0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.34 % Computer : n024.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 1440 0.13/0.34 % WCLimit : 180 0.13/0.34 % DateTime : Mon Jul 3 11:39:38 EDT 2023 0.13/0.34 % CPUTime : 1.35/1.64 ============================== Prover9 =============================== 1.35/1.64 Prover9 (32) version 2009-11A, November 2009. 1.35/1.64 Process 5457 was started by sandbox on n024.cluster.edu, 1.35/1.64 Mon Jul 3 11:39:39 2023 1.35/1.64 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1440 -f /tmp/Prover9_5294_n024.cluster.edu". 1.35/1.64 ============================== end of head =========================== 1.35/1.64 1.35/1.64 ============================== INPUT ================================= 1.35/1.64 1.35/1.64 % Reading from file /tmp/Prover9_5294_n024.cluster.edu 1.35/1.64 1.35/1.64 set(prolog_style_variables). 1.35/1.64 set(auto2). 1.35/1.64 % set(auto2) -> set(auto). 1.35/1.64 % set(auto) -> set(auto_inference). 1.35/1.64 % set(auto) -> set(auto_setup). 1.35/1.64 % set(auto_setup) -> set(predicate_elim). 1.35/1.64 % set(auto_setup) -> assign(eq_defs, unfold). 1.35/1.64 % set(auto) -> set(auto_limits). 1.35/1.64 % set(auto_limits) -> assign(max_weight, "100.000"). 1.35/1.64 % set(auto_limits) -> assign(sos_limit, 20000). 1.35/1.64 % set(auto) -> set(auto_denials). 1.35/1.64 % set(auto) -> set(auto_process). 1.35/1.64 % set(auto2) -> assign(new_constants, 1). 1.35/1.64 % set(auto2) -> assign(fold_denial_max, 3). 1.35/1.64 % set(auto2) -> assign(max_weight, "200.000"). 1.35/1.64 % set(auto2) -> assign(max_hours, 1). 1.35/1.64 % assign(max_hours, 1) -> assign(max_seconds, 3600). 1.35/1.64 % set(auto2) -> assign(max_seconds, 0). 1.35/1.64 % set(auto2) -> assign(max_minutes, 5). 1.35/1.64 % assign(max_minutes, 5) -> assign(max_seconds, 300). 1.35/1.64 % set(auto2) -> set(sort_initial_sos). 1.35/1.64 % set(auto2) -> assign(sos_limit, -1). 1.35/1.64 % set(auto2) -> assign(lrs_ticks, 3000). 1.35/1.64 % set(auto2) -> assign(max_megs, 400). 1.35/1.64 % set(auto2) -> assign(stats, some). 1.35/1.64 % set(auto2) -> clear(echo_input). 1.35/1.64 % set(auto2) -> set(quiet). 1.35/1.64 % set(auto2) -> clear(print_initial_clauses). 1.35/1.64 % set(auto2) -> clear(print_given). 1.35/1.64 assign(lrs_ticks,-1). 1.35/1.64 assign(sos_limit,10000). 1.35/1.64 assign(order,kbo). 1.35/1.64 set(lex_order_vars). 1.35/1.64 clear(print_given). 1.35/1.64 1.35/1.64 % formulas(sos). % not echoed (444 formulas) 1.35/1.64 1.35/1.64 ============================== end of input ========================== 1.35/1.64 1.35/1.64 % From the command line: assign(max_seconds, 1440). 1.35/1.64 1.35/1.64 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 1.35/1.64 1.35/1.64 % Formulas that are not ordinary clauses: 1.35/1.64 1 (all X0 all X12 all X22 all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1567857808d_d_Pi,X0),X12))) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X32),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,X22),X32)),aa_TPTP_ind_TPTP_ind(X12,X32)))))) # label(fact_ap__Pi) # label(axiom) # label(non_clause). [assumption]. 1.35/1.64 2 (all X all Xa (pp(scratc718232188_d_not(scratc2095815101d_l_ec(X,Xa))) <-> pp(scratc610767008_d_and(X,Xa)))) # label(fact_def__d__and) # label(axiom) # label(non_clause). [assumption]. 1.35/1.64 3 (all X7 all Y (X7 != Y | pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)))) # label(help_fequal_2_1_fequal_001t__TPTP____Interpret__Oind_T) # label(axiom) # label(non_clause). [assumption]. 1.35/1.64 4 (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]. 1.35/1.64 5 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fc,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2069016971nd_nis,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__10) # label(axiom) # label(non_clause). [assumption]. 1.35/1.64 6 (all Uu all Uua all Uub ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X3),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,Uub),X3)),aa_TPTP_ind_TPTP_ind(Uua,X3)))))) <-> pp(aa_TPTP_ind_bool(aa_fun1913827119d_bool(aTP_Lamm_be(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__144) # label(axiom) # label(non_clause). [assumption]. 1.35/1.64 7 (all X all Xa aa_fun1431113780TP_ind(scratc494515559_d_Sep(X),aa_TPT43085870d_bool(aTP_Lamm_bl,Xa)) = aa_TPTP_ind_TPTP_ind(scratc1223447707tminus(X),Xa)) # label(fact_def__setminus) # label(axiom) # label(non_clause). [assumption]. 1.35/1.64 8 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2069016971nd_nis,Uua),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ef,Uu),Uua)))) # label(fact_ATP_Olambda__90) # label(axiom) # label(non_clause). [assumption]. 1.35/1.64 9 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,scratc2095348162ptyset),Uub),Uu),Uua) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_bn(Uu),Uua),Uub)) # label(fact_ATP_Olambda__111) # label(axiom) # label(non_clause). [assumption]. 1.35/1.64 10 (all X (pp(aa_bool_bool(scratc2096471106d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,X),scratc98832752nd_n_1)),aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(aTP_Lamm_ae,X)))) <-> pp(aa_TPTP_ind_bool(scratc1984139126_prop1,X)))) # label(fact_def__d__23__prop1) # label(axiom) # label(non_clause). [assumption]. 1.35/1.64 11 (all X all Xa (pp(aa_fun171081125l_bool(scratc846727211all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,X)),scratc2069410560nd_non(X,aa_TPT43085870d_bool(aTP_Lamm_at(X),Xa)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc893548160_empty,X),Xa)))) # label(fact_def__empty) # label(axiom) # label(non_clause). [assumption]. 1.35/1.64 12 (all Uu all Uua aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1124382172d_repl,Uu),Uua)) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(aTP_Lamm_bk,Uu),Uua)) # label(fact_ATP_Olambda__89) # label(axiom) # label(non_clause). [assumption]. 1.35/1.64 13 (all X all Xa all Xb all Xc all Xd scratc2028037426nd_ind(Xb,aa_TPT43085870d_bool(scratc143298178_prop2(X,Xa,Xb,Xc),Xd)) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1837303166_indeq(X,Xa,Xb),Xc),Xd)) # label(fact_def__indeq) # label(axiom) # label(non_clause). [assumption]. 1.35/1.64 14 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X22),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2059486350_Sigma,X0),X12)),X22) = aa_TPTP_ind_TPTP_ind(X12,X22))) # label(fact_beta) # label(axiom) # label(non_clause). [assumption]. 1.35/1.64 15 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,Uub),aa_fun1431113780TP_ind(scratc494515559_d_Sep(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_gc(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__141) # label(axiom) # label(non_clause). [assumption]. 1.35/1.64 16 (all P all X7 (pp(fEx_TPTP_ind(P)) | -pp(aa_TPTP_ind_bool(P,X7)))) # label(help_fEx_1_1_fEx_001t__TPTP____Interpret__Oind_U) # label(axiom) # label(non_clause). [assumption]. 1.35/1.64 17 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cf(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cg,Uu),Uua)))) # label(fact_ATP_Olambda__101) # label(axiom) # label(non_clause). [assumption]. 1.35/1.64 18 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),scratc98832752nd_n_1))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_er,Uu)))) # label(fact_ATP_Olambda__7) # label(axiom) # label(non_clause). [assumption]. 1.35/1.64 19 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fy(Uu),Uua),Uub)) <-> scratc1623311406_is_of(aa_TPTP_ind_TPTP_ind(scratc1074704707_first(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_ai,Uu)))) # label(fact_ATP_Olambda__117) # label(axiom) # label(non_clause). [assumption]. 1.35/1.64 20 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1475084483nverse(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2059486350_Sigma,Xa),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_aw(X),Xa),Xb))) # label(fact_def__inverse) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 21 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032062638_image(aa_fun1431113780TP_ind(scratc494515559_d_Sep(Uu),Uua),Uu),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2059486350_Sigma,aa_fun1431113780TP_ind(scratc494515559_d_Sep(Uu),Uua)),scratc561578429d_e_in(Uu,Uua))),Uub))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_gb(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__130) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 22 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cx,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc414529904lessis,Uu),Uua)) -> pp(scratc718232188_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,Uu),Uua)))))) # label(fact_ATP_Olambda__78) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 23 (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]. 1.35/1.65 24 (all X scratc561578434d_e_is(X) = fequal_TPTP_ind) # label(fact_def__e__is) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 25 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_eg,Uu)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ef,Uu))))) # label(fact_ATP_Olambda__23) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 26 (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(scratc1802667954bnd_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(scratc1118156403_rec_G(X),Xa),Xb)))) # label(fact_def__d__In__rec__G) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 27 (all X aa_TPTP_ind_TPTP_ind(scratc1768849959d_plus,X) = scratc2028037426nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1567857808d_d_Pi,scratc2068492180nd_nat),aTP_Lamm_ab),aa_TPT43085870d_bool(scratc425017654_prop2,X))) # label(fact_def__plus) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 28 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bb(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(scratc561578434d_e_is(Uu),Uub),Uuc)))))) # label(fact_ATP_Olambda__157) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 29 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_bh,Uu)) <-> (exists X2 (gg_TPTP_ind(X2) & aa_TPTP_ind_TPTP_ind(scratc696190755d_Inj1,X2) = Uu))))) # label(fact_ATP_Olambda__55) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 30 (all X all Xa (pp(scratc2077868803nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1219344880_prop1,X),Xa)))) # label(fact_def__d__29__prop1) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 31 (all B_1 all B_2 gg_TPTP_ind(scratc2028037426nd_ind(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__45846__17029_ONUM669__thf__4__p_Obnd__ind) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 32 (all X aa_fun277296641TP_ind(scratc1807233176eplSep(X,aTP_Lamm_bi),scratc511628954_d_Unj) = aa_TPTP_ind_TPTP_ind(scratc142904582_proj0,X)) # label(fact_def__proj0) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 33 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_eq,Uu)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ep,Uu))))) # label(fact_ATP_Olambda__19) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 34 (all Uu all Uua (scratc1067749701_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(aTP_Lamm_dt(Uu),Uua)),aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(aTP_Lamm_du(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dv,Uu),Uua)))) # label(fact_ATP_Olambda__60) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 35 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ca,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bz(Uu),Uua))))) # label(fact_ATP_Olambda__103) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 36 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X33),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,aa_TPTP_ind_TPTP_ind(X22,X33)),aa_TPTP_ind_TPTP_ind(X12,X33)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2059486350_Sigma,X0),X22)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1567857808d_d_Pi,X0),X12))))) # label(fact_lam__Pi) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 37 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bu,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bt(Uu),Uua))))) # label(fact_ATP_Olambda__105) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 38 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_di,Uu)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dh,Uu))))) # label(fact_ATP_Olambda__33) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 39 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dd,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc548513516moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc414529904lessis,Uua),Uu))))) # label(fact_ATP_Olambda__73) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 40 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc846727211all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_gj(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_gk(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__132) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 41 (all P all Q (-pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)) | pp(Q))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 42 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),Uu)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu)))) # label(fact_ATP_Olambda__9) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 43 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_br,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua)),Uu)))) # label(fact_ATP_Olambda__80) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 44 (all Uu all Uua aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1124382172d_repl,aa_TPTP_ind_TPTP_ind(Uu,Uua)),aa_TPT1424761345TP_ind(scratc1677186215d_pair,Uua)) = aa_TPTP_ind_TPTP_ind(aTP_Lamm_bg(Uu),Uua)) # label(fact_ATP_Olambda__81) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 