0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.12/0.33 % Computer : n014.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 180 0.12/0.33 % DateTime : Thu Aug 29 17:14:09 EDT 2019 0.12/0.34 % CPUTime : 0.96/1.25 ============================== Prover9 =============================== 0.96/1.25 Prover9 (32) version 2009-11A, November 2009. 0.96/1.25 Process 18271 was started by sandbox2 on n014.cluster.edu, 0.96/1.25 Thu Aug 29 17:14:09 2019 0.96/1.25 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 180 -f /tmp/Prover9_18118_n014.cluster.edu". 0.96/1.25 ============================== end of head =========================== 0.96/1.25 0.96/1.25 ============================== INPUT ================================= 0.96/1.25 0.96/1.25 % Reading from file /tmp/Prover9_18118_n014.cluster.edu 0.96/1.25 0.96/1.25 set(prolog_style_variables). 0.96/1.25 set(auto2). 0.96/1.25 % set(auto2) -> set(auto). 0.96/1.25 % set(auto) -> set(auto_inference). 0.96/1.25 % set(auto) -> set(auto_setup). 0.96/1.25 % set(auto_setup) -> set(predicate_elim). 0.96/1.25 % set(auto_setup) -> assign(eq_defs, unfold). 0.96/1.25 % set(auto) -> set(auto_limits). 0.96/1.25 % set(auto_limits) -> assign(max_weight, "100.000"). 0.96/1.25 % set(auto_limits) -> assign(sos_limit, 20000). 0.96/1.25 % set(auto) -> set(auto_denials). 0.96/1.25 % set(auto) -> set(auto_process). 0.96/1.25 % set(auto2) -> assign(new_constants, 1). 0.96/1.25 % set(auto2) -> assign(fold_denial_max, 3). 0.96/1.25 % set(auto2) -> assign(max_weight, "200.000"). 0.96/1.25 % set(auto2) -> assign(max_hours, 1). 0.96/1.25 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.96/1.25 % set(auto2) -> assign(max_seconds, 0). 0.96/1.25 % set(auto2) -> assign(max_minutes, 5). 0.96/1.25 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.96/1.25 % set(auto2) -> set(sort_initial_sos). 0.96/1.25 % set(auto2) -> assign(sos_limit, -1). 0.96/1.25 % set(auto2) -> assign(lrs_ticks, 3000). 0.96/1.25 % set(auto2) -> assign(max_megs, 400). 0.96/1.25 % set(auto2) -> assign(stats, some). 0.96/1.25 % set(auto2) -> clear(echo_input). 0.96/1.25 % set(auto2) -> set(quiet). 0.96/1.25 % set(auto2) -> clear(print_initial_clauses). 0.96/1.25 % set(auto2) -> clear(print_given). 0.96/1.25 assign(lrs_ticks,-1). 0.96/1.25 assign(sos_limit,10000). 0.96/1.25 assign(order,kbo). 0.96/1.25 set(lex_order_vars). 0.96/1.25 clear(print_given). 0.96/1.25 0.96/1.25 % formulas(sos). % not echoed (320 formulas) 0.96/1.25 0.96/1.25 ============================== end of input ========================== 0.96/1.25 0.96/1.25 % From the command line: assign(max_seconds, 180). 0.96/1.25 0.96/1.25 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.96/1.25 0.96/1.25 % Formulas that are not ordinary clauses: 0.96/1.25 1 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc96293030_image(aa_fun1431113780TP_ind(scratc764078447_d_Sep(Uu),Uua),Uu),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc828961942_Sigma,aa_fun1431113780TP_ind(scratc764078447_d_Sep(Uu),Uua)),scratc1773292469d_e_in(Uu,Uua))),Uub))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_da(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__53) # label(axiom) # label(non_clause). [assumption]. 0.96/1.25 2 (all X0 pp(aa_fun171081125l_bool(scratc1522259491all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_dk,X0)))) # label(fact_refis) # label(axiom) # label(non_clause). [assumption]. 0.96/1.25 3 (all X all Xa ((pp(X) -> pp(scratc987795076_d_not(Xa))) <-> scratc1554980283d_r_ec(X,Xa))) # label(fact_def__r__ec) # label(axiom) # label(non_clause). [assumption]. 0.96/1.25 4 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_by,Uu)) <-> pp(aa_fun171081125l_bool(scratc503482417nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc632088200d_d_Pi,scratc494368140nd_nat),aTP_Lamm_ac)),aa_TPT43085870d_bool(aTP_Lamm_bx,Uu))))) # label(fact_ATP_Olambda__5) # label(axiom) # label(non_clause). [assumption]. 0.96/1.25 5 (all Uu (gg_TPTP_ind(Uu) -> ((exists X2 (gg_TPTP_ind(X2) & Uu = aa_TPTP_ind_TPTP_ind(scratc1371723034d_Inj0,X2))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_bj,Uu))))) # label(fact_ATP_Olambda__21) # label(axiom) # label(non_clause). [assumption]. 0.96/1.25 6 (all X aa_fun277296641TP_ind(scratc1836604576eplSep(X,aTP_Lamm_bj),scratc781191842_d_Unj) = aa_TPTP_ind_TPTP_ind(scratc1354618622_proj0,X)) # label(fact_def__proj0) # label(axiom) # label(non_clause). [assumption]. 0.96/1.25 7 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cf,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1291952830d_n_in,Uua),Uu)))) # label(fact_ATP_Olambda__36) # label(axiom) # label(non_clause). [assumption]. 0.96/1.25 8 (all X0 (scratc568984073nd_wel(X0) -> pp(X0))) # label(fact_l__et) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 9 (all X all Xa scratc1354618622_proj0 = scratc138935099_first(X,Xa)) # label(fact_def__first) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 10 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1522259491all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_cr(X0),X12)))) # label(fact_secondis1) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 11 (all X0 scratc864823754ptyset != aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,X0)) # label(fact_neq__ordsucc__0) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 12 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,Uu),aa_TPTP_ind_TPTP_ind(scratc1226104784_power,scratc494368140nd_nat))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ce,Uu)))) # label(fact_ATP_Olambda__11) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 13 (all X0 all X12 (gg_TPTP_ind(X12) -> X12 = aa_TPTP_ind_TPTP_ind(scratc1354618623_proj1,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc318016687d_pair,X0),X12)))) # label(fact_proj1__pair__eq) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 14 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc17092065hangef(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc828961942_Sigma,X),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_av(X),Xb),Xc),Xd))) # label(fact_def__changef) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 15 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1733366650_union,aa_TPTP_ind_TPTP_ind(scratc723448320_UPair(X),Xa)) = aa_TPTP_ind_TPTP_ind(scratc76637757nunion(X),Xa)) # label(fact_def__binunion) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 16 (all B_1 gg_bool(fEx_TPTP_ind(B_1))) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 17 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dk,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1773292474d_e_is(Uu),Uua),Uua)))) # label(fact_ATP_Olambda__22) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 18 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1212513688sel_wa(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc454306981nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1773292474d_e_is(X),Xc),Xa),X,Xb),Xc)) # label(fact_def__wissel__wa) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 19 (all X7 all Y (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) | Y != X7)) # label(help_fequal_2_1_fequal_001t__TPTP____Interpret__Oind_T) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 20 (all X scratc453913386nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc632088200d_d_Pi,scratc494368140nd_nat),aTP_Lamm_ac),aa_TPT43085870d_bool(scratc1773136190_prop2,X)) = aa_TPTP_ind_TPTP_ind(scratc409680431d_plus,X)) # label(fact_def__plus) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 21 (all Uu all Uua all Uub all Uuc (pp(aa_bool_bool(aa_boo1142376798l_bool(scratc453847799nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc470920760d_esti(Uu),Uuc),Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc470920760d_esti(Uu),Uuc),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_at(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__74) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 22 scratc868215762bvious <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc453847799nd_imp,fFalse),fFalse)) # label(fact_def__obvious) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 23 (all X aa_TPTP_ind_TPTP_ind(scratc76637757nunion(X),aa_TPTP_ind_TPTP_ind(scratc546615358d_Sing,X)) = aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,X)) # label(fact_def__ordsucc) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 24 (all B_1 all B_2 all B_3 gg_bool(scratc503744763nd_or3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__40153__8903_ONUM640__thf__4__p_Obnd__or3) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 25 (all Uu all Uua all Uub ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X3),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,Uub),X3)),aa_TPTP_ind_TPTP_ind(Uua,X3)))))) <-> pp(aa_TPTP_ind_bool(aa_fun1913827119d_bool(aTP_Lamm_bf(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__65) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 26 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc650439802_ecelt(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc764078447_d_Sep(X),aa_TPT43085870d_bool(Xa,Xb))) # label(fact_def__ecelt) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 27 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc828961942_Sigma,X),aTP_Lamm_ai(Xa)) = aa_TPTP_ind_TPTP_ind(scratc238808516etprod(X),Xa)) # label(fact_def__setprod) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 28 (all X all Xa all Xb all Xc all Xd (pp(scratc880329896_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc453847799nd_imp,X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1773292474d_e_is(Xa),Xd),Xb)),aa_bool_bool(aa_boo1142376798l_bool(scratc453847799nd_imp,scratc987795076_d_not(X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1773292474d_e_is(Xa),Xd),Xc)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1355012217_prop1(X,Xa,Xb),Xc),Xd)))) # label(fact_def__prop1) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 29 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bz,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc494892931nd_nis,Uu),scratc887146872nd_n_1)) -> pp(aa_fun171081125l_bool(scratc421095981_n_one,aa_TPT43085870d_bool(aTP_Lamm_af,Uu)))))) # label(fact_ATP_Olambda__2) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 30 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,Uub),aa_fun1431113780TP_ind(scratc764078447_d_Sep(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_db(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__62) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 31 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1291952835d_n_is,aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1291952835d_n_is,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ch,Uu),Uua)))) # label(fact_ATP_Olambda__24) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 32 (all Uu all Uua (pp(scratc880329896_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1291952835d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,Uua),scratc887146872nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,Uu)),aa_fun171081125l_bool(scratc305303720_n_all,aa_TPT43085870d_bool(aTP_Lamm_ae,Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bx,Uu),Uua)))) # label(fact_ATP_Olambda__23) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 33 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc828961942_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,aa_TPTP_ind_TPTP_ind(scratc1354618622_proj0,X22)),X0)))) # label(fact_proj0__Sigma) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 34 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_dd(Uu),Uua),Uub)) <-> scratc1892874294_is_of(aa_TPTP_ind_TPTP_ind(scratc1773292469d_e_in(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)))) # label(fact_ATP_Olambda__50) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 35 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc454306981nd_ite(X,Xa,Xb),Xc) = scratc453913386nd_ind(Xa,aa_TPT43085870d_bool(scratc1355012217_prop1(X,Xa,Xb),Xc))) # label(fact_def__ite) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 36 (all Uu (gg_TPTP_ind(Uu) -> ((exists X2 (aa_TPTP_ind_TPTP_ind(scratc1371723035d_Inj1,X2) = Uu & gg_TPTP_ind(X2))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_bi,Uu))))) # label(fact_ATP_Olambda__20) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 37 (all X all Xa all Xb aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc828961942_Sigma,Xa),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ax(X),Xa),Xb)) = aa_TPTP_ind_TPTP_ind(scratc3133115nverse(X,Xa),Xb)) # label(fact_def__inverse) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 38 (all P all Q (-pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)) | pp(Q))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 39 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc65091634univof,X0)))) # label(fact_k__UnivOf__In) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 40 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_au(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc470920760d_esti(Uu),Uub),Uua)))) # label(fact_ATP_Olambda__45) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 41 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc1226104784_power,X0)))) # label(fact_k__Self__In__Power) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 42 (all X (pp(scratc987795076_d_not(scratc987795076_d_not(X))) <-> scratc568984073nd_wel(X))) # label(fact_def__wel) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 43 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1522259491all_of(aa_fun1584354236d_bool(aTP_Lamm_db(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_dc(X0),X12)))) # label(fact_e__inp) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 44 (all X all Xa scratc627758911d_soft(aa_fun1431113780TP_ind(scratc764078447_d_Sep(X),Xa),X,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc828961942_Sigma,aa_fun1431113780TP_ind(scratc764078447_d_Sep(X),Xa)),scratc1773292469d_e_in(X,Xa))) = scratc503941625nd_out(X,Xa)) # label(fact_def__out) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 45 (all Uu all Uua all Uub all Uuc all Uud aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,aa_TPTP_ind_TPTP_ind(scratc744232494wissel(Uu,Uub),Uuc)),Uud)) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_av(Uu),Uua),Uub),Uuc),Uud)) # label(fact_ATP_Olambda__85) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 46 (all X all Xa all Xb (pp(scratc503744763nd_or3(X,Xa,Xb)) <-> pp(aa_bool_bool(scratc1160701498d_l_or(X),aa_bool_bool(scratc1160701498d_l_or(Xa),Xb))))) # label(fact_def__or3) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 47 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc2140406947tminus(X),Xa) = aa_fun1431113780TP_ind(scratc764078447_d_Sep(X),aa_TPT43085870d_bool(aTP_Lamm_bm,Xa))) # label(fact_def__setminus) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 48 (all X0 (pp(aa_TPTP_ind_bool(scratc1779518500_nat_p,X0)) -> pp(aa_TPTP_ind_bool(scratc1779518500_nat_p,aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,X0))))) # label(fact_nat__ordsucc) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 49 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1522259491all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_dj(X0),X12)))) # label(fact_e__isp) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 50 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1522259491all_of(aa_TPT43085870d_bool(aTP_Lamm_cu(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_cv(X0),X12)))) # label(fact_pairis1) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 51 (all X aa_TPTP_ind_TPTP_ind(scratc546615358d_Sing,X) = aa_TPTP_ind_TPTP_ind(scratc723448320_UPair(X),X)) # label(fact_def__d__Sing) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 52 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1291952835d_n_is,aa_TPTP_ind_TPTP_ind(scratc1292412021d_n_pl(aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,aa_TPTP_ind_TPTP_ind(scratc1292412021d_n_pl(Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_br,Uu),Uua)))) # label(fact_ATP_Olambda__25) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 53 (all X0 (gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(scratc1779518500_nat_p,X0)) -> X0 = scratc864823754ptyset | (exists X13 (pp(aa_TPTP_ind_bool(scratc1779518500_nat_p,X13)) & aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,X13) = X0 & gg_TPTP_ind(X13)))))) # label(fact_nat__inv) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 54 (all Uu all Uua aa_fun277296641TP_ind(aa_TPT494704832TP_ind(aTP_Lamm_bl,Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc76637757nunion(aa_TPTP_ind_TPTP_ind(scratc546615358d_Sing,scratc864823754ptyset)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1912696292d_repl,Uu),Uua))) # label(fact_ATP_Olambda__33) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 55 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1522259491all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_cp(X0),X12)))) # label(fact_estii) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 56 (all B_1 gg_TPTP_ind(scratc420998579nd_eps(B_1))) # label(gsy_c_Scratch__tptp__translate__40153__8903_ONUM640__thf__4__p_Obnd__eps) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 57 (all X aa_boo1142376798l_bool(scratc453847799nd_imp,scratc987795076_d_not(X)) = scratc1160701498d_l_or(X)) # label(fact_def__l__or) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 58 (all B_1 gg_bool(scratc987795076_d_not(B_1))) # label(gsy_c_Scratch__tptp__translate__40153__8903_ONUM640__thf__4__p_Obnd__d__not) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 59 (all B_1 all B_2 gg_TPTP_ind(scratc420145793nd_ect(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__40153__8903_ONUM640__thf__4__p_Obnd__ect) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 60 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cr(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1522259491all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cq(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__59) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 61 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc982323043unmore(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc764078447_d_Sep(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ar(X),Xa),Xb))) # label(fact_def__unmore) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 62 (all B_1 all B_2 gg_bool(scratc880329896_d_and(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__40153__8903_ONUM640__thf__4__p_Obnd__d__and) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 63 (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_am(Uu),Uua),Uub),Uuc),Uud),Uue)) <-> pp(aa_fun171081125l_bool(scratc1522259491all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_al(Uu),Uua),Uub),Uuc),Uud),Uue))))) # label(fact_ATP_Olambda__86) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 64 (all B_1 all B_2 gg_bool(scratc1160045493d_l_ec(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__40153__8903_ONUM640__thf__4__p_Obnd__l__ec) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 65 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1522259491all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_cz(X0),X12)))) # label(fact_e__pair__p) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 66 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1230264306munion,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1733366650_union,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1912696292d_repl,X),Xa))) # label(fact_def__famunion) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 67 (all X all Xa (pp(aa_fun171081125l_bool(scratc1522259491all_of(X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (scratc1892874294_is_of(X2,X) -> pp(aa_TPTP_ind_bool(Xa,X2))))))) # label(fact_def__all__of) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 68 (all X all Xa aa_fun1431113780TP_ind(scratc764078447_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1226104784_power,X)),scratc1601247744d_anec(X,Xa)) = scratc420145793nd_ect(X,Xa)) # label(fact_def__ect) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 69 (all Q all P (pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) | -pp(Q))) # label(help_fimplies_2_1_U) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 70 (all B_1 all B_2 gg_TPTP_ind(aa_fun1431113780TP_ind(B_1,B_2))) # label(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 71 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1773292474d_e_is(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__71) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 72 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc901533558_indeq(X,Xa,Xb),Xc),Xd) = scratc453913386nd_ind(Xb,aa_TPT43085870d_bool(scratc1355012218_prop2(X,Xa,Xb,Xc),Xd))) # label(fact_def__indeq) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 73 (all Uu aa_TPTP_ind_TPTP_ind(aTP_Lamm_ac,Uu) = scratc494368140nd_nat) # label(fact_ATP_Olambda__90) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 74 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1291952835d_n_is,aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,aa_TPTP_ind_TPTP_ind(scratc1292412021d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc1292412021d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,Uua)))))) # label(fact_ATP_Olambda__32) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 75 (all X (gg_TPTP_ind(X) -> (X = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc318016687d_pair,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,X),scratc864823754ptyset)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,X),aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,scratc864823754ptyset))) <-> pp(aa_TPTP_ind_bool(scratc461635393pair_p,X))))) # label(fact_def__pair__p) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 