact_ATP_Olambda__286) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 163 (all X all Xa scratc1952701419d_pair(X,Xa) = scratc266622957d_pair) # label(fact_def__d__pair) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 164 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cn,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_co,Uu)))) # label(fact_ATP_Olambda__165) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 165 (all Uu all Uua (pp(scratc1933184573nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qm,Uu),Uua)))) # label(fact_ATP_Olambda__179) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 166 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1351969473d_incl(Uu),Uua),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1351969473d_incl(Uu),Uub),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1945325564d_e_is(aa_TPTP_ind_TPTP_ind(scratc1398137874_power,Uu)),Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_so(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__347) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 167 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mg,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_mf(Uu),Uua))))) # label(fact_ATP_Olambda__284) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 168 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463723527d_n_eq,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1925119923nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc1841455290nd_den,Xa))),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1925119923nd_num,Xa)),aa_TPTP_ind_TPTP_ind(scratc1841455290nd_den,X)))))) # label(fact_def__n__eq) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 169 (all X0 all X12 all X22 (gg_TPTP_ind(X12) -> (pp(X0) -> X12 = aa_TPTP_ind_TPTP_ind(scratc1747570160bnd_if(X0,X12),X22)))) # label(fact_if__i__1) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 170 (all Uu all Uua aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,Uu),Uua)) = aa_TPTP_ind_TPTP_ind(aTP_Lamm_al(Uu),Uua)) # label(fact_ATP_Olambda__339) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 171 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1924332741nd_nis,Uua),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rg,Uu),Uua)))) # label(fact_ATP_Olambda__247) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 172 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_et,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_es,Uu))))) # label(fact_ATP_Olambda__145) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 173 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_jy,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_jz,Uu)))) # label(fact_ATP_Olambda__99) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 174 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463723527d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1464445105d_n_pf(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1463789127d_n_fr,Uu),Uub)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1463789127d_n_fr,Uua),Uub))),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1463789127d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uua)),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ci(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__352) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 175 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fm,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_fl(Uu),Uua))))) # label(fact_ATP_Olambda__321) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 176 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_pv,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_pu,Uu))))) # label(fact_ATP_Olambda__50) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 177 (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]. 1.22/1.59 178 (all X all Xa scratc2104322782eplSep(X,Xa) = aa_TPT494704832TP_ind(scratc1861302562d_repl,aa_fun1431113780TP_ind(scratc936179117_d_Sep(X),Xa))) # label(fact_def__d__ReplSep) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 179 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gk(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uua),Uuc))))))) # label(fact_ATP_Olambda__473) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 180 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gq,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_gp(Uu),Uua))))) # label(fact_ATP_Olambda__316) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 181 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hc,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_hb(Uu),Uua))))) # label(fact_ATP_Olambda__313) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 182 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fs(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ft,Uu),Uua)))) # label(fact_ATP_Olambda__325) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 183 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_pe,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_pf,Uu)))) # label(fact_ATP_Olambda__57) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 184 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_od,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_oe,Uu)))) # label(fact_ATP_Olambda__66) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 185 (all B_1 all B_2 gg_TPTP_ind(scratc1849585603nd_ect(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__57749__12314_ONUM749__thf__4__p_Obnd__ect) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 186 (all X all Xa all Xb all Xc all Xd scratc1883353196nd_ind(Xb,aa_TPT43085870d_bool(scratc1527045308_prop2(X,Xa,Xb,Xc),Xd)) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1073566648_indeq(X,Xa,Xb),Xc),Xd)) # label(fact_def__indeq) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 187 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1905399740_union,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1861302562d_repl,X),Xa)) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1507337520munion,X),Xa)) # label(fact_def__famunion) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 188 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_ci(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cj,Uu),Uua)))) # label(fact_ATP_Olambda__323) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 189 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nq,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_np(Uu),Uua))))) # label(fact_ATP_Olambda__273) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 190 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463723527d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1464445105d_n_pf(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1464445105d_n_pf(Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cc,Uu),Uua)))) # label(fact_ATP_Olambda__210) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 191 (all X all Xa (scratc2064974964_is_of(X,Xa) <-> pp(aa_TPTP_ind_bool(Xa,X)))) # label(fact_def__is__of) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 192 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1398137874_power,X0))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc955280034d_Subq,X12),X0)))) # label(fact_k__PowerE) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 193 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_fi(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fj,Uu),Uua)))) # label(fact_ATP_Olambda__322) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 194 (all X all Xa (pp(scratc1159895746_d_not(scratc1332078583d_l_ec(X,Xa))) <-> pp(scratc1052430566_d_and(X,Xa)))) # label(fact_def__d__and) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 195 (all X0 all X12 all X22 all X32 (pp(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1747570160bnd_if(X0,X22),X32))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X12),X22))))) # label(fact_k__If__In__then__E) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 196 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qu(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__415) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 197 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_rd(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_re,Uu),Uua)))) # label(fact_ATP_Olambda__258) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 198 (all X all Xa scratc1933381435nd_out(aa_TPTP_ind_TPTP_ind(scratc1398137874_power,X),scratc1549854014d_anec(X,Xa)) = scratc1048306367ectset(X,Xa)) # label(fact_def__ectset) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 199 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_du,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dt(Uu),Uua))))) # label(fact_ATP_Olambda__329) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 200 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ho,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_hn(Uu),Uua))))) # label(fact_ATP_Olambda__309) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 201 (all X all Xa all Xb (pp(aa_bool_bool(scratc1332734588d_l_or(X),aa_bool_bool(scratc1332734588d_l_or(Xa),Xb))) <-> pp(scratc1933184573nd_or3(X,Xa,Xb)))) # label(fact_def__or3) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 202 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,scratc835753142nd_n_1),aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_kt,Uu)))) # label(fact_ATP_Olambda__172) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 203 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_of(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__401) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 204 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_oi(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__395) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 205 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qe,Uu),Uua)))) # label(fact_ATP_Olambda__212) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 206 (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(scratc1463985925d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uuc),Uua))))))) # label(fact_ATP_Olambda__484) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 207 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc972514770ective(X),Xa),Xb)) <-> pp(scratc1052430566_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788795540ective(X),Xa),Xb),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1076607503ective(X),Xa),Xb))))) # label(fact_def__bijective) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 208 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1922233568nd_nIn,Uua),Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bt,Uu),Uua)))) # label(fact_ATP_Olambda__255) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 209 (all Uu all Uua all Uub all Uuc (pp(aa_fun171081125l_bool(scratc1817129966nd_all(Uu),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_bg(Uu),Uua),Uub),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bh(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__494) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 210 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc353710971nunion(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1905399740_union,aa_TPTP_ind_TPTP_ind(scratc1000521534_UPair(X),Xa))) # label(fact_def__binunion) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 211 (all X all Xa (pp(aa_TPTP_ind_bool(scratc1916071231nd_min(X),Xa)) <-> pp(scratc1052430566_d_and(aa_TPTP_ind_bool(scratc1464182705d_n_lb(X),Xa),aa_TPTP_ind_bool(X,Xa))))) # label(fact_def__min) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 212 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_nm,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_nn,Uu)))) # label(fact_ATP_Olambda__71) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 213 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_oj,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ok,Uu)))) # label(fact_ATP_Olambda__64) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 214 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_oc(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__374) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 215 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_mv,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_mw,Uu)))) # label(fact_ATP_Olambda__76) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 216 (all X aa_TPTP_ind_TPTP_ind(scratc353710971nunion(X),aa_TPTP_ind_TPTP_ind(scratc856929152d_Sing,X)) = aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,X)) # label(fact_def__ordsucc) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 217 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_in,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_im(Uu),Uua))))) # label(fact_ATP_Olambda__302) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 218 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cm(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cl(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__448) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 219 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1687058735n_some,aa_TPT43085870d_bool(scratc276310267ffprop(Xa),X))))) # label(fact_def__iii) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 220 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc855931064lesseq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463723527d_n_eq,Uu),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463723527d_n_eq,Uua),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc855931064lesseq,Uub),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ds(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__475) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 221 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_rb,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_rc,Uu)))) # label(fact_ATP_Olambda__35) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 222 (all X0 (pp(aa_fun171081125l_bool(scratc1687058735n_some,X0)) -> pp(aa_fun171081125l_bool(scratc593196651_n_one,scratc1916071231nd_min(X0))))) # label(fact_satz27a) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 223 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),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__292) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 224 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_gu,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_gv,Uu)))) # label(fact_ATP_Olambda__125) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 225 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,Uub),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc804121290d_d_Pi,Uu),aTP_Lamm_af(Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tg(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__414) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 226 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788795540ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1817129966nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bh(X),Xa),Xb))))) # label(fact_def__injective) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 227 (all X all Xa (pp(aa_TPTP_ind_bool(scratc1464182705d_n_lb(X),Xa)) <-> pp(aa_fun171081125l_bool(scratc477404390_n_all,aa_TPT43085870d_bool(scratc1530322028lbprop(X),Xa))))) # label(fact_def__n__lb) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 228 (all X aa_fun1431113780TP_ind(scratc936179117_d_Sep(scratc1923807950nd_nat),aa_TPT43085870d_bool(aTP_Lamm_ag,X)) = aa_TPTP_ind_TPTP_ind(scratc656271931_d_1to,X)) # label(fact_def__d__1to) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 229 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_sm,Uu)) <-> scratc2064974964_is_of(aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uu),aTP_Lamm_ce))) # label(fact_ATP_Olambda__14) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 230 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_qk,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ql,Uu)))) # label(fact_ATP_Olambda__42) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 231 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ca,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cb,Uu)))) # label(fact_ATP_Olambda__167) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 232 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1009239625_right(X,Xa,Xb),Xc) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1106035156_Sigma,aa_TPTP_ind_TPTP_ind(scratc656271931_d_1to,Xb)),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ac(Xa),Xb),Xc))) # label(fact_def__right) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 233 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc31338806_prop1,X),Xa)) <-> pp(scratc1933184573nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,X),Xa))))) # label(fact_def__d__29__prop1) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 234 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_kg,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_kf,Uu))))) # label(fact_ATP_Olambda__97) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 235 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_og,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_oh,Uu)))) # label(fact_ATP_Olambda__65) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 236 (all Uu all Uua ((pp(scratc1159895746_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pw,Uu),Uua)))) # label(fact_ATP_Olambda__236) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 237 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mj,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_mi(Uu),Uua))))) # label(fact_ATP_Olambda__283) # label(axiom) # label(non_clause). [assumption]. 1.22/1.59 238 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_gt(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gu,Uu),Uua)))) # label(fact_ATP_Olambda__315) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 239 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_il(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__479) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 240 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_hr,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_hs,Uu)))) # label(fact_ATP_Olambda__118) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 241 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1106035156_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc266622957d_pair,aa_TPTP_ind_TPTP_ind(scratc1526651712_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1526651713_proj1,X22)) = X22))) # label(fact_proj__Sigma__eta) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 242 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jc,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_jb(Uu),Uua))))) # label(fact_ATP_Olambda__297) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 243 (all X all Xa scratc1526651712_proj0 = scratc310968189_first(X,Xa)) # label(fact_def__first) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 244 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_go(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__465) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 245 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fg,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fh,Uu)))) # label(fact_ATP_Olambda__139) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 246 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_kj,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_kk,Uu)))) # label(fact_ATP_Olambda__95) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 247 (all Uu (gg_TPTP_ind(Uu) -> aa_TPTP_ind_TPTP_ind(aTP_Lamm_aj,Uu) = Uu)) # label(fact_ATP_Olambda__507) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 248 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rw,Uu),Uua)))) # label(fact_ATP_Olambda__200) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 249 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ez,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ey,Uu))))) # label(fact_ATP_Olambda__143) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 250 (all X (pp(aa_fun171081125l_bool(scratc943234093l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc804121290d_d_Pi,scratc1923807950nd_nat),aTP_Lamm_ah)),aa_TPT43085870d_bool(scratc1991612902_prop2,X))) <-> pp(aa_TPTP_ind_bool(scratc1991612904_prop4,X)))) # label(fact_def__d__428__prop4) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 251 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,X0) = aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,X12) -> X0 = X12))) # label(fact_ordsucc__inj) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 252 (all P all Q (-pp(Q) | pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)) | -pp(P))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 253 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dk,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dj,Uu))))) # label(fact_ATP_Olambda__159) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 254 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mm,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_ml(Uu),Uua))))) # label(fact_ATP_Olambda__282) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 255 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fi(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463723527d_n_eq,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1463789127d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uua),Uub))),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1463789127d_n_fr,Uu),Uua))))) # label(fact_ATP_Olambda__353) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 256 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_ai(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,Uu),Uua)),Uua)) # label(fact_ATP_Olambda__231) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 257 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nd(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__378) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 258 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fg,Uu),Uua)) <-> scratc304013183_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463723527d_n_eq,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc85621118_moref,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1886782970_lessf,Uu),Uua)))) # label(fact_ATP_Olambda__178) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 259 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_mq,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_mp,Uu))))) # label(fact_ATP_Olambda__78) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 260 (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]. 