0.03/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.35 % Computer : n027.cluster.edu 0.13/0.35 % Model : x86_64 x86_64 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.35 % Memory : 8042.1875MB 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.35 % CPULimit : 960 0.13/0.35 % DateTime : Thu Jul 2 15:36:16 EDT 2020 0.13/0.35 % CPUTime : 1.11/1.42 ============================== Prover9 =============================== 1.11/1.42 Prover9 (32) version 2009-11A, November 2009. 1.11/1.42 Process 2258 was started by sandbox on n027.cluster.edu, 1.11/1.42 Thu Jul 2 15:36:17 2020 1.11/1.42 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 960 -f /tmp/Prover9_2082_n027.cluster.edu". 1.11/1.42 ============================== end of head =========================== 1.11/1.42 1.11/1.42 ============================== INPUT ================================= 1.11/1.42 1.11/1.42 % Reading from file /tmp/Prover9_2082_n027.cluster.edu 1.11/1.42 1.11/1.42 set(prolog_style_variables). 1.11/1.42 set(auto2). 1.11/1.42 % set(auto2) -> set(auto). 1.11/1.42 % set(auto) -> set(auto_inference). 1.11/1.42 % set(auto) -> set(auto_setup). 1.11/1.42 % set(auto_setup) -> set(predicate_elim). 1.11/1.42 % set(auto_setup) -> assign(eq_defs, unfold). 1.11/1.42 % set(auto) -> set(auto_limits). 1.11/1.42 % set(auto_limits) -> assign(max_weight, "100.000"). 1.11/1.42 % set(auto_limits) -> assign(sos_limit, 20000). 1.11/1.42 % set(auto) -> set(auto_denials). 1.11/1.42 % set(auto) -> set(auto_process). 1.11/1.42 % set(auto2) -> assign(new_constants, 1). 1.11/1.42 % set(auto2) -> assign(fold_denial_max, 3). 1.11/1.42 % set(auto2) -> assign(max_weight, "200.000"). 1.11/1.42 % set(auto2) -> assign(max_hours, 1). 1.11/1.42 % assign(max_hours, 1) -> assign(max_seconds, 3600). 1.11/1.42 % set(auto2) -> assign(max_seconds, 0). 1.11/1.42 % set(auto2) -> assign(max_minutes, 5). 1.11/1.42 % assign(max_minutes, 5) -> assign(max_seconds, 300). 1.11/1.42 % set(auto2) -> set(sort_initial_sos). 1.11/1.42 % set(auto2) -> assign(sos_limit, -1). 1.11/1.42 % set(auto2) -> assign(lrs_ticks, 3000). 1.11/1.42 % set(auto2) -> assign(max_megs, 400). 1.11/1.42 % set(auto2) -> assign(stats, some). 1.11/1.42 % set(auto2) -> clear(echo_input). 1.11/1.42 % set(auto2) -> set(quiet). 1.11/1.42 % set(auto2) -> clear(print_initial_clauses). 1.11/1.42 % set(auto2) -> clear(print_given). 1.11/1.42 assign(lrs_ticks,-1). 1.11/1.42 assign(sos_limit,10000). 1.11/1.42 assign(order,kbo). 1.11/1.42 set(lex_order_vars). 1.11/1.42 clear(print_given). 1.11/1.42 1.11/1.42 % formulas(sos). % not echoed (583 formulas) 1.11/1.42 1.11/1.42 ============================== end of input ========================== 1.11/1.42 1.11/1.42 % From the command line: assign(max_seconds, 960). 1.11/1.42 1.11/1.42 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 1.11/1.42 1.11/1.42 % Formulas that are not ordinary clauses: 1.11/1.42 1 (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_TPTP_ind_bool(aa_TPT43085870d_bool(scratc937796165d_e_is(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__242) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 2 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bt,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,Uu)),scratc1396187181nd_n_1)))) # label(fact_ATP_Olambda__12) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 3 (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]. 1.11/1.42 4 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1561761582all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jt(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ju(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__215) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 5 (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_ao(Uu),Uua),Uub),Uuc),Uud)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc937796165d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,Uub),Uud)))))) # label(fact_ATP_Olambda__265) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 6 (all X0 pp(aa_fun171081125l_bool(scratc1561761582all_of(aa_TPT43085870d_bool(aTP_Lamm_jm,X0)),aa_TPT43085870d_bool(aTP_Lamm_jo,X0)))) # label(fact_isseti) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 7 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ew,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ex,Uu)))) # label(fact_ATP_Olambda__61) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 8 (all X all Xa scratc57161220nd_out(aa_TPTP_ind_TPTP_ind(scratc390608475_power,X),scratc2110288053d_anec(X,Xa)) = scratc1231495862ectset(X,Xa)) # label(fact_def__ectset) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 9 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_il,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ik,Uu))))) # label(fact_ATP_Olambda__24) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 10 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc979961069d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc1119368612_d_Sep(Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_jq(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__211) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 11 (all B_1 all B_2 gg_bool(scratc1235620061_d_and(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__50754__14833_ONUM697__thf__4__p_Obnd__d__and) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 12 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1913649887d_invf(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc113866315_Sigma,Xa),scratc1136799220d_soft(X,Xa,Xb))) # label(fact_def__invf) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 13 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fd,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fc,Uu))))) # label(fact_ATP_Olambda__59) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 14 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bz(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ca(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__233) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 15 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ey(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ez,Uu),Uua)))) # label(fact_ATP_Olambda__146) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 16 (all X all Xa (scratc100680811_is_of(X,Xa) <-> pp(aa_TPTP_ind_bool(Xa,X)))) # label(fact_def__is__of) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 17 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1173366569moreis,Uua),aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,Uu)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,Uu),Uua)))) # label(fact_ATP_Olambda__106) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 18 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456521d_n_in,Uua),Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jg,Uu),Uua)))) # label(fact_ATP_Olambda__130) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 19 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ia,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hz(Uu),Uua))))) # label(fact_ATP_Olambda__135) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 20 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc113866315_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,aa_TPTP_ind_TPTP_ind(scratc519122314_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc519122313_proj0,X22)))) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,aa_TPTP_ind_TPTP_ind(scratc519122313_proj0,X22)),X0)) & X22 = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc827056996d_pair,aa_TPTP_ind_TPTP_ind(scratc519122313_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc519122314_proj1,X22))))) # label(fact_k__Sigma__eta__proj0__proj1) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 21 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1039382957lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1039382957lessis,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dt(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__199) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 22 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc937796165d_e_is(aa_TPTP_ind_TPTP_ind(scratc390608475_power,X)),Xb),aa_TPTP_ind_TPTP_ind(scratc1962427141_ecelt(X,Xa),Xc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2120849032nd_ecp(X,Xa),Xb),Xc)))) # label(fact_def__ecp) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 23 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc56702012nd_one(X0),X12)) -> pp(aa_TPTP_ind_bool(X12,scratc7132981nd_ind(X0,X12))))) # label(fact_oneax) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 24 (all X (pp(aa_TPTP_ind_bool(scratc212847509closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X1),X)) -> (all X2 ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X3),X1)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,aa_TPTP_ind_TPTP_ind(X2,X3)),X))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc274252953d_repl,X1),X2)),X))))))))) # label(fact_def__d__Repl__closed) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 25 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ct(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__259) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 26 (all B_1 gg_bool(scratc1343085241_d_not(B_1))) # label(gsy_c_Scratch__tptp__translate__50754__14833_ONUM697__thf__4__p_Obnd__d__not) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 27 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(scratc995845351bnd_if(aa_TPTP_ind_bool(Uua,Uub),Uub),scratc2121701822nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bb(Uu),Uua))) = aa_TPTP_ind_TPTP_ind(aa_fun1235454963TP_ind(aTP_Lamm_bn(Uu),Uua),Uub)) # label(fact_ATP_Olambda__176) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 28 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_db(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dc,Uu),Uua)))) # label(fact_ATP_Olambda__161) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 29 (all X (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc48112526nd_nis,aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,X)),X)) <-> pp(aa_TPTP_ind_bool(scratc988492404_prop1,X)))) # label(fact_def__d__22__prop1) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 30 (all X7 all Y (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) | X7 != Y)) # label(help_fequal_2_1_fequal_001t__TPTP____Interpret__Oind_T) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 31 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc1909019605eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bg,Xa)),scratc519122314_proj1)) # label(fact_def__ap) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 32 (all X all Xa all Xb (pp(aa_fun171081125l_bool(scratc2088393399nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ba(X),Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1439398365ective(X),Xa),Xb)))) # label(fact_def__injective) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 33 (all Uu all Uua (gg_TPTP_ind(Uu) -> Uu = aa_TPTP_ind_TPTP_ind(aTP_Lamm_ai(Uu),Uua))) # label(fact_ATP_Olambda__272) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 34 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cw,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cv,Uu))))) # label(fact_ATP_Olambda__77) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 35 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1173366569moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1173366569moreis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1173366569moreis,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bz(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__251) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 36 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dg,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_df,Uu))))) # label(fact_ATP_Olambda__74) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 37 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bc(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(Uua,Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc937796165d_e_is(Uu),Uub),Uuc)))))) # label(fact_ATP_Olambda__261) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 38 (all B_1 all B_2 gg_TPTP_ind(scratc7132981nd_ind(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__50754__14833_ONUM697__thf__4__p_Obnd__ind) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 39 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eg(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ef(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__226) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 40 (all X0 all X12 scratc100680811_is_of(aa_fun1431113780TP_ind(scratc1119368612_d_Sep(X0),X12),aa_TPT43085870d_bool(aTP_Lamm_jm,X0))) # label(fact_setof__p) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 41 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> ((exists X3 (aa_TPTP_ind_TPTP_ind(X12,X3) = X22 & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X3),X0)) & gg_TPTP_ind(X3))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc274252953d_repl,X0),X12)))))) # label(fact_k__ReplEq) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 42 (all B_1 all B_2 gg_bool(scratc997820912_amone(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__50754__14833_ONUM697__thf__4__p_Obnd__amone) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 43 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cy(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cx(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__227) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 44 (all P all Q (-pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) | -pp(P) | pp(Q))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 45 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uuc),Uua))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ef(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__257) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 46 (all Uu ((pp(aa_TPTP_ind_bool(scratc534239045_cond1,Uu)) -> (pp(aa_TPTP_ind_bool(scratc534239046_cond2,Uu)) -> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jg,Uu))))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_jh,Uu)))) # label(fact_ATP_Olambda__6) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 47 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gf(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1039382957lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__201) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 48 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ja,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc48112526nd_nis,Uu),scratc1396187181nd_n_1)) -> pp(aa_fun171081125l_bool(scratc776386146_n_one,aa_TPT43085870d_bool(aTP_Lamm_af,Uu)))))) # label(fact_ATP_Olambda__2) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 49 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ei,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eh,Uu))))) # label(fact_ATP_Olambda__65) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 50 (all X all Xa all Xb (scratc2110222406d_and3(X,Xa,Xb) <-> pp(scratc1235620061_d_and(X,scratc1235620061_d_and(Xa,Xb))))) # label(fact_def__and3) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 51 (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]. 