0.06/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.11 % Command : tptp2X_and_run_prover9 %d %s 0.10/0.32 % Computer : n004.cluster.edu 0.10/0.32 % Model : x86_64 x86_64 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.32 % Memory : 8042.1875MB 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.32 % CPULimit : 1200 0.10/0.32 % DateTime : Tue Jul 13 16:26:54 EDT 2021 0.10/0.32 % CPUTime : 1.42/1.72 ============================== Prover9 =============================== 1.42/1.72 Prover9 (32) version 2009-11A, November 2009. 1.42/1.72 Process 11871 was started by sandbox on n004.cluster.edu, 1.42/1.72 Tue Jul 13 16:26:55 2021 1.42/1.72 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1200 -f /tmp/Prover9_11718_n004.cluster.edu". 1.42/1.72 ============================== end of head =========================== 1.42/1.72 1.42/1.72 ============================== INPUT ================================= 1.42/1.72 1.42/1.72 % Reading from file /tmp/Prover9_11718_n004.cluster.edu 1.42/1.72 1.42/1.72 set(prolog_style_variables). 1.42/1.72 set(auto2). 1.42/1.72 % set(auto2) -> set(auto). 1.42/1.72 % set(auto) -> set(auto_inference). 1.42/1.72 % set(auto) -> set(auto_setup). 1.42/1.72 % set(auto_setup) -> set(predicate_elim). 1.42/1.72 % set(auto_setup) -> assign(eq_defs, unfold). 1.42/1.72 % set(auto) -> set(auto_limits). 1.42/1.72 % set(auto_limits) -> assign(max_weight, "100.000"). 1.42/1.72 % set(auto_limits) -> assign(sos_limit, 20000). 1.42/1.72 % set(auto) -> set(auto_denials). 1.42/1.72 % set(auto) -> set(auto_process). 1.42/1.72 % set(auto2) -> assign(new_constants, 1). 1.42/1.72 % set(auto2) -> assign(fold_denial_max, 3). 1.42/1.72 % set(auto2) -> assign(max_weight, "200.000"). 1.42/1.72 % set(auto2) -> assign(max_hours, 1). 1.42/1.72 % assign(max_hours, 1) -> assign(max_seconds, 3600). 1.42/1.72 % set(auto2) -> assign(max_seconds, 0). 1.42/1.72 % set(auto2) -> assign(max_minutes, 5). 1.42/1.72 % assign(max_minutes, 5) -> assign(max_seconds, 300). 1.42/1.72 % set(auto2) -> set(sort_initial_sos). 1.42/1.72 % set(auto2) -> assign(sos_limit, -1). 1.42/1.72 % set(auto2) -> assign(lrs_ticks, 3000). 1.42/1.72 % set(auto2) -> assign(max_megs, 400). 1.42/1.72 % set(auto2) -> assign(stats, some). 1.42/1.72 % set(auto2) -> clear(echo_input). 1.42/1.72 % set(auto2) -> set(quiet). 1.42/1.72 % set(auto2) -> clear(print_initial_clauses). 1.42/1.72 % set(auto2) -> clear(print_given). 1.42/1.72 assign(lrs_ticks,-1). 1.42/1.72 assign(sos_limit,10000). 1.42/1.72 assign(order,kbo). 1.42/1.72 set(lex_order_vars). 1.42/1.72 clear(print_given). 1.42/1.72 1.42/1.72 % formulas(sos). % not echoed (632 formulas) 1.42/1.72 1.42/1.72 ============================== end of input ========================== 1.42/1.72 1.42/1.72 % From the command line: assign(max_seconds, 1200). 1.42/1.72 1.42/1.72 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 1.42/1.72 1.42/1.72 % Formulas that are not ordinary clauses: 1.42/1.72 1 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uua),aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,Uu))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc605409850lessis,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ce,Uu),Uua)))) # label(fact_ATP_Olambda__119) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 2 (all X0 (gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(scratc1700835558_nat_p,X0)) -> scratc351358348ptyset = X0 | (exists X13 (gg_TPTP_ind(X13) & aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,X13) = X0 & pp(aa_TPTP_ind_bool(scratc1700835558_nat_p,X13))))))) # label(fact_nat__inv) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 3 (all Uu all Uua (pp(scratc755465763_amone(scratc272482122nd_nat,aa_TPT43085870d_bool(aTP_Lamm_ir(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iv,Uu),Uua)))) # label(fact_ATP_Olambda__192) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 4 (all X aa_TPTP_ind_TPTP_ind(scratc2087855887_times,X) = scratc232027368nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1701720390d_d_Pi,scratc272482122nd_nat),aTP_Lamm_ab),aa_TPT43085870d_bool(scratc1990322274_prop2,X))) # label(fact_def__times) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 5 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cc,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uua),scratc1030418234nd_n_1)),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc739393462moreis,Uua),Uu))))) # label(fact_ATP_Olambda__111) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 6 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc860077246_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(X),Xa)),Xb)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(X),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Xa),Xb)))))) # label(fact_def__d__25__prop1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 7 (all X (pp(aa_TPTP_ind_bool(scratc271715071_prop1,X)) <-> pp(aa_fun171081125l_bool(scratc226620778_n_all,aa_TPT43085870d_bool(aTP_Lamm_ag,X))))) # label(fact_def__d__24__prop1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 8 (all Uu all Uua (scratc1201612283_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc257638827n_some,aa_TPT43085870d_bool(aTP_Lamm_ir(Uu),Uua)),aa_fun171081125l_bool(scratc257638827n_some,aa_TPT43085870d_bool(aTP_Lamm_is(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_it,Uu),Uua)))) # label(fact_ATP_Olambda__106) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 9 (all X0 (pp(aa_fun171081125l_bool(scratc257638827n_some,X0)) -> pp(aa_fun171081125l_bool(scratc257638827n_some,scratc264745403nd_min(X0))))) # label(fact_satz27) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 10 (all X all Xa (pp(scratc755465763_amone(X,Xa)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X)),aa_fun1584354236d_bool(aTP_Lamm_bf(X),Xa))))) # label(fact_def__amone) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 11 (all X scratc403153377all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X)) = scratc165804138nd_all(X)) # label(fact_def__all) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 12 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bf(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aa_TPT43085870d_bool(aTP_Lamm_al,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_be(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__236) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 13 (all X0 all X12 (gg_TPTP_ind(X0) -> X0 = aa_TPTP_ind_TPTP_ind(scratc276767164_proj0,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc461288049d_pair,X0),X12)))) # label(fact_proj0__pair__eq) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 14 (all X all Xa scratc1551617471d_tofs(X,Xa) = scratc1764370566bnd_ap) # label(fact_def__tofs) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 15 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ck,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cl,Uu)))) # label(fact_ATP_Olambda__90) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 16 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cr,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,Uu)),scratc1030418234nd_n_1)))) # label(fact_ATP_Olambda__15) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 17 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_kf,Uu)) <-> (pp(aa_TPTP_ind_bool(scratc291883896_cond1,Uu)) -> (pp(aa_TPTP_ind_bool(scratc291883897_cond2,Uu)) -> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ke,Uu))))))) # label(fact_ATP_Olambda__9) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 18 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_il,Uu),Uua)) <-> scratc1201612283_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uu),Uua)))) # label(fact_ATP_Olambda__103) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 19 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hx,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc739393462moreis,Uu),Uua)) -> pp(scratc909112134_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uu),Uua)))))) # label(fact_ATP_Olambda__134) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 20 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ex(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ey,Uu),Uua)))) # label(fact_ATP_Olambda__175) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 21 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ci,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cj,Uu)))) # label(fact_ATP_Olambda__91) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 22 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fj,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fk,Uu)))) # label(fact_ATP_Olambda__68) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 23 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cg,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uua),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),scratc1030418234nd_n_1))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc605409850lessis,Uua),Uu))))) # label(fact_ATP_Olambda__117) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 24 (all X all Xa scratc695441011d_e_in(aa_TPTP_ind_TPTP_ind(scratc148253326_power,X),scratc1744519106d_anec(X,Xa)) = scratc1719481601_ecect(X,Xa)) # label(fact_def__ecect) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 25 (all X all Xa (pp(aa_TPTP_ind_bool(Xa,X)) <-> scratc1814191352_is_of(X,Xa))) # label(fact_def__is__of) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 26 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc461288049d_pair,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1710655999nunion(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2055967654d_repl,X),scratc252616920d_Inj0)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2055967654d_repl,Xa),scratc252616921d_Inj1))) # label(fact_def__pair) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 27 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc232420963nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc695441016d_e_is(X),Xc),Xb),X,Xa),aa_TPTP_ind_TPTP_ind(scratc1657856090sel_wa(X,Xa,Xb),Xc)) = aa_TPTP_ind_TPTP_ind(scratc1657856091sel_wb(X,Xa,Xb),Xc)) # label(fact_def__wissel__wb) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 28 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ep,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eo(Uu),Uua))))) # label(fact_ATP_Olambda__178) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 29 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_a,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,Uu),scratc272482122nd_nat)))) # label(fact_ATP_Olambda__21) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 30 (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]. 1.42/1.72 31 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_az(Uu),Uua),Uub),Uuc) = aa_TPTP_ind_TPTP_ind(scratc1764895348bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1165925220_image(Uu,Uua),Uub),Uuc),aa_TPTP_ind_TPTP_ind(scratc771030273d_soft(Uu,Uua,Uub),Uuc)),scratc351358348ptyset)) # label(fact_ATP_Olambda__260) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 32 (all X all Xa all Xb all Xc all Xd all Xe all Xf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc819037698_prop1(X,Xa,Xb,Xc,Xd),Xe),Xf)) <-> pp(scratc801646954_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc614192122d_esti(X),Xf),aa_TPTP_ind_TPTP_ind(scratc1719481601_ecect(X,Xa),Xd)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc695441016d_e_is(Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,Xc),Xf)),Xe))))) # label(fact_def__d__10__prop1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 33 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc739393462moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dn(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__273) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 34 (all Uu all Uua (pp(aa_bool_bool(aa_boo1142376798l_bool(scratc231961781nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101372d_n_in,Uua),Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101372d_n_in,aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,Uua)),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ai,Uu),Uua)))) # label(fact_ATP_Olambda__124) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 35 (all X0 all X12 pp(aa_fun171081125l_bool(scratc403153377all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X0)),aa_fun1584354236d_bool(aTP_Lamm_ko(X0),X12)))) # label(fact_estii) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 36 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_is(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uua),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uub))))) # label(fact_ATP_Olambda__242) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 37 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ik,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ij,Uu))))) # label(fact_ATP_Olambda__38) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 38 (all Uu all Uua aa_fun277296641TP_ind(aa_TPT494704832TP_ind(aTP_Lamm_bn,Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1710655999nunion(aa_TPTP_ind_TPTP_ind(scratc1574992892d_Sing,scratc351358348ptyset)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2055967654d_repl,Uu),Uua))) # label(fact_ATP_Olambda__147) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 39 (all B_1 all B_2 gg_TPTP_ind(scratc198259775nd_ect(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__52628__31704_ONUM706__thf__4__p_Obnd__ect) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 40 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ev,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eu(Uu),Uua))))) # label(fact_ATP_Olambda__176) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 41 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fi(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fh(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__248) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 42 (all X all Xa all Xb scratc1971165748_indeq(X,Xa,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1701720390d_d_Pi,X),aTP_Lamm_ak(Xb))) = scratc1542279420d_11_i(X,Xa,Xb)) # label(fact_def__d__11__i) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 43 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cx(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc739393462moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc739393462moreis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc739393462moreis,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__274) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 44 (all X0 all X12 pp(aa_fun171081125l_bool(scratc403153377all_of(aa_TPT43085870d_bool(aTP_Lamm_kt(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_kv(X0),X12)))) # label(fact_second__p) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 45 (all X all Xa (pp(scratc82194035d_l_ec(X,Xa)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc231961781nd_imp,X),scratc909112134_d_not(Xa))))) # label(fact_def__l__ec) # label(axiom) # label(non_clause). [assumption]. 1.42/1.72 46 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc605409850lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc605409850lessis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc605409850lessis,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ct(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__275) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 47 (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_bb(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc231961781nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc695441016d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,Uub),Uud))),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc695441016d_e_is(Uu),Uuc),Uud))))) # label(fact_ATP_Olambda__287) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 48 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc315496536_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,aa_TPTP_ind_TPTP_ind(scratc276767164_proj0,X22)),X0)))) # label(fact_proj0__Sigma) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 49 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fx,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fw(Uu),Uua))))) # label(fact_ATP_Olambda__168) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 50 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101372d_n_in,Uua),Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ke,Uu),Uua)))) # label(fact_ATP_Olambda__152) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 51 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_it,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_iu,Uu)))) # label(fact_ATP_Olambda__34) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 52 (all X0 all X12 all X22 all X32 (pp(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1764895348bnd_if(X0,X22),X32))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X12),X22))))) # label(fact_k__If__In__then__E) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 53 (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]. 