1.22/1.60 261 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_bv(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc1747570160bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,scratc1141896968ptyset),Uub),Uu),Uua)) # label(fact_ATP_Olambda__343) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 262 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1832573285all_of(aa_fun1584354236d_bool(aTP_Lamm_td(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_tf(X0),X12)))) # label(fact_e__in__p) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 263 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cs,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1886782970_lessf,Uua),Uu)))) # label(fact_ATP_Olambda__253) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 264 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kr,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,Uua),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),scratc835753142nd_n_1)))))) # label(fact_ATP_Olambda__206) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 265 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_ij,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ik,Uu)))) # label(fact_ATP_Olambda__113) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 266 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cy,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cx,Uu))))) # label(fact_ATP_Olambda__163) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 267 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sw(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,Uub),aa_TPTP_ind_TPTP_ind(scratc549122310etprod(Uu),Uua))))) # label(fact_ATP_Olambda__417) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 268 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_da,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cz(Uu),Uua))))) # label(fact_ATP_Olambda__334) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 269 (all Uu (pp(aa_fun171081125l_bool(scratc1932922227nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc804121290d_d_Pi,scratc1923807950nd_nat),aTP_Lamm_ah)),aa_TPT43085870d_bool(aTP_Lamm_rz,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_sa,Uu)))) # label(fact_ATP_Olambda__7) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 270 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_ox(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_oy,Uu),Uua)))) # label(fact_ATP_Olambda__264) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 271 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_la(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__470) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 272 (all X0 (gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(scratc1951619170_nat_p,X0)) -> scratc1141896968ptyset = X0 | (exists X13 (aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,X13) = X0 & pp(aa_TPTP_ind_bool(scratc1951619170_nat_p,X13)) & gg_TPTP_ind(X13)))))) # label(fact_nat__inv) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 273 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ie(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_id(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__434) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 274 (all X all Xa scratc1356952379d_tofs(X,Xa) = scratc1747045378bnd_ap) # label(fact_def__tofs) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 275 (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]. 1.22/1.60 276 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_il(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_im(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__432) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 277 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dz,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dy,Uu))))) # label(fact_ATP_Olambda__154) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 278 (all X0 all X12 scratc2064974964_is_of(aa_fun1431113780TP_ind(scratc936179117_d_Sep(X0),X12),aa_TPT43085870d_bool(aTP_Lamm_sn,X0))) # label(fact_setof__p) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 279 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hv,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_hu,Uu))))) # label(fact_ATP_Olambda__117) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 280 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1154423713unmore(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc936179117_d_Sep(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(X),Xa),Xb))) # label(fact_def__unmore) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 281 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1480231894sel_wa(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc1883746791nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1945325564d_e_is(X),Xc),Xa),X,Xb),Xc)) # label(fact_def__wissel__wa) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 282 (all X all Xa (pp(aa_fun171081125l_bool(scratc1832573285all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,X)),scratc1924726330nd_non(X,aa_TPT43085870d_bool(aTP_Lamm_bb(X),Xa)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc129811642_empty,X),Xa)))) # label(fact_def__empty) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 283 (all B_1 gg_TPTP_ind(scratc1850438389nd_eps(B_1))) # label(gsy_c_Scratch__tptp__translate__57749__12314_ONUM749__thf__4__p_Obnd__eps) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 284 (all X (gg_TPTP_ind(X) -> (X = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc266622957d_pair,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,X),scratc1141896968ptyset)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,X),aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,scratc1141896968ptyset))) <-> pp(aa_TPTP_ind_bool(scratc771949187pair_p,X))))) # label(fact_def__pair__p) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 285 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fv,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fw,Uu)))) # label(fact_ATP_Olambda__137) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 286 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uua)),Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_os,Uu),Uua)))) # label(fact_ATP_Olambda__229) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 287 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_lu(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__491) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 288 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qs,Uu),Uua)) <-> pp(scratc1933184573nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1687058735n_some,aa_TPT43085870d_bool(scratc276310267ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc1687058735n_some,aa_TPT43085870d_bool(scratc276310267ffprop(Uua),Uu)))))) # label(fact_ATP_Olambda__184) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 289 (all X all Xa all Xb (pp(scratc1052430566_d_and(X,scratc1052430566_d_and(Xa,Xb))) <-> scratc1549788367d_and3(X,Xa,Xb))) # label(fact_def__and3) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 290 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_ip(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iq,Uu),Uua)))) # label(fact_ATP_Olambda__301) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 291 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fe,Uu),Uua)) <-> pp(scratc1933184573nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463723527d_n_eq,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc85621118_moref,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1886782970_lessf,Uu),Uua))))) # label(fact_ATP_Olambda__180) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 292 (all B_1 all B_2 all B_3 gg_bool(scratc1933184573nd_or3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__57749__12314_ONUM749__thf__4__p_Obnd__or3) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 293 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1905399740_union,X0))) <-> (exists X2 (gg_TPTP_ind(X2) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X2),X0)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X12),X2)))))) # label(fact_k__UnionEq) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 294 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ct,Uu)) <-> pp(aa_fun171081125l_bool(scratc943234093l_some(scratc1190606337d_frac),aa_TPT43085870d_bool(aTP_Lamm_cs,Uu))))) # label(fact_ATP_Olambda__171) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 295 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(Uua,aa_TPTP_ind_TPTP_ind(scratc1945325559d_e_in(Uu,Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_te(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__449) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 296 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_ou(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ov,Uu),Uua)))) # label(fact_ATP_Olambda__265) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 297 (all X all Xa all Xb scratc1850438389nd_eps(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bw(X),Xa),Xb)) = aa_TPTP_ind_TPTP_ind(scratc1747570160bnd_if(X,Xa),Xb)) # label(fact_def__if) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 298 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1832573285all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_tk(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_tl(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__409) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 299 (all X (pp(scratc1159895746_d_not(X)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1883287609nd_imp,X),fFalse)))) # label(fact_def__d__not) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 300 (all X0 scratc1141896968ptyset != aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,X0)) # label(fact_neq__ordsucc__0) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 301 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1353215848d_invf(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1106035156_Sigma,Xa),scratc576365181d_soft(X,Xa,Xb))) # label(fact_def__invf) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 302 (all X scratc1799471091d_outn(X) = scratc1933381435nd_out(scratc1923807950nd_nat,aa_TPT43085870d_bool(aTP_Lamm_ag,X))) # label(fact_def__outn) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 303 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc576365181d_soft(X,Xa,Xb),Xc) = scratc1883353196nd_ind(X,aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bf(Xa),Xb),Xc))) # label(fact_def__soft) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 304 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_em,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc855931064lesseq,Uu),Uua)) -> pp(scratc1159895746_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc85621118_moref,Uu),Uua)))))) # label(fact_ATP_Olambda__224) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 305 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),scratc835753142nd_n_1))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ju,Uu)))) # label(fact_ATP_Olambda__17) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 306 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_oi(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_oj,Uu),Uua)))) # label(fact_ATP_Olambda__267) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 307 (all X all Xa all Xb (pp(aa_fun171081125l_bool(scratc1817129966nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ba(X),Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1351969473d_incl(X),Xa),Xb)))) # label(fact_def__incl) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 308 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rb,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_ra(Uu),Uua))))) # label(fact_ATP_Olambda__259) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 309 (all X0 all X12 all X22 ((pp(X0) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X12),X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,aa_TPTP_ind_TPTP_ind(scratc1747570160bnd_if(X0,X12),scratc1141896968ptyset)),aa_TPTP_ind_TPTP_ind(scratc1747570160bnd_if(X0,X22),aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,scratc1141896968ptyset)))))) # label(fact_k__If__In__01) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 310 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bx,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_by,Uu)))) # label(fact_ATP_Olambda__168) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 311 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pj(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__404) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 312 (all Uu all Uua all Uub ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X3),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,Uub),X3)),aa_TPTP_ind_TPTP_ind(Uua,X3)))))) <-> pp(aa_TPTP_ind_bool(aa_fun1913827119d_bool(aTP_Lamm_bm(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__450) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 313 (all X (pp(aa_TPTP_ind_bool(scratc1587817897closed,X)) <-> pp(aa_TPTP_ind_bool(scratc233918976closed,X)) & pp(aa_TPTP_ind_bool(scratc1381490636closed,X)) & pp(aa_TPTP_ind_bool(scratc69185962closed,X)))) # label(fact_def__d__ZF__closed) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 314 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cp(Uu),Uua),Uub)) <-> pp(scratc1052430566_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1886782970_lessf,Uu),Uub),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1886782970_lessf,Uub),Uua))))) # label(fact_ATP_Olambda__405) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 315 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gc(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gd(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__442) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 316 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1886782970_lessf,Uu),Uua)) -> pp(scratc1159895746_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc85621129_moreq,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ee,Uu),Uua)))) # label(fact_ATP_Olambda__227) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 317 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jq,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_jp,Uu))))) # label(fact_ATP_Olambda__102) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 318 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc419527030d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc936179117_d_Sep(Uu),Uua))) -> pp(aa_TPTP_ind_bool(Uua,Uub))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_sq(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__346) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 319 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,Uua),Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aq,Uu),Uua)))) # label(fact_ATP_Olambda__256) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 320 (all X all Xa ((all X2 (gg_TPTP_ind(X2) -> (scratc2064974964_is_of(X2,X) -> pp(aa_TPTP_ind_bool(Xa,X2))))) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(X),Xa)))) # label(fact_def__all__of) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 321 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_az(Uu),Uua),Uub),Uuc)) <-> pp(scratc1332078583d_l_ec(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc419527030d_esti(Uu),Uuc),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc419527030d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__459) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 322 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_pw,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_px,Uu)))) # label(fact_ATP_Olambda__49) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 323 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_rs,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),scratc835753142nd_n_1))))) # label(fact_ATP_Olambda__10) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 324 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cm(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cn,Uu),Uua)))) # label(fact_ATP_Olambda__336) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 325 (all Uu all Uua all Uub all Uuc ((pp(aa_fun171081125l_bool(scratc1832573285all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_th(Uua),Uub),Uuc))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1945325564d_e_is(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc804121290d_d_Pi,Uu),aTP_Lamm_af(Uua))),Uub),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ti(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__461) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 326 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ia(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_hz(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__435) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 327 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ae(Uu),Uua),Uub),Uuc) = aa_TPTP_ind_TPTP_ind(scratc1883746791nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1945325564d_e_is(aa_TPTP_ind_TPTP_ind(scratc656271931_d_1to,scratc835753143nd_n_2)),Uuc),scratc1460312382d_n_1t),Uu,Uua),Uub)) # label(fact_ATP_Olambda__451) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 328 (all B_1 gg_bool(fEx_TPTP_ind(B_1))) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 329 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1464445105d_n_pf(X),Xa) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1463789127d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1925119923nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc1841455290nd_den,Xa))),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1925119923nd_num,Xa)),aa_TPTP_ind_TPTP_ind(scratc1841455290nd_den,X)))),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1841455290nd_den,X)),aa_TPTP_ind_TPTP_ind(scratc1841455290nd_den,Xa)))) # label(fact_def__n__pf) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 