45 (all X all Xa ((pp(X) -> pp(scratc718232188_d_not(Xa))) <-> scratc343266243d_r_ec(X,Xa))) # label(fact_def__r__ec) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 46 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,Uub),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1567857808d_d_Pi,Uu),aTP_Lamm_ah(Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gf(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__137) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 47 (all B_1 all B_2 gg_bool(scratc621603181_amone(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__45846__17029_ONUM669__thf__4__p_Obnd__amone) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 48 (all X aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(X),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,X))) # label(fact_def__ordsucc) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 49 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dh,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uua),Uu))))) # label(fact_ATP_Olambda__72) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 50 (all X (pp(scratc718232188_d_not(X)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc2027971839nd_imp,X),fFalse)))) # label(fact_def__d__not) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 51 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),Uua)) -> pp(scratc718232188_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc548513516moreis,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cp,Uu),Uua)))) # label(fact_ATP_Olambda__79) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 52 (all X0 pp(aa_fun171081125l_bool(scratc846727211all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,X0)),aa_TPT43085870d_bool(aTP_Lamm_gl,X0)))) # label(fact_refis) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 53 (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(scratc2095815101d_l_ec(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1830090288d_esti(Uu),Uuc),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1830090288d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__152) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 54 (all X all Xa all Xb (scratc1067749701_orec3(X,Xa,Xb) <-> pp(scratc610767008_d_and(scratc2077868803nd_or3(X,Xa,Xb),scratc1994269768nd_ec3(X,Xa,Xb))))) # label(fact_def__orec3) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 55 (all X0 all X12 (gg_TPTP_ind(X12) -> X12 = aa_TPTP_ind_TPTP_ind(scratc142904583_proj1,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1677186215d_pair,X0),X12)))) # label(fact_proj1__pair__eq) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 56 (all X (gg_TPTP_ind(X) -> (pp(aa_TPTP_ind_bool(scratc1933586761pair_p,X)) <-> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1677186215d_pair,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,X),scratc2095348162ptyset)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,X),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset))) = X))) # label(fact_def__pair__p) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 57 (all B_1 all B_2 all B_3 gg_bool(scratc2077868803nd_or3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__45846__17029_ONUM669__thf__4__p_Obnd__or3) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 58 (all X all Xa all Xb (pp(scratc2077868803nd_or3(X,Xa,Xb)) <-> pp(aa_bool_bool(scratc2096471106d_l_or(X),aa_bool_bool(scratc2096471106d_l_or(Xa),Xb))))) # label(fact_def__or3) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 59 (all X all Xa aa_TPT494704832TP_ind(scratc1124382172d_repl,aa_fun1431113780TP_ind(scratc494515559_d_Sep(X),Xa)) = scratc1807233176eplSep(X,Xa)) # label(fact_def__d__ReplSep) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 60 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2059486350_Sigma,X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc313305066munion,X),aTP_Lamm_bg(Xa))) # label(fact_def__d__Sigma) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 61 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> pp(X0) & X12 = aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(X0,X12),X22) | -pp(X0) & X22 = aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(X0,X12),X22))) # label(fact_if__i__correct) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 62 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2059486350_Sigma,X),aTP_Lamm_ah(Xa)) = aa_TPTP_ind_TPTP_ind(scratc1710759884etprod(X),Xa)) # label(fact_def__setprod) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 63 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_af,Uu),Uua)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc2027971839nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238790d_n_in,Uua),Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238790d_n_in,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uua)),Uu))))) # label(fact_ATP_Olambda__70) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 64 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cd,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cc(Uu),Uua))))) # label(fact_ATP_Olambda__102) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 65 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,Uu),Uua)) -> pp(scratc718232188_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc414529904lessis,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cr,Uu),Uua)))) # label(fact_ATP_Olambda__76) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 66 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc2028431021nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(X),Xc),Xa),X,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc1183142288sel_wa(X,Xa,Xb),Xc)) # label(fact_def__wissel__wa) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 67 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,Uub),Uu)) & pp(aa_TPTP_ind_bool(Uua,Uub)) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ba(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__129) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 68 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238790d_n_in,Uua),Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fg,Uu),Uua)))) # label(fact_ATP_Olambda__94) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 69 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(Uua,aa_TPTP_ind_TPTP_ind(scratc561578429d_e_in(Uu,Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_gd(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__143) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 70 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2069016971nd_nis,Xa),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc42620530_prop1,X),Xa)))) # label(fact_def__d__27__prop1) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 71 (all Uu (pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_br,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_bs,Uu)))) # label(fact_ATP_Olambda__51) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 72 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ec(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2069016971nd_nis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2069016971nd_nis,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uub)))))) # label(fact_ATP_Olambda__126) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 73 (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(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),Uua))))) # label(fact_ATP_Olambda__83) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 74 (all Uu (pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bu,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_bv,Uu)))) # label(fact_ATP_Olambda__50) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 75 (all X0 (scratc2143108113nd_wel(X0) -> pp(X0))) # label(fact_l__et) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 76 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fl,Uu)) <-> scratc1623311406_is_of(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu),aTP_Lamm_a))) # label(fact_ATP_Olambda__11) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 77 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ff,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,Uu),aa_TPTP_ind_TPTP_ind(scratc14390744_power,scratc2068492180nd_nat))))) # label(fact_ATP_Olambda__13) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 78 (all X0 all X12 all X22 (gg_TPTP_ind(X12) -> (pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(X0,X12),X22) = X12))) # label(fact_if__i__1) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 79 (all X0 all X12 pp(aa_fun171081125l_bool(scratc846727211all_of(aa_TPT43085870d_bool(aTP_Lamm_fv(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_fx(X0),X12)))) # label(fact_second__p) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 80 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc615049083d_incl(Uu),Uua),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc615049083d_incl(Uu),Uub),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(aa_TPTP_ind_TPTP_ind(scratc14390744_power,Uu)),Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fn(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__115) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 81 (all X0 all X12 (gg_TPTP_ind(X0) -> X0 = aa_TPTP_ind_TPTP_ind(scratc142904582_proj0,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1677186215d_pair,X0),X12)))) # label(fact_proj0__pair__eq) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 82 (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]. 1.35/1.65 83 (all X all Xa (pp(scratc610767008_d_and(aa_bool_bool(scratc2096471106d_l_or(X),Xa),scratc2095815101d_l_ec(X,Xa))) <-> scratc1036782190d_orec(X,Xa))) # label(fact_def__orec) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 84 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,Uu),scratc2068492180nd_nat)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_a,Uu)))) # label(fact_ATP_Olambda__14) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 85 (all X all Xa scratc1995122619nd_eps(aa_fun1584354236d_bool(aTP_Lamm_ba(X),Xa)) = scratc2028037426nd_ind(X,Xa)) # label(fact_def__ind) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 86 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (-pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(X0,X12),X22) = X22))) # label(fact_if__i__0) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 87 (all X all Xa aa_fun1431113780TP_ind(scratc494515559_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1802667954bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1124382172d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc2095348162ptyset)) # label(fact_def__d__Sep) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 88 (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]. 1.35/1.65 89 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dt(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__138) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 90 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_co,Uu)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cn,Uu))))) # label(fact_ATP_Olambda__43) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 91 (all Uu aa_TPT494704832TP_ind(aTP_Lamm_bj,Uu) = aa_TPT494704832TP_ind(scratc1124382172d_repl,aa_TPTP_ind_TPTP_ind(scratc1223447707tminus(Uu),aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,scratc2095348162ptyset)))) # label(fact_ATP_Olambda__53) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 92 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dx,Uu),Uua)) <-> pp(scratc621603181_amone(scratc2068492180nd_nat,aa_TPT43085870d_bool(aTP_Lamm_dt(Uu),Uua))))) # label(fact_ATP_Olambda__106) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 93 (all Uu all Uua (gg_TPTP_ind(Uua) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bf,Uu),Uua)) <-> (exists X3 (aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1677186215d_pair,Uu),X3) = Uua & gg_TPTP_ind(X3)))))) # label(fact_ATP_Olambda__109) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 94 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1677186215d_pair,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1124382172d_repl,X),scratc696190754d_Inj0)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1124382172d_repl,Xa),scratc696190755d_Inj1))) # label(fact_def__pair) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 95 (all X0 all X12 pp(aa_fun171081125l_bool(scratc846727211all_of(aa_TPT43085870d_bool(aTP_Lamm_gf(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_gi(X0),X12)))) # label(fact_e__fisi) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 96 (all X0 all X12 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc772422746ective(aa_fun1431113780TP_ind(scratc494515559_d_Sep(X0),X12)),X0),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2059486350_Sigma,aa_fun1431113780TP_ind(scratc494515559_d_Sep(X0),X12)),scratc561578429d_e_in(X0,X12))))) # label(fact_otax1) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 97 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_et,Uu)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_es,Uu))))) # label(fact_ATP_Olambda__18) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 98 (all X all Xa all Xb all Xc all Xd (pp(scratc610767008_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc2027971839nd_imp,X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(Xa),Xd),Xb)),aa_bool_bool(aa_boo1142376798l_bool(scratc2027971839nd_imp,scratc718232188_d_not(X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(Xa),Xd),Xc)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc143298177_prop1(X,Xa,Xb),Xc),Xd)))) # label(fact_def__prop1) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 