1.11/1.42 52 (all X all Xa all Xb all Xc all Xd aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc113866315_Sigma,X),aa_TPT1424761345TP_ind(aTP_Lamm_aw(Xc),Xd)) = aa_TPTP_ind_TPTP_ind(scratc840785325_inj_h(X,Xa,Xb,Xc),Xd)) # label(fact_def__inj__h) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 53 -(exists X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X0),scratc149728127ptyset))) # label(fact_k__EmptyAx) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 54 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc390608475_power,X0))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc684468331d_Subq,X12),X0)))) # label(fact_k__PowerE) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 55 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ft(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1039382957lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1039382957lessis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1039382957lessis,Uu),Uub)))))) # label(fact_ATP_Olambda__200) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 56 (all B_1 all B_2 all B_3 gg_bool(scratc56964358nd_or3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__50754__14833_ONUM697__thf__4__p_Obnd__or3) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 57 (all P all Q (pp(P) | pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)))) # label(help_fimplies_1_1_U) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 58 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1173366569moreis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fw(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__194) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 59 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_is,Uu),Uua)))) # label(fact_ATP_Olambda__100) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 60 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ki(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aa_TPT43085870d_bool(aTP_Lamm_kf(Uu),Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kh(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__183) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 61 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1039382957lessis,X),Xa)) <-> pp(aa_bool_bool(scratc325205189d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,X),Xa))))) # label(fact_def__lessis) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 62 (all X aa_TPTP_ind_TPTP_ind(scratc918720740d_plus,X) = scratc7132981nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1944075539d_d_Pi,scratc47587735nd_nat),aTP_Lamm_ac),aa_TPT43085870d_bool(scratc17733107_prop2,X))) # label(fact_def__plus) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 63 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1408280369_image(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc672422390l_some(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(Xa),Xb),Xc))))) # label(fact_def__image) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 64 (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]. 1.11/1.42 65 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ca(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cb,Uu),Uua)))) # label(fact_ATP_Olambda__168) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 66 (all Uu aa_TPTP_ind_TPTP_ind(aTP_Lamm_ac,Uu) = scratc47587735nd_nat) # label(fact_ATP_Olambda__273) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 67 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ce(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cd(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__232) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 68 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eg(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eh,Uu),Uua)))) # label(fact_ATP_Olambda__151) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 69 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc48112526nd_nis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc48112526nd_nis,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ic(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__204) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 70 (all X all Xa (pp(aa_fun171081125l_bool(scratc56702012nd_one(X),Xa)) <-> pp(scratc1235620061_d_and(scratc997820912_amone(X,Xa),aa_fun171081125l_bool(scratc672422390l_some(X),Xa))))) # label(fact_def__one) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 71 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ih,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uua),Uu))))) # label(fact_ATP_Olambda__107) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 72 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_co,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cn,Uu))))) # label(fact_ATP_Olambda__79) # label(axiom) # label(non_clause). [assumption]. 1.11/1.42 73 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_er(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__254) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 74 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X22),X0)) -> (all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X32),aa_TPTP_ind_TPTP_ind(X12,X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc827056996d_pair,X22),X32)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc113866315_Sigma,X0),X12))))))) # label(fact_pair__Sigma) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 75 (all X0 pp(aa_fun171081125l_bool(scratc1561761582all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_kl,X0)))) # label(fact_refis) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 76 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1173366569moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1039382957lessis,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hd,Uu),Uua)))) # label(fact_ATP_Olambda__109) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 77 (all X all Xa (scratc2129761511_l_iff(X,Xa) <-> pp(scratc1235620061_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc7067394nd_imp,X),Xa),aa_bool_bool(aa_boo1142376798l_bool(scratc7067394nd_imp,Xa),X))))) # label(fact_def__l__iff) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 78 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jz(Uu),Uua),Uub),Uuc)) <-> scratc100680811_is_of(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1681889716d_pair(Uu,Uua),Uub),Uuc),aa_TPT43085870d_bool(aTP_Lamm_jv(Uu),Uua)))) # label(fact_ATP_Olambda__243) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 79 (all Uu (gg_TPTP_ind(Uu) -> (Uu != scratc149728127ptyset <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ah,Uu))))) # label(fact_ATP_Olambda__88) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 80 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dr,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dq(Uu),Uua))))) # label(fact_ATP_Olambda__156) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 81 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc684468331d_Subq,X12),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc390608475_power,X0))))) # label(fact_k__PowerI) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 82 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1912403512d_incl(Uu),Uua),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1912403512d_incl(Uu),Uub),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc937796165d_e_is(aa_TPTP_ind_TPTP_ind(scratc390608475_power,Uu)),Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jn(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__179) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 83 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> X12 = aa_TPTP_ind_TPTP_ind(scratc995845351bnd_if(X0,X12),X22) | aa_TPTP_ind_TPTP_ind(scratc995845351bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__or) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 84 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(Uua,aa_TPTP_ind_TPTP_ind(scratc937796160d_e_in(Uu,Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_kd(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__235) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 85 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hi,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hh,Uu))))) # label(fact_ATP_Olambda__36) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 86 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bb(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(Uua,Uub)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,Uub),Uu)))) # label(fact_ATP_Olambda__209) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 87 (all X all Xa all Xb all Xc all Xd (pp(scratc1235620061_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc7067394nd_imp,X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc937796165d_e_is(Xa),Xd),Xb)),aa_bool_bool(aa_boo1142376798l_bool(scratc7067394nd_imp,scratc1343085241_d_not(X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc937796165d_e_is(Xa),Xd),Xc)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc519515908_prop1(X,Xa,Xb),Xc),Xd)))) # label(fact_def__prop1) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 88 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_el,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_em,Uu)))) # label(fact_ATP_Olambda__64) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 89 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X22),aa_fun1431113780TP_ind(scratc1119368612_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(X12,X22)))) # label(fact_k__SepE2) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 90 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hs,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hr,Uu))))) # label(fact_ATP_Olambda__31) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 91 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fk(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__192) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 92 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cb,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cc,Uu)))) # label(fact_ATP_Olambda__82) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 93 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_be(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc897870341_union,aa_TPTP_ind_TPTP_ind(Uu,Uua))) # label(fact_ATP_Olambda__172) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 94 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc937796165d_e_is(Uu),Uub),Uuc)) -> pp(aa_TPTP_ind_bool(Uua,Uuc)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_kj(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__260) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 95 (all X all Xa scratc827056996d_pair = scratc1681889716d_pair(X,Xa)) # label(fact_def__d__pair) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 96 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bx,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bw(Uu),Uua))))) # label(fact_ATP_Olambda__169) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 97 (all Uu all Uua (pp(scratc56964358nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1416247032n_some,aa_TPT43085870d_bool(scratc1431625074ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc1416247032n_some,aa_TPT43085870d_bool(scratc1431625074ffprop(Uua),Uu)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hr,Uu),Uua)))) # label(fact_ATP_Olambda__95) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 98 (all X all Xa all Xb all Xc all Xd aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc113866315_Sigma,X),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_av(X),Xb),Xc),Xd)) = aa_TPTP_ind_TPTP_ind(scratc56594156hangef(X,Xa,Xb,Xc),Xd)) # label(fact_def__changef) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 99 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gl,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_gm,Uu)))) # label(fact_ATP_Olambda__47) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 100 (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]. 1.11/1.43 101 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_di,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dh(Uu),Uua))))) # label(fact_ATP_Olambda__159) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 102 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_in,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_im,Uu))))) # label(fact_ATP_Olambda__23) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 103 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1509025778nunion(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc897870341_union,aa_TPTP_ind_TPTP_ind(scratc8352693_UPair(X),Xa))) # label(fact_def__binunion) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 104 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1173366569moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1173366569moreis,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ec(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__195) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 105 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dx,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_dy,Uu)))) # label(fact_ATP_Olambda__68) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 106 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ej(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__256) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 107 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aq(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc979961069d_esti(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__241) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 108 (all X (pp(aa_TPTP_ind_bool(scratc1576854579_prop1,X)) <-> pp(aa_bool_bool(scratc325205189d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,X),scratc1396187181nd_n_1)),aa_fun171081125l_bool(scratc1416247032n_some,aa_TPT43085870d_bool(aTP_Lamm_af,X)))))) # label(fact_def__d__23__prop1) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 109 (all Uu all Uua all Uub all Uuc (gg_TPTP_ind(Uua) & gg_TPTP_ind(Uuc) & gg_TPTP_ind(Uub) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bp(Uu),Uua),Uub),Uuc)) <-> Uuc = Uua & pp(Uu) | Uuc = Uub & -pp(Uu)))) # label(fact_ATP_Olambda__247) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 110 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc48112526nd_nis,aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,Uu)),scratc1396187181nd_n_1)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_jk,Uu)))) # label(fact_ATP_Olambda__13) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 111 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1561761582all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_js(X0),X12)))) # label(fact_secondis1) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 112 (all X all Xa all Xb (pp(scratc1235620061_d_and(scratc56964358nd_or3(X,Xa,Xb),scratc2120848971nd_ec3(X,Xa,Xb))) <-> scratc1443967432_orec3(X,Xa,Xb))) # label(fact_def__orec3) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 113 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bq,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1173366569moreis,Uua),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),scratc1396187181nd_n_1)))))) # label(fact_ATP_Olambda__105) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 114 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1561761582all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jr(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_js(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__216) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 115 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,Uu),Uua)) -> pp(scratc1343085241_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1173366569moreis,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gp,Uu),Uua)))) # label(fact_ATP_Olambda__115) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 116 (all Uu all Uua (gg_TPTP_ind(Uua) -> ((exists X3 (gg_TPTP_ind(X3) & aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc827056996d_pair,Uu),X3) = Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bg,Uu),Uua))))) # label(fact_ATP_Olambda__173) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 117 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),scratc1396187181nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ix,Uu)))) # label(fact_ATP_Olambda__3) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 118 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_kb(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1408280369_image(aa_fun1431113780TP_ind(scratc1119368612_d_Sep(Uu),Uua),Uu),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc113866315_Sigma,aa_fun1431113780TP_ind(scratc1119368612_d_Sep(Uu),Uua)),scratc937796160d_e_in(Uu,Uua))),Uub))))) # label(fact_ATP_Olambda__210) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 119 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gc(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gd,Uu),Uua)))) # label(fact_ATP_Olambda__138) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 120 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1912403512d_incl(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc2088393399nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_at(X),Xa),Xb))))) # label(fact_def__incl) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 121 (all P (gg_bool(P) -> P = fFalse | P = fTrue)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 122 