330 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_ol(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_om,Uu),Uua)))) # label(fact_ATP_Olambda__266) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 331 (all X0 all X12 (gg_TPTP_ind(X12) -> aa_TPTP_ind_TPTP_ind(scratc1526651713_proj1,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc266622957d_pair,X0),X12)) = X12)) # label(fact_proj1__pair__eq) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 332 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gr,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_gq,Uu))))) # label(fact_ATP_Olambda__126) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 333 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bl(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1905399740_union,aa_TPTP_ind_TPTP_ind(Uu,Uua))) # label(fact_ATP_Olambda__340) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 334 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sn,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,Uua),aa_TPTP_ind_TPTP_ind(scratc1398137874_power,Uu))))) # label(fact_ATP_Olambda__250) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 335 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ic,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_ib,Uu))))) # label(fact_ATP_Olambda__115) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 336 (all X all Xa (pp(scratc1052430566_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,Xa),scratc835753142nd_n_1)),X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1991612901_prop1,X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1991612902_prop2,X),Xa)))) # label(fact_def__d__428__prop2) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 337 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hg,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_hf,Uu))))) # label(fact_ATP_Olambda__122) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 338 (all Uu ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1924332741nd_nis,Uu),scratc835753142nd_n_1)) -> pp(aa_fun171081125l_bool(scratc593196651_n_one,aa_TPT43085870d_bool(aTP_Lamm_an,Uu)))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_sb,Uu)))) # label(fact_ATP_Olambda__2) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 339 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_og,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_of(Uu),Uua))))) # label(fact_ATP_Olambda__268) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 340 (all P all Q (pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) | pp(P))) # label(help_fimplies_1_1_U) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 341 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_li(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lj(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__428) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 342 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_js,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),Uua)),Uu)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uua)))))) # label(fact_ATP_Olambda__189) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 343 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_pb,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_pc,Uu)))) # label(fact_ATP_Olambda__58) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 344 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hk(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__354) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 345 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kf,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uua),scratc835753142nd_n_1)),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,Uua),Uu))))) # label(fact_ATP_Olambda__191) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 346 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gy,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_gx(Uu),Uua))))) # label(fact_ATP_Olambda__314) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 347 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gz,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_gy,Uu))))) # label(fact_ATP_Olambda__124) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 348 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ke,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_kd,Uu))))) # label(fact_ATP_Olambda__98) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 349 (all Uu all Uua all Uub (scratc2064974964_is_of(aa_TPTP_ind_TPTP_ind(scratc1945325559d_e_in(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aq,Uu)) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_tf(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__350) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 350 (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]. 1.22/1.60 351 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_eu(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ev(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__444) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 352 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_di(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc855931064lesseq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1886782970_lessf,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1886782970_lessf,Uu),Uub)))))) # label(fact_ATP_Olambda__388) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 353 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(Uu),Uua),Uub),Uuc)) <-> pp(aa_fun171081125l_bool(scratc943234093l_some(Uua),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ax(Uu),Uub),Uuc))))) # label(fact_ATP_Olambda__495) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 354 -(exists X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X0),scratc1141896968ptyset))) # label(fact_k__EmptyAx) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 355 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jf,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_je(Uu),Uua))))) # label(fact_ATP_Olambda__296) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 356 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_fj,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fk,Uu)))) # label(fact_ATP_Olambda__134) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 357 (all X all Xa all Xb (gg_TPTP_ind(Xb) -> aa_TPTP_ind_TPTP_ind(scratc1945325559d_e_in(X,Xa),Xb) = Xb)) # label(fact_def__e__in) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 358 (all X scratc1883353206nd_inn(X) = scratc1945325559d_e_in(scratc1923807950nd_nat,aa_TPT43085870d_bool(aTP_Lamm_ag,X))) # label(fact_def__inn) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 359 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1002098104_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1924332741nd_nis,Xa),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(X),Xa))))) # label(fact_def__d__27__prop1) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 360 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qv(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,Uua),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uub))))) # label(fact_ATP_Olambda__416) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 361 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dl(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dm,Uu),Uua)))) # label(fact_ATP_Olambda__330) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 362 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ka,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),scratc835753142nd_n_1)),Uu)))) # label(fact_ATP_Olambda__4) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 363 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dy,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dx(Uu),Uua))))) # label(fact_ATP_Olambda__328) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 364 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_ap,Uu)) <-> scratc1141896968ptyset != Uu))) # label(fact_ATP_Olambda__174) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 365 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ip(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uub),Uua)))))) # label(fact_ATP_Olambda__400) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 366 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_ji,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_jj,Uu)))) # label(fact_ATP_Olambda__105) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 367 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X33),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,aa_TPTP_ind_TPTP_ind(X22,X33)),aa_TPTP_ind_TPTP_ind(X12,X33)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1106035156_Sigma,X0),X22)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc804121290d_d_Pi,X0),X12))))) # label(fact_lam__Pi) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 368 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc432491428_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Xa),X))))) # label(fact_def__d__429__prop1) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 369 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_qb,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_qa,Uu))))) # label(fact_ATP_Olambda__47) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 370 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_sg,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,Uu),aa_TPTP_ind_TPTP_ind(scratc1398137874_power,scratc1923807950nd_nat))))) # label(fact_ATP_Olambda__20) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 371 (all X all Xa (pp(aa_fun171081125l_bool(scratc943234093l_some(X),aa_TPT43085870d_bool(aTP_Lamm_bb(X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1427491955nempty,X),Xa)))) # label(fact_def__nonempty) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 372 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jg,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_jf,Uu))))) # label(fact_ATP_Olambda__106) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 373 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_oy,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_oz,Uu)))) # label(fact_ATP_Olambda__59) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 374 (all Uu all Uua all Uub all Uuc (pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1883287609nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc419527030d_esti(Uu),Uuc),Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc419527030d_esti(Uu),Uuc),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ba(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__460) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 375 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1540862208etprop(X,Xa),Xb),Xc)) <-> pp(scratc1052430566_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc419527030d_esti(X),Xc),Xa),scratc1159895746_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc419527030d_esti(X),Xc),Xb)))))) # label(fact_def__nissetprop) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 376 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_si,Uu)) <-> (pp(aa_TPTP_ind_bool(scratc1541768444_cond1,Uu)) -> (pp(aa_TPTP_ind_bool(scratc1541768445_cond2,Uu)) -> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_sh,Uu))))))) # label(fact_ATP_Olambda__9) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 377 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1925119923nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc1841455290nd_den,Xa))),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1925119923nd_num,Xa)),aa_TPTP_ind_TPTP_ind(scratc1841455290nd_den,X)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1886782970_lessf,X),Xa)))) # label(fact_def__lessf) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 378 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jb(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__393) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 379 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),Uua)),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jv,Uu),Uua)))) # label(fact_ATP_Olambda__194) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 380 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_du,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_dv,Uu)))) # label(fact_ATP_Olambda__155) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 381 (all X all Xa (pp(aa_fun171081125l_bool(scratc1687058735n_some,aa_TPT43085870d_bool(scratc276310267ffprop(X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,X),Xa)))) # label(fact_def__d__29__ii) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 382 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ku,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uu)),scratc835753142nd_n_1)))) # label(fact_ATP_Olambda__15) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 383 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1092526980_pair1(X),Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1106035156_Sigma,aa_TPTP_ind_TPTP_ind(scratc656271931_d_1to,scratc835753143nd_n_2)),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ae(X),Xa),Xb))) # label(fact_def__pair1) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 384 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gh(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gg(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__441) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 385 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_qo,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_qp,Uu)))) # label(fact_ATP_Olambda__40) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 386 (all X all Xa all Xb all Xc all Xd aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1106035156_Sigma,X),aa_TPT1424761345TP_ind(aTP_Lamm_bd(Xc),Xd)) = aa_TPTP_ind_TPTP_ind(scratc657595830_inj_h(X,Xa,Xb,Xc),Xd)) # label(fact_def__inj__h) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 387 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_bp,Uu)) <-> (exists X2 (gg_TPTP_ind(X2) & Uu = aa_TPTP_ind_TPTP_ind(scratc1682036829d_Inj1,X2)))))) # label(fact_ATP_Olambda__175) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 388 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_nr,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_nq,Uu))))) # label(fact_ATP_Olambda__70) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 389 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc686833008t_disj(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1817129966nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_az(X),Xa),Xb))))) # label(fact_def__st__disj) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 390 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1925119923nd_num,X)),aa_TPTP_ind_TPTP_ind(scratc1841455290nd_den,Xa))),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1925119923nd_num,Xa)),aa_TPTP_ind_TPTP_ind(scratc1841455290nd_den,X)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc85621118_moref,X),Xa)))) # label(fact_def__moref) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 391 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ej,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ei,Uu))))) # label(fact_ATP_Olambda__149) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 392 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uu),Uua)) -> pp(scratc1159895746_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ps,Uu),Uua)))) # label(fact_ATP_Olambda__221) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 393 (all X all Xa scratc1883353196nd_ind(scratc1923807950nd_nat,aa_TPT43085870d_bool(scratc276310267ffprop(X),Xa)) = aa_TPTP_ind_TPTP_ind(scratc1464248316d_n_mn(X),Xa)) # label(fact_def__n__mn) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 394 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_sk,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_sj,Uu))))) # label(fact_ATP_Olambda__25) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 395 (all X (pp(scratc1159895746_d_not(scratc1159895746_d_not(X))) <-> scratc1998423883nd_wel(X))) # label(fact_def__wel) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 396 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),scratc835753142nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ry,Uu)))) # label(fact_ATP_Olambda__3) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 397 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nw(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__402) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 398 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc419527030d_esti(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,Uua),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ax(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__456) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 399 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_qt,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_qs,Uu))))) # label(fact_ATP_Olambda__38) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 400 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_is(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__394) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 401 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc266622957d_pair,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc353710971nunion(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1861302562d_repl,X),scratc1682036828d_Inj0)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1861302562d_repl,Xa),scratc1682036829d_Inj1))) # label(fact_def__pair) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 402 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_nv,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_nu,Uu))))) # label(fact_ATP_Olambda__69) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 403 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jr,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(scratc835753142nd_n_1),Uu))))) # label(fact_ATP_Olambda__18) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 404 (all Uu scratc1923807950nd_nat = aa_TPTP_ind_TPTP_ind(aTP_Lamm_ah,Uu)) # label(fact_ATP_Olambda__508) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 405 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_go(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gp(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__439) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 406 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ha(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hb(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__436) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 407 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_qq,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_qr,Uu)))) # label(fact_ATP_Olambda__39) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 408 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc268326120_image(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc943234093l_some(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bf(Xa),Xb),Xc))))) # label(fact_def__image) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 409 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mc(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__363) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 410 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463723527d_n_eq,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1463789127d_n_fr,Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1463789127d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fl(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__370) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 411 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gw(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uua),Uuc))))))) # label(fact_ATP_Olambda__490) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 412 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dx(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dw(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__446) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 