99 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_ay(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc2027971839nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,Uub),Uud))),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(Uu),Uuc),Uud))))) # label(fact_ATP_Olambda__160) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 100 (all X all Xa all Xb (gg_TPTP_ind(Xb) -> Xb = aa_TPTP_ind_TPTP_ind(scratc561578429d_e_in(X,Xa),Xb))) # label(fact_def__e__in) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 101 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cv,Uu),Uua)) <-> (pp(scratc718232188_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc414529904lessis,Uu),Uua))))) # label(fact_ATP_Olambda__85) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 102 (all X all Xa scratc1802143164bnd_ap = scratc620031989d_tofs(X,Xa)) # label(fact_def__tofs) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 103 (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_ak(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_aj(Uua),Uub),Uuc),Uud),Uue),Uuf))))) # label(fact_ATP_Olambda__167) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 104 (all Uu (pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dp,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_dq,Uu)))) # label(fact_ATP_Olambda__29) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 105 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1994269829nd_ecp(X,Xa),Xb),Xc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(aa_TPTP_ind_TPTP_ind(scratc14390744_power,X)),Xb),aa_TPTP_ind_TPTP_ind(scratc1586209410_ecelt(X,Xa),Xc))))) # label(fact_def__ecp) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 106 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(scratc98832752nd_n_1),Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_eo,Uu)))) # label(fact_ATP_Olambda__8) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 107 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ap(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1830090288d_esti(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__149) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 108 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(Uu),aa_TPTP_ind_TPTP_ind(scratc1074704707_first(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc966855345d_pair(Uu,Uua),Uub),Uuc))),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ft(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__146) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 109 (all B_1 all B_2 gg_bool(scratc610767008_d_and(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__45846__17029_ONUM669__thf__4__p_Obnd__d__and) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 110 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc2077606457nd_one(X0),X12)) -> scratc1623311406_is_of(scratc2028037426nd_ind(X0,X12),aa_TPT43085870d_bool(aTP_Lamm_ai,X0)))) # label(fact_ind__p) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 111 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ev,Uu),Uua)))) # label(fact_ATP_Olambda__67) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 112 (all X aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1124382172d_repl,X),scratc696190755d_Inj1) = aa_TPTP_ind_TPTP_ind(scratc696190754d_Inj0,X)) # label(fact_def__d__Inj0) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 113 (all P (gg_bool(P) -> fFalse = P | fTrue = P)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 114 (all X0 all X12 pp(aa_fun171081125l_bool(scratc846727211all_of(aa_fun1584354236d_bool(aTP_Lamm_gc(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_ge(X0),X12)))) # label(fact_e__in__p) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 115 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1986928439d_soft(X,Xa,Xb),Xc) = scratc2028037426nd_ind(X,aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ax(Xa),Xb),Xc))) # label(fact_def__soft) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 116 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fb,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2069016971nd_nis,Uu),scratc98832752nd_n_1)) -> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(aTP_Lamm_ae,Uu)))))) # label(fact_ATP_Olambda__1) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 117 (all X aa_boo1142376798l_bool(scratc2027971839nd_imp,scratc718232188_d_not(X)) = scratc2096471106d_l_or(X)) # label(fact_def__l__or) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 118 (all X0 all X12 pp(aa_fun171081125l_bool(scratc846727211all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,X0)),aa_fun1584354236d_bool(aTP_Lamm_fq(X0),X12)))) # label(fact_estii) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 119 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_eu,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(scratc98832752nd_n_1),Uu)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu))))) # label(fact_ATP_Olambda__4) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 120 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ez,Uu)) <-> pp(aa_fun171081125l_bool(scratc2077606457nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1567857808d_d_Pi,scratc2068492180nd_nat),aTP_Lamm_ab)),aa_TPT43085870d_bool(aTP_Lamm_ey,Uu))))) # label(fact_ATP_Olambda__5) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 121 (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]. 1.35/1.65 122 (all X all Xa all Xb all Xc all Xd all Xe all Xf (pp(scratc610767008_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1830090288d_esti(X),Xf),aa_TPTP_ind_TPTP_ind(scratc1585619019_ecect(X,Xa),Xd)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,Xc),Xf)),Xe))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc972340280_prop1(X,Xa,Xb,Xc,Xd),Xe),Xf)))) # label(fact_def__d__10__prop1) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 123 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ga(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fz(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__134) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 124 (all B_1 gg_bool(fEx_TPTP_ind(B_1))) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 125 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_el,Uu)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ek,Uu))))) # label(fact_ATP_Olambda__21) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 126 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(X),Xa))))) # label(fact_def__d__29__ii) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 127 (all Uu (pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cv,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cw,Uu)))) # label(fact_ATP_Olambda__39) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 128 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc521652610_union,aa_TPTP_ind_TPTP_ind(scratc1953972728_UPair(X),Xa)) = aa_TPTP_ind_TPTP_ind(scratc1307162165nunion(X),Xa)) # label(fact_def__binunion) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 129 (all X all Xa all Xb (pp(scratc718232188_d_not(aa_TPTP_ind_bool(Xa,Xb))) <-> pp(aa_TPTP_ind_bool(scratc2069410560nd_non(X,Xa),Xb)))) # label(fact_def__non) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 130 (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]. 1.35/1.65 131 (all X all Xa (-pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2066917798nd_nIn,X),Xa)))) # label(fact_def__nIn) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 132 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ce,Uu)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cd,Uu))))) # label(fact_ATP_Olambda__47) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 133 (all X scratc1961814196nd_all(X) = scratc846727211all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,X))) # label(fact_def__all) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 134 -(exists X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X0),scratc2095348162ptyset))) # label(fact_k__EmptyAx) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 135 (all Uu all Uua all Uub all Uuc all Uud all Uue (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_al(Uu),Uua),Uub),Uuc),Uud),Uue)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_ak(Uu),Uua),Uub),Uuc),Uud),Uue))))) # label(fact_ATP_Olambda__165) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 136 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cb,Uu)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ca,Uu))))) # label(fact_ATP_Olambda__48) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 137 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,X),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1229761461ffprop(X),Xa),Xb)))) # label(fact_def__diffprop) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 138 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc414529904lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc548513516moreis,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_db,Uu),Uua)))) # label(fact_ATP_Olambda__74) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 139 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1567857808d_d_Pi,X0),X12))) -> (all X32 (gg_TPTP_ind(X32) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X32),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1567857808d_d_Pi,X0),X12))) -> ((all X42 (gg_TPTP_ind(X42) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X42),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,X32),X42) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,X22),X42)))) -> X22 = X32))))))) # label(fact_k__Pi__ext) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 140 (all X all Xa all Xb aa_fun1431113780TP_ind(scratc494515559_d_Sep(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aq(X),Xa),Xb)) = aa_TPTP_ind_TPTP_ind(scratc712760155unmore(X,Xa),Xb)) # label(fact_def__unmore) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 141 (all Uu all Uua ((pp(scratc718232188_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc548513516moreis,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ct,Uu),Uua)))) # label(fact_ATP_Olambda__88) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 142 (all Uu all Uua all Uub all Uuc (scratc1623311406_is_of(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc966855345d_pair(Uu,Uua),Uub),Uuc),aa_TPT43085870d_bool(aTP_Lamm_fv(Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fz(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__151) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 143 (all X ((all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,aa_TPTP_ind_TPTP_ind(scratc521652610_union,X1)),X))))) <-> pp(aa_TPTP_ind_bool(scratc136593508closed,X)))) # label(fact_def__d__Union__closed) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 144 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dc,Uu)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_db,Uu))))) # label(fact_ATP_Olambda__36) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 145 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_fun171081125l_bool(scratc846727211all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_al(Uu),Uua),Uub),Uuc),Uud))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_am(Uu),Uua),Uub),Uuc),Uud)))) # label(fact_ATP_Olambda__162) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 146 (all X (pp(aa_fun171081125l_bool(scratc2104871667l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1567857808d_d_Pi,scratc2068492180nd_nat),aTP_Lamm_ab)),aa_TPT43085870d_bool(scratc425017654_prop2,X))) <-> pp(aa_TPTP_ind_bool(scratc143298180_prop4,X)))) # label(fact_def__prop4) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 147 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))))) # label(fact_ATP_Olambda__52) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 148 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dm,Uu)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dl,Uu))))) # label(fact_ATP_Olambda__31) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 149 (all Uu all Uua all Uub (scratc1623311406_is_of(aa_TPTP_ind_TPTP_ind(scratc1233885537second(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_ai,Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fx(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__116) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 150 (all Uu (pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dx,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_dy,Uu)))) # label(fact_ATP_Olambda__26) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 151 (all Uu all Uua ((pp(scratc718232188_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc548513516moreis,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cn,Uu),Uua)))) # label(fact_ATP_Olambda__86) # label(axiom) # label(non_clause). [assumption]. 1.35/1.65 152 (all X0 all X12 pp(aa_fun171081125l_bool(scratc846727211all_of(aa_fun1584354236d_bool(aTP_Lamm_gc(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_gd(X0),X12)))) # label(fact_e__inp) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 153 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2069016971nd_nis,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),scratc98832752nd_n_1)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fk,Uu)))) # label(fact_ATP_Olambda__12) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 154 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc14390744_power,X0)))) # label(fact_k__Self__In__Power) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 155 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fr(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(Uua),aa_TPTP_ind_TPTP_ind(scratc1233885537second(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc966855345d_pair(Uu,Uua),Uub),Uuc))),Uuc)))) # label(fact_ATP_Olambda__147) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 156 (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]. 