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eo(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_en(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__224) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 123 (all X aa_TPTP_ind_TPTP_ind(scratc1411225125d_Inj0,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc274252953d_repl,X),scratc1411225126d_Inj1)) # label(fact_def__d__Inj0) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 124 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1561761582all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_jp(X0),X12)))) # label(fact_estie) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 125 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1039382957lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1173366569moreis,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hb,Uu),Uua)))) # label(fact_ATP_Olambda__110) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 126 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc995845351bnd_if(X,Xa),Xb) = scratc2121701822nd_eps(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bp(X),Xa),Xb))) # label(fact_def__if) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 127 (all X scratc979961069d_esti(X) = scratc995845359bnd_in) # label(fact_def__esti) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 128 (all X all Xa all Xb all Xc (pp(aa_fun171081125l_bool(scratc1561761582all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_an(X),Xa),Xb),Xc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc719469336fixfu2(X,Xa),Xb),Xc)))) # label(fact_def__fixfu2) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 129 (all Uu all Uua all Uub all Uuc (pp(aa_fun171081125l_bool(scratc2088393399nd_all(Uu),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_az(Uu),Uua),Uub),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ba(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__262) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 130 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_aw(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,Uu),Uub))) # label(fact_ATP_Olambda__222) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 131 (all X all Xa (pp(scratc1343085241_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc48112526nd_nis,X),Xa)))) # label(fact_def__nis) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 132 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1561761582all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_kb(X0),X12)))) # label(fact_otax2) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 133 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fb(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__193) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 134 (all X all Xa all Xb all Xc all Xd scratc502979185indeq2(X,Xa,Xb,Xc,Xd) = aa_TPT1424761345TP_ind(scratc66037249_indeq(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1340649199d_11_i(X,Xa,Xb),Xc),Xd))) # label(fact_def__indeq2) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 135 (all B_1 all B_2 all B_3 gg_bool(scratc2120848971nd_ec3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__50754__14833_ONUM697__thf__4__p_Obnd__ec3) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 136 (all X all Xa ((pp(X) -> pp(scratc1343085241_d_not(Xa))) <-> scratc719483974d_r_ec(X,Xa))) # label(fact_def__r__ec) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 137 (all X all Xa all Xb (pp(aa_fun171081125l_bool(scratc672422390l_some(X),aa_TPT43085870d_bool(scratc2120849032nd_ecp(X,Xa),Xb))) <-> pp(aa_TPTP_ind_bool(scratc2110288053d_anec(X,Xa),Xb)))) # label(fact_def__anec) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 138 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hz(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__186) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 139 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc113866315_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,aa_TPTP_ind_TPTP_ind(scratc519122313_proj0,X22)),X0)))) # label(fact_proj0__Sigma) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 140 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ck,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cj,Uu))))) # label(fact_ATP_Olambda__80) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 141 (all X (pp(scratc1343085241_d_not(X)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc7067394nd_imp,X),fFalse)))) # label(fact_def__d__not) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 142 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ew,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ev(Uu),Uua))))) # label(fact_ATP_Olambda__147) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 143 (all X all Xa all Xb all Xc all Xd all Xe (pp(aa_fun171081125l_bool(scratc672422390l_some(X),aa_TPT43085870d_bool(scratc565055733_prop1(X,Xa,Xb,Xc,Xd),Xe))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc519515909_prop2(X,Xa,Xb,Xc),Xd),Xe)))) # label(fact_def__prop2) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 144 (all Q all P (pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) | -pp(Q))) # label(help_fimplies_2_1_U) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 145 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fo,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__9) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 146 (all X all Xa all Xb scratc66037249_indeq(X,Xa,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1944075539d_d_Pi,X),aTP_Lamm_ai(Xb))) = scratc1340649199d_11_i(X,Xa,Xb)) # label(fact_def__d__11__i) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 147 (all X (pp(aa_TPTP_ind_bool(scratc2134808665_nat_p,X)) <-> (all X1 (pp(aa_TPTP_ind_bool(X1,scratc149728127ptyset)) -> ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(X1,X2)) -> pp(aa_TPTP_ind_bool(X1,aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,X2)))))) -> pp(aa_TPTP_ind_bool(X1,X))))))) # label(fact_def__nat__p) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 148 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hv,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_hw,Uu)))) # label(fact_ATP_Olambda__30) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 149 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cq(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cr,Uu),Uua)))) # label(fact_ATP_Olambda__164) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 150 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gj,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gi(Uu),Uua))))) # label(fact_ATP_Olambda__136) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 151 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jl,Uu)) <-> scratc100680811_is_of(aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,Uu),aTP_Lamm_a))) # label(fact_ATP_Olambda__11) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 152 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gr,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_gs,Uu)))) # label(fact_ATP_Olambda__44) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 153 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_af,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,Uua))))) # label(fact_ATP_Olambda__128) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 154 (all X all Xa (pp(scratc1235620061_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,Xa),scratc1396187181nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,X)),aa_TPTP_ind_bool(scratc17733106_prop1,Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc17733107_prop2,X),Xa)))) # label(fact_def__d__24__prop2) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 155 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dj,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_di,Uu))))) # label(fact_ATP_Olambda__73) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 156 (all X scratc456915712d_n_pl(X) = aa_TPT1424761345TP_ind(scratc995320569bnd_ap,aa_TPTP_ind_TPTP_ind(scratc918720740d_plus,X))) # label(fact_def__n__pl) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 157 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cm(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cl(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__230) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 158 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gn,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_go,Uu)))) # label(fact_ATP_Olambda__46) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 159 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1284928718sel_wb(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc7526576nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc937796165d_e_is(X),Xc),Xb),X,Xa),aa_TPTP_ind_TPTP_ind(scratc1284928717sel_wa(X,Xa,Xb),Xc))) # label(fact_def__wissel__wb) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 160 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1194457456_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Xa),X))))) # label(fact_def__d__26__prop1) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 161 (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]. 1.11/1.43 162 (all Uu all Uua ((pp(scratc1343085241_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1039382957lessis,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gv,Uu),Uua)))) # label(fact_ATP_Olambda__121) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 163 (all Uu aa_TPT494704832TP_ind(aTP_Lamm_bk,Uu) = aa_TPT494704832TP_ind(scratc274252953d_repl,aa_TPTP_ind_TPTP_ind(scratc1425311320tminus(Uu),aa_TPTP_ind_TPTP_ind(scratc586117449d_Sing,scratc149728127ptyset)))) # label(fact_ATP_Olambda__87) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 164 (all X0 (pp(aa_TPTP_ind_bool(scratc2134808665_nat_p,X0)) -> pp(aa_TPTP_ind_bool(scratc2134808665_nat_p,aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,X0))))) # label(fact_nat__ordsucc) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 165 (all Uu all Uua all Uub all Uuc (pp(aa_fun171081125l_bool(scratc672422390l_some(Uua),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aq(Uu),Uub),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ar(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__263) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 166 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X22),aa_fun1431113780TP_ind(scratc1119368612_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X22),X0)))) # label(fact_k__SepE1) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 167 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fz(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1173366569moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,Uu),Uub)))))) # label(fact_ATP_Olambda__197) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 168 (all X all Xa all Xb all Xc scratc7132981nd_ind(X,aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(Xa),Xb),Xc)) = aa_TPTP_ind_TPTP_ind(scratc1136799220d_soft(X,Xa,Xb),Xc)) # label(fact_def__soft) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 169 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_if,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc48112526nd_nis,Uua),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__126) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 170 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,Uua),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hu(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__219) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 171 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hf,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_hg,Uu)))) # label(fact_ATP_Olambda__37) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 172 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jt(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc937796165d_e_is(Uu),aa_TPTP_ind_TPTP_ind(scratc1450922438_first(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1681889716d_pair(Uu,Uua),Uub),Uuc))),Uub)))) # label(fact_ATP_Olambda__238) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 173 (all X all Xa all Xb (gg_TPTP_ind(Xb) -> aa_TPTP_ind_TPTP_ind(scratc937796160d_e_in(X,Xa),Xb) = Xb)) # label(fact_def__e__in) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 174 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hj,Uu),Uua)) <-> pp(scratc2120848971nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__93) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 175 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ip,Uu),Uua)))) # label(fact_ATP_Olambda__120) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 176 (all B_1 gg_TPTP_ind(scratc2121701822nd_eps(B_1))) # label(gsy_c_Scratch__tptp__translate__50754__14833_ONUM697__thf__4__p_Obnd__eps) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 177 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc995845351bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc995845359bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc274252953d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bn(X),Xa))),scratc149728127ptyset) = aa_fun1431113780TP_ind(scratc1119368612_d_Sep(X),Xa)) # label(fact_def__d__Sep) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 178 (all X all Xa all Xb all Xc all Xd all Xe all Xf (pp(scratc1235620061_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc979961069d_esti(X),Xf),aa_TPTP_ind_TPTP_ind(scratc1961836750_ecect(X,Xa),Xd)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc937796165d_e_is(Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,Xc),Xf)),Xe))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc565055733_prop1(X,Xa,Xb,Xc,Xd),Xe),Xf)))) # label(fact_def__d__10__prop1) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 179 (all X (pp(aa_TPTP_ind_bool(scratc17733106_prop1,X)) <-> pp(aa_fun171081125l_bool(scratc660593885_n_all,aa_TPT43085870d_bool(aTP_Lamm_ae,X))))) # label(fact_def__d__24__prop1) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 180 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1269765891_empty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),scratc48506115nd_non(X,aa_TPT43085870d_bool(aTP_Lamm_au(X),Xa)))))) # label(fact_def__empty) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 181 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dk(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__189) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 182 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ax(Uu),Uua),Uub),Uuc) = aa_TPTP_ind_TPTP_ind(scratc995845351bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1408280369_image(Uu,Uua),Uub),Uuc),aa_TPTP_ind_TPTP_ind(scratc1136799220d_soft(Uu,Uua,Uub),Uuc)),scratc149728127ptyset)) # label(fact_ATP_Olambda__237) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 183 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_kk(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_kj(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__212) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 184 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ha,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gz,Uu))))) # label(fact_ATP_Olambda__40) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 185 (all X all Xa scratc2121701822nd_eps(aa_TPT43085870d_bool(scratc503222518_rec_G(X),Xa)) = aa_TPTP_ind_TPTP_ind(scratc1636783185In_rec(X),Xa)) # label(fact_def__d__In__rec) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 186 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ho,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hn,Uu))))) # label(fact_ATP_Olambda__33) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 187 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1173366569moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1173366569moreis,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dz(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__196) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 188 (all X aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc113866315_Sigma,scratc47587735nd_nat),aTP_Lamm_ad(X)) = aa_TPTP_ind_TPTP_ind(scratc527007787d_24_g,X)) # label(fact_def__d__24__g) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 189 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc113866315_Sigma,X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc515168679munion,X),aTP_Lamm_bh(Xa))) # label(fact_def__d__Sigma) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 190 (all X0 scratc149728127ptyset != aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,X0)) # label(fact_neq__ordsucc__0) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 191 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1284928717sel_wa(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc7526576nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc937796165d_e_is(X),Xc),Xa),X,Xb),Xc)) # label(fact_def__wissel__wa) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 192 (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]. 