413 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_es,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_er(Uu),Uua))))) # label(fact_ATP_Olambda__327) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 414 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ng(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uuc),Uua))))))) # label(fact_ATP_Olambda__486) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 415 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1924332741nd_nis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1924332741nd_nis,aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_se,Uu),Uua)))) # label(fact_ATP_Olambda__203) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 416 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc933104490ectelt(X,Xa),Xb) = aa_TPTP_ind_TPTP_ind(scratc1048306367ectset(X,Xa),aa_TPTP_ind_TPTP_ind(scratc822472892_ecelt(X,Xa),Xb))) # label(fact_def__ectelt) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 417 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_do,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc855931064lesseq,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc85621129_moreq,Uua),Uu))))) # label(fact_ATP_Olambda__214) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 418 (all Uu all Uua (pp(scratc1849585538nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463723527d_n_eq,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc85621118_moref,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1886782970_lessf,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fc,Uu),Uua)))) # label(fact_ATP_Olambda__182) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 419 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1832573285all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,X0)),aa_fun1584354236d_bool(aTP_Lamm_sr(X0),X12)))) # label(fact_estii) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 420 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ki,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_kh,Uu))))) # label(fact_ATP_Olambda__96) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 421 (all Uu (gg_TPTP_ind(Uu) -> ((exists X2 (gg_TPTP_ind(X2) & Uu = aa_TPTP_ind_TPTP_ind(scratc1682036828d_Inj0,X2))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu))))) # label(fact_ATP_Olambda__176) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 422 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gs(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__467) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 423 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ir,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_iq,Uu))))) # label(fact_ATP_Olambda__111) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 424 (all X aa_TPTP_ind_TPTP_ind(scratc358286701d_plus,X) = scratc1883353196nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc804121290d_d_Pi,scratc1923807950nd_nat),aTP_Lamm_ah),aa_TPT43085870d_bool(scratc1384495228_prop2,X))) # label(fact_def__plus) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 425 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nu,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_nt(Uu),Uua))))) # label(fact_ATP_Olambda__272) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 426 (all Uu all Uua (scratc304013183_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qo,Uu),Uua)))) # label(fact_ATP_Olambda__177) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 427 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dt(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ds(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__447) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 428 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fo,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463723527d_n_eq,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1463789127d_n_fr,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1925119923nd_num,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1841455290nd_den,Uu)),Uua))),Uu)))) # label(fact_ATP_Olambda__187) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 429 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_fo,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fp,Uu)))) # label(fact_ATP_Olambda__132) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 430 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ja,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_iz,Uu))))) # label(fact_ATP_Olambda__108) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 431 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rk(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__366) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 432 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_le(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__489) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 433 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1430363820air_q0(X),Xa) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1092526980_pair1(X),aa_TPTP_ind_TPTP_ind(scratc255057908first1(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1837011018econd1(X),Xa))) # label(fact_def__pair__q0) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 434 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ew,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ex,Uu)))) # label(fact_ATP_Olambda__144) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 435 (all X all Xa scratc1850438389nd_eps(aa_TPT43085870d_bool(scratc1289293997_rec_G(X),Xa)) = aa_TPTP_ind_TPTP_ind(scratc1832086362In_rec(X),Xa)) # label(fact_def__d__In__rec) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 436 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536279841fixfu2(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_au(X),Xa),Xb),Xc))))) # label(fact_def__fixfu2) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 437 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_qf,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_qe,Uu))))) # label(fact_ATP_Olambda__45) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 438 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nx,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_nw(Uu),Uua))))) # label(fact_ATP_Olambda__271) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 439 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qg,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uua),Uu))))) # label(fact_ATP_Olambda__219) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 440 (all B_1 gg_bool(scratc1159895746_d_not(B_1))) # label(gsy_c_Scratch__tptp__translate__57749__12314_ONUM749__thf__4__p_Obnd__d__not) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 441 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ib,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_ia(Uu),Uua))))) # label(fact_ATP_Olambda__305) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 442 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uua)),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kl,Uu),Uua)))) # label(fact_ATP_Olambda__205) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 443 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1945325564d_e_is(Uu),aa_TPTP_ind_TPTP_ind(scratc310968189_first(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1952701419d_pair(Uu,Uua),Uub),Uuc))),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_su(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__453) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 444 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1832573285all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ta(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tb(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__411) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 445 (all Uu all Uua aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1861302562d_repl,aa_TPTP_ind_TPTP_ind(Uu,Uua)),aa_TPT1424761345TP_ind(scratc266622957d_pair,Uua)) = aa_TPTP_ind_TPTP_ind(aTP_Lamm_bo(Uu),Uua)) # label(fact_ATP_Olambda__232) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 446 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc255057908first1(X),Xa) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,Xa),scratc1460312382d_n_1t)) # label(fact_def__first1) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 447 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_gi,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_gj,Uu)))) # label(fact_ATP_Olambda__128) # label(axiom) # label(non_clause). [assumption]. 1.22/1.60 448 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pk,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_pj(Uu),Uua))))) # label(fact_ATP_Olambda__260) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 449 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fs(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463723527d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463723527d_n_eq,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463723527d_n_eq,Uu),Uub)))))) # label(fact_ATP_Olambda__397) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 450 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_pk,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_pl,Uu)))) # label(fact_ATP_Olambda__55) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 451 (all X all Xa all Xb all Xc all Xd all Xe all Xf (pp(scratc1052430566_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc419527030d_esti(X),Xf),aa_TPTP_ind_TPTP_ind(scratc821882501_ecect(X,Xa),Xd)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1945325564d_e_is(Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,Xc),Xf)),Xe))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1931817854_prop1(X,Xa,Xb,Xc,Xd),Xe),Xf)))) # label(fact_def__d__10__prop1) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 452 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uu)),Uu)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_op,Uu)))) # label(fact_ATP_Olambda__12) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 453 (all X0 (pp(aa_TPTP_ind_bool(scratc1951619170_nat_p,X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X0),scratc696306926_omega)))) # label(fact_nat__p__omega) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 454 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pu,Uu),Uua)) <-> (pp(scratc1159895746_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,Uu),Uua))))) # label(fact_ATP_Olambda__243) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 455 (all X all Xa (scratc1946572016_l_iff(X,Xa) <-> pp(scratc1052430566_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1883287609nd_imp,X),Xa),aa_bool_bool(aa_boo1142376798l_bool(scratc1883287609nd_imp,Xa),X))))) # label(fact_def__l__iff) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 456 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dq,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc85621129_moreq,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc855931064lesseq,Uua),Uu))))) # label(fact_ATP_Olambda__215) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 457 (all Uu all Uua all Uub (scratc2064974964_is_of(aa_TPTP_ind_TPTP_ind(scratc1675549095second(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aq,Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sy(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__348) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 458 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cq,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1886782970_lessf,Uu),Uua)) -> pp(aa_fun171081125l_bool(scratc943234093l_some(scratc1190606337d_frac),aa_TPT43085870d_bool(aTP_Lamm_cp(Uu),Uua)))))) # label(fact_ATP_Olambda__220) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 459 (all X0 pp(aa_fun171081125l_bool(scratc1832573285all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,X0)),aa_TPT43085870d_bool(aTP_Lamm_tm,X0)))) # label(fact_refis) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 460 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_kc,Uu)) <-> pp(aa_fun171081125l_bool(scratc1932922227nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc804121290d_d_Pi,scratc1923807950nd_nat),aTP_Lamm_ah)),aa_TPT43085870d_bool(aTP_Lamm_kb,Uu))))) # label(fact_ATP_Olambda__8) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 461 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_nl(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nm,Uu),Uua)))) # label(fact_ATP_Olambda__274) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 462 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc822472892_ecelt(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc936179117_d_Sep(X),aa_TPT43085870d_bool(Xa,Xb))) # label(fact_def__ecelt) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 463 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ix,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_iw,Uu))))) # label(fact_ATP_Olambda__109) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 464 (all X scratc1945325564d_e_is(X) = fequal_TPTP_ind) # label(fact_def__e__is) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 465 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_rg,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_rh,Uu)))) # label(fact_ATP_Olambda__33) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 466 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gf,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_ge,Uu))))) # label(fact_ATP_Olambda__129) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 467 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uua),scratc835753142nd_n_1)),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kn,Uu),Uua)))) # label(fact_ATP_Olambda__202) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 468 (all Uu all Uua ((pp(scratc1159895746_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1886782970_lessf,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc85621129_moreq,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ei,Uu),Uua)))) # label(fact_ATP_Olambda__242) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 469 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_qh,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_qg,Uu))))) # label(fact_ATP_Olambda__44) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 470 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gb,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_ga,Uu))))) # label(fact_ATP_Olambda__130) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 471 (all Uu all Uua (gg_TPTP_ind(Uua) -> ((exists X3 (gg_TPTP_ind(X3) & aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc266622957d_pair,Uu),X3) = Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bn,Uu),Uua))))) # label(fact_ATP_Olambda__341) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 472 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gc(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uua),Uuc))))))) # label(fact_ATP_Olambda__469) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 473 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc85621118_moref,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463723527d_n_eq,Uu),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463723527d_n_eq,Uua),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc85621118_moref,Uub),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_eu(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__477) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 474 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,Uu),scratc1923807950nd_nat)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ce,Uu)))) # label(fact_ATP_Olambda__24) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 475 (all X all Xa ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X2),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X2),Xa))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc955280034d_Subq,X),Xa)))) # label(fact_def__d__Subq) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 476 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_my,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_mx(Uu),Uua))))) # label(fact_ATP_Olambda__278) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 477 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hm,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_hl,Uu))))) # label(fact_ATP_Olambda__120) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 478 (all X scratc1883353196nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc804121290d_d_Pi,scratc1923807950nd_nat),aTP_Lamm_ah),aa_TPT43085870d_bool(scratc1991612902_prop2,X)) = aa_TPTP_ind_TPTP_ind(scratc1190256787_times,X)) # label(fact_def__times) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 479 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ly(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lz(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__424) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 480 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,Uua),aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uu)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kp,Uu),Uua)))) # label(fact_ATP_Olambda__207) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 481 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Xa),X))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc413735929_prop1,X),Xa)))) # label(fact_def__d__26__prop1) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 482 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_th(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1945325564d_e_is(Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,Uua),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,Uub),Uuc))))) # label(fact_ATP_Olambda__455) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 483 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,Uu),Uub)) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_bd(Uu),Uua),Uub)) # label(fact_ATP_Olambda__419) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 484 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_nk(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__485) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 485 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_lj(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lk,Uu),Uua)))) # label(fact_ATP_Olambda__290) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 486 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kx(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kw(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__431) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 487 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ol(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__373) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 488 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_gh(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gi,Uu),Uua)))) # label(fact_ATP_Olambda__318) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 489 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_no(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uuc),Uua))))))) # label(fact_ATP_Olambda__482) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 490 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1832573285all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ss(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_st(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__413) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 491 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ji,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_jh(Uu),Uua))))) # label(fact_ATP_Olambda__295) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 492 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hp,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_ho,Uu))))) # label(fact_ATP_Olambda__119) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 493 (all B_1 all B_2 all B_3 gg_bool(scratc1849585538nd_ec3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__57749__12314_ONUM749__thf__4__p_Obnd__ec3) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 494 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_mo(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mp,Uu),Uua)))) # label(fact_ATP_Olambda__281) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 495 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),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__420) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 496 (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(scratc1945325564d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,Uub),Uuc)),Uue)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,Uub),Uud)),Uuf))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_ar(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)))) # label(fact_ATP_Olambda__504) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 497 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1832573285all_of(aa_TPT43085870d_bool(aTP_Lamm_sw(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_sy(X0),X12)))) # label(fact_second__p) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 498 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_it,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_iu,Uu)))) # label(fact_ATP_Olambda__110) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 499 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_sf,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_se,Uu))))) # label(fact_ATP_Olambda__26) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 500 (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]. 