0.05/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.05/0.11 % Command : tptp2X_and_run_prover9 %d %s 0.10/0.31 % Computer : n018.cluster.edu 0.10/0.31 % Model : x86_64 x86_64 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.31 % Memory : 8042.1875MB 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.31 % CPULimit : 960 0.10/0.31 % DateTime : Thu Jul 2 15:46:37 EDT 2020 0.10/0.31 % CPUTime : 1.18/1.49 ============================== Prover9 =============================== 1.18/1.49 Prover9 (32) version 2009-11A, November 2009. 1.18/1.49 Process 23314 was started by sandbox2 on n018.cluster.edu, 1.18/1.49 Thu Jul 2 15:46:38 2020 1.18/1.49 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_23161_n018.cluster.edu". 1.18/1.49 ============================== end of head =========================== 1.18/1.49 1.18/1.49 ============================== INPUT ================================= 1.18/1.49 1.18/1.49 % Reading from file /tmp/Prover9_23161_n018.cluster.edu 1.18/1.49 1.18/1.49 set(prolog_style_variables). 1.18/1.49 set(auto2). 1.18/1.49 % set(auto2) -> set(auto). 1.18/1.49 % set(auto) -> set(auto_inference). 1.18/1.49 % set(auto) -> set(auto_setup). 1.18/1.49 % set(auto_setup) -> set(predicate_elim). 1.18/1.49 % set(auto_setup) -> assign(eq_defs, unfold). 1.18/1.49 % set(auto) -> set(auto_limits). 1.18/1.49 % set(auto_limits) -> assign(max_weight, "100.000"). 1.18/1.49 % set(auto_limits) -> assign(sos_limit, 20000). 1.18/1.49 % set(auto) -> set(auto_denials). 1.18/1.49 % set(auto) -> set(auto_process). 1.18/1.49 % set(auto2) -> assign(new_constants, 1). 1.18/1.49 % set(auto2) -> assign(fold_denial_max, 3). 1.18/1.49 % set(auto2) -> assign(max_weight, "200.000"). 1.18/1.49 % set(auto2) -> assign(max_hours, 1). 1.18/1.49 % assign(max_hours, 1) -> assign(max_seconds, 3600). 1.18/1.49 % set(auto2) -> assign(max_seconds, 0). 1.18/1.49 % set(auto2) -> assign(max_minutes, 5). 1.18/1.49 % assign(max_minutes, 5) -> assign(max_seconds, 300). 1.18/1.49 % set(auto2) -> set(sort_initial_sos). 1.18/1.49 % set(auto2) -> assign(sos_limit, -1). 1.18/1.49 % set(auto2) -> assign(lrs_ticks, 3000). 1.18/1.49 % set(auto2) -> assign(max_megs, 400). 1.18/1.49 % set(auto2) -> assign(stats, some). 1.18/1.49 % set(auto2) -> clear(echo_input). 1.18/1.49 % set(auto2) -> set(quiet). 1.18/1.49 % set(auto2) -> clear(print_initial_clauses). 1.18/1.49 % set(auto2) -> clear(print_given). 1.18/1.49 assign(lrs_ticks,-1). 1.18/1.49 assign(sos_limit,10000). 1.18/1.49 assign(order,kbo). 1.18/1.49 set(lex_order_vars). 1.18/1.49 clear(print_given). 1.18/1.49 1.18/1.49 % formulas(sos). % not echoed (454 formulas) 1.18/1.49 1.18/1.49 ============================== end of input ========================== 1.18/1.49 1.18/1.49 % From the command line: assign(max_seconds, 960). 1.18/1.49 1.18/1.49 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 1.18/1.49 1.18/1.49 % Formulas that are not ordinary clauses: 1.18/1.49 1 (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]. 1.18/1.49 2 (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]. 1.18/1.49 3 (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]. 1.18/1.49 4 (all X0 all X12 (gg_TPTP_ind(X12) -> X12 = aa_TPTP_ind_TPTP_ind(scratc2055805578_proj1,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1340651108d_pair,X0),X12)))) # label(fact_proj1__pair__eq) # label(axiom) # label(non_clause). [assumption]. 1.18/1.49 5 (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]. 1.18/1.49 6 (all X0 all X12 all X22 (gg_TPTP_ind(X22) & gg_TPTP_ind(X12) -> aa_TPTP_ind_TPTP_ind(scratc1710340071bnd_if(X0,X12),X22) = X12 & pp(X0) | -pp(X0) & X22 = aa_TPTP_ind_TPTP_ind(scratc1710340071bnd_if(X0,X12),X22))) # label(fact_if__i__correct) # label(axiom) # label(non_clause). [assumption]. 1.18/1.49 7 (all X all Xa all 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)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1113004721_prop1(X),Xa),Xb)))) # label(fact_def__d__25__prop1) # label(axiom) # label(non_clause). [assumption]. 1.18/1.49 8 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ay(Uu),Uua),Uub),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)) # label(fact_ATP_Olambda__152) # label(axiom) # label(non_clause). [assumption]. 1.18/1.49 9 (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]. 1.18/1.49 10 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ct,Uu)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cs,Uu))))) # label(fact_ATP_Olambda__45) # label(axiom) # label(non_clause). [assumption]. 1.18/1.49 11 (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]. 1.18/1.49 12 (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]. 1.18/1.49 13 (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]. 1.18/1.49 14 (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]. 1.18/1.49 15 (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]. 1.18/1.49 16 (all X all Xa (pp(aa_fun171081125l_bool(scratc294126638all_of(X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (scratc2103678827_is_of(X2,X) -> pp(aa_TPTP_ind_bool(Xa,X2))))))) # label(fact_def__all__of) # label(axiom) # label(non_clause). [assumption]. 1.18/1.49 17 (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]. 1.18/1.49 18 (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]. 1.18/1.49 19 (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]. 1.18/1.49 20 (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]. 1.18/1.49 21 (all X all Xa all Xb (gg_TPTP_ind(Xb) -> Xb = aa_TPTP_ind_TPTP_ind(scratc326995776d_e_in(X,Xa),Xb))) # label(fact_def__e__in) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 22 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_by,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_bz,Uu)))) # label(fact_ATP_Olambda__52) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 23 (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]. 1.18/1.50 24 (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]. 1.18/1.50 25 (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]. 1.18/1.50 26 (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]. 1.18/1.50 27 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1315324671nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bw,Uu),Uua)))) # label(fact_ATP_Olambda__94) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 28 (all Uu all Uua all 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))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_gr(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__139) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 29 (all X all 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)) = aa_TPTP_ind_TPTP_ind(scratc1432962741_UPair(X),Xa)) # label(fact_def__d__UPair) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 30 (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]. 1.18/1.50 31 (all X all Xa (pp(scratc1091134429_d_and(scratc387020528_amone(X,Xa),aa_fun171081125l_bool(scratc1552271094l_some(X),Xa))) <-> pp(aa_fun171081125l_bool(scratc1365221692nd_one(X),Xa)))) # label(fact_def__one) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 32 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,Uu),scratc1356107415nd_nat)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_a,Uu)))) # label(fact_ATP_Olambda__15) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 33 (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]. 