0.09/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.09/0.14 % Command : tptp2X_and_run_prover9 %d %s 0.10/0.35 % Computer : n009.cluster.edu 0.10/0.35 % Model : x86_64 x86_64 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.35 % Memory : 8042.1875MB 0.10/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.35 % CPULimit : 1440 0.10/0.35 % WCLimit : 180 0.10/0.35 % DateTime : Mon Jul 3 12:08:41 EDT 2023 0.10/0.35 % CPUTime : 0.85/1.19 ============================== Prover9 =============================== 0.85/1.19 Prover9 (32) version 2009-11A, November 2009. 0.85/1.19 Process 3467 was started by sandbox2 on n009.cluster.edu, 0.85/1.19 Mon Jul 3 12:08:42 2023 0.85/1.19 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1440 -f /tmp/Prover9_3313_n009.cluster.edu". 0.85/1.19 ============================== end of head =========================== 0.85/1.19 0.85/1.19 ============================== INPUT ================================= 0.85/1.19 0.85/1.19 % Reading from file /tmp/Prover9_3313_n009.cluster.edu 0.85/1.19 0.85/1.19 set(prolog_style_variables). 0.85/1.19 set(auto2). 0.85/1.19 % set(auto2) -> set(auto). 0.85/1.19 % set(auto) -> set(auto_inference). 0.85/1.19 % set(auto) -> set(auto_setup). 0.85/1.19 % set(auto_setup) -> set(predicate_elim). 0.85/1.19 % set(auto_setup) -> assign(eq_defs, unfold). 0.85/1.19 % set(auto) -> set(auto_limits). 0.85/1.19 % set(auto_limits) -> assign(max_weight, "100.000"). 0.85/1.19 % set(auto_limits) -> assign(sos_limit, 20000). 0.85/1.19 % set(auto) -> set(auto_denials). 0.85/1.19 % set(auto) -> set(auto_process). 0.85/1.19 % set(auto2) -> assign(new_constants, 1). 0.85/1.19 % set(auto2) -> assign(fold_denial_max, 3). 0.85/1.19 % set(auto2) -> assign(max_weight, "200.000"). 0.85/1.19 % set(auto2) -> assign(max_hours, 1). 0.85/1.19 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.85/1.19 % set(auto2) -> assign(max_seconds, 0). 0.85/1.19 % set(auto2) -> assign(max_minutes, 5). 0.85/1.19 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.85/1.19 % set(auto2) -> set(sort_initial_sos). 0.85/1.19 % set(auto2) -> assign(sos_limit, -1). 0.85/1.19 % set(auto2) -> assign(lrs_ticks, 3000). 0.85/1.19 % set(auto2) -> assign(max_megs, 400). 0.85/1.19 % set(auto2) -> assign(stats, some). 0.85/1.19 % set(auto2) -> clear(echo_input). 0.85/1.19 % set(auto2) -> set(quiet). 0.85/1.19 % set(auto2) -> clear(print_initial_clauses). 0.85/1.19 % set(auto2) -> clear(print_given). 0.85/1.19 assign(lrs_ticks,-1). 0.85/1.19 assign(sos_limit,10000). 0.85/1.19 assign(order,kbo). 0.85/1.19 set(lex_order_vars). 0.85/1.19 clear(print_given). 0.85/1.19 0.85/1.19 % formulas(sos). % not echoed (454 formulas) 0.85/1.19 0.85/1.19 ============================== end of input ========================== 0.85/1.19 0.85/1.19 % From the command line: assign(max_seconds, 1440). 0.85/1.19 0.85/1.19 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.85/1.19 0.85/1.19 % Formulas that are not ordinary clauses: 0.85/1.19 1 (all X all Xa (pp(scratc1091134429_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1315587074nd_imp,X),Xa),aa_bool_bool(aa_boo1142376798l_bool(scratc1315587074nd_imp,Xa),X))) <-> scratc1985275879_l_iff(X,Xa))) # label(fact_def__l__iff) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 2 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gd(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc326995781d_e_is(aa_TPTP_ind_TPTP_ind(scratc1158159311etprod(Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc414254772d_pair(Uu,Uua),aa_TPTP_ind_TPTP_ind(scratc840122054_first(Uu,Uua),Uub)),aa_TPTP_ind_TPTP_ind(scratc1714252958second(Uu,Uua),Uub))),Uub)))) # label(fact_ATP_Olambda__115) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 3 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1356632206nd_nis,X),Xa)) <-> pp(scratc1198599609_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,X),Xa))))) # label(fact_def__nis) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 4 (all X0 (scratc1430723348nd_wel(X0) -> pp(X0))) # label(fact_l__et) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 5 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(Uua,aa_TPTP_ind_TPTP_ind(scratc326995776d_e_in(Uu,Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_gk(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__150) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 6 (all X ((all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,aa_TPTP_ind_TPTP_ind(scratc1927291739_power,X1)),X))))) <-> pp(aa_TPTP_ind_bool(scratc1340156791closed,X)))) # label(fact_def__d__Power__closed) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 7 (all X all Xa (-pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1354533033nd_nIn,X),Xa)))) # label(fact_def__nIn) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 8 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_be(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bd(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__140) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 9 (all X all Xa (pp(aa_bool_bool(scratc1861888453d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1315324671nd_iii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc894897325lessis,X),Xa)))) # label(fact_def__lessis) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 10 (all Uu all Uua (pp(scratc1281885003nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1196184449_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1315324671nd_iii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dq,Uu),Uua)))) # label(fact_ATP_Olambda__62) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 11 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(scratc1909781293nd_n_1),Uu)),aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fb,Uu)))) # label(fact_ATP_Olambda__4) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 12 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_et,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_eu,Uu)))) # label(fact_ATP_Olambda__21) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 13 (all X all Xa scratc1340651108d_pair = scratc414254772d_pair(X,Xa)) # label(fact_def__d__pair) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 14 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_er,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_es,Uu)))) # label(fact_ATP_Olambda__22) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 15 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_br(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bs,Uu),Uua)))) # label(fact_ATP_Olambda__109) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 16 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1333275155d_d_Pi,X0),X12))) -> (all X32 (gg_TPTP_ind(X32) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X32),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1333275155d_d_Pi,X0),X12))) -> ((all X42 (gg_TPTP_ind(X42) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X42),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,X22),X42) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,X32),X42)))) -> X22 = X32))))))) # label(fact_k__Pi__ext) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 17 (all X all Xa scratc1365680900nd_out(aa_TPTP_ind_TPTP_ind(scratc1927291739_power,X),scratc476398517d_anec(X,Xa)) = scratc1087010230ectset(X,Xa)) # label(fact_def__ectset) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 18 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1701366896_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Xa),X))))) # label(fact_def__d__26__prop1) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 19 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(scratc1909781293nd_n_1),Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ev,Uu)))) # label(fact_ATP_Olambda__8) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 20 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fp,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fq,Uu)))) # label(fact_ATP_Olambda__16) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 21 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bb(Uu),Uua),Uub),Uuc)) <-> pp(aa_fun171081125l_bool(scratc1249429431nd_all(Uu),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_ba(Uu),Uua),Uub),Uuc))))) # label(fact_ATP_Olambda__165) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 22 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_do,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_dp,Uu)))) # label(fact_ATP_Olambda__34) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 23 pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1315587074nd_imp,fFalse),fFalse)) <-> scratc1787566557bvious # label(fact_def__obvious) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 24 (all P all Q (pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) | pp(P))) # label(help_fimplies_1_1_U) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 25 (all X all Xa scratc283496882d_tofs(X,Xa) = scratc1709815289bnd_ap) # label(fact_def__tofs) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 26 (all X all Xa (pp(aa_fun171081125l_bool(scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X)),scratc1357025795nd_non(X,aa_TPT43085870d_bool(aTP_Lamm_av(X),Xa)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc658965507_empty,X),Xa)))) # label(fact_def__empty) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 27 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_de,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_df,Uu)))) # label(fact_ATP_Olambda__39) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 28 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc971808353ectelt(X,Xa),Xb) = aa_TPTP_ind_TPTP_ind(scratc1087010230ectset(X,Xa),aa_TPTP_ind_TPTP_ind(scratc1351626757_ecelt(X,Xa),Xb))) # label(fact_def__ectelt) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 29 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (-pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc1710340071bnd_if(X0,X12),X22) = X22))) # label(fact_if__i__0) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 30 (all X0 (pp(aa_TPTP_ind_bool(scratc1990323033_nat_p,X0)) -> pp(aa_TPTP_ind_bool(scratc1990323033_nat_p,aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,X0))))) # label(fact_nat__ordsucc) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 31 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1196184449_29_ii,aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,Uu)),Uu)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_bv,Uu)))) # label(fact_ATP_Olambda__9) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 32 (all X scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X)) = scratc1249429431nd_all(X)) # label(fact_def__all) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 33 (all B_1 all B_2 gg_TPTP_ind(scratc1281885068nd_ect(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__46248__31143_ONUM671__thf__4__p_Obnd__ect) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 34 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc278513976d_incl(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1249429431nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_au(X),Xa),Xb))))) # label(fact_def__incl) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 35 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1316046256nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc326995781d_e_is(X),Xc),Xa),X,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc600229837sel_wa(X,Xa,Xb),Xc)) # label(fact_def__wissel__wa) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 36 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eo,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ep,Uu)))) # label(fact_ATP_Olambda__23) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 37 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc524642547_prop2,X),Xa)) <-> pp(scratc1091134429_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,Xa),scratc1909781293nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,X)),aa_TPTP_ind_bool(scratc524642546_prop1,Xa))))) # label(fact_def__d__24__prop2) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 38 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_au(Uu),Uua),Uub),Uuc)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1315587074nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1493555181d_esti(Uu),Uuc),Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1493555181d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__160) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 39 (all X0 all X12 pp(aa_fun171081125l_bool(scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X0)),aa_fun1584354236d_bool(aTP_Lamm_fw(X0),X12)))) # label(fact_estie) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 40 (all X all Xa (pp(scratc1091134429_d_and(X,Xa)) <-> pp(scratc1198599609_d_not(scratc1861232448d_l_ec(X,Xa))))) # label(fact_def__d__and) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 41 (all X all Xa (pp(aa_fun171081125l_bool(scratc148612088n_some,aa_TPT43085870d_bool(scratc708751474ffprop(X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1196184449_29_ii,X),Xa)))) # label(fact_def__d__29__ii) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 42 (all X all Xa all Xb aa_fun1431113780TP_ind(scratc974882980_d_Sep(X),aa_TPT43085870d_bool(Xa,Xb)) = aa_TPTP_ind_TPTP_ind(scratc1351626757_ecelt(X,Xa),Xb)) # label(fact_def__ecelt) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 43 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1927291739_power,X0))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564317035d_Subq,X12),X0)))) # label(fact_k__PowerEq) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 44 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dq,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_dr,Uu)))) # label(fact_ATP_Olambda__33) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 45 (all Uu (pp(aa_fun171081125l_bool(scratc1365221692nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1333275155d_d_Pi,scratc1356107415nd_nat),aTP_Lamm_ad)),aa_TPT43085870d_bool(aTP_Lamm_ff,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fg,Uu)))) # label(fact_ATP_Olambda__5) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 46 (all X0 (pp(aa_TPTP_ind_bool(scratc1990323033_nat_p,X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X0),scratc1225460791_omega)))) # label(fact_nat__p__omega) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 47 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dz,Uu)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dy,Uu))))) # label(fact_ATP_Olambda__29) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 48 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fy(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc326995781d_e_is(Uua),aa_TPTP_ind_TPTP_ind(scratc1714252958second(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc414254772d_pair(Uu,Uua),Uub),Uuc))),Uuc)))) # label(fact_ATP_Olambda__154) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 49 (all X all Xa all Xb scratc617775599d_11_i(X,Xa,Xb) = scratc1602720513_indeq(X,Xa,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1333275155d_d_Pi,X),aTP_Lamm_aj(Xb)))) # label(fact_def__d__11__i) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 50 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bs,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_bt,Uu)))) # label(fact_ATP_Olambda__54) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 51 (all X0 pp(aa_fun171081125l_bool(scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X0)),aa_TPT43085870d_bool(aTP_Lamm_gs,X0)))) # label(fact_refis) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 52 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bz,Uu)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_by,Uu))))) # label(fact_ATP_Olambda__52) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 53 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,Uub),aa_TPTP_ind_TPTP_ind(scratc1158159311etprod(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gc(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__147) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 54 (all B_1 gg_bool(scratc1198599609_d_not(B_1))) # label(gsy_c_Scratch__tptp__translate__46248__31143_ONUM671__thf__4__p_Obnd__d__not) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 55 (all X aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc787847065d_repl,X),scratc143590182d_Inj1) = aa_TPTP_ind_TPTP_ind(scratc143590181d_Inj0,X)) # label(fact_def__d__Inj0) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 56 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fo,Uu)) <-> (pp(aa_TPTP_ind_bool(scratc2070922309_cond1,Uu)) -> (pp(aa_TPTP_ind_bool(scratc2070922310_cond2,Uu)) -> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fn,Uu))))))) # label(fact_ATP_Olambda__6) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 57 (all X0 all X12 pp(aa_fun171081125l_bool(scratc294126638all_of(aa_fun1584354236d_bool(aTP_Lamm_gj(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_gl(X0),X12)))) # label(fact_e__in__p) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 58 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1315324671nd_iii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc148612088n_some,aa_TPT43085870d_bool(scratc708751474ffprop(Xa),X))))) # label(fact_def__iii) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 59 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fi,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1356632206nd_nis,Uu),scratc1909781293nd_n_1)) -> pp(aa_fun171081125l_bool(scratc148612088n_some,aa_TPT43085870d_bool(aTP_Lamm_ag,Uu)))))) # label(fact_ATP_Olambda__1) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 60 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1859933162nempty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1552271094l_some(X),aa_TPT43085870d_bool(aTP_Lamm_av(X),Xa))))) # label(fact_def__nonempty) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 61 (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]. 0.85/1.19 62 (all Uu all Uua ((pp(scratc1198599609_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1315324671nd_iii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1028880937moreis,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_da,Uu),Uua)))) # label(fact_ATP_Olambda__91) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 63 (all X all Xa all Xb (pp(aa_fun171081125l_bool(scratc1249429431nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_at(X),Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1119274215t_disj(X),Xa),Xb)))) # label(fact_def__st__disj) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 64 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bw,Uu))))) # label(fact_ATP_Olambda__53) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 65 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fz(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fy(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__143) # label(axiom) # label(non_clause). [assumption]. 0.85/1.19 66 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_du,Uu),Uua)) <-> scratc833167048_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1196184449_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1315324671nd_iii,Uu),Uua)))) # label(fact_ATP_Olambda__60) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 67 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_av(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1493555181d_esti(Uu),Uub),Uua)))) # label(fact_ATP_Olambda__118) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 68 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eh,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eg(Uu),Uua))))) # label(fact_ATP_Olambda__102) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 69 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bc(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,Uub),Uu)) & pp(aa_TPTP_ind_bool(Uua,Uub)))) # label(fact_ATP_Olambda__136) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 70 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1538476363_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,aa_TPTP_ind_TPTP_ind(scratc2055805577_proj0,X22)),X0)))) # label(fact_proj0__Sigma) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 71 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fh,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1356632206nd_nis,Uu),scratc1909781293nd_n_1)) -> pp(aa_fun171081125l_bool(scratc631900514_n_one,aa_TPT43085870d_bool(aTP_Lamm_ag,Uu)))))) # label(fact_ATP_Olambda__2) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 72 (all X aa_TPTP_ind_TPTP_ind(scratc2055805577_proj0,X) = aa_fun277296641TP_ind(scratc1224320725eplSep(X,aTP_Lamm_bk),scratc991996375_d_Unj)) # label(fact_def__proj0) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 73 (all X all Xa (pp(scratc1198599609_d_not(aa_fun171081125l_bool(scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X)),scratc1357025795nd_non(X,Xa)))) <-> pp(aa_fun171081125l_bool(scratc1552271094l_some(X),Xa)))) # label(fact_def__l__some) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 74 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_em,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_en,Uu)))) # label(fact_ATP_Olambda__24) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 75 (all Uu all Uua ((pp(scratc1198599609_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1196184449_29_ii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc894897325lessis,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dc,Uu),Uua)))) # label(fact_ATP_Olambda__88) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 76 (all Uu all Uua all Uub all Uuc (pp(scratc1861232448d_l_ec(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1493555181d_esti(Uu),Uuc),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1493555181d_esti(Uu),Uuc),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_at(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__159) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 77 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc922483910nverse(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1538476363_Sigma,Xa),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ay(X),Xa),Xb))) # label(fact_def__inverse) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 78 (all X0 all X12 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc240543453ective(aa_fun1431113780TP_ind(scratc974882980_d_Sep(X0),X12)),X0),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1538476363_Sigma,aa_fun1431113780TP_ind(scratc974882980_d_Sep(X0),X12)),scratc326995776d_e_in(X0,X12))))) # label(fact_otax1) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 79 (all Uu (gg_TPTP_ind(Uu) -> ((exists X2 (Uu = aa_TPTP_ind_TPTP_ind(scratc143590181d_Inj0,X2) & gg_TPTP_ind(X2))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_bk,Uu))))) # label(fact_ATP_Olambda__59) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 80 (all X all Xa scratc2055805577_proj0 = scratc840122054_first(X,Xa)) # label(fact_def__first) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 81 (all X all Xa all Xb all Xc all Xd scratc1315652661nd_ind(Xb,aa_TPT43085870d_bool(scratc2056199173_prop2(X,Xa,Xb,Xc),Xd)) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1602720513_indeq(X,Xa,Xb),Xc),Xd)) # label(fact_def__indeq) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 82 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc797479985_image(aa_fun1431113780TP_ind(scratc974882980_d_Sep(Uu),Uua),Uu),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1538476363_Sigma,aa_fun1431113780TP_ind(scratc974882980_d_Sep(Uu),Uua)),scratc326995776d_e_in(Uu,Uua))),Uub))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_gi(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__137) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 83 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1493555181d_esti(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,Uua),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ar(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__156) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 84 (all P (gg_bool(P) -> fFalse = P | P = fTrue)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 85 (all X0 all X12 pp(aa_fun171081125l_bool(scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_gm(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_gp(X0),X12)))) # label(fact_e__fisi) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 86 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc894897325lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc894897325lessis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc894897325lessis,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ca(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__130) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 87 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,Uua),Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ak,Uu),Uua)))) # label(fact_ATP_Olambda__99) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 88 (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(scratc1993139790d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,Uu),aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,Uu),Uua)))))) # label(fact_ATP_Olambda__71) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 89 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc797479985_image(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1552271094l_some(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_az(Xa),Xb),Xc))))) # label(fact_def__image) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 90 (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]. 0.85/1.20 91 (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]. 0.85/1.20 92 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Uu),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eg(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__125) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 93 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fu(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc278513976d_incl(Uu),Uua),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc278513976d_incl(Uu),Uub),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc326995781d_e_is(aa_TPTP_ind_TPTP_ind(scratc1927291739_power,Uu)),Uua),Uub)))))) # label(fact_ATP_Olambda__120) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 94 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ey,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Uu),scratc1909781293nd_n_1))))) # label(fact_ATP_Olambda__7) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 95 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1315324671nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc894897325lessis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1315324671nd_iii,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cj(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__134) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 96 (all Uu all Uua all Uub all Uuc (gg_TPTP_ind(Uua) & gg_TPTP_ind(Uub) & gg_TPTP_ind(Uuc) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bq(Uu),Uua),Uub),Uuc)) <-> Uuc = Uua & pp(Uu) | Uub = Uuc & -pp(Uu)))) # label(fact_ATP_Olambda__162) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 97 (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]. 