1.42/1.73 54 (all X all Xa aa_TPT494704832TP_ind(scratc2055967654d_repl,aa_fun1431113780TP_ind(scratc685395505_d_Sep(X),Xa)) = scratc134463330eplSep(X,Xa)) # label(fact_def__d__ReplSep) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 55 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gu(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gv,Uu),Uua)))) # label(fact_ATP_Olambda__162) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 56 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc1744519106d_anec(X,Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1661297833l_some(X),aa_TPT43085870d_bool(scratc198259771nd_ecp(X,Xa),Xb))))) # label(fact_def__anec) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 57 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc605409850lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc605409850lessis,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_er(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__222) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 58 (all X (pp(scratc909112134_d_not(X)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc231961781nd_imp,X),fFalse)))) # label(fact_def__d__not) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 59 (all X all Xa all Xb (pp(aa_fun171081125l_bool(scratc165804138nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_av(X),Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1546634565d_incl(X),Xa),Xb)))) # label(fact_def__incl) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 60 (all Uu all Uua all Uub (scratc1814191352_is_of(aa_TPTP_ind_TPTP_ind(scratc695441011d_e_in(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_al,Uu)) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_lc(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__204) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 61 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jf,Uu),Uua)))) # label(fact_ATP_Olambda__128) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 62 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dl,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dk(Uu),Uua))))) # label(fact_ATP_Olambda__187) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 63 (all X0 all X12 pp(aa_fun171081125l_bool(scratc403153377all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X0)),aa_fun1584354236d_bool(aTP_Lamm_li(X0),X12)))) # label(fact_e__isp) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 64 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_kc,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_kb,Uu))))) # label(fact_ATP_Olambda__23) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 65 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cy(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cx(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__256) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 66 (all X0 all X12 scratc1814191352_is_of(aa_fun1431113780TP_ind(scratc685395505_d_Sep(X0),X12),aa_TPT43085870d_bool(aTP_Lamm_kk,X0))) # label(fact_setof__p) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 67 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2012196942ective(X),Xa),Xb)) <-> pp(scratc801646954_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1828477712ective(X),Xa),Xb),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1254231699ective(X),Xa),Xb))))) # label(fact_def__bijective) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 68 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_au(Uu),Uua),Uub),Uuc)) <-> pp(scratc82194035d_l_ec(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc614192122d_esti(Uu),Uuc),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc614192122d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__267) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 69 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jk,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,Uu)),Uua))))) # label(fact_ATP_Olambda__141) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 70 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ia,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hz,Uu))))) # label(fact_ATP_Olambda__43) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 71 (all X0 scratc351358348ptyset != aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,X0)) # label(fact_neq__ordsucc__0) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 72 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_ay(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,Uu),Uub))) # label(fact_ATP_Olambda__245) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 73 (all X ((all X1 (pp(aa_TPTP_ind_bool(X1,scratc351358348ptyset)) -> ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(X1,X2)) -> pp(aa_TPTP_ind_bool(X1,aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,X2)))))) -> pp(aa_TPTP_ind_bool(X1,X))))) <-> pp(aa_TPTP_ind_bool(scratc1700835558_nat_p,X)))) # label(fact_def__nat__p) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 74 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dc(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_db(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__255) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 75 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fm(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fl(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__247) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 76 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc315496536_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc461288049d_pair,aa_TPTP_ind_TPTP_ind(scratc276767164_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc276767165_proj1,X22)) = X22 & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,aa_TPTP_ind_TPTP_ind(scratc276767165_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc276767164_proj0,X22)))) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,aa_TPTP_ind_TPTP_ind(scratc276767164_proj0,X22)),X0))))) # label(fact_k__Sigma__eta__proj0__proj1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 77 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cg,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ch,Uu)))) # label(fact_ATP_Olambda__92) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 78 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jq,Uu),Uua)))) # label(fact_ATP_Olambda__116) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 79 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ck,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc605409850lessis,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uua),scratc1030418234nd_n_1)),Uu))))) # label(fact_ATP_Olambda__122) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 80 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_bk,Uu)) <-> (exists X2 (gg_TPTP_ind(X2) & aa_TPTP_ind_TPTP_ind(scratc252616921d_Inj1,X2) = Uu))))) # label(fact_ATP_Olambda__101) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 81 (all Uu (gg_TPTP_ind(Uu) -> ((exists X2 (gg_TPTP_ind(X2) & aa_TPTP_ind_TPTP_ind(scratc252616920d_Inj0,X2) = Uu)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_bl,Uu))))) # label(fact_ATP_Olambda__102) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 82 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc614192122d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc685395505_d_Sep(Uu),Uua))) -> pp(aa_TPTP_ind_bool(Uua,Uub))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_kn(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__200) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 83 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),Uua)),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bv,Uu),Uua)))) # label(fact_ATP_Olambda__118) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 84 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1027410742_empty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X)),scratc273400502nd_non(X,aa_TPT43085870d_bool(aTP_Lamm_aw(X),Xa)))))) # label(fact_def__empty) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 85 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dt,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_du,Uu)))) # label(fact_ATP_Olambda__81) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 86 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ah,Uu),Uua)))) # label(fact_ATP_Olambda__150) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 87 (all X all Xa (pp(scratc801646954_d_and(aa_bool_bool(scratc82850040d_l_or(X),Xa),scratc82194035d_l_ec(X,Xa))) <-> scratc1968367672d_orec(X,Xa))) # label(fact_def__orec) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 88 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cd,Uu)))) # label(fact_ATP_Olambda__94) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 89 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ig,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_if,Uu))))) # label(fact_ATP_Olambda__40) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 90 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fd(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uuc),Uua))))))) # label(fact_ATP_Olambda__280) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 91 (all X aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,aa_TPTP_ind_TPTP_ind(scratc2087855887_times,X)) = scratc214822966d_n_ts(X)) # label(fact_def__n__ts) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 92 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gg,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_gh,Uu)))) # label(fact_ATP_Olambda__61) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 93 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc273006913nd_nis,Uua),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jd,Uu),Uua)))) # label(fact_ATP_Olambda__148) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 94 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bz,Uu)) <-> pp(aa_fun171081125l_bool(scratc281596399nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1701720390d_d_Pi,scratc272482122nd_nat),aTP_Lamm_ab)),aa_TPT43085870d_bool(aTP_Lamm_by,Uu))))) # label(fact_ATP_Olambda__8) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 95 (all X0 pp(aa_fun171081125l_bool(scratc403153377all_of(aa_TPT43085870d_bool(aTP_Lamm_kk,X0)),aa_TPT43085870d_bool(aTP_Lamm_km,X0)))) # label(fact_isseti) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 96 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ft(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__229) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 97 (all P all Q (pp(Q) | -pp(P) | -pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 98 (all Uu all Uua (gg_TPTP_ind(Uu) -> aa_TPTP_ind_TPTP_ind(aTP_Lamm_ak(Uu),Uua) = Uu)) # label(fact_ATP_Olambda__295) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 99 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hv,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc605409850lessis,Uu),Uua)) -> pp(scratc909112134_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,Uu),Uua)))))) # label(fact_ATP_Olambda__135) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 100 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1)),Uu)))) # label(fact_ATP_Olambda__4) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 101 (all X0 all X12 all X22 all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1701720390d_d_Pi,X0),X12))) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X32),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,X22),X32)),aa_TPTP_ind_TPTP_ind(X12,X32)))))) # label(fact_ap__Pi) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 102 (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(scratc214101377d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__226) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 103 (all P (gg_bool(P) -> P = fTrue | fFalse = P)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 104 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc406812218_inj_h(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc315496536_Sigma,X),aa_TPT1424761345TP_ind(aTP_Lamm_ay(Xc),Xd))) # label(fact_def__inj__h) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 105 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc148253326_power,X0))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1673343774d_Subq,X12),X0)))) # label(fact_k__PowerEq) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 106 (all X all Xa all Xb (pp(aa_fun171081125l_bool(scratc165804138nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bc(X),Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1828477712ective(X),Xa),Xb)))) # label(fact_def__injective) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 107 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_he,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_hf,Uu)))) # label(fact_ATP_Olambda__53) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 108 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc273006913nd_nis,X),Xa)) <-> pp(scratc909112134_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,X),Xa))))) # label(fact_def__nis) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 109 (all X0 (pp(aa_TPTP_ind_bool(scratc1700835558_nat_p,X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X0),scratc1593906026_omega)))) # label(fact_nat__p__omega) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 110 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fb,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fa(Uu),Uua))))) # label(fact_ATP_Olambda__174) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 111 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hk,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hj,Uu))))) # label(fact_ATP_Olambda__51) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 112 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gj,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gi(Uu),Uua))))) # label(fact_ATP_Olambda__164) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 113 (all X all Xa all Xb all Xc (pp(aa_fun171081125l_bool(scratc1661297833l_some(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ba(Xa),Xb),Xc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1165925220_image(X,Xa),Xb),Xc)))) # label(fact_def__image) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 114 (all X0 all X12 pp(aa_fun171081125l_bool(scratc403153377all_of(aa_TPT43085870d_bool(aTP_Lamm_ld(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_lg(X0),X12)))) # label(fact_e__fisi) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 115 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_gl,Uu)))) # label(fact_ATP_Olambda__18) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 116 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc605409850lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc605409850lessis,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eu(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__221) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 117 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,Uu),Uua)) -> pp(scratc909112134_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc605409850lessis,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hp,Uu),Uua)))) # label(fact_ATP_Olambda__133) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 118 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X33),X0)) -> aa_TPTP_ind_TPTP_ind(X22,X33) = aa_TPTP_ind_TPTP_ind(X12,X33)))) -> aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc315496536_Sigma,X0),X22) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc315496536_Sigma,X0),X12))) # label(fact_xi__ext) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 119 (all X (pp(aa_TPTP_ind_bool(scratc1242474369_prop1,X)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc273006913nd_nis,aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,X)),X)))) # label(fact_def__d__22__prop1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 120 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_kg,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_kh,Uu)))) # label(fact_ATP_Olambda__22) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 121 (all B_1 all B_2 all B_3 gg_bool(scratc281858745nd_or3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__52628__31704_ONUM706__thf__4__p_Obnd__or3) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 122 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ih,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ii,Uu)))) # label(fact_ATP_Olambda__39) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 123 (all X all Xa (pp(aa_fun171081125l_bool(scratc403153377all_of(X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (scratc1814191352_is_of(X2,X) -> pp(aa_TPTP_ind_bool(Xa,X2))))))) # label(fact_def__all__of) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 124 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ib,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ic,Uu)))) # label(fact_ATP_Olambda__42) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 125 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc739393462moreis,Uu),scratc1030418234nd_n_1)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cs,Uu)))) # label(fact_ATP_Olambda__20) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 126 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fr,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fq(Uu),Uua))))) # label(fact_ATP_Olambda__170) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 127 (all X all Xa all Xb (pp(aa_fun171081125l_bool(scratc165804138nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_au(X),Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2043778036t_disj(X),Xa),Xb)))) # label(fact_def__st__disj) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 128 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1673343774d_Subq,X12),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc148253326_power,X0))))) # label(fact_k__PowerI) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 129 (all Uu all Uua all Uub all Uuc all Uud aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_ax(Uu),Uua),Uub),Uuc),Uud) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,aa_TPTP_ind_TPTP_ind(scratc665549552wissel(Uu,Uub),Uuc)),Uud))) # label(fact_ATP_Olambda__291) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 130 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc605409850lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc605409850lessis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc605409850lessis,Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gr(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__223) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 131 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hg(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hh,Uu),Uua)))) # label(fact_ATP_Olambda__158) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 