1.18/1.50 34 (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]. 1.18/1.50 35 (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]. 1.18/1.50 36 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bs,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_br(Uu),Uua))))) # label(fact_ATP_Olambda__109) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 37 (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]. 1.18/1.50 38 (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]. 1.18/1.50 39 (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]. 1.18/1.50 40 (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]. 1.18/1.50 41 (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]. 1.18/1.50 42 (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]. 1.18/1.50 43 (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]. 1.18/1.50 44 (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]. 1.18/1.50 45 (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]. 1.18/1.50 46 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gs,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc326995781d_e_is(Uu),Uua),Uua)))) # label(fact_ATP_Olambda__66) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 47 (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 (gg_TPTP_ind(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)))))) # label(fact_k__UnionEq) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 48 (all Uu all Uua all 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)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gm(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__144) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 49 (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]. 1.18/1.50 50 (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]. 1.18/1.50 51 (all Uu all 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)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ff,Uu),Uua)))) # label(fact_ATP_Olambda__67) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 52 (all X all Xa all Xb all Xc all 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)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2056199172_prop1(X,Xa,Xb),Xc),Xd)))) # label(fact_def__prop1) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 53 (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]. 1.18/1.50 54 (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]. 1.18/1.50 55 (all P all Q all R aa_TPTP_ind_bool(aa_TPT43085870d_bool(P,R),Q) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(cOMBC_1555011498d_bool(P),Q),R)) # label(help_COMBC_1_1_COMBC_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind_001t__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 56 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1602720513_indeq(X,Xa,Xb),Xc),Xd) = scratc1315652661nd_ind(Xb,aa_TPT43085870d_bool(scratc2056199173_prop2(X,Xa,Xb,Xc),Xd))) # label(fact_def__indeq) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 57 (all Uu all 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))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cs,Uu),Uua)))) # label(fact_ATP_Olambda__90) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 58 (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]. 1.18/1.50 59 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1281885064nd_ecp(X,Xa),Xb),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))))) # label(fact_def__ecp) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 60 (all X0 all X12 (gg_TPTP_ind(X12) & gg_TPTP_ind(X0) -> (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]. 1.18/1.50 61 (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]. 1.18/1.50 62 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cv,Uu)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cu,Uu))))) # label(fact_ATP_Olambda__44) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 63 (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]. 1.18/1.50 64 (all Uu aa_TPT494704832TP_ind(scratc787847065d_repl,aa_TPTP_ind_TPTP_ind(scratc702437720tminus(Uu),aa_TPTP_ind_TPTP_ind(scratc1465966153d_Sing,scratc1574338175ptyset))) = aa_TPT494704832TP_ind(aTP_Lamm_bl,Uu)) # label(fact_ATP_Olambda__56) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 65 (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]. 1.18/1.50 66 (all X scratc1493555181d_esti(X) = scratc1710340079bnd_in) # label(fact_def__esti) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 67 (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]. 1.18/1.50 68 (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]. 1.18/1.50 69 (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(X12,X33) = aa_TPTP_ind_TPTP_ind(X22,X33)))) -> aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1538476363_Sigma,X0),X22) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1538476363_Sigma,X0),X12))) # label(fact_xi__ext) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 70 (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]. 1.18/1.50 71 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ea(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Uua),Uub))))) # label(fact_ATP_Olambda__145) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 72 (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]. 1.18/1.50 73 (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]. 1.18/1.50 74 (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]. 1.18/1.50 75 (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(Uua,Uub)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,Uub),Uu)))) # label(fact_ATP_Olambda__136) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 76 (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]. 1.18/1.50 77 (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]. 1.18/1.50 78 (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]. 1.18/1.50 79 (all Q all P (pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) | -pp(Q))) # label(help_fimplies_2_1_U) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 80 (all X aa_TPTP_ind_TPTP_ind(scratc1432962741_UPair(X),X) = aa_TPTP_ind_TPTP_ind(scratc1465966153d_Sing,X)) # label(fact_def__d__Sing) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 81 (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]. 1.18/1.50 82 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eq(Uu),Uua),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)))))) # label(fact_ATP_Olambda__126) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 83 (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]. 1.18/1.50 84 (all X7 all Y (gg_TPTP_ind(Y) & gg_TPTP_ind(X7) -> -pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) | Y = X7)) # label(help_fequal_1_1_fequal_001t__TPTP____Interpret__Oind_T) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 85 (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]. 1.18/1.50 86 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_co,Uu)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cn,Uu))))) # label(fact_ATP_Olambda__47) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 87 (all B_1 all B_2 gg_TPTP_ind(aa_fun1431113780TP_ind(B_1,B_2))) # label(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 88 (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]. 