76 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1291952835d_n_is,aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1292412021d_n_pl(Uu),scratc887146872nd_n_1))))) # label(fact_ATP_Olambda__7) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 77 (all X all Xa (pp(aa_fun171081125l_bool(scratc632920299l_some(X),aa_TPT43085870d_bool(aTP_Lamm_au(X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1150418741nempty,X),Xa)))) # label(fact_def__nonempty) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 78 (all Uu (pp(aa_fun171081125l_bool(scratc1522259491all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_br,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_bs,Uu)))) # label(fact_ATP_Olambda__16) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 79 (all P (gg_bool(P) -> fFalse = P | fTrue = P)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 80 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc485495160_inj_h(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc828961942_Sigma,X),aa_TPT1424761345TP_ind(aTP_Lamm_aw(Xc),Xd))) # label(fact_def__inj__h) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 81 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,X0) = aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,X12) -> X0 = X12))) # label(fact_ordsucc__inj) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 82 (all X all Xa (pp(scratc880329896_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1291952835d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,Xa),scratc887146872nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,X)),aa_TPTP_ind_bool(scratc1773136189_prop1,Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1773136190_prop2,X),Xa)))) # label(fact_def__d__24__prop2) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 83 (all X all Xa aa_fun1431113780TP_ind(scratc764078447_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc534561714bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc534561722bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1912696292d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bn(X),Xa))),scratc864823754ptyset)) # label(fact_def__d__Sep) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 84 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_ah,Uu)) <-> scratc864823754ptyset != Uu))) # label(fact_ATP_Olambda__19) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 85 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X33),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,aa_TPTP_ind_TPTP_ind(X22,X33)),aa_TPTP_ind_TPTP_ind(X12,X33)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc828961942_Sigma,X0),X22)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc632088200d_d_Pi,X0),X12))))) # label(fact_lam__Pi) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 86 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cx(Uu),Uua),Uub)) <-> scratc1892874294_is_of(aa_TPTP_ind_TPTP_ind(scratc138935099_first(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)))) # label(fact_ATP_Olambda__49) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 87 (all P all Q (-pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)) | pp(P))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 88 (all X all Xa (pp(aa_fun171081125l_bool(scratc1522259491all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),aa_fun1584354236d_bool(aTP_Lamm_bd(X),Xa))) <-> pp(scratc1833317221_amone(X,Xa)))) # label(fact_def__amone) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 89 (all X aa_TPTP_ind_TPTP_ind(scratc1354618623_proj1,X) = aa_fun277296641TP_ind(scratc1836604576eplSep(X,aTP_Lamm_bi),scratc781191842_d_Unj)) # label(fact_def__proj1) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 90 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1291952835d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_af,Uu),Uua)))) # label(fact_ATP_Olambda__34) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 91 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X22),X0)) -> (pp(aa_TPTP_ind_bool(X12,X22)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X22),aa_fun1431113780TP_ind(scratc764078447_d_Sep(X0),X12)))))) # label(fact_k__SepI) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 92 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1522259491all_of(aa_TPT43085870d_bool(aTP_Lamm_cu(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_cx(X0),X12)))) # label(fact_first__p) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 93 (all X all Xa (pp(scratc880329896_d_and(X,Xa)) <-> pp(scratc987795076_d_not(scratc1160045493d_l_ec(X,Xa))))) # label(fact_def__d__and) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 94 (all X all Xa (pp(scratc1160045493d_l_ec(X,Xa)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc453847799nd_imp,X),scratc987795076_d_not(Xa))))) # label(fact_def__l__ec) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 95 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1291952835d_n_is,aa_TPTP_ind_TPTP_ind(scratc1292412021d_n_pl(Uu),scratc887146872nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_bw,Uu)))) # label(fact_ATP_Olambda__3) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 96 (all X all Xa (pp(aa_TPTP_ind_bool(Xa,X)) <-> scratc1892874294_is_of(X,Xa))) # label(fact_def__is__of) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 97 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc492793758nd_nIn,Uua),Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bm,Uu),Uua)))) # label(fact_ATP_Olambda__37) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 98 (all X all Xa all Xb (pp(scratc987795076_d_not(aa_TPTP_ind_bool(Xa,Xb))) <-> pp(aa_TPTP_ind_bool(scratc495286520nd_non(X,Xa),Xb)))) # label(fact_def__non) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 99 (all X all Xa all Xb all Xc scratc453913386nd_ind(X,aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(Xa),Xb),Xc)) = aa_TPTP_ind_TPTP_ind(scratc627758911d_soft(X,Xa,Xb),Xc)) # label(fact_def__soft) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 100 (all X0 all X12 all X22 (gg_TPTP_ind(X22) & gg_TPTP_ind(X12) -> -pp(X0) & X22 = aa_TPTP_ind_TPTP_ind(scratc534561714bnd_if(X0,X12),X22) | X12 = aa_TPTP_ind_TPTP_ind(scratc534561714bnd_if(X0,X12),X22) & pp(X0))) # label(fact_if__i__correct) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 101 (all Uu (pp(aa_fun171081125l_bool(scratc1522259491all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cd,Uu)))) # label(fact_ATP_Olambda__14) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 102 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cq(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1773292474d_e_is(Uua),aa_TPTP_ind_TPTP_ind(scratc1503448425second(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1642387625d_pair(Uu,Uua),Uub),Uuc))),Uuc)))) # label(fact_ATP_Olambda__68) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 103 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc644966240d_Subq,X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X2),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X2),Xa))))))) # label(fact_def__d__Subq) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 104 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,Uua),Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu),Uua)))) # label(fact_ATP_Olambda__38) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 105 (all X fequal_TPTP_ind = scratc1773292474d_e_is(X)) # label(fact_def__e__is) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 106 (all X0 (pp(aa_TPTP_ind_bool(X0,scratc864823754ptyset)) -> ((all X13 (gg_TPTP_ind(X13) -> (pp(aa_TPTP_ind_bool(scratc1779518500_nat_p,X13)) -> (pp(aa_TPTP_ind_bool(X0,X13)) -> pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,X13))))))) -> (all X12 (pp(aa_TPTP_ind_bool(scratc1779518500_nat_p,X12)) -> pp(aa_TPTP_ind_bool(X0,X12))))))) # label(fact_nat__ind) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 107 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ca,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc494892931nd_nis,Uu),scratc887146872nd_n_1)) -> pp(aa_fun171081125l_bool(scratc1376744941n_some,aa_TPT43085870d_bool(aTP_Lamm_af,Uu)))))) # label(fact_ATP_Olambda__1) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 108 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364179171fixfu2(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1522259491all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_an(X),Xa),Xb),Xc))))) # label(fact_def__fixfu2) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 109 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc632088200d_d_Pi,X),Xa) = aa_fun1431113780TP_ind(scratc764078447_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1226104784_power,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc828961942_Sigma,X),aTP_Lamm_be(Xa)))),aa_fun1913827119d_bool(aTP_Lamm_bf(X),Xa))) # label(fact_def__d__Pi) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 110 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc1836604576eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bg,Xa)),scratc1354618623_proj1)) # label(fact_def__ap) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 111 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ap(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_fun171081125l_bool(scratc1522259491all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_ao(Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__84) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 112 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cb,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc494892931nd_nis,aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__8) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 113 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc828961942_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,aa_TPTP_ind_TPTP_ind(scratc1354618623_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1354618622_proj0,X22)))))) # label(fact_proj1__Sigma) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 114 (all X all Xa scratc420998579nd_eps(aa_TPT43085870d_bool(scratc821891179_rec_G(X),Xa)) = aa_TPTP_ind_TPTP_ind(scratc1564368156In_rec(X),Xa)) # label(fact_def__d__In__rec) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 115 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1773292474d_e_is(Uu),aa_TPTP_ind_TPTP_ind(scratc138935099_first(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1642387625d_pair(Uu,Uua),Uub),Uuc))),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cs(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__67) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 116 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1226104784_power,X0))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc644966240d_Subq,X12),X0)))) # label(fact_k__PowerE) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 