TSTP Solution File: NUM686+4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM686+4 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 13:30:38 EDT 2022
% Result : Timeout 300.08s 300.39s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM686+4 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.11 % Command : tptp2X_and_run_prover9 %d %s
% 0.10/0.32 % Computer : n016.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 600
% 0.10/0.32 % DateTime : Wed Jul 6 08:20:19 EDT 2022
% 0.10/0.32 % CPUTime :
% 1.00/1.32 ============================== Prover9 ===============================
% 1.00/1.32 Prover9 (32) version 2009-11A, November 2009.
% 1.00/1.32 Process 9661 was started by sandbox on n016.cluster.edu,
% 1.00/1.32 Wed Jul 6 08:20:20 2022
% 1.00/1.32 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_9508_n016.cluster.edu".
% 1.00/1.32 ============================== end of head ===========================
% 1.00/1.32
% 1.00/1.32 ============================== INPUT =================================
% 1.00/1.32
% 1.00/1.32 % Reading from file /tmp/Prover9_9508_n016.cluster.edu
% 1.00/1.32
% 1.00/1.32 set(prolog_style_variables).
% 1.00/1.32 set(auto2).
% 1.00/1.32 % set(auto2) -> set(auto).
% 1.00/1.32 % set(auto) -> set(auto_inference).
% 1.00/1.32 % set(auto) -> set(auto_setup).
% 1.00/1.32 % set(auto_setup) -> set(predicate_elim).
% 1.00/1.32 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.00/1.32 % set(auto) -> set(auto_limits).
% 1.00/1.32 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.00/1.32 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.00/1.32 % set(auto) -> set(auto_denials).
% 1.00/1.32 % set(auto) -> set(auto_process).
% 1.00/1.32 % set(auto2) -> assign(new_constants, 1).
% 1.00/1.32 % set(auto2) -> assign(fold_denial_max, 3).
% 1.00/1.32 % set(auto2) -> assign(max_weight, "200.000").
% 1.00/1.32 % set(auto2) -> assign(max_hours, 1).
% 1.00/1.32 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.00/1.32 % set(auto2) -> assign(max_seconds, 0).
% 1.00/1.32 % set(auto2) -> assign(max_minutes, 5).
% 1.00/1.32 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.00/1.32 % set(auto2) -> set(sort_initial_sos).
% 1.00/1.32 % set(auto2) -> assign(sos_limit, -1).
% 1.00/1.32 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.00/1.32 % set(auto2) -> assign(max_megs, 400).
% 1.00/1.32 % set(auto2) -> assign(stats, some).
% 1.00/1.32 % set(auto2) -> clear(echo_input).
% 1.00/1.32 % set(auto2) -> set(quiet).
% 1.00/1.32 % set(auto2) -> clear(print_initial_clauses).
% 1.00/1.32 % set(auto2) -> clear(print_given).
% 1.00/1.32 assign(lrs_ticks,-1).
% 1.00/1.32 assign(sos_limit,10000).
% 1.00/1.32 assign(order,kbo).
% 1.00/1.32 set(lex_order_vars).
% 1.00/1.32 clear(print_given).
% 1.00/1.32
% 1.00/1.32 % formulas(sos). % not echoed (535 formulas)
% 1.00/1.32
% 1.00/1.32 ============================== end of input ==========================
% 1.00/1.32
% 1.00/1.32 % From the command line: assign(max_seconds, 300).