1.35/1.66 157 scratc192683482bvious <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc2027971839nd_imp,fFalse),fFalse)) # label(fact_def__obvious) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 158 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bx,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bw(Uu),Uua))))) # label(fact_ATP_Olambda__104) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 159 (all X0 all X12 (gg_TPTP_ind(X12) & gg_TPTP_ind(X0) -> (aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X12) = aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X0) -> X0 = X12))) # label(fact_ordsucc__inj) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 160 (all Uu (pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eh,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ei,Uu)))) # label(fact_ATP_Olambda__22) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 161 (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_aj(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(scratc561578434d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,Uub),Uuc)),Uue)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,Uub),Uud)),Uuf))))))) # label(fact_ATP_Olambda__166) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 162 (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]. 1.35/1.66 163 (all X all Xa all Xb (pp(scratc610767008_d_and(X,scratc610767008_d_and(Xa,Xb))) <-> scratc812867977d_and3(X,Xa,Xb))) # label(fact_def__and3) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 164 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,Uua),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ax(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__150) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 165 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X22),X0)) -> (pp(aa_TPTP_ind_bool(X12,X22)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X22),aa_fun1431113780TP_ind(scratc494515559_d_Sep(X0),X12)))))) # label(fact_k__SepI) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 166 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gi(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aa_TPT43085870d_bool(aTP_Lamm_gf(Uu),Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gh(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__119) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 167 (all X0 all X12 pp(aa_fun171081125l_bool(scratc846727211all_of(aa_TPT43085870d_bool(aTP_Lamm_fv(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_fw(X0),X12)))) # label(fact_pairis1) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 168 (all Uu all Uua all Uub all Uuc (pp(aa_fun171081125l_bool(scratc1961814196nd_all(Uu),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_ay(Uu),Uua),Uub),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_az(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__158) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 169 (all B_1 gg_TPTP_ind(scratc1995122619nd_eps(B_1))) # label(gsy_c_Scratch__tptp__translate__45846__17029_ONUM669__thf__4__p_Obnd__eps) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 170 (all X all Xa all Xb (pp(scratc1994269768nd_ec3(X,Xa,Xb)) <-> scratc812867977d_and3(scratc2095815101d_l_ec(X,Xa),scratc2095815101d_l_ec(Xa,Xb),scratc2095815101d_l_ec(Xb,X)))) # label(fact_def__ec3) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 171 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(X),Xa)),Xb)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(X),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Xa),Xb)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1013379828_prop1(X),Xa),Xb)))) # label(fact_def__d__25__prop1) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 172 (all X0 all X12 pp(aa_fun171081125l_bool(scratc846727211all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,X0)),aa_fun1584354236d_bool(aTP_Lamm_gb(X0),X12)))) # label(fact_otax2) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 173 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dg,Uu)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_df,Uu))))) # label(fact_ATP_Olambda__34) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 174 (all X aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1768849959d_plus,X)) = scratc80697981d_n_pl(X)) # label(fact_def__n__pl) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 175 (all X aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2059486350_Sigma,scratc2068492180nd_nat),aTP_Lamm_ac(X)) = aa_TPTP_ind_TPTP_ind(scratc325144174d_24_g,X)) # label(fact_def__d__24__g) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 176 (all X0 (gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(scratc1509955612_nat_p,X0)) -> X0 = scratc2095348162ptyset | (exists X13 (gg_TPTP_ind(X13) & pp(aa_TPTP_ind_bool(scratc1509955612_nat_p,X13)) & aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X13) = X0))))) # label(fact_nat__inv) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 177 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Xa),X))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1601742003_prop1,X),Xa)))) # label(fact_def__d__26__prop1) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 178 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc846727211all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bb(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bc(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__133) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 179 (all X all Xa all Xb all Xc (pp(aa_fun171081125l_bool(scratc846727211all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ao(X),Xa),Xb),Xc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1123420951_fixfu(X,Xa),Xb),Xc)))) # label(fact_def__fixfu) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 180 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fj,Uu)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fi,Uu))))) # label(fact_ATP_Olambda__15) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 181 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2116917608d_Subq,X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X2),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X2),Xa))))))) # label(fact_def__d__Subq) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 182 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_an(Uu),Uua),Uub),Uuc),Uud)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,Uub),Uud)))))) # label(fact_ATP_Olambda__161) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 183 (all Uu all Uua all Uub all Uuc (gg_TPTP_ind(Uua) & gg_TPTP_ind(Uuc) & gg_TPTP_ind(Uub) -> (pp(Uu) & Uuc = Uua | Uuc = Uub & -pp(Uu) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bo(Uu),Uua),Uub),Uuc))))) # label(fact_ATP_Olambda__155) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 184 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ej(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__121) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 185 (all B_1 all B_2 all B_3 gg_bool(scratc1994269768nd_ec3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__45846__17029_ONUM669__thf__4__p_Obnd__ec3) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 186 (all X all Xa (pp(aa_bool_bool(scratc2096471106d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc548513516moreis,X),Xa)))) # label(fact_def__moreis) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 187 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__91) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 188 (all Uu (pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ev,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ew,Uu)))) # label(fact_ATP_Olambda__17) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 189 (all Uu (pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cx,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cy,Uu)))) # label(fact_ATP_Olambda__38) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 190 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ee,Uu)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ed,Uu))))) # label(fact_ATP_Olambda__24) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 191 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1640284202t_disj(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1961814196nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ar(X),Xa),Xb))))) # label(fact_def__st__disj) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 192 (all X (pp(aa_TPTP_ind_bool(scratc1416680303closed,X)) <-> pp(aa_TPTP_ind_bool(scratc1134690962closed,X)) & pp(aa_TPTP_ind_bool(scratc301326522closed,X)) & pp(aa_TPTP_ind_bool(scratc136593508closed,X)))) # label(fact_def__d__ZF__closed) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 193 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cs,Uu)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cr,Uu))))) # label(fact_ATP_Olambda__41) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 194 (all X all Xa scratc561578429d_e_in(aa_TPTP_ind_TPTP_ind(scratc14390744_power,X),scratc812933624d_anec(X,Xa)) = scratc1585619019_ecect(X,Xa)) # label(fact_def__ecect) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 195 (all X all Xa (pp(scratc610767008_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc2027971839nd_imp,X),Xa),aa_bool_bool(aa_boo1142376798l_bool(scratc2027971839nd_imp,Xa),X))) <-> scratc1504908458_l_iff(X,Xa))) # label(fact_def__l__iff) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 196 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1953972728_UPair(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1124382172d_repl,aa_TPTP_ind_TPTP_ind(scratc14390744_power,aa_TPTP_ind_TPTP_ind(scratc14390744_power,scratc2095348162ptyset))),aa_TPT1424761345TP_ind(aTP_Lamm_bn(X),Xa))) # label(fact_def__d__UPair) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 197 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc14390744_power,X0))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2116917608d_Subq,X12),X0)))) # label(fact_k__PowerE) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 198 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ch,Uu)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cg,Uu))))) # label(fact_ATP_Olambda__46) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 199 (all X all Xa all Xb all Xc (pp(aa_fun171081125l_bool(scratc2104871667l_some(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ax(Xa),Xb),Xc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032062638_image(X,Xa),Xb),Xc)))) # label(fact_def__image) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 200 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1567857808d_d_Pi,X),Xa) = aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc14390744_power,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2059486350_Sigma,X),aTP_Lamm_bd(Xa)))),aa_fun1913827119d_bool(aTP_Lamm_be(X),Xa))) # label(fact_def__d__Pi) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 201 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fd,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2069016971nd_nis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2069016971nd_nis,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uua)))))) # label(fact_ATP_Olambda__69) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 202 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ed,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ec(Uu),Uua))))) # label(fact_ATP_Olambda__98) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 203 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cf(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc414529904lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__125) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 204 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dn,Uu),Uua)) <-> scratc1067749701_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),Uua)))) # label(fact_ATP_Olambda__57) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 205 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(X,Xa),Xb) = scratc1995122619nd_eps(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bo(X),Xa),Xb))) # label(fact_def__if) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 206 (all X all Xa all Xb all Xc all Xd all Xe (pp(aa_fun171081125l_bool(scratc2104871667l_some(X),aa_TPT43085870d_bool(scratc972340280_prop1(X,Xa,Xb,Xc,Xd),Xe))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc143298178_prop2(X,Xa,Xb,Xc),Xd),Xe)))) # label(fact_def__prop2) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 207 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc14390744_power,X0))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2116917608d_Subq,X12),X0)))) # label(fact_k__PowerEq) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 208 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_aw(Uu),Uua),Uub),Uuc) = aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032062638_image(Uu,Uua),Uub),Uuc),aa_TPTP_ind_TPTP_ind(scratc1986928439d_soft(Uu,Uua,Uub),Uuc)),scratc2095348162ptyset)) # label(fact_ATP_Olambda__145) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 209 (all X0 all X12 pp(aa_fun171081125l_bool(scratc846727211all_of(aa_TPT43085870d_bool(aTP_Lamm_fv(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_fy(X0),X12)))) # label(fact_first__p) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 210 