0.85/1.20 98 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,X),Xb)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2056199174_prop3(X),Xa),Xb)))) # label(fact_def__prop3) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 99 (all X all Xa all Xb all Xc all Xd (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2056199172_prop1(X,Xa,Xb),Xc),Xd)) <-> pp(scratc1091134429_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1315587074nd_imp,X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc326995781d_e_is(Xa),Xd),Xb)),aa_bool_bool(aa_boo1142376798l_bool(scratc1315587074nd_imp,scratc1198599609_d_not(X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc326995781d_e_is(Xa),Xd),Xc)))))) # label(fact_def__prop1) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 100 (all X0 all X12 pp(aa_fun171081125l_bool(scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X0)),aa_fun1584354236d_bool(aTP_Lamm_fx(X0),X12)))) # label(fact_estii) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 101 (all Uu all Uua all Uub all Uuc all Uud all Uue (pp(aa_fun171081125l_bool(scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_am(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_an(Uu),Uua),Uub),Uuc),Uud),Uue)))) # label(fact_ATP_Olambda__172) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 102 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc142245423_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1356632206nd_nis,Xa),aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(X),Xa))))) # label(fact_def__d__27__prop1) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 103 (all X (pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1315587074nd_imp,X),fFalse)) <-> pp(scratc1198599609_d_not(X)))) # label(fact_def__d__not) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 104 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> X12 = aa_TPTP_ind_TPTP_ind(scratc1710340071bnd_if(X0,X12),X22) | X22 = aa_TPTP_ind_TPTP_ind(scratc1710340071bnd_if(X0,X12),X22))) # label(fact_if__i__or) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 105 (all B_1 all B_2 gg_bool(scratc1861232448d_l_ec(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__46248__31143_ONUM671__thf__4__p_Obnd__l__ec) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 106 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc1927291739_power,X0)))) # label(fact_k__Self__In__Power) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 107 (all B_1 all B_2 all B_3 gg_bool(scratc1365484038nd_or3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__46248__31143_ONUM671__thf__4__p_Obnd__or3) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 108 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc294126638all_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__104) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 109 (all X all Xa ((pp(X) -> pp(scratc1198599609_d_not(Xa))) <-> scratc108683590d_r_ec(X,Xa))) # label(fact_def__r__ec) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 110 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cy,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1196184449_29_ii,Uu),Uua)) -> pp(scratc1198599609_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc894897325lessis,Uu),Uua)))))) # label(fact_ATP_Olambda__79) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 111 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1196184449_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1315324671nd_iii,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_do,Uu),Uua)))) # label(fact_ATP_Olambda__75) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 112 (all X0 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X0),scratc1225460791_omega)) -> pp(aa_TPTP_ind_bool(scratc1990323033_nat_p,X0)))) # label(fact_omega__nat__p) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 113 (all X (gg_TPTP_ind(X) -> (pp(aa_TPTP_ind_bool(scratc1380986188pair_p,X)) <-> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1340651108d_pair,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,X),scratc1574338175ptyset)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,X),aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,scratc1574338175ptyset))) = X))) # label(fact_def__pair__p) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 114 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc326995781d_e_is(aa_TPTP_ind_TPTP_ind(scratc1927291739_power,X)),Xb),aa_TPTP_ind_TPTP_ind(scratc1351626757_ecelt(X,Xa),Xc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1281885064nd_ecp(X,Xa),Xb),Xc)))) # label(fact_def__ecp) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 115 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gb(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ga(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__142) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 116 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_go(Uu),Uua),Uub),Uuc)) <-> (pp(aa_fun171081125l_bool(scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gn(Uua),Uub),Uuc))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc326995781d_e_is(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1333275155d_d_Pi,Uu),aTP_Lamm_aj(Uua))),Uub),Uuc))))) # label(fact_ATP_Olambda__161) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 117 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_a,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,Uu),scratc1356107415nd_nat)))) # label(fact_ATP_Olambda__15) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 118 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ez,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fa,Uu)))) # label(fact_ATP_Olambda__19) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 119 (all X all Xa all Xb all Xc scratc1315652661nd_ind(X,aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_az(Xa),Xb),Xc)) = aa_TPTP_ind_TPTP_ind(scratc1650393332d_soft(X,Xa,Xb),Xc)) # label(fact_def__soft) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 120 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dj,Uu)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_di,Uu))))) # label(fact_ATP_Olambda__37) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 121 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc888838298_fixfu(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_aq(X),Xa),Xb),Xc))))) # label(fact_def__fixfu) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 122 (all Uu (gg_TPTP_ind(Uu) -> (Uu != scratc1574338175ptyset <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ai,Uu))))) # label(fact_ATP_Olambda__57) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 123 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ef,Uu)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ee,Uu))))) # label(fact_ATP_Olambda__27) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 124 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1927291739_power,X0))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564317035d_Subq,X12),X0)))) # label(fact_k__PowerE) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 125 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc275896167univof,X0)))) # label(fact_k__UnivOf__In) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 126 (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_ao(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_an(Uu),Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__169) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 127 (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]. 0.85/1.20 128 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ge(Uu),Uua),Uub)) <-> scratc2103678827_is_of(aa_TPTP_ind_TPTP_ind(scratc1714252958second(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_ak,Uua)))) # label(fact_ATP_Olambda__121) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 129 (all X0 all X12 (gg_TPTP_ind(X12) -> aa_TPTP_ind_TPTP_ind(scratc2055805578_proj1,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1340651108d_pair,X0),X12)) = X12)) # label(fact_proj1__pair__eq) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 130 (all X (pp(aa_TPTP_ind_bool(scratc1175423777closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,aa_TPTP_ind_TPTP_ind(scratc287069957_union,X1)),X))))))) # label(fact_def__d__Union__closed) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 131 (all X all Xa all Xb aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1538476363_Sigma,Xa),scratc1650393332d_soft(X,Xa,Xb)) = aa_TPTP_ind_TPTP_ind(scratc279760351d_invf(X,Xa),Xb)) # label(fact_def__invf) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 132 (all X (pp(aa_TPTP_ind_bool(scratc524642546_prop1,X)) <-> pp(aa_fun171081125l_bool(scratc516108253_n_all,aa_TPT43085870d_bool(aTP_Lamm_af,X))))) # label(fact_def__d__24__prop1) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 133 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1196184449_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1196184449_29_ii,aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_br(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__127) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 134 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ck,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cj(Uu),Uua))))) # label(fact_ATP_Olambda__105) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 135 (all P all Q (-pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)) | pp(Q))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 136 (all X0 all X12 pp(aa_fun171081125l_bool(scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X0)),aa_TPT43085870d_bool(aTP_Lamm_fz(X0),X12)))) # label(fact_secondis1) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 137 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ea(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__145) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 138 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gf(Uu),Uua),Uub)) <-> scratc2103678827_is_of(aa_TPTP_ind_TPTP_ind(scratc840122054_first(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_ak,Uu)))) # label(fact_ATP_Olambda__122) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 139 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,Uua),aa_TPTP_ind_TPTP_ind(scratc1927291739_power,Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ft,Uu),Uua)))) # label(fact_ATP_Olambda__96) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 140 (all X0 ((all X13 (gg_TPTP_ind(X13) -> ((all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_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]. 0.85/1.20 141 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ej(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ek,Uu),Uua)))) # label(fact_ATP_Olambda__101) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 142 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1356632206nd_nis,aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,Uu)),scratc1909781293nd_n_1)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fr,Uu)))) # label(fact_ATP_Olambda__12) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 143 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ei,Uu)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eh,Uu))))) # label(fact_ATP_Olambda__26) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 144 (all X0 all X12 pp(aa_fun171081125l_bool(scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X0)),aa_TPT43085870d_bool(aTP_Lamm_gb(X0),X12)))) # label(fact_firstis1) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 145 (all X all Xa all Xb all Xc all Xd scratc358493553indeq2(X,Xa,Xb,Xc,Xd) = aa_TPT1424761345TP_ind(scratc1602720513_indeq(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc617775599d_11_i(X,Xa,Xb),Xc),Xd))) # label(fact_def__indeq2) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 146 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ec,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ed,Uu)))) # label(fact_ATP_Olambda__28) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 147 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc1224320725eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bh,Xa)),scratc2055805578_proj1)) # label(fact_def__ap) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 148 (all X0 all X12 all X22 (gg_TPTP_ind(X12) -> (pp(X0) -> X12 = aa_TPTP_ind_TPTP_ind(scratc1710340071bnd_if(X0,X12),X22)))) # label(fact_if__i__1) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 149 (all X0 all X12 pp(aa_fun171081125l_bool(scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_gc(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_gf(X0),X12)))) # label(fact_first__p) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 150 (all Uu all Uua aa_TPTP_ind_TPTP_ind(scratc786152178nunion(aa_TPTP_ind_TPTP_ind(scratc1465966153d_Sing,scratc1574338175ptyset)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc787847065d_repl,Uu),Uua)) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(aTP_Lamm_bm,Uu),Uua)) # label(fact_ATP_Olambda__92) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 151 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_gr(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_gq(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__139) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 152 (all X aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc786152178nunion(X),aa_TPTP_ind_TPTP_ind(scratc1465966153d_Sing,X))) # label(fact_def__ordsucc) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 153 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc294126638all_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__108) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 154 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cz,Uu)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cy,Uu))))) # label(fact_ATP_Olambda__42) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 155 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc326995781d_e_is(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,Uua),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_az(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__157) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 156 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_du,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_dv,Uu)))) # label(fact_ATP_Olambda__31) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 