% 1.00/1.32
% 1.00/1.32 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.00/1.32
% 1.00/1.32 % Formulas that are not ordinary clauses:
% 1.00/1.32 1 (all B_1 all B_2 gg_bool(scratc1769573999_amone(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__48475__25370_ONUM686__thf__4__p_Obnd__amone) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 2 (all B_1 all B_2 gg_bool(scratc539372574_d_and(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__48475__25370_ONUM686__thf__4__p_Obnd__d__and) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 3 (all B_1 gg_bool(scratc646837754_d_not(B_1))) # label(gsy_c_Scratch__tptp__translate__48475__25370_ONUM686__thf__4__p_Obnd__d__not) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 4 (all B_1 all B_2 all B_3 gg_bool(scratc2008132170nd_ec3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__48475__25370_ONUM686__thf__4__p_Obnd__ec3) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 5 (all B_1 all B_2 gg_TPTP_ind(scratc2008132235nd_ect(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__48475__25370_ONUM686__thf__4__p_Obnd__ect) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 6 (all B_1 gg_TPTP_ind(scratc2008985021nd_eps(B_1))) # label(gsy_c_Scratch__tptp__translate__48475__25370_ONUM686__thf__4__p_Obnd__eps) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 7 (all B_1 all B_2 gg_TPTP_ind(scratc2041899828nd_ind(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__48475__25370_ONUM686__thf__4__p_Obnd__ind) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 8 (all B_1 all B_2 gg_bool(scratc1096302271d_l_ec(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__48475__25370_ONUM686__thf__4__p_Obnd__l__ec) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 9 (all B_1 all B_2 all B_3 gg_bool(scratc2091731205nd_or3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__48475__25370_ONUM686__thf__4__p_Obnd__or3) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 10 (all B_1 all B_2 gg_bool(aa_bool_bool(B_1,B_2))) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 11 (all B_1 all B_2 gg_bool(aa_TPTP_ind_bool(B_1,B_2))) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 12 (all B_1 all B_2 gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2))) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 13 (all B_1 all B_2 gg_bool(aa_fun171081125l_bool(B_1,B_2))) # label(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__HOL__Obool) # label(hypothesis) # label(non_clause). [assumption].
% 1.00/1.32 14 (all B_1 all B_2 gg_TPTP_ind(aa_fun1431113780TP_ind(B_1,B_2))) # label(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 15 (all B_1 all B_2 gg_TPTP_ind(aa_fun277296641TP_ind(B_1,B_2))) # label(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__TPTP____Interpret__Oind_J_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 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].
% 1.00/1.32 17 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc343135470lessis,X),Xa)) <-> pp(aa_bool_bool(scratc1096958276d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,X),Xa))))) # label(fact_def__lessis) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 18 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc477119082moreis,X),Xa)) <-> pp(aa_bool_bool(scratc1096958276d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,X),Xa))))) # label(fact_def__moreis) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 19 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc787822702_prop1,X),Xa)) <-> pp(scratc2091731205nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,X),Xa))))) # label(fact_def__d__29__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 20 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc959572983n_some,aa_TPT43085870d_bool(scratc1467574323ffprop(Xa),X))))) # label(fact_def__iii) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 21 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc959572983n_some,aa_TPT43085870d_bool(scratc1467574323ffprop(X),Xa))))) # label(fact_def__d__29__ii) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 22 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1467574323ffprop(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,X),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Xa),Xb))))) # label(fact_def__diffprop) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 23 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc199460527_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2082879373nd_nis,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(X),Xb))))) # label(fact_def__d__28__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 24 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1758582000_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2082879373nd_nis,Xa),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(X),Xa))))) # label(fact_def__d__27__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 25 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1170219825_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Xa),X))))) # label(fact_def__d__26__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 26 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc581857650_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(X),Xa)),Xb)),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(X),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Xa),Xb)))))) # label(fact_def__d__25__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 27 (all X