132 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X22),aa_fun1431113780TP_ind(scratc685395505_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X22),X0)))) # label(fact_k__SepE1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 133 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jt,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ju,Uu)))) # label(fact_ATP_Olambda__24) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 134 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc716798900munion,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc655515192_union,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2055967654d_repl,X),Xa))) # label(fact_def__famunion) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 135 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc273006913nd_nis,aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,Uu)),Uu)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ka,Uu)))) # label(fact_ATP_Olambda__13) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 136 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fj,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fi(Uu),Uua))))) # label(fact_ATP_Olambda__172) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 137 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc403153377all_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__183) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 138 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hr,Uu),Uua)) <-> (pp(scratc909112134_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc739393462moreis,Uu),Uua))))) # label(fact_ATP_Olambda__146) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 139 (all X all Xa all Xb all Xc all Xd scratc232027368nd_ind(Xb,aa_TPT43085870d_bool(scratc277160760_prop2(X,Xa,Xb,Xc),Xd)) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1971165748_indeq(X,Xa,Xb),Xc),Xd)) # label(fact_def__indeq) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 140 (all Uu all Uua all Uub all Uuc (scratc1814191352_is_of(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc523281511d_pair(Uu,Uua),Uub),Uuc),aa_TPT43085870d_bool(aTP_Lamm_kt(Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kx(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__266) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 141 (all X all Xa (pp(scratc801646954_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc231961781nd_imp,X),Xa),aa_bool_bool(aa_boo1142376798l_bool(scratc231961781nd_imp,Xa),X))) <-> scratc1695788404_l_iff(X,Xa))) # label(fact_def__l__iff) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 142 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ge,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gd,Uu))))) # label(fact_ATP_Olambda__62) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 143 scratc1896593296bvious <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc231961781nd_imp,fFalse),fFalse)) # label(fact_def__obvious) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 144 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jx,Uu)) <-> pp(aa_fun171081125l_bool(scratc281596399nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1701720390d_d_Pi,scratc272482122nd_nat),aTP_Lamm_ab)),aa_TPT43085870d_bool(aTP_Lamm_jw,Uu))))) # label(fact_ATP_Olambda__7) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 145 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hb,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_hc,Uu)))) # label(fact_ATP_Olambda__54) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 146 (all X all Xa (scratc477128825d_r_ec(X,Xa) <-> (pp(X) -> pp(scratc909112134_d_not(Xa))))) # label(fact_def__r__ec) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 147 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gp,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_gq,Uu)))) # label(fact_ATP_Olambda__58) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 148 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_fun1235454963TP_ind(aTP_Lamm_bp(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc1764895348bnd_if(aa_TPTP_ind_bool(Uua,Uub),Uub),scratc199112561nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bd(Uu),Uua)))) # label(fact_ATP_Olambda__198) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 149 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dr(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__282) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 150 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ec(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__210) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 151 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dl,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_dm,Uu)))) # label(fact_ATP_Olambda__83) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 152 (all B_1 all B_2 gg_bool(scratc755465763_amone(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__52628__31704_ONUM706__thf__4__p_Obnd__amone) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 153 (all X0 all X12 pp(aa_fun171081125l_bool(scratc403153377all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X0)),aa_TPT43085870d_bool(aTP_Lamm_ks(X0),X12)))) # label(fact_firstis1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 154 (all X0 all X12 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1828477712ective(aa_fun1431113780TP_ind(scratc685395505_d_Sep(X0),X12)),X0),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc315496536_Sigma,aa_fun1431113780TP_ind(scratc685395505_d_Sep(X0),X12)),scratc695441011d_e_in(X0,X12))))) # label(fact_otax1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 155 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc257638827n_some,aa_TPT43085870d_bool(scratc1633255295ffprop(X),Xa))))) # label(fact_def__d__29__ii) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 156 (all Uu all Uua aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,Uu),Uua)) = aa_TPTP_ind_TPTP_ind(aTP_Lamm_af(Uu),Uua)) # label(fact_ATP_Olambda__193) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 157 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc148253326_power,X0)))) # label(fact_k__Self__In__Power) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 158 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_je,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jd,Uu))))) # label(fact_ATP_Olambda__30) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 159 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1546634565d_incl(Uu),Uua),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1546634565d_incl(Uu),Uub),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc695441016d_e_is(aa_TPTP_ind_TPTP_ind(scratc148253326_power,Uu)),Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kl(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__201) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 160 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1547880940d_invf(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc315496536_Sigma,Xa),scratc771030273d_soft(X,Xa,Xb))) # label(fact_def__invf) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 161 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ew,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ev,Uu))))) # label(fact_ATP_Olambda__72) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 162 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jp,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),scratc1030418234nd_n_1))))) # label(fact_ATP_Olambda__10) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 163 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gu(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc739393462moreis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,Uu),Uub)))))) # label(fact_ATP_Olambda__217) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 164 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uuc),Uua))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fl(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__278) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 165 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,Uua),Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_al,Uu),Uua)))) # label(fact_ATP_Olambda__154) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 166 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_id,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,Uua),Uu))))) # label(fact_ATP_Olambda__132) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 167 (all X all Xa all Xb all Xc (pp(aa_fun171081125l_bool(scratc403153377all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ap(X),Xa),Xb),Xc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc285496229fixfu2(X,Xa),Xb),Xc)))) # label(fact_def__fixfu2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 168 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,Uua),aa_TPTP_ind_TPTP_ind(scratc148253326_power,Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kk,Uu),Uua)))) # label(fact_ATP_Olambda__151) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 169 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_id,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ie,Uu)))) # label(fact_ATP_Olambda__41) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 170 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1764895348bnd_if(X,Xa),Xb) = scratc199112561nd_eps(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_br(X),Xa),Xb))) # label(fact_def__if) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 171 (all X all Xa (pp(scratc909112134_d_not(scratc82194035d_l_ec(X,Xa))) <-> pp(scratc801646954_d_and(X,Xa)))) # label(fact_def__d__and) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 172 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc2133892340univof,X0)))) # label(fact_k__UnivOf__In) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 173 (all Uu all Uua all Uub all Uuc all Uud ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc695441016d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,Uub),Uud)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_aq(Uu),Uua),Uub),Uuc),Uud)))) # label(fact_ATP_Olambda__288) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 174 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dd,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_de,Uu)))) # label(fact_ATP_Olambda__85) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 175 (all X0 all X12 ((exists X2 (gg_TPTP_ind(X2) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X2),X0)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X12),X2)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc655515192_union,X0))))) # label(fact_k__UnionEq) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 176 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc2009710558In_rec(X),Xa) = scratc199112561nd_eps(aa_TPT43085870d_bool(scratc1288003369_rec_G(X),Xa))) # label(fact_def__d__In__rec) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 177 (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]. 1.42/1.73 178 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gy,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_gz,Uu)))) # label(fact_ATP_Olambda__55) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 179 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (-pp(X0) -> X22 = aa_TPTP_ind_TPTP_ind(scratc1764895348bnd_if(X0,X12),X22)))) # label(fact_if__i__0) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 180 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bc(Uu),Uua),Uub),Uuc)) <-> pp(aa_fun171081125l_bool(scratc165804138nd_all(Uu),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_bb(Uu),Uua),Uub),Uuc))))) # label(fact_ATP_Olambda__285) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 181 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cq,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,scratc1030418234nd_n_1),aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,Uu))))) # label(fact_ATP_Olambda__98) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 182 (all X all Xa scratc797522755ectset(X,Xa) = scratc282055607nd_out(aa_TPTP_ind_TPTP_ind(scratc148253326_power,X),scratc1744519106d_anec(X,Xa))) # label(fact_def__ectset) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 183 (all X0 all X12 all X22 (gg_TPTP_ind(X22) & gg_TPTP_ind(X12) -> X22 = aa_TPTP_ind_TPTP_ind(scratc1764895348bnd_if(X0,X12),X22) & -pp(X0) | pp(X0) & X12 = aa_TPTP_ind_TPTP_ind(scratc1764895348bnd_if(X0,X12),X22))) # label(fact_if__i__correct) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 184 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_aj,Uu)) <-> scratc351358348ptyset != Uu))) # label(fact_ATP_Olambda__100) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 185 (all X all Xa all Xb (scratc1201612283_orec3(X,Xa,Xb) <-> pp(scratc801646954_d_and(scratc281858745nd_or3(X,Xa,Xb),scratc198259710nd_ec3(X,Xa,Xb))))) # label(fact_def__orec3) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 186 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gk,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gj,Uu))))) # label(fact_ATP_Olambda__60) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 187 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc281596399nd_one(X0),X12)) -> pp(aa_TPTP_ind_bool(X12,scratc232027368nd_ind(X0,X12))))) # label(fact_oneax) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 188 (all X0 pp(aa_TPTP_ind_bool(scratc1586527269closed,aa_TPTP_ind_TPTP_ind(scratc2133892340univof,X0)))) # label(fact_k__UnivOf__ZF__closed) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 189 (all Uu all Uua all Uub all Uuc all Uud all Uue all Uuf (pp(aa_fun171081125l_bool(scratc403153377all_of(aa_TPT43085870d_bool(aTP_Lamm_al,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_am(Uua),Uub),Uuc),Uud),Uue),Uuf))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_an(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)))) # label(fact_ATP_Olambda__294) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 190 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cm,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc739393462moreis,Uua),aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,Uu)))))) # label(fact_ATP_Olambda__127) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 191 (all X all Xa scratc523281511d_pair(X,Xa) = scratc461288049d_pair) # label(fact_def__d__pair) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 192 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc695441016d_e_is(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,Uua),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ba(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__265) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 193 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_il,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_im,Uu)))) # label(fact_ATP_Olambda__37) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 194 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jo,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jn,Uu))))) # label(fact_ATP_Olambda__26) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 195 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bj(Uu),Uua) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2055967654d_repl,aa_TPTP_ind_TPTP_ind(Uu,Uua)),aa_TPT1424761345TP_ind(scratc461288049d_pair,Uua))) # label(fact_ATP_Olambda__139) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 196 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,Uub))),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,Uua),Uub)),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ae(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__214) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 197 (all X all Xa all Xb (gg_TPTP_ind(Xb) -> aa_TPTP_ind_TPTP_ind(scratc695441011d_e_in(X,Xa),Xb) = Xb)) # label(fact_def__e__in) # label(axiom) # label(non_clause). [assumption]. 1.42/1.73 198 (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_am(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(scratc695441016d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,Uub),Uuc)),Uue)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,Uub),Uud)),Uuf))))))) # label(fact_ATP_Olambda__293) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 199 (all X0 all X12 all X22 (gg_TPTP_ind(X22) & gg_TPTP_ind(X12) -> X22 = aa_TPTP_ind_TPTP_ind(scratc1764895348bnd_if(X0,X12),X22) | aa_TPTP_ind_TPTP_ind(scratc1764895348bnd_if(X0,X12),X22) = X12)) # label(fact_if__i__or) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 200 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_km,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aa_TPT43085870d_bool(aTP_Lamm_kk,Uu)),aa_TPT43085870d_bool(aTP_Lamm_kl(Uu),Uua))))) # label(fact_ATP_Olambda__140) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 201 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hj,Uu),Uua)) <-> (pp(scratc909112134_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc605409850lessis,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__145) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 202 (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]. 