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc956141976ective(X),Xa),Xb)) <-> pp(scratc610767008_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc772422746ective(X),Xa),Xb),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc779517897ective(X),Xa),Xb))))) # label(fact_def__bijective) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 211 (all Uu (pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dr,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ds,Uu)))) # label(fact_ATP_Olambda__28) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 212 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eh,Uu),Uua)))) # label(fact_ATP_Olambda__71) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 213 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ai,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,Uua),Uu)))) # label(fact_ATP_Olambda__96) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 214 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_ag,Uu)) <-> scratc2095348162ptyset != Uu))) # label(fact_ATP_Olambda__54) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 215 (all X0 pp(aa_fun171081125l_bool(scratc846727211all_of(aa_TPT43085870d_bool(aTP_Lamm_fm,X0)),aa_TPT43085870d_bool(aTP_Lamm_fo,X0)))) # label(fact_isseti) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 216 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_es,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__66) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 217 (all Uu aa_TPTP_ind_TPTP_ind(aTP_Lamm_ab,Uu) = scratc2068492180nd_nat) # label(fact_ATP_Olambda__169) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 218 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1534996756In_rec(X),Xa) = scratc1995122619nd_eps(aa_TPT43085870d_bool(scratc1118156403_rec_G(X),Xa))) # label(fact_def__d__In__rec) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 219 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X22),aa_fun1431113780TP_ind(scratc494515559_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X22),X0)))) # label(fact_k__SepE1) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 220 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X22),X0)) -> (all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X32),aa_TPTP_ind_TPTP_ind(X12,X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1677186215d_pair,X22),X32)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2059486350_Sigma,X0),X12))))))) # label(fact_pair__Sigma) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 221 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_as(Uu),Uua),Uub),Uuc)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc2027971839nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1830090288d_esti(Uu),Uuc),Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1830090288d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__153) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 222 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fe,Uu)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fd,Uu))))) # label(fact_ATP_Olambda__16) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 223 (all X aa_TPTP_ind_TPTP_ind(scratc1953972728_UPair(X),X) = aa_TPTP_ind_TPTP_ind(scratc2018566726d_Sing,X)) # label(fact_def__d__Sing) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 224 (all X all Xa scratc1986928439d_soft(aa_fun1431113780TP_ind(scratc494515559_d_Sep(X),Xa),X,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2059486350_Sigma,aa_fun1431113780TP_ind(scratc494515559_d_Sep(X),Xa)),scratc561578429d_e_in(X,Xa))) = scratc2078065665nd_out(X,Xa)) # label(fact_def__out) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 225 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc548513516moreis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bw(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__122) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 226 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc846727211all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ft(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fu(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__135) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 227 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc2077606457nd_one(X0),X12)) -> pp(aa_TPTP_ind_bool(X12,scratc2028037426nd_ind(X0,X12))))) # label(fact_oneax) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 228 (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]. 1.35/1.66 229 (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]. 1.35/1.66 230 (all X all Xa all Xb all Xc scratc2028037426nd_ind(Xa,aa_TPT43085870d_bool(scratc143298177_prop1(X,Xa,Xb),Xc)) = aa_TPTP_ind_TPTP_ind(scratc2028431021nd_ite(X,Xa,Xb),Xc)) # label(fact_def__ite) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 231 (all X ((all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,aa_TPTP_ind_TPTP_ind(scratc14390744_power,X1)),X))))) <-> pp(aa_TPTP_ind_bool(scratc301326522closed,X)))) # label(fact_def__d__Power__closed) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 232 (all X all Xa (pp(scratc718232188_d_not(aa_fun171081125l_bool(scratc846727211all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,X)),scratc2069410560nd_non(X,Xa)))) <-> pp(aa_fun171081125l_bool(scratc2104871667l_some(X),Xa)))) # label(fact_def__l__some) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 233 (all Uu ((pp(aa_TPTP_ind_bool(scratc158021314_cond1,Uu)) -> (pp(aa_TPTP_ind_bool(scratc158021315_cond2,Uu)) -> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fg,Uu))))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fh,Uu)))) # label(fact_ATP_Olambda__6) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 234 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_av(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,Uu),Uub))) # label(fact_ATP_Olambda__142) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 235 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1830090288d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc494515559_d_Sep(Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_fq(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__131) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 236 (all X (pp(scratc718232188_d_not(scratc718232188_d_not(X))) <-> scratc2143108113nd_wel(X))) # label(fact_def__wel) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 237 (all X0 (pp(aa_TPTP_ind_bool(X0,scratc2095348162ptyset)) -> ((all X13 (gg_TPTP_ind(X13) -> (pp(aa_TPTP_ind_bool(scratc1509955612_nat_p,X13)) -> (pp(aa_TPTP_ind_bool(X0,X13)) -> pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X13))))))) -> (all X12 (pp(aa_TPTP_ind_bool(scratc1509955612_nat_p,X12)) -> pp(aa_TPTP_ind_bool(X0,X12))))))) # label(fact_nat__ind) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 238 (all X all Xa scratc142904583_proj1 = scratc1233885537second(X,Xa)) # label(fact_def__second) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 239 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc2028431021nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(X),Xc),Xb),X,Xa),aa_TPTP_ind_TPTP_ind(scratc1183142288sel_wa(X,Xa,Xb),Xc)) = aa_TPTP_ind_TPTP_ind(scratc1183142289sel_wb(X,Xa,Xb),Xc)) # label(fact_def__wissel__wb) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 240 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ad,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,Uu),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,Uu),Uua)))))) # label(fact_ATP_Olambda__68) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 241 (all B_1 all B_2 gg_bool(scratc2095815101d_l_ec(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__45846__17029_ONUM669__thf__4__p_Obnd__l__ec) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 242 (all Uu (pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ct,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cu,Uu)))) # label(fact_ATP_Olambda__40) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 243 (all P all Q (pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)) | -pp(Q) | -pp(P))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 244 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc846727211all_of(aa_TPT43085870d_bool(aTP_Lamm_fm,Uu)),aa_TPT43085870d_bool(aTP_Lamm_fn(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fo,Uu),Uua)))) # label(fact_ATP_Olambda__82) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 245 (all X0 ((all X13 (gg_TPTP_ind(X13) -> ((all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_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]. 1.35/1.66 246 (all X (pp(aa_TPTP_ind_bool(scratc1395776951_prop1,X)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2069016971nd_nis,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X)),X)))) # label(fact_def__d__22__prop1) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 247 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dw,Uu)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dv,Uu))))) # label(fact_ATP_Olambda__27) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 248 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dz(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__120) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 249 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_df,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,Uua),Uu))))) # label(fact_ATP_Olambda__75) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 250 (all X all Xa (pp(scratc610767008_d_and(scratc621603181_amone(X,Xa),aa_fun171081125l_bool(scratc2104871667l_some(X),Xa))) <-> pp(aa_fun171081125l_bool(scratc2077606457nd_one(X),Xa)))) # label(fact_def__one) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 251 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gh(Uu),Uua),Uub),Uuc)) <-> (pp(aa_fun171081125l_bool(scratc846727211all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gg(Uua),Uub),Uuc))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1567857808d_d_Pi,Uu),aTP_Lamm_ah(Uua))),Uub),Uuc))))) # label(fact_ATP_Olambda__154) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 252 (all X all Xa ((all X2 (gg_TPTP_ind(X2) -> (scratc1623311406_is_of(X2,X) -> pp(aa_TPTP_ind_bool(Xa,X2))))) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(X),Xa)))) # label(fact_def__all__of) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 253 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(X0,X12),X22) = X22 | aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(X0,X12),X22) = X12)) # label(fact_if__i__or) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 254 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dr,Uu),Uua)) <-> pp(scratc2077868803nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(Uua),Uu)))))) # label(fact_ATP_Olambda__61) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 255 (all X0 all X12 pp(aa_fun171081125l_bool(scratc846727211all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,X0)),aa_fun1584354236d_bool(aTP_Lamm_fp(X0),X12)))) # label(fact_estie) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 256 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc313305066munion,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc521652610_union,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1124382172d_repl,X),Xa))) # label(fact_def__famunion) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 257 (all X all Xa all Xb all Xc all Xd aa_TPT1424761345TP_ind(scratc1837303166_indeq(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1138785586d_11_i(X,Xa,Xb),Xc),Xd)) = scratc2025609780indeq2(X,Xa,Xb,Xc,Xd)) # label(fact_def__indeq2) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 258 (all X all Xa all Xb all Xc all Xd aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2059486350_Sigma,X),aa_TPT1424761345TP_ind(aTP_Lamm_av(Xc),Xd)) = aa_TPTP_ind_TPTP_ind(scratc215932272_inj_h(X,Xa,Xb,Xc),Xd)) # label(fact_def__inj__h) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 259 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc548513516moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bz(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__123) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 260 (all Uu all Uua (gg_TPTP_ind(Uu) -> Uu = aa_TPTP_ind_TPTP_ind(aTP_Lamm_ah(Uu),Uua))) # label(fact_ATP_Olambda__168) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 261 (all X all Xa all Xb aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2059486350_Sigma,Xa),scratc1986928439d_soft(X,Xa,Xb)) = aa_TPTP_ind_TPTP_ind(scratc616295458d_invf(X,Xa),Xb)) # label(fact_def__invf) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 262 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ex,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),scratc98832752nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu))))) # label(fact_ATP_Olambda__3) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 263 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> ((exists X3 (gg_TPTP_ind(X3) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X3),X0)) & X22 = aa_TPTP_ind_TPTP_ind(X12,X3))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1124382172d_repl,X0),X12)))))) # label(fact_k__ReplEq) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 264 (all X all Xa (pp(aa_TPTP_ind_bool(Xa,X)) <-> scratc1623311406_is_of(X,Xa))) # label(fact_def__is__of) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 265 (all X aa_TPTP_ind_TPTP_ind(scratc142904583_proj1,X) = aa_fun277296641TP_ind(scratc1807233176eplSep(X,aTP_Lamm_bh),scratc511628954_d_Unj)) # label(fact_def__proj1) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 266 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,Uua),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,Uub),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gg(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__148) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 