scratc1228668799d_n_pl(X) = aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,aa_TPTP_ind_TPTP_ind(scratc595492005d_plus,X))) # label(fact_def__n__pl) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 28 (all X aa_TPTP_ind_TPTP_ind(scratc595492005d_plus,X) = scratc2041899828nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc568344978d_d_Pi,scratc2082354582nd_nat),aTP_Lamm_ae),aa_TPT43085870d_bool(scratc2140979124_prop2,X))) # label(fact_def__plus) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 29 (all X aa_TPTP_ind_TPTP_ind(scratc562957036d_24_g,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc149815564_Sigma,scratc2082354582nd_nat),aTP_Lamm_af(X))) # label(fact_def__d__24__g) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 30 (all X (pp(aa_TPTP_ind_bool(scratc1291268998_prop4,X)) <-> pp(aa_fun171081125l_bool(scratc215748341l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc568344978d_d_Pi,scratc2082354582nd_nat),aTP_Lamm_ae)),aa_TPT43085870d_bool(scratc2140979124_prop2,X))))) # label(fact_def__prop4) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 31 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1291268997_prop3(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,X),Xb)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,Xa),Xb))))) # label(fact_def__prop3) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 32 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2140979124_prop2,X),Xa)) <-> pp(scratc539372574_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,Xa),scratc1072958446nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,X)),aa_TPTP_ind_bool(scratc2140979123_prop1,Xa))))) # label(fact_def__d__24__prop2) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 33 (all X (pp(aa_TPTP_ind_bool(scratc2140979123_prop1,X)) <-> pp(aa_fun171081125l_bool(scratc2111830046_n_all,aa_TPT43085870d_bool(aTP_Lamm_ag,X))))) # label(fact_def__d__24__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 34 (all X (pp(aa_TPTP_ind_bool(scratc1552616948_prop1,X)) <-> pp(aa_bool_bool(scratc1096958276d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,X),scratc1072958446nd_n_1)),aa_fun171081125l_bool(scratc959572983n_some,aa_TPT43085870d_bool(aTP_Lamm_ah,X)))))) # label(fact_def__d__23__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 35 (all X (pp(aa_TPTP_ind_bool(scratc964254773_prop1,X)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2082879373nd_nis,aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,X)),X)))) # label(fact_def__d__22__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 36 (all X (pp(aa_TPTP_ind_bool(scratc1305992133_cond2,X)) <-> pp(aa_fun171081125l_bool(scratc2111830046_n_all,aa_TPT43085870d_bool(aTP_Lamm_ai,X))))) # label(fact_def__cond2) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 37 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2082879373nd_nis,X),Xa)) <-> pp(scratc646837754_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,X),Xa))))) # label(fact_def__nis) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 38 (all X all Xa all Xb all Xc all Xd scratc1954215346indeq2(X,Xa,Xb,Xc,Xd) = aa_TPT1424761345TP_ind(scratc837790336_indeq(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1376598448d_11_i(X,Xa,Xb),Xc),Xd))) # label(fact_def__indeq2) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.32 39 (all X all Xa all Xb scratc1376598448d_11_i(X,Xa,Xb) = scratc837790336_indeq(X,Xa,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc568344978d_d_Pi,X),aTP_Lamm_ak(Xb)))) # label(fact_def__d__11__i) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 40 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc23221849fixfu2(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ap(X),Xa),Xb),Xc))))) # label(fact_def__fixfu2) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 41 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc837790336_indeq(X,Xa,Xb),Xc),Xd) = scratc2041899828nd_ind(Xb,aa_TPT43085870d_bool(scratc1291268996_prop2(X,Xa,Xb,Xc),Xd))) # label(fact_def__indeq) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 42 (all X all Xa all Xb all Xc all Xd all Xe (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1291268996_prop2(X,Xa,Xb,Xc),Xd),Xe)) <-> pp(aa_fun171081125l_bool(scratc215748341l_some(X),aa_TPT43085870d_bool(scratc540818102_prop1(X,Xa,Xb,Xc,Xd),Xe))))) # label(fact_def__prop2) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 43 (all X all Xa all Xb all Xc all Xd all Xe all Xf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc540818102_prop1(X,Xa,Xb,Xc,Xd),Xe),Xf)) <-> pp(scratc539372574_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc656732334d_esti(X),Xf),aa_TPTP_ind_TPTP_ind(scratc586106189_ecect(X,Xa),Xd)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1709549252d_e_is(Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,Xc),Xf)),Xe))))) # label(fact_def__d__10__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 44 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc123908121_fixfu(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ar(X),Xa),Xb),Xc))))) # label(fact_def__fixfu) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 45 (all X all Xa scratc586106189_ecect(X,Xa) = scratc1709549247d_e_in(aa_TPTP_ind_TPTP_ind(scratc1162361562_power,X),scratc1787059318d_anec(X,Xa))) # label(fact_def__ecect) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 46 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc420046498ectelt(X,Xa),Xb) = aa_TPTP_ind_TPTP_ind(scratc535248375ectset(X,Xa),aa_TPTP_ind_TPTP_ind(scratc586696580_ecelt(X,Xa),Xb))) # label(fact_def__ectelt) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 47 (all X all Xa