1.22/1.61 501 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ff,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fe,Uu))))) # label(fact_ATP_Olambda__140) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 502 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1832573285all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_su(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sv(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__412) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 503 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ra(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,Uua),Uub))))) # label(fact_ATP_Olambda__358) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 504 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iw,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_iv(Uu),Uua))))) # label(fact_ATP_Olambda__299) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 505 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),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__317) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 506 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_md,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_mc(Uu),Uua))))) # label(fact_ATP_Olambda__285) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 507 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dh,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dg,Uu))))) # label(fact_ATP_Olambda__160) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 508 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ad(Uu),Uua),Uub),Uuc) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,Uub),aa_TPTP_ind_TPTP_ind(scratc683642354eft1to(Uu,Uua),Uuc))) # label(fact_ATP_Olambda__497) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 509 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_pn,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_pm,Uu))))) # label(fact_ATP_Olambda__54) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 510 (all X all Xa all Xb scratc1073566648_indeq(X,Xa,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc804121290d_d_Pi,X),aTP_Lamm_af(Xb))) = scratc185334392d_11_i(X,Xa,Xb)) # label(fact_def__d__11__i) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 511 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_da,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_db,Uu)))) # label(fact_ATP_Olambda__162) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 512 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uu)),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rn,Uu),Uua)))) # label(fact_ATP_Olambda__234) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 513 (all X aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1106035156_Sigma,scratc1923807950nd_nat),aTP_Lamm_al(X)) = aa_TPTP_ind_TPTP_ind(scratc1519176628d_24_g,X)) # label(fact_def__d__24__g) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 514 (all X all Xa (pp(scratc1332078583d_l_ec(X,Xa)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1883287609nd_imp,X),scratc1159895746_d_not(Xa))))) # label(fact_def__l__ec) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 515 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1945325564d_e_is(aa_TPTP_ind_TPTP_ind(scratc1398137874_power,X)),Xb),aa_TPTP_ind_TPTP_ind(scratc822472892_ecelt(X,Xa),Xc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1849585599nd_ecp(X,Xa),Xb),Xc)))) # label(fact_def__ecp) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 516 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,X),Xa)) <-> pp(aa_bool_bool(scratc1332734588d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,X),Xa))))) # label(fact_def__lessis) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 517 (all Uu all Uua (pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1883287609nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985920d_n_in,Uua),Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985920d_n_in,aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uua)),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ao,Uu),Uua)))) # label(fact_ATP_Olambda__204) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 518 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_he(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__361) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 519 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_oo,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uu))))) # label(fact_ATP_Olambda__19) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 520 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ml(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__362) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 521 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_do,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_dp,Uu)))) # label(fact_ATP_Olambda__157) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 522 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1480231895sel_wb(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc1883746791nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1945325564d_e_is(X),Xc),Xb),X,Xa),aa_TPTP_ind_TPTP_ind(scratc1480231894sel_wa(X,Xa,Xb),Xc))) # label(fact_def__wissel__wb) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 523 (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_bc(Uu),Uua),Uub),Uuc),Uud) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,aa_TPTP_ind_TPTP_ind(scratc916333164wissel(Uu,Uub),Uuc)),Uud))) # label(fact_ATP_Olambda__502) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 524 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(X),Xa)),Xb)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(X),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Xa),Xb)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1414757293_prop1(X),Xa),Xb)))) # label(fact_def__d__431__prop1) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 525 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_ky,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_kz,Uu)))) # label(fact_ATP_Olambda__90) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 526 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1832573285all_of(aa_TPT43085870d_bool(aTP_Lamm_tg(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_tj(X0),X12)))) # label(fact_e__fisi) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 527 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_jv,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_jw,Uu)))) # label(fact_ATP_Olambda__100) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 528 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cl(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463723527d_n_eq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463723527d_n_eq,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463723527d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1464445105d_n_pf(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464445105d_n_pf(Uua),Uuc))))))) # label(fact_ATP_Olambda__487) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 529 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rz,Uu),Uua)) <-> pp(scratc1052430566_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,Uua),scratc835753142nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uu)),aa_fun171081125l_bool(scratc477404390_n_all,aa_TPT43085870d_bool(aTP_Lamm_am,Uua)))))) # label(fact_ATP_Olambda__190) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 530 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_lm(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__466) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 531 (all X all Xa all Xb (scratc1549788367d_and3(scratc1332078583d_l_ec(X,Xa),scratc1332078583d_l_ec(Xa,Xb),scratc1332078583d_l_ec(Xb,X)) <-> pp(scratc1849585538nd_ec3(X,Xa,Xb)))) # label(fact_def__ec3) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 532 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc85621129_moreq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463723527d_n_eq,Uu),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463723527d_n_eq,Uua),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc85621129_moreq,Uub),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dw(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__476) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 533 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1832573285all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,X0)),aa_fun1584354236d_bool(aTP_Lamm_tc(X0),X12)))) # label(fact_otax2) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 534 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tm,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1945325564d_e_is(Uu),Uua),Uua)))) # label(fact_ATP_Olambda__186) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 535 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),Uua)),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jy,Uu),Uua)))) # label(fact_ATP_Olambda__198) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 536 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gt(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gs(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__438) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 537 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_rw,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_rx,Uu)))) # label(fact_ATP_Olambda__27) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 538 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_tc(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc268326120_image(aa_fun1431113780TP_ind(scratc936179117_d_Sep(Uu),Uua),Uu),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1106035156_Sigma,aa_fun1431113780TP_ind(scratc936179117_d_Sep(Uu),Uua)),scratc1945325559d_e_in(Uu,Uua))),Uub))))) # label(fact_ATP_Olambda__407) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 539 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_jn,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_jo,Uu)))) # label(fact_ATP_Olambda__103) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 540 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_sd,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1924332741nd_nis,aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__13) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 541 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hu,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_ht(Uu),Uua))))) # label(fact_ATP_Olambda__307) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 542 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1106035156_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,aa_TPTP_ind_TPTP_ind(scratc1526651712_proj0,X22)),X0)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,aa_TPTP_ind_TPTP_ind(scratc1526651713_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1526651712_proj0,X22)))) & aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc266622957d_pair,aa_TPTP_ind_TPTP_ind(scratc1526651712_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1526651713_proj1,X22)) = X22))) # label(fact_k__Sigma__eta__proj0__proj1) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 543 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gg(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__488) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 544 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_os,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ot,Uu)))) # label(fact_ATP_Olambda__61) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 545 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ox(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__375) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 546 (all P all X7 (-pp(aa_TPTP_ind_bool(P,X7)) | pp(fEx_TPTP_ind(P)))) # label(help_fEx_1_1_fEx_001t__TPTP____Interpret__Oind_U) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 547 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1886782970_lessf,Uu),aa_TPTP_ind_TPTP_ind(scratc1464445105d_n_pf(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,Uu),Uua)))) # label(fact_ATP_Olambda__246) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 548 (all B_1 all B_2 gg_TPTP_ind(scratc1883353196nd_ind(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__57749__12314_ONUM749__thf__4__p_Obnd__ind) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 549 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_jl,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_jm,Uu)))) # label(fact_ATP_Olambda__104) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 550 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mr(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__355) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 551 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hn(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uub),Uua)))))) # label(fact_ATP_Olambda__382) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 552 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ou(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__385) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 553 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jp,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),Uua)),Uua)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uu)),Uua))))) # label(fact_ATP_Olambda__188) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 554 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mi(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__356) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 555 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1832573285all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,X0)),aa_fun1584354236d_bool(aTP_Lamm_tl(X0),X12)))) # label(fact_e__isp) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 556 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X22),X0)) -> (pp(aa_TPTP_ind_bool(X12,X22)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X22),aa_fun1431113780TP_ind(scratc936179117_d_Sep(X0),X12)))))) # label(fact_k__SepI) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 557 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uu),Uua)) -> pp(scratc1159895746_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pq,Uu),Uua)))) # label(fact_ATP_Olambda__228) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 558 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ca,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bz(Uu),Uua))))) # label(fact_ATP_Olambda__337) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 559 (all X all Xa (-pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1922233568nd_nIn,X),Xa)))) # label(fact_def__nIn) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 560 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rq,Uu),Uua)))) # label(fact_ATP_Olambda__235) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 561 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pd(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__403) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 562 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_fq,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fr,Uu)))) # label(fact_ATP_Olambda__131) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 563 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ms,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_mr(Uu),Uua))))) # label(fact_ATP_Olambda__280) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 564 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eg,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_eh,Uu)))) # label(fact_ATP_Olambda__150) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 565 pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1883287609nd_imp,fFalse),fFalse)) <-> scratc1178529556bvious # label(fact_def__obvious) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 566 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_ie(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_if,Uu),Uua)))) # label(fact_ATP_Olambda__304) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 567 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1972857402_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(X),Xa)),Xb)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(X),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Xa),Xb)))))) # label(fact_def__d__25__prop1) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 568 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gw(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__437) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 569 (all X0 (pp(aa_TPTP_ind_bool(X0,scratc1141896968ptyset)) -> ((all X13 (gg_TPTP_ind(X13) -> (pp(aa_TPTP_ind_bool(scratc1951619170_nat_p,X13)) -> (pp(aa_TPTP_ind_bool(X0,X13)) -> pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,X13))))))) -> (all X12 (pp(aa_TPTP_ind_bool(scratc1951619170_nat_p,X12)) -> pp(aa_TPTP_ind_bool(X0,X12))))))) # label(fact_nat__ind) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 570 (all X aa_TPTP_ind_TPTP_ind(scratc185317865d_xout,X) = aa_TPTP_ind_TPTP_ind(scratc1799471091d_outn(X),X)) # label(fact_def__xout) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 571 (all X scratc1747570168bnd_in = scratc419527030d_esti(X)) # label(fact_def__esti) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 572 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_qj,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_qi,Uu))))) # label(fact_ATP_Olambda__43) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 573 (all P all Q (pp(P) | -pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 574 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_oq,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_or,Uu)))) # label(fact_ATP_Olambda__62) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 575 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_li(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__474) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 576 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_lu(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lv(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__425) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 577 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ii(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ih(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__433) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 578 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc1932922227nd_one(X0),X12)) -> pp(aa_TPTP_ind_bool(X12,scratc1883353196nd_ind(X0,X12))))) # label(fact_oneax) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 579 (all X all Xa