1.11/1.43 193 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gf(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gg,Uu),Uua)))) # label(fact_ATP_Olambda__137) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 194 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ga,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_gb,Uu)))) # label(fact_ATP_Olambda__51) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 195 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ap(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_ao(Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__267) # label(axiom) # label(non_clause). [assumption]. 1.11/1.43 196 (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]. 1.11/1.44 197 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dr,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ds,Uu)))) # label(fact_ATP_Olambda__70) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 198 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1944075539d_d_Pi,X0),X12))) -> (all X32 (gg_TPTP_ind(X32) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X32),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1944075539d_d_Pi,X0),X12))) -> ((all X42 (gg_TPTP_ind(X42) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X42),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,X22),X42) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,X32),X42)))) -> X32 = X22))))))) # label(fact_k__Pi__ext) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 199 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dx,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dw(Uu),Uua))))) # label(fact_ATP_Olambda__154) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 200 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc420381799univof,X0)))) # label(fact_k__UnivOf__In) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 201 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1561761582all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_kk(X0),X12)))) # label(fact_e__isp) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 202 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1561761582all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jz(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ka(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__214) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 203 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc42635206nverse(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc113866315_Sigma,Xa),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ax(X),Xa),Xb))) # label(fact_def__inverse) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 204 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1039382957lessis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cd(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__258) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 205 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ed,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ec(Uu),Uua))))) # label(fact_ATP_Olambda__152) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 206 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ci(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ch(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__231) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 207 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dn(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_do,Uu),Uua)))) # label(fact_ATP_Olambda__157) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 208 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,X),Xb)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc519515910_prop3(X),Xa),Xb)))) # label(fact_def__prop3) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 209 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc66037249_indeq(X,Xa,Xb),Xc),Xd) = scratc7132981nd_ind(Xb,aa_TPT43085870d_bool(scratc519515909_prop2(X,Xa,Xb,Xc),Xd))) # label(fact_def__indeq) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 210 (all X0 all X12 all X22 ((pp(X0) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X12),X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,aa_TPTP_ind_TPTP_ind(scratc995845351bnd_if(X0,X12),scratc149728127ptyset)),aa_TPTP_ind_TPTP_ind(scratc995845351bnd_if(X0,X22),aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,scratc149728127ptyset)))))) # label(fact_k__If__In__01) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 211 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1099522659wissel(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc113866315_Sigma,X),scratc1284928718sel_wb(X,Xa,Xb))) # label(fact_def__wissel) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 212 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jr(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc937796165d_e_is(Uua),aa_TPTP_ind_TPTP_ind(scratc1858738590second(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1681889716d_pair(Uu,Uua),Uub),Uuc))),Uuc)))) # label(fact_ATP_Olambda__239) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 213 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ek(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_el,Uu),Uua)))) # label(fact_ATP_Olambda__150) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 214 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gk,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gj,Uu))))) # label(fact_ATP_Olambda__48) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 215 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fb(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fc,Uu),Uua)))) # label(fact_ATP_Olambda__145) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 216 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1425311320tminus(X),Xa) = aa_fun1431113780TP_ind(scratc1119368612_d_Sep(X),aa_TPT43085870d_bool(aTP_Lamm_bm,Xa))) # label(fact_def__setminus) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 217 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc8352693_UPair(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc274252953d_repl,aa_TPTP_ind_TPTP_ind(scratc390608475_power,aa_TPTP_ind_TPTP_ind(scratc390608475_power,scratc149728127ptyset))),aa_TPT1424761345TP_ind(aTP_Lamm_bo(X),Xa))) # label(fact_def__d__UPair) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 218 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jb,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc48112526nd_nis,Uu),scratc1396187181nd_n_1)) -> pp(aa_fun171081125l_bool(scratc1416247032n_some,aa_TPT43085870d_bool(aTP_Lamm_af,Uu)))))) # label(fact_ATP_Olambda__1) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 219 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1416247032n_some,aa_TPT43085870d_bool(scratc1431625074ffprop(X),Xa))))) # label(fact_def__d__29__ii) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 220 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc979961069d_esti(Uu),Uub),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_au(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__177) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 221 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fp,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__127) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 222 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fe(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__205) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 223 (all X aa_boo1142376798l_bool(scratc7067394nd_imp,scratc1343085241_d_not(X)) = scratc325205189d_l_or(X)) # label(fact_def__l__or) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 224 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jw(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc937796165d_e_is(aa_TPTP_ind_TPTP_ind(scratc278310607etprod(Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1681889716d_pair(Uu,Uua),aa_TPTP_ind_TPTP_ind(scratc1450922438_first(Uu,Uua),Uub)),aa_TPTP_ind_TPTP_ind(scratc1858738590second(Uu,Uua),Uub))),Uub)))) # label(fact_ATP_Olambda__174) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 225 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ht(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__218) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 226 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hp,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_hq,Uu)))) # label(fact_ATP_Olambda__32) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 227 (all B_1 gg_bool(fEx_TPTP_ind(B_1))) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 228 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bm,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc46013353nd_nIn,Uua),Uu)))) # label(fact_ATP_Olambda__131) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 229 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iv,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__101) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 230 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ce(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cf,Uu),Uua)))) # label(fact_ATP_Olambda__167) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 231 (all X (pp(aa_TPTP_ind_bool(scratc1267447841closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,aa_TPTP_ind_TPTP_ind(scratc897870341_union,X1)),X))))))) # label(fact_def__d__Union__closed) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 232 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(scratc1396187181nd_n_1),Uu)),aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_iu,Uu)))) # label(fact_ATP_Olambda__4) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 233 (all X all Xa scratc57161220nd_out(X,Xa) = scratc1136799220d_soft(aa_fun1431113780TP_ind(scratc1119368612_d_Sep(X),Xa),X,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc113866315_Sigma,aa_fun1431113780TP_ind(scratc1119368612_d_Sep(X),Xa)),scratc937796160d_e_in(X,Xa)))) # label(fact_def__out) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 234 (all X aa_fun277296641TP_ind(scratc1909019605eplSep(X,aTP_Lamm_bi),scratc1136482007_d_Unj) = aa_TPTP_ind_TPTP_ind(scratc519122314_proj1,X)) # label(fact_def__proj1) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 235 (all Uu all Uua all Uub (scratc100680811_is_of(aa_TPTP_ind_TPTP_ind(scratc1858738590second(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jx(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__180) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 236 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jc,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc48112526nd_nis,aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__10) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 237 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc684468331d_Subq,X12),X0)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc390608475_power,X0))))) # label(fact_k__PowerEq) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 238 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cx(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__248) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 239 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dn(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__187) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 240 (all X0 all X12 (gg_TPTP_ind(X12) & gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc684468331d_Subq,X0),X12)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc684468331d_Subq,X12),X0)) -> X0 = X12)))) # label(fact_set__ext) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 241 (all X scratc1561761582all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)) = scratc2088393399nd_all(X)) # label(fact_def__all) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 242 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1561761582all_of(aa_TPT43085870d_bool(aTP_Lamm_jv(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_jw(X0),X12)))) # label(fact_pairis1) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 243 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fk(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fl,Uu),Uua)))) # label(fact_ATP_Olambda__142) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 244 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ag,Uu),Uua)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc7067394nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456521d_n_in,Uua),Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456521d_n_in,aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,Uua)),Uu))))) # label(fact_ATP_Olambda__104) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 245 (all X all Xa all Xb (pp(scratc56964358nd_or3(X,Xa,Xb)) <-> pp(aa_bool_bool(scratc325205189d_l_or(X),aa_bool_bool(scratc325205189d_l_or(Xa),Xb))))) # label(fact_def__or3) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 246 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_de(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__188) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 247 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gp,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_gq,Uu)))) # label(fact_ATP_Olambda__45) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 248 (all X0 (gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(scratc2134808665_nat_p,X0)) -> (exists X13 (gg_TPTP_ind(X13) & aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,X13) = X0 & pp(aa_TPTP_ind_bool(scratc2134808665_nat_p,X13)))) | scratc149728127ptyset = X0))) # label(fact_nat__inv) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 249 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_db(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__190) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 250 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(scratc1396187181nd_n_1),Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_io,Uu)))) # label(fact_ATP_Olambda__8) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 251 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(scratc995845351bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,scratc149728127ptyset),Uub),Uu),Uua) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_bo(Uu),Uua),Uub)) # label(fact_ATP_Olambda__175) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 252 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1499638682_fixfu(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ap(X),Xa),Xb),Xc))))) # label(fact_def__fixfu) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 253 (all X all Xa aa_fun1431113780TP_ind(scratc1119368612_d_Sep(aa_TPTP_ind_TPTP_ind(scratc390608475_power,X)),scratc2110288053d_anec(X,Xa)) = scratc2120849036nd_ect(X,Xa)) # label(fact_def__ect) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 254 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_id,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ie,Uu)))) # label(fact_ATP_Olambda__27) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 255 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X22),X0)) -> (pp(aa_TPTP_ind_bool(X12,X22)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X22),aa_fun1431113780TP_ind(scratc1119368612_d_Sep(X0),X12)))))) # label(fact_k__SepI) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 256 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_is,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_it,Uu)))) # label(fact_ATP_Olambda__21) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 257 (all X all Xa all Xb (scratc2110222406d_and3(scratc324549184d_l_ec(X,Xa),scratc324549184d_l_ec(Xa,Xb),scratc324549184d_l_ec(Xb,X)) <-> pp(scratc2120848971nd_ec3(X,Xa,Xb)))) # label(fact_def__ec3) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 258 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,Uua),Uu)))) # label(fact_ATP_Olambda__132) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 259 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc897870341_union,X0))) <-> (exists