1.42/1.74 203 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gy,Uu),Uua)))) # label(fact_ATP_Olambda__161) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 204 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_df(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc605409850lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__276) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 205 (all X0 all X12 pp(aa_fun171081125l_bool(scratc403153377all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X0)),aa_fun1584354236d_bool(aTP_Lamm_kn(X0),X12)))) # label(fact_estie) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 206 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fp(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__277) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 207 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ez,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ey,Uu))))) # label(fact_ATP_Olambda__71) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 208 (all X0 (pp(aa_TPTP_ind_bool(X0,scratc351358348ptyset)) -> ((all X13 (gg_TPTP_ind(X13) -> (pp(aa_TPTP_ind_bool(scratc1700835558_nat_p,X13)) -> (pp(aa_TPTP_ind_bool(X0,X13)) -> pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,X13))))))) -> (all X12 (pp(aa_TPTP_ind_bool(scratc1700835558_nat_p,X12)) -> pp(aa_TPTP_ind_bool(X0,X12))))))) # label(fact_nat__ind) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 209 (all X all Xa all Xb (pp(scratc198259710nd_ec3(X,Xa,Xb)) <-> scratc1744453459d_and3(scratc82194035d_l_ec(X,Xa),scratc82194035d_l_ec(Xa,Xb),scratc82194035d_l_ec(Xb,X)))) # label(fact_def__ec3) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 210 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aw(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc614192122d_esti(Uu),Uub),Uua)))) # label(fact_ATP_Olambda__199) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 211 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ja(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jb,Uu),Uua)))) # label(fact_ATP_Olambda__156) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 212 (all B_1 all B_2 gg_bool(scratc82194035d_l_ec(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__52628__31704_ONUM706__thf__4__p_Obnd__l__ec) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 213 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kg,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__113) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 214 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,X),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1633255295ffprop(X),Xa),Xb)))) # label(fact_def__diffprop) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 215 (all X (gg_TPTP_ind(X) -> (pp(aa_TPTP_ind_bool(scratc1490012927pair_p,X)) <-> X = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc461288049d_pair,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,X),scratc351358348ptyset)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,X),aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,scratc351358348ptyset)))))) # label(fact_def__pair__p) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 216 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ex(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc739393462moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc739393462moreis,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__219) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 217 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_iw,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_iv,Uu))))) # label(fact_ATP_Olambda__33) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 218 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fd(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fe(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__249) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 219 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ei(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__211) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 220 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc739393462moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,Uu),Uub)))))) # label(fact_ATP_Olambda__220) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 221 (all P all Q (pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) | pp(P))) # label(help_fimplies_1_1_U) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 222 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc695441016d_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_lh(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__283) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 223 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gc(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__228) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 224 (all X all Xa all Xb all Xc scratc232027368nd_ind(Xa,aa_TPT43085870d_bool(scratc277160759_prop1(X,Xa,Xb),Xc)) = aa_TPTP_ind_TPTP_ind(scratc232420963nd_ite(X,Xa,Xb),Xc)) # label(fact_def__ite) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 225 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1165925220_image(aa_fun1431113780TP_ind(scratc685395505_d_Sep(Uu),Uua),Uu),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc315496536_Sigma,aa_fun1431113780TP_ind(scratc685395505_d_Sep(Uu),Uua)),scratc695441011d_e_in(Uu,Uua))),Uub))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_kz(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__233) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 226 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_le(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc695441016d_e_is(Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,Uua),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,Uub),Uuc))))) # label(fact_ATP_Olambda__263) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 227 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc315496536_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,aa_TPTP_ind_TPTP_ind(scratc276767165_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc276767164_proj0,X22)))))) # label(fact_proj1__Sigma) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 228 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc273006913nd_nis,aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,Uu)),scratc1030418234nd_n_1)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ki,Uu)))) # label(fact_ATP_Olambda__16) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 229 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_el(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__209) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 230 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_by,Uu),Uua)) <-> pp(scratc801646954_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,Uua),scratc1030418234nd_n_1)),Uu),aa_fun171081125l_bool(scratc226620778_n_all,aa_TPT43085870d_bool(aTP_Lamm_ae(Uu),Uua)))))) # label(fact_ATP_Olambda__112) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 231 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_io,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_in,Uu))))) # label(fact_ATP_Olambda__36) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 232 (all Uu all Uua (gg_TPTP_ind(Uua) -> ((exists X3 (gg_TPTP_ind(X3) & Uua = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc461288049d_pair,Uu),X3))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bi,Uu),Uua))))) # label(fact_ATP_Olambda__195) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 233 (all X all Xa (pp(aa_TPTP_ind_bool(scratc264745403nd_min(X),Xa)) <-> pp(scratc801646954_d_and(aa_TPTP_ind_bool(scratc214298157d_n_lb(X),Xa),aa_TPTP_ind_bool(X,Xa))))) # label(fact_def__min) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 234 (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_ao(Uu),Uua),Uub),Uuc),Uud),Uue)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aa_TPT43085870d_bool(aTP_Lamm_al,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_an(Uu),Uua),Uub),Uuc),Uud),Uue))))) # label(fact_ATP_Olambda__292) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 235 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ht,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_hu,Uu)))) # label(fact_ATP_Olambda__46) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 236 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dz(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__212) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 237 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc403153377all_of(aa_TPT43085870d_bool(aTP_Lamm_al,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_lh(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_li(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__235) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 238 (all X0 pp(aa_fun171081125l_bool(scratc403153377all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X0)),aa_TPT43085870d_bool(aTP_Lamm_lj,X0)))) # label(fact_refis) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 239 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1673343774d_Subq,X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X2),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X2),Xa))))))) # label(fact_def__d__Subq) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 240 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jm,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(scratc1030418234nd_n_1),Uu))))) # label(fact_ATP_Olambda__11) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 241 (all X all Xa all Xb all Xc all Xd aa_TPT1424761345TP_ind(scratc1971165748_indeq(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1542279420d_11_i(X,Xa,Xb),Xc),Xd)) = scratc69006078indeq2(X,Xa,Xb,Xc,Xd)) # label(fact_def__indeq2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 242 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_es,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_et,Uu)))) # label(fact_ATP_Olambda__73) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 243 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ix(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uua),Uub))))) # label(fact_ATP_Olambda__208) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 244 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ks(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aa_TPT43085870d_bool(aTP_Lamm_al,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kr(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__238) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 245 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dd,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dc(Uu),Uua))))) # label(fact_ATP_Olambda__189) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 246 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gn,Uu),Uua)))) # label(fact_ATP_Olambda__149) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 247 (all Uu all Uua all Uub all Uuc (pp(aa_fun171081125l_bool(scratc1661297833l_some(Uua),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_as(Uu),Uub),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_at(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__286) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 248 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_do(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dp,Uu),Uua)))) # label(fact_ATP_Olambda__186) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 249 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_lf(Uu),Uua),Uub),Uuc)) <-> (pp(aa_fun171081125l_bool(scratc403153377all_of(aa_TPT43085870d_bool(aTP_Lamm_al,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_le(Uua),Uub),Uuc))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc695441016d_e_is(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1701720390d_d_Pi,Uu),aTP_Lamm_ak(Uua))),Uub),Uuc))))) # label(fact_ATP_Olambda__269) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 250 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc273006913nd_nis,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(X),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc477680123_prop1(X),Xa),Xb)))) # label(fact_def__d__28__prop1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 251 (all B_1 gg_TPTP_ind(scratc199112561nd_eps(B_1))) # label(gsy_c_Scratch__tptp__translate__52628__31704_ONUM706__thf__4__p_Obnd__eps) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 252 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hq,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hp,Uu))))) # label(fact_ATP_Olambda__48) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 253 (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]. 1.42/1.74 254 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc148253326_power,X0))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1673343774d_Subq,X12),X0)))) # label(fact_k__PowerE) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 255 (all X all Xa (pp(aa_fun171081125l_bool(scratc281596399nd_one(X),Xa)) <-> pp(scratc801646954_d_and(scratc755465763_amone(X,Xa),aa_fun171081125l_bool(scratc1661297833l_some(X),Xa))))) # label(fact_def__one) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 256 (all X all Xa aa_fun1431113780TP_ind(scratc685395505_d_Sep(aa_TPTP_ind_TPTP_ind(scratc148253326_power,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc315496536_Sigma,X),aTP_Lamm_bg(Xa)))),aa_fun1913827119d_bool(aTP_Lamm_bh(X),Xa)) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1701720390d_d_Pi,X),Xa)) # label(fact_def__d__Pi) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 257 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hi,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hh,Uu))))) # label(fact_ATP_Olambda__52) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 258 (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]. 1.42/1.74 259 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dq,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dp,Uu))))) # label(fact_ATP_Olambda__82) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 260 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jb,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_jc,Uu)))) # label(fact_ATP_Olambda__31) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 261 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hx,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_hy,Uu)))) # label(fact_ATP_Olambda__44) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 262 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_in,Uu),Uua)) <-> pp(scratc198259710nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc257638827n_some,aa_TPT43085870d_bool(scratc1633255295ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc257638827n_some,aa_TPT43085870d_bool(scratc1633255295ffprop(Uua),Uu)))))) # label(fact_ATP_Olambda__108) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 263 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bd(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(Uua,Uub)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,Uub),Uu)))) # label(fact_ATP_Olambda__232) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 264 (all X all Xa all Xb aa_fun1431113780TP_ind(scratc685395505_d_Sep(X),aa_TPT43085870d_bool(Xa,Xb)) = aa_TPTP_ind_TPTP_ind(scratc1720071992_ecelt(X,Xa),Xb)) # label(fact_def__ecelt) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 265 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jl,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jk,Uu))))) # label(fact_ATP_Olambda__27) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 266 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ip,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_iq,Uu)))) # label(fact_ATP_Olambda__35) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 267 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jq,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_jr,Uu)))) # label(fact_ATP_Olambda__25) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 268 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dg(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_df(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__254) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 269 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fq(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fp(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__246) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 270 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ag,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,Uu),aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,Uu),Uua)))))) # label(fact_ATP_Olambda__121) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 271 (all Uu (gg_TPTP_ind(Uu) -> aa_TPTP_ind_TPTP_ind(aTP_Lamm_ad,Uu) = Uu)) # label(fact_ATP_Olambda__296) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 272 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cw,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cv,Uu))))) # label(fact_ATP_Olambda__87) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 273 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ci,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc605409850lessis,aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,Uua)),Uu))))) # label(fact_ATP_Olambda__125) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 274 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gb,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ga,Uu))))) # label(fact_ATP_Olambda__63) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 275 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1257283533_fixfu(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ar(X),Xa),Xb),Xc))))) # label(fact_def__fixfu) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 276 (all X all Xa scratc276767164_proj0 = scratc1208567289_first(X,Xa)) # label(fact_def__first) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 277 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ef(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__207) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 278 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eo(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__206) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 279 (all X (pp(aa_TPTP_ind_bool(scratc1108127816closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X1),X)) -> (all X2 ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X3),X1)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,aa_TPTP_ind_TPTP_ind(X2,X3)),X))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2055967654d_repl,X1),X2)),X))))))))) # label(fact_def__d__Repl__closed) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 280 (all X0 all X12 pp(aa_fun171081125l_bool(scratc403153377all_of(aa_fun1584354236d_bool(aTP_Lamm_la(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_lb(X0),X12)))) # label(fact_e__inp) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 281 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hl,Uu),Uua)) <-> (pp(scratc909112134_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc739393462moreis,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__144) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 282 (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]. 