1.18/1.50 89 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> X22 = aa_TPTP_ind_TPTP_ind(scratc1710340071bnd_if(X0,X12),X22) | aa_TPTP_ind_TPTP_ind(scratc1710340071bnd_if(X0,X12),X22) = X12)) # label(fact_if__i__or) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 90 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1650393332d_soft(X,Xa,Xb),Xc) = scratc1315652661nd_ind(X,aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_az(Xa),Xb),Xc))) # label(fact_def__soft) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 91 (all B_1 all B_2 gg_bool(aa_TPTP_ind_bool(B_1,B_2))) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 92 (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]. 1.18/1.50 93 (all X all Xa scratc840122054_first(X,Xa) = scratc2055805577_proj0) # label(fact_def__first) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 94 (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]. 1.18/1.50 95 (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]. 1.18/1.50 96 (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]. 1.18/1.50 97 (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]. 1.18/1.50 98 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ee,Uu),Uua)) <-> pp(scratc387020528_amone(scratc1356107415nd_nat,aa_TPT43085870d_bool(aTP_Lamm_ea(Uu),Uua))))) # label(fact_ATP_Olambda__111) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 99 (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(scratc787847065d_repl,X0),X12))) <-> (exists X3 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X3),X0)) & X22 = aa_TPTP_ind_TPTP_ind(X12,X3) & gg_TPTP_ind(X3)))))) # label(fact_k__ReplEq) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 100 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dl,Uu)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dk,Uu))))) # label(fact_ATP_Olambda__36) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 101 (all X all Xa all Xb (pp(scratc1091134429_d_and(X,scratc1091134429_d_and(Xa,Xb))) <-> scratc476332870d_and3(X,Xa,Xb))) # label(fact_def__and3) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 102 (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]. 1.18/1.50 103 (all P all Q all R aa_TPT2142672771l_bool(cOMBB_658106424TP_ind(P,Q),R) = aa_boo1142376798l_bool(P,aa_TPTP_ind_bool(Q,R))) # label(help_COMBB_1_1_COMBB_001t__HOL__Obool_001t__fun_It__HOL__Obool_Mt__HOL__Obool_J_001t__TPTP____Interpret__Oind_U) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 104 (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]. 1.18/1.50 105 (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]. 1.18/1.50 106 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dw,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_dx,Uu)))) # label(fact_ATP_Olambda__30) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 107 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_di,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_dj,Uu)))) # label(fact_ATP_Olambda__37) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 108 (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]. 1.18/1.50 109 (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]. 1.18/1.50 110 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fj,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1356632206nd_nis,aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__10) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 111 (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]. 1.18/1.50 112 (all X (pp(scratc1198599609_d_not(X)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1315587074nd_imp,X),fFalse)))) # label(fact_def__d__not) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 113 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cr,Uu)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cq,Uu))))) # label(fact_ATP_Olambda__46) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 114 (all X (pp(aa_fun171081125l_bool(scratc516108253_n_all,aa_TPT43085870d_bool(aTP_Lamm_af,X))) <-> pp(aa_TPTP_ind_bool(scratc524642546_prop1,X)))) # label(fact_def__d__24__prop1) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 115 (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]. 1.18/1.50 116 (all X (pp(scratc1198599609_d_not(scratc1198599609_d_not(X))) <-> scratc1430723348nd_wel(X))) # label(fact_def__wel) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 117 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ar(Uu),Uua),Uub),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))))) # label(fact_ATP_Olambda__156) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 118 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc658965507_empty,X),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)))))) # label(fact_def__empty) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 119 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eg(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eh,Uu),Uua)))) # label(fact_ATP_Olambda__102) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 120 (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]. 1.18/1.50 121 (all X all Xa all 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))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc730607598_prop1(X),Xa),Xb)))) # label(fact_def__d__28__prop1) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 122 (all B_1 all B_2 gg_bool(aa_fun171081125l_bool(B_1,B_2))) # label(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__HOL__Obool) # label(hypothesis) # label(non_clause). [assumption]. 1.18/1.50 123 (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]. 1.18/1.50 124 (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__PowerEq) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 125 (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]. 1.18/1.50 126 (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]. 1.18/1.50 127 (all X aa_TPTP_ind_TPTP_ind(scratc1951617835d_24_g,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1538476363_Sigma,scratc1356107415nd_nat),aTP_Lamm_ae(X))) # label(fact_def__d__24__g) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 128 (all P (gg_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 129 (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]. 1.18/1.50 130 (all X all Xa aa_fun1431113780TP_ind(scratc974882980_d_Sep(X),aa_TPT43085870d_bool(aTP_Lamm_bn,Xa)) = aa_TPTP_ind_TPTP_ind(scratc702437720tminus(X),Xa)) # label(fact_def__setminus) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 131 (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]. 1.18/1.50 132 (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]. 1.18/1.50 133 (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]. 1.18/1.50 134 (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]. 1.18/1.50 135 (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]. 1.18/1.50 136 (all X all 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))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1028880937moreis,X),Xa)))) # label(fact_def__moreis) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 137 (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]. 1.18/1.50 138 (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]. 1.18/1.50 139 (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]. 