117 (all X all Xa (pp(aa_fun171081125l_bool(scratc503482417nd_one(X),Xa)) <-> pp(scratc880329896_d_and(scratc1833317221_amone(X,Xa),aa_fun171081125l_bool(scratc632920299l_some(X),Xa))))) # label(fact_def__one) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 118 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1548346256ective(X),Xa),Xb)) <-> pp(scratc880329896_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1364627026ective(X),Xa),Xb),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc808889297ective(X),Xa),Xb))))) # label(fact_def__bijective) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 119 (all X all Xa all Xb all Xc all Xd all Xe (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1355012218_prop2(X,Xa,Xb,Xc),Xd),Xe)) <-> pp(aa_fun171081125l_bool(scratc632920299l_some(X),aa_TPT43085870d_bool(scratc172975168_prop1(X,Xa,Xb,Xc,Xd),Xe))))) # label(fact_def__prop2) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 120 (all X scratc1292412021d_n_pl(X) = aa_TPT1424761345TP_ind(scratc534036932bnd_ap,aa_TPTP_ind_TPTP_ind(scratc409680431d_plus,X))) # label(fact_def__n__pl) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 121 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc761003820ectelt(X,Xa),Xb) = aa_TPTP_ind_TPTP_ind(scratc876205697ectset(X,Xa),aa_TPTP_ind_TPTP_ind(scratc650439802_ecelt(X,Xa),Xb))) # label(fact_def__ectelt) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 122 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X33),X0)) -> aa_TPTP_ind_TPTP_ind(X22,X33) = aa_TPTP_ind_TPTP_ind(X12,X33)))) -> aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc828961942_Sigma,X0),X22) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc828961942_Sigma,X0),X12))) # label(fact_xi__ext) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 123 (all X (pp(aa_TPTP_ind_bool(scratc1773136189_prop1,X)) <-> pp(aa_fun171081125l_bool(scratc305303720_n_all,aa_TPT43085870d_bool(aTP_Lamm_ae,X))))) # label(fact_def__d__24__prop1) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 124 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> X22 = aa_TPTP_ind_TPTP_ind(scratc534561714bnd_if(X0,X12),X22) | aa_TPTP_ind_TPTP_ind(scratc534561714bnd_if(X0,X12),X22) = X12)) # label(fact_if__i__or) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 125 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_dj(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1522259491all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_di(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__55) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 126 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc644966240d_Subq,X12),X0)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1226104784_power,X0))))) # label(fact_k__PowerEq) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 127 (all B_1 all B_2 gg_TPTP_ind(aa_fun277296641TP_ind(B_1,B_2))) # label(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__TPTP____Interpret__Oind_J_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 128 (all P all Q (-pp(P) | pp(Q) | -pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 129 (all Uu ((pp(aa_TPTP_ind_bool(scratc1369735354_cond1,Uu)) -> (pp(aa_TPTP_ind_bool(scratc1369735355_cond2,Uu)) -> pp(aa_fun171081125l_bool(scratc1522259491all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cf,Uu))))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cg,Uu)))) # label(fact_ATP_Olambda__6) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 130 (all Uu aa_TPT494704832TP_ind(aTP_Lamm_bk,Uu) = aa_TPT494704832TP_ind(scratc1912696292d_repl,aa_TPTP_ind_TPTP_ind(scratc2140406947tminus(Uu),aa_TPTP_ind_TPTP_ind(scratc546615358d_Sing,scratc864823754ptyset)))) # label(fact_ATP_Olambda__18) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 131 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1212513689sel_wb(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc454306981nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1773292474d_e_is(X),Xc),Xb),X,Xa),aa_TPTP_ind_TPTP_ind(scratc1212513688sel_wa(X,Xa,Xb),Xc))) # label(fact_def__wissel__wb) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 132 (all X0 pp(aa_TPTP_ind_bool(scratc1120415079closed,aa_TPTP_ind_TPTP_ind(scratc65091634univof,X0)))) # label(fact_k__UnivOf__ZF__closed) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 133 (all X all Xa all Xb scratc420998579nd_eps(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bp(X),Xa),Xb)) = aa_TPTP_ind_TPTP_ind(scratc534561714bnd_if(X,Xa),Xb)) # label(fact_def__if) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 134 (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]. 0.96/1.26 135 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1355012219_prop3(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1291952835d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,X),Xb)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,Xa),Xb))))) # label(fact_def__prop3) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 136 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1733366650_union,X0))) <-> (exists X2 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X12),X2)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X2),X0)) & gg_TPTP_ind(X2))))) # label(fact_k__UnionEq) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 137 (all X all Xa scratc534036932bnd_ap = scratc1408346109d_tofs(X,Xa)) # label(fact_def__tofs) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 138 (all X all Xa (-pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc492793758nd_nIn,X),Xa)))) # label(fact_def__nIn) # label(axiom) # label(non_clause). [assumption]. 0.96/1.26 139 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc828961942_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc318016687d_pair,aa_TPTP_ind_TPTP_ind(scratc1354618622_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1354618623_proj1,X22)) = X22 & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,aa_TPTP_ind_TPTP_ind(scratc1354618623_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1354618622_proj0,X22)))) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,aa_TPTP_ind_TPTP_ind(scratc1354618622_proj0,X22)),X0))))) # label(fact_k__Sigma__eta__proj0__proj1) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 140 (all P all Q all R aa_TPTP_ind_bool(aa_TPT43085870d_bool(P,R),Q) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(cOMBC_1555011498d_bool(P),Q),R)) # label(help_COMBC_1_1_COMBC_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind_001t__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 141 (all X aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc828961942_Sigma,scratc494368140nd_nat),aTP_Lamm_ad(X)) = aa_TPTP_ind_TPTP_ind(scratc1242103414d_24_g,X)) # label(fact_def__d__24__g) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 142 (all Uu all Uua all Uub all Uuc all Uud all Uue all Uuf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_al(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)) <-> pp(aa_fun171081125l_bool(scratc1522259491all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_ak(Uua),Uub),Uuc),Uud),Uue),Uuf))))) # label(fact_ATP_Olambda__88) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 143 (all P all Q all R aa_bool_bool(aa_TPT2142672771l_bool(P,R),aa_TPTP_ind_bool(Q,R)) = aa_TPTP_ind_bool(cOMBS_2003118649l_bool(P,Q),R)) # label(help_COMBS_1_1_COMBS_001t__TPTP____Interpret__Oind_001t__HOL__Obool_001t__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 144 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1291952835d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,Uu),aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ae,Uu),Uua)))) # label(fact_ATP_Olambda__27) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 145 (all X all Xa scratc503941625nd_out(aa_TPTP_ind_TPTP_ind(scratc1226104784_power,X),scratc1601247744d_anec(X,Xa)) = scratc876205697ectset(X,Xa)) # label(fact_def__ectset) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 146 (all X all Xa scratc1836604576eplSep(X,Xa) = aa_TPT494704832TP_ind(scratc1912696292d_repl,aa_fun1431113780TP_ind(scratc764078447_d_Sep(X),Xa))) # label(fact_def__d__ReplSep) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 147 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bb(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,Uub),Uu)) & pp(aa_TPTP_ind_bool(Uua,Uub)))) # label(fact_ATP_Olambda__52) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 148 (all Uu all Uua all Uub all Uuc (gg_TPTP_ind(Uub) & gg_TPTP_ind(Uuc) & gg_TPTP_ind(Uua) -> (Uub = Uuc & -pp(Uu) | Uua = Uuc & pp(Uu) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bp(Uu),Uua),Uub),Uuc))))) # label(fact_ATP_Olambda__76) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 149 (all X all Xa all Xb all Xc all Xd scratc147689020indeq2(X,Xa,Xb,Xc,Xd) = aa_TPT1424761345TP_ind(scratc901533558_indeq(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2055744826d_11_i(X,Xa,Xb),Xc),Xd))) # label(fact_def__indeq2) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 150 (all B_1 all B_2 gg_bool(aa_bool_bool(B_1,B_2))) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 151 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_fun171081125l_bool(scratc1522259491all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_am(Uu),Uua),Uub),Uuc),Uud))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_an(Uu),Uua),Uub),Uuc),Uud)))) # label(fact_ATP_Olambda__83) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 152 (all Uu all Uua all Uub all Uuc all Uud all Uue all Uuf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_ak(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uue),Uuf)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1773292474d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,Uub),Uuc)),Uue)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,Uub),Uud)),Uuf))))))) # label(fact_ATP_Olambda__87) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 153 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dh(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1522259491all_of(aa_TPT43085870d_bool(aTP_Lamm_de(Uu),Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dg(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__51) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 154 (all X aa_TPTP_ind_TPTP_ind(scratc1371723034d_Inj0,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1912696292d_repl,X),scratc1371723035d_Inj1)) # label(fact_def__d__Inj0) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 155 (all P all Q all R aa_boo1142376798l_bool(P,aa_TPTP_ind_bool(Q,R)) = aa_TPT2142672771l_bool(cOMBB_658106424TP_ind(P,Q),R)) # label(help_COMBB_1_1_COMBB_001t__HOL__Obool_001t__fun_It__HOL__Obool_Mt__HOL__Obool_J_001t__TPTP____Interpret__Oind_U) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 156 (all Uu (pp(aa_fun171081125l_bool(scratc1522259491all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ch,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ci,Uu)))) # label(fact_ATP_Olambda__13) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 157 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1522259491all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cs(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ct(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__58) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 158 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1230264306munion,X),aTP_Lamm_bh(Xa)) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc828961942_Sigma,X),Xa)) # label(fact_def__d__Sigma) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 159 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc632088200d_d_Pi,X0),X12))) -> (all X32 (gg_TPTP_ind(X32) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X32),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc632088200d_d_Pi,X0),X12))) -> ((all X42 (gg_TPTP_ind(X42) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X42),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,X32),X42) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,X22),X42)))) -> X22 = X32))))))) # label(fact_k__Pi__ext) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 160 (all Uu all Uua (gg_TPTP_ind(Uua) -> ((exists X3 (gg_TPTP_ind(X3) & aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc318016687d_pair,Uu),X3) = Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bg,Uu),Uua))))) # label(fact_ATP_Olambda__41) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 161 -(exists X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X0),scratc864823754ptyset))) # label(fact_k__EmptyAx) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 162 (all X (pp(aa_bool_bool(scratc1160701498d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1291952835d_n_is,X),scratc887146872nd_n_1)),aa_fun171081125l_bool(scratc1376744941n_some,aa_TPT43085870d_bool(aTP_Lamm_af,X)))) <-> pp(aa_TPTP_ind_bool(scratc1184774014_prop1,X)))) # label(fact_def__d__23__prop1) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 163 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cu(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,Uub),aa_TPTP_ind_TPTP_ind(scratc238808516etprod(Uu),Uua))))) # label(fact_ATP_Olambda__61) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 164 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> ((exists X3 (X22 = aa_TPTP_ind_TPTP_ind(X12,X3) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X3),X0)) & gg_TPTP_ind(X3))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1912696292d_repl,X0),X12)))))) # label(fact_k__ReplEq) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 165 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_bo(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc534561714bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,scratc864823754ptyset),Uub),Uu),Uua)) # label(fact_ATP_Olambda__43) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 166 (all X all Xa all Xb (gg_TPTP_ind(Xb) -> aa_TPTP_ind_TPTP_ind(scratc1773292469d_e_in(X,Xa),Xb) = Xb)) # label(fact_def__e__in) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 167 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1522259491all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bc(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bd(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__56) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 168 (all X (pp(aa_TPTP_ind_bool(scratc596411839_prop1,X)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc494892931nd_nis,aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,X)),X)))) # label(fact_def__d__22__prop1) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 169 (all Uu all Uua (pp(aa_bool_bool(aa_boo1142376798l_bool(scratc453847799nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1291952830d_n_in,Uua),Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1291952830d_n_in,aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,Uua)),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ag,Uu),Uua)))) # label(fact_ATP_Olambda__29) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 170 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,Uub),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc632088200d_d_Pi,Uu),aTP_Lamm_ai(Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_de(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__60) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 171 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc821891179_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(scratc534561722bnd_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]. 0.96/1.27 172 (all X all Xa all Xb (scratc131980093_orec3(X,Xa,Xb) <-> pp(scratc880329896_d_and(scratc503744763nd_or3(X,Xa,Xb),scratc420145728nd_ec3(X,Xa,Xb))))) # label(fact_def__orec3) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 173 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bv,Uu)) <-> pp(aa_fun171081125l_bool(scratc1522259491all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bu,Uu))))) # label(fact_ATP_Olambda__15) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 174 (all X all Xa scratc453913386nd_ind(X,Xa) = scratc420998579nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bb(X),Xa))) # label(fact_def__ind) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 175 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X22),aa_fun1431113780TP_ind(scratc764078447_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(X12,X22)))) # label(fact_k__SepE2) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 176 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1522259491all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cy(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cz(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__57) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 177 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc644966240d_Subq,X12),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1226104784_power,X0))))) # label(fact_k__PowerI) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 178 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cy(Uu),Uua),Uub),Uuc)) <-> scratc1892874294_is_of(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1642387625d_pair(Uu,Uua),Uub),Uuc),aa_TPT43085870d_bool(aTP_Lamm_cu(Uu),Uua)))) # label(fact_ATP_Olambda__72) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 179 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1404609578d_invf(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc828961942_Sigma,Xa),scratc627758911d_soft(X,Xa,Xb))) # label(fact_def__invf) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 180 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cn,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1522259491all_of(aa_TPT43085870d_bool(aTP_Lamm_cl,Uu)),aa_TPT43085870d_bool(aTP_Lamm_cm(Uu),Uua))))) # label(fact_ATP_Olambda__31) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 181 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_di(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1773292474d_e_is(Uu),Uub),Uuc)) -> pp(aa_TPTP_ind_bool(Uua,Uuc)))))) # label(fact_ATP_Olambda__77) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 182 (all X ((all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,aa_TPTP_ind_TPTP_ind(scratc1226104784_power,X1)),X))))) <-> pp(aa_TPTP_ind_bool(scratc101417154closed,X)))) # label(fact_def__d__Power__closed) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 183 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc409759794t_disj(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc387690156nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_as(X),Xa),Xb))))) # label(fact_def__st__disj) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 184 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bt,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1291952835d_n_is,aa_TPTP_ind_TPTP_ind(scratc1292412021d_n_pl(scratc887146872nd_n_1),Uu)),aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,Uu))))) # label(fact_ATP_Olambda__4) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 185 (all X all Xa all Xb all Xc (pp(aa_fun171081125l_bool(scratc632920299l_some(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(Xa),Xb),Xc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc96293030_image(X,Xa),Xb),Xc)))) # label(fact_def__image) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 186 (all Uu all Uua all Uub all Uuc (pp(aa_fun171081125l_bool(scratc387690156nd_all(Uu),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_az(Uu),Uua),Uub),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ba(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__79) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 187 (all Uu (pp(aa_fun171081125l_bool(scratc1522259491all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ab,Uu)))) # label(fact_ATP_Olambda__17) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 188 (all X (pp(aa_fun171081125l_bool(scratc305303720_n_all,aa_TPT43085870d_bool(aTP_Lamm_ag,X))) <-> pp(aa_TPTP_ind_bool(scratc1369735355_cond2,X)))) # label(fact_def__cond2) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 189 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ar(Uu),Uua),Uub),Uuc)) <-> pp(aa_fun171081125l_bool(scratc632920299l_some(Uua),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aq(Uu),Uub),Uuc))))) # label(fact_ATP_Olambda__80) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 190 (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(scratc1773292474d_e_is(Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,Uua),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,Uub),Uuc))))) # label(fact_ATP_Olambda__69) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 191 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cv(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1773292474d_e_is(aa_TPTP_ind_TPTP_ind(scratc238808516etprod(Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1642387625d_pair(Uu,Uua),aa_TPTP_ind_TPTP_ind(scratc138935099_first(Uu,Uua),Uub)),aa_TPTP_ind_TPTP_ind(scratc1503448425second(Uu,Uua),Uub))),Uub)))) # label(fact_ATP_Olambda__42) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 192 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1773292474d_e_is(aa_TPTP_ind_TPTP_ind(scratc1226104784_power,X)),Xb),aa_TPTP_ind_TPTP_ind(scratc650439802_ecelt(X,Xa),Xc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc420145789nd_ecp(X,Xa),Xb),Xc)))) # label(fact_def__ecp) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 193 (all B_1 all B_2 gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2))) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 194 