157 (all X0 all X12 pp(aa_fun171081125l_bool(scratc294126638all_of(aa_fun1584354236d_bool(aTP_Lamm_gj(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_gk(X0),X12)))) # label(fact_e__inp) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 158 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_gl(Uu),Uua),Uub)) <-> scratc2103678827_is_of(aa_TPTP_ind_TPTP_ind(scratc326995776d_e_in(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_ak,Uu)))) # label(fact_ATP_Olambda__123) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 159 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eq(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__126) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 160 (all X (pp(aa_fun171081125l_bool(scratc1552271094l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1333275155d_d_Pi,scratc1356107415nd_nat),aTP_Lamm_ad)),aa_TPT43085870d_bool(scratc524642547_prop2,X))) <-> pp(aa_TPTP_ind_bool(scratc2056199175_prop4,X)))) # label(fact_def__prop4) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 161 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bw,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1315324671nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__94) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 162 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X22),X0)) -> (all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X32),aa_TPTP_ind_TPTP_ind(X12,X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1340651108d_pair,X22),X32)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1538476363_Sigma,X0),X12))))))) # label(fact_pair__Sigma) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 163 (all X all Xa (scratc700247083d_orec(X,Xa) <-> pp(scratc1091134429_d_and(aa_bool_bool(scratc1861888453d_l_or(X),Xa),scratc1861232448d_l_ec(X,Xa))))) # label(fact_def__orec) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 164 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ch,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cg(Uu),Uua))))) # label(fact_ATP_Olambda__106) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 165 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eo,Uu),Uua)))) # label(fact_ATP_Olambda__74) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 166 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1316046256nd_ite(X,Xa,Xb),Xc) = scratc1315652661nd_ind(Xa,aa_TPT43085870d_bool(scratc2056199172_prop1(X,Xa,Xb),Xc))) # label(fact_def__ite) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 167 (all X (pp(aa_TPTP_ind_bool(scratc1990323033_nat_p,X)) <-> (all X1 (pp(aa_TPTP_ind_bool(X1,scratc1574338175ptyset)) -> ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(X1,X2)) -> pp(aa_TPTP_ind_bool(X1,aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,X2)))))) -> pp(aa_TPTP_ind_bool(X1,X))))))) # label(fact_def__nat__p) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 168 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X22),aa_fun1431113780TP_ind(scratc974882980_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X22),X0)))) # label(fact_k__SepE1) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 169 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ac,Uu)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ab,Uu))))) # label(fact_ATP_Olambda__55) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 170 (all X scratc1993598976d_n_pl(X) = aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1432314852d_plus,X))) # label(fact_def__n__pl) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 171 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ag,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,Uua))))) # label(fact_ATP_Olambda__95) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 172 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1315324671nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,Uu))))) # label(fact_ATP_Olambda__13) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 173 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bi(Uu),Uua) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc787847065d_repl,aa_TPTP_ind_TPTP_ind(Uu,Uua)),aa_TPT1424761345TP_ind(scratc1340651108d_pair,Uua))) # label(fact_ATP_Olambda__84) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 174 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cu,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cv,Uu)))) # label(fact_ATP_Olambda__44) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 175 (all X0 (gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(scratc1990323033_nat_p,X0)) -> (exists X13 (aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,X13) = X0 & pp(aa_TPTP_ind_bool(scratc1990323033_nat_p,X13)) & gg_TPTP_ind(X13))) | X0 = scratc1574338175ptyset))) # label(fact_nat__inv) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 176 (all X (pp(aa_TPTP_ind_bool(scratc1175423777closed,X)) & pp(aa_TPTP_ind_bool(scratc1340156791closed,X)) & pp(aa_TPTP_ind_bool(scratc352794773closed,X)) <-> pp(aa_TPTP_ind_bool(scratc1917295346closed,X)))) # label(fact_def__d__ZF__closed) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 177 (all Uu all Uua all Uub all Uuc all Uud aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,aa_TPTP_ind_TPTP_ind(scratc955037027wissel(Uu,Uub),Uuc)),Uud)) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_aw(Uu),Uua),Uub),Uuc),Uud)) # label(fact_ATP_Olambda__171) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 178 (all X all Xa all Xb (scratc476332870d_and3(scratc1861232448d_l_ec(X,Xa),scratc1861232448d_l_ec(Xa,Xb),scratc1861232448d_l_ec(Xb,X)) <-> pp(scratc1281885003nd_ec3(X,Xa,Xb)))) # label(fact_def__ec3) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 179 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_fun171081125l_bool(scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_ap(Uua),Uub),Uuc),Uud))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_aq(Uu),Uua),Uub),Uuc),Uud)))) # label(fact_ATP_Olambda__170) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 180 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_da,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_db,Uu)))) # label(fact_ATP_Olambda__41) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 181 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dg,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_dh,Uu)))) # label(fact_ATP_Olambda__38) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 182 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc730607598_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1356632206nd_nis,aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(X),Xb))))) # label(fact_def__d__28__prop1) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 183 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X33),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,aa_TPTP_ind_TPTP_ind(X22,X33)),aa_TPTP_ind_TPTP_ind(X12,X33)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1538476363_Sigma,X0),X22)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1333275155d_d_Pi,X0),X12))))) # label(fact_lam__Pi) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 184 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ex,Uu)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ew,Uu))))) # label(fact_ATP_Olambda__20) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 185 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ga(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc326995781d_e_is(Uu),aa_TPTP_ind_TPTP_ind(scratc840122054_first(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc414254772d_pair(Uu,Uua),Uub),Uuc))),Uub)))) # label(fact_ATP_Olambda__153) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 186 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cs,Uu),Uua)) <-> (pp(scratc1198599609_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc894897325lessis,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1196184449_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__90) # label(axiom) # label(non_clause). [assumption]. 0.85/1.20 187 (all X aa_TPTP_ind_TPTP_ind(scratc1432314852d_plus,X) = scratc1315652661nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1333275155d_d_Pi,scratc1356107415nd_nat),aTP_Lamm_ad),aa_TPT43085870d_bool(scratc524642547_prop2,X))) # label(fact_def__plus) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 188 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__132) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 189 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc952084305In_rec(X),Xa) = scratc1282737854nd_eps(aa_TPT43085870d_bool(scratc1618771446_rec_G(X),Xa))) # label(fact_def__d__In__rec) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 190 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fd,Uu)))) # label(fact_ATP_Olambda__18) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 191 (all X0 all X12 pp(aa_fun171081125l_bool(scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X0)),aa_fun1584354236d_bool(aTP_Lamm_gi(X0),X12)))) # label(fact_otax2) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 192 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564317035d_Subq,X0),X12)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564317035d_Subq,X12),X0)) -> X12 = X0)))) # label(fact_set__ext) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 193 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1316046256nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc326995781d_e_is(X),Xc),Xb),X,Xa),aa_TPTP_ind_TPTP_ind(scratc600229837sel_wa(X,Xa,Xb),Xc)) = aa_TPTP_ind_TPTP_ind(scratc600229838sel_wb(X,Xa,Xb),Xc)) # label(fact_def__wissel__wb) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 194 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> ((exists X3 (gg_TPTP_ind(X3) & X22 = aa_TPTP_ind_TPTP_ind(X12,X3) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X3),X0)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc787847065d_repl,X0),X12)))))) # label(fact_k__ReplEq) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 195 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc240543453ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1249429431nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bb(X),Xa),Xb))))) # label(fact_def__injective) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 196 (all Uu all Uua (gg_TPTP_ind(Uua) -> ((exists X3 (gg_TPTP_ind(X3) & aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1340651108d_pair,Uu),X3) = Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bh,Uu),Uua))))) # label(fact_ATP_Olambda__114) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 197 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cs,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ct,Uu)))) # label(fact_ATP_Olambda__45) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 198 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gp(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_gm(Uu),Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_go(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__124) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 199 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_em,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1356632206nd_nis,Uua),aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__93) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 200 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc326995781d_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_gq(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__163) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 201 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_dd,Uu)))) # label(fact_ATP_Olambda__40) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 202 (all X scratc326995781d_e_is(X) = fequal_TPTP_ind) # label(fact_def__e__is) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 203 (all X0 all X12 pp(aa_fun171081125l_bool(scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X0)),aa_fun1584354236d_bool(aTP_Lamm_gr(X0),X12)))) # label(fact_e__isp) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 204 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gm(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,Uub),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1333275155d_d_Pi,Uu),aTP_Lamm_aj(Uua)))))) # label(fact_ATP_Olambda__144) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 205 (all Uu all Uua (scratc833167048_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc148612088n_some,aa_TPT43085870d_bool(aTP_Lamm_ea(Uu),Uua)),aa_fun171081125l_bool(scratc148612088n_some,aa_TPT43085870d_bool(aTP_Lamm_eb(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ec,Uu),Uua)))) # label(fact_ATP_Olambda__63) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 206 (all Uu all Uua aa_TPTP_ind_TPTP_ind(scratc287069957_union,aa_TPTP_ind_TPTP_ind(Uu,Uua)) = aa_TPTP_ind_TPTP_ind(aTP_Lamm_bf(Uu),Uua)) # label(fact_ATP_Olambda__113) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 207 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1356632206nd_nis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1356632206nd_nis,aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ej(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__133) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 208 (all Uu all Uua (pp(scratc1365484038nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1196184449_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1315324671nd_iii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ds,Uu),Uua)))) # label(fact_ATP_Olambda__61) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 209 (all X all Xa all Xb (scratc476332870d_and3(X,Xa,Xb) <-> pp(scratc1091134429_d_and(X,scratc1091134429_d_and(Xa,Xb))))) # label(fact_def__and3) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 210 (all X all Xa all Xb all Xc all Xd all Xe (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2056199173_prop2(X,Xa,Xb,Xc),Xd),Xe)) <-> pp(aa_fun171081125l_bool(scratc1552271094l_some(X),aa_TPT43085870d_bool(scratc1071965173_prop1(X,Xa,Xb,Xc,Xd),Xe))))) # label(fact_def__prop2) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 211 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fv,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_ft,Uu)),aa_TPT43085870d_bool(aTP_Lamm_fu(Uu),Uua))))) # label(fact_ATP_Olambda__85) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 212 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gh(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gg(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__141) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 213 (all X0 all X12 all X22 ((pp(X0) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X12),X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,aa_TPTP_ind_TPTP_ind(scratc1710340071bnd_if(X0,X12),scratc1574338175ptyset)),aa_TPTP_ind_TPTP_ind(scratc1710340071bnd_if(X0,X22),aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,scratc1574338175ptyset)))))) # label(fact_k__If__In__01) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 214 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1538476363_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1340651108d_pair,aa_TPTP_ind_TPTP_ind(scratc2055805577_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc2055805578_proj1,X22)) = X22))) # label(fact_proj__Sigma__eta) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 215 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1318969773_prop1,X),Xa)) <-> pp(scratc1365484038nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1196184449_29_ii,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1315324671nd_iii,X),Xa))))) # label(fact_def__d__29__prop1) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 216 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_fun1235454963TP_ind(aTP_Lamm_bo(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc1710340071bnd_if(aa_TPTP_ind_bool(Uua,Uub),Uub),scratc1282737854nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bc(Uu),Uua)))) # label(fact_ATP_Olambda__117) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 217 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1432962741_UPair(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc787847065d_repl,aa_TPTP_ind_TPTP_ind(scratc1927291739_power,aa_TPTP_ind_TPTP_ind(scratc1927291739_power,scratc1574338175ptyset))),aa_TPT1424761345TP_ind(aTP_Lamm_bp(X),Xa))) # label(fact_def__d__UPair) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 218 (all Uu aa_TPT494704832TP_ind(aTP_Lamm_bl,Uu) = aa_TPT494704832TP_ind(scratc787847065d_repl,aa_TPTP_ind_TPTP_ind(scratc702437720tminus(Uu),aa_TPTP_ind_TPTP_ind(scratc1465966153d_Sing,scratc1574338175ptyset)))) # label(fact_ATP_Olambda__56) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 219 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1493555181d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc974882980_d_Sep(Uu),Uua))) -> pp(aa_TPTP_ind_bool(Uua,Uub))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_fw(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__119) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 220 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,Uu)),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_et,Uu),Uua)))) # label(fact_ATP_Olambda__86) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 221 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fs,Uu)) <-> scratc2103678827_is_of(aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,Uu),aTP_Lamm_a))) # label(fact_ATP_Olambda__11) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 222 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_by,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1196184449_29_ii,aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Uu),Uua)),Uu)))) # label(fact_ATP_Olambda__83) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 223 (all X0 all X12 all X22 all X32 (pp(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1710340071bnd_if(X0,X22),X32))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X12),X22))))) # label(fact_k__If__In__then__E) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 224 (all X0 all X12 pp(aa_fun171081125l_bool(scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X0)),aa_TPT43085870d_bool(aTP_Lamm_gh(X0),X12)))) # label(fact_e__pair__p) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 225 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1538476363_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,aa_TPTP_ind_TPTP_ind(scratc2055805578_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc2055805577_proj0,X22)))) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,aa_TPTP_ind_TPTP_ind(scratc2055805577_proj0,X22)),X0)) & X22 = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1340651108d_pair,aa_TPTP_ind_TPTP_ind(scratc2055805577_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc2055805578_proj1,X22))))) # label(fact_k__Sigma__eta__proj0__proj1) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 226 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139785d_n_in,Uua),Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fn,Uu),Uua)))) # label(fact_ATP_Olambda__97) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 227 (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]. 0.85/1.21 228 (all B_1 all B_2 gg_TPTP_ind(scratc1315652661nd_ind(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__46248__31143_ONUM671__thf__4__p_Obnd__ind) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 229 (all Uu all Uua all Uub all Uuc all Uud all Uue all Uuf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_am(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_al(Uua),Uub),Uuc),Uud),Uue),Uuf))))) # label(fact_ATP_Olambda__174) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 230 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_fx(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1493555181d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc974882980_d_Sep(Uu),Uua)))))) # label(fact_ATP_Olambda__138) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 231 (all Uu all Uua all Uub ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X3),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,Uub),X3)),aa_TPTP_ind_TPTP_ind(Uua,X3)))))) <-> pp(aa_TPTP_ind_bool(aa_fun1913827119d_bool(aTP_Lamm_bg(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__151) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 232 (all Uu all Uua (pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1315587074nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139785d_n_in,Uua),Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139785d_n_in,aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,Uua)),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ah,Uu),Uua)))) # label(fact_ATP_Olambda__73) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 233 (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]. 0.85/1.21 234 (all X all Xa all Xb all Xc all Xd aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1538476363_Sigma,X),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_aw(X),Xb),Xc),Xd)) = aa_TPTP_ind_TPTP_ind(scratc936442860hangef(X,Xa,Xb,Xc),Xd)) # label(fact_def__changef) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 235 (all B_1 all B_2 gg_bool(scratc387020528_amone(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__46248__31143_ONUM671__thf__4__p_Obnd__amone) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 236 (all Uu all Uua (pp(scratc387020528_amone(scratc1356107415nd_nat,aa_TPT43085870d_bool(aTP_Lamm_ea(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ee,Uu),Uua)))) # label(fact_ATP_Olambda__111) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 237 (all X0 all X12 all X22 all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1333275155d_d_Pi,X0),X12))) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X32),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,X22),X32)),aa_TPTP_ind_TPTP_ind(X12,X32)))))) # label(fact_ap__Pi) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 238 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc894897325lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1315324671nd_iii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1315324671nd_iii,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cm(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__131) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 239 (all B_1 gg_TPTP_ind(scratc1282737854nd_eps(B_1))) # label(gsy_c_Scratch__tptp__translate__46248__31143_ONUM671__thf__4__p_Obnd__eps) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 240 (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_ap(Uu),Uua),Uub),Uuc),Uud)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc326995781d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,Uub),Uud)))))) # label(fact_ATP_Olambda__168) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 241 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dx,Uu)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dw,Uu))))) # label(fact_ATP_Olambda__30) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 242 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1028880937moreis,X),Xa)) <-> pp(aa_bool_bool(scratc1861888453d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1196184449_29_ii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,X),Xa))))) # label(fact_def__moreis) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 243 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1939778727munion,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc287069957_union,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc787847065d_repl,X),Xa))) # label(fact_def__famunion) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 244 (all X all Xa all Xb ((all X3 ((all X4 all X5 (gg_TPTP_ind(X4) -> ((all X6 (gg_TPTP_ind(X6) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X6),X4)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(X3,X6),aa_TPTP_ind_TPTP_ind(X5,X6)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(X3,X4),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(X,X4),X5)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(X3,Xa),Xb)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1618771446_rec_G(X),Xa),Xb)))) # label(fact_def__d__In__rec__G) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 245 (all X all Xa aa_TPT494704832TP_ind(scratc787847065d_repl,aa_fun1431113780TP_ind(scratc974882980_d_Sep(X),Xa)) = scratc1224320725eplSep(X,Xa)) # label(fact_def__d__ReplSep) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 246 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1158159311etprod(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1538476363_Sigma,X),aTP_Lamm_aj(Xa))) # label(fact_def__setprod) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 247 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1538476363_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,aa_TPTP_ind_TPTP_ind(scratc2055805578_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc2055805577_proj0,X22)))))) # label(fact_proj1__Sigma) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 248 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fl,Uu)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fk,Uu))))) # label(fact_ATP_Olambda__17) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 249 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gg(Uu),Uua),Uub),Uuc)) <-> scratc2103678827_is_of(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc414254772d_pair(Uu,Uua),Uub),Uuc),aa_TPT43085870d_bool(aTP_Lamm_gc(Uu),Uua)))) # label(fact_ATP_Olambda__158) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 250 (all X (scratc1430723348nd_wel(X) <-> pp(scratc1198599609_d_not(scratc1198599609_d_not(X))))) # label(fact_def__wel) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 251 (all X all Xa scratc1282737854nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bc(X),Xa)) = scratc1315652661nd_ind(X,Xa)) # label(fact_def__ind) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 252 (all B_1 gg_bool(fEx_TPTP_ind(B_1))) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 253 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bd(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(scratc326995781d_e_is(Uu),Uub),Uuc)))))) # label(fact_ATP_Olambda__164) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 254 (all Uu all Uua (pp(scratc1365484038nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc148612088n_some,aa_TPT43085870d_bool(scratc708751474ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc148612088n_some,aa_TPT43085870d_bool(scratc708751474ffprop(Uua),Uu)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dy,Uu),Uua)))) # label(fact_ATP_Olambda__64) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 255 (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]. 