1.18/1.50 140 (all P all Q all R aa_bool_bool(aa_TPT2142672771l_bool(P,R),aa_TPTP_ind_bool(Q,R)) = aa_TPTP_ind_bool(cOMBS_2003118649l_bool(P,Q),R)) # label(help_COMBS_1_1_COMBS_001t__TPTP____Interpret__Oind_001t__HOL__Obool_001t__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 141 (all Uu all Uua all 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))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gb(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__142) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 142 (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]. 1.18/1.50 143 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cg(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ch,Uu),Uua)))) # label(fact_ATP_Olambda__106) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 144 (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]. 1.18/1.50 145 (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]. 1.18/1.50 146 (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]. 1.18/1.50 147 (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]. 1.18/1.50 148 (all X0 (scratc1430723348nd_wel(X0) -> pp(X0))) # label(fact_l__et) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 149 (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]. 1.18/1.50 150 (all B_1 gg_bool(fEx_TPTP_ind(B_1))) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 151 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_et,Uu),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))))) # label(fact_ATP_Olambda__86) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 152 (all X all Xa all Xb aa_fun1431113780TP_ind(scratc974882980_d_Sep(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_as(X),Xa),Xb)) = aa_TPTP_ind_TPTP_ind(scratc1193127576unmore(X,Xa),Xb)) # label(fact_def__unmore) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 153 (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]. 1.18/1.50 154 (all X all Xa scratc326995776d_e_in(aa_TPTP_ind_TPTP_ind(scratc1927291739_power,X),scratc476398517d_anec(X,Xa)) = scratc1351036366_ecect(X,Xa)) # label(fact_def__ecect) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 155 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc424262683ective(X),Xa),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))))) # label(fact_def__bijective) # label(axiom) # label(non_clause). [assumption]. 1.18/1.50 156 (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]. 1.18/1.50 157 (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]. 1.18/1.50 158 (all X all Xa all Xb all Xc (pp(aa_fun171081125l_bool(scratc1552271094l_some(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_az(Xa),Xb),Xc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc797479985_image(X,Xa),Xb),Xc)))) # label(fact_def__image) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 159 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_da,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(scratc1028880937moreis,Uu),Uua))))) # label(fact_ATP_Olambda__91) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 160 (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(scratc1028880937moreis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1196184449_29_ii,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cd(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__128) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 161 (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]. 1.18/1.51 162 (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]. 1.18/1.51 163 (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]. 1.18/1.51 164 (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]. 1.18/1.51 165 (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]. 1.18/1.51 166 (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]. 1.18/1.51 167 (all Uu all 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))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dm,Uu),Uua)))) # label(fact_ATP_Olambda__78) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 168 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1538476363_Sigma,X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1939778727munion,X),aTP_Lamm_bi(Xa))) # label(fact_def__d__Sigma) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 169 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fa,Uu)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ez,Uu))))) # label(fact_ATP_Olambda__19) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 170 (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(Uu),scratc1909781293nd_n_1))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ey,Uu)))) # label(fact_ATP_Olambda__7) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 171 (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]. 1.18/1.51 172 (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]. 1.18/1.51 173 (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]. 1.18/1.51 174 (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]. 1.18/1.51 175 (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(scratc287069957_union,X1)),X))))) <-> pp(aa_TPTP_ind_bool(scratc1175423777closed,X)))) # label(fact_def__d__Union__closed) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 176 (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]. 1.18/1.51 177 (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]. 1.18/1.51 178 (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]. 1.18/1.51 179 (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]. 1.18/1.51 180 (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]. 1.18/1.51 181 (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]. 1.18/1.51 182 (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]. 1.18/1.51 183 (all P all Q (-pp(P) | -pp(Q) | pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 184 (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]. 1.18/1.51 185 (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]. 1.18/1.51 186 (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]. 1.18/1.51 187 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dy,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_dz,Uu)))) # label(fact_ATP_Olambda__29) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 188 (all Uu all Uua (gg_TPTP_ind(Uua) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bh,Uu),Uua)) <-> (exists X3 (gg_TPTP_ind(X3) & aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1340651108d_pair,Uu),X3) = Uua))))) # label(fact_ATP_Olambda__114) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 189 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_gk(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(Uua,aa_TPTP_ind_TPTP_ind(scratc326995776d_e_in(Uu,Uua),Uub))))) # label(fact_ATP_Olambda__150) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 190 (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]. 1.18/1.51 191 (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]. 1.18/1.51 192 (all X0 (gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(scratc1990323033_nat_p,X0)) -> X0 = scratc1574338175ptyset | (exists X13 (X0 = aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,X13) & pp(aa_TPTP_ind_bool(scratc1990323033_nat_p,X13)) & gg_TPTP_ind(X13)))))) # label(fact_nat__inv) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 193 (all X scratc1861888453d_l_or(X) = aa_boo1142376798l_bool(scratc1315587074nd_imp,scratc1198599609_d_not(X))) # label(fact_def__l__or) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 194 (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]. 