1.42/1.74 283 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ee,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ed,Uu))))) # label(fact_ATP_Olambda__78) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 284 (all X scratc214560563d_n_pl(X) = aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,aa_TPTP_ind_TPTP_ind(scratc552951793d_plus,X))) # label(fact_def__n__pl) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 285 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gp,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uua)),Uu)))) # label(fact_ATP_Olambda__137) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 286 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_da,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cz,Uu))))) # label(fact_ATP_Olambda__86) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 287 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uub),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fz(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__216) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 288 (all X scratc82850040d_l_or(X) = aa_boo1142376798l_bool(scratc231961781nd_imp,scratc909112134_d_not(X))) # label(fact_def__l__or) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 289 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ku(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc695441016d_e_is(aa_TPTP_ind_TPTP_ind(scratc1267186050etprod(Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc523281511d_pair(Uu,Uua),aa_TPTP_ind_TPTP_ind(scratc1208567289_first(Uu,Uua),Uub)),aa_TPTP_ind_TPTP_ind(scratc1424765483second(Uu,Uua),Uub))),Uub)))) # label(fact_ATP_Olambda__196) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 290 (all X all Xa (pp(aa_fun171081125l_bool(scratc226620778_n_all,aa_TPT43085870d_bool(scratc1279538416lbprop(X),Xa))) <-> pp(aa_TPTP_ind_bool(scratc214298157d_n_lb(X),Xa)))) # label(fact_def__n__lb) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 291 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fh(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__279) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 292 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dn(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_do(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__252) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 293 (all X all Xa (pp(aa_bool_bool(scratc82850040d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc605409850lessis,X),Xa)))) # label(fact_def__lessis) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 294 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc614192122d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc685395505_d_Sep(Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ko(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__234) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 295 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jv,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),scratc1030418234nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,Uu))))) # label(fact_ATP_Olambda__3) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 296 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gn,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_go,Uu)))) # label(fact_ATP_Olambda__59) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 297 (all X all Xa all Xb (pp(aa_fun171081125l_bool(scratc165804138nd_all(Xa),aa_TPT43085870d_bool(scratc1165925220_image(X,Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1254231699ective(X),Xa),Xb)))) # label(fact_def__surjective) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 298 (all X (pp(aa_TPTP_ind_bool(scratc291883897_cond2,X)) <-> pp(aa_fun171081125l_bool(scratc226620778_n_all,aa_TPT43085870d_bool(aTP_Lamm_ai,X))))) # label(fact_def__cond2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 299 (all X (pp(aa_TPTP_ind_bool(scratc1586527269closed,X)) <-> pp(aa_TPTP_ind_bool(scratc1377501230closed,X)) & pp(aa_TPTP_ind_bool(scratc1542234244closed,X)) & pp(aa_TPTP_ind_bool(scratc1108127816closed,X)))) # label(fact_def__d__ZF__closed) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 300 (all X all Xa scratc198259775nd_ect(X,Xa) = aa_fun1431113780TP_ind(scratc685395505_d_Sep(aa_TPTP_ind_TPTP_ind(scratc148253326_power,X)),scratc1744519106d_anec(X,Xa))) # label(fact_def__ect) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 301 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fx,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fy,Uu)))) # label(fact_ATP_Olambda__64) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 302 (all X all Xa all Xb (pp(scratc801646954_d_and(X,scratc801646954_d_and(Xa,Xb))) <-> scratc1744453459d_and3(X,Xa,Xb))) # label(fact_def__and3) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 303 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gm,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__12) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 304 (all X0 all X12 pp(aa_fun171081125l_bool(scratc403153377all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X0)),aa_TPT43085870d_bool(aTP_Lamm_kq(X0),X12)))) # label(fact_secondis1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 305 (all X (pp(aa_TPTP_ind_bool(scratc1377501230closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,aa_TPTP_ind_TPTP_ind(scratc655515192_union,X1)),X))))))) # label(fact_def__d__Union__closed) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 306 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cu(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ct(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__257) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 307 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ga,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fz(Uu),Uua))))) # label(fact_ATP_Olambda__167) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 308 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dk(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dj(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__253) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 309 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc739393462moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc605409850lessis,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ib,Uu),Uua)))) # label(fact_ATP_Olambda__130) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 310 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cf,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ce,Uu))))) # label(fact_ATP_Olambda__93) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 311 (all X all Xa all Xb all Xc all Xd aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc315496536_Sigma,X),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_ax(X),Xb),Xc),Xd)) = aa_TPTP_ind_TPTP_ind(scratc1045469599hangef(X,Xa,Xb,Xc),Xd)) # label(fact_def__changef) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 312 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jh(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ji,Uu),Uua)))) # label(fact_ATP_Olambda__155) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 313 -(exists X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X0),scratc351358348ptyset))) # label(fact_k__EmptyAx) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 314 (all X (pp(aa_TPTP_ind_bool(scratc1830836544_prop1,X)) <-> pp(aa_bool_bool(scratc82850040d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,X),scratc1030418234nd_n_1)),aa_fun171081125l_bool(scratc257638827n_some,aa_TPT43085870d_bool(aTP_Lamm_ah,X)))))) # label(fact_def__d__23__prop1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 315 (all Uu all Uua (pp(scratc281858745nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc257638827n_some,aa_TPT43085870d_bool(scratc1633255295ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc257638827n_some,aa_TPT43085870d_bool(scratc1633255295ffprop(Uua),Uu)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ip,Uu),Uua)))) # label(fact_ATP_Olambda__107) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 316 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_ac(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,Uu),Uua)),Uua)) # label(fact_ATP_Olambda__138) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 317 (all X0 (pp(aa_fun171081125l_bool(scratc257638827n_some,X0)) -> pp(aa_fun171081125l_bool(scratc342413039_n_one,scratc264745403nd_min(X0))))) # label(fact_satz27a) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 318 (all X aa_fun277296641TP_ind(scratc134463330eplSep(X,aTP_Lamm_bl),scratc702508900_d_Unj) = aa_TPTP_ind_TPTP_ind(scratc276767164_proj0,X)) # label(fact_def__proj0) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 319 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dv(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__271) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 320 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1710655999nunion(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc655515192_union,aa_TPTP_ind_TPTP_ind(scratc209982914_UPair(X),Xa))) # label(fact_def__binunion) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 321 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dt,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ds(Uu),Uua))))) # label(fact_ATP_Olambda__185) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 322 (all X (scratc347098055nd_wel(X) <-> pp(scratc909112134_d_not(scratc909112134_d_not(X))))) # label(fact_def__wel) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 323 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gf(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__225) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 324 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ca,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,Uua)),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc739393462moreis,Uua),Uu))))) # label(fact_ATP_Olambda__115) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 325 (all X0 all X12 pp(aa_fun171081125l_bool(scratc403153377all_of(aa_TPT43085870d_bool(aTP_Lamm_kt(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_kw(X0),X12)))) # label(fact_first__p) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 326 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jg,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jf,Uu))))) # label(fact_ATP_Olambda__29) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 327 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gt,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gs,Uu))))) # label(fact_ATP_Olambda__57) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 328 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc665549552wissel(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc315496536_Sigma,X),scratc1657856091sel_wb(X,Xa,Xb))) # label(fact_def__wissel) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 329 (all P all Q all R aa_TPTP_ind_bool(cOMBS_2003118649l_bool(P,Q),R) = aa_bool_bool(aa_TPT2142672771l_bool(P,R),aa_TPTP_ind_bool(Q,R))) # label(help_COMBS_1_1_COMBS_001t__TPTP____Interpret__Oind_001t__HOL__Obool_001t__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 330 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc739393462moreis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dj(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__272) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 331 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ef(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eg,Uu),Uua)))) # label(fact_ATP_Olambda__181) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 332 (all Uu aa_TPT494704832TP_ind(scratc2055967654d_repl,aa_TPTP_ind_TPTP_ind(scratc1626941541tminus(Uu),aa_TPTP_ind_TPTP_ind(scratc1574992892d_Sing,scratc351358348ptyset))) = aa_TPT494704832TP_ind(aTP_Lamm_bm,Uu)) # label(fact_ATP_Olambda__99) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 333 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hr,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_hs,Uu)))) # label(fact_ATP_Olambda__47) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 334 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ec(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ed,Uu),Uua)))) # label(fact_ATP_Olambda__182) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 335 (all X all Xa (pp(aa_fun171081125l_bool(scratc1661297833l_some(X),Xa)) <-> pp(scratc909112134_d_not(aa_fun171081125l_bool(scratc403153377all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X)),scratc273400502nd_non(X,Xa)))))) # label(fact_def__l__some) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 336 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_lb(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(Uua,aa_TPTP_ind_TPTP_ind(scratc695441011d_e_in(Uu,Uua),Uub))))) # label(fact_ATP_Olambda__258) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 337 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kw(Uu),Uua),Uub)) <-> scratc1814191352_is_of(aa_TPTP_ind_TPTP_ind(scratc1208567289_first(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_al,Uu)))) # label(fact_ATP_Olambda__203) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 338 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cn,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cm,Uu))))) # label(fact_ATP_Olambda__89) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 339 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ds(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dr(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__251) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 340 (all Uu all Uua all Uub all Uuc (pp(aa_bool_bool(aa_boo1142376798l_bool(scratc231961781nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc614192122d_esti(Uu),Uuc),Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc614192122d_esti(Uu),Uuc),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_av(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__268) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 341 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2055967654d_repl,X0),X12))) <-> (exists X3 (gg_TPTP_ind(X3) & X22 = aa_TPTP_ind_TPTP_ind(X12,X3) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X3),X0))))))) # label(fact_k__ReplEq) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 342 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1990322274_prop2,X),Xa)) <-> pp(scratc801646954_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,Xa),scratc1030418234nd_n_1)),X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1990322273_prop1,X),Xa))))) # label(fact_def__d__428__prop2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 343 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fa(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc739393462moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc739393462moreis,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__218) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 344 (all X0 all X12 pp(aa_fun171081125l_bool(scratc403153377all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X0)),aa_fun1584354236d_bool(aTP_Lamm_kz(X0),X12)))) # label(fact_otax2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 345 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cv,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cu(Uu),Uua))))) # label(fact_ATP_Olambda__191) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 346 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kb,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc273006913nd_nis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc273006913nd_nis,aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,Uua)))))) # label(fact_ATP_Olambda__123) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 347 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(scratc1764895348bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,scratc351358348ptyset),Uub),Uu),Uua) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_bq(Uu),Uua),Uub)) # label(fact_ATP_Olambda__197) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 348 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc315496536_Sigma,X),aTP_Lamm_ak(Xa)) = aa_TPTP_ind_TPTP_ind(scratc1267186050etprod(X),Xa)) # label(fact_def__setprod) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 349 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_he,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hd(Uu),Uua))))) # label(fact_ATP_Olambda__159) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 350 (all X0 ((all X13 (gg_TPTP_ind(X13) -> ((all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_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]. 