scratc535248375ectset(X,Xa) = scratc2091928067nd_out(aa_TPTP_ind_TPTP_ind(scratc1162361562_power,X),scratc1787059318d_anec(X,Xa))) # label(fact_def__ectset) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 48 (all X all Xa scratc2008132235nd_ect(X,Xa) = aa_fun1431113780TP_ind(scratc423121125_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1162361562_power,X)),scratc1787059318d_anec(X,Xa))) # label(fact_def__ect) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 49 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc1787059318d_anec(X,Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc215748341l_some(X),aa_TPT43085870d_bool(scratc2008132231nd_ecp(X,Xa),Xb))))) # label(fact_def__anec) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 50 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2008132231nd_ecp(X,Xa),Xb),Xc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1709549252d_e_is(aa_TPTP_ind_TPTP_ind(scratc1162361562_power,X)),Xb),aa_TPTP_ind_TPTP_ind(scratc586696580_ecelt(X,Xa),Xc))))) # label(fact_def__ecp) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 51 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc586696580_ecelt(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc423121125_d_Sep(X),aa_TPT43085870d_bool(Xa,Xb))) # label(fact_def__ecelt) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 52 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc641365721unmore(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc423121125_d_Sep(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_at(X),Xa),Xb))) # label(fact_def__unmore) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 53 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1404884024etprop(X,Xa),Xb),Xc)) <-> pp(scratc539372574_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc656732334d_esti(X),Xc),Xa),scratc646837754_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc656732334d_esti(X),Xc),Xb)))))) # label(fact_def__nissetprop) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 54 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1878097064t_disj(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1975676598nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_au(X),Xa),Xb))))) # label(fact_def__st__disj) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 55 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1589174777d_incl(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1975676598nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_av(X),Xa),Xb))))) # label(fact_def__incl) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 56 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc471272363nempty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc215748341l_some(X),aa_TPT43085870d_bool(aTP_Lamm_aw(X),Xa))))) # label(fact_def__nonempty) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 57 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041518978_empty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X)),scratc2083272962nd_non(X,aa_TPT43085870d_bool(aTP_Lamm_aw(X),Xa)))))) # label(fact_def__empty) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 58 (all X scratc656732334d_esti(X) = scratc2085839152bnd_in) # label(fact_def__esti) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 59 (all X all Xa (scratc1491237061d_r_ec(X,Xa) <-> (pp(X) -> pp(scratc646837754_d_not(Xa))))) # label(fact_def__r__ec) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 60 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc1747403755hangef(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc149815564_Sigma,X),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_ax(X),Xb),Xc),Xd))) # label(fact_def__changef) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 61 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc403275172wissel(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc149815564_Sigma,X),scratc1344253711sel_wb(X,Xa,Xb))) # label(fact_def__wissel) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 62 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1344253711sel_wb(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc2042293423nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1709549252d_e_is(X),Xc),Xb),X,Xa),aa_TPTP_ind_TPTP_ind(scratc1344253710sel_wa(X,Xa,Xb),Xc))) # label(fact_def__wissel__wb) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 63 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1344253710sel_wa(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc2042293423nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1709549252d_e_is(X),Xc),Xa),X,Xb),Xc)) # label(fact_def__wissel__wa) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 64 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc2042293423nd_ite(X,Xa,Xb),Xc) = scratc2041899828nd_ind(Xa,aa_TPT43085870d_bool(scratc1291268995_prop1(X,Xa,Xb),Xc))) # label(fact_def__ite) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 65 (all X all Xa all Xb all Xc all Xd (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1291268995_prop1(X,Xa,Xb),Xc),Xd)) <-> pp(scratc539372574_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc2041834241nd_imp,X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1709549252d_e_is(Xa),Xd),Xb)),aa_bool_bool(aa_boo1142376798l_bool(scratc2041834241nd_imp,scratc646837754_d_not(X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1709549252d_e_is(Xa),Xd),Xc)))))) # label(fact_def__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 66 (all X all Xa scratc1162491103second(X,Xa) = scratc1290875401_proj1) # label(fact_def__second) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 