scratc1883353196nd_ind(X,Xa) = scratc1850438389nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bi(X),Xa))) # label(fact_def__ind) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 580 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lf(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_le(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__429) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 581 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc85621118_moref,Uua),Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cu,Uu),Uua)))) # label(fact_ATP_Olambda__252) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 582 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_lr(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ls,Uu),Uua)))) # label(fact_ATP_Olambda__288) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 583 (all Uu aa_TPT494704832TP_ind(aTP_Lamm_br,Uu) = aa_TPT494704832TP_ind(scratc1861302562d_repl,aa_TPTP_ind_TPTP_ind(scratc269996513tminus(Uu),aa_TPTP_ind_TPTP_ind(scratc856929152d_Sing,scratc1141896968ptyset)))) # label(fact_ATP_Olambda__173) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 584 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iy(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__399) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 585 (all B_1 all B_2 gg_bool(scratc1332078583d_l_ec(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__57749__12314_ONUM749__thf__4__p_Obnd__l__ec) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 586 (all Uu all Uua all Uub all Uuc all Uud all Uue all Uuf (pp(aa_fun171081125l_bool(scratc1832573285all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_ar(Uua),Uub),Uuc),Uud),Uue),Uuf))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_as(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)))) # label(fact_ATP_Olambda__505) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 587 (all X (pp(aa_TPTP_ind_bool(scratc796133052_prop1,X)) <-> pp(aa_bool_bool(scratc1332734588d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,X),scratc835753142nd_n_1)),aa_fun171081125l_bool(scratc1687058735n_some,aa_TPT43085870d_bool(aTP_Lamm_an,X)))))) # label(fact_def__d__23__prop1) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 588 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hi,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_hh(Uu),Uua))))) # label(fact_ATP_Olambda__311) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 589 (all X all Xa (scratc1727013373d_r_ec(X,Xa) <-> (pp(X) -> pp(scratc1159895746_d_not(Xa))))) # label(fact_def__r__ec) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 590 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc85621129_moreq,X),Xa)) <-> pp(aa_bool_bool(scratc1332734588d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc85621118_moref,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463723527d_n_eq,X),Xa))))) # label(fact_def__moreq) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 591 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1832573285all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bj(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bk(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__410) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 592 (all X (pp(aa_fun171081125l_bool(scratc477404390_n_all,aa_TPT43085870d_bool(aTP_Lamm_ao,X))) <-> pp(aa_TPTP_ind_bool(scratc1541768445_cond2,X)))) # label(fact_def__cond2) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 593 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_lk,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ll,Uu)))) # label(fact_ATP_Olambda__87) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 594 (all X all Xa (pp(scratc1052430566_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,Xa),scratc835753142nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,X)),aa_TPTP_ind_bool(scratc1384495227_prop1,Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1384495228_prop2,X),Xa)))) # label(fact_def__d__24__prop2) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 595 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_on,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_om,Uu))))) # label(fact_ATP_Olambda__63) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 596 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mo(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__359) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 597 (all B_1 all B_2 gg_bool(scratc2005350311_amone(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__57749__12314_ONUM749__thf__4__p_Obnd__amone) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 598 (all X aa_TPTP_ind_TPTP_ind(scratc136796398d_1out,X) = aa_TPTP_ind_TPTP_ind(scratc1799471091d_outn(X),scratc835753142nd_n_1)) # label(fact_def__d__1out) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 599 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cv,Uu)) <-> pp(aa_fun171081125l_bool(scratc943234093l_some(scratc1190606337d_frac),aa_TPT43085870d_bool(aTP_Lamm_cu,Uu))))) # label(fact_ATP_Olambda__170) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 600 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_td(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,Uub),aa_fun1431113780TP_ind(scratc936179117_d_Sep(Uu),Uua))))) # label(fact_ATP_Olambda__418) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 601 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jk(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uua),Uub))),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),Uub)))))) # label(fact_ATP_Olambda__368) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 602 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_de,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dd,Uu))))) # label(fact_ATP_Olambda__161) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 603 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_nh(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ni,Uu),Uua)))) # label(fact_ATP_Olambda__275) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 604 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_rl,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_rm,Uu)))) # label(fact_ATP_Olambda__31) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 605 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc955280034d_Subq,X12),X0)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1398137874_power,X0))))) # label(fact_k__PowerEq) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 606 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_rt,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ru,Uu)))) # label(fact_ATP_Olambda__28) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 607 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ng(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nh(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__423) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 608 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_lc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ld,Uu)))) # label(fact_ATP_Olambda__89) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 609 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sx(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1945325564d_e_is(aa_TPTP_ind_TPTP_ind(scratc549122310etprod(Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1952701419d_pair(Uu,Uua),aa_TPTP_ind_TPTP_ind(scratc310968189_first(Uu,Uua),Uub)),aa_TPTP_ind_TPTP_ind(scratc1675549095second(Uu,Uua),Uub))),Uub)))) # label(fact_ATP_Olambda__342) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 610 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ha(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uua),Uuc))))))) # label(fact_ATP_Olambda__463) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 611 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cr,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cq,Uu))))) # label(fact_ATP_Olambda__164) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 612 (all X all Xa all Xb (pp(aa_fun171081125l_bool(scratc943234093l_some(X),aa_TPT43085870d_bool(scratc1849585599nd_ecp(X,Xa),Xb))) <-> pp(aa_TPTP_ind_bool(scratc1549854014d_anec(X,Xa),Xb)))) # label(fact_def__anec) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 613 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(scratc1747570160bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc268326120_image(Uu,Uua),Uub),Uuc),aa_TPTP_ind_TPTP_ind(scratc576365181d_soft(Uu,Uua,Uub),Uuc)),scratc1141896968ptyset) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_be(Uu),Uua),Uub),Uuc)) # label(fact_ATP_Olambda__452) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 614 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_tk(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1945325564d_e_is(Uu),Uub),Uuc)) -> pp(aa_TPTP_ind_bool(Uua,Uuc)))))) # label(fact_ATP_Olambda__492) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 615 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_ms,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_mt,Uu)))) # label(fact_ATP_Olambda__77) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 616 (all Uu all Uua all Uub all Uuc all Uud all Uue (pp(aa_fun171081125l_bool(scratc1832573285all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_as(Uu),Uua),Uub),Uuc),Uud),Uue))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_at(Uu),Uua),Uub),Uuc),Uud),Uue)))) # label(fact_ATP_Olambda__503) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 617 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jn,Uu),Uua)))) # label(fact_ATP_Olambda__208) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 618 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_nf,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_ne,Uu))))) # label(fact_ATP_Olambda__73) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 619 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lo,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_ln(Uu),Uua))))) # label(fact_ATP_Olambda__289) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 620 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_od,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_oc(Uu),Uua))))) # label(fact_ATP_Olambda__269) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 621 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_mk,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_mj,Uu))))) # label(fact_ATP_Olambda__80) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 622 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mu(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__384) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 623 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lr(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_lq(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__426) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 624 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ac(Uu),Uua),Uub),Uuc) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,Uub),aa_TPTP_ind_TPTP_ind(scratc865293603ght1to(Uu,Uua),Uuc))) # label(fact_ATP_Olambda__496) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 625 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ft,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fu,Uu)))) # label(fact_ATP_Olambda__138) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 626 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qi,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uua),Uu))))) # label(fact_ATP_Olambda__211) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 627 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (-pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc1747570160bnd_if(X0,X12),X22) = X22))) # label(fact_if__i__0) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 628 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,X),Xb)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1527045309_prop3(X),Xa),Xb)))) # label(fact_def__prop3) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 629 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rl,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_rk(Uu),Uua))))) # label(fact_ATP_Olambda__257) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 630 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ly(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__464) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 631 (all Uu all Uua ((pp(scratc1159895746_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pm,Uu),Uua)))) # label(fact_ATP_Olambda__238) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 632 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1886782970_lessf,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463723527d_n_eq,Uu),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463723527d_n_eq,Uua),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1886782970_lessf,Uub),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_eq(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__478) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 633 (all B_1 all B_2 gg_bool(scratc1052430566_d_and(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__57749__12314_ONUM749__thf__4__p_Obnd__d__and) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 634 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463723527d_n_eq,aa_TPTP_ind_TPTP_ind(scratc1464445105d_n_pf(aa_TPTP_ind_TPTP_ind(scratc1464445105d_n_pf(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464445105d_n_pf(Uu),aa_TPTP_ind_TPTP_ind(scratc1464445105d_n_pf(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bz(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__367) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 635 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_js,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_jt,Uu)))) # label(fact_ATP_Olambda__101) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 636 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1106035156_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,aa_TPTP_ind_TPTP_ind(scratc1526651712_proj0,X22)),X0)))) # label(fact_proj0__Sigma) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 637 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cd,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cc,Uu))))) # label(fact_ATP_Olambda__166) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 638 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_kr,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ks,Uu)))) # label(fact_ATP_Olambda__91) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 639 (all X0 ((all X13 (gg_TPTP_ind(X13) -> ((all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_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]. 1.22/1.61 640 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc2104322782eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bn,Xa)),scratc1526651713_proj1)) # label(fact_def__ap) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 641 (all X0 (pp(aa_TPTP_ind_bool(scratc1951619170_nat_p,X0)) -> pp(aa_TPTP_ind_bool(scratc1951619170_nat_p,aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,X0))))) # label(fact_nat__ordsucc) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 642 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_sr(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc419527030d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc936179117_d_Sep(Uu),Uua)))))) # label(fact_ATP_Olambda__408) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 643 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_bg(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1883287609nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1945325564d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,Uub),Uud))),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1945325564d_e_is(Uu),Uuc),Uud))))) # label(fact_ATP_Olambda__498) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 644 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fn,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_fm,Uu))))) # label(fact_ATP_Olambda__133) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 645 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hr,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_hq(Uu),Uua))))) # label(fact_ATP_Olambda__308) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 646 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc85621118_moref,Uu),Uua)) -> pp(scratc1159895746_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc855931064lesseq,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eg,Uu),Uua)))) # label(fact_ATP_Olambda__226) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 647 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_hx,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_hy,Uu)))) # label(fact_ATP_Olambda__116) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 648 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1832573285all_of(aa_TPT43085870d_bool(aTP_Lamm_sw(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_sx(X0),X12)))) # label(fact_pairis1) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 649 (all X aa_TPTP_ind_TPTP_ind(scratc856929152d_Sing,X) = aa_TPTP_ind_TPTP_ind(scratc1000521534_UPair(X),X)) # label(fact_def__d__Sing) # label(axiom) # label(non_clause). [assumption]. 