0.85/1.21 256 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ek,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_el,Uu)))) # label(fact_ATP_Olambda__25) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 257 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X22),aa_fun1431113780TP_ind(scratc974882980_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(X12,X22)))) # label(fact_k__SepE2) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 258 (all X (pp(aa_fun171081125l_bool(scratc516108253_n_all,aa_TPT43085870d_bool(aTP_Lamm_ah,X))) <-> pp(aa_TPTP_ind_bool(scratc2070922310_cond2,X)))) # label(fact_def__cond2) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 259 (all Uu all Uua (gg_TPTP_ind(Uu) -> aa_TPTP_ind_TPTP_ind(aTP_Lamm_aj(Uu),Uua) = Uu)) # label(fact_ATP_Olambda__175) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 260 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cc,Uu)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cb,Uu))))) # label(fact_ATP_Olambda__51) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 261 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1315324671nd_iii,Uu),Uua)) -> pp(scratc1198599609_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1028880937moreis,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cw,Uu),Uua)))) # label(fact_ATP_Olambda__82) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 262 (all X0 pp(aa_TPTP_ind_bool(scratc1917295346closed,aa_TPTP_ind_TPTP_ind(scratc275896167univof,X0)))) # label(fact_k__UnivOf__ZF__closed) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 263 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fc,Uu),Uua)))) # label(fact_ATP_Olambda__70) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 264 (all X all Xa aa_fun1431113780TP_ind(scratc974882980_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1927291739_power,X)),scratc476398517d_anec(X,Xa)) = scratc1281885068nd_ect(X,Xa)) # label(fact_def__ect) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 265 (all X all Xa all Xb all Xc all Xd aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1538476363_Sigma,X),aa_TPT1424761345TP_ind(aTP_Lamm_ax(Xc),Xd)) = aa_TPTP_ind_TPTP_ind(scratc696299693_inj_h(X,Xa,Xb,Xc),Xd)) # label(fact_def__inj__h) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 266 (all X0 all X12 pp(aa_fun171081125l_bool(scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_gc(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_ge(X0),X12)))) # label(fact_second__p) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 267 (all X all Xa all Xb (pp(scratc1198599609_d_not(aa_TPTP_ind_bool(Xa,Xb))) <-> pp(aa_TPTP_ind_bool(scratc1357025795nd_non(X,Xa),Xb)))) # label(fact_def__non) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 268 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ds,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_dt,Uu)))) # label(fact_ATP_Olambda__32) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 269 (all X0 aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,X0) != scratc1574338175ptyset) # label(fact_neq__ordsucc__0) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 270 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc955037027wissel(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1538476363_Sigma,X),scratc600229838sel_wb(X,Xa,Xb))) # label(fact_def__wissel) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 271 (all X all Xa (pp(aa_fun171081125l_bool(scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X)),aa_fun1584354236d_bool(aTP_Lamm_be(X),Xa))) <-> pp(scratc387020528_amone(X,Xa)))) # label(fact_def__amone) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 272 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc476398517d_anec(X,Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1552271094l_some(X),aa_TPT43085870d_bool(scratc1281885064nd_ecp(X,Xa),Xb))))) # label(fact_def__anec) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 273 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc326995781d_e_is(Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,Uua),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,Uub),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gn(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__155) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 274 (all X0 (pp(aa_TPTP_ind_bool(X0,scratc1574338175ptyset)) -> ((all X13 (gg_TPTP_ind(X13) -> (pp(aa_TPTP_ind_bool(scratc1990323033_nat_p,X13)) -> (pp(aa_TPTP_ind_bool(X0,X13)) -> pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,X13))))))) -> (all X12 (pp(aa_TPTP_ind_bool(scratc1990323033_nat_p,X12)) -> pp(aa_TPTP_ind_bool(X0,X12))))))) # label(fact_nat__ind) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 275 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_gj(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,Uub),aa_fun1431113780TP_ind(scratc974882980_d_Sep(Uu),Uua))))) # label(fact_ATP_Olambda__148) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 276 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1356632206nd_nis,aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,Uu)),Uu)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fj,Uu)))) # label(fact_ATP_Olambda__10) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 277 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1028880937moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc894897325lessis,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dk,Uu),Uua)))) # label(fact_ATP_Olambda__76) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 278 (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_al(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(scratc326995781d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,Uub),Uuc)),Uue)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,Uub),Uud)),Uuf))))))) # label(fact_ATP_Olambda__173) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 279 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1356632206nd_nis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1356632206nd_nis,aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fk,Uu),Uua)))) # label(fact_ATP_Olambda__72) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 280 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc660860151etprop(X,Xa),Xb),Xc)) <-> pp(scratc1091134429_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1493555181d_esti(X),Xc),Xa),scratc1198599609_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1493555181d_esti(X),Xc),Xb)))))) # label(fact_def__nissetprop) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 281 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dk,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_dl,Uu)))) # label(fact_ATP_Olambda__36) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 282 (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]. 0.85/1.21 283 (all X all Xa all Xb all Xc all Xd all Xe all Xf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1071965173_prop1(X,Xa,Xb,Xc,Xd),Xe),Xf)) <-> pp(scratc1091134429_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1493555181d_esti(X),Xf),aa_TPTP_ind_TPTP_ind(scratc1351036366_ecect(X,Xa),Xd)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc326995781d_e_is(Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,Xc),Xf)),Xe))))) # label(fact_def__d__10__prop1) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 284 (all X all Xa ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X2),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X2),Xa))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564317035d_Subq,X),Xa)))) # label(fact_def__d__Subq) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 285 (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]. 0.85/1.21 286 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cp(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cq,Uu),Uua)))) # label(fact_ATP_Olambda__103) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 287 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(scratc1710340071bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc797479985_image(Uu,Uua),Uub),Uuc),aa_TPTP_ind_TPTP_ind(scratc1650393332d_soft(Uu,Uua,Uub),Uuc)),scratc1574338175ptyset) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ay(Uu),Uua),Uub),Uuc)) # label(fact_ATP_Olambda__152) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 288 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X33),X0)) -> aa_TPTP_ind_TPTP_ind(X22,X33) = aa_TPTP_ind_TPTP_ind(X12,X33)))) -> aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1538476363_Sigma,X0),X12) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1538476363_Sigma,X0),X22))) # label(fact_xi__ext) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 289 (all P all X7 (pp(fEx_TPTP_ind(P)) | -pp(aa_TPTP_ind_bool(P,X7)))) # label(help_fEx_1_1_fEx_001t__TPTP____Interpret__Oind_U) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 290 (all X aa_boo1142376798l_bool(scratc1315587074nd_imp,scratc1198599609_d_not(X)) = scratc1861888453d_l_or(X)) # label(fact_def__l__or) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 291 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dm,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1315324671nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1196184449_29_ii,Uua),Uu))))) # label(fact_ATP_Olambda__78) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 292 (all X scratc1710340079bnd_in = scratc1493555181d_esti(X)) # label(fact_def__esti) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 293 (all X all Xa (scratc2103678827_is_of(X,Xa) <-> pp(aa_TPTP_ind_bool(Xa,X)))) # label(fact_def__is__of) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 294 (all X0 pp(aa_fun171081125l_bool(scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_ft,X0)),aa_TPT43085870d_bool(aTP_Lamm_fv,X0)))) # label(fact_isseti) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 295 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X22),X0)) -> (pp(aa_TPTP_ind_bool(X12,X22)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X22),aa_fun1431113780TP_ind(scratc974882980_d_Sep(X0),X12)))))) # label(fact_k__SepI) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 296 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_ax(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,Uu),Uub))) # label(fact_ATP_Olambda__149) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 297 (all Uu all Uua ((pp(scratc1198599609_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1028880937moreis,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1315324671nd_iii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cu,Uu),Uua)))) # label(fact_ATP_Olambda__89) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 298 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc1365221692nd_one(X0),X12)) -> pp(aa_TPTP_ind_bool(X12,scratc1315652661nd_ind(X0,X12))))) # label(fact_oneax) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 299 (all X all Xa all Xb (pp(scratc1091134429_d_and(scratc1365484038nd_or3(X,Xa,Xb),scratc1281885003nd_ec3(X,Xa,Xb))) <-> scratc833167048_orec3(X,Xa,Xb))) # label(fact_def__orec3) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 300 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cg(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1028880937moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1196184449_29_ii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1196184449_29_ii,Uu),Uub)))))) # label(fact_ATP_Olambda__129) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 301 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ch,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ci,Uu)))) # label(fact_ATP_Olambda__49) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 302 (all X0 all X12 (gg_TPTP_ind(X0) -> X0 = aa_TPTP_ind_TPTP_ind(scratc2055805577_proj0,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1340651108d_pair,X0),X12)))) # label(fact_proj0__pair__eq) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 303 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc786152178nunion(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc787847065d_repl,X),scratc143590181d_Inj0)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc787847065d_repl,Xa),scratc143590182d_Inj1)) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1340651108d_pair,X),Xa)) # label(fact_def__pair) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 304 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc326995781d_e_is(Uu),Uua),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gs,Uu),Uua)))) # label(fact_ATP_Olambda__66) # label(axiom) # label(non_clause). [assumption]. 0.85/1.21 305 (all X all Xa (pp(scratc1861232448d_l_ec(X,Xa)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1315587074nd_imp,X),scratc1198599609_d_not(Xa))))) # label(fact_def__l__ec) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 306 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ff,Uu),Uua)) <-> pp(scratc1091134429_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,Uua),scratc1909781293nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,Uu)),aa_fun171081125l_bool(scratc516108253_n_all,aa_TPT43085870d_bool(aTP_Lamm_af,Uua)))))) # label(fact_ATP_Olambda__67) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 307 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dn,Uu)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dm,Uu))))) # label(fact_ATP_Olambda__35) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 308 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_bp(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc1710340071bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,scratc1574338175ptyset),Uub),Uu),Uua)) # label(fact_ATP_Olambda__116) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 309 (all B_1 all B_2 gg_bool(scratc1091134429_d_and(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__46248__31143_ONUM671__thf__4__p_Obnd__d__and) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 310 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_di,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc894897325lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1028880937moreis,Uua),Uu))))) # label(fact_ATP_Olambda__77) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 311 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc708751474ffprop(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,X),aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Xa),Xb))))) # label(fact_def__diffprop) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 312 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1028880937moreis,Uu),Uua)) -> pp(scratc1198599609_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1315324671nd_iii,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dg,Uu),Uua)))) # label(fact_ATP_Olambda__80) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 313 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fe,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Uu),scratc1909781293nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,Uu))))) # label(fact_ATP_Olambda__3) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 314 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1939778727munion,X),aTP_Lamm_bi(Xa)) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1538476363_Sigma,X),Xa)) # label(fact_def__d__Sigma) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 315 -(exists X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X0),scratc1574338175ptyset))) # label(fact_k__EmptyAx) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 316 (all X7 all Y (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) | Y != X7)) # label(help_fequal_2_1_fequal_001t__TPTP____Interpret__Oind_T) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 317 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cw,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cx,Uu)))) # label(fact_ATP_Olambda__43) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 318 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_ae(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,Uu),Uua))) # label(fact_ATP_Olambda__112) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 319 (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]. 