1.42/1.75 351 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dv(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dw(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__250) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 352 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_js,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(scratc1030418234nd_n_1),Uu)),aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,Uu))))) # label(fact_ATP_Olambda__5) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 353 (all X all Xa all Xb aa_fun1431113780TP_ind(scratc685395505_d_Sep(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_at(X),Xa),Xb)) = aa_TPTP_ind_TPTP_ind(scratc903640101unmore(X,Xa),Xb)) # label(fact_def__unmore) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 354 (all X all Xa scratc232027368nd_ind(X,Xa) = scratc199112561nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bd(X),Xa))) # label(fact_def__ind) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 355 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X22),aa_fun1431113780TP_ind(scratc685395505_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(X12,X22)))) # label(fact_k__SepE2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 356 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_em,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_en,Uu)))) # label(fact_ATP_Olambda__75) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 357 (all X0 all X12 pp(aa_fun171081125l_bool(scratc403153377all_of(aa_TPT43085870d_bool(aTP_Lamm_kt(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_ku(X0),X12)))) # label(fact_pairis1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 358 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jh(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__213) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 359 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(scratc1030418234nd_n_1),Uu)),Uu)))) # label(fact_ATP_Olambda__6) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 360 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X33),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,aa_TPTP_ind_TPTP_ind(X22,X33)),aa_TPTP_ind_TPTP_ind(X12,X33)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc315496536_Sigma,X0),X22)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1701720390d_d_Pi,X0),X12))))) # label(fact_lam__Pi) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 361 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ep,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_eq,Uu)))) # label(fact_ATP_Olambda__74) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 362 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_es,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_er(Uu),Uua))))) # label(fact_ATP_Olambda__177) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 363 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lj,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc695441016d_e_is(Uu),Uua),Uua)))) # label(fact_ATP_Olambda__109) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 364 (all X all Xa scratc282055607nd_out(X,Xa) = scratc771030273d_soft(aa_fun1431113780TP_ind(scratc685395505_d_Sep(X),Xa),X,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc315496536_Sigma,aa_fun1431113780TP_ind(scratc685395505_d_Sep(X),Xa)),scratc695441011d_e_in(X,Xa)))) # label(fact_def__out) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 365 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cp,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_co,Uu))))) # label(fact_ATP_Olambda__88) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 366 (all X aa_TPTP_ind_TPTP_ind(scratc276767165_proj1,X) = aa_fun277296641TP_ind(scratc134463330eplSep(X,aTP_Lamm_bk),scratc702508900_d_Unj)) # label(fact_def__proj1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 367 (all Q all P (-pp(Q) | pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)))) # label(help_fimplies_2_1_U) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 368 (all P all X7 (-pp(aa_TPTP_ind_bool(P,X7)) | pp(fEx_TPTP_ind(P)))) # label(help_fEx_1_1_fEx_001t__TPTP____Interpret__Oind_U) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 369 (all X all Xa scratc276767165_proj1 = scratc1424765483second(X,Xa)) # label(fact_def__second) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 370 (all X aa_TPTP_ind_TPTP_ind(scratc552951793d_plus,X) = scratc232027368nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1701720390d_d_Pi,scratc272482122nd_nat),aTP_Lamm_ab),aa_TPT43085870d_bool(scratc271715072_prop2,X))) # label(fact_def__plus) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 371 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dh,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_di,Uu)))) # label(fact_ATP_Olambda__84) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 372 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ih,Uu),Uua)) <-> pp(scratc198259710nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__105) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 373 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bw,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bv,Uu))))) # label(fact_ATP_Olambda__96) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 374 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1626941541tminus(X),Xa) = aa_fun1431113780TP_ind(scratc685395505_d_Sep(X),aa_TPT43085870d_bool(aTP_Lamm_bo,Xa))) # label(fact_def__setminus) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 375 (all B_1 all B_2 gg_TPTP_ind(scratc232027368nd_ind(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__52628__31704_ONUM706__thf__4__p_Obnd__ind) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 376 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ei(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ej,Uu),Uua)))) # label(fact_ATP_Olambda__180) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 377 (all X0 all X12 (gg_TPTP_ind(X12) -> X12 = aa_TPTP_ind_TPTP_ind(scratc276767165_proj1,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc461288049d_pair,X0),X12)))) # label(fact_proj1__pair__eq) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 378 (all X all Xa all Xb all Xc all Xd all Xe (pp(aa_fun171081125l_bool(scratc1661297833l_some(X),aa_TPT43085870d_bool(scratc819037698_prop1(X,Xa,Xb,Xc,Xd),Xe))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc277160760_prop2(X,Xa,Xb,Xc),Xd),Xe)))) # label(fact_def__prop2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 379 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lg(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aa_TPT43085870d_bool(aTP_Lamm_ld(Uu),Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_lf(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__205) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 380 (all X0 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X0),scratc1593906026_omega)) -> pp(aa_TPTP_ind_bool(scratc1700835558_nat_p,X0)))) # label(fact_omega__nat__p) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 381 (all X aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1710655999nunion(X),aa_TPTP_ind_TPTP_ind(scratc1574992892d_Sing,X))) # label(fact_def__ordsucc) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 382 (all X all Xa all Xb (pp(scratc281858745nd_or3(X,Xa,Xb)) <-> pp(aa_bool_bool(scratc82850040d_l_or(X),aa_bool_bool(scratc82850040d_l_or(Xa),Xb))))) # label(fact_def__or3) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 383 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bo,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc270907740nd_nIn,Uua),Uu)))) # label(fact_ATP_Olambda__153) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 384 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc273006913nd_nis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc273006913nd_nis,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ja(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__227) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 385 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc695441016d_e_is(Uua),aa_TPTP_ind_TPTP_ind(scratc1424765483second(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc523281511d_pair(Uu,Uua),Uub),Uuc))),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kp(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__262) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 386 (all X scratc695441016d_e_is(X) = fequal_TPTP_ind) # label(fact_def__e__is) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 387 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Xa),X))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1448439421_prop1,X),Xa)))) # label(fact_def__d__26__prop1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 388 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1657856090sel_wa(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc232420963nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc695441016d_e_is(X),Xc),Xa),X,Xb),Xc)) # label(fact_def__wissel__wa) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 389 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc605409850lessis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uua),Uuc))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_db(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__281) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 390 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hd(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc605409850lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__224) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 391 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jt,Uu),Uua)))) # label(fact_ATP_Olambda__120) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 392 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X22),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc315496536_Sigma,X0),X12)),X22) = aa_TPTP_ind_TPTP_ind(X12,X22))) # label(fact_beta) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 393 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hv,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_hw,Uu)))) # label(fact_ATP_Olambda__45) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 394 (all X (pp(aa_TPTP_ind_bool(scratc1542234244closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,aa_TPTP_ind_TPTP_ind(scratc148253326_power,X1)),X))))))) # label(fact_def__d__Power__closed) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 395 (all X all Xa all Xb aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc315496536_Sigma,Xa),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_az(X),Xa),Xb)) = aa_TPTP_ind_TPTP_ind(scratc1031510649nverse(X,Xa),Xb)) # label(fact_def__inverse) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 396 (all X (pp(aa_TPTP_ind_bool(scratc277160762_prop4,X)) <-> pp(aa_fun171081125l_bool(scratc1661297833l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1701720390d_d_Pi,scratc272482122nd_nat),aTP_Lamm_ab)),aa_TPT43085870d_bool(scratc271715072_prop2,X))))) # label(fact_def__prop4) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 397 (all Uu all Uua ((pp(scratc909112134_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc605409850lessis,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ht,Uu),Uua)))) # label(fact_ATP_Olambda__143) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 398 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc281596399nd_one(X0),X12)) -> scratc1814191352_is_of(scratc232027368nd_ind(X0,X12),aa_TPT43085870d_bool(aTP_Lamm_al,X0)))) # label(fact_ind__p) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 399 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fm(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fn,Uu),Uua)))) # label(fact_ATP_Olambda__171) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 400 (all X0 all X12 pp(aa_fun171081125l_bool(scratc403153377all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X0)),aa_TPT43085870d_bool(aTP_Lamm_ky(X0),X12)))) # label(fact_e__pair__p) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 401 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718486404etprop(X,Xa),Xb),Xc)) <-> pp(scratc801646954_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc614192122d_esti(X),Xc),Xa),scratc909112134_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc614192122d_esti(X),Xc),Xb)))))) # label(fact_def__nissetprop) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 402 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cy(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cz,Uu),Uua)))) # label(fact_ATP_Olambda__190) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 403 (all Uu ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc273006913nd_nis,Uu),scratc1030418234nd_n_1)) -> pp(aa_fun171081125l_bool(scratc257638827n_some,aa_TPT43085870d_bool(aTP_Lamm_ah,Uu)))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_jz,Uu)))) # label(fact_ATP_Olambda__1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 404 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ix(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iy,Uu),Uua)))) # label(fact_ATP_Olambda__157) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 405 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jn,Uu),Uua)))) # label(fact_ATP_Olambda__142) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 406 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ky(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aa_TPT43085870d_bool(aTP_Lamm_al,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kx(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__237) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 407 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hn,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uu),Uua)) -> pp(scratc909112134_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc739393462moreis,Uu),Uua)))))) # label(fact_ATP_Olambda__136) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 408 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc270907740nd_nIn,X),Xa)) <-> -pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X),Xa)))) # label(fact_def__nIn) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 409 (all X all Xa (pp(aa_fun171081125l_bool(scratc257638827n_some,aa_TPT43085870d_bool(scratc1633255295ffprop(Xa),X))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,X),Xa)))) # label(fact_def__iii) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 410 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gw,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gv,Uu))))) # label(fact_ATP_Olambda__56) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 411 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc277160761_prop3(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,X),Xb)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,Xa),Xb))))) # label(fact_def__prop3) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 412 (all X aa_TPTP_ind_TPTP_ind(scratc1574992892d_Sing,X) = aa_TPTP_ind_TPTP_ind(scratc209982914_UPair(X),X)) # label(fact_def__d__Sing) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 413 (all X0 all X12 all X22 (gg_TPTP_ind(X12) -> (pp(X0) -> X12 = aa_TPTP_ind_TPTP_ind(scratc1764895348bnd_if(X0,X12),X22)))) # label(fact_if__i__1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 414 (all X0 all X12 all X22 ((pp(X0) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X12),X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,aa_TPTP_ind_TPTP_ind(scratc1764895348bnd_if(X0,X12),scratc351358348ptyset)),aa_TPTP_ind_TPTP_ind(scratc1764895348bnd_if(X0,X22),aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,scratc351358348ptyset)))))) # label(fact_k__If__In__01) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 415 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,X12) = aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,X0) -> X0 = X12))) # label(fact_ordsucc__inj) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 416 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fu,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fv,Uu)))) # label(fact_ATP_Olambda__65) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 417 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dx,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_dy,Uu)))) # label(fact_ATP_Olambda__80) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 418 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ha(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc605409850lessis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__230) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 419 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc315496536_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc461288049d_pair,aa_TPTP_ind_TPTP_ind(scratc276767164_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc276767165_proj1,X22)) = X22))) # label(fact_proj__Sigma__eta) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 420 (all X all Xa (pp(aa_fun171081125l_bool(scratc1661297833l_some(X),aa_TPT43085870d_bool(aTP_Lamm_aw(X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636953335nempty,X),Xa)))) # label(fact_def__nonempty) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 421 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc682320878ectelt(X,Xa),Xb) = aa_TPTP_ind_TPTP_ind(scratc797522755ectset(X,Xa),aa_TPTP_ind_TPTP_ind(scratc1720071992_ecelt(X,Xa),Xb))) # label(fact_def__ectelt) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 422 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fe(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ff,Uu),Uua)))) # label(fact_ATP_Olambda__173) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 423 (all Uu aa_TPTP_ind_TPTP_ind(aTP_Lamm_ab,Uu) = scratc272482122nd_nat) # label(fact_ATP_Olambda__297) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 424 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jw,Uu),Uua)) <-> pp(scratc801646954_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,Uua),scratc1030418234nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,Uu)),aa_fun171081125l_bool(scratc226620778_n_all,aa_TPT43085870d_bool(aTP_Lamm_ag,Uua)))))) # label(fact_ATP_Olambda__110) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 425 