X2 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X12),X2)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X2),X0)) & gg_TPTP_ind(X2))))) # label(fact_k__UnionEq) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 260 (all X all Xa scratc519122314_proj1 = scratc1858738590second(X,Xa)) # label(fact_def__second) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 261 (all X0 pp(aa_TPTP_ind_bool(scratc801746418closed,aa_TPTP_ind_TPTP_ind(scratc420381799univof,X0)))) # label(fact_k__UnivOf__ZF__closed) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 262 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (-pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc995845351bnd_if(X0,X12),X22) = X22))) # label(fact_if__i__0) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 263 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dq(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__184) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 264 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cz,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_da,Uu)))) # label(fact_ATP_Olambda__76) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 265 (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_av(Uu),Uua),Uub),Uuc),Uud) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1099522659wissel(Uu,Uub),Uuc)),Uud))) # label(fact_ATP_Olambda__268) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 266 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jv(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,Uub),aa_TPTP_ind_TPTP_ind(scratc278310607etprod(Uu),Uua))))) # label(fact_ATP_Olambda__220) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 267 (all X all Xa scratc519122313_proj0 = scratc1450922438_first(X,Xa)) # label(fact_def__first) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 268 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fr,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fs,Uu)))) # label(fact_ATP_Olambda__54) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 269 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1561761582all_of(aa_TPT43085870d_bool(aTP_Lamm_jv(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_jx(X0),X12)))) # label(fact_second__p) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 270 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ab,Uu)))) # label(fact_ATP_Olambda__85) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 271 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_if,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ig,Uu)))) # label(fact_ATP_Olambda__26) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 272 (all X all Xa scratc937796160d_e_in(aa_TPTP_ind_TPTP_ind(scratc390608475_power,X),scratc2110288053d_anec(X,Xa)) = scratc1961836750_ecect(X,Xa)) # label(fact_def__ecect) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 273 (all X0 ((all X13 (gg_TPTP_ind(X13) -> ((all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_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]. 1.11/1.44 274 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dz(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ea,Uu),Uua)))) # label(fact_ATP_Olambda__153) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 275 (all X7 all Y (gg_TPTP_ind(X7) & gg_TPTP_ind(Y) -> -pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) | Y = X7)) # label(help_fequal_1_1_fequal_001t__TPTP____Interpret__Oind_T) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 276 (all Uu all Uua all Uub all Uuc all Uud all Uue all Uuf (pp(aa_fun171081125l_bool(scratc1561761582all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_ak(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_al(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)))) # label(fact_ATP_Olambda__271) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 277 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1561761582all_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__165) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 278 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc503222518_rec_G(X),Xa),Xb)) <-> (all X3 ((all X4 all X5 (gg_TPTP_ind(X4) -> ((all X6 (gg_TPTP_ind(X6) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X6),X4)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(X3,X6),aa_TPTP_ind_TPTP_ind(X5,X6)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(X3,X4),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(X,X4),X5)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(X3,Xa),Xb)))))) # label(fact_def__d__In__rec__G) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 279 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),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__166) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 280 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_iz,Uu)) <-> pp(aa_fun171081125l_bool(scratc56702012nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1944075539d_d_Pi,scratc47587735nd_nat),aTP_Lamm_ac)),aa_TPT43085870d_bool(aTP_Lamm_iy,Uu))))) # label(fact_ATP_Olambda__5) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 281 (all X all Xa (pp(aa_fun171081125l_bool(scratc672422390l_some(X),Xa)) <-> pp(scratc1343085241_d_not(aa_fun171081125l_bool(scratc1561761582all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),scratc48506115nd_non(X,Xa)))))) # label(fact_def__l__some) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 282 (all Uu all Uua aa_fun277296641TP_ind(aa_TPT494704832TP_ind(aTP_Lamm_bl,Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1509025778nunion(aa_TPTP_ind_TPTP_ind(scratc586117449d_Sing,scratc149728127ptyset)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc274252953d_repl,Uu),Uua))) # label(fact_ATP_Olambda__125) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 283 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gh,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gg,Uu))))) # label(fact_ATP_Olambda__49) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 284 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_de(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_df,Uu),Uua)))) # label(fact_ATP_Olambda__160) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 285 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fh(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__202) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 286 (all Uu all Uua all Uub all Uuc all Uud all Uue (pp(aa_fun171081125l_bool(scratc1561761582all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_al(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_am(Uu),Uua),Uub),Uuc),Uud),Uue)))) # label(fact_ATP_Olambda__269) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 287 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hx,Uu),Uua)) <-> pp(scratc997820912_amone(scratc47587735nd_nat,aa_TPT43085870d_bool(aTP_Lamm_ht(Uu),Uua))))) # label(fact_ATP_Olambda__170) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 288 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_eu,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_et,Uu))))) # label(fact_ATP_Olambda__62) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 289 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_an(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_am(Uu),Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__266) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 290 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jf,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,Uu),aa_TPTP_ind_TPTP_ind(scratc390608475_power,scratc47587735nd_nat))))) # label(fact_ATP_Olambda__15) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 291 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ij(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ik,Uu),Uua)))) # label(fact_ATP_Olambda__133) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 292 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gw,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gv,Uu))))) # label(fact_ATP_Olambda__42) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 293 (all X all Xa scratc1909019605eplSep(X,Xa) = aa_TPT494704832TP_ind(scratc274252953d_repl,aa_fun1431113780TP_ind(scratc1119368612_d_Sep(X),Xa))) # label(fact_def__d__ReplSep) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 294 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1116293985ectelt(X,Xa),Xb) = aa_TPTP_ind_TPTP_ind(scratc1231495862ectset(X,Xa),aa_TPTP_ind_TPTP_ind(scratc1962427141_ecelt(X,Xa),Xb))) # label(fact_def__ectelt) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 295 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_im,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,Uu)),Uua))))) # label(fact_ATP_Olambda__119) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 296 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dv,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_du,Uu))))) # label(fact_ATP_Olambda__69) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 297 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc278310607etprod(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc113866315_Sigma,X),aTP_Lamm_ai(Xa))) # label(fact_def__setprod) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 298 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cy(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cz,Uu),Uua)))) # label(fact_ATP_Olambda__162) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 299 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ge,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gd,Uu))))) # label(fact_ATP_Olambda__50) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 300 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X33),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,aa_TPTP_ind_TPTP_ind(X22,X33)),aa_TPTP_ind_TPTP_ind(X12,X33)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc113866315_Sigma,X0),X22)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1944075539d_d_Pi,X0),X12))))) # label(fact_lam__Pi) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 301 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc390608475_power,X0)))) # label(fact_k__Self__In__Power) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 302 (all X0 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X0),scratc1836261175_omega)) -> pp(aa_TPTP_ind_bool(scratc2134808665_nat_p,X0)))) # label(fact_omega__nat__p) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 303 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc897870341_union,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc274252953d_repl,X),Xa)) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc515168679munion,X),Xa)) # label(fact_def__famunion) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 304 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc113866315_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc827056996d_pair,aa_TPTP_ind_TPTP_ind(scratc519122313_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc519122314_proj1,X22)) = X22))) # label(fact_proj__Sigma__eta) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 305 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc7526576nd_ite(X,Xa,Xb),Xc) = scratc7132981nd_ind(Xa,aa_TPT43085870d_bool(scratc519515908_prop1(X,Xa,Xb),Xc))) # label(fact_def__ite) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 306 (all X0 (pp(aa_TPTP_ind_bool(X0,scratc149728127ptyset)) -> ((all X13 (gg_TPTP_ind(X13) -> (pp(aa_TPTP_ind_bool(scratc2134808665_nat_p,X13)) -> (pp(aa_TPTP_ind_bool(X0,X13)) -> pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,X13))))))) -> (all X12 (pp(aa_TPTP_ind_bool(scratc2134808665_nat_p,X12)) -> pp(aa_TPTP_ind_bool(X0,X12))))))) # label(fact_nat__ind) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 307 (all X ((all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,aa_TPTP_ind_TPTP_ind(scratc390608475_power,X1)),X))))) <-> pp(aa_TPTP_ind_bool(scratc1432180855closed,X)))) # label(fact_def__d__Power__closed) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 308 (all Uu all Uua (pp(scratc56964358nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hl,Uu),Uua)))) # label(fact_ATP_Olambda__92) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 309 (all Uu all Uua (pp(scratc2120848971nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1416247032n_some,aa_TPT43085870d_bool(scratc1431625074ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc1416247032n_some,aa_TPT43085870d_bool(scratc1431625074ffprop(Uua),Uu)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hp,Uu),Uua)))) # label(fact_ATP_Olambda__96) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 310 (all X all Xa aa_fun1431113780TP_ind(scratc1119368612_d_Sep(aa_TPTP_ind_TPTP_ind(scratc390608475_power,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc113866315_Sigma,X),aTP_Lamm_be(Xa)))),aa_fun1913827119d_bool(aTP_Lamm_bf(X),Xa)) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1944075539d_d_Pi,X),Xa)) # label(fact_def__d__Pi) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 311 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ic(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_id,Uu),Uua)))) # label(fact_ATP_Olambda__134) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 312 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fx,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fw(Uu),Uua))))) # label(fact_ATP_Olambda__140) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 313 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ea,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_eb,Uu)))) # label(fact_ATP_Olambda__67) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 314 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ch(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1039382957lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__253) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 315 scratc907717853bvious <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc7067394nd_imp,fFalse),fFalse)) # label(fact_def__obvious) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 316 (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(scratc247555713_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1173366569moreis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__249) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 317 (all X all Xa (pp(scratc1343085241_d_not(scratc324549184d_l_ec(X,Xa))) <-> pp(scratc1235620061_d_and(X,Xa)))) # label(fact_def__d__and) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 318 (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]. 1.11/1.44 319 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hc,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hb,Uu))))) # label(fact_ATP_Olambda__39) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 320 (all X0 all X12 all X22 (gg_TPTP_ind(X12) -> (pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc995845351bnd_if(X0,X12),X22) = X12))) # label(fact_if__i__1) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 321 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fu,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ft(Uu),Uua))))) # label(fact_ATP_Olambda__141) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 322 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kf(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,Uub),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1944075539d_d_Pi,Uu),aTP_Lamm_ai(Uua)))))) # label(fact_ATP_Olambda__217) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 323 (all Uu all Uua (scratc1443967432_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hn,Uu),Uua)))) # label(fact_ATP_Olambda__91) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 324 (all Uu all Uua ((pp(scratc1343085241_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1173366569moreis,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gt,Uu),Uua)))) # label(fact_ATP_Olambda__124) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 325 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_et,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_es(Uu),Uua))))) # label(fact_ATP_Olambda__148) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 326 (all X all Xa (pp(aa_fun171081125l_bool(scratc1561761582all_of(X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (scratc100680811_is_of(X2,X) -> pp(aa_TPTP_ind_bool(Xa,X2))))))) # label(fact_def__all__of) # label(axiom) # label(non_clause). [assumption]. 