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc503482417nd_one(X0),X12)) -> pp(aa_TPTP_ind_bool(X12,scratc453913386nd_ind(X0,X12))))) # label(fact_oneax) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 195 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1403363203d_incl(Uu),Uua),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1403363203d_incl(Uu),Uub),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1773292474d_e_is(aa_TPTP_ind_TPTP_ind(scratc1226104784_power,Uu)),Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cm(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__47) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 196 (all X0 all X12 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1364627026ective(aa_fun1431113780TP_ind(scratc764078447_d_Sep(X0),X12)),X0),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc828961942_Sigma,aa_fun1431113780TP_ind(scratc764078447_d_Sep(X0),X12)),scratc1773292469d_e_in(X0,X12))))) # label(fact_otax1) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 197 (all X all Xa all Xb (pp(aa_fun171081125l_bool(scratc632920299l_some(X),aa_TPT43085870d_bool(scratc420145789nd_ecp(X,Xa),Xb))) <-> pp(aa_TPTP_ind_bool(scratc1601247744d_anec(X,Xa),Xb)))) # label(fact_def__anec) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 198 (all Uu all Uua all Uub (scratc1892874294_is_of(aa_TPTP_ind_TPTP_ind(scratc1503448425second(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cw(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__48) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 199 (all X scratc534561722bnd_in = scratc470920760d_esti(X)) # label(fact_def__esti) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 200 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc828961942_Sigma,X0),X12))) -> X22 = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc318016687d_pair,aa_TPTP_ind_TPTP_ind(scratc1354618622_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1354618623_proj1,X22))))) # label(fact_proj__Sigma__eta) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 201 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X22),aa_fun1431113780TP_ind(scratc764078447_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X22),X0)))) # label(fact_k__SepE1) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 202 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1522259491all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_ct(X0),X12)))) # label(fact_firstis1) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 203 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_cp(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc470920760d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc764078447_d_Sep(Uu),Uua)))))) # label(fact_ATP_Olambda__54) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 204 (all B_1 all B_2 gg_bool(aa_TPTP_ind_bool(B_1,B_2))) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 205 (all X all Xa scratc1642387625d_pair(X,Xa) = scratc318016687d_pair) # label(fact_def__d__pair) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 206 (all B_1 all B_2 gg_bool(aa_fun171081125l_bool(B_1,B_2))) # label(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__HOL__Obool) # label(hypothesis) # label(non_clause). [assumption]. 0.96/1.27 207 (all X all Xa scratc1773292469d_e_in(aa_TPTP_ind_TPTP_ind(scratc1226104784_power,X),scratc1601247744d_anec(X,Xa)) = scratc649849411_ecect(X,Xa)) # label(fact_def__ecect) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 208 (all Uu all Uua all Uub all Uuc ((pp(aa_fun171081125l_bool(scratc1522259491all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_df(Uua),Uub),Uuc))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1773292474d_e_is(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc632088200d_d_Pi,Uu),aTP_Lamm_ai(Uua))),Uub),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dg(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__75) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 209 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc494892931nd_nis,X),Xa)) <-> pp(scratc987795076_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1291952835d_n_is,X),Xa))))) # label(fact_def__nis) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 210 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1522259491all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_da(X0),X12)))) # label(fact_otax2) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 211 (all X all Xa all Xb all Xc (pp(scratc880329896_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc470920760d_esti(X),Xc),Xa),scratc987795076_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc470920760d_esti(X),Xc),Xb)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1273144002etprop(X,Xa),Xb),Xc)))) # label(fact_def__nissetprop) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 212 (all X all Xa all Xb scratc901533558_indeq(X,Xa,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc632088200d_d_Pi,X),aTP_Lamm_ai(Xb))) = scratc2055744826d_11_i(X,Xa,Xb)) # label(fact_def__d__11__i) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 213 (all X0 all X12 (gg_TPTP_ind(X12) & gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc644966240d_Subq,X0),X12)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc644966240d_Subq,X12),X0)) -> X12 = X0)))) # label(fact_set__ext) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 214 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc723448320_UPair(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1912696292d_repl,aa_TPTP_ind_TPTP_ind(scratc1226104784_power,aa_TPTP_ind_TPTP_ind(scratc1226104784_power,scratc864823754ptyset))),aa_TPT1424761345TP_ind(aTP_Lamm_bo(X),Xa))) # label(fact_def__d__UPair) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 215 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2105262200_empty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1522259491all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),scratc495286520nd_non(X,aa_TPT43085870d_bool(aTP_Lamm_au(X),Xa)))))) # label(fact_def__empty) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 216 (all X all Xa (pp(scratc987795076_d_not(aa_fun171081125l_bool(scratc1522259491all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),scratc495286520nd_non(X,Xa)))) <-> pp(aa_fun171081125l_bool(scratc632920299l_some(X),Xa)))) # label(fact_def__l__some) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 217 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,Uua),aa_TPTP_ind_TPTP_ind(scratc1226104784_power,Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cl,Uu),Uua)))) # label(fact_ATP_Olambda__35) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 218 (all X all Xa (scratc1774471346_l_iff(X,Xa) <-> pp(scratc880329896_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc453847799nd_imp,X),Xa),aa_bool_bool(aa_boo1142376798l_bool(scratc453847799nd_imp,Xa),X))))) # label(fact_def__l__iff) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 219 (all X0 (pp(aa_TPTP_ind_bool(scratc1779518500_nat_p,X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X0),scratc524273836_omega)))) # label(fact_nat__p__omega) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 220 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc187651343_fixfu(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1522259491all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ap(X),Xa),Xb),Xc))))) # label(fact_def__fixfu) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 221 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc744232494wissel(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc828961942_Sigma,X),scratc1212513689sel_wb(X,Xa,Xb))) # label(fact_def__wissel) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 222 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(Uua,Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1773292474d_e_is(Uu),Uub),Uuc)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bc(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__78) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 223 (all X all Xa scratc1503448425second(X,Xa) = scratc1354618623_proj1) # label(fact_def__second) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 224 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,Uu),Uub)) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_aw(Uu),Uua),Uub)) # label(fact_ATP_Olambda__63) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 225 (all B_1 all B_2 gg_TPTP_ind(scratc453913386nd_ind(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__40153__8903_ONUM640__thf__4__p_Obnd__ind) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 226 (all Uu all Uua aa_TPTP_ind_TPTP_ind(scratc1733366650_union,aa_TPTP_ind_TPTP_ind(Uu,Uua)) = aa_TPTP_ind_TPTP_ind(aTP_Lamm_be(Uu),Uua)) # label(fact_ATP_Olambda__40) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 227 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1403363203d_incl(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc387690156nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_at(X),Xa),Xb))))) # label(fact_def__incl) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 228 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bh(Uu),Uua) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1912696292d_repl,aa_TPTP_ind_TPTP_ind(Uu,Uua)),aa_TPT1424761345TP_ind(scratc318016687d_pair,Uua))) # label(fact_ATP_Olambda__30) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 229 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(scratc534561714bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc96293030_image(Uu,Uua),Uub),Uuc),aa_TPTP_ind_TPTP_ind(scratc627758911d_soft(Uu,Uua,Uub),Uuc)),scratc864823754ptyset) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ax(Uu),Uua),Uub),Uuc)) # label(fact_ATP_Olambda__66) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 230 (all P all Q (pp(P) | pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)))) # label(help_fimplies_1_1_U) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 231 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_ao(Uu),Uua),Uub),Uuc),Uud)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1773292474d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,Uub),Uud)))))) # label(fact_ATP_Olambda__82) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 232 (all X all Xa (scratc1825096310d_orec(X,Xa) <-> pp(scratc880329896_d_and(aa_bool_bool(scratc1160701498d_l_or(X),Xa),scratc1160045493d_l_ec(X,Xa))))) # label(fact_def__orec) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 233 (all B_1 all B_2 all B_3 gg_bool(scratc420145728nd_ec3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__40153__8903_ONUM640__thf__4__p_Obnd__ec3) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 234 (all Uu all Uua (gg_TPTP_ind(Uu) -> aa_TPTP_ind_TPTP_ind(aTP_Lamm_ai(Uu),Uua) = Uu)) # label(fact_ATP_Olambda__89) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 235 (all X all Xa all Xb (pp(scratc880329896_d_and(X,scratc880329896_d_and(Xa,Xb))) <-> scratc1601182097d_and3(X,Xa,Xb))) # label(fact_def__and3) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 236 (all X0 all X12 all X22 ((pp(X0) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X12),X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,aa_TPTP_ind_TPTP_ind(scratc534561714bnd_if(X0,X12),scratc864823754ptyset)),aa_TPTP_ind_TPTP_ind(scratc534561714bnd_if(X0,X22),aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,scratc864823754ptyset)))))) # label(fact_k__If__In__01) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 237 (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(scratc1160045493d_l_ec(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc470920760d_esti(Uu),Uuc),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc470920760d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__73) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 238 (all X (pp(aa_TPTP_ind_bool(scratc2084167788closed,X)) & pp(aa_TPTP_ind_bool(scratc1140580490closed,X)) & pp(aa_TPTP_ind_bool(scratc101417154closed,X)) <-> pp(aa_TPTP_ind_bool(scratc1120415079closed,X)))) # label(fact_def__d__ZF__closed) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 239 (all X (pp(aa_TPTP_ind_bool(scratc2084167788closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,aa_TPTP_ind_TPTP_ind(scratc1733366650_union,X1)),X))))))) # label(fact_def__d__Union__closed) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 240 (all X0 all X12 (gg_TPTP_ind(X0) -> X0 = aa_TPTP_ind_TPTP_ind(scratc1354618622_proj0,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc318016687d_pair,X0),X12)))) # label(fact_proj0__pair__eq) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 241 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1291952835d_n_is,aa_TPTP_ind_TPTP_ind(scratc1292412021d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,aa_TPTP_ind_TPTP_ind(scratc1292412021d_n_pl(Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bu,Uu),Uua)))) # label(fact_ATP_Olambda__26) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 242 (all X0 all X12 all X22 all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc632088200d_d_Pi,X0),X12))) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X32),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,X22),X32)),aa_TPTP_ind_TPTP_ind(X12,X32)))))) # label(fact_ap__Pi) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 243 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc503482417nd_one(X0),X12)) -> scratc1892874294_is_of(scratc453913386nd_ind(X0,X12),aa_TPT43085870d_bool(aTP_Lamm_aj,X0)))) # label(fact_ind__p) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 244 (all Uu (scratc1892874294_is_of(aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,Uu),aTP_Lamm_a) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ck,Uu)))) # label(fact_ATP_Olambda__9) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 245 (all X0 pp(aa_fun171081125l_bool(scratc1522259491all_of(aa_TPT43085870d_bool(aTP_Lamm_cl,X0)),aa_TPT43085870d_bool(aTP_Lamm_cn,X0)))) # label(fact_isseti) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 246 (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_az(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc453847799nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1773292474d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,Uub),Uud))),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1773292474d_e_is(Uu),Uuc),Uud))))) # label(fact_ATP_Olambda__81) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 247 (all X0 ((all X13 (gg_TPTP_ind(X13) -> ((all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X22),X13)) -> pp(aa_TPTP_ind_bool(X0,X22)))) -> pp(aa_TPTP_ind_bool(X0,X13))))) -> (all X14 pp(aa_TPTP_ind_bool(X0,X14))))) # label(fact_k__In__ind) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 248 (all X0 all X12 scratc1892874294_is_of(aa_fun1431113780TP_ind(scratc764078447_d_Sep(X0),X12),aa_TPT43085870d_bool(aTP_Lamm_cl,X0))) # label(fact_setof__p) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 249 (all Uu all Uua aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,Uu),Uua)) = aa_TPTP_ind_TPTP_ind(aTP_Lamm_ad(Uu),Uua)) # label(fact_ATP_Olambda__39) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 250 (all X0 all X12 all X22 (gg_TPTP_ind(X12) -> (pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc534561714bnd_if(X0,X12),X22) = X12))) # label(fact_if__i__1) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 251 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc470920760d_esti(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,Uua),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aq(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__70) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 252 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1522259491all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_co(X0),X12)))) # label(fact_estie) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 253 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(scratc534561714bnd_if(aa_TPTP_ind_bool(Uua,Uub),Uub),scratc420998579nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bb(Uu),Uua))) = aa_TPTP_ind_TPTP_ind(aa_fun1235454963TP_ind(aTP_Lamm_bn(Uu),Uua),Uub)) # label(fact_ATP_Olambda__44) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 254 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,Uu),scratc494368140nd_nat)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_a,Uu)))) # label(fact_ATP_Olambda__12) # label(axiom) # label(non_clause). [assumption]. 0.96/1.27 255 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1522259491all_of(aa_TPT43085870d_bool(aTP_Lamm_cu(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_cw(X0),X12)))) # label(fact_second__p) # label(axiom) # label(non_clause). [assumption]. 0.96/1.28 256 (all B_1 all B_2 gg_bool(scratc1833317221_amone(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__40153__8903_ONUM640__thf__4__p_Obnd__amone) # label(axiom) # label(non_clause). [assumption]. 0.96/1.28 257 (all X7 all Y (gg_TPTP_ind(Y) & gg_TPTP_ind(X7) -> X7 = Y | -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]. 0.96/1.28 258 (all X0 all X12 all X22 all X32 (pp(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc534561714bnd_if(X0,X22),X32))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X12),X22))))) # label(fact_k__If__In__then__E) # label(axiom) # label(non_clause). [assumption]. 0.96/1.28 259 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_dc(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(Uua,aa_TPTP_ind_TPTP_ind(scratc1773292469d_e_in(Uu,Uua),Uub))))) # label(fact_ATP_Olambda__64) # label(axiom) # label(non_clause). [assumption]. 0.96/1.28 260 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc318016687d_pair,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc76637757nunion(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1912696292d_repl,X),scratc1371723034d_Inj0)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1912696292d_repl,Xa),scratc1371723035d_Inj1))) # label(fact_def__pair) # label(axiom) # label(non_clause). [assumption]. 0.96/1.28 261 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc808889297ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc387690156nd_all(Xa),aa_TPT43085870d_bool(scratc96293030_image(X,Xa),Xb))))) # label(fact_def__surjective) # label(axiom) # label(non_clause). [assumption]. 0.96/1.28 262 (all X scratc387690156nd_all(X) = scratc1522259491all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X))) # label(fact_def__all) # label(axiom) # label(non_clause). [assumption]. 0.96/1.28 263 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1522259491all_of(aa_TPT43085870d_bool(aTP_Lamm_de(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_dh(X0),X12)))) # label(fact_e__fisi) # label(axiom) # label(non_clause). [assumption]. 0.96/1.28 264 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X22),X0)) -> aa_TPTP_ind_TPTP_ind(X12,X22) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc828961942_Sigma,X0),X12)),X22))) # label(fact_beta) # label(axiom) # label(non_clause). [assumption]. 0.96/1.28 265 (all X (pp(aa_TPTP_ind_bool(scratc1355012220_prop4,X)) <-> pp(aa_fun171081125l_bool(scratc632920299l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc632088200d_d_Pi,scratc494368140nd_nat),aTP_Lamm_ac)),aa_TPT43085870d_bool(scratc1773136190_prop2,X))))) # label(fact_def__prop4) # label(axiom) # label(non_clause). [assumption]. 0.96/1.28 266 (all X ((all X1 (pp(aa_TPTP_ind_bool(X1,scratc864823754ptyset)) -> ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(X1,X2)) -> pp(aa_TPTP_ind_bool(X1,aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,X2)))))) -> pp(aa_TPTP_ind_bool(X1,X))))) <-> pp(aa_TPTP_ind_bool(scratc1779518500_nat_p,X)))) # label(fact_def__nat__p) # label(axiom) # label(non_clause). [assumption]. 0.96/1.28 267 (all P all Q (-pp(Q) | pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)) | -pp(P))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption]. 0.96/1.28 268 (all X all Xa all Xb all Xc all Xd all Xe all Xf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc172975168_prop1(X,Xa,Xb,Xc,Xd),Xe),Xf)) <-> pp(scratc880329896_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc470920760d_esti(X),Xf),aa_TPTP_ind_TPTP_ind(scratc649849411_ecect(X,Xa),Xd)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1773292474d_e_is(Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc534036932bnd_ap,Xc),Xf)),Xe))))) # label(fact_def__d__10__prop1) # label(axiom) # label(non_clause). [assumption]. 0.96/1.28 269 (all X all Xa all Xb (pp(scratc420145728nd_ec3(X,Xa,Xb)) <-> scratc1601182097d_and3(scratc1160045493d_l_ec(X,Xa),scratc1160045493d_l_ec(Xa,Xb),scratc1160045493d_l_ec(Xb,X)))) # label(fact_def__ec3) # label(axiom) # label(non_clause). [assumption]. 0.96/1.28 270 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (-pp(X0) -> X22 = aa_TPTP_ind_TPTP_ind(scratc534561714bnd_if(X0,X12),X22)))) # label(fact_if__i__0) # label(axiom) # label(non_clause). [assumption]. 0.96/1.28 271 (all X (pp(aa_TPTP_ind_bool(scratc1140580490closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X1),X)) -> (all X2 ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X3),X1)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,aa_TPTP_ind_TPTP_ind(X2,X3)),X))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1912696292d_repl,X1),X2)),X))))))))) # label(fact_def__d__Repl__closed) # label(axiom) # label(non_clause). [assumption]. 0.96/1.28 272 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X22),X0)) -> (all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X32),aa_TPTP_ind_TPTP_ind(X12,X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc318016687d_pair,X22),X32)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc828961942_Sigma,X0),X12))))))) # label(fact_pair__Sigma) # label(axiom) # label(non_clause). [assumption]. 