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_co,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc739393462moreis,Uua),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),scratc1030418234nd_n_1)))))) # label(fact_ATP_Olambda__126) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 426 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fg,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ff,Uu))))) # label(fact_ATP_Olambda__69) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 427 (all X all Xa all Xb all Xc all Xd (pp(scratc801646954_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc231961781nd_imp,X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc695441016d_e_is(Xa),Xd),Xb)),aa_bool_bool(aa_boo1142376798l_bool(scratc231961781nd_imp,scratc909112134_d_not(X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc695441016d_e_is(Xa),Xd),Xc)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc277160759_prop1(X,Xa,Xb),Xc),Xd)))) # label(fact_def__prop1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 428 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_iy,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_iz,Uu)))) # label(fact_ATP_Olambda__32) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 429 (all X all Xa (pp(aa_bool_bool(scratc82850040d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc739393462moreis,X),Xa)))) # label(fact_def__moreis) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 430 (all X all Xa aa_fun277296641TP_ind(scratc134463330eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bi,Xa)),scratc276767165_proj1) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,X),Xa)) # label(fact_def__ap) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 431 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hz,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc605409850lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc739393462moreis,Uua),Uu))))) # label(fact_ATP_Olambda__131) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 432 (all Uu all Uua (pp(scratc281858745nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ij,Uu),Uua)))) # label(fact_ATP_Olambda__104) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 433 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dh,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dg(Uu),Uua))))) # label(fact_ATP_Olambda__188) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 434 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hb,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ha(Uu),Uua))))) # label(fact_ATP_Olambda__160) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 435 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ft(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fu,Uu),Uua)))) # label(fact_ATP_Olambda__169) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 436 (all X all Xa all Xb (pp(scratc909112134_d_not(aa_TPTP_ind_bool(Xa,Xb))) <-> pp(aa_TPTP_ind_bool(scratc273400502nd_non(X,Xa),Xb)))) # label(fact_def__non) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 437 (all B_1 gg_bool(fEx_TPTP_ind(B_1))) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 438 (all X0 all X12 (gg_TPTP_ind(X12) & gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1673343774d_Subq,X0),X12)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1673343774d_Subq,X12),X0)) -> X12 = X0)))) # label(fact_set__ext) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 439 (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_TPTP_ind_bool(aa_TPT43085870d_bool(scratc614192122d_esti(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__264) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 440 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_el(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_em,Uu),Uua)))) # label(fact_ATP_Olambda__179) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 441 (all X all Xa all Xb (pp(aa_bool_bool(aa_boo1142376798l_bool(scratc231961781nd_imp,aa_TPTP_ind_bool(X,Xb)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc605409850lessis,Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1279538416lbprop(X),Xa),Xb)))) # label(fact_def__lbprop) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 442 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fn,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fo,Uu)))) # label(fact_ATP_Olambda__67) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 443 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1990322273_prop1,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc226620778_n_all,aa_TPT43085870d_bool(aTP_Lamm_ae(X),Xa))))) # label(fact_def__d__428__prop1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 444 (all B_1 all B_2 all B_3 gg_bool(scratc198259710nd_ec3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__52628__31704_ONUM706__thf__4__p_Obnd__ec3) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 445 (all X0 all X12 pp(aa_fun171081125l_bool(scratc403153377all_of(aa_fun1584354236d_bool(aTP_Lamm_la(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_lc(X0),X12)))) # label(fact_e__in__p) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 446 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ir(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__241) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 447 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ek,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ej,Uu))))) # label(fact_ATP_Olambda__76) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 448 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_be(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(scratc695441016d_e_is(Uu),Uub),Uuc)))))) # label(fact_ATP_Olambda__284) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 449 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X22),X0)) -> (pp(aa_TPTP_ind_bool(X12,X22)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X22),aa_fun1431113780TP_ind(scratc685395505_d_Sep(X0),X12)))))) # label(fact_k__SepI) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 450 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kr(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc695441016d_e_is(Uu),aa_TPTP_ind_TPTP_ind(scratc1208567289_first(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc523281511d_pair(Uu,Uua),Uub),Uuc))),Uub)))) # label(fact_ATP_Olambda__261) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 451 (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]. 1.42/1.75 452 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ca,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cb,Uu)))) # label(fact_ATP_Olambda__95) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 453 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kq(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aa_TPT43085870d_bool(aTP_Lamm_al,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kp(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__239) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 454 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bg(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc655515192_union,aa_TPTP_ind_TPTP_ind(Uu,Uua))) # label(fact_ATP_Olambda__194) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 455 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ld(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,Uub),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1701720390d_d_Pi,Uu),aTP_Lamm_ak(Uua)))))) # label(fact_ATP_Olambda__240) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 456 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1913827119d_bool(aTP_Lamm_bh(Uu),Uua),Uub)) <-> (all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X3),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,Uub),X3)),aa_TPTP_ind_TPTP_ind(Uua,X3)))))))) # label(fact_ATP_Olambda__259) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 457 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fs,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fr,Uu))))) # label(fact_ATP_Olambda__66) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 458 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_kd,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,Uu),aa_TPTP_ind_TPTP_ind(scratc148253326_power,scratc272482122nd_nat))))) # label(fact_ATP_Olambda__19) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 459 (all B_1 gg_bool(scratc909112134_d_not(B_1))) # label(gsy_c_Scratch__tptp__translate__52628__31704_ONUM706__thf__4__p_Obnd__d__not) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 460 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gg,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gf(Uu),Uua))))) # label(fact_ATP_Olambda__165) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 461 (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]. 1.42/1.75 462 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),scratc1030418234nd_n_1))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu)))) # label(fact_ATP_Olambda__17) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 463 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2055967654d_repl,aa_TPTP_ind_TPTP_ind(scratc148253326_power,aa_TPTP_ind_TPTP_ind(scratc148253326_power,scratc351358348ptyset))),aa_TPT1424761345TP_ind(aTP_Lamm_bq(X),Xa)) = aa_TPTP_ind_TPTP_ind(scratc209982914_UPair(X),Xa)) # label(fact_def__d__UPair) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 464 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc273006913nd_nis,Xa),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2036801596_prop1,X),Xa)))) # label(fact_def__d__27__prop1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 465 (all X all Xa (pp(scratc801646954_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,Xa),scratc1030418234nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,X)),aa_TPTP_ind_bool(scratc271715071_prop1,Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc271715072_prop2,X),Xa)))) # label(fact_def__d__24__prop2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 466 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hm,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hl,Uu))))) # label(fact_ATP_Olambda__50) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 467 (all X0 (pp(aa_TPTP_ind_bool(scratc1700835558_nat_p,X0)) -> pp(aa_TPTP_ind_bool(scratc1700835558_nat_p,aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,X0))))) # label(fact_nat__ordsucc) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 468 (all X (pp(aa_fun171081125l_bool(scratc1661297833l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1701720390d_d_Pi,scratc272482122nd_nat),aTP_Lamm_ab)),aa_TPT43085870d_bool(scratc1990322274_prop2,X))) <-> pp(aa_TPTP_ind_bool(scratc1990322276_prop4,X)))) # label(fact_def__d__428__prop4) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 469 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hg(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__231) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 470 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gs,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gr(Uu),Uua))))) # label(fact_ATP_Olambda__163) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 471 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(aa_TPTP_ind_TPTP_ind(scratc214822966d_n_ts(Uu),Uua)),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bs,Uu),Uua)))) # label(fact_ATP_Olambda__114) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 472 (all X all Xa aa_fun1431113780TP_ind(scratc685395505_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1764895348bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1764895356bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2055967654d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bp(X),Xa))),scratc351358348ptyset)) # label(fact_def__d__Sep) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 473 (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_ar(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aa_TPT43085870d_bool(aTP_Lamm_al,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_aq(Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__290) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 474 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jj,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ji,Uu))))) # label(fact_ATP_Olambda__28) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 475 (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]. 1.42/1.76 476 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_if,Uu),Uua)))) # label(fact_ATP_Olambda__129) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 477 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_fun171081125l_bool(scratc403153377all_of(aa_TPT43085870d_bool(aTP_Lamm_al,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_ao(Uu),Uua),Uub),Uuc),Uud))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ap(Uu),Uua),Uub),Uuc),Uud)))) # label(fact_ATP_Olambda__289) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 478 (all X aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc315496536_Sigma,scratc272482122nd_nat),aTP_Lamm_ac(X)) = aa_TPTP_ind_TPTP_ind(scratc1614848410_428_g,X)) # label(fact_def__d__428__g) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 479 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc214560563d_n_pl(Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gi(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__215) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 480 (all X7 all Y (Y != X7 | 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]. 1.42/1.76 481 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc198259771nd_ecp(X,Xa),Xb),Xc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc695441016d_e_is(aa_TPTP_ind_TPTP_ind(scratc148253326_power,X)),Xb),aa_TPTP_ind_TPTP_ind(scratc1720071992_ecelt(X,Xa),Xc))))) # label(fact_def__ecp) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 482 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X22),X0)) -> (all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X32),aa_TPTP_ind_TPTP_ind(X12,X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc461288049d_pair,X22),X32)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc315496536_Sigma,X0),X12))))))) # label(fact_pair__Sigma) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 483 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gd,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gc(Uu),Uua))))) # label(fact_ATP_Olambda__166) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 484 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fb,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_fc,Uu)))) # label(fact_ATP_Olambda__70) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 485 (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]. 1.42/1.76 486 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1288003369_rec_G(X),Xa),Xb)) <-> (all X3 ((all X4 all X5 (gg_TPTP_ind(X4) -> ((all X6 (gg_TPTP_ind(X6) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X6),X4)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(X3,X6),aa_TPTP_ind_TPTP_ind(X5,X6)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(X3,X4),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(X,X4),X5)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(X3,Xa),Xb)))))) # label(fact_def__d__In__rec__G) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 487 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc315496536_Sigma,X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc716798900munion,X),aTP_Lamm_bj(Xa))) # label(fact_def__d__Sigma) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 488 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_kj,Uu)) <-> scratc1814191352_is_of(aa_TPTP_ind_TPTP_ind(scratc1633262956rdsucc,Uu),aTP_Lamm_a))) # label(fact_ATP_Olambda__14) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 489 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc771030273d_soft(X,Xa,Xb),Xc) = scratc232027368nd_ind(X,aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ba(Xa),Xb),Xc))) # label(fact_def__soft) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 490 (all Uu all Uua all Uub all Uuc (gg_TPTP_ind(Uub) & gg_TPTP_ind(Uuc) & gg_TPTP_ind(Uua) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_br(Uu),Uua),Uub),Uuc)) <-> Uub = Uuc & -pp(Uu) | pp(Uu) & Uua = Uuc))) # label(fact_ATP_Olambda__270) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 491 (all X scratc1764895356bnd_in = scratc614192122d_esti(X)) # label(fact_def__esti) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 492 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,Uub),aa_fun1431113780TP_ind(scratc685395505_d_Sep(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_la(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__244) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 493 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hn,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ho,Uu)))) # label(fact_ATP_Olambda__49) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 494 (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]. 