1.11/1.44 327 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jj,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ji,Uu))))) # label(fact_ATP_Olambda__18) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 328 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,X),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1431625074ffprop(X),Xa),Xb)))) # label(fact_def__diffprop) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 329 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ia,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ib,Uu)))) # label(fact_ATP_Olambda__28) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 330 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hf,Uu),Uua)))) # label(fact_ATP_Olambda__111) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 331 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc435323114nempty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc672422390l_some(X),aa_TPT43085870d_bool(aTP_Lamm_au(X),Xa))))) # label(fact_def__nonempty) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 332 (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]. 1.11/1.45 333 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1561761582all_of(aa_fun1584354236d_bool(aTP_Lamm_kc(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_ke(X0),X12)))) # label(fact_e__in__p) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 334 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bv(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1039382957lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1039382957lessis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1039382957lessis,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__252) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 335 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bq,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_br,Uu)))) # label(fact_ATP_Olambda__84) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 336 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kg(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc937796165d_e_is(Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,Uua),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,Uub),Uuc))))) # label(fact_ATP_Olambda__240) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 337 (all Uu all Uua ((pp(scratc1343085241_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1173366569moreis,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gn,Uu),Uua)))) # label(fact_ATP_Olambda__122) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 338 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cf,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cg,Uu)))) # label(fact_ATP_Olambda__81) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 339 (all Uu all Uua all Uub (scratc100680811_is_of(aa_TPTP_ind_TPTP_ind(scratc937796160d_e_in(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ke(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__182) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 340 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_he,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hd,Uu))))) # label(fact_ATP_Olambda__38) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 341 (all X0 all X12 (gg_TPTP_ind(X12) -> aa_TPTP_ind_TPTP_ind(scratc519122314_proj1,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc827056996d_pair,X0),X12)) = X12)) # label(fact_proj1__pair__eq) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 342 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ji,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__99) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 343 (all B_1 all B_2 gg_TPTP_ind(scratc2120849036nd_ect(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__50754__14833_ONUM697__thf__4__p_Obnd__ect) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 344 (all B_1 all B_2 gg_bool(scratc324549184d_l_ec(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__50754__14833_ONUM697__thf__4__p_Obnd__l__ec) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 345 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc48506115nd_non(X,Xa),Xb)) <-> pp(scratc1343085241_d_not(aa_TPTP_ind_bool(Xa,Xb))))) # label(fact_def__non) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 346 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_er(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_es(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__223) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 347 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ff,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fe(Uu),Uua))))) # label(fact_ATP_Olambda__144) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 348 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_eq,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ep,Uu))))) # label(fact_ATP_Olambda__63) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 349 (all X all Xa ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X2),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X2),Xa))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc684468331d_Subq,X),Xa)))) # label(fact_def__d__Subq) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 350 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1039382957lessis,Uu),Uua)) -> pp(scratc1343085241_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,Uu),Uua)))))) # label(fact_ATP_Olambda__114) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 351 (all X fequal_TPTP_ind = scratc937796165d_e_is(X)) # label(fact_def__e__is) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 352 (all X (pp(aa_TPTP_ind_bool(scratc534239046_cond2,X)) <-> pp(aa_fun171081125l_bool(scratc660593885_n_all,aa_TPT43085870d_bool(aTP_Lamm_ag,X))))) # label(fact_def__cond2) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 353 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1782819631_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc48112526nd_nis,Xa),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(X),Xa))))) # label(fact_def__d__27__prop1) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 354 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_bool_bool(aa_boo1142376798l_bool(scratc7067394nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc937796165d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,Uub),Uud))),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc937796165d_e_is(Uu),Uuc),Uud))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_az(Uu),Uua),Uub),Uuc),Uud)))) # label(fact_ATP_Olambda__264) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 355 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cu(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cv,Uu),Uua)))) # label(fact_ATP_Olambda__163) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 356 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc606095281_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(X),Xa)),Xb)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(X),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Xa),Xb)))))) # label(fact_def__d__25__prop1) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 357 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ey(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__203) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 358 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bh(Uu),Uua) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc274252953d_repl,aa_TPTP_ind_TPTP_ind(Uu,Uua)),aa_TPT1424761345TP_ind(scratc827056996d_pair,Uua))) # label(fact_ATP_Olambda__117) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 359 (all X all Xa (pp(aa_fun171081125l_bool(scratc1561761582all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),aa_fun1584354236d_bool(aTP_Lamm_bd(X),Xa))) <-> pp(scratc997820912_amone(X,Xa)))) # label(fact_def__amone) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 360 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1561761582all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_jq(X0),X12)))) # label(fact_estii) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 361 (all P all Q (pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)) | -pp(Q) | -pp(P))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 362 (all Uu all Uua aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,Uu),Uua)) = aa_TPTP_ind_TPTP_ind(aTP_Lamm_ad(Uu),Uua)) # label(fact_ATP_Olambda__171) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 363 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fi,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fj,Uu)))) # label(fact_ATP_Olambda__57) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 364 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hk,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hj,Uu))))) # label(fact_ATP_Olambda__35) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 365 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1561761582all_of(aa_TPT43085870d_bool(aTP_Lamm_kf(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_ki(X0),X12)))) # label(fact_e__fisi) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 366 (all X0 all X12 (gg_TPTP_ind(X0) -> X0 = aa_TPTP_ind_TPTP_ind(scratc519122313_proj0,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc827056996d_pair,X0),X12)))) # label(fact_proj0__pair__eq) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 367 (all Uu (gg_TPTP_ind(Uu) -> ((exists X2 (gg_TPTP_ind(X2) & aa_TPTP_ind_TPTP_ind(scratc1411225126d_Inj1,X2) = Uu)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_bi,Uu))))) # label(fact_ATP_Olambda__89) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 368 (all X all Xa (-pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc46013353nd_nIn,X),Xa)))) # label(fact_def__nIn) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 369 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_as(Uu),Uua),Uub),Uuc)) <-> pp(scratc324549184d_l_ec(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc979961069d_esti(Uu),Uuc),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc979961069d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__244) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 370 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ev(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__206) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 371 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1842147815t_disj(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc2088393399nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_as(X),Xa),Xb))))) # label(fact_def__st__disj) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 372 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ez,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fa,Uu)))) # label(fact_ATP_Olambda__60) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 373 (all X all Xa (pp(scratc1235620061_d_and(aa_bool_bool(scratc325205189d_l_or(X),Xa),scratc324549184d_l_ec(X,Xa))) <-> scratc186652971d_orec(X,Xa))) # label(fact_def__orec) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 374 (all X (pp(aa_TPTP_ind_bool(scratc519515911_prop4,X)) <-> pp(aa_fun171081125l_bool(scratc672422390l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1944075539d_d_Pi,scratc47587735nd_nat),aTP_Lamm_ac)),aa_TPT43085870d_bool(scratc17733107_prop2,X))))) # label(fact_def__prop4) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 375 (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]. 1.11/1.45 376 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jy(Uu),Uua),Uub)) <-> scratc100680811_is_of(aa_TPTP_ind_TPTP_ind(scratc1450922438_first(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)))) # label(fact_ATP_Olambda__181) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 377 (all X all Xa (pp(scratc324549184d_l_ec(X,Xa)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc7067394nd_imp,X),scratc1343085241_d_not(Xa))))) # label(fact_def__l__ec) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 378 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hh,Uu),Uua)))) # label(fact_ATP_Olambda__108) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 379 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1561761582all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_ka(X0),X12)))) # label(fact_e__pair__p) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 380 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bv(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bw(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__234) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 381 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fy,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fx,Uu))))) # label(fact_ATP_Olambda__52) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 382 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fl,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fm,Uu)))) # label(fact_ATP_Olambda__56) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 383 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> pp(X0) & X12 = aa_TPTP_ind_TPTP_ind(scratc995845351bnd_if(X0,X12),X22) | -pp(X0) & aa_TPTP_ind_TPTP_ind(scratc995845351bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__correct) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 384 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),scratc1396187181nd_n_1))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ir,Uu)))) # label(fact_ATP_Olambda__7) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 385 (all Uu (gg_TPTP_ind(Uu) -> ((exists X2 (gg_TPTP_ind(X2) & Uu = aa_TPTP_ind_TPTP_ind(scratc1411225125d_Inj0,X2))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_bj,Uu))))) # label(fact_ATP_Olambda__90) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 386 (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]. 1.11/1.45 387 (all X all Xa (pp(scratc56964358nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc812060333_prop1,X),Xa)))) # label(fact_def__d__29__prop1) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 388 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_a,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,Uu),scratc47587735nd_nat)))) # label(fact_ATP_Olambda__17) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 389 (all X (pp(aa_TPTP_ind_bool(scratc1267447841closed,X)) & pp(aa_TPTP_ind_bool(scratc1432180855closed,X)) & pp(aa_TPTP_ind_bool(scratc212847509closed,X)) <-> pp(aa_TPTP_ind_bool(scratc801746418closed,X)))) # label(fact_def__d__ZF__closed) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 390 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iy,Uu),Uua)) <-> pp(scratc1235620061_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,Uua),scratc1396187181nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,Uu)),aa_fun171081125l_bool(scratc660593885_n_all,aa_TPT43085870d_bool(aTP_Lamm_ae,Uua)))))) # label(fact_ATP_Olambda__98) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 391 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cu(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ct(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__228) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 392 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,Uu),Uua)) -> pp(scratc1343085241_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1039382957lessis,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gr,Uu),Uua)))) # label(fact_ATP_Olambda__112) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 393 (all X aa_TPTP_ind_TPTP_ind(scratc586117449d_Sing,X) = aa_TPTP_ind_TPTP_ind(scratc8352693_UPair(X),X)) # label(fact_def__d__Sing) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 394 (all X0 (scratc122203668nd_wel(X0) -> pp(X0))) # label(fact_l__et) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 395 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X33),X0)) -> aa_TPTP_ind_TPTP_ind(X12,X33) = aa_TPTP_ind_TPTP_ind(X22,X33)))) -> aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc113866315_Sigma,X0),X12) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc113866315_Sigma,X0),X22))) # label(fact_xi__ext) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 396 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bs,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,scratc1396187181nd_n_1),aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,Uu))))) # label(fact_ATP_Olambda__86) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 397 (all X all Xa