1.18/1.51 195 (all X all Xa all Xb aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1538476363_Sigma,X),scratc600229838sel_wb(X,Xa,Xb)) = aa_TPTP_ind_TPTP_ind(scratc955037027wissel(X,Xa),Xb)) # label(fact_def__wissel) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 196 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ep,Uu)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eo,Uu))))) # label(fact_ATP_Olambda__23) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 197 (all B_1 all B_2 gg_TPTP_ind(aa_fun277296641TP_ind(B_1,B_2))) # label(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__TPTP____Interpret__Oind_J_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 198 (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]. 1.18/1.51 199 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc696299693_inj_h(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1538476363_Sigma,X),aa_TPT1424761345TP_ind(aTP_Lamm_ax(Xc),Xd))) # label(fact_def__inj__h) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 200 (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]. 1.18/1.51 201 (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]. 1.18/1.51 202 (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]. 1.18/1.51 203 (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]. 1.18/1.51 204 (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]. 1.18/1.51 205 (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]. 1.18/1.51 206 (all X scratc326995781d_e_is(X) = fequal_TPTP_ind) # label(fact_def__e__is) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 207 (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]. 1.18/1.51 208 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cb,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ca(Uu),Uua))))) # label(fact_ATP_Olambda__108) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 209 (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]. 1.18/1.51 210 (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]. 1.18/1.51 211 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1340651108d_pair,X),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))) # label(fact_def__pair) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 212 (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]. 1.18/1.51 213 (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]. 1.18/1.51 214 (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]. 1.18/1.51 215 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cb,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cc,Uu)))) # label(fact_ATP_Olambda__51) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 216 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eh,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ei,Uu)))) # label(fact_ATP_Olambda__26) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 217 (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]. 1.18/1.51 218 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fq,Uu)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fp,Uu))))) # label(fact_ATP_Olambda__16) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 219 (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]. 1.18/1.51 220 (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]. 1.18/1.51 221 (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(aa_fun845057962d_bool(aTP_Lamm_an(Uu),Uua),Uub),Uuc),Uud))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ao(Uu),Uua),Uub),Uuc),Uud)))) # label(fact_ATP_Olambda__169) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 222 -(exists X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,X0),scratc1574338175ptyset))) # label(fact_k__EmptyAx) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 223 (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]. 1.18/1.51 224 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cn,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cm(Uu),Uua))))) # label(fact_ATP_Olambda__104) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 225 (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]. 1.18/1.51 226 (all X all Xa (pp(aa_fun171081125l_bool(scratc148612088n_some,aa_TPT43085870d_bool(scratc708751474ffprop(Xa),X))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1315324671nd_iii,X),Xa)))) # label(fact_def__iii) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 227 (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]. 1.18/1.51 228 (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]. 1.18/1.51 229 (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]. 1.18/1.51 230 (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]. 1.18/1.51 231 (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]. 1.18/1.51 232 (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]. 1.18/1.51 233 (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]. 1.18/1.51 234 (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]. 1.18/1.51 235 (all P all Q (pp(P) | pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)))) # label(help_fimplies_1_1_U) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 236 (all X7 all Y (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) | Y != X7)) # label(help_fequal_2_1_fequal_001t__TPTP____Interpret__Oind_T) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 237 (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]. 1.18/1.51 238 (all X0 all X12 (gg_TPTP_ind(X12) & gg_TPTP_ind(X0) -> (aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,X12) = aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,X0) -> X0 = X12))) # label(fact_ordsucc__inj) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 239 (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]. 1.18/1.51 240 (all X (pp(aa_TPTP_ind_bool(scratc2070922310_cond2,X)) <-> pp(aa_fun171081125l_bool(scratc516108253_n_all,aa_TPT43085870d_bool(aTP_Lamm_ah,X))))) # label(fact_def__cond2) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 241 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ew,Uu),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)))))) # label(fact_ATP_Olambda__87) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 242 (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]. 1.18/1.51 243 (all Uu all Uua all Uub all Uuc (gg_TPTP_ind(Uub) & gg_TPTP_ind(Uuc) & gg_TPTP_ind(Uua) -> (pp(Uu) & Uua = Uuc | Uub = Uuc & -pp(Uu) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bq(Uu),Uua),Uub),Uuc))))) # label(fact_ATP_Olambda__162) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 244 (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]. 1.18/1.51 245 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cx,Uu)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cw,Uu))))) # label(fact_ATP_Olambda__43) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 246 (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]. 1.18/1.51 247 (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]. 1.18/1.51 248 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ds,Uu),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))))) # label(fact_ATP_Olambda__61) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 249 (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]. 1.18/1.51 250 (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]. 