267 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc1489043433hangef(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2059486350_Sigma,X),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_au(X),Xb),Xc),Xd))) # label(fact_def__changef) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 268 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ae,Uu),Uua)))) # label(fact_ATP_Olambda__92) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 269 (all X (pp(aa_fun171081125l_bool(scratc35740832_n_all,aa_TPT43085870d_bool(aTP_Lamm_ad,X))) <-> pp(aa_TPTP_ind_bool(scratc425017653_prop1,X)))) # label(fact_def__d__24__prop1) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 270 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_fp(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1830090288d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc494515559_d_Sep(Uu),Uua))) -> pp(aa_TPTP_ind_bool(Uua,Uub))))) # label(fact_ATP_Olambda__114) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 271 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_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_gj(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__156) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 272 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dp,Uu),Uua)) <-> pp(scratc1994269768nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(Uua),Uu)))))) # label(fact_ATP_Olambda__62) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 273 (all X all Xa all Xb (pp(aa_fun171081125l_bool(scratc1961814196nd_all(Xa),aa_TPT43085870d_bool(scratc1032062638_image(X,Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc779517897ective(X),Xa),Xb)))) # label(fact_def__surjective) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 274 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_bi,Uu)) <-> (exists X2 (gg_TPTP_ind(X2) & aa_TPTP_ind_TPTP_ind(scratc696190754d_Inj0,X2) = Uu))))) # label(fact_ATP_Olambda__56) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 275 (all X all Xa scratc1994269833nd_ect(X,Xa) = aa_fun1431113780TP_ind(scratc494515559_d_Sep(aa_TPTP_ind_TPTP_ind(scratc14390744_power,X)),scratc812933624d_anec(X,Xa))) # label(fact_def__ect) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 276 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,Uua),aa_TPTP_ind_TPTP_ind(scratc14390744_power,Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fm,Uu),Uua)))) # label(fact_ATP_Olambda__93) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 277 (all Uu all Uua ((pp(scratc718232188_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc414529904lessis,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cl,Uu),Uua)))) # label(fact_ATP_Olambda__87) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 278 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ge(Uu),Uua),Uub)) <-> scratc1623311406_is_of(aa_TPTP_ind_TPTP_ind(scratc561578429d_e_in(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_ai,Uu)))) # label(fact_ATP_Olambda__118) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 279 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2116917608d_Subq,X12),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc14390744_power,X0))))) # label(fact_k__PowerI) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 280 (all X all Xa scratc1677186215d_pair = scratc966855345d_pair(X,Xa)) # label(fact_def__d__pair) # label(axiom) # label(non_clause). [assumption]. 1.35/1.66 281 (all X all Xa all Xb scratc1837303166_indeq(X,Xa,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1567857808d_d_Pi,X),aTP_Lamm_ah(Xb))) = scratc1138785586d_11_i(X,Xa,Xb)) # label(fact_def__d__11__i) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 282 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dz(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ea,Uu),Uua)))) # label(fact_ATP_Olambda__99) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 283 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2059486350_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,aa_TPTP_ind_TPTP_ind(scratc142904583_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc142904582_proj0,X22)))))) # label(fact_proj1__Sigma) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 284 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,Uua),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_du(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__139) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 285 (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]. 1.35/1.67 286 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc701212661n_some,aa_TPT43085870d_bool(scratc1229761461ffprop(Xa),X))))) # label(fact_def__iii) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 287 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ek,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ej(Uu),Uua))))) # label(fact_ATP_Olambda__97) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 288 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ep,Uu),Uua)))) # label(fact_ATP_Olambda__84) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 289 (all X all Xa all Xb aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2059486350_Sigma,X),scratc1183142289sel_wb(X,Xa,Xb)) = aa_TPTP_ind_TPTP_ind(scratc474669606wissel(X,Xa),Xb)) # label(fact_def__wissel) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 290 (all X0 all X12 pp(aa_fun171081125l_bool(scratc846727211all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,X0)),aa_TPT43085870d_bool(aTP_Lamm_ga(X0),X12)))) # label(fact_e__pair__p) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 291 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc491440932ectelt(X,Xa),Xb) = aa_TPTP_ind_TPTP_ind(scratc606642809ectset(X,Xa),aa_TPTP_ind_TPTP_ind(scratc1586209410_ecelt(X,Xa),Xb))) # label(fact_def__ectelt) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 292 (all Uu ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2069016971nd_nis,Uu),scratc98832752nd_n_1)) -> pp(aa_fun171081125l_bool(scratc151533093_n_one,aa_TPT43085870d_bool(aTP_Lamm_ae,Uu)))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fa,Uu)))) # label(fact_ATP_Olambda__2) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 293 (all X ((all X1 (pp(aa_TPTP_ind_bool(X1,scratc2095348162ptyset)) -> ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(X1,X2)) -> pp(aa_TPTP_ind_bool(X1,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X2)))))) -> pp(aa_TPTP_ind_bool(X1,X))))) <-> pp(aa_TPTP_ind_bool(scratc1509955612_nat_p,X)))) # label(fact_def__nat__p) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 294 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2059486350_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,aa_TPTP_ind_TPTP_ind(scratc142904583_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc142904582_proj0,X22)))) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,aa_TPTP_ind_TPTP_ind(scratc142904582_proj0,X22)),X0)) & aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1677186215d_pair,aa_TPTP_ind_TPTP_ind(scratc142904582_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc142904583_proj1,X22)) = X22))) # label(fact_k__Sigma__eta__proj0__proj1) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 295 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc414529904lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc414529904lessis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc414529904lessis,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bt(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__124) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 296 (all X all Xa scratc142904582_proj0 = scratc1074704707_first(X,Xa)) # label(fact_def__first) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 297 (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]. 1.35/1.67 298 (all Uu all Uua (pp(scratc610767008_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,Uua),scratc98832752nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),aa_fun171081125l_bool(scratc35740832_n_all,aa_TPT43085870d_bool(aTP_Lamm_ad,Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ey,Uu),Uua)))) # label(fact_ATP_Olambda__64) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 299 (all X0 all X12 scratc1623311406_is_of(aa_fun1431113780TP_ind(scratc494515559_d_Sep(X0),X12),aa_TPT43085870d_bool(aTP_Lamm_fm,X0))) # label(fact_setof__p) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 300 (all X scratc1830090288d_esti(X) = scratc1802667954bnd_in) # label(fact_def__esti) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 301 (all X (pp(aa_TPTP_ind_bool(scratc158021315_cond2,X)) <-> pp(aa_fun171081125l_bool(scratc35740832_n_all,aa_TPT43085870d_bool(aTP_Lamm_af,X))))) # label(fact_def__cond2) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 302 (all X7 all Y (gg_TPTP_ind(X7) & gg_TPTP_ind(Y) -> Y = X7 | -pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)))) # label(help_fequal_1_1_fequal_001t__TPTP____Interpret__Oind_T) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 303 (all Uu all Uua (pp(scratc2077868803nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dl,Uu),Uua)))) # label(fact_ATP_Olambda__58) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 304 (all X0 all X12 pp(aa_fun171081125l_bool(scratc846727211all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,X0)),aa_fun1584354236d_bool(aTP_Lamm_gk(X0),X12)))) # label(fact_e__isp) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 305 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(Uu),Uua),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gl,Uu),Uua)))) # label(fact_ATP_Olambda__63) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 306 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,X),Xb)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc143298179_prop3(X),Xa),Xb)))) # label(fact_def__prop3) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 307 (all Uu all Uua all Uub all Uuc (pp(aa_fun171081125l_bool(scratc2104871667l_some(Uua),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ap(Uu),Uub),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aq(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__159) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 308 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc1807233176eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bf,Xa)),scratc142904583_proj1)) # label(fact_def__ap) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 309 (all B_1 gg_bool(scratc718232188_d_not(B_1))) # label(gsy_c_Scratch__tptp__translate__45846__17029_ONUM669__thf__4__p_Obnd__d__not) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 310 (all X0 (pp(aa_TPTP_ind_bool(scratc1509955612_nat_p,X0)) -> pp(aa_TPTP_ind_bool(scratc1509955612_nat_p,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X0))))) # label(fact_nat__ordsucc) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 311 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_da,Uu)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cz,Uu))))) # label(fact_ATP_Olambda__37) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 312 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ci(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__128) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 313 (all X all Xa (pp(scratc621603181_amone(X,Xa)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,X)),aa_fun1584354236d_bool(aTP_Lamm_bc(X),Xa))))) # label(fact_def__amone) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 314 (all X all Xa all Xb (pp(aa_fun171081125l_bool(scratc1961814196nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_az(X),Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc772422746ective(X),Xa),Xb)))) # label(fact_def__injective) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 315 (all Uu all Uua aa_TPTP_ind_TPTP_ind(scratc521652610_union,aa_TPTP_ind_TPTP_ind(Uu,Uua)) = aa_TPTP_ind_TPTP_ind(aTP_Lamm_bd(Uu),Uua)) # label(fact_ATP_Olambda__108) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 316 (all X0 all X12 pp(aa_fun171081125l_bool(scratc846727211all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,X0)),aa_TPT43085870d_bool(aTP_Lamm_fs(X0),X12)))) # label(fact_secondis1) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 317 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cz,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc548513516moreis,Uu),Uua)) -> pp(scratc718232188_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),Uua)))))) # label(fact_ATP_Olambda__77) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 318 (all X0 all X12 ((exists X2 (gg_TPTP_ind(X2) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X12),X2)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X2),X0)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc521652610_union,X0))))) # label(fact_k__UnionEq) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 319 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc1943012394univof,X0)))) # label(fact_k__UnivOf__In) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 320 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dj,Uu),Uua)) <-> pp(scratc1994269768nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728063742_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__59) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 321 (all X0 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X0),scratc1460043444_omega)) -> pp(aa_TPTP_ind_bool(scratc1509955612_nat_p,X0)))) # label(fact_omega__nat__p) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 322 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_ac(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,Uu),Uua))) # label(fact_ATP_Olambda__107) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 