67 (all X all Xa scratc75191877_first(X,Xa) = scratc1290875400_proj0) # label(fact_def__first) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 68 (all X all Xa scratc1225215667d_pair(X,Xa) = scratc503828261d_pair) # label(fact_def__d__pair) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 69 (all X all Xa scratc2091928067nd_out(X,Xa) = scratc813570485d_soft(aa_fun1431113780TP_ind(scratc423121125_d_Sep(X),Xa),X,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc149815564_Sigma,aa_fun1431113780TP_ind(scratc423121125_d_Sep(X),Xa)),scratc1709549247d_e_in(X,Xa)))) # label(fact_def__out) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 70 (all X all Xa all Xb (gg_TPTP_ind(Xb) -> aa_TPTP_ind_TPTP_ind(scratc1709549247d_e_in(X,Xa),Xb) = Xb)) # label(fact_def__e__in) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 71 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc144537838_inj_h(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc149815564_Sigma,X),aa_TPT1424761345TP_ind(aTP_Lamm_ay(Xc),Xd))) # label(fact_def__inj__h) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 72 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1590421152d_invf(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc149815564_Sigma,Xa),scratc813570485d_soft(X,Xa,Xb))) # label(fact_def__invf) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 73 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1920857242ective(X),Xa),Xb)) <-> pp(scratc539372574_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1737138012ective(X),Xa),Xb),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc940629319ective(X),Xa),Xb))))) # label(fact_def__bijective) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 74 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc940629319ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1975676598nd_all(Xa),aa_TPT43085870d_bool(scratc32549808_image(X,Xa),Xb))))) # label(fact_def__surjective) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 75 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1733444805nverse(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc149815564_Sigma,Xa),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_az(X),Xa),Xb))) # label(fact_def__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 76 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc813570485d_soft(X,Xa,Xb),Xc) = scratc2041899828nd_ind(X,aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ba(Xa),Xb),Xc))) # label(fact_def__soft) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 77 (all X all Xa scratc1594157683d_tofs(X,Xa) = scratc2085314362bnd_ap) # label(fact_def__tofs) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 78 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc32549808_image(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc215748341l_some(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ba(Xa),Xb),Xc))))) # label(fact_def__image) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 79 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1737138012ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1975676598nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bc(X),Xa),Xb))))) # label(fact_def__injective) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 80 (all X all Xa scratc2041899828nd_ind(X,Xa) = scratc2008985021nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bd(X),Xa))) # label(fact_def__ind) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 81 (all X all Xa (pp(aa_fun171081125l_bool(scratc2091468859nd_one(X),Xa)) <-> pp(scratc539372574_d_and(scratc1769573999_amone(X,Xa),aa_fun171081125l_bool(scratc215748341l_some(X),Xa))))) # label(fact_def__one) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 82 (all X all Xa (pp(scratc1769573999_amone(X,Xa)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X)),aa_fun1584354236d_bool(aTP_Lamm_bf(X),Xa))))) # label(fact_def__amone) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 83 (all X scratc1709549252d_e_is(X) = fequal_TPTP_ind) # label(fact_def__e__is) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 84 (all X all Xa all Xb (scratc68236871_orec3(X,Xa,Xb) <-> pp(scratc539372574_d_and(scratc2091731205nd_or3(X,Xa,Xb),scratc2008132170nd_ec3(X,Xa,Xb))))) # label(fact_def__orec3) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 85 (all X all Xa all Xb (pp(scratc2008132170nd_ec3(X,Xa,Xb)) <-> scratc1786993671d_and3(scratc1096302271d_l_ec(X,Xa),scratc1096302271d_l_ec(Xa,Xb),scratc1096302271d_l_ec(Xb,X)))) # label(fact_def__ec3) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 86 (all X all Xa all Xb (scratc1786993671d_and3(X,Xa,Xb) <-> pp(scratc539372574_d_and(X,scratc539372574_d_and(Xa,Xb))))) # label(fact_def__and3) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 87 (all X all Xa all Xb (pp(scratc2091731205nd_or3(X,Xa,Xb)) <-> pp(aa_bool_bool(scratc1096958276d_l_or(X),aa_bool_bool(scratc1096958276d_l_or(Xa),Xb))))) # label(fact_def__or3) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 88 (all X all Xa (pp(aa_fun171081125l_bool(scratc215748341l_some(X),Xa)) <-> pp(scratc646837754_d_not(aa_fun171081125l_bool(scratc1105087533all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X)),scratc2083272962nd_non(X,Xa)))))) # label(fact_def__l__some) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 89 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc2083272962nd_non(X,Xa),Xb)) <-> pp(scratc646837754_d_not(aa_TPTP_ind_bool(Xa,Xb))))) # label(fact_def__non) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 90 (all X