1.22/1.61 650 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_fun171081125l_bool(scratc1832573285all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_at(Uu),Uua),Uub),Uuc),Uud))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_au(Uu),Uua),Uub),Uuc),Uud)))) # label(fact_ATP_Olambda__500) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 651 (all X0 (scratc1998423883nd_wel(X0) -> pp(X0))) # label(fact_l__et) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 652 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_gd(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ge,Uu),Uua)))) # label(fact_ATP_Olambda__319) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 653 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_md,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_me,Uu)))) # label(fact_ATP_Olambda__82) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 654 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ko,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_kn,Uu))))) # label(fact_ATP_Olambda__93) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 655 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_tj(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aa_TPT43085870d_bool(aTP_Lamm_tg(Uu),Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ti(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__351) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 656 (all Uu ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1924332741nd_nis,Uu),scratc835753142nd_n_1)) -> pp(aa_fun171081125l_bool(scratc1687058735n_some,aa_TPT43085870d_bool(aTP_Lamm_an,Uu)))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_sc,Uu)))) # label(fact_ATP_Olambda__1) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 657 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jh(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uua),Uub)))))) # label(fact_ATP_Olambda__365) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 658 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_nb,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_nc,Uu)))) # label(fact_ATP_Olambda__74) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 659 (all X scratc1332734588d_l_or(X) = aa_boo1142376798l_bool(scratc1883287609nd_imp,scratc1159895746_d_not(X))) # label(fact_def__l__or) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 660 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X22),X0)) -> (all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X32),aa_TPTP_ind_TPTP_ind(X12,X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc266622957d_pair,X22),X32)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1106035156_Sigma,X0),X12))))))) # label(fact_pair__Sigma) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 661 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_pz,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_py,Uu))))) # label(fact_ATP_Olambda__48) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 662 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1883025206nd_iii,Uua),aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uu))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kh,Uu),Uua)))) # label(fact_ATP_Olambda__199) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 663 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pb,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_pa(Uu),Uua))))) # label(fact_ATP_Olambda__263) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 664 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1832573285all_of(aa_TPT43085870d_bool(aTP_Lamm_sw(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_sz(X0),X12)))) # label(fact_first__p) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 665 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_no(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_np(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__421) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 666 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,X),Xa)) <-> pp(aa_bool_bool(scratc1332734588d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,X),Xa))))) # label(fact_def__moreis) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 667 (all X ((all X1 (pp(aa_TPTP_ind_bool(X1,scratc1141896968ptyset)) -> ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(X1,X2)) -> pp(aa_TPTP_ind_bool(X1,aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,X2)))))) -> pp(aa_TPTP_ind_bool(X1,X))))) <-> pp(aa_TPTP_ind_bool(scratc1951619170_nat_p,X)))) # label(fact_def__nat__p) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 668 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc855931064lesseq,X),Xa)) <-> pp(aa_bool_bool(scratc1332734588d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1886782970_lessf,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463723527d_n_eq,X),Xa))))) # label(fact_def__lesseq) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 669 (all Uu all Uua (scratc304013183_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1687058735n_some,aa_TPT43085870d_bool(aTP_Lamm_qu(Uu),Uua)),aa_fun171081125l_bool(scratc1687058735n_some,aa_TPT43085870d_bool(aTP_Lamm_qv(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qw,Uu),Uua)))) # label(fact_ATP_Olambda__183) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 670 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_cg,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ch,Uu)))) # label(fact_ATP_Olambda__136) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 671 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_hw(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hx,Uu),Uua)))) # label(fact_ATP_Olambda__306) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 672 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ne,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_nd(Uu),Uua))))) # label(fact_ATP_Olambda__276) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 673 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1837011018econd1(X),Xa) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,Xa),scratc1460377981d_n_2t)) # label(fact_def__second1) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 674 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_it,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_is(Uu),Uua))))) # label(fact_ATP_Olambda__300) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 675 (all Uu all Uua aa_TPTP_ind_TPTP_ind(scratc353710971nunion(aa_TPTP_ind_TPTP_ind(scratc856929152d_Sing,scratc1141896968ptyset)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1861302562d_repl,Uu),Uua)) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(aTP_Lamm_bs,Uu),Uua)) # label(fact_ATP_Olambda__244) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 676 (all Uu all Uua all Uub all Uuc (gg_TPTP_ind(Uua) & gg_TPTP_ind(Uub) & gg_TPTP_ind(Uuc) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bw(Uu),Uua),Uub),Uuc)) <-> Uua = Uuc & pp(Uu) | Uuc = Uub & -pp(Uu)))) # label(fact_ATP_Olambda__462) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 677 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gl(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gk(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__440) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 678 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),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__331) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 679 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ek,Uu),Uua)) <-> (pp(scratc1159895746_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc85621118_moref,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc855931064lesseq,Uu),Uua))))) # label(fact_ATP_Olambda__241) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 680 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_ni,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_nj,Uu)))) # label(fact_ATP_Olambda__72) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 681 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_an,Uu),Uua)))) # label(fact_ATP_Olambda__249) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 682 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_mu(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_mv,Uu),Uua)))) # label(fact_ATP_Olambda__279) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 683 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_rf,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_re,Uu))))) # label(fact_ATP_Olambda__34) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 684 (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(scratc1747570168bnd_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(scratc1289293997_rec_G(X),Xa),Xb)))) # label(fact_def__d__In__rec__G) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 685 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nz(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__396) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 686 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ht(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uub),Uua)))))) # label(fact_ATP_Olambda__377) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 687 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hw(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__376) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 688 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1886782970_lessf,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1886782970_lessf,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1886782970_lessf,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dl(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__392) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 689 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc85621118_moref,aa_TPTP_ind_TPTP_ind(scratc1464445105d_n_pf(Uu),Uua)),Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bx,Uu),Uua)))) # label(fact_ATP_Olambda__230) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 690 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_lq(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__468) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 691 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_lx,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_lw,Uu))))) # label(fact_ATP_Olambda__84) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 692 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_pa(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc990177074moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744436536_29_ii,Uu),Uub)))))) # label(fact_ATP_Olambda__380) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 693 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sj,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__193) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 694 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_qx,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_qw,Uu))))) # label(fact_ATP_Olambda__37) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 695 (all Uu all Uua (pp(scratc2005350311_amone(scratc1923807950nd_nat,aa_TPT43085870d_bool(aTP_Lamm_qu(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_qy,Uu),Uua)))) # label(fact_ATP_Olambda__338) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 696 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ob,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_oa,Uu))))) # label(fact_ATP_Olambda__67) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 697 (all X aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,aa_TPTP_ind_TPTP_ind(scratc358286701d_plus,X)) = scratc1464445111d_n_pl(X)) # label(fact_def__n__pl) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 698 (all X0 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X0),scratc696306926_omega)) -> pp(aa_TPTP_ind_bool(scratc1951619170_nat_p,X0)))) # label(fact_omega__nat__p) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 699 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bb(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc419527030d_esti(Uu),Uub),Uua)))) # label(fact_ATP_Olambda__345) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 700 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eo,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc85621129_moreq,Uu),Uua)) -> pp(scratc1159895746_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1886782970_lessf,Uu),Uua)))))) # label(fact_ATP_Olambda__225) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 701 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1883746791nd_ite(X,Xa,Xb),Xc) = scratc1883353196nd_ind(Xa,aa_TPT43085870d_bool(scratc1527045307_prop1(X,Xa,Xb),Xc))) # label(fact_def__ite) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 702 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> aa_TPTP_ind_TPTP_ind(scratc1747570160bnd_if(X0,X12),X22) = X12 & pp(X0) | X22 = aa_TPTP_ind_TPTP_ind(scratc1747570160bnd_if(X0,X12),X22) & -pp(X0))) # label(fact_if__i__correct) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 703 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ph,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_pg(Uu),Uua))))) # label(fact_ATP_Olambda__261) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 704 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X22),aa_fun1431113780TP_ind(scratc936179117_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X22),X0)))) # label(fact_k__SepE1) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 705 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ed,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ec,Uu))))) # label(fact_ATP_Olambda__152) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 706 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc856193462lessis,aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1464707514d_n_ts(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fy(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__471) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 707 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1832573285all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,X0)),aa_TPT43085870d_bool(aTP_Lamm_tb(X0),X12)))) # label(fact_e__pair__p) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 708 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rt,Uu),Uua)))) # label(fact_ATP_Olambda__196) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 709 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ow,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_ov,Uu))))) # label(fact_ATP_Olambda__60) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 710 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc1398137874_power,X0)))) # label(fact_k__Self__In__Power) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 711 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc804121290d_d_Pi,X0),X12))) -> (all X32 (gg_TPTP_ind(X32) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X32),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc804121290d_d_Pi,X0),X12))) -> ((all X42 (gg_TPTP_ind(X42) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X42),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,X22),X42) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,X32),X42)))) -> X22 = X32))))))) # label(fact_k__Pi__ext) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 712 (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(scratc1883025206nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__248) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 713 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_nk(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_nl(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__422) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 714 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985920d_n_in,Uua),Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_sh,Uu),Uua)))) # label(fact_ATP_Olambda__254) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 715 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1106035156_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,aa_TPTP_ind_TPTP_ind(scratc1526651713_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1526651712_proj0,X22)))))) # label(fact_proj1__Sigma) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 716 (all X7 all Y (gg_TPTP_ind(Y) & gg_TPTP_ind(X7) -> Y = X7 | -pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)))) # label(help_fequal_1_1_fequal_001t__TPTP____Interpret__Oind_T) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 717 (all X aa_fun277296641TP_ind(scratc2104322782eplSep(X,aTP_Lamm_bq),scratc953292512_d_Unj) = aa_TPTP_ind_TPTP_ind(scratc1526651712_proj0,X)) # label(fact_def__proj0) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 718 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1832573285all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,X0)),aa_TPT43085870d_bool(aTP_Lamm_sv(X0),X12)))) # label(fact_firstis1) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 719 (all P all Q all R aa_TPTP_ind_bool(cOMBS_2003118649l_bool(P,Q),R) = aa_bool_bool(aa_TPT2142672771l_bool(P,R),aa_TPTP_ind_bool(Q,R))) # label(help_COMBS_1_1_COMBS_001t__TPTP____Interpret__Oind_001t__HOL__Obool_001t__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 720 (all X all Xa scratc1933381435nd_out(X,Xa) = scratc576365181d_soft(aa_fun1431113780TP_ind(scratc936179117_d_Sep(X),Xa),X,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1106035156_Sigma,aa_fun1431113780TP_ind(scratc936179117_d_Sep(X),Xa)),scratc1945325559d_e_in(X,Xa)))) # label(fact_def__out) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 721 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_lh,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_lg,Uu))))) # label(fact_ATP_Olambda__88) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 722 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ta(Uu),Uua),Uub),Uuc)) <-> scratc2064974964_is_of(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1952701419d_pair(Uu,Uua),Uub),Uuc),aa_TPT43085870d_bool(aTP_Lamm_sw(Uu),Uua)))) # label(fact_ATP_Olambda__458) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 723 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1726949702eft_f2(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc1472090682d_left(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(scratc1726949701eft_f1(X,Xa,Xb),Xc))) # label(fact_def__left__f2) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 724 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ak(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,Uub))),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,Uua),Uub)),Uu))))) # label(fact_ATP_Olambda__369) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 725 (all X (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1924332741nd_nis,aa_TPTP_ind_TPTP_ind(scratc915199216rdsucc,X)),X)) <-> pp(aa_TPTP_ind_bool(scratc207770877_prop1,X)))) # label(fact_def__d__22__prop1) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 726 (all X scratc1817129966nd_all(X) = scratc1832573285all_of(aa_TPT43085870d_bool(aTP_Lamm_aq,X))) # label(fact_def__all) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 727 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc1932922227nd_one(X0),X12)) -> scratc2064974964_is_of(scratc1883353196nd_ind(X0,X12),aa_TPT43085870d_bool(aTP_Lamm_aq,X0)))) # label(fact_ind__p) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 728 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_pp,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_po,Uu))))) # label(fact_ATP_Olambda__53) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 729 (all Uu (pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_hi,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_hj,Uu)))) # label(fact_ATP_Olambda__121) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 730 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1924332741nd_nis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1924332741nd_nis,aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_rd(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__398) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 731 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ew,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ev(Uu),Uua))))) # label(fact_ATP_Olambda__326) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 732 (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]. 1.22/1.62 733 (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(scratc1945325564d_e_is(Uu),Uub),Uuc)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bj(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__493) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 734 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1861302562d_repl,X0),X12))) <-> (exists X3 (gg_TPTP_ind(X3) & aa_TPTP_ind_TPTP_ind(X12,X3) = X22 & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X3),X0))))))) # label(fact_k__ReplEq) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 735 (all Uu all Uua ((pp(scratc1159895746_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc855931064lesseq,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc85621118_moref,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ea,Uu),Uua)))) # label(fact_ATP_Olambda__239) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 736 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X22),X0)) -> aa_TPTP_ind_TPTP_ind(X12,X22) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1106035156_Sigma,X0),X12)),X22))) # label(fact_beta) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 737 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jl,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_jk(Uu),Uua))))) # label(fact_ATP_Olambda__294) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 738 (all Uu all Uua (pp(scratc1052430566_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1747045378bnd_ap,Uua),scratc835753142nd_n_1)),Uu),aa_fun171081125l_bool(scratc477404390_n_all,aa_TPT43085870d_bool(aTP_Lamm_ak(Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kb,Uu),Uua)))) # label(fact_ATP_Olambda__192) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 739 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dc(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc85621129_moreq,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc85621118_moref,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc85621118_moref,Uu),Uub)))))) # label(fact_ATP_Olambda__389) # label(axiom) # label(non_clause). [assumption]. 1.22/1.62 740 (all X all Xa (pp(scratc1159895746_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1924332741nd_nis,X),Xa)))) # label(fact_def__nis) # label(axiom) # label(non_clause). [assumption]. 1.38/1.67 741 (all X (pp(aa_TPTP_ind_bool(scratc1527045310_prop4,X)) <-> pp(aa_fun171081125l_bool(scratc943234093l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc804121290d_d_Pi,scratc1923807950nd_nat),aTP_Lamm_ah)),aa_TPT43085870d_bool(scratc1384495228_prop2,X))))) # label(fact_def__prop4) # label(axiom) # label(non_clause). [assumption]. 1.38/1.67 742 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_qz,Uu)) <-> pp(aa_fun171081125l_bool(scratc1832573285all_of(aTP_Lamm_ce),aa_TPT43085870d_bool(aTP_Lamm_qy,Uu))))) # label(fact_ATP_Olambda__36) # label(axiom) # label(non_clause). [assumption]. 