0.96/1.28 273 (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(scratc494892931nd_nis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc494892931nd_nis,aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,Uua)))))) # label(fact_ATP_Olambda__28) # label(axiom) # label(non_clause). [assumption]. 0.96/1.28 274 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc470920760d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc764078447_d_Sep(Uu),Uua))) -> pp(aa_TPTP_ind_bool(Uua,Uub))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_co(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__46) # label(axiom) # label(non_clause). [assumption]. 0.96/1.28 275 (all X all Xa all Xb (pp(aa_fun171081125l_bool(scratc387690156nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ba(X),Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1364627026ective(X),Xa),Xb)))) # label(fact_def__injective) # label(axiom) # label(non_clause). [assumption]. 0.96/1.28 276 (all X0 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc534561722bnd_in,X0),scratc524273836_omega)) -> pp(aa_TPTP_ind_bool(scratc1779518500_nat_p,X0)))) # label(fact_omega__nat__p) # label(axiom) # label(non_clause). [assumption]. 0.96/1.28 277 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1522259491all_of(aa_fun1584354236d_bool(aTP_Lamm_db(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_dd(X0),X12)))) # label(fact_e__in__p) # label(axiom) # label(non_clause). [assumption]. 0.96/1.28 278 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc494892931nd_nis,aa_TPTP_ind_TPTP_ind(scratc604885422rdsucc,Uu)),scratc887146872nd_n_1)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cj,Uu)))) # label(fact_ATP_Olambda__10) # label(axiom) # label(non_clause). [assumption]. 0.96/1.28 279 (all X (pp(aa_bool_bool(aa_boo1142376798l_bool(scratc453847799nd_imp,X),fFalse)) <-> pp(scratc987795076_d_not(X)))) # label(fact_def__d__not) # label(axiom) # label(non_clause). [assumption]. 0.96/1.28 0.96/1.28 ============================== end of process non-clausal formulas === 0.96/1.28 0.96/1.28 ============================== PROCESS INITIAL CLAUSES =============== 0.96/1.28 0.96/1.28 ============================== PREDICATE ELIMINATION ================= 0.96/1.28 280 -pp(A) | pp(scratc987795076_d_not(B)) | -scratc1554980283d_r_ec(A,B) # label(fact_def__r__ec) # label(axiom). [clausify(3)]. 0.96/1.28 281 pp(A) | scratc1554980283d_r_ec(A,B) # label(fact_def__r__ec) # label(axiom). [clausify(3)]. 0.96/1.28 282 -pp(scratc987795076_d_not(A)) | scratc1554980283d_r_ec(B,A) # label(fact_def__r__ec) # label(axiom). [clausify(3)]. 0.96/1.35 283 -pp(scratc987795076_d_not(scratc987795076_d_not(A))) | scratc568984073nd_wel(A) # label(fact_def__wel) # label(axiom). [clausify(42)]. 0.96/1.35 284 -scratc568984073nd_wel(A) | pp(A) # label(fact_l__et) # label(axiom). [clausify(8)]. 0.96/1.35 Derived: -pp(scratc987795076_d_not(scratc987795076_d_not(A))) | pp(A). [resolve(283,b,284,a)]. 0.96/1.35 285 pp(scratc987795076_d_not(scratc987795076_d_not(A))) | -scratc568984073nd_wel(A) # label(fact_def__wel) # label(axiom). [clausify(42)]. 0.96/1.35 286 -gg_bool(A) | A = fFalse | fTrue = A # label(help_fFalse_1_1_T) # label(axiom). [clausify(79)]. 0.96/1.35 287 gg_bool(fEx_TPTP_ind(A)) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom). [clausify(16)]. 0.96/1.35 288 gg_bool(scratc503744763nd_or3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__40153__8903_ONUM640__thf__4__p_Obnd__or3) # label(axiom). [clausify(24)]. 0.96/1.35 289 gg_bool(scratc987795076_d_not(A)) # label(gsy_c_Scratch__tptp__translate__40153__8903_ONUM640__thf__4__p_Obnd__d__not) # label(axiom). [clausify(58)]. 0.96/1.35 290 gg_bool(scratc880329896_d_and(A,B)) # label(gsy_c_Scratch__tptp__translate__40153__8903_ONUM640__thf__4__p_Obnd__d__and) # label(axiom). [clausify(62)]. 0.96/1.35 291 gg_bool(scratc1160045493d_l_ec(A,B)) # label(gsy_c_Scratch__tptp__translate__40153__8903_ONUM640__thf__4__p_Obnd__l__ec) # label(axiom). [clausify(64)]. 0.96/1.35 Derived: fEx_TPTP_ind(A) = fFalse | fTrue = fEx_TPTP_ind(A). [resolve(286,a,287,a)]. 0.96/1.35 Derived: scratc503744763nd_or3(A,B,C) = fFalse | fTrue = scratc503744763nd_or3(A,B,C). [resolve(286,a,288,a)]. 0.96/1.35 Derived: scratc987795076_d_not(A) = fFalse | fTrue = scratc987795076_d_not(A). [resolve(286,a,289,a)]. 0.96/1.35 Derived: scratc880329896_d_and(A,B) = fFalse | fTrue = scratc880329896_d_and(A,B). [resolve(286,a,290,a)]. 0.96/1.35 Derived: scratc1160045493d_l_ec(A,B) = fFalse | fTrue = scratc1160045493d_l_ec(A,B). [resolve(286,a,291,a)]. 0.96/1.35 292 gg_bool(aa_bool_bool(A,B)) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom). [clausify(150)]. 0.96/1.35 Derived: aa_bool_bool(A,B) = fFalse | fTrue = aa_bool_bool(A,B). [resolve(292,a,286,a)]. 0.96/1.35 293 gg_bool(undefined_bool(bool)) # label(gsy_c_HOL_Oundefined_001t__HOL__Obool) # label(axiom). [assumption]. 0.96/1.35 Derived: undefined_bool(bool) = fFalse | fTrue = undefined_bool(bool). [resolve(293,a,286,a)]. 0.96/1.35 294 gg_bool(aa_TPTP_ind_bool(A,B)) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom). [clausify(204)]. 0.96/1.35 Derived: aa_TPTP_ind_bool(A,B) = fFalse | fTrue = aa_TPTP_ind_bool(A,B). [resolve(294,a,286,a)]. 0.96/1.35 295 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(206)]. 0.96/1.35 Derived: aa_fun171081125l_bool(A,B) = fFalse | fTrue = aa_fun171081125l_bool(A,B). [resolve(295,a,286,a)]. 0.96/1.35 296 gg_bool(fTrue) # label(gsy_c_fTrue) # label(axiom). [assumption]. 0.96/1.35 Derived: fTrue = fFalse | fTrue = fTrue. [resolve(296,a,286,a)]. 0.96/1.35 297 gg_bool(scratc420145728nd_ec3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__40153__8903_ONUM640__thf__4__p_Obnd__ec3) # label(axiom). [clausify(233)]. 0.96/1.35 Derived: scratc420145728nd_ec3(A,B,C) = fFalse | fTrue = scratc420145728nd_ec3(A,B,C). [resolve(297,a,286,a)]. 0.96/1.35 298 gg_bool(fFalse) # label(gsy_c_fFalse) # label(axiom). [assumption]. 0.96/1.35 Derived: fFalse = fFalse | fTrue = fFalse. [resolve(298,a,286,a)]. 0.96/1.35 299 gg_bool(scratc1833317221_amone(A,B)) # label(gsy_c_Scratch__tptp__translate__40153__8903_ONUM640__thf__4__p_Obnd__amone) # label(axiom). [clausify(256)]. 0.96/1.35 Derived: scratc1833317221_amone(A,B) = fFalse | fTrue = scratc1833317221_amone(A,B). [resolve(299,a,286,a)]. 0.96/1.35 300 scratc131980093_orec3(A,B,C) | -pp(scratc880329896_d_and(scratc503744763nd_or3(A,B,C),scratc420145728nd_ec3(A,B,C))) # label(fact_def__orec3) # label(axiom). [clausify(172)]. 0.96/1.35 301 -scratc131980093_orec3(A,B,C) | pp(scratc880329896_d_and(scratc503744763nd_or3(A,B,C),scratc420145728nd_ec3(A,B,C))) # label(fact_def__orec3) # label(axiom). [clausify(172)]. 0.96/1.35 302 scratc1774471346_l_iff(A,B) | -pp(scratc880329896_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc453847799nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc453847799nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(218)]. 0.96/1.50 303 -scratc1774471346_l_iff(A,B) | pp(scratc880329896_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc453847799nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc453847799nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(218)]. 0.96/1.50 304 scratc1825096310d_orec(A,B) | -pp(scratc880329896_d_and(aa_bool_bool(scratc1160701498d_l_or(A),B),scratc1160045493d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(232)]. 0.96/1.50 305 -scratc1825096310d_orec(A,B) | pp(scratc880329896_d_and(aa_bool_bool(scratc1160701498d_l_or(A),B),scratc1160045493d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(232)]. 0.96/1.50 0.96/1.50 ============================== end predicate elimination ============= 0.96/1.50 0.96/1.50 Auto_denials: (non-Horn, no changes). 0.96/1.50 0.96/1.50 Term ordering decisions: 0.96/1.50 Function symbol KB weights: scratc534561722bnd_in=1. scratc604885422rdsucc=1. scratc534036932bnd_ap=1. aTP_Lamm_aj=1. scratc864823754ptyset=1. scratc1291952835d_n_is=1. aTP_Lamm_a=1. scratc828961942_Sigma=1. scratc887146872nd_n_1=1. fFalse=1. scratc1226104784_power=1. scratc1779518500_nat_p=1. scratc632088200d_d_Pi=1. scratc494368140nd_nat=1. scratc1912696292d_repl=1. scratc453847799nd_imp=1. fTrue=1. scratc494892931nd_nis=1. scratc318016687d_pair=1. scratc644966240d_Subq=1. scratc1140580490closed=1. scratc1354618622_proj0=1. scratc1733366650_union=1. aTP_Lamm_af=1. scratc1291952830d_n_in=1. scratc1354618623_proj1=1. scratc305303720_n_all=1. aTP_Lamm_ac=1. aTP_Lamm_ae=1. aTP_Lamm_cl=1. scratc101417154closed=1. scratc2084167788closed=1. aTP_Lamm_cc=1. aTP_Lamm_cg=1. aTP_Lamm_ch=1. scratc1120415079closed=1. scratc1371723035d_Inj1=1. scratc1376744941n_some=1. scratc1773136190_prop2=1. scratc524273836_omega=1. aTP_Lamm_aa=1. aTP_Lamm_ag=1. aTP_Lamm_bg=1. aTP_Lamm_bi=1. aTP_Lamm_bj=1. aTP_Lamm_br=1. aTP_Lamm_bu=1. aTP_Lamm_bx=1. aTP_Lamm_bz=1. aTP_Lamm_ca=1. aTP_Lamm_cf=1. fconj=1. fimplies=1. scratc1369735355_cond2=1. scratc1371723034d_Inj0=1. scratc1773136189_prop1=1. scratc546615358d_Sing=1. aTP_Lamm_bm=1. aTP_Lamm_bq=1. aTP_Lamm_bs=1. aTP_Lamm_bt=1. aTP_Lamm_bv=1. aTP_Lamm_bw=1. aTP_Lamm_by=1. aTP_Lamm_cb=1. aTP_Lamm_cd=1. aTP_Lamm_ce=1. aTP_Lamm_ci=1. aTP_Lamm_cj=1. aTP_Lamm_ck=1. aTP_Lamm_cn=1. aTP_Lamm_dk=1. fequal_TPTP_ind=1. scratc1369735354_cond1=1. scratc421095981_n_one=1. scratc492793758nd_nIn=1. scratc65091634univof=1. scratc781191842_d_Unj=1. aTP_Lamm_ab=1. aTP_Lamm_ah=1. aTP_Lamm_bk=1. aTP_Lamm_bl=1. bool=1. scratc1150418741nempty=1. scratc1184774014_prop1=1. scratc1230264306munion=1. scratc1355012220_prop4=1. scratc2105262200_empty=1. scratc409680431d_plus=1. scratc461635393pair_p=1. scratc596411839_prop1=1. scratc1242103414d_24_g=1. scratc488653558d_i1_s=1. tPTP_ind=1. aa_TPTP_ind_bool=1. aa_TPT43085870d_bool=1. aa_TPTP_ind_TPTP_ind=1. aa_fun171081125l_bool=1. aa_TPT1424761345TP_ind=1. aa_TPT60673477d_bool=1. aa_fun277296641TP_ind=1. aa_TPT494704832TP_ind=1. aa_fun1584354236d_bool=1. aa_bool_bool=1. aa_fun1431113780TP_ind=1. aa_boo1142376798l_bool=1. aa_TPT1123896796d_bool=1. scratc880329896_d_and=1. scratc534561714bnd_if=1. scratc1160045493d_l_ec=1. aa_fun1212484691d_bool=1. aa_TPT985247859d_bool=1. scratc1773292469d_e_in=1. scratc1642387625d_pair=1. aa_fun987228051d_bool=1. scratc453913386nd_ind=1. scratc138935099_first=1. scratc1503448425second=1. scratc96293030_image=1. aa_TPT125613450d_bool=1. scratc1833317221_amone=1. scratc495286520nd_non=1. aa_fun1913827119d_bool=1. scratc1601247744d_anec=1. aa_TPT1791839040TP_ind=1. aa_fun1107270209d_bool=1. aa_fun845057962d_bool=1. scratc1836604576eplSep=1. scratc420145789nd_ecp=1. scratc650439802_ecelt=1. scratc649849411_ecect=1. aa_TPT1781712639TP_ind=1. aa_TPT2142672771l_bool=1. aa_fun1235454963TP_ind=1. cOMBB_658106424TP_ind=1. cOMBS_2003118649l_bool=1. scratc1273144002etprop=1. scratc187651343_fixfu=1. scratc364179171fixfu2=1. scratc420145793nd_ect=1. scratc503941625nd_out=1. scratc744232494wissel=1. scratc876205697ectset=1. scratc1404609578d_invf=1. scratc140834610Cputime limit exceeded (core dumped) 180.10/180.37 EOF