323 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1830090288d_esti(Uu),Uub),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_at(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__113) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 324 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_eb,Uu)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ea,Uu))))) # label(fact_ATP_Olambda__25) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 325 (all X all Xa all Xb aa_fun1431113780TP_ind(scratc494515559_d_Sep(X),aa_TPT43085870d_bool(Xa,Xb)) = aa_TPTP_ind_TPTP_ind(scratc1586209410_ecelt(X,Xa),Xb)) # label(fact_def__ecelt) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 326 (all X all Xa scratc606642809ectset(X,Xa) = scratc2078065665nd_out(aa_TPTP_ind_TPTP_ind(scratc14390744_power,X),scratc812933624d_anec(X,Xa))) # label(fact_def__ectset) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 327 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ck,Uu)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cj,Uu))))) # label(fact_ATP_Olambda__45) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 328 (all X all Xa (pp(aa_bool_bool(scratc2096471106d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc414529904lessis,X),Xa)))) # label(fact_def__lessis) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 329 (all Uu (pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_em,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_en,Uu)))) # label(fact_ATP_Olambda__20) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 330 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2059486350_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,aa_TPTP_ind_TPTP_ind(scratc142904582_proj0,X22)),X0)))) # label(fact_proj0__Sigma) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 331 (all X all Xa all Xb (pp(aa_fun171081125l_bool(scratc1961814196nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_as(X),Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc615049083d_incl(X),Xa),Xb)))) # label(fact_def__incl) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 332 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ao(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_an(Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__163) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 333 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fv(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,Uub),aa_TPTP_ind_TPTP_ind(scratc1710759884etprod(Uu),Uua))))) # label(fact_ATP_Olambda__140) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 334 (all X0 pp(aa_TPTP_ind_bool(scratc1416680303closed,aa_TPTP_ind_TPTP_ind(scratc1943012394univof,X0)))) # label(fact_k__UnivOf__ZF__closed) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 335 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2059486350_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1677186215d_pair,aa_TPTP_ind_TPTP_ind(scratc142904582_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc142904583_proj1,X22)) = X22))) # label(fact_proj__Sigma__eta) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 336 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc630982705_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2069016971nd_nis,aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc80697981d_n_pl(X),Xb))))) # label(fact_def__d__28__prop1) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 337 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cj,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ci(Uu),Uua))))) # label(fact_ATP_Olambda__100) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 338 (all X0 all X12 all X22 all X32 (pp(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(X0,X22),X32))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X12),X22))))) # label(fact_k__If__In__then__E) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 339 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X22),aa_fun1431113780TP_ind(scratc494515559_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(X12,X22)))) # label(fact_k__SepE2) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 340 (all X0 aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X0) != scratc2095348162ptyset) # label(fact_neq__ordsucc__0) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 341 (all X ((all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X1),X)) -> (all X2 ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X3),X1)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,aa_TPTP_ind_TPTP_ind(X2,X3)),X))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1124382172d_repl,X1),X2)),X))))))) <-> pp(aa_TPTP_ind_bool(scratc1134690962closed,X)))) # label(fact_def__d__Repl__closed) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 342 (all X0 all X12 pp(aa_fun171081125l_bool(scratc846727211all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,X0)),aa_TPT43085870d_bool(aTP_Lamm_fu(X0),X12)))) # label(fact_firstis1) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 343 (all Uu (pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dd,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_de,Uu)))) # label(fact_ATP_Olambda__35) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 344 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fi,Uu),Uua)))) # label(fact_ATP_Olambda__65) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 345 (all X all Xa all Xb all Xc (pp(scratc610767008_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1830090288d_esti(X),Xc),Xa),scratc718232188_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1830090288d_esti(X),Xc),Xb)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1243772602etprop(X,Xa),Xb),Xc)))) # label(fact_def__nissetprop) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 346 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2069016971nd_nis,X),Xa)) <-> pp(scratc718232188_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,X),Xa))))) # label(fact_def__nis) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 347 (all Uu (pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dj,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_dk,Uu)))) # label(fact_ATP_Olambda__32) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 348 (all Uu (pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bx,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_by,Uu)))) # label(fact_ATP_Olambda__49) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 349 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fw(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561578434d_e_is(aa_TPTP_ind_TPTP_ind(scratc1710759884etprod(Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc966855345d_pair(Uu,Uua),aa_TPTP_ind_TPTP_ind(scratc1074704707_first(Uu,Uua),Uub)),aa_TPTP_ind_TPTP_ind(scratc1233885537second(Uu,Uua),Uub))),Uub)))) # label(fact_ATP_Olambda__110) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 350 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc425017654_prop2,X),Xa)) <-> pp(scratc610767008_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc80238795d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,Xa),scratc98832752nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,X)),aa_TPTP_ind_bool(scratc425017653_prop1,Xa))))) # label(fact_def__d__24__prop2) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 351 (all Uu (pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dn,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_do,Uu)))) # label(fact_ATP_Olambda__30) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 352 (all B_1 all B_2 gg_TPTP_ind(scratc1994269833nd_ect(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__45846__17029_ONUM669__thf__4__p_Obnd__ect) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 353 (all Uu all Uua all Uub all Uuc all Uud aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1802143164bnd_ap,aa_TPTP_ind_TPTP_ind(scratc474669606wissel(Uu,Uub),Uuc)),Uud)) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_au(Uu),Uua),Uub),Uuc),Uud)) # label(fact_ATP_Olambda__164) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 354 (all Uu (pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cl,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cm,Uu)))) # label(fact_ATP_Olambda__44) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 355 (all X all Xa (pp(scratc2095815101d_l_ec(X,Xa)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc2027971839nd_imp,X),scratc718232188_d_not(Xa))))) # label(fact_def__l__ec) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 356 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc846727211all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fr(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fs(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__136) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 357 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2116917608d_Subq,X0),X12)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2116917608d_Subq,X12),X0)) -> X0 = X12)))) # label(fact_set__ext) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 358 (all P all Q all R aa_boo1142376798l_bool(P,aa_TPTP_ind_bool(Q,R)) = aa_TPT2142672771l_bool(cOMBB_658106424TP_ind(P,Q),R)) # label(help_COMBB_1_1_COMBB_001t__HOL__Obool_001t__fun_It__HOL__Obool_Mt__HOL__Obool_J_001t__TPTP____Interpret__Oind_U) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 359 (all Uu (pp(aa_fun171081125l_bool(scratc846727211all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cp,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cq,Uu)))) # label(fact_ATP_Olambda__42) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 360 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cc(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc414529904lessis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2027709436nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__127) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 361 (all X all Xa all Xb (pp(aa_fun171081125l_bool(scratc2104871667l_some(X),aa_TPT43085870d_bool(scratc1994269829nd_ecp(X,Xa),Xb))) <-> pp(aa_TPTP_ind_bool(scratc812933624d_anec(X,Xa),Xb)))) # label(fact_def__anec) # label(axiom) # label(non_clause). [assumption]. 1.35/1.67 362 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc94616283fixfu2(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc846727211all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_am(X),Xa),Xb),Xc))))) # label(fact_def__fixfu2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.70 363 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_fun1235454963TP_ind(aTP_Lamm_bm(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(aa_TPTP_ind_bool(Uua,Uub),Uub),scratc1995122619nd_eps(aa_fun1584354236d_bool(aTP_Lamm_ba(Uu),Uua)))) # label(fact_ATP_Olambda__112) # label(axiom) # label(non_clause). [assumption]. 1.42/1.70 364 (all X0 all X12 all X22 ((pp(X0) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X12),X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(X0,X12),scratc2095348162ptyset)),aa_TPTP_ind_TPTP_ind(scratc1802667946bnd_if(X0,X22),aa_TPTP_ind_TPTP_ind(scratc2076836790rdsucc,scratc2095348162ptyset)))))) # label(fact_k__If__In__01) # label(axiom) # label(non_clause). [assumption]. 1.42/1.70 365 (all X all Xa (pp(aa_fun171081125l_bool(scratc2104871667l_some(X),aa_TPT43085870d_bool(aTP_Lamm_at(X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc233459501nempty,X),Xa)))) # label(fact_def__nonempty) # label(axiom) # label(non_clause). [assumption]. 1.42/1.70 366 (all X0 (pp(aa_TPTP_ind_bool(scratc1509955612_nat_p,X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X0),scratc1460043444_omega)))) # label(fact_nat__p__omega) # label(axiom) # label(non_clause). [assumption]. 1.42/1.70 367 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bl,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2066917798nd_nIn,Uua),Uu)))) # label(fact_ATP_Olambda__95) # label(axiom) # label(non_clause). [assumption]. 1.42/1.70 368 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802667954bnd_in,X33),X0)) -> aa_TPTP_ind_TPTP_ind(X12,X33) = aa_TPTP_ind_TPTP_ind(X22,X33)))) -> aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2059486350_Sigma,X0),X22) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2059486350_Sigma,X0),X12))) # label(fact_xi__ext) # label(axiom) # label(non_clause). [assumption]. 1.42/1.70 1.42/1.70 ============================== end of process non-clausal formulas === 1.42/1.70 1.42/1.70 ============================== PROCESS INITIAL CLAUSES =============== 1.42/1.70 1.42/1.70 ============================== PREDICATE ELIMINATION ================= 1.42/1.70 369 -pp(A) | pp(scratc718232188_d_not(B)) | -scratc343266243d_r_ec(A,B) # label(fact_def__r__ec) # label(axiom). [clausify(45)]. 1.42/1.70 370 pp(A) | scratc343266243d_r_ec(A,B) # label(fact_def__r__ec) # label(axiom). [clausify(45)]. 1.42/1.70 371 -pp(scratc718232188_d_not(A)) | scratc343266243d_r_ec(B,A) # label(fact_def__r__ec) # label(axiom). [clausify(45)]. 1.42/1.70 372 -gg_bool(A) | fFalse = A | fTrue = A # label(help_fFalse_1_1_T) # label(axiom). [clausify(113)]. 1.42/1.70 373 gg_bool(scratc621603181_amone(A,B)) # label(gsy_c_Scratch__tptp__translate__45846__17029_ONUM669__thf__4__p_Obnd__amone) # label(axiom). [clausify(47)]. 1.42/1.70 374 gg_bool(scratc2077868803nd_or3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__45846__17029_ONUM669__thf__4__p_Obnd__or3) # label(axiom). [clausify(57)]. 1.42/1.70 375 gg_bool(fFalse) # label(gsy_c_fFalse) # label(axiom). [assumption]. 1.42/1.70 376 gg_bool(scratc610767008_d_and(A,B)) # label(gsy_c_Scratch__tptp__translate__45846__17029_ONUM669__thf__4__p_Obnd__d__and) # label(axiom). [clausify(109)]. 