all Xb (pp(aa_fun171081125l_bool(scratc2088393399nd_all(Xa),aa_TPT43085870d_bool(scratc1408280369_image(X,Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc881304326ective(X),Xa),Xb)))) # label(fact_def__surjective) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 398 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1561761582all_of(aa_TPT43085870d_bool(aTP_Lamm_jm,Uu)),aa_TPT43085870d_bool(aTP_Lamm_jn(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jo,Uu),Uua)))) # label(fact_ATP_Olambda__118) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 399 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_at(Uu),Uua),Uub),Uuc)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc7067394nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc979961069d_esti(Uu),Uuc),Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc979961069d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__245) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 400 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gc(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1039382957lessis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__207) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 401 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1509025778nunion(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc274252953d_repl,X),scratc1411225125d_Inj0)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc274252953d_repl,Xa),scratc1411225126d_Inj1)) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc827056996d_pair,X),Xa)) # label(fact_def__pair) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 402 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,Uua),aa_TPTP_ind_TPTP_ind(scratc390608475_power,Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jm,Uu),Uua)))) # label(fact_ATP_Olambda__129) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 403 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_je,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jd,Uu))))) # label(fact_ATP_Olambda__19) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 404 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dp,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_do,Uu))))) # label(fact_ATP_Olambda__71) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 405 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cr,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cs,Uu)))) # label(fact_ATP_Olambda__78) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 406 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1561761582all_of(aa_TPT43085870d_bool(aTP_Lamm_jv(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_jy(X0),X12)))) # label(fact_first__p) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 407 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dk(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dl,Uu),Uua)))) # label(fact_ATP_Olambda__158) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 408 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc979961069d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc1119368612_d_Sep(Uu),Uua))) -> pp(aa_TPTP_ind_bool(Uua,Uub))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_jp(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__178) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 409 (all Uu all Uua all Uub all Uuc ((pp(aa_fun171081125l_bool(scratc1561761582all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kg(Uua),Uub),Uuc))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc937796165d_e_is(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1944075539d_d_Pi,Uu),aTP_Lamm_ai(Uua))),Uub),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kh(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__246) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 410 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gz,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1173366569moreis,Uu),Uua)) -> pp(scratc1343085241_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,Uu),Uua)))))) # label(fact_ATP_Olambda__113) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 411 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fi,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fh(Uu),Uua))))) # label(fact_ATP_Olambda__143) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 412 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kl,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc937796165d_e_is(Uu),Uua),Uua)))) # label(fact_ATP_Olambda__97) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 413 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jd,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc48112526nd_nis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc48112526nd_nis,aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,Uua)))))) # label(fact_ATP_Olambda__103) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 414 (all X0 all X12 all X22 all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1944075539d_d_Pi,X0),X12))) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X32),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,X22),X32)),aa_TPTP_ind_TPTP_ind(X12,X32)))))) # label(fact_ap__Pi) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 415 (all X0 (pp(aa_TPTP_ind_bool(scratc2134808665_nat_p,X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X0),scratc1836261175_omega)))) # label(fact_nat__p__omega) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 416 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,Uub),aa_fun1431113780TP_ind(scratc1119368612_d_Sep(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_kc(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__221) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 417 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ae,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,Uu),aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,Uu),Uua)))))) # label(fact_ATP_Olambda__102) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 418 (all X all Xa all Xb aa_fun1431113780TP_ind(scratc1119368612_d_Sep(X),aa_TPT43085870d_bool(Xa,Xb)) = aa_TPTP_ind_TPTP_ind(scratc1962427141_ecelt(X,Xa),Xb)) # label(fact_def__ecelt) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 419 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dt(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_du,Uu),Uua)))) # label(fact_ATP_Olambda__155) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 420 (all X aa_TPTP_ind_TPTP_ind(scratc1509025778nunion(X),aa_TPTP_ind_TPTP_ind(scratc586117449d_Sing,X)) = aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,X)) # label(fact_def__ordsucc) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 421 (all X (gg_TPTP_ind(X) -> (pp(aa_TPTP_ind_bool(scratc501137484pair_p,X)) <-> X = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc827056996d_pair,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,X),scratc149728127ptyset)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,X),aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,scratc149728127ptyset)))))) # label(fact_def__pair__p) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 422 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eo(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ep,Uu),Uua)))) # label(fact_ATP_Olambda__149) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 423 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fq,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fp,Uu))))) # label(fact_ATP_Olambda__55) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 424 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ij(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__191) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 425 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1623117595ective(X),Xa),Xb)) <-> pp(scratc1235620061_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1439398365ective(X),Xa),Xb),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc881304326ective(X),Xa),Xb))))) # label(fact_def__bijective) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 426 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1561761582all_of(aa_fun1584354236d_bool(aTP_Lamm_kc(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_kd(X0),X12)))) # label(fact_e__inp) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 427 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ii,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ih,Uu))))) # label(fact_ATP_Olambda__25) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 428 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gi(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__208) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 429 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hm,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hl,Uu))))) # label(fact_ATP_Olambda__34) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 430 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1561761582all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_ju(X0),X12)))) # label(fact_firstis1) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 431 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cp(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cq(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__229) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 432 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bd(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bc(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__213) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 433 (all X all Xa (pp(aa_bool_bool(scratc325205189d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1173366569moreis,X),Xa)))) # label(fact_def__moreis) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 434 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dd,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dc,Uu))))) # label(fact_ATP_Olambda__75) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 435 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc113866315_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,aa_TPTP_ind_TPTP_ind(scratc519122314_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc519122313_proj0,X22)))))) # label(fact_proj1__Sigma) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 436 (all X all Xa all Xb all Xc (pp(scratc1235620061_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc979961069d_esti(X),Xc),Xa),scratc1343085241_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc979961069d_esti(X),Xc),Xb)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1345559031etprop(X,Xa),Xb),Xc)))) # label(fact_def__nissetprop) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 437 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cp(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1173366569moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__250) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 438 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fv,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fu,Uu))))) # label(fact_ATP_Olambda__53) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 439 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dh(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__185) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 440 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ga,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fz(Uu),Uua))))) # label(fact_ATP_Olambda__139) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 441 (all Uu all Uua (scratc1443967432_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1416247032n_some,aa_TPT43085870d_bool(aTP_Lamm_ht(Uu),Uua)),aa_fun171081125l_bool(scratc1416247032n_some,aa_TPT43085870d_bool(aTP_Lamm_hu(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hv,Uu),Uua)))) # label(fact_ATP_Olambda__94) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 442 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fn,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,Uu))))) # label(fact_ATP_Olambda__14) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 443 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X22),X0)) -> aa_TPTP_ind_TPTP_ind(X12,X22) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc113866315_Sigma,X0),X12)),X22))) # label(fact_beta) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 444 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fg,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ff,Uu))))) # label(fact_ATP_Olambda__58) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 445 (all X0 all X12 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1439398365ective(aa_fun1431113780TP_ind(scratc1119368612_d_Sep(X0),X12)),X0),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc113866315_Sigma,aa_fun1431113780TP_ind(scratc1119368612_d_Sep(X0),X12)),scratc937796160d_e_in(X0,X12))))) # label(fact_otax1) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 446 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,X0) = aa_TPTP_ind_TPTP_ind(scratc644387513rdsucc,X12) -> X0 = X12))) # label(fact_ordsucc__inj) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 447 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_iw,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_iv,Uu))))) # label(fact_ATP_Olambda__20) # label(axiom) # label(non_clause). [assumption]. 1.11/1.45 448 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1913827119d_bool(aTP_Lamm_bf(Uu),Uua),Uub)) <-> (all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X3),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,Uub),X3)),aa_TPTP_ind_TPTP_ind(Uua,X3)))))))) # label(fact_ATP_Olambda__236) # label(axiom) # label(non_clause). [assumption]. 1.11/1.46 449 (all X all Xa scratc2121701822nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bb(X),Xa)) = scratc7132981nd_ind(X,Xa)) # label(fact_def__ind) # label(axiom) # label(non_clause). [assumption]. 1.11/1.46 450 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_gy,Uu)))) # label(fact_ATP_Olambda__41) # label(axiom) # label(non_clause). [assumption]. 1.11/1.46 451 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ek(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ej(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__225) # label(axiom) # label(non_clause). [assumption]. 1.11/1.46 452 (all P all Q (-pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)) | pp(P))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption]. 1.11/1.46 453 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1337613208unmore(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc1119368612_d_Sep(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ar(X),Xa),Xb))) # label(fact_def__unmore) # label(axiom) # label(non_clause). [assumption]. 1.11/1.46 454 (all Uu all Uua all Uub all Uuc all Uud all Uue all Uuf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_ak(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uue),Uuf)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc937796165d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,Uub),Uuc)),Uue)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc995320569bnd_ap,Uub),Uud)),Uuf))))))) # label(fact_ATP_Olambda__270) # label(axiom) # label(non_clause). [assumption]. 1.11/1.46 455 (all X (pp(scratc1343085241_d_not(scratc1343085241_d_not(X))) <-> scratc122203668nd_wel(X))) # label(fact_def__wel) # label(axiom) # label(non_clause). [assumption]. 1.11/1.46 456 (all X0 all X12 all X22 all X32 (pp(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc995845351bnd_if(X0,X22),X32))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc995845359bnd_in,X12),X22))))) # label(fact_k__If__In__then__E) # label(axiom) # label(non_clause). [assumption]. 1.11/1.46 457 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bx,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_by,Uu)))) # label(fact_ATP_Olambda__83) # label(axiom) # label(non_clause). [assumption]. 1.11/1.46 458 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gu,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gt,Uu))))) # label(fact_ATP_Olambda__43) # label(axiom) # label(non_clause). [assumption]. 1.11/1.46 459 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uua)),Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fr,Uu),Uua)))) # label(fact_ATP_Olambda__116) # label(axiom) # label(non_clause). [assumption]. 