1.18/1.51 251 (all X (gg_TPTP_ind(X) -> (pp(aa_TPTP_ind_bool(scratc1380986188pair_p,X)) <-> 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)))))) # label(fact_def__pair__p) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 252 (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]. 1.18/1.51 253 (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]. 1.18/1.51 254 (all B_1 all B_2 gg_bool(aa_bool_bool(B_1,B_2))) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 255 (all P all Q (-pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) | pp(Q) | -pp(P))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 256 (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]. 1.18/1.51 257 (all X aa_TPTP_ind_TPTP_ind(scratc2055805578_proj1,X) = aa_fun277296641TP_ind(scratc1224320725eplSep(X,aTP_Lamm_bj),scratc991996375_d_Unj)) # label(fact_def__proj1) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 258 (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]. 1.18/1.51 259 (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]. 1.18/1.51 260 (all X all Xa scratc1714252958second(X,Xa) = scratc2055805578_proj1) # label(fact_def__second) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 261 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ck,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cl,Uu)))) # label(fact_ATP_Olambda__48) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 262 (all Uu all 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)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cy,Uu),Uua)))) # label(fact_ATP_Olambda__79) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 263 (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]. 1.18/1.51 264 (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]. 1.18/1.51 265 (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]. 1.18/1.51 266 scratc1787566557bvious <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1315587074nd_imp,fFalse),fFalse)) # label(fact_def__obvious) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 267 (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]. 1.18/1.51 268 (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]. 1.18/1.51 269 (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]. 1.18/1.51 270 (all Uu (pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ce,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cf,Uu)))) # label(fact_ATP_Olambda__50) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 271 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eb(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,Uua),aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Uu),Uub))))) # label(fact_ATP_Olambda__146) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 272 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dy,Uu),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)))))) # label(fact_ATP_Olambda__64) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 273 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ci,Uu)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ch,Uu))))) # label(fact_ATP_Olambda__49) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 274 (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]. 1.18/1.51 275 (all X all Xa all Xb all 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)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc660860151etprop(X,Xa),Xb),Xc)))) # label(fact_def__nissetprop) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 276 (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]. 1.18/1.51 277 (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]. 1.18/1.51 278 (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]. 1.18/1.51 279 (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]. 1.18/1.51 280 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cj(Uu),Uua),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)))))) # label(fact_ATP_Olambda__134) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 281 (all X0 scratc1574338175ptyset != aa_TPTP_ind_TPTP_ind(scratc1524236217rdsucc,X0)) # label(fact_neq__ordsucc__0) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 282 (all Uu all Uua all 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))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gh(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__141) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 283 (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]. 1.18/1.51 284 (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]. 1.18/1.51 285 (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]. 1.18/1.51 286 (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]. 1.18/1.51 287 (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]. 1.18/1.51 288 (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]. 1.18/1.51 289 (all Uu all Uua all 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))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fz(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__143) # label(axiom) # label(non_clause). [assumption]. 1.18/1.51 290 (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]. 1.18/1.52 291 (all Uu all 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)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dw,Uu),Uua)))) # label(fact_ATP_Olambda__65) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 292 (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]. 1.18/1.52 293 (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]. 1.18/1.52 294 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eo,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1993139790d_n_is,aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1993598976d_n_pl(Uua),Uu))))) # label(fact_ATP_Olambda__74) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 295 (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]. 1.18/1.52 296 (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_aq(X),Xa),Xb),Xc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc888838298_fixfu(X,Xa),Xb),Xc)))) # label(fact_def__fixfu) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 297 (all X all Xa all Xb all Xc scratc1315652661nd_ind(Xa,aa_TPT43085870d_bool(scratc2056199172_prop1(X,Xa,Xb),Xc)) = aa_TPTP_ind_TPTP_ind(scratc1316046256nd_ite(X,Xa,Xb),Xc)) # label(fact_def__ite) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 298 (all P all X7 (-pp(aa_TPTP_ind_bool(P,X7)) | pp(fEx_TPTP_ind(P)))) # label(help_fEx_1_1_fEx_001t__TPTP____Interpret__Oind_U) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 299 (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]. 1.18/1.52 300 (all Uu (gg_TPTP_ind(Uu) -> ((exists X2 (gg_TPTP_ind(X2) & aa_TPTP_ind_TPTP_ind(scratc143590181d_Inj0,X2) = Uu)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_bk,Uu))))) # label(fact_ATP_Olambda__59) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 301 (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]. 1.18/1.52 302 (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]. 1.18/1.52 303 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(scratc1710340071bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,scratc1574338175ptyset),Uub),Uu),Uua) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_bp(Uu),Uua),Uub)) # label(fact_ATP_Olambda__116) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 304 (all Uu all Uua all 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))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gp(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__124) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 305 (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]. 