1.42/1.76 495 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dw(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dx,Uu),Uua)))) # label(fact_ATP_Olambda__184) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 496 (all Uu all Uua all Uub (scratc1814191352_is_of(aa_TPTP_ind_TPTP_ind(scratc1424765483second(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_al,Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kv(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__202) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 497 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1701720390d_d_Pi,X0),X12))) -> (all X32 (gg_TPTP_ind(X32) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X32),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1701720390d_d_Pi,X0),X12))) -> ((all X42 (gg_TPTP_ind(X42) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,X42),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,X22),X42) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1764370566bnd_ap,X32),X42)))) -> X22 = X32))))))) # label(fact_k__Pi__ext) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 498 (all Uu (pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ea,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_eb,Uu)))) # label(fact_ATP_Olambda__79) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 499 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764895356bnd_in,Uub),aa_TPTP_ind_TPTP_ind(scratc1267186050etprod(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kt(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__243) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 500 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_eh,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eg,Uu))))) # label(fact_ATP_Olambda__77) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 501 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bt,Uu)) <-> pp(aa_fun171081125l_bool(scratc403153377all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bs,Uu))))) # label(fact_ATP_Olambda__97) # label(axiom) # label(non_clause). [assumption]. 1.54/1.84 502 (all X0 (scratc347098055nd_wel(X0) -> pp(X0))) # label(fact_l__et) # label(axiom) # label(non_clause). [assumption]. 1.54/1.84 503 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jy,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc273006913nd_nis,Uu),scratc1030418234nd_n_1)) -> pp(aa_fun171081125l_bool(scratc342413039_n_one,aa_TPT43085870d_bool(aTP_Lamm_ah,Uu)))))) # label(fact_ATP_Olambda__2) # label(axiom) # label(non_clause). [assumption]. 1.54/1.84 504 (all X aa_TPTP_ind_TPTP_ind(scratc252616920d_Inj0,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2055967654d_repl,X),scratc252616921d_Inj1)) # label(fact_def__d__Inj0) # label(axiom) # label(non_clause). [assumption]. 1.54/1.84 505 (all X aa_TPTP_ind_TPTP_ind(scratc728638008d_24_g,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc315496536_Sigma,scratc272482122nd_nat),aTP_Lamm_af(X))) # label(fact_def__d__24__g) # label(axiom) # label(non_clause). [assumption]. 1.54/1.84 506 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1066042298_prop1,X),Xa)) <-> pp(scratc281858745nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214101377d_n_is,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc636635060_29_ii,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231699378nd_iii,X),Xa))))) # label(fact_def__d__29__prop1) # label(axiom) # label(non_clause). [assumption]. 1.54/1.84 507 (all B_1 all B_2 gg_bool(scratc801646954_d_and(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__52628__31704_ONUM706__thf__4__p_Obnd__d__and) # label(axiom) # label(non_clause). [assumption]. 1.54/1.84 1.54/1.84 ============================== end of process non-clausal formulas === 1.54/1.84 1.54/1.84 ============================== PROCESS INITIAL CLAUSES =============== 1.54/1.84 1.54/1.84 ============================== PREDICATE ELIMINATION ================= 1.54/1.84 508 pp(scratc801646954_d_and(aa_bool_bool(scratc82850040d_l_or(A),B),scratc82194035d_l_ec(A,B))) | -scratc1968367672d_orec(A,B) # label(fact_def__orec) # label(axiom). [clausify(87)]. 1.54/1.84 509 -pp(scratc801646954_d_and(aa_bool_bool(scratc82850040d_l_or(A),B),scratc82194035d_l_ec(A,B))) | scratc1968367672d_orec(A,B) # label(fact_def__orec) # label(axiom). [clausify(87)]. 1.54/1.84 510 gg_bool(scratc281858745nd_or3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__52628__31704_ONUM706__thf__4__p_Obnd__or3) # label(axiom). [clausify(121)]. 1.54/1.84 511 -gg_bool(A) | A = fTrue | fFalse = A # label(help_fFalse_1_1_T) # label(axiom). [clausify(103)]. 1.54/1.84 Derived: scratc281858745nd_or3(A,B,C) = fTrue | fFalse = scratc281858745nd_or3(A,B,C). [resolve(510,a,511,a)]. 1.54/1.84 512 gg_bool(fFalse) # label(gsy_c_fFalse) # label(axiom). [assumption]. 1.54/1.84 Derived: fFalse = fTrue | fFalse = fFalse. [resolve(512,a,511,a)]. 1.54/1.84 513 gg_bool(undefined_bool(bool)) # label(gsy_c_HOL_Oundefined_001t__HOL__Obool) # label(axiom). [assumption]. 1.54/1.84 Derived: undefined_bool(bool) = fTrue | fFalse = undefined_bool(bool). [resolve(513,a,511,a)]. 1.54/1.84 514 gg_bool(scratc755465763_amone(A,B)) # label(gsy_c_Scratch__tptp__translate__52628__31704_ONUM706__thf__4__p_Obnd__amone) # label(axiom). [clausify(152)]. 1.54/1.84 Derived: scratc755465763_amone(A,B) = fTrue | fFalse = scratc755465763_amone(A,B). [resolve(514,a,511,a)]. 1.54/1.84 515 gg_bool(aa_TPTP_ind_bool(A,B)) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom). [clausify(202)]. 1.54/1.84 Derived: aa_TPTP_ind_bool(A,B) = fTrue | fFalse = aa_TPTP_ind_bool(A,B). [resolve(515,a,511,a)]. 1.54/1.84 516 gg_bool(scratc82194035d_l_ec(A,B)) # label(gsy_c_Scratch__tptp__translate__52628__31704_ONUM706__thf__4__p_Obnd__l__ec) # label(axiom). [clausify(212)]. 1.54/1.84 Derived: scratc82194035d_l_ec(A,B) = fTrue | fFalse = scratc82194035d_l_ec(A,B). [resolve(516,a,511,a)]. 1.54/1.84 517 gg_bool(fTrue) # label(gsy_c_fTrue) # label(axiom). [assumption]. 1.54/1.84 Derived: fTrue = fTrue | fFalse = fTrue. [resolve(517,a,511,a)]. 1.54/1.84 518 gg_bool(aa_bool_bool(A,B)) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom). [clausify(253)]. 1.54/1.84 Derived: aa_bool_bool(A,B) = fTrue | fFalse = aa_bool_bool(A,B). [resolve(518,a,511,a)]. 1.54/1.84 519 gg_bool(fEx_TPTP_ind(A)) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom). [clausify(437)]. 2.59/2.91 Derived: fEx_TPTP_ind(A) = fTrue | fFalse = fEx_TPTP_ind(A). [resolve(519,a,511,a)]. 2.59/2.91 520 gg_bool(scratc198259710nd_ec3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__52628__31704_ONUM706__thf__4__p_Obnd__ec3) # label(axiom). [clausify(444)]. 2.59/2.91 Derived: scratc198259710nd_ec3(A,B,C) = fTrue | fFalse = scratc198259710nd_ec3(A,B,C). [resolve(520,a,511,a)]. 2.59/2.91 521 gg_bool(scratc909112134_d_not(A)) # label(gsy_c_Scratch__tptp__translate__52628__31704_ONUM706__thf__4__p_Obnd__d__not) # label(axiom). [clausify(459)]. 2.59/2.91 Derived: scratc909112134_d_not(A) = fTrue | fFalse = scratc909112134_d_not(A). [resolve(521,a,511,a)]. 2.59/2.91 522 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(494)]. 2.59/2.91 Derived: aa_fun171081125l_bool(A,B) = fTrue | fFalse = aa_fun171081125l_bool(A,B). [resolve(522,a,511,a)]. 2.59/2.91 523 gg_bool(scratc801646954_d_and(A,B)) # label(gsy_c_Scratch__tptp__translate__52628__31704_ONUM706__thf__4__p_Obnd__d__and) # label(axiom). [clausify(507)]. 2.59/2.91 Derived: scratc801646954_d_and(A,B) = fTrue | fFalse = scratc801646954_d_and(A,B). [resolve(523,a,511,a)]. 2.59/2.91 524 pp(scratc801646954_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc231961781nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc231961781nd_imp,B),A))) | -scratc1695788404_l_iff(A,B) # label(fact_def__l__iff) # label(axiom). [clausify(141)]. 2.59/2.91 525 -pp(scratc801646954_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc231961781nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc231961781nd_imp,B),A))) | scratc1695788404_l_iff(A,B) # label(fact_def__l__iff) # label(axiom). [clausify(141)]. 2.59/2.91 526 scratc477128825d_r_ec(A,B) | pp(A) # label(fact_def__r__ec) # label(axiom). [clausify(146)]. 2.59/2.91 527 -scratc477128825d_r_ec(A,B) | -pp(A) | pp(scratc909112134_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(146)]. 2.59/2.91 528 scratc477128825d_r_ec(A,B) | -pp(scratc909112134_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(146)]. 2.59/2.91 529 scratc347098055nd_wel(A) | -pp(scratc909112134_d_not(scratc909112134_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(322)]. 2.59/2.91 530 -scratc347098055nd_wel(A) | pp(scratc909112134_d_not(scratc909112134_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(322)]. 2.59/2.91 531 -scratc347098055nd_wel(A) | pp(A) # label(fact_l__et) # label(axiom). [clausify(502)]. 2.59/2.91 Derived: pp(A) | -pp(scratc909112134_d_not(scratc909112134_d_not(A))). [resolve(531,a,529,a)]. 2.59/2.91 2.59/2.91 ============================== end predicate elimination ============= 2.59/2.91 2.59/2.91 Auto_denials: (non-Horn, no changes). 2.59/2.91 2.59/2.91 Term ordering decisions: 2.59/2.91 Function symbol KB weights: aTP_Lamm_a=1. scratc1764895356bnd_in=1. scratc214101377d_n_is=1. scratc1633262956rdsucc=1. scratc231699378nd_iii=1. scratc636635060_29_ii=1. scratc1764370566bnd_ap=1. scratc605409850lessis=1. scratc1030418234nd_n_1=1. aTP_Lamm_al=1. scratc739393462moreis=1. scratc315496536_Sigma=1. scratc351358348ptyset=1. scratc272482122nd_nat=1. scratc1701720390d_d_Pi=1. scratc273006913nd_nis=1. scratc257638827n_some=1. fFalse=1. scratc148253326_power=1. scratc1700835558_nat_p=1. scratc231961781nd_imp=1. scratc2055967654d_repl=1. fTrue=1. scratc226620778_n_all=1. scratc461288049d_pair=1. aTP_Lamm_ab=1. scratc1673343774d_Subq=1. scratc1108127816closed=1. scratc276767164_proj0=1. scratc655515192_union=1. aTP_Lamm_ah=1. scratc214101372d_n_in=1. scratc276767165_proj1=1. aTP_Lamm_ag=1. aTP_Lamm_kk=1. scratc1377501230closed=1. scratc1542234244closed=1. aTP_Lamm_ca=1. aTP_Lamm_cc=1. aTP_Lamm_ce=1. aTP_Lamm_cg=1. aTP_Lamm_ci=1. aTP_Lamm_ck=1. aTP_Lamm_cm=1. aTP_Lamm_co=1. aTP_Lamm_hj=1. aTP_Lamm_hl=1. aTP_Lamm_hn=1. aTP_Lamm_hp=1. aTP_Lamm_hr=1. aTP_Lamm_ht=1. aTP_Lamm_hv=1. aTP_Lamm_hx=1. aTP_Lamm_hz=1. aTP_Lamm_ib=1. aTP_Lamm_id=1. aTP_Lamm_if=1. aTP_Lamm_kb=1. aTP_Lamm_kf=1. aTP_Lamm_kg=1. scratc1586527269closed=1. scratc1593906026_omega=1. scratc1990322274_prop2=1. scratc252616921d_Inj1=1. scratc271715072_prop2=1. aTP_Lamm_ai=1. aTP_Lamm_bi=1. aTP_Lamm_bk=1. aTP_Lamm_bl=1. aTP_Lamm_bs=1. aTP_Lamm_bv=1. aTP_Lamm_by=1. aTP_Lamm_cv=1. aTP_Lamm_cz=1. aTP_Lamm_dd=1. aTP_Lamm_dh=1. aTP_Lamm_dl=1. aTP_Lamm_dp=1. aTP_Lamm_dt=1. aTP_Lamm_dx=1. aTP_Lamm_ea=1. aTP_Lamm_ed=1. aTP_Lamm_eg=1. aTP_Lamm_ej=1. aTP_Lamm_em=1. aTP_Lamm_ep=1. aTP_Lamm_es=1. aTP_Lamm_ev=1. aTP_Lamm_ey=1. aTP_Lamm_fb=1. aTP_Lamm_ff=1. aTP_Lamm_fj=1. aTP_Lamm_fn=1. aTP_Lamm_fr=1. aTP_Lamm_fu=1. aTP_Lamm_fx=1. aTP_Lamm_ga=1. aTP_Lamm_gd=1. aTP_Lamm_gg=1. aTP_Lamm_gj=1. aTP_Lamm_gn=1. aTP_Lamm_gp=1. aTP_Lamm_gs=1. aTP_Lamm_gv=1. aTP_Lamm_gy=1. aTP_Lamm_hb=1. aTP_Lamm_he=1. aTP_Lamm_hh=1. aTP_Lamm_ih=1. aTP_Lamm_ij=1. aTP_Lamm_il=1. aTP_Lamm_in=1. aTP_Lamm_ip=1. aTP_Lamm_it=1. aTP_Lamm_iv=1. aTP_Lamm_iy=1. aTP_Lamm_jb=1. aTP_Lamm_jd=1. aTP_Lamm_jf=1. aTP_Lamm_ji=1. aTP_Lamm_jk=1. aTP_Lamm_jn=1. aTP_Lamm_jq=1. aTP_Lamm_jt=1. aTP_Lamm_jw=1. aTP_Lamm_jy=1. aTP_Lamm_jz=1. aTP_Lamm_ke=1. fconj=1. fimplies=1. scratc1574992892d_Sing=1. scratc1990322273_prop1=1. scratc252616920d_Inj0=1. scratc271715071_prop1=1. scratc291883897_cond2=1. scratc342413039_n_one=1. aTP_Lamm_bo=1. aTP_Lamm_bt=1. aTP_Lamm_bu=1. aTP_Lamm_bw=1. aTP_Lamm_bx=1. aTP_Lamm_bz=1. aTP_Lamm_cb=1. aTP_Lamm_cd=1. aTP_Lamm_cf=1. aTP_Lamm_ch=1. aTP_Lamm_cj=1. aTP_Lamm_cl=1. aTP_Lamm_cn=1. aTP_Lamm_cp=1. aTP_Lamm_cq=1. aTP_Lamm_cr=1. aTP_Lamm_cs=1. aTP_Lamm_cw=1. aTP_Lamm_da=1. aTP_Lamm_de=1. aTP_Lamm_di=1. aTP_Lamm_dm=1. aTP_Lamm_dq=1. aTP_Lamm_du=1. aTP_Lamm_dy=1. aTP_Lamm_eb=1. aTP_Lamm_ee=1. aTP_Lamm_eh=1. aTP_Lamm_ek=1. aTP_Lamm_en=1. aTP_Lamm_eq=1. aTP_Lamm_et=1. aTP_Lamm_ew=1. aTP_Lamm_ez=1. aTP_Lamm_fc=1. aTP_Lamm_fg=1. aTP_Lamm_fk=1. aTP_Lamm_fo=1. aTP_Lamm_fs=1. aTP_Lamm_fv=1. aTP_Lamm_fy=1. aTP_Lamm_gb=1. aTP_Lamm_ge=1. aTP_Lamm_gh=1. aTP_Lamm_gk=1. aTP_Lamm_gl=1. aTP_Lamm_gm=1. aTP_Lamm_go=1. aTP_Lamm_gq=1. aTP_Lamm_gt=1. aTP_Lamm_gw=1. aTP_Lamm_gz=1. aTP_Lamm_hc=1. aTP_Lamm_hf=1. aTP_Lamm_hi=1. aTP_Lamm_hk=1. aTP_Lamm_hm=1. aTP_Lamm_ho=1. aTP_Lamm_hq=1. aTP_Lamm_hs=1. aTP_Lamm_hu=1. aTP_Lamm_hw=1. aTP_Lamm_hy=1. aTP_Lamm_ia=1. aTP_Lamm_ic=1. aTP_Lamm_ie=1. aTP_Lamm_ig=1. aTP_Lamm_ii=1. aTP_Lamm_ik=1. aTP_Lamm_im=1. aTP_Lamm_io=1. aTP_Lamm_iq=1. aTP_Lamm_iu=1. aTP_Lamm_iw=1. aTP_Lamm_iz=1. aTP_Lamm_jc=1. aTP_Lamm_je=1. aTP_Lamm_jg=1. aTP_Lamm_jj=1. aTP_Lamm_jl=1. aTP_Lamm_jm=1. aTP_Lamm_jo=1. aTP_Lamm_jp=1. aTP_Lamm_jr=1. aTP_Lamm_js=1. aTP_Lamm_ju=1. aTP_Lamm_jv=1. aTP_Lamm_jx=1. aTP_Lamm_ka=1. aTP_Lamm_kc=1. aTP_Lamm_kd=1. aTP_Lamm_kh=1. aTP_Lamm_ki=1. aTP_Lamm_kj=1. aTP_Lamm_km=1. aTP_Lamm_lj=1. fequal_TPTP_ind=1. scratc2133892340univof=1. scratc270907740nd_nIn=1. scratc291883896_cond1=1. scratc702508900_d_Unj=1. aTP_Lamm_aa=1. aTP_Lamm_ad=1. aTP_Lamm_aj=1. aTP_Lamm_bm=1. aTP_Lamm_bn=1. bool=1. scratc1027410742_empty=1. scratc1066042298_prop1=1. scratc1242474369_prop1=1. scratc1367590344428_id=1. scratc1448439421_prop1=1. scratc1490012927pair_p=1. scratc1830836544_prop1=1. scratc1990322276_prop4=1. scratc2036801596_prop1=1. scratc2087855887_times=1. scratc277160762_prop4=1. scratc552951793d_plus=1. scratc636953335nempty=1. scratc716798900munion=1. scratc1558285748d_i1_s=1. scratc1614848410_428_g=1. scratc728638008d_24_g=1. tPTP_ind=1. aa_TPT43085870d_bool=1. aa_TPTP_ind_bool=1. aa_TPTP_ind_TPTP_ind=1. aa_fun171081125l_bool=1. aa_TPT60673477d_bool=1. aa_TPT1424761345TP_ind=1. aa_fun277296641TP_ind=1. aa_TPT494704832TP_ind=1. aa_bool_bool=1. aa_fun1584354236d_bool=1. scratc801646954_d_and=1. aa_fun1431113780TP_ind=1. aa_boo1142376798l_bool=1. aa_TPT1123896796d_bool=1. scratc1764895348bnd_if=1. scratc82194035d_l_ec=1. aa_fun1212484691d_bool=1. aa_TPT985247859d_bool=1. scratc695441011d_e_in=1. scratc232027368nd_ind=1. scratc523281511d_pair=1. aa_fun987228051d_bool=1. scratc755465763_amone=1. scratc1165925220_image=1. scratc1208567289_first=1. scratc1424765483second=1. aa_TPT125613450d_bool=1. scratc273400502nd_non=1. aa_fun1913827119d_bool=1. scratc1744519106d_anec=1. aa_TPT1791839040TP_ind=1. aa_fun1107270209d_bool=1. aa_fun845057962d_bool=1. scratc134463330eplSep=1. scratc1720071992_ecelt=1. scratc198259771nd_ecp=1. scratc1719481601_ecect=1. aa_TPT1781712639TP_ind=1. aa_TPT2142672771l_bool=1. aa_fun1235454963TP_ind=1. cOMBB_658106424TP_ind=1. cOMBS_2003118649l_bool=1. scratc1257283533_fixfu=1. scratc1718486404etprop=1. scratc198259775nd_ect=1. scratc282055607nd_out=1. scratc285496229fixfu2=1. scratc665549552wissel=1. scratc797522755ectset=1. scratc1031510649nverse=1. scratc1547880940d_invf=1. scratc1551617471d_tofs=1. scratc682320878ectelt=1. scratc903640101unmore=1. f3=1. f7=1. f8=1. f10=1. f11=1. scratc403153377all_of=1. scratc214560563d_n_pl=1. scratc695441016d_e_is=1. scratc909112134_d_not=1. scratc685395505_d_Sep=1. scratc614192122d_esti=1. scratc1661297833l_some=1. scratc214822966d_n_ts=1. scratc1633255295ffprop=1. scratc165804138nd_all=1. scratc82850040d_l_or=1. scratc281596399nd_one=1. scratc1288003369_rec_G=1. aTP_Lamm_ak=1. aTP_Lamm_kt=1. aTP_Lamm_ae=1. aTP_Lamm_am=1. aTP_Lamm_aw=1. aTP_Lamm_be=1. aTP_Lamm_br=1. aTP_Lamm_ct=1. aTP_Lamm_cx=1. aTP_Lamm_db=1. aTP_Lamm_df=1. aTP_Lamm_dj=1. aTP_Lamm_dn=1. aTP_Lamm_dr=1. aTP_Lamm_dv=1. aTP_Lamm_fd=1. aTP_Lamm_fh=1. aTP_Lamm_fl=1. aTP_Lamm_fp=1. aTP_Lamm_gr=1. aTP_Lamm_gu=1. aTP_Lamm_gx=1. aTP_Lamm_ha=1. aTP_Lamm_hd=1. aTP_Lamm_hg=1. aTP_Lamm_ir=1. aTP_Lamm_kl=1. aTP_Lamm_lh=1. scratc1546634565d_incl=1. aTP_Lamm_aq=1. aTP_Lamm_ba=1. aTP_Lamm_bd=1. aTP_Lamm_bh=1. aTP_Lamm_dz=1. aTP_Lamm_ec=1. aTP_Lamm_ef=1. aTP_Lamm_ei=1. aTP_Lamm_el=1. aTP_Lamm_eo=1. aTP_Lamm_er=1. aTP_Lamm_eu=1. aTP_Lamm_ex=1. aTP_Lamm_fa=1. aTP_Lamm_ft=1. aTP_Lamm_fw=1. aTP_Lamm_fz=1. aTP_Lamm_gc=1. aTP_Lamm_gf=1. aTP_Lamm_gi=1. aTP_Lamm_ix=1. aTP_Lamm_ja=1. aTP_Lamm_ld=1. aTP_Lamm_lf=1. scratc1267186050etprod=1. scratc1828477712ective=1. scratc199112561nd_eps=1. aTP_Lamm_an=1. aTP_Lamm_ao=1. aTP_Lamm_ap=1. aTP_Lamm_ar=1. aTP_Lamm_as=1. aTP_Lamm_au=1. aTP_Lamm_av=1. aTP_Lamm_bb=1. aTP_Lamm_bc=1. aTP_Lamm_bf=1. aTP_Lamm_cu=1. aTP_Lamm_cy=1. aTP_Lamm_dc=1. aTP_Lamm_dg=1. aTP_Lamm_dk=1. aTP_Lamm_do=1. aTP_Lamm_ds=1. aTP_Lamm_dw=1. aTP_Lamm_fe=1. aTP_Lamm_fi=1. aTP_Lamm_fm=1. aTP_Lamm_fq=1. aTP_Lamm_is=1. aTP_Lamm_jh=1. aTP_Lamm_kn=1. aTP_Lamm_ko=1. aTP_Lamm_kp=1. aTP_Lamm_kr=1. aTP_Lamm_kx=1. aTP_Lamm_kz=1. aTP_Lamm_la=1. aTP_Lamm_le=1. fEx_TPTP_ind=1. scratc1254231699ective=1. scratc1279538416lbprop=1. scratc1710655999nunion=1. scratc214298157d_n_lb=1. scratc264745403nd_min=1. aTP_Lamm_at=1. aTP_Lamm_kq=1. aTP_Lamm_ks=1. aTP_Lamm_ku=1. aTP_Lamm_kv=1. aTP_Lamm_kw=1. aTP_Lamm_ky=1. aTP_Lamm_lb=1. aTP_Lamm_lc=1. aTP_Lamm_lg=1. aTP_Lamm_li=1. scratc2009710558In_rec=1. scratc209982914_UPair=1. aTP_Lamm_ac=1. aTP_Lamm_af=1. aTP_Lamm_ax=1. aTP_Lamm_ay=1. aTP_Lamm_az=1. aTP_Lamm_bg=1. aTP_Lamm_bj=1. aTP_Lamm_bp=1. aTP_Lamm_bq=1. cOMBC_1555011498d_bool=1. scratc1626941541tminus=1. scratc2012196942ective=1. scratc2043778036t_disj=1. scratc277160761_prop3=1. scratc477680123_prop1=1. scratc860077246_prop1=1. undefined_bool=1. undefined_TPTP_ind=1. f1=1. f2=1. f4=1. f5=1. f9=1. f13=1. f14=1. f15=1. f17=1. f19=1. scratc281858745nd_or3=1. scratc198259710nd_ec3=1. scratc771030273d_soft=1. scratc1971165748_indeq=1. scratc232420963nd_ite=1. scratc277160759_prop1=1. scratc1542279420d_11_i=1. scratc1657856090sel_wa=1. scratc1657856091sel_wb=1. f6=1. f12=1. f16=1. f18=1. f20=1. f23=1. scratc277160760_prop2=1. scratc1045469599hangef=1. scratc406812218_inj_h=1. f21=1. f22=1. f25=1. scratc819037698_prop1=1. scratc69006078indeq2=1. f24=1. 4.72/5.02 4.72/5.02 ============================== end of process initial clauses ======== 4.72/5.02 4.72/5.02 ============================== CLAUSES FOR SEARCH ==================== 4.72/5.02 4.72/5.02 ============================== end of clauses for search ============= 4.72/5.02 4.72/5.02 ============================== SEARCH ================================ 4.72/5.02 4.72/5.02 % Starting search at 1.23 seconds. 4.72/5.02 4.72/5.02 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 509 (0.00 of 2.07 sec). 4.72/5.02 4.72/5.02 Low Water (keep): wt=42.000, iters=3703 4.72/5.02 4.72/5.02 Low Water (keep): wt=32.000, iters=3490 4.72/5.02 4.72/5.02 Low Water (keep): wt=29.000, iters=3367 4.72/5.02 4.72/5.02 Low Water (keep): wt=28.000, iters=3368 4.72/5.02 4.72/5.02 Low Water (keep): wt=27.000, iters=3358 4.72/5.02 4.72/5.02 Low Water (keep): wt=26.000, iters=3350 4.72/5.02 4.72/5.02 Low Water (keep): wt=25.000, iters=3373 4.72/5.02 4.72/5.02 Low Water (keep): wt=24.000, iters=3Alarm clock 118.86/120.09 Prover9 interrupted 118.86/120.09 EOF