1.11/1.46 460 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gl,Uu),Uua)) <-> (pp(scratc1343085241_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1039382957lessis,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__123) # label(axiom) # label(non_clause). [assumption]. 1.11/1.46 461 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc223698158_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc48112526nd_nis,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(X),Xb))))) # label(fact_def__d__28__prop1) # label(axiom) # label(non_clause). [assumption]. 1.11/1.47 462 (all X aa_fun277296641TP_ind(scratc1909019605eplSep(X,aTP_Lamm_bj),scratc1136482007_d_Unj) = aa_TPTP_ind_TPTP_ind(scratc519122313_proj0,X)) # label(fact_def__proj0) # label(axiom) # label(non_clause). [assumption]. 1.11/1.47 463 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dl,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_dm,Uu)))) # label(fact_ATP_Olambda__72) # label(axiom) # label(non_clause). [assumption]. 1.11/1.47 464 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ed,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ee,Uu)))) # label(fact_ATP_Olambda__66) # label(axiom) # label(non_clause). [assumption]. 1.11/1.47 465 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1173366569moreis,Uu),scratc1396187181nd_n_1)))) # label(fact_ATP_Olambda__16) # label(axiom) # label(non_clause). [assumption]. 1.11/1.47 466 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ip,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_iq,Uu)))) # label(fact_ATP_Olambda__22) # label(axiom) # label(non_clause). [assumption]. 1.11/1.47 467 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_en(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc456456526d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc247555713_29_ii,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uuc),Uua))))))) # label(fact_ATP_Olambda__255) # label(axiom) # label(non_clause). [assumption]. 1.11/1.47 468 (all Uu (pp(aa_fun171081125l_bool(scratc1561761582all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hx,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_hy,Uu)))) # label(fact_ATP_Olambda__29) # label(axiom) # label(non_clause). [assumption]. 1.11/1.47 469 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc56702012nd_one(X0),X12)) -> scratc100680811_is_of(scratc7132981nd_ind(X0,X12),aa_TPT43085870d_bool(aTP_Lamm_aj,X0)))) # label(fact_ind__p) # label(axiom) # label(non_clause). [assumption]. 1.11/1.47 470 (all X all Xa scratc995320569bnd_ap = scratc1917386418d_tofs(X,Xa)) # label(fact_def__tofs) # label(axiom) # label(non_clause). [assumption]. 1.11/1.47 471 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6804991nd_iii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1416247032n_some,aa_TPT43085870d_bool(scratc1431625074ffprop(Xa),X))))) # label(fact_def__iii) # label(axiom) # label(non_clause). [assumption]. 1.11/1.47 472 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1039382957lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1039382957lessis,aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc456915712d_n_pl(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dw(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__198) # label(axiom) # label(non_clause). [assumption]. 1.11/1.47 1.11/1.47 ============================== end of process non-clausal formulas === 1.11/1.47 1.11/1.47 ============================== PROCESS INITIAL CLAUSES =============== 1.11/1.47 1.11/1.47 ============================== PREDICATE ELIMINATION ================= 1.11/1.47 473 -gg_bool(A) | fFalse = A | fTrue = A # label(help_fFalse_1_1_T) # label(axiom). [clausify(121)]. 1.11/1.47 474 gg_bool(scratc1235620061_d_and(A,B)) # label(gsy_c_Scratch__tptp__translate__50754__14833_ONUM697__thf__4__p_Obnd__d__and) # label(axiom). [clausify(11)]. 1.11/1.47 475 gg_bool(scratc1343085241_d_not(A)) # label(gsy_c_Scratch__tptp__translate__50754__14833_ONUM697__thf__4__p_Obnd__d__not) # label(axiom). [clausify(26)]. 1.11/1.47 476 gg_bool(undefined_bool(bool)) # label(gsy_c_HOL_Oundefined_001t__HOL__Obool) # label(axiom). [assumption]. 1.11/1.47 477 gg_bool(scratc997820912_amone(A,B)) # label(gsy_c_Scratch__tptp__translate__50754__14833_ONUM697__thf__4__p_Obnd__amone) # label(axiom). [clausify(42)]. 1.38/1.64 478 gg_bool(scratc56964358nd_or3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__50754__14833_ONUM697__thf__4__p_Obnd__or3) # label(axiom). [clausify(56)]. 1.38/1.64 Derived: fFalse = scratc1235620061_d_and(A,B) | fTrue = scratc1235620061_d_and(A,B). [resolve(473,a,474,a)]. 1.38/1.64 Derived: fFalse = scratc1343085241_d_not(A) | fTrue = scratc1343085241_d_not(A). [resolve(473,a,475,a)]. 1.38/1.64 Derived: fFalse = undefined_bool(bool) | fTrue = undefined_bool(bool). [resolve(473,a,476,a)]. 1.38/1.64 Derived: fFalse = scratc997820912_amone(A,B) | fTrue = scratc997820912_amone(A,B). [resolve(473,a,477,a)]. 1.38/1.64 Derived: fFalse = scratc56964358nd_or3(A,B,C) | fTrue = scratc56964358nd_or3(A,B,C). [resolve(473,a,478,a)]. 1.38/1.64 479 gg_bool(scratc2120848971nd_ec3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__50754__14833_ONUM697__thf__4__p_Obnd__ec3) # label(axiom). [clausify(135)]. 1.38/1.64 Derived: fFalse = scratc2120848971nd_ec3(A,B,C) | fTrue = scratc2120848971nd_ec3(A,B,C). [resolve(479,a,473,a)]. 1.38/1.64 480 gg_bool(aa_TPTP_ind_bool(A,B)) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom). [clausify(161)]. 1.38/1.64 Derived: fFalse = aa_TPTP_ind_bool(A,B) | fTrue = aa_TPTP_ind_bool(A,B). [resolve(480,a,473,a)]. 1.38/1.64 481 gg_bool(fEx_TPTP_ind(A)) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom). [clausify(227)]. 1.38/1.64 Derived: fFalse = fEx_TPTP_ind(A) | fTrue = fEx_TPTP_ind(A). [resolve(481,a,473,a)]. 1.38/1.64 482 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(332)]. 1.38/1.64 Derived: fFalse = aa_fun171081125l_bool(A,B) | fTrue = aa_fun171081125l_bool(A,B). [resolve(482,a,473,a)]. 1.38/1.64 483 gg_bool(scratc324549184d_l_ec(A,B)) # label(gsy_c_Scratch__tptp__translate__50754__14833_ONUM697__thf__4__p_Obnd__l__ec) # label(axiom). [clausify(344)]. 1.38/1.64 Derived: fFalse = scratc324549184d_l_ec(A,B) | fTrue = scratc324549184d_l_ec(A,B). [resolve(483,a,473,a)]. 1.38/1.64 484 gg_bool(aa_bool_bool(A,B)) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom). [clausify(386)]. 1.38/1.64 Derived: fFalse = aa_bool_bool(A,B) | fTrue = aa_bool_bool(A,B). [resolve(484,a,473,a)]. 1.38/1.64 485 gg_bool(fTrue) # label(gsy_c_fTrue) # label(axiom). [assumption]. 1.38/1.64 Derived: fFalse = fTrue | fTrue = fTrue. [resolve(485,a,473,a)]. 1.38/1.64 486 gg_bool(fFalse) # label(gsy_c_fFalse) # label(axiom). [assumption]. 1.38/1.64 Derived: fFalse = fFalse | fTrue = fFalse. [resolve(486,a,473,a)]. 1.38/1.64 487 scratc2129761511_l_iff(A,B) | -pp(scratc1235620061_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc7067394nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc7067394nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(77)]. 1.38/1.64 488 -scratc2129761511_l_iff(A,B) | pp(scratc1235620061_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc7067394nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc7067394nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(77)]. 1.38/1.64 489 -pp(A) | pp(scratc1343085241_d_not(B)) | -scratc719483974d_r_ec(A,B) # label(fact_def__r__ec) # label(axiom). [clausify(136)]. 1.38/1.64 490 pp(A) | scratc719483974d_r_ec(A,B) # label(fact_def__r__ec) # label(axiom). [clausify(136)]. 1.38/1.64 491 -pp(scratc1343085241_d_not(A)) | scratc719483974d_r_ec(B,A) # label(fact_def__r__ec) # label(axiom). [clausify(136)]. 1.38/1.64 492 pp(scratc1235620061_d_and(aa_bool_bool(scratc325205189d_l_or(A),B),scratc324549184d_l_ec(A,B))) | -scratc186652971d_orec(A,B) # label(fact_def__orec) # label(axiom). [clausify(373)]. 1.38/1.64 493 -pp(scratc1235620061_d_and(aa_bool_bool(scratc325205189d_l_or(A),B),scratc324549184d_l_ec(A,B))) | scratc186652971d_orec(A,B) # label(fact_def__orec) # label(axiom). [clausify(373)]. 1.38/1.64 494 -pp(scratc1343085241_d_not(scratc1343085241_d_not(A))) | scratc122203668nd_wel(A) # label(fact_def__wel) # label(axiom). [clausify(455)]. 1.38/1.64 495 -scratc122203668nd_wel(A) | pp(A) # label(fact_l__et) # label(axiom). [clausify(394)]. 1.38/1.64 Derived: -pp(scratc1343085241_d_not(scratc1343085241_d_not(A))) | pp(A). [resolve(494,b,495,a)]. 1.38/1.64 496 pp(scratc1343085241_d_not(scratc1343085241_d_not(A))) | -scratc122203668nd_wel(A) # label(fact_def__wel) # label(axiom). [clausify(455)]. 1.90/2.17 1.90/2.17 ============================== end predicate elimination ============= 1.90/2.17 1.90/2.17 Auto_denials: (non-Horn, no changes). 1.90/2.17 1.90/2.17 Term ordering decisions: 1.90/2.17 Function symbol KB weights: aTP_Lamm_a=1. scratc995845359bnd_in=1. scratc456456526d_n_is=1. scratc6804991nd_iii=1. scratc247555713_29_ii=1. scratc644387513rdsucc=1. scratc995320569bnd_ap=1. aTP_Lamm_aj=1. scratc1039382957lessis=1. scratc1173366569moreis=1. scratc1396187181nd_n_1=1. scratc149728127ptyset=1. scratc113866315_Sigma=1. scratc48112526nd_nis=1. fFalse=1. scratc1416247032n_some=1. scratc1944075539d_d_Pi=1. scratc2134808665_nat_p=1. scratc390608475_power=1. scratc47587735nd_nat=1. scratc274252953d_repl=1. scratc7067394nd_imp=1. fTrue=1. scratc827056996d_pair=1. scratc684468331d_Subq=1. scratc212847509closed=1. scratc519122313_proj0=1. scratc897870341_union=1. aTP_Lamm_af=1. scratc456456521d_n_in=1. scratc519122314_proj1=1. scratc660593885_n_all=1. aTP_Lamm_ac=1. aTP_Lamm_ae=1. aTP_Lamm_jm=1. scratc1267447841closed=1. scratc1432180855closed=1. aTP_Lamm_aa=1. aTP_Lamm_bq=1. aTP_Lamm_gl=1. aTP_Lamm_gn=1. aTP_Lamm_gp=1. aTP_Lamm_gr=1. aTP_Lamm_gt=1. aTP_Lamm_gv=1. aTP_Lamm_gx=1. aTP_Lamm_gz=1. aTP_Lamm_hb=1. aTP_Lamm_hd=1. aTP_Lamm_hf=1. aTP_Lamm_hh=1. aTP_Lamm_jd=1. aTP_Lamm_jh=1. aTP_Lamm_ji=1. scratc1411225126d_Inj1=1. scratc17733107_prop2=1. scratc1836261175_omega=1. scratc801746418closed=1. aTP_Lamm_ag=1. aTP_Lamm_bg=1. aTP_Lamm_bi=1. aTP_Lamm_bj=1. aTP_Lamm_bx=1. aTP_Lamm_cb=1. aTP_Lamm_cf=1. aTP_Lamm_cj=1. aTP_Lamm_cn=1. aTP_Lamm_cr=1. aTP_Lamm_cv=1. aTP_Lamm_cz=1. aTP_Lamm_dc=1. aTP_Lamm_df=1. aTP_Lamm_di=1. aTP_Lamm_dl=1. aTP_Lamm_do=1. aTP_Lamm_dr=1. aTP_Lamm_du=1. aTP_Lamm_dx=1. aTP_Lamm_ea=1. aTP_Lamm_ed=1. aTP_Lamm_eh=1. aTP_Lamm_el=1. aTP_Lamm_ep=1. aTP_Lamm_et=1. aTP_Lamm_ew=1. aTP_Lamm_ez=1. aTP_Lamm_fc=1. aTP_Lamm_ff=1. aTP_Lamm_fi=1. aTP_Lamm_fl=1. aTP_Lamm_fp=1. aTP_Lamm_fr=1. aTP_Lamm_fu=1. aTP_Lamm_fx=1. aTP_Lamm_ga=1. aTP_Lamm_gd=1. aTP_Lamm_gg=1. aTP_Lamm_gj=1. aTP_Lamm_hj=1. aTP_Lamm_hl=1. aTP_Lamm_hn=1. aTP_Lamm_hp=1. aTP_Lamm_hr=1. aTP_Lamm_hv=1. aTP_Lamm_hx=1. aTP_Lamm_ia=1. aTP_Lamm_id=1. aTP_Lamm_if=1. aTP_Lamm_ih=1. aTP_Lamm_ik=1. aTP_Lamm_im=1. aTP_Lamm_ip=1. aTP_Lamm_is=1. aTP_Lamm_iv=1. aTP_Lamm_iy=1. aTP_Lamm_ja=1. aTP_Lamm_jb=1. aTP_Lamm_jg=1. fconj=1. fimplies=1. scratc1411225125d_Inj0=1. scratc17733106_prop1=1. scratc534239046_cond2=1. scratc586117449d_Sing=1. aTP_Lamm_bm=1. aTP_Lamm_br=1. aTP_Lamm_bs=1. aTP_Lamm_bt=1. aTP_Lamm_bu=1. aTP_Lamm_by=1. aTP_Lamm_cc=1. aTP_Lamm_cg=1. aTP_Lamm_ck=1. aTP_Lamm_co=1. aTP_Lamm_cs=1. aTP_Lamm_cw=1. aTP_Lamm_da=1. aTP_Lamm_dd=1. aTP_Lamm_dg=1. aTP_Lamm_dj=1. aTP_Lamm_dm=1. aTP_Lamm_dp=1. aTP_Lamm_ds=1. aTP_Lamm_dv=1. aTP_Lamm_dy=1. aTP_Lamm_eb=1. aTP_Lamm_ee=1. aTP_Lamm_ei=1. aTP_Lamm_em=1. aTP_Lamm_eq=1. aTP_Lamm_eu=1. aTP_Lamm_ex=1. aTP_Lamm_fa=1. aTP_Lamm_fd=1. aTP_Lamm_fg=1. aTP_Lamm_fj=1. aTP_Lamm_fm=1. aTP_Lamm_fn=1. aTP_Lamm_fo=1. aTP_Lamm_fq=1. aTP_Lamm_fs=1. aTP_Lamm_fv=1. aTP_Lamm_fy=1. aTP_Lamm_gb=1. aTP_Lamm_ge=1. aTP_Lamm_gh=1. aTP_Lamm_gk=1. aTP_Lamm_gm=1. aTP_Lamm_go=1. aTP_Lamm_gq=1. aTP_Lamm_gs=1. aTP_Lamm_gu=1. aTP_Lamm_gw=1. aTP_Lamm_gy=1. aTP_Lamm_ha=1. aTP_Lamm_hc=1. aTP_Lamm_he=1. aTP_Lamm_hg=1. aTP_Lamm_hi=1. aTP_Lamm_hk=1. aTP_Lamm_hm=1. aTP_Lamm_ho=1. aTP_Lamm_hq=1. aTP_Lamm_hs=1. aTP_Lamm_hw=1. aTP_Lamm_hy=1. aTP_Lamm_ib=1. aTP_Lamm_ie=1. aTP_Lamm_ig=1. aTP_Lamm_ii=1. aTP_Lamm_il=1. aTP_Lamm_in=1. aTP_Lamm_io=1. aTP_Lamm_iq=1. aTP_Lamm_ir=1. aTP_Lamm_it=1. aTP_Lamm_iu=1. aTP_Lamm_iw=1. aTP_Lamm_ix=1. aTP_Lamm_iz=1. aTP_Lamm_jc=1. aTP_Lamm_je=1. aTP_Lamm_jf=1. aTP_Lamm_jj=1. aTP_Lamm_jk=1. aTP_Lamm_jl=1. aTP_Lamm_jo=1. aTP_Lamm_kl=1. fequal_TPTP_ind=1. scratc1136482007_d_Unj=1. scratc420381799univof=1. scratc46013353nd_nIn=1. scratc534239045_cond1=1. scratc776386146_n_one=1. aTP_Lamm_ab=1. aTP_Lamm_ah=1. aTP_Lamm_bk=1. aTP_Lamm_bl=1. bool=1. scratc1194457456_prop1=1. scratc1269765891_empty=1. scratc1576854579_prop1=1. scratc1782819631_prop1=1. scratc435323114nempty=1. scratc501137484pair_p=1. scratc515168679munion=1. scratc519515911_prop4=1. scratc812060333_prop1=1. scratc918720740d_plus=1. scratc988492404_prop1=1. scratc1800640897d_i1_s=1. scratc527007787d_24_g=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. aa_fun1431113780TP_ind=1. aa_boo1142376798l_bool=1. scratc1235620061_d_and=1. aa_TPT1123896796d_bool=1. scratc995845351bnd_if=1. scratc324549184d_l_ec=1. aa_fun1212484691d_bool=1. aa_TPT985247859d_bool=1. scratc937796160d_e_in=1. scratc1681889716d_pair=1. aa_fun987228051d_bool=1. scratc7132981nd_ind=1. scratc997820912_amone=1. scratc1408280369_image=1. scratc1450922438_first=1. scratc1858738590second=1. aa_TPT125613450d_bool=1. scratc48506115nd_non=1. aa_fun1913827119d_bool=1. scratc2110288053d_anec=1. aa_TPT1791839040TP_ind=1. aa_fun1107270209d_bool=1. aa_fun845057962d_bool=1. scratc1909019605eplSep=1. scratc1962427141_ecelt=1. scratc2120849032nd_ecp=1. scratc1961836750_ecect=1. aa_TPT1781712639TP_ind=1. aa_TPT2142672771l_bool=1. aa_fun1235454963TP_ind=1. cOMBB_658106424TP_ind=1. cOMBS_2003118649l_bool=1. scratc1099522659wissel=1. scratc1231495862ectset=1. scratc1345559031etprop=1. scratc1499638682_fixfu=1. scratc2120849036nd_ect=1. scratc57161220nd_out=1. scratc719469336fixfu2=1. scratc1116293985ectelt=1. scratc1337613208unmore=1. scratc1913649887d_invf=1. scratc1917386418d_tofs=1. scratc42635206nverse=1. f5=1. f6=1. f11=1. f20=1. f21=1. scratc1561761582all_of=1. scratc456915712d_n_pl=1. scratc937796165d_e_is=1. scratc1343085241_d_not=1. scratc1119368612_d_Sep=1. scratc979961069d_esti=1. scratc672422390l_some=1. scratc1431625074ffprop=1. scratc2088393399nd_all=1. scratc325205189d_l_or=1. scratc503222518_rec_G=1. aTP_Lamm_ai=1. aTP_Lamm_jv=1. scratc56702012nd_one=1. aTP_Lamm_ak=1. aTP_Lamm_au=1. aTP_Lamm_bc=1. aTP_Lamm_bp=1. aTP_Lamm_bv=1. aTP_Lamm_bz=1. aTP_Lamm_cd=1. aTP_Lamm_ch=1. aTP_Lamm_cl=1. aTP_Lamm_cp=1. aTP_Lamm_ct=1. aTP_Lamm_cx=1. aTP_Lamm_ef=1. aTP_Lamm_ej=1. aTP_Lamm_en=1. aTP_Lamm_er=1. aTP_Lamm_ft=1. aTP_Lamm_fw=1. aTP_Lamm_fz=1. aTP_Lamm_gc=1. aTP_Lamm_gf=1. aTP_Lamm_gi=1. aTP_Lamm_ht=1. aTP_Lamm_jn=1. aTP_Lamm_kj=1. scratc1912403512d_incl=1. aTP_Lamm_ao=1. aTP_Lamm_ay=1. aTP_Lamm_bb=1. aTP_Lamm_bf=1. aTP_Lamm_db=1. aTP_Lamm_de=1. aTP_Lamm_dh=1. aTP_Lamm_dk=1. aTP_Lamm_dn=1. aTP_Lamm_dq=1. aTP_Lamm_dt=1. aTP_Lamm_dw=1. aTP_Lamm_dz=1. aTP_Lamm_ec=1. aTP_Lamm_ev=1. aTP_Lamm_ey=1. aTP_Lamm_fb=1. aTP_Lamm_fe=1. aTP_Lamm_fh=1. aTP_Lamm_fk=1. aTP_Lamm_hz=1. aTP_Lamm_ic=1. aTP_Lamm_kf=1. aTP_Lamm_kh=1. scratc1439398365ective=1. scratc2121701822nd_eps=1. scratc278310607etprod=1. aTP_Lamm_al=1. aTP_Lamm_am=1. aTP_Lamm_an=1. aTP_Lamm_ap=1. aTP_Lamm_aq=1. aTP_Lamm_as=1. aTP_Lamm_at=1. aTP_Lamm_az=1. aTP_Lamm_ba=1. aTP_Lamm_bd=1. aTP_Lamm_bw=1. aTP_Lamm_ca=1. aTP_Lamm_ce=1. aTP_Lamm_ci=1. aTP_Lamm_cm=1. aTP_Lamm_cq=1. aTP_Lamm_cu=1. aTP_Lamm_cy=1. aTP_Lamm_eg=1. aTP_Lamm_ek=1. aTP_Lamm_eo=1. aTP_Lamm_es=1. aTP_Lamm_hu=1. aTP_Lamm_ij=1. aTP_Lamm_jp=1. aTP_Lamm_jq=1. aTP_Lamm_jr=1. aTP_Lamm_jt=1. aTP_Lamm_jz=1. aTP_Lamm_kb=1. aTP_Lamm_kc=1. aTP_Lamm_kg=1. fEx_TPTP_ind=1. scratc1509025778nunion=1. scratc881304326ective=1. aTP_Lamm_ar=1. aTP_Lamm_js=1. aTP_Lamm_ju=1. aTP_Lamm_jw=1. aTP_Lamm_jx=1. aTP_Lamm_jy=1. aTP_Lamm_ka=1. aTP_Lamm_kd=1. aTP_Lamm_ke=1. aTP_Lamm_ki=1. aTP_Lamm_kk=1. scratc1636783185In_rec=1. scratc8352693_UPair=1. aTP_Lamm_ad=1. aTP_Lamm_av=1. aTP_Lamm_aw=1. aTP_Lamm_ax=1. aTP_Lamm_be=1. aTP_Lamm_bh=1. aTP_Lamm_bn=1. aTP_Lamm_bo=1. cOMBC_1555011498d_bool=1. scratc1425311320tminus=1. scratc1623117595ective=1. scratc1842147815t_disj=1. scratc223698158_prop1=1. scratc519515910_prop3=1. scratc606095281_prop1=1. undefined_bool=1. undefined_TPTP_ind=1. f2=1. f3=1. f7=1. f9=1. f10=1. f12=1. f18=1. f19=1. f22=1. f23=1. scratc56964358nd_or3=1. scratc2120848971nd_ec3=1. scratc1136799220d_soft=1. scratc519515908_prop1=1. scratc66037249_indeq=1. scratc7526576nd_ite=1. scratc1284928717sel_wa=1. scratc1284928718sel_wb=1. scratc1340649199d_11_i=1. f1=1. f4=1. f15Alarm clock 119.81/120.07 Prover9 interrupted 119.81/120.07 EOF