0.85/1.22 320 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cq,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cr,Uu)))) # label(fact_ATP_Olambda__46) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 321 (all X all Xa scratc1351036366_ecect(X,Xa) = scratc326995776d_e_in(aa_TPTP_ind_TPTP_ind(scratc1927291739_power,X),scratc476398517d_anec(X,Xa))) # label(fact_def__ecect) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 322 (all X all Xa all Xb (pp(scratc1091134429_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc240543453ective(X),Xa),Xb),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc196605446ective(X),Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc424262683ective(X),Xa),Xb)))) # label(fact_def__bijective) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 323 (all X (pp(aa_TPTP_ind_bool(scratc1495401844_prop1,X)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1356632206nd_nis,aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,X)),X)))) # label(fact_def__d__22__prop1) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 324 (all X all Xa all Xb (pp(aa_fun171081125l_bool(scratc1249429431nd_all(Xa),aa_TPT43085870d_bool(scratc797479985_image(X,Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc196605446ective(X),Xa),Xb)))) # label(fact_def__surjective) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 325 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cd(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ce,Uu),Uua)))) # label(fact_ATP_Olambda__107) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 326 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eq(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_er,Uu),Uua)))) # label(fact_ATP_Olambda__100) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 327 (all Uu aa_TPTP_ind_TPTP_ind(aTP_Lamm_ad,Uu) = scratc1356107415nd_nat) # label(fact_ATP_Olambda__176) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 328 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_de,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc894897325lessis,Uu),Uua)) -> pp(scratc1198599609_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1196184449_29_ii,Uu),Uua)))))) # label(fact_ATP_Olambda__81) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 329 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cn,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_co,Uu)))) # label(fact_ATP_Olambda__47) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 330 (all X aa_fun277296641TP_ind(scratc1224320725eplSep(X,aTP_Lamm_bj),scratc991996375_d_Unj) = aa_TPTP_ind_TPTP_ind(scratc2055805578_proj1,X)) # label(fact_def__proj1) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 331 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,X0) = aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,X12) -> X12 = X0))) # label(fact_ordsucc__inj) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 332 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1315324671nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1315324671nd_iii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1315324671nd_iii,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cp(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__135) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 333 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc287069957_union,X0))) <-> (exists X2 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X12),X2)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X2),X0)) & gg_TPTP_ind(X2))))) # label(fact_k__UnionEq) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 334 (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(scratc1993139790d_n_is,aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__68) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 335 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1193127576unmore(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc974882980_d_Sep(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_as(X),Xa),Xb))) # label(fact_def__unmore) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 336 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1710340071bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1710340079bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc787847065d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bo(X),Xa))),scratc1574338175ptyset) = aa_fun1431113780TP_ind(scratc974882980_d_Sep(X),Xa)) # label(fact_def__d__Sep) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 337 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ab,Uu),Uua)))) # label(fact_ATP_Olambda__110) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 338 (all P all Q all R aa_boo1142376798l_bool(P,aa_TPTP_ind_bool(Q,R)) = aa_TPT2142672771l_bool(cOMBB_658106424TP_ind(P,Q),R)) # label(help_COMBB_1_1_COMBB_001t__HOL__Obool_001t__fun_It__HOL__Obool_Mt__HOL__Obool_J_001t__TPTP____Interpret__Oind_U) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 339 (all X0 all X12 scratc2103678827_is_of(aa_fun1431113780TP_ind(scratc974882980_d_Sep(X0),X12),aa_TPT43085870d_bool(aTP_Lamm_ft,X0))) # label(fact_setof__p) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 340 (all X all Xa (pp(aa_fun171081125l_bool(scratc1365221692nd_one(X),Xa)) <-> pp(scratc1091134429_d_and(scratc387020528_amone(X,Xa),aa_fun171081125l_bool(scratc1552271094l_some(X),Xa))))) # label(fact_def__one) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 341 (all X all Xa all Xb all Xc (pp(aa_fun171081125l_bool(scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ao(X),Xa),Xb),Xc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc574983704fixfu2(X,Xa),Xb),Xc)))) # label(fact_def__fixfu2) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 342 (all X all Xa all Xb (gg_TPTP_ind(Xb) -> aa_TPTP_ind_TPTP_ind(scratc326995776d_e_in(X,Xa),Xb) = Xb)) # label(fact_def__e__in) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 343 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ez,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__69) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 344 (all X aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1538476363_Sigma,scratc1356107415nd_nat),aTP_Lamm_ae(X)) = aa_TPTP_ind_TPTP_ind(scratc1951617835d_24_g,X)) # label(fact_def__d__24__g) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 345 (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]. 0.85/1.22 346 (all B_1 all B_2 gg_bool(aa_fun171081125l_bool(B_1,B_2))) # label(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__HOL__Obool) # label(hypothesis) # label(non_clause). [assumption]. 0.85/1.22 347 (all X all Xa ((all X2 (gg_TPTP_ind(X2) -> (scratc2103678827_is_of(X2,X) -> pp(aa_TPTP_ind_bool(Xa,X2))))) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(X),Xa)))) # label(fact_def__all__of) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 348 (all Uu (gg_TPTP_ind(Uu) -> ((exists X2 (gg_TPTP_ind(X2) & Uu = aa_TPTP_ind_TPTP_ind(scratc143590182d_Inj1,X2))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_bj,Uu))))) # label(fact_ATP_Olambda__58) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 349 (all X all Xa all Xb scratc1282737854nd_eps(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bq(X),Xa),Xb)) = aa_TPTP_ind_TPTP_ind(scratc1710340071bnd_if(X,Xa),Xb)) # label(fact_def__if) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 350 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc287069957_union,aa_TPTP_ind_TPTP_ind(scratc1432962741_UPair(X),Xa)) = aa_TPTP_ind_TPTP_ind(scratc786152178nunion(X),Xa)) # label(fact_def__binunion) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 351 (all X0 all X12 pp(aa_fun171081125l_bool(scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_gc(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_gd(X0),X12)))) # label(fact_pairis1) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 352 (all X all Xa scratc1714252958second(X,Xa) = scratc2055805578_proj1) # label(fact_def__second) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 353 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc1365221692nd_one(X0),X12)) -> scratc2103678827_is_of(scratc1315652661nd_ind(X0,X12),aa_TPT43085870d_bool(aTP_Lamm_ak,X0)))) # label(fact_ind__p) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 354 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1315587074nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc326995781d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,Uub),Uud))),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc326995781d_e_is(Uu),Uuc),Uud))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_ba(Uu),Uua),Uub),Uuc),Uud)))) # label(fact_ATP_Olambda__167) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 355 (all X (pp(aa_TPTP_ind_bool(scratc2083764019_prop1,X)) <-> pp(aa_bool_bool(scratc1861888453d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,X),scratc1909781293nd_n_1)),aa_fun171081125l_bool(scratc148612088n_some,aa_TPT43085870d_bool(aTP_Lamm_ag,X)))))) # label(fact_def__d__23__prop1) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 356 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X22),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1709815289bnd_ap,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1538476363_Sigma,X0),X12)),X22) = aa_TPTP_ind_TPTP_ind(X12,X22))) # label(fact_beta) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 357 (all B_1 all B_2 all B_3 gg_bool(scratc1281885003nd_ec3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__46248__31143_ONUM671__thf__4__p_Obnd__ec3) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 358 (all X (pp(aa_TPTP_ind_bool(scratc352794773closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X1),X)) -> (all X2 ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X3),X1)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,aa_TPTP_ind_TPTP_ind(X2,X3)),X))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc787847065d_repl,X1),X2)),X))))))))) # label(fact_def__d__Repl__closed) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 359 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564317035d_Subq,X12),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1927291739_power,X0))))) # label(fact_k__PowerI) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 360 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cd(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1196184449_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1028880937moreis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1196184449_29_ii,Uu),Uub)))))) # label(fact_ATP_Olambda__128) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 361 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> pp(X0) & aa_TPTP_ind_TPTP_ind(scratc1710340071bnd_if(X0,X12),X22) = X12 | X22 = aa_TPTP_ind_TPTP_ind(scratc1710340071bnd_if(X0,X12),X22) & -pp(X0))) # label(fact_if__i__correct) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 362 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ew,Uu),Uua)))) # label(fact_ATP_Olambda__87) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 363 (all Uu all Uua all Uub all Uuc (pp(aa_fun171081125l_bool(scratc1552271094l_some(Uua),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ar(Uu),Uub),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_as(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__166) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 364 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fm,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,Uu),aa_TPTP_ind_TPTP_ind(scratc1927291739_power,scratc1356107415nd_nat))))) # label(fact_ATP_Olambda__14) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 365 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc702437720tminus(X),Xa) = aa_fun1431113780TP_ind(scratc974882980_d_Sep(X),aa_TPT43085870d_bool(aTP_Lamm_bn,Xa))) # label(fact_def__setminus) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 366 (all X all Xa all Xb (pp(scratc1365484038nd_or3(X,Xa,Xb)) <-> pp(aa_bool_bool(scratc1861888453d_l_or(X),aa_bool_bool(scratc1861888453d_l_or(Xa),Xb))))) # label(fact_def__or3) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 367 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,Uua),aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Uu),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eb(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__146) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 368 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cl,Uu)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ck,Uu))))) # label(fact_ATP_Olambda__48) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 369 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1333275155d_d_Pi,X),Xa) = aa_fun1431113780TP_ind(scratc974882980_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1927291739_power,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1538476363_Sigma,X),aTP_Lamm_bf(Xa)))),aa_fun1913827119d_bool(aTP_Lamm_bg(X),Xa))) # label(fact_def__d__Pi) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 370 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cf,Uu)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ce,Uu))))) # label(fact_ATP_Olambda__50) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 371 (all X aa_TPTP_ind_TPTP_ind(scratc1465966153d_Sing,X) = aa_TPTP_ind_TPTP_ind(scratc1432962741_UPair(X),X)) # label(fact_def__d__Sing) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 372 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dw,Uu),Uua)) <-> pp(scratc1281885003nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc148612088n_some,aa_TPT43085870d_bool(scratc708751474ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc148612088n_some,aa_TPT43085870d_bool(scratc708751474ffprop(Uua),Uu)))))) # label(fact_ATP_Olambda__65) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 373 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bn,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1354533033nd_nIn,Uua),Uu)))) # label(fact_ATP_Olambda__98) # label(axiom) # label(non_clause). [assumption]. 