1.38/1.67 743 (all X ((all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1747570168bnd_in,aa_TPTP_ind_TPTP_ind(scratc1905399740_union,X1)),X))))) <-> pp(aa_TPTP_ind_bool(scratc69185962closed,X)))) # label(fact_def__d__Union__closed) # label(axiom) # label(non_clause). [assumption]. 1.38/1.67 744 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc276310267ffprop(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1463985925d_n_is,X),aa_TPTP_ind_TPTP_ind(scratc1464445111d_n_pl(Xa),Xb))))) # label(fact_def__diffprop) # label(axiom) # label(non_clause). [assumption]. 1.38/1.67 1.38/1.67 ============================== end of process non-clausal formulas === 1.38/1.67 1.38/1.67 ============================== PROCESS INITIAL CLAUSES =============== 1.38/1.67 1.38/1.67 ============================== PREDICATE ELIMINATION ================= 1.38/1.67 745 -gg_bool(A) | fFalse = A | A = fTrue # label(help_fFalse_1_1_T) # label(axiom). [clausify(71)]. 1.38/1.67 746 gg_bool(fTrue) # label(gsy_c_fTrue) # label(axiom). [assumption]. 1.38/1.67 Derived: fFalse = fTrue | fTrue = fTrue. [resolve(745,a,746,a)]. 1.38/1.67 747 gg_bool(aa_TPTP_ind_bool(A,B)) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom). [clausify(73)]. 1.38/1.67 Derived: fFalse = aa_TPTP_ind_bool(A,B) | aa_TPTP_ind_bool(A,B) = fTrue. [resolve(747,a,745,a)]. 1.38/1.67 748 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(147)]. 1.38/1.67 Derived: fFalse = aa_fun171081125l_bool(A,B) | aa_fun171081125l_bool(A,B) = fTrue. [resolve(748,a,745,a)]. 1.38/1.67 749 gg_bool(aa_bool_bool(A,B)) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom). [clausify(260)]. 1.38/1.67 Derived: fFalse = aa_bool_bool(A,B) | aa_bool_bool(A,B) = fTrue. [resolve(749,a,745,a)]. 1.38/1.67 750 gg_bool(scratc1933184573nd_or3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__57749__12314_ONUM749__thf__4__p_Obnd__or3) # label(axiom). [clausify(292)]. 1.38/1.67 Derived: fFalse = scratc1933184573nd_or3(A,B,C) | scratc1933184573nd_or3(A,B,C) = fTrue. [resolve(750,a,745,a)]. 1.38/1.67 751 gg_bool(fEx_TPTP_ind(A)) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom). [clausify(328)]. 1.38/1.67 Derived: fFalse = fEx_TPTP_ind(A) | fEx_TPTP_ind(A) = fTrue. [resolve(751,a,745,a)]. 1.38/1.67 752 gg_bool(fFalse) # label(gsy_c_fFalse) # label(axiom). [assumption]. 1.38/1.67 Derived: fFalse = fFalse | fFalse = fTrue. [resolve(752,a,745,a)]. 1.38/1.67 753 gg_bool(scratc1159895746_d_not(A)) # label(gsy_c_Scratch__tptp__translate__57749__12314_ONUM749__thf__4__p_Obnd__d__not) # label(axiom). [clausify(440)]. 1.38/1.67 Derived: fFalse = scratc1159895746_d_not(A) | scratc1159895746_d_not(A) = fTrue. [resolve(753,a,745,a)]. 1.38/1.67 754 gg_bool(scratc1849585538nd_ec3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__57749__12314_ONUM749__thf__4__p_Obnd__ec3) # label(axiom). [clausify(493)]. 1.38/1.67 Derived: fFalse = scratc1849585538nd_ec3(A,B,C) | scratc1849585538nd_ec3(A,B,C) = fTrue. [resolve(754,a,745,a)]. 1.38/1.67 755 gg_bool(undefined_bool(bool)) # label(gsy_c_HOL_Oundefined_001t__HOL__Obool) # label(axiom). [assumption]. 1.38/1.67 Derived: fFalse = undefined_bool(bool) | undefined_bool(bool) = fTrue. [resolve(755,a,745,a)]. 1.38/1.67 756 gg_bool(scratc1332078583d_l_ec(A,B)) # label(gsy_c_Scratch__tptp__translate__57749__12314_ONUM749__thf__4__p_Obnd__l__ec) # label(axiom). [clausify(585)]. 1.38/1.67 Derived: fFalse = scratc1332078583d_l_ec(A,B) | scratc1332078583d_l_ec(A,B) = fTrue. [resolve(756,a,745,a)]. 3.07/3.35 757 gg_bool(scratc2005350311_amone(A,B)) # label(gsy_c_Scratch__tptp__translate__57749__12314_ONUM749__thf__4__p_Obnd__amone) # label(axiom). [clausify(597)]. 3.07/3.35 Derived: fFalse = scratc2005350311_amone(A,B) | scratc2005350311_amone(A,B) = fTrue. [resolve(757,a,745,a)]. 3.07/3.35 758 gg_bool(scratc1052430566_d_and(A,B)) # label(gsy_c_Scratch__tptp__translate__57749__12314_ONUM749__thf__4__p_Obnd__d__and) # label(axiom). [clausify(633)]. 3.07/3.35 Derived: fFalse = scratc1052430566_d_and(A,B) | scratc1052430566_d_and(A,B) = fTrue. [resolve(758,a,745,a)]. 3.07/3.35 759 pp(scratc1052430566_d_and(aa_bool_bool(scratc1332734588d_l_or(A),B),scratc1332078583d_l_ec(A,B))) | -scratc1773702580d_orec(A,B) # label(fact_def__orec) # label(axiom). [clausify(23)]. 3.07/3.35 760 -pp(scratc1052430566_d_and(aa_bool_bool(scratc1332734588d_l_or(A),B),scratc1332078583d_l_ec(A,B))) | scratc1773702580d_orec(A,B) # label(fact_def__orec) # label(axiom). [clausify(23)]. 3.07/3.35 761 pp(scratc1159895746_d_not(scratc1159895746_d_not(A))) | -scratc1998423883nd_wel(A) # label(fact_def__wel) # label(axiom). [clausify(395)]. 3.07/3.35 762 -pp(scratc1159895746_d_not(scratc1159895746_d_not(A))) | scratc1998423883nd_wel(A) # label(fact_def__wel) # label(axiom). [clausify(395)]. 3.07/3.35 763 -scratc1998423883nd_wel(A) | pp(A) # label(fact_l__et) # label(axiom). [clausify(651)]. 3.07/3.35 Derived: pp(A) | -pp(scratc1159895746_d_not(scratc1159895746_d_not(A))). [resolve(763,a,762,b)]. 3.07/3.35 764 scratc1946572016_l_iff(A,B) | -pp(scratc1052430566_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1883287609nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc1883287609nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(455)]. 3.07/3.35 765 -scratc1946572016_l_iff(A,B) | pp(scratc1052430566_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1883287609nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc1883287609nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(455)]. 3.07/3.35 766 scratc1727013373d_r_ec(A,B) | pp(A) # label(fact_def__r__ec) # label(axiom). [clausify(589)]. 3.07/3.35 767 -scratc1727013373d_r_ec(A,B) | -pp(A) | pp(scratc1159895746_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(589)]. 3.07/3.35 768 scratc1727013373d_r_ec(A,B) | -pp(scratc1159895746_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(589)]. 3.07/3.35 3.07/3.35 ============================== end predicate elimination ============= 3.07/3.35 3.07/3.35 Auto_denials: (non-Horn, no changes). 3.07/3.35 3.07/3.35 Term ordering decisions: 3.07/3.35 Function symbol KB weights: aTP_Lamm_ce=1. scratc1463985925d_n_is=1. aTP_Lamm_a=1. scratc1883025206nd_iii=1. scratc1744436536_29_ii=1. scratc1747570168bnd_in=1. scratc915199216rdsucc=1. scratc856193462lessis=1. scratc1747045378bnd_ap=1. scratc990177074moreis=1. scratc1463723527d_n_eq=1. scratc835753142nd_n_1=1. scratc1886782970_lessf=1. aTP_Lamm_aq=1. scratc85621118_moref=1. scratc1923807950nd_nat=1. scratc1106035156_Sigma=1. scratc1141896968ptyset=1. scratc855931064lesseq=1. scratc804121290d_d_Pi=1. scratc1463789127d_n_fr=1. scratc1924332741nd_nis=1. scratc1687058735n_some=1. scratc85621129_moreq=1. fFalse=1. scratc1398137874_power=1. scratc1841455290nd_den=1. scratc1951619170_nat_p=1. scratc1883287609nd_imp=1. scratc1925119923nd_num=1. scratc1861302562d_repl=1. fTrue=1. scratc477404390_n_all=1. scratc266622957d_pair=1. aTP_Lamm_ah=1. scratc1190606337d_frac=1. scratc955280034d_Subq=1. scratc1381490636closed=1. scratc1526651712_proj0=1. scratc1905399740_union=1. scratc835753143nd_n_2=1. aTP_Lamm_an=1. scratc1463985920d_n_in=1. scratc1526651713_proj1=1. aTP_Lamm_am=1. aTP_Lamm_sn=1. scratc233918976closed=1. scratc656271931_d_1to=1. scratc69185962closed=1. aTP_Lamm_ag=1. aTP_Lamm_cq=1. aTP_Lamm_do=1. aTP_Lamm_dq=1. aTP_Lamm_ea=1. aTP_Lamm_ec=1. aTP_Lamm_ee=1. aTP_Lamm_eg=1. aTP_Lamm_ei=1. aTP_Lamm_ek=1. aTP_Lamm_em=1. aTP_Lamm_eo=1. aTP_Lamm_ey=1. aTP_Lamm_fa=1. aTP_Lamm_fv=1. aTP_Lamm_kd=1. aTP_Lamm_kf=1. aTP_Lamm_kh=1. aTP_Lamm_kj=1. aTP_Lamm_kl=1. aTP_Lamm_kn=1. aTP_Lamm_kp=1. aTP_Lamm_kr=1. aTP_Lamm_pm=1. aTP_Lamm_po=1. aTP_Lamm_pq=1. aTP_Lamm_ps=1. aTP_Lamm_pu=1. aTP_Lamm_pw=1. aTP_Lamm_py=1. aTP_Lamm_qa=1. aTP_Lamm_qc=1. aTP_Lamm_qe=1. aTP_Lamm_qg=1. aTP_Lamm_qi=1. aTP_Lamm_se=1. aTP_Lamm_si=1. aTP_Lamm_sj=1. scratc1384495228_prop2=1. scratc1587817897closed=1. scratc1682036829d_Inj1=1. scratc1991612902_prop2=1. scratc696306926_omega=1. aTP_Lamm_aa=1. aTP_Lamm_ao=1. aTP_Lamm_bn=1. aTP_Lamm_bp=1. aTP_Lamm_bq=1. aTP_Lamm_bx=1. aTP_Lamm_ca=1. aTP_Lamm_cc=1. aTP_Lamm_cg=1. aTP_Lamm_cj=1. aTP_Lamm_cn=1. aTP_Lamm_cs=1. aTP_Lamm_cu=1. aTP_Lamm_cx=1. aTP_Lamm_da=1. aTP_Lamm_dd=1. aTP_Lamm_dg=1. aTP_Lamm_dj=1. aTP_Lamm_dm=1. aTP_Lamm_du=1. aTP_Lamm_dy=1. aTP_Lamm_es=1. aTP_Lamm_ew=1. aTP_Lamm_fc=1. aTP_Lamm_fe=1. aTP_Lamm_fg=1. aTP_Lamm_fj=1. aTP_Lamm_fm=1. aTP_Lamm_fo=1. aTP_Lamm_fq=1. aTP_Lamm_ft=1. aTP_Lamm_ga=1. aTP_Lamm_ge=1. aTP_Lamm_gi=1. aTP_Lamm_gm=1. aTP_Lamm_gq=1. aTP_Lamm_gu=1. aTP_Lamm_gy=1. aTP_Lamm_hc=1. aTP_Lamm_hf=1. aTP_Lamm_hi=1. aTP_Lamm_hl=1. aTP_Lamm_ho=1. aTP_Lamm_hr=1. aTP_Lamm_hu=1. aTP_Lamm_hx=1. aTP_Lamm_ib=1. aTP_Lamm_if=1. aTP_Lamm_ij=1. aTP_Lamm_in=1. aTP_Lamm_iq=1. aTP_Lamm_it=1. aTP_Lamm_iw=1. aTP_Lamm_iz=1. aTP_Lamm_jc=1. aTP_Lamm_jf=1. aTP_Lamm_ji=1. aTP_Lamm_jl=1. aTP_Lamm_jn=1. aTP_Lamm_jp=1. aTP_Lamm_js=1. aTP_Lamm_jv=1. aTP_Lamm_jy=1. aTP_Lamm_kb=1. aTP_Lamm_ky=1. aTP_Lamm_lc=1. aTP_Lamm_lg=1. aTP_Lamm_lk=1. aTP_Lamm_lo=1. aTP_Lamm_ls=1. aTP_Lamm_lw=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_ms=1. aTP_Lamm_mv=1. aTP_Lamm_my=1. aTP_Lamm_nb=1. aTP_Lamm_ne=1. aTP_Lamm_ni=1. aTP_Lamm_nm=1. aTP_Lamm_nq=1. aTP_Lamm_nu=1. aTP_Lamm_nx=1. aTP_Lamm_oa=1. aTP_Lamm_od=1. aTP_Lamm_og=1. aTP_Lamm_oj=1. aTP_Lamm_om=1. aTP_Lamm_oq=1. aTP_Lamm_os=1. aTP_Lamm_ov=1. aTP_Lamm_oy=1. aTP_Lamm_pb=1. aTP_Lamm_pe=1. aTP_Lamm_ph=1. aTP_Lamm_pk=1. aTP_Lamm_qk=1. aTP_Lamm_qm=1. aTP_Lamm_qo=1. aTP_Lamm_qq=1. aTP_Lamm_qs=1. aTP_Lamm_qw=1. aTP_Lamm_qy=1. aTP_Lamm_rb=1. aTP_Lamm_re=1. aTP_Lamm_rg=1. aTP_Lamm_ri=1. aTP_Lamm_rl=1. aTP_Lamm_rn=1. aTP_Lamm_rq=1. aTP_Lamm_rt=1. aTP_Lamm_rw=1. aTP_Lamm_rz=1. aTP_Lamm_sb=1. aTP_Lamm_sc=1. aTP_Lamm_sh=1. fconj=1. fimplies=1. scratc1384495227_prop1=1. scratc1460312382d_n_1t=1. scratc1541768445_cond2=1. scratc1682036828d_Inj0=1. scratc1991612901_prop1=1. scratc593196651_n_one=1. scratc856929152d_Sing=1. aTP_Lamm_bt=1. aTP_Lamm_by=1. aTP_Lamm_cb=1. aTP_Lamm_cd=1. aTP_Lamm_ch=1. aTP_Lamm_ck=1. aTP_Lamm_co=1. aTP_Lamm_cr=1. aTP_Lamm_ct=1. aTP_Lamm_cv=1. aTP_Lamm_cy=1. aTP_Lamm_db=1. aTP_Lamm_de=1. aTP_Lamm_dh=1. aTP_Lamm_dk=1. aTP_Lamm_dn=1. aTP_Lamm_dp=1. aTP_Lamm_dr=1. aTP_Lamm_dv=1. aTP_Lamm_dz=1. aTP_Lamm_eb=1. aTP_Lamm_ed=1. aTP_Lamm_ef=1. aTP_Lamm_eh=1. aTP_Lamm_ej=1. aTP_Lamm_el=1. aTP_Lamm_en=1. aTP_Lamm_ep=1. aTP_Lamm_et=1. aTP_Lamm_ex=1. aTP_Lamm_ez=1. aTP_Lamm_fb=1. aTP_Lamm_fd=1. aTP_Lamm_ff=1. aTP_Lamm_fh=1. aTP_Lamm_fk=1. aTP_Lamm_fn=1. aTP_Lamm_fp=1. aTP_Lamm_fr=1. aTP_Lamm_fu=1. aTP_Lamm_fw=1. aTP_Lamm_fx=1. aTP_Lamm_gb=1. aTP_Lamm_gf=1. aTP_Lamm_gj=1. aTP_Lamm_gn=1. aTP_Lamm_gr=1. aTP_Lamm_gv=1. aTP_Lamm_gz=1. aTP_Lamm_hd=1. aTP_Lamm_hg=1. aTP_Lamm_hj=1. aTP_Lamm_hm=1. aTP_Lamm_hp=1. aTP_Lamm_hs=1. aTP_Lamm_hv=1. aTP_Lamm_hy=1. aTP_Lamm_ic=1. aTP_Lamm_ig=1. aTP_Lamm_ik=1. aTP_Lamm_io=1. aTP_Lamm_ir=1. aTP_Lamm_iu=1. aTP_Lamm_ix=1. aTP_Lamm_ja=1. aTP_Lamm_jd=1. aTP_Lamm_jg=1. aTP_Lamm_jj=1. aTP_Lamm_jm=1. aTP_Lamm_jo=1. aTP_Lamm_jq=1. aTP_Lamm_jr=1. aTP_Lamm_jt=1. aTP_Lamm_ju=1. aTP_Lamm_jw=1. aTP_Lamm_jx=1. aTP_Lamm_jz=1. aTP_Lamm_ka=1. aTP_Lamm_kc=1. aTP_Lamm_ke=1. aTP_Lamm_kg=1. aTP_Lamm_ki=1. aTP_Lamm_kk=1. aTP_Lamm_km=1. aTP_Lamm_ko=1. aTP_Lamm_kq=1. aTP_Lamm_ks=1. aTP_Lamm_kt=1. aTP_Lamm_ku=1. aTP_Lamm_kv=1. aTP_Lamm_kz=1. aTP_Lamm_ld=1. aTP_Lamm_lh=1. aTP_Lamm_ll=1. aTP_Lamm_lp=1. aTP_Lamm_lt=1. aTP_Lamm_lx=1. aTP_Lamm_mb=1. aTP_Lamm_me=1. aTP_Lamm_mh=1. aTP_Lamm_mk=1. aTP_Lamm_mn=1. aTP_Lamm_mq=1. aTP_Lamm_mt=1. aTP_Lamm_mw=1. aTP_Lamm_mz=1. aTP_Lamm_nc=1. aTP_Lamm_nf=1. aTP_Lamm_nj=1. aTP_Lamm_nn=1. aTP_Lamm_nr=1. aTP_Lamm_nv=1. aTP_Lamm_ny=1. aTP_Lamm_ob=1. aTP_Lamm_oe=1. aTP_Lamm_oh=1. aTP_Lamm_ok=1. aTP_Lamm_on=1. aTP_Lamm_oo=1. aTP_Lamm_op=1. aTP_Lamm_or=1. aTP_Lamm_ot=1. aTP_Lamm_ow=1. aTP_Lamm_oz=1. aTP_Lamm_pc=1. aTP_Lamm_pf=1. aTP_Lamm_pi=1. aTP_Lamm_pl=1. aTP_Lamm_pn=1. aTP_Lamm_pp=1. aTP_Lamm_pr=1. aTP_Lamm_pt=1. aTP_Lamm_pv=1. aTP_Lamm_px=1. aTP_Lamm_pz=1. aTP_Lamm_qb=1. aTP_Lamm_qd=1. aTP_Lamm_qf=1. aTP_Lamm_qh=1. aTP_Lamm_qj=1. aTP_Lamm_ql=1. aTP_Lamm_qn=1. aTP_Lamm_qp=1. aTP_Lamm_qr=1. aTP_Lamm_qt=1. aTP_Lamm_qx=1. aTP_Lamm_qz=1. aTP_Lamm_rc=1. aTP_Lamm_rf=1. aTP_Lamm_rh=1. aTP_Lamm_rj=1. aTP_Lamm_rm=1. aTP_Lamm_ro=1. aTP_Lamm_rp=1. aTP_Lamm_rr=1. aTP_Lamm_rs=1. aTP_Lamm_ru=1. aTP_Lamm_rv=1. aTP_Lamm_rx=1. aTP_Lamm_ry=1. aTP_Lamm_sa=1. aTP_Lamm_sd=1. aTP_Lamm_sf=1. aTP_Lamm_sg=1. aTP_Lamm_sk=1. aTP_Lamm_sl=1. aTP_Lamm_sm=1. aTP_Lamm_sp=1. aTP_Lamm_tm=1. fequal_TPTP_ind=1. scratc1460377981d_n_2t=1. scratc1541768444_cond1=1. scratc1922233568nd_nIn=1. scratc237192304univof=1. scratc953292512_d_Unj=1. aTP_Lamm_ab=1. aTP_Lamm_aj=1. aTP_Lamm_ap=1. aTP_Lamm_br=1. aTP_Lamm_bs=1. bool=1. scratc1002098104_prop1=1. scratc1189966148428_id=1. scratc1190256787_times=1. scratc129811642_empty=1. scratc1427491955nempty=1. scratc1460312377d_n_1o=1. scratc1507337520munion=1. scratc1527045310_prop4=1. scratc1991612904_prop4=1. scratc207770877_prop1=1. scratc31338806_prop1=1. scratc358286701d_plus=1. scratc413735929_prop1=1. scratc432491428_prop1=1. scratc771949187pair_p=1. scratc796133052_prop1=1. scratc983082494r1type=1. scratc136796398d_1out=1. scratc1430626216air_u0=1. scratc1519176628d_24_g=1. scratc185317865d_xout=1. scratc575166238_428_g=1. scratc660686648d_i1_s=1. scratc706896276let_u0=1. tPTP_ind=1. aa_TPT43085870d_bool=1. aa_TPTP_ind_bool=1. aa_TPTP_ind_TPTP_ind=1. aa_fun171081125l_bool=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. scratc1052430566_d_and=1. aa_fun1431113780TP_ind=1. aa_boo1142376798l_bool=1. aa_TPT1123896796d_bool=1. scratc1747570160bnd_if=1. scratc1332078583d_l_ec=1. aa_fun1212484691d_bool=1. scratc1945325559d_e_in=1. aa_TPT1791839040TP_ind=1. aa_TPT985247859d_bool=1. scratc1883353196nd_ind=1. scratc1952701419d_pair=1. aa_fun987228051d_bool=1. scratc2005350311_amone=1. scratc1675549095second=1. scratc268326120_image=1. scratc310968189_first=1. aa_TPT125613450d_bool=1. scratc1924726330nd_non=1. aa_fun1913827119d_bool=1. scratc1549854014d_anec=1. aa_fun1107270209d_bool=1. aa_fun845057962d_bool=1. scratc1849585599nd_ecp=1. scratc2104322782eplSep=1. scratc822472892_ecelt=1. scratc1933381435nd_out=1. scratc821882501_ecect=1. aa_TPT1781712639TP_ind=1. aa_TPT2142672771l_bool=1. aa_fun1235454963TP_ind=1. cOMBB_658106424TP_ind=1. cOMBS_2003118649l_bool=1. scratc1048306367ectset=1. scratc1540862208etprop=1. scratc1849585603nd_ect=1. scratc359684433_fixfu=1. scratc536279841fixfu2=1. scratc683642354eft1to=1. scratc865293603ght1to=1. scratc916333164wissel=1. scratc1154423713unmore=1. scratc1353215848d_invf=1. scratc1356952379d_tofs=1. scratc313446909nverse=1. scratc933104490ectelt=1. f7=1. f9=1. f13=1. f14=1. f18=1. scratc1832573285all_of=1. scratc1464445111d_n_pl=1. scratc1464707514d_n_ts=1. scratc1159895746_d_not=1. scratc1945325564d_e_is=1. scratc936179117_d_Sep=1. scratc1464445105d_n_pf=1. scratc943234093l_some=1. scratc419527030d_esti=1. scratc1332734588d_l_or=1. scratc276310267ffprop=1. scratc1817129966nd_all=1. scratc1932922227nd_one=1. aTP_Lamm_af=1. scratc1289293997_rec_G=1. scratc1799471091d_outn=1. aTP_Lamm_ds=1. aTP_Lamm_dw=1. aTP_Lamm_eq=1. aTP_Lamm_eu=1. aTP_Lamm_sw=1. aTP_Lamm_ak=1. aTP_Lamm_ar=1. aTP_Lamm_bb=1. aTP_Lamm_bj=1. aTP_Lamm_bw=1. aTP_Lamm_cl=1. aTP_Lamm_cw=1. aTP_Lamm_cz=1. aTP_Lamm_dc=1. aTP_Lamm_df=1. aTP_Lamm_di=1. aTP_Lamm_dl=1. aTP_Lamm_fs=1. aTP_Lamm_fy=1. aTP_Lamm_gc=1. aTP_Lamm_gg=1. aTP_Lamm_gk=1. aTP_Lamm_go=1. aTP_Lamm_gs=1. aTP_Lamm_gw=1. aTP_Lamm_ha=1. aTP_Lamm_hz=1. aTP_Lamm_id=1. aTP_Lamm_ih=1. aTP_Lamm_il=1. aTP_Lamm_kw=1. aTP_Lamm_la=1. aTP_Lamm_le=1. aTP_Lamm_li=1. aTP_Lamm_lm=1. aTP_Lamm_lq=1. aTP_Lamm_lu=1. aTP_Lamm_ly=1. aTP_Lamm_ng=1. aTP_Lamm_nk=1. aTP_Lamm_no=1. aTP_Lamm_ns=1. aTP_Lamm_ou=1. aTP_Lamm_ox=1. aTP_Lamm_pa=1. aTP_Lamm_pd=1. aTP_Lamm_pg=1. aTP_Lamm_pj=1. aTP_Lamm_qu=1. aTP_Lamm_so=1. aTP_Lamm_tk=1. scratc1351969473d_incl=1. aTP_Lamm_av=1. aTP_Lamm_bf=1. aTP_Lamm_bi=1. aTP_Lamm_bm=1. aTP_Lamm_he=1. aTP_Lamm_hh=1. aTP_Lamm_hk=1. aTP_Lamm_hn=1. aTP_Lamm_hq=1. aTP_Lamm_ht=1. aTP_Lamm_hw=1. aTP_Lamm_ip=1. aTP_Lamm_is=1. aTP_Lamm_iv=1. aTP_Lamm_iy=1. aTP_Lamm_jb=1. aTP_Lamm_je=1. aTP_Lamm_mc=1. aTP_Lamm_mf=1. aTP_Lamm_mi=1. aTP_Lamm_ml=1. aTP_Lamm_mo=1. aTP_Lamm_mr=1. aTP_Lamm_mu=1. aTP_Lamm_mx=1. aTP_Lamm_na=1. aTP_Lamm_nd=1. aTP_Lamm_nw=1. aTP_Lamm_nz=1. aTP_Lamm_oc=1. aTP_Lamm_of=1. aTP_Lamm_oi=1. aTP_Lamm_ol=1. aTP_Lamm_ra=1. aTP_Lamm_rd=1. aTP_Lamm_tg=1. aTP_Lamm_ti=1. scratc1850438389nd_eps=1. scratc1883353206nd_inn=1. scratc549122310etprod=1. scratc788795540ective=1. aTP_Lamm_as=1. aTP_Lamm_at=1. aTP_Lamm_au=1. aTP_Lamm_aw=1. aTP_Lamm_ax=1. aTP_Lamm_az=1. aTP_Lamm_ba=1. aTP_Lamm_bg=1. aTP_Lamm_bh=1. aTP_Lamm_bk=1. aTP_Lamm_bz=1. aTP_Lamm_cf=1. aTP_Lamm_ci=1. aTP_Lamm_cm=1. aTP_Lamm_cp=1. aTP_Lamm_dt=1. aTP_Lamm_dx=1. aTP_Lamm_er=1. aTP_Lamm_ev=1. aTP_Lamm_fi=1. aTP_Lamm_fl=1. aTP_Lamm_fz=1. aTP_Lamm_gd=1. aTP_Lamm_gh=1. aTP_Lamm_gl=1. aTP_Lamm_gp=1. aTP_Lamm_gt=1. aTP_Lamm_gx=1. aTP_Lamm_hb=1. aTP_Lamm_ia=1. aTP_Lamm_ie=1. aTP_Lamm_ii=1. aTP_Lamm_im=1. aTP_Lamm_jh=1. aTP_Lamm_jk=1. aTP_Lamm_kx=1. aTP_Lamm_lb=1. aTP_Lamm_lf=1. aTP_Lamm_lj=1. aTP_Lamm_ln=1. aTP_Lamm_lr=1. aTP_Lamm_lv=1. aTP_Lamm_lz=1. aTP_Lamm_nh=1. aTP_Lamm_nl=1. aTP_Lamm_np=1. aTP_Lamm_nt=1. aTP_Lamm_qv=1. aTP_Lamm_rk=1. aTP_Lamm_sq=1. aTP_Lamm_sr=1. aTP_Lamm_ss=1. aTP_Lamm_su=1. aTP_Lamm_ta=1. aTP_Lamm_tc=1. aTP_Lamm_td=1. aTP_Lamm_th=1. fEx_TPTP_ind=1. scratc1076607503ective=1. scratc1464182705d_n_lb=1. scratc1530322028lbprop=1. scratc1916071231nd_min=1. scratc353710971nunion=1. aTP_Lamm_ay=1. aTP_Lamm_st=1. aTP_Lamm_sv=1. aTP_Lamm_sx=1. aTP_Lamm_sy=1. aTP_Lamm_sz=1. aTP_Lamm_tb=1. aTP_Lamm_te=1. aTP_Lamm_tf=1. aTP_Lamm_tj=1. aTP_Lamm_tl=1. scratc1000521534_UPair=1. scratc1092526980_pair1=1. scratc1832086362In_rec=1. scratc1837011018econd1=1. scratc255057908first1=1. aTP_Lamm_ac=1. aTP_Lamm_ad=1. aTP_Lamm_ae=1. aTP_Lamm_ai=1. aTP_Lamm_al=1. aTP_Lamm_bc=1. aTP_Lamm_bd=1. aTP_Lamm_be=1. aTP_Lamm_bl=1. aTP_Lamm_bo=1. aTP_Lamm_bu=1. aTP_Lamm_bv=1. cOMBC_1555011498d_bool=1. scratc1414757293_prop1=1. scratc1527045309_prop3=1. scratc1590460279_prop1=1. scratc1972857402_prop1=1. scratc269996513tminus=1. scratc686833008t_disj=1. scratc826395118_prop1=1. scratc972514770ective=1. undefined_bool=1. scratc1430363820air_q0=1. scratc1464248316d_n_mn=1. undefined_TPTP_ind=1. f2=1. f4=1. f5=1. f6=1. f11=1. f12=1. f15=1. f16=1. f17=1. f25=1. scratc1933184573nd_or3=1. scratc1849585538nd_ec3=1. scratc1883746791nd_ite=1. scratc576365181d_soft=1. scratc1073566648_indeq=1. scratc1472090682d_left=1. scratc1527045307_prop1=1. scratc1480231894sel_wa=1. scratc1480231895sel_wb=1. scratc1726949701eft_f1=1. scratc185334392d_11_i=1. scratc1009239625_right=1. scratc1726949702eft_f2=1. f1=1. f3=1. f8=1. f10=1. f19=1. f24=1. scratc1527045308_prop2=1. scratc327405859hangef=1. scratc657595830_inj_h=1. f21=1. f22=1. f23=1. scratc1931817854_prop1=1. scratc319789690indeq2=1. f20=1. 6.29/6.56 6.29/6.56 ============================== end of process initial clauses ======== 6.29/6.56 6.29/6.56 ============================== CLAUSES FOR SEARCH ==================== 6.29/6.56 6.29/6.56 ============================== end of clauses for search ============= 6.29/6.56 6.29/6.56 ============================== SEARCH ================================ 6.29/6.56 6.29/6.56 % Starting search at 1.88 seconds. 6.29/6.56 6.29/6.56 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 649 (0.00 of 2.18 sec). 6.29/6.56 6.29/6.56 Low Water (keep): wt=27.000, iters=3356 6.29/6.56 6.29/6.56 Low Water (keep): wt=26.000, iters=3343 6.29/6.56 6.29/6.56 Low Water (keep): wt=25.000, iters=3336 6.29/6.56 6.29/6.56 Low Water (keep): wt=24.000, iters=3374 6.29/6.56 6.29/6.56 Low Water (keep): wt=23.000, iters=3442 6.29/6.56 6.29/6.56 Low Water (keep): wt=22.000, iters=3343 6.29/6.56 6.29/6.56 Low Water (keep): wt=21.000, iters=3490 6.29/6.56 6.29/6.56 Low Water (keep): wt=20.000, iters=3336 6.29/6.56 6.29/6.56 Low Water (keep): wt=18.000, iters=3490 6.29/6.56 6.29/6.56 Low Water (keep): wt=17.000, iters=3476 6.29/6.56 6.29/6.56 Low Water (keep): wt=16.000, iters=3478 6.29/6.56 6.29/6.56 Low Water (keep): wt=15.000, iters=3335 6.29/6.56 6.29/6.56 Low Water (keep): wt=14.000, iters=4515 6.29/6.56 6.29/6.56 Low Water (keep): wt=13.000, iters=4001 6.29/6.56 6.29/6.56 Low Water (keep): wt=12.000, iAlarm clock 119.79/120.05 Prover9 interrupted 119.79/120.05 EOF