1.18/1.52 306 (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]. 1.18/1.52 307 (all X all 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))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1701366896_prop1,X),Xa)))) # label(fact_def__d__26__prop1) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 308 (all Uu aa_TPTP_ind_TPTP_ind(aTP_Lamm_ad,Uu) = scratc1356107415nd_nat) # label(fact_ATP_Olambda__176) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 309 (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]. 1.18/1.52 310 (all P all Q (pp(Q) | -pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 311 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1087010230ectset(X,Xa),aa_TPTP_ind_TPTP_ind(scratc1351626757_ecelt(X,Xa),Xb)) = aa_TPTP_ind_TPTP_ind(scratc971808353ectelt(X,Xa),Xb)) # label(fact_def__ectelt) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 312 (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]. 1.18/1.52 313 (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]. 1.18/1.52 314 (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]. 1.18/1.52 315 (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]. 1.18/1.52 316 (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]. 1.18/1.52 317 (all X aa_TPTP_ind_TPTP_ind(scratc143590181d_Inj0,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc787847065d_repl,X),scratc143590182d_Inj1)) # label(fact_def__d__Inj0) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 318 (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]. 1.18/1.52 319 (all X all Xa scratc283496882d_tofs(X,Xa) = scratc1709815289bnd_ap) # label(fact_def__tofs) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 320 (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]. 1.18/1.52 321 (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]. 1.18/1.52 322 (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]. 1.18/1.52 323 (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]. 1.18/1.52 324 (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]. 1.18/1.52 325 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ek,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ej(Uu),Uua))))) # label(fact_ATP_Olambda__101) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 326 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc574983704fixfu2(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_ao(X),Xa),Xb),Xc))))) # label(fact_def__fixfu2) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 327 (all X scratc1249429431nd_all(X) = scratc294126638all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X))) # label(fact_def__all) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 328 (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]. 1.18/1.52 329 (all X all 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)) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1333275155d_d_Pi,X),Xa)) # label(fact_def__d__Pi) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 330 (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]. 1.18/1.52 331 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1538476363_Sigma,X),aTP_Lamm_aj(Xa)) = aa_TPTP_ind_TPTP_ind(scratc1158159311etprod(X),Xa)) # label(fact_def__setprod) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 332 (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]. 1.18/1.52 333 (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]. 1.18/1.52 334 (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(scratc840122054_first(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc414254772d_pair(Uu,Uua),Uub),Uuc))),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ga(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__153) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 335 (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]. 1.18/1.52 336 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc600229837sel_wa(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc1316046256nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc326995781d_e_is(X),Xc),Xa),X,Xb),Xc)) # label(fact_def__wissel__wa) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 337 (all Uu all 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))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fp,Uu),Uua)))) # label(fact_ATP_Olambda__68) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 338 (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]. 1.18/1.52 339 (all B_1 all B_2 gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2))) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 340 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_es,Uu)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_er,Uu))))) # label(fact_ATP_Olambda__22) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 341 (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]. 1.18/1.52 342 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_df,Uu)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_de,Uu))))) # label(fact_ATP_Olambda__39) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 343 (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]. 1.18/1.52 344 (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]. 1.18/1.52 345 (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]. 1.18/1.52 346 (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]. 1.18/1.52 347 (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]. 1.18/1.52 348 (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]. 1.18/1.52 349 (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]. 1.18/1.52 350 (all X all Xa scratc1315652661nd_ind(X,Xa) = scratc1282737854nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bc(X),Xa))) # label(fact_def__ind) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 351 (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]. 1.18/1.52 352 (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]. 1.18/1.52 353 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_gi(Uu),Uua),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))))) # label(fact_ATP_Olambda__137) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 354 (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]. 1.18/1.52 355 (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]. 1.18/1.52 356 (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]. 1.18/1.52 357 (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]. 1.18/1.52 358 (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]. 1.18/1.52 359 (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]. 1.18/1.52 360 (all P all Q (-pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)) | pp(P))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 361 (all X all Xa all Xb all Xc all Xd all Xe (pp(aa_fun171081125l_bool(scratc1552271094l_some(X),aa_TPT43085870d_bool(scratc1071965173_prop1(X,Xa,Xb,Xc,Xd),Xe))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2056199173_prop2(X,Xa,Xb,Xc),Xd),Xe)))) # label(fact_def__prop2) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 362 (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]. 