0.85/1.22 374 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1113004721_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(X),Xa)),Xb)),aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(X),aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Xa),Xb)))))) # label(fact_def__d__25__prop1) # label(axiom) # label(non_clause). [assumption]. 0.85/1.29 375 (all X all Xa scratc1365680900nd_out(X,Xa) = scratc1650393332d_soft(aa_fun1431113780TP_ind(scratc974882980_d_Sep(X),Xa),X,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1538476363_Sigma,aa_fun1431113780TP_ind(scratc974882980_d_Sep(X),Xa)),scratc326995776d_e_in(X,Xa)))) # label(fact_def__out) # label(axiom) # label(non_clause). [assumption]. 0.85/1.29 0.85/1.29 ============================== end of process non-clausal formulas === 0.85/1.29 0.85/1.29 ============================== PROCESS INITIAL CLAUSES =============== 0.85/1.29 0.85/1.29 ============================== PREDICATE ELIMINATION ================= 0.85/1.29 376 pp(scratc1091134429_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1315587074nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc1315587074nd_imp,B),A))) | -scratc1985275879_l_iff(A,B) # label(fact_def__l__iff) # label(axiom). [clausify(1)]. 0.85/1.29 377 -pp(scratc1091134429_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1315587074nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc1315587074nd_imp,B),A))) | scratc1985275879_l_iff(A,B) # label(fact_def__l__iff) # label(axiom). [clausify(1)]. 0.85/1.29 378 scratc1430723348nd_wel(A) | -pp(scratc1198599609_d_not(scratc1198599609_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(250)]. 0.85/1.29 379 -scratc1430723348nd_wel(A) | pp(A) # label(fact_l__et) # label(axiom). [clausify(4)]. 0.85/1.29 380 -scratc1430723348nd_wel(A) | pp(scratc1198599609_d_not(scratc1198599609_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(250)]. 0.85/1.29 Derived: -pp(scratc1198599609_d_not(scratc1198599609_d_not(A))) | pp(A). [resolve(378,a,379,a)]. 0.85/1.29 381 -gg_bool(A) | A = fFalse | fTrue = A # label(help_fFalse_1_1_T) # label(axiom). [clausify(84)]. 0.85/1.29 382 gg_bool(fTrue) # label(gsy_c_fTrue) # label(axiom). [assumption]. 0.85/1.29 383 gg_bool(scratc1198599609_d_not(A)) # label(gsy_c_Scratch__tptp__translate__46248__31143_ONUM671__thf__4__p_Obnd__d__not) # label(axiom). [clausify(54)]. 0.85/1.29 384 gg_bool(undefined_bool(bool)) # label(gsy_c_HOL_Oundefined_001t__HOL__Obool) # label(axiom). [assumption]. 0.85/1.29 Derived: fTrue = fFalse | fTrue = fTrue. [resolve(381,a,382,a)]. 0.85/1.29 Derived: scratc1198599609_d_not(A) = fFalse | fTrue = scratc1198599609_d_not(A). [resolve(381,a,383,a)]. 0.85/1.29 Derived: undefined_bool(bool) = fFalse | fTrue = undefined_bool(bool). [resolve(381,a,384,a)]. 0.85/1.29 385 gg_bool(scratc1861232448d_l_ec(A,B)) # label(gsy_c_Scratch__tptp__translate__46248__31143_ONUM671__thf__4__p_Obnd__l__ec) # label(axiom). [clausify(105)]. 0.85/1.29 Derived: scratc1861232448d_l_ec(A,B) = fFalse | fTrue = scratc1861232448d_l_ec(A,B). [resolve(385,a,381,a)]. 0.85/1.29 386 gg_bool(scratc1365484038nd_or3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__46248__31143_ONUM671__thf__4__p_Obnd__or3) # label(axiom). [clausify(107)]. 0.85/1.29 Derived: scratc1365484038nd_or3(A,B,C) = fFalse | fTrue = scratc1365484038nd_or3(A,B,C). [resolve(386,a,381,a)]. 0.85/1.29 387 gg_bool(scratc387020528_amone(A,B)) # label(gsy_c_Scratch__tptp__translate__46248__31143_ONUM671__thf__4__p_Obnd__amone) # label(axiom). [clausify(235)]. 0.85/1.29 Derived: scratc387020528_amone(A,B) = fFalse | fTrue = scratc387020528_amone(A,B). [resolve(387,a,381,a)]. 0.85/1.29 388 gg_bool(fEx_TPTP_ind(A)) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom). [clausify(252)]. 0.85/1.29 Derived: fEx_TPTP_ind(A) = fFalse | fTrue = fEx_TPTP_ind(A). [resolve(388,a,381,a)]. 0.85/1.29 389 gg_bool(aa_bool_bool(A,B)) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom). [clausify(255)]. 0.85/1.29 Derived: aa_bool_bool(A,B) = fFalse | fTrue = aa_bool_bool(A,B). [resolve(389,a,381,a)]. 0.85/1.29 390 gg_bool(scratc1091134429_d_and(A,B)) # label(gsy_c_Scratch__tptp__translate__46248__31143_ONUM671__thf__4__p_Obnd__d__and) # label(axiom). [clausify(309)]. 0.85/1.29 Derived: scratc1091134429_d_and(A,B) = fFalse | fTrue = scratc1091134429_d_and(A,B). [resolve(390,a,381,a)]. 0.85/1.29 391 gg_bool(fFalse) # label(gsy_c_fFalse) # label(axiom). [assumption]. 0.85/1.29 Derived: fFalse = fFalse | fTrue = fFalse. [resolve(391,a,381,a)]. 0.85/1.52 392 gg_bool(aa_TPTP_ind_bool(A,B)) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom). [clausify(345)]. 0.85/1.52 Derived: aa_TPTP_ind_bool(A,B) = fFalse | fTrue = aa_TPTP_ind_bool(A,B). [resolve(392,a,381,a)]. 0.85/1.52 393 gg_bool(aa_fun171081125l_bool(A,B)) # label(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__HOL__Obool) # label(hypothesis). [clausify(346)]. 0.85/1.52 Derived: aa_fun171081125l_bool(A,B) = fFalse | fTrue = aa_fun171081125l_bool(A,B). [resolve(393,a,381,a)]. 0.85/1.52 394 gg_bool(scratc1281885003nd_ec3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__46248__31143_ONUM671__thf__4__p_Obnd__ec3) # label(axiom). [clausify(357)]. 0.85/1.52 Derived: scratc1281885003nd_ec3(A,B,C) = fFalse | fTrue = scratc1281885003nd_ec3(A,B,C). [resolve(394,a,381,a)]. 0.85/1.52 395 -pp(A) | pp(scratc1198599609_d_not(B)) | -scratc108683590d_r_ec(A,B) # label(fact_def__r__ec) # label(axiom). [clausify(109)]. 0.85/1.52 396 pp(A) | scratc108683590d_r_ec(A,B) # label(fact_def__r__ec) # label(axiom). [clausify(109)]. 0.85/1.52 397 -pp(scratc1198599609_d_not(A)) | scratc108683590d_r_ec(B,A) # label(fact_def__r__ec) # label(axiom). [clausify(109)]. 0.85/1.52 398 scratc700247083d_orec(A,B) | -pp(scratc1091134429_d_and(aa_bool_bool(scratc1861888453d_l_or(A),B),scratc1861232448d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(163)]. 0.85/1.52 399 -scratc700247083d_orec(A,B) | pp(scratc1091134429_d_and(aa_bool_bool(scratc1861888453d_l_or(A),B),scratc1861232448d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(163)]. 0.85/1.52 0.85/1.52 ============================== end predicate elimination ============= 0.85/1.52 0.85/1.52 Auto_denials: (non-Horn, no changes). 0.85/1.52 0.85/1.52 Term ordering decisions: 0.85/1.52 Function symbol KB weights: aTP_Lamm_a=1. scratc1710340079bnd_in=1. scratc1993139790d_n_is=1. scratc1524236217rdsucc=1. scratc1709815289bnd_ap=1. aTP_Lamm_ak=1. scratc1315324671nd_iii=1. scratc1196184449_29_ii=1. scratc1574338175ptyset=1. scratc1538476363_Sigma=1. scratc1356632206nd_nis=1. scratc1909781293nd_n_1=1. scratc894897325lessis=1. fFalse=1. scratc1333275155d_d_Pi=1. scratc1356107415nd_nat=1. scratc148612088n_some=1. scratc1927291739_power=1. scratc1990323033_nat_p=1. scratc1028880937moreis=1. scratc1315587074nd_imp=1. scratc787847065d_repl=1. fTrue=1. scratc1340651108d_pair=1. scratc1564317035d_Subq=1. scratc2055805577_proj0=1. scratc287069957_union=1. scratc352794773closed=1. aTP_Lamm_ag=1. scratc1993139785d_n_in=1. scratc2055805578_proj1=1. scratc516108253_n_all=1. aTP_Lamm_ad=1. aTP_Lamm_af=1. aTP_Lamm_ft=1. scratc1175423777closed=1. scratc1340156791closed=1. aTP_Lamm_cs=1. aTP_Lamm_cu=1. aTP_Lamm_cw=1. aTP_Lamm_cy=1. aTP_Lamm_da=1. aTP_Lamm_dc=1. aTP_Lamm_de=1. aTP_Lamm_dg=1. aTP_Lamm_di=1. aTP_Lamm_dk=1. aTP_Lamm_dm=1. aTP_Lamm_do=1. aTP_Lamm_fk=1. aTP_Lamm_fo=1. aTP_Lamm_fp=1. scratc1225460791_omega=1. scratc143590182d_Inj1=1. scratc1917295346closed=1. scratc524642547_prop2=1. aTP_Lamm_ab=1. aTP_Lamm_ah=1. aTP_Lamm_bh=1. aTP_Lamm_bj=1. aTP_Lamm_bk=1. aTP_Lamm_bs=1. aTP_Lamm_bw=1. aTP_Lamm_by=1. aTP_Lamm_cb=1. aTP_Lamm_ce=1. aTP_Lamm_ch=1. aTP_Lamm_ck=1. aTP_Lamm_cn=1. aTP_Lamm_cq=1. aTP_Lamm_dq=1. aTP_Lamm_ds=1. aTP_Lamm_du=1. aTP_Lamm_dw=1. aTP_Lamm_dy=1. aTP_Lamm_ec=1. aTP_Lamm_ee=1. aTP_Lamm_eh=1. aTP_Lamm_ek=1. aTP_Lamm_em=1. aTP_Lamm_eo=1. aTP_Lamm_er=1. aTP_Lamm_et=1. aTP_Lamm_ew=1. aTP_Lamm_ez=1. aTP_Lamm_fc=1. aTP_Lamm_ff=1. aTP_Lamm_fh=1. aTP_Lamm_fi=1. aTP_Lamm_fn=1. fconj=1. fimplies=1. scratc143590181d_Inj0=1. scratc1465966153d_Sing=1. scratc2070922310_cond2=1. scratc524642546_prop1=1. aTP_Lamm_bn=1. aTP_Lamm_bt=1. aTP_Lamm_bu=1. aTP_Lamm_bv=1. aTP_Lamm_bx=1. aTP_Lamm_bz=1. aTP_Lamm_cc=1. aTP_Lamm_cf=1. aTP_Lamm_ci=1. aTP_Lamm_cl=1. aTP_Lamm_co=1. aTP_Lamm_cr=1. aTP_Lamm_ct=1. aTP_Lamm_cv=1. aTP_Lamm_cx=1. aTP_Lamm_cz=1. aTP_Lamm_db=1. aTP_Lamm_dd=1. aTP_Lamm_df=1. aTP_Lamm_dh=1. aTP_Lamm_dj=1. aTP_Lamm_dl=1. aTP_Lamm_dn=1. aTP_Lamm_dp=1. aTP_Lamm_dr=1. aTP_Lamm_dt=1. aTP_Lamm_dv=1. aTP_Lamm_dx=1. aTP_Lamm_dz=1. aTP_Lamm_ed=1. aTP_Lamm_ef=1. aTP_Lamm_ei=1. aTP_Lamm_el=1. aTP_Lamm_en=1. aTP_Lamm_ep=1. aTP_Lamm_es=1. aTP_Lamm_eu=1. aTP_Lamm_ev=1. aTP_Lamm_ex=1. aTP_Lamm_ey=1. aTP_Lamm_fa=1. aTP_Lamm_fb=1. aTP_Lamm_fd=1. aTP_Lamm_fe=1. aTP_Lamm_fg=1. aTP_Lamm_fj=1. aTP_Lamm_fl=1. aTP_Lamm_fm=1. aTP_Lamm_fq=1. aTP_Lamm_fr=1. aTP_Lamm_fs=1. aTP_Lamm_fv=1. aTP_Lamm_gs=1. fequal_TPTP_ind=1. scratc1354533033nd_nIn=1. scratc2070922309_cond1=1. scratc275896167univof=1. scratc631900514_n_one=1. scratc991996375_d_Unj=1. aTP_Lamm_ac=1. aTP_Lamm_ai=1. aTP_Lamm_bl=1. aTP_Lamm_bm=1. bool=1. scratc1318969773_prop1=1. scratc1380986188pair_p=1. scratc142245423_prop1=1. scratc1432314852d_plus=1. scratc1495401844_prop1=1. scratc1701366896_prop1=1. scratc1859933162nempty=1. scratc1939778727munion=1. scratc2056199175_prop4=1. scratc2083764019_prop1=1. scratc658965507_empty=1. scratc1189840513d_i1_s=1. scratc1951617835d_24_g=1. tPTP_ind=1. aa_TPTP_ind_bool=1. aa_TPT43085870d_bool=1. aa_TPTP_ind_TPTP_ind=1. aa_fun171081125l_bool=1. aa_TPT1424761345TP_ind=1. aa_TPT60673477d_bool=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. scratc1091134429_d_and=1. aa_TPT1123896796d_bool=1. scratc1710340071bnd_if=1. scratc1861232448d_l_ec=1. aa_fun1212484691d_bool=1. aa_TPT985247859d_bool=1. scratc326995776d_e_in=1. scratc414254772d_pair=1. aa_fun987228051d_bool=1. scratc1315652661nd_ind=1. scratc387020528_amone=1. scratc1714252958second=1. scratc797479985_image=1. scratc840122054_first=1. aa_TPT125613450d_bool=1. scratc1357025795nd_non=1. aa_fun1913827119d_bool=1. scratc476398517d_anec=1. aa_TPT1791839040TP_ind=1. aa_fun1107270209d_bool=1. aa_fun845057962d_bool=1. scratc1224320725eplSep=1. scratc1281885064nd_ecp=1. scratc1351626757_ecelt=1. scratc1351036366_ecect=1. aa_TPT1781712639TP_ind=1. aa_TPT2142672771l_bool=1. aa_fun1235454963TP_ind=1. cOMBB_658106424TP_ind=1. cOMBS_2003118649l_bool=1. scratc1087010230ectset=1. scratc1281885068nd_ect=1. scratc1365680900nd_out=1. scratc574983704fixfu2=1. scratc660860151etprop=1. scratc888838298_fixfu=1. scratc955037027wissel=1. scratc1193127576unmore=1. scratc279760351d_invf=1. scratc283496882d_tofs=1. scratc922483910nverse=1. scratc971808353ectelt=1. f6=1. f11=1. f18=1. f20=1. f21=1. scratc294126638all_of=1. scratc1993598976d_n_pl=1. scratc326995781d_e_is=1. scratc1198599609_d_not=1. scratc974882980_d_Sep=1. scratc1493555181d_esti=1. scratc1552271094l_some=1. scratc708751474ffprop=1. scratc1249429431nd_all=1. scratc1861888453d_l_or=1. scratc1618771446_rec_G=1. aTP_Lamm_aj=1. aTP_Lamm_gc=1. scratc1365221692nd_one=1. aTP_Lamm_al=1. aTP_Lamm_av=1. aTP_Lamm_bd=1. aTP_Lamm_bq=1. aTP_Lamm_ca=1. aTP_Lamm_cd=1. aTP_Lamm_cg=1. aTP_Lamm_cj=1. aTP_Lamm_cm=1. aTP_Lamm_cp=1. aTP_Lamm_ea=1. aTP_Lamm_fu=1. aTP_Lamm_gq=1. scratc278513976d_incl=1. aTP_Lamm_aa=1. aTP_Lamm_ap=1. aTP_Lamm_az=1. aTP_Lamm_bc=1. aTP_Lamm_bg=1. aTP_Lamm_br=1. aTP_Lamm_eg=1. aTP_Lamm_ej=1. aTP_Lamm_gm=1. aTP_Lamm_go=1. scratc1158159311etprod=1. scratc1282737854nd_eps=1. scratc240543453ective=1. aTP_Lamm_am=1. aTP_Lamm_an=1. aTP_Lamm_ao=1. aTP_Lamm_aq=1. aTP_Lamm_ar=1. aTP_Lamm_at=1. aTP_Lamm_au=1. aTP_Lamm_ba=1. aTP_Lamm_bb=1. aTP_Lamm_be=1. aTP_Lamm_eb=1. aTP_Lamm_eq=1. aTP_Lamm_fw=1. aTP_Lamm_fx=1. aTP_Lamm_fy=1. aTP_Lamm_ga=1. aTP_Lamm_gg=1. aTP_Lamm_gi=1. aTP_Lamm_gj=1. aTP_Lamm_gn=1. fEx_TPTP_ind=1. scratc196605446ective=1. scratc786152178nunion=1. aTP_Lamm_as=1. aTP_Lamm_fz=1. aTP_Lamm_gb=1. aTP_Lamm_gd=1. aTP_Lamm_ge=1. aTP_Lamm_gf=1. aTP_Lamm_gh=1. aTP_Lamm_gk=1. aTP_Lamm_gl=1. aTP_Lamm_gp=1. aTP_Lamm_gr=1. scratc1432962741_UPair=1. scratc952084305In_rec=1. aTP_Lamm_ae=1. aTP_Lamm_aw=1. aTP_Lamm_ax=1. aTP_Lamm_ay=1. aTP_Lamm_bf=1. aTP_Lamm_bi=1. aTP_Lamm_bo=1. aTP_Lamm_bp=1. cOMBC_1555011498d_bool=1. scratc1113004721_prop1=1. scratc1119274215t_disj=1. scratc2056199174_prop3=1. scratc424262683ective=1. scratc702437720tminus=1. scratc730607598_prop1=1. undefined_bool=1. undefined_TPTP_ind=1. f1=1. f3=1. f4=1. f5=1. f7=1. f8=1. f17=1. f22=1. f24=1. f25=1. scratc1365484038nd_or3=1. scratc1281885003nd_ec3=1. scratc1650393332d_soft=1. scratc1316046256nd_ite=1. scratc1602720513_indeq=1. scratc2056199172_prop1=1. Alarm clock 179.75/180.07 Prover9 interrupted 179.75/180.07 EOF