1.42/1.70 Derived: fFalse = scratc621603181_amone(A,B) | fTrue = scratc621603181_amone(A,B). [resolve(372,a,373,a)]. 1.42/1.70 Derived: fFalse = scratc2077868803nd_or3(A,B,C) | fTrue = scratc2077868803nd_or3(A,B,C). [resolve(372,a,374,a)]. 1.42/1.70 Derived: fFalse = fFalse | fTrue = fFalse. [resolve(372,a,375,a)]. 1.42/1.70 Derived: fFalse = scratc610767008_d_and(A,B) | fTrue = scratc610767008_d_and(A,B). [resolve(372,a,376,a)]. 1.42/1.70 377 gg_bool(aa_bool_bool(A,B)) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom). [clausify(121)]. 1.42/1.70 Derived: fFalse = aa_bool_bool(A,B) | fTrue = aa_bool_bool(A,B). [resolve(377,a,372,a)]. 1.88/2.22 378 gg_bool(fEx_TPTP_ind(A)) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom). [clausify(124)]. 1.88/2.22 Derived: fFalse = fEx_TPTP_ind(A) | fTrue = fEx_TPTP_ind(A). [resolve(378,a,372,a)]. 1.88/2.22 379 gg_bool(fTrue) # label(gsy_c_fTrue) # label(axiom). [assumption]. 1.88/2.22 Derived: fFalse = fTrue | fTrue = fTrue. [resolve(379,a,372,a)]. 1.88/2.22 380 gg_bool(scratc1994269768nd_ec3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__45846__17029_ONUM669__thf__4__p_Obnd__ec3) # label(axiom). [clausify(185)]. 1.88/2.22 Derived: fFalse = scratc1994269768nd_ec3(A,B,C) | fTrue = scratc1994269768nd_ec3(A,B,C). [resolve(380,a,372,a)]. 1.88/2.22 381 gg_bool(aa_TPTP_ind_bool(A,B)) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom). [clausify(229)]. 1.88/2.22 Derived: fFalse = aa_TPTP_ind_bool(A,B) | fTrue = aa_TPTP_ind_bool(A,B). [resolve(381,a,372,a)]. 1.88/2.22 382 gg_bool(scratc2095815101d_l_ec(A,B)) # label(gsy_c_Scratch__tptp__translate__45846__17029_ONUM669__thf__4__p_Obnd__l__ec) # label(axiom). [clausify(241)]. 1.88/2.22 Derived: fFalse = scratc2095815101d_l_ec(A,B) | fTrue = scratc2095815101d_l_ec(A,B). [resolve(382,a,372,a)]. 1.88/2.22 383 gg_bool(undefined_bool(bool)) # label(gsy_c_HOL_Oundefined_001t__HOL__Obool) # label(axiom). [assumption]. 1.88/2.22 Derived: fFalse = undefined_bool(bool) | fTrue = undefined_bool(bool). [resolve(383,a,372,a)]. 1.88/2.22 384 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(285)]. 1.88/2.22 Derived: fFalse = aa_fun171081125l_bool(A,B) | fTrue = aa_fun171081125l_bool(A,B). [resolve(384,a,372,a)]. 1.88/2.22 385 gg_bool(scratc718232188_d_not(A)) # label(gsy_c_Scratch__tptp__translate__45846__17029_ONUM669__thf__4__p_Obnd__d__not) # label(axiom). [clausify(309)]. 1.88/2.22 Derived: fFalse = scratc718232188_d_not(A) | fTrue = scratc718232188_d_not(A). [resolve(385,a,372,a)]. 1.88/2.22 386 -pp(scratc718232188_d_not(scratc718232188_d_not(A))) | scratc2143108113nd_wel(A) # label(fact_def__wel) # label(axiom). [clausify(236)]. 1.88/2.22 387 -scratc2143108113nd_wel(A) | pp(A) # label(fact_l__et) # label(axiom). [clausify(75)]. 1.88/2.22 Derived: -pp(scratc718232188_d_not(scratc718232188_d_not(A))) | pp(A). [resolve(386,b,387,a)]. 1.88/2.22 388 pp(scratc718232188_d_not(scratc718232188_d_not(A))) | -scratc2143108113nd_wel(A) # label(fact_def__wel) # label(axiom). [clausify(236)]. 1.88/2.22 389 pp(scratc610767008_d_and(aa_bool_bool(scratc2096471106d_l_or(A),B),scratc2095815101d_l_ec(A,B))) | -scratc1036782190d_orec(A,B) # label(fact_def__orec) # label(axiom). [clausify(83)]. 1.88/2.22 390 -pp(scratc610767008_d_and(aa_bool_bool(scratc2096471106d_l_or(A),B),scratc2095815101d_l_ec(A,B))) | scratc1036782190d_orec(A,B) # label(fact_def__orec) # label(axiom). [clausify(83)]. 1.88/2.22 391 pp(scratc610767008_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc2027971839nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc2027971839nd_imp,B),A))) | -scratc1504908458_l_iff(A,B) # label(fact_def__l__iff) # label(axiom). [clausify(195)]. 1.88/2.22 392 -pp(scratc610767008_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc2027971839nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc2027971839nd_imp,B),A))) | scratc1504908458_l_iff(A,B) # label(fact_def__l__iff) # label(axiom). [clausify(195)]. 1.88/2.22 1.88/2.22 ============================== end predicate elimination ============= 1.88/2.22 1.88/2.22 Auto_denials: (non-Horn, no changes). 1.88/2.22 1.88/2.22 Term ordering decisions: 1.88/2.22 Function symbol KB weights: aTP_Lamm_a=1. scratc1802667954bnd_in=1. scratc80238795d_n_is=1. scratc2076836790rdsucc=1. scratc1802143164bnd_ap=1. aTP_Lamm_ai=1. scratc2027709436nd_iii=1. scratc1728063742_29_ii=1. scratc2095348162ptyset=1. scratc2059486350_Sigma=1. scratc2069016971nd_nis=1. scratc414529904lessis=1. scratc98832752nd_n_1=1. fFalse=1. scratc14390744_power=1. scratc1509955612_nat_p=1. scratc1567857808d_d_Pi=1. scratc2068492180nd_nat=1. scratc701212661n_some=1. scratc1124382172d_repl=1. scratc2027971839nd_imp=1. scratc548513516moreis=1. fTrue=1. scratc1677186215d_pair=1. scratc2116917608d_Subq=1. scratc1134690962closed=1. scratc142904582_proj0=1. scratc521652610_union=1. aTP_Lamm_ae=1. scratc142904583_proj1=1. scratc80238790d_n_in=1. scratc35740832_n_all=1. aTP_Lamm_ab=1. aTP_Lamm_ad=1. aTP_Lamm_fm=1. scratc136593508closed=1. scratc301326522closed=1. aTP_Lamm_cl=1. aTP_Lamm_cn=1. aTP_Lamm_cp=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_fd=1. aTP_Lamm_fh=1. aTP_Lamm_fi=1. scratc1416680303closed=1. scratc1460043444_omega=1. scratc425017654_prop2=1. scratc696190755d_Inj1=1. aTP_Lamm_af=1. aTP_Lamm_bf=1. aTP_Lamm_bh=1. aTP_Lamm_bi=1. aTP_Lamm_bp=1. aTP_Lamm_br=1. aTP_Lamm_bu=1. aTP_Lamm_bx=1. aTP_Lamm_ca=1. aTP_Lamm_cd=1. aTP_Lamm_cg=1. aTP_Lamm_cj=1. aTP_Lamm_dj=1. aTP_Lamm_dl=1. aTP_Lamm_dn=1. aTP_Lamm_dp=1. aTP_Lamm_dr=1. aTP_Lamm_dv=1. aTP_Lamm_dx=1. aTP_Lamm_ea=1. aTP_Lamm_ed=1. aTP_Lamm_ef=1. aTP_Lamm_eh=1. aTP_Lamm_ek=1. aTP_Lamm_em=1. aTP_Lamm_ep=1. aTP_Lamm_es=1. aTP_Lamm_ev=1. aTP_Lamm_ey=1. aTP_Lamm_fa=1. aTP_Lamm_fb=1. aTP_Lamm_fg=1. fconj=1. fimplies=1. scratc158021315_cond2=1. scratc2018566726d_Sing=1. scratc425017653_prop1=1. scratc696190754d_Inj0=1. aTP_Lamm_bl=1. aTP_Lamm_bq=1. aTP_Lamm_bs=1. aTP_Lamm_bv=1. aTP_Lamm_by=1. aTP_Lamm_cb=1. aTP_Lamm_ce=1. aTP_Lamm_ch=1. aTP_Lamm_ck=1. aTP_Lamm_cm=1. aTP_Lamm_co=1. aTP_Lamm_cq=1. aTP_Lamm_cs=1. aTP_Lamm_cu=1. aTP_Lamm_cw=1. aTP_Lamm_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_dq=1. aTP_Lamm_ds=1. aTP_Lamm_dw=1. aTP_Lamm_dy=1. aTP_Lamm_eb=1. aTP_Lamm_ee=1. aTP_Lamm_eg=1. aTP_Lamm_ei=1. aTP_Lamm_el=1. aTP_Lamm_en=1. aTP_Lamm_eo=1. aTP_Lamm_eq=1. aTP_Lamm_er=1. aTP_Lamm_et=1. aTP_Lamm_eu=1. aTP_Lamm_ew=1. aTP_Lamm_ex=1. aTP_Lamm_ez=1. aTP_Lamm_fc=1. aTP_Lamm_fe=1. aTP_Lamm_ff=1. aTP_Lamm_fj=1. aTP_Lamm_fk=1. aTP_Lamm_fl=1. aTP_Lamm_fo=1. aTP_Lamm_gl=1. fequal_TPTP_ind=1. scratc151533093_n_one=1. scratc158021314_cond1=1. scratc1943012394univof=1. scratc2066917798nd_nIn=1. scratc511628954_d_Unj=1. aTP_Lamm_aa=1. aTP_Lamm_ag=1. aTP_Lamm_bj=1. aTP_Lamm_bk=1. bool=1. scratc1219344880_prop1=1. scratc1395776951_prop1=1. scratc143298180_prop4=1. scratc1601742003_prop1=1. scratc1768849959d_plus=1. scratc1933586761pair_p=1. scratc1984139126_prop1=1. scratc233459501nempty=1. scratc313305066munion=1. scratc42620530_prop1=1. scratc893548160_empty=1. scratc1424423166d_i1_s=1. scratc325144174d_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. scratc610767008_d_and=1. aa_TPT1123896796d_bool=1. scratc1802667946bnd_if=1. scratc2095815101d_l_ec=1. aa_fun1212484691d_bool=1. aa_TPT985247859d_bool=1. scratc561578429d_e_in=1. scratc966855345d_pair=1. aa_fun987228051d_bool=1. scratc2028037426nd_ind=1. scratc621603181_amone=1. scratc1032062638_image=1. scratc1074704707_first=1. scratc1233885537second=1. aa_TPT125613450d_bool=1. scratc2069410560nd_non=1. aa_fun1913827119d_bool=1. scratc812933624d_anec=1. aa_TPT1791839040TP_ind=1. aa_fun1107270209d_bool=1. aa_fun845057962d_bool=1. scratc1586209410_ecelt=1. scratc1807233176eplSep=1. scratc1994269829nd_ecp=1. scratc1585619019_ecect=1. aa_TPT1781712639TP_ind=1. aa_TPT2142672771l_bool=1. aa_fun1235454963TP_ind=1. cOMBB_658106424TP_ind=1. cOMBS_2003118649l_bool=1. scratc1123420951_fixfu=1. scratc1243772602etprop=1. scratc1994269833nd_ect=1. scratc2078065665nd_out=1. scratc474669606wissel=1. scratc606642809ectset=1. scratc94616283fixfu2=1. scratc1475084483nverse=1. scratc491440932ectelt=1. scratc616295458d_invf=1. scratc620031989d_tofs=1. scratc712760155unmore=1. f8=1. f12=1. f16=1. f20=1. f21=1. scratc846727211all_of=1. scratc80697981d_n_pl=1. scratc561578434d_e_is=1. scratc718232188_d_not=1. scratc494515559_d_Sep=1. scratc1830090288d_esti=1. scratc2104871667l_some=1. scratc1229761461ffprop=1. scratc1961814196nd_all=1. scratc2096471106d_l_or=1. scratc1118156403_rec_G=1. aTP_Lamm_ah=1. aTP_Lamm_fv=1. scratc2077606457nd_one=1. aTP_Lamm_aj=1. aTP_Lamm_at=1. aTP_Lamm_bb=1. aTP_Lamm_bo=1. aTP_Lamm_bt=1. aTP_Lamm_bw=1. aTP_Lamm_bz=1. aTP_Lamm_cc=1. aTP_Lamm_cf=1. aTP_Lamm_ci=1. aTP_Lamm_dt=1. aTP_Lamm_fn=1. aTP_Lamm_gj=1. scratc615049083d_incl=1. aTP_Lamm_an=1. aTP_Lamm_ax=1. aTP_Lamm_ba=1. aTP_Lamm_be=1. aTP_Lamm_dz=1. aTP_Lamm_ec=1. aTP_Lamm_gf=1. aTP_Lamm_gh=1. scratc1710759884etprod=1. scratc1995122619nd_eps=1. scratc772422746ective=1. aTP_Lamm_ak=1. aTP_Lamm_al=1. aTP_Lamm_am=1. aTP_Lamm_ao=1. aTP_Lamm_ap=1. aTP_Lamm_ar=1. aTP_Lamm_as=1. aTP_Lamm_ay=1. aTP_Lamm_az=1. aTP_Lamm_bc=1. aTP_Lamm_du=1. aTP_Lamm_ej=1. aTP_Lamm_fp=1. aTP_Lamm_fq=1. aTP_Lamm_fr=1. aTP_Lamm_ft=1. aTP_Lamm_fz=1. aTP_Lamm_gb=1. aTP_Lamm_gc=1. aTP_Lamm_gg=1. fEx_TPTP_ind=1. scratc1307162165nunion=1. scratc779517897ective=1. aTP_Lamm_aq=1. aTP_Lamm_fs=1. aTP_Lamm_fu=1. aTP_Lamm_fw=1. aTP_Lamm_fx=1. aTP_Lamm_fy=1. aTP_Lamm_ga=1. aTP_Lamm_gd=1. aTP_Lamm_ge=1. aTP_Lamm_gi=1. aTP_Lamm_gk=1. scratc1534996756In_rec=1. scratc1953972728_UPair=1. aTP_Lamm_ac=1. aTP_Lamm_au=1. aTP_Lamm_av=1. aTP_Lamm_aw=1. aTP_Lamm_bd=1. aTP_Lamm_bg=1. aTP_Lamm_bm=1. aTP_Lamm_bn=1. cOMBC_1555011498d_bool=1. scratc1013379828_prop1=1. scratc1223447707tminus=1. scratc143298179_prop3=1. scratc1640284202t_disj=1. scratc630982705_prop1=1. scratc956141976ective=1. undefined_bool=1. undefined_TPTP_ind=1. f6=1. f10=1. f11=1. f13=1. f14=1. f15=1. f18=1. f19=1. f22=1. f23=1. scratc2077868803nd_or3=1. scratc1994269768nd_ec3=1. scratc1986928439d_soft=1. scratc143298177_prop1=1. scratc1837303166_indeq=1. scratc2028431021nd_ite=1. scratc1138785586d_11_i=1. scratc1183142288sel_wa=1. scratc1183142289sel_wb=1. f1=1. f2=1. f7=1. f17=1. f24=1. f25=1. scratc143298178_prop2=1. scratc1489043433hangef=1. scratc215932272_inj_h=1. f4=1. f5=1. f9=1. scratc972340280_prop1=1. scratc2025609780indeq2=1. f3=1. 10.87/11.18 10.87/11.18 ============================== end of process initial clauses ======== 10.87/11.18 10.87/11.18 ============================== CLAUSES FOR SEARCH ==================== 10.87/11.18 10.87/11.18 ============================== end of clauses for search ============= 10.87/11.18 10.87/11.18 ============================== SEARCH ================================ 10.87/11.18 10.87/11.18 % Starting search at 0.61 seconds. 10.87/11.18 10.87/11.18 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 104 (0.00 of 2.00 sec). 10.87/11.18 10.87/11.18 Low Water (keep): wt=34.000, iters=3449 10.87/11.18 10.87/11.18 Low Water (keep): wt=32.000, iters=3365 10.87/11.18 10.87/11.18 Low Water (keep): wt=30.000, iters=3377 10.87/11.18 10.87/11.18 Low Water (keep): wt=28.000, iters=3383 10.87/11.18 10.87/11.18 Low Water (keep): wt=27.000, iters=3355 10.87/11.18 10.87/11.18 Low Water (keep): wt=26.000, iters=3348 10.87/11.18 10.87/11.18 Low Water (keep): wt=25.000, iters=3403 10.87/11.18 10.87/11.18 Low Water (keep): wt=24.000, iters=3343 10.87/11.18 10.87/11.18 Low Water (keep): wt=23.000, iters=3372 10.87/11.18 10.87/11.18 Low Water (keep): wt=19.000, iters=4534 10.87/11.18 10.87/11.18 Low Water (keep): wt=17.000, iters=3866 10.87/11.18 10.87/11.18 Low Water (keep): wt=16.000, iters=3555 10.87/11.18 10.87/11.18 Low Water (keep): wt=15.000, iters=3701 10.87/11.18 10.87/11.18 Low Water (keep): wt=14.000, iters=3335 10.87/11.18 10.87/11.18 Low Water (keep): wt=13.000, iters=3489 10.87/11.18 10.87/11.18 Low Water (keep): wt=12.000, iters=3458 10.87/11.18 10.87/11.18 Low Water (displace): id=6748, wt=125.000 10.87/11.18 10.87/11.18 Low Water (displace): id=6675, wt=117.000 10.87/11.18 10.87/11.18 Low Water (displace): id=6696, wt=106.000 10.87/11.18 10.87/11.18 Low Water (displace): id=6865, wt=103.000 10.87/11.18 10.87/11.18 Low Water (displace): id=6750, wt=99.000 10.87/11.18 10.87/11.18 Low Water (displace): id=6697, wt=96.000 10.87/11.18 10.87/11.18 Low Water (displace): id=6632, wt=94.000 10.87/11.18 10.87/11.18 Low Water (displace): id=6886, wt=93.000 10.87/11.18 10.87/11.18 Low Water (displace): id=6695, wt=92.000 10.87/11.18 10.87/11.18 Low Water (displace): id=6751, wt=89.000 10.87/11.18 10.87/11.18 Low Water (displace): id=6724, wt=88.000 10.87/11.18 10.87/11.18 Low Water (displace): id=6638, wt=86.000 10.87/11.18 10.87/11.18 Low Water (displace): id=6698, wt=84.000 10.87/11.18 10.87/11.18 Low Water (displace): id=6887, wt=83.000 10.87/11.18 10.87/11.18 Low Water (displace): id=6739, wt=82.000 10.87/11.18 10.87/11.18 Low Water (displace): id=6822, wt=81.000 10.87/11.18 10.87/11.18 Low Water (displace): id=6885, wt=80.000 10.87/11.18 10.87/11.18 Low Water (displace): id=6604, wt=79.000 10.87/11.18 10.87/11.18 Low Water (displace): id=6669, wt=78.000 10.87/11.18 10.87/11.18 Low Water (displace): id=6752, wt=77.000 10.87/11.18 10.87/11.18 Low Water (displace): id=6869, wt=76.000 10.87/11.18 10.87/11.18 Low Water (displace): id=6644, wt=75.000 10.87/11.18 10.87/11.18 Low Water (displace): id=6908, wt=74.000 10.87/11.18 10.87/11.18 Low Water (displace): id=6828, wt=73.000 10.87/11.18 10.87/11.18 Low Water (displace): id=13314, wt=11.000 10.87/11.18 10.87/11.18 Low Water (displace): id=13316, wt=10.000 10.87/11.18 10.87/11.18 Low Water (displace): id=14073, wt=9.000 10.87/11.18 10.87/11.18 Low Water (keep): wt=11.000, iters=3344 10.87/11.18 10.87/11.18 Low WaAlarm clock 179.39/180.04 Prover9 interrupted 179.39/180.04 EOF