1.18/1.52 363 (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]. 1.18/1.52 364 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cu,Uu),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))))) # label(fact_ATP_Olambda__89) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 365 (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]. 1.18/1.52 366 (all Uu all Uua all Uub all Uuc all Uud ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(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)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_ap(Uu),Uua),Uub),Uuc),Uud)))) # label(fact_ATP_Olambda__168) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 367 (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]. 1.18/1.52 368 (all X all Xa scratc1340651108d_pair = scratc414254772d_pair(X,Xa)) # label(fact_def__d__pair) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 369 (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]. 1.18/1.52 370 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_br(Uu),Uua),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)))))) # label(fact_ATP_Olambda__127) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 371 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dt,Uu)) <-> pp(aa_fun171081125l_bool(scratc294126638all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ds,Uu))))) # label(fact_ATP_Olambda__32) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 372 (all Uu all Uua all Uub all 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)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gg(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__158) # label(axiom) # label(non_clause). [assumption]. 1.18/1.52 373 (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]. 1.18/1.52 374 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564317035d_Subq,X),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))))))) # label(fact_def__d__Subq) # label(axiom) # label(non_clause). [assumption]. 1.18/1.55 375 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ak,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1710340079bnd_in,Uua),Uu)))) # label(fact_ATP_Olambda__99) # label(axiom) # label(non_clause). [assumption]. 1.18/1.55 1.18/1.55 ============================== end of process non-clausal formulas === 1.18/1.55 1.18/1.55 ============================== PROCESS INITIAL CLAUSES =============== 1.18/1.55 1.18/1.55 ============================== PREDICATE ELIMINATION ================= 1.18/1.55 376 -gg_bool(A) | fTrue = A | A = fFalse # label(help_fFalse_1_1_T) # label(axiom). [clausify(128)]. 1.18/1.55 377 gg_bool(scratc1198599609_d_not(A)) # label(gsy_c_Scratch__tptp__translate__46248__31143_ONUM671__thf__4__p_Obnd__d__not) # label(axiom). [clausify(2)]. 1.18/1.55 378 gg_bool(scratc387020528_amone(A,B)) # label(gsy_c_Scratch__tptp__translate__46248__31143_ONUM671__thf__4__p_Obnd__amone) # label(axiom). [clausify(33)]. 1.18/1.55 379 gg_bool(fFalse) # label(gsy_c_fFalse) # label(axiom). [assumption]. 1.18/1.55 380 gg_bool(scratc1365484038nd_or3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__46248__31143_ONUM671__thf__4__p_Obnd__or3) # label(axiom). [clausify(63)]. 1.18/1.55 381 gg_bool(aa_TPTP_ind_bool(A,B)) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom). [clausify(91)]. 1.18/1.55 382 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(94)]. 1.18/1.55 383 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(122)]. 1.18/1.55 Derived: fTrue = scratc1198599609_d_not(A) | scratc1198599609_d_not(A) = fFalse. [resolve(376,a,377,a)]. 1.18/1.55 Derived: fTrue = scratc387020528_amone(A,B) | scratc387020528_amone(A,B) = fFalse. [resolve(376,a,378,a)]. 1.18/1.55 Derived: fTrue = fFalse | fFalse = fFalse. [resolve(376,a,379,a)]. 1.18/1.55 Derived: fTrue = scratc1365484038nd_or3(A,B,C) | scratc1365484038nd_or3(A,B,C) = fFalse. [resolve(376,a,380,a)]. 1.18/1.55 Derived: fTrue = aa_TPTP_ind_bool(A,B) | aa_TPTP_ind_bool(A,B) = fFalse. [resolve(376,a,381,a)]. 1.18/1.55 Derived: fTrue = scratc1861232448d_l_ec(A,B) | scratc1861232448d_l_ec(A,B) = fFalse. [resolve(376,a,382,a)]. 1.18/1.55 Derived: fTrue = aa_fun171081125l_bool(A,B) | aa_fun171081125l_bool(A,B) = fFalse. [resolve(376,a,383,a)]. 1.18/1.55 384 gg_bool(fEx_TPTP_ind(A)) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom). [clausify(150)]. 1.18/1.55 Derived: fTrue = fEx_TPTP_ind(A) | fEx_TPTP_ind(A) = fFalse. [resolve(384,a,376,a)]. 1.18/1.55 385 gg_bool(undefined_bool(bool)) # label(gsy_c_HOL_Oundefined_001t__HOL__Obool) # label(axiom). [assumption]. 1.18/1.55 Derived: fTrue = undefined_bool(bool) | undefined_bool(bool) = fFalse. [resolve(385,a,376,a)]. 1.18/1.55 386 gg_bool(scratc1281885003nd_ec3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__46248__31143_ONUM671__thf__4__p_Obnd__ec3) # label(axiom). [clausify(237)]. 1.18/1.55 Derived: fTrue = scratc1281885003nd_ec3(A,B,C) | scratc1281885003nd_ec3(A,B,C) = fFalse. [resolve(386,a,376,a)]. 1.18/1.55 387 gg_bool(fTrue) # label(gsy_c_fTrue) # label(axiom). [assumption]. 1.18/1.55 Derived: fTrue = fTrue | fTrue = fFalse. [resolve(387,a,376,a)]. 1.18/1.55 388 gg_bool(aa_bool_bool(A,B)) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom). [clausify(254)]. 1.18/1.55 Derived: fTrue = aa_bool_bool(A,B) | aa_bool_bool(A,B) = fFalse. [resolve(388,a,376,a)]. 1.18/1.55 389 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(343)]. 1.18/1.55 Derived: fTrue = scratc1091134429_d_and(A,B) | scratc1091134429_d_and(A,B) = fFalse. [resolve(389,a,376,a)]. 1.18/1.55 390 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(26)]. 1.71/2.02 391 -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(26)]. 1.71/2.02 392 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(49)]. 1.71/2.02 393 -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(49)]. 1.71/2.02 394 pp(scratc1198599609_d_not(scratc1198599609_d_not(A))) | -scratc1430723348nd_wel(A) # label(fact_def__wel) # label(axiom). [clausify(116)]. 1.71/2.02 395 -pp(scratc1198599609_d_not(scratc1198599609_d_not(A))) | scratc1430723348nd_wel(A) # label(fact_def__wel) # label(axiom). [clausify(116)]. 1.71/2.02 396 -scratc1430723348nd_wel(A) | pp(A) # label(fact_l__et) # label(axiom). [clausify(148)]. 1.71/2.02 Derived: pp(A) | -pp(scratc1198599609_d_not(scratc1198599609_d_not(A))). [resolve(396,a,395,b)]. 1.71/2.02 397 -pp(A) | pp(scratc1198599609_d_not(B)) | -scratc108683590d_r_ec(A,B) # label(fact_def__r__ec) # label(axiom). [clausify(344)]. 1.71/2.02 398 pp(A) | scratc108683590d_r_ec(A,B) # label(fact_def__r__ec) # label(axiom). [clausify(344)]. 1.71/2.02 399 -pp(scratc1198599609_d_not(A)) | scratc108683590d_r_ec(B,A) # label(fact_def__r__ec) # label(axiom). [clausify(344)]. 1.71/2.02 1.71/2.02 ============================== end predicate elimination ============= 1.71/2.02 1.71/2.02 Auto_denials: (non-Horn, no changes). 1.71/2.02 1.71/2.02 Term ordering decisions: 1.71/2.02 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. f1=1. f2=1. f14=1. f18=1. f25=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. f9=1. f10=1. f13=1. f15=1. f16=1. f17=1. f19=1. f21=1. f23=1. f24=1. scratc1365484038nd_or3=1. scratc1281885003nd_ec3=1. scratc1650393332d_soft=1. scratc1316046256nd_ite=1. scratc1602720513_indeq=1. scratc2056199172_prop1=Alarm clock 119.51/120.06 Prover9 interrupted 119.51/120.06 EOF