scratc1975676598nd_all(X) = scratc1105087533all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X))) # label(fact_def__all) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 91 (all X all Xa (scratc1433514024_l_iff(X,Xa) <-> pp(scratc539372574_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc2041834241nd_imp,X),Xa),aa_bool_bool(aa_boo1142376798l_bool(scratc2041834241nd_imp,Xa),X))))) # label(fact_def__l__iff) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 92 (all X all Xa (scratc2010907884d_orec(X,Xa) <-> pp(scratc539372574_d_and(aa_bool_bool(scratc1096958276d_l_or(X),Xa),scratc1096302271d_l_ec(X,Xa))))) # label(fact_def__orec) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 93 (all X scratc1096958276d_l_or(X) = aa_boo1142376798l_bool(scratc2041834241nd_imp,scratc646837754_d_not(X))) # label(fact_def__l__or) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 94 (all X all Xa (pp(scratc539372574_d_and(X,Xa)) <-> pp(scratc646837754_d_not(scratc1096302271d_l_ec(X,Xa))))) # label(fact_def__d__and) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 95 (all X all Xa (pp(scratc1096302271d_l_ec(X,Xa)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc2041834241nd_imp,X),scratc646837754_d_not(Xa))))) # label(fact_def__l__ec) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 96 scratc451043804bvious <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc2041834241nd_imp,fFalse),fFalse)) # label(fact_def__obvious) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 97 (all X (scratc9486867nd_wel(X) <-> pp(scratc646837754_d_not(scratc646837754_d_not(X))))) # label(fact_def__wel) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 98 (all X (pp(scratc646837754_d_not(X)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc2041834241nd_imp,X),fFalse)))) # label(fact_def__d__not) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 99 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc568344978d_d_Pi,X),Xa) = aa_fun1431113780TP_ind(scratc423121125_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1162361562_power,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc149815564_Sigma,X),aTP_Lamm_bg(Xa)))),aa_fun1913827119d_bool(aTP_Lamm_bh(X),Xa))) # label(fact_def__d__Pi) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 100 (all X (gg_TPTP_ind(X) -> (pp(aa_TPTP_ind_bool(scratc44463435pair_p,X)) <-> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc503828261d_pair,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,X),scratc185677376ptyset)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,X),aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,scratc185677376ptyset))) = X))) # label(fact_def__pair__p) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 101 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc1968344598eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bi,Xa)),scratc1290875401_proj1)) # label(fact_def__ap) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 102 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1969120206etprod(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc149815564_Sigma,X),aTP_Lamm_ak(Xa))) # label(fact_def__setprod) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 103 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc149815564_Sigma,X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc551117928munion,X),aTP_Lamm_bj(Xa))) # label(fact_def__d__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 104 (all X aa_TPTP_ind_TPTP_ind(scratc1290875401_proj1,X) = aa_fun277296641TP_ind(scratc1968344598eplSep(X,aTP_Lamm_bk),scratc440234520_d_Unj)) # label(fact_def__proj1) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 105 (all X aa_TPTP_ind_TPTP_ind(scratc1290875400_proj0,X) = aa_fun277296641TP_ind(scratc1968344598eplSep(X,aTP_Lamm_bl),scratc440234520_d_Unj)) # label(fact_def__proj0) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 106 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc503828261d_pair,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1544975027nunion(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2098507866d_repl,X),scratc954551076d_Inj0)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2098507866d_repl,Xa),scratc954551077d_Inj1))) # label(fact_def__pair) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 107 (all X aa_TPTP_ind_TPTP_ind(scratc954551076d_Inj0,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2098507866d_repl,X),scratc954551077d_Inj1)) # label(fact_def__d__Inj0) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 108 (all X (pp(aa_TPTP_ind_bool(scratc1438561178_nat_p,X)) <-> (all X1 (pp(aa_TPTP_ind_bool(X1,scratc185677376ptyset)) -> ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(X1,X2)) -> pp(aa_TPTP_ind_bool(X1,aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,X2)))))) -> pp(aa_TPTP_ind_bool(X1,X))))))) # label(fact_def__nat__p) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 109 (all X aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1544975027nunion(X),aa_TPTP_ind_TPTP_ind(scratc129443400d_Sing,X))) # label(fact_def__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 110 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1696108178In_rec(X),Xa) = scratc2008985021nd_eps(aa_TPT43085870d_bool(scratc1824249717_rec_G(X),Xa))) # label(fact_def__d__In__rec) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 111 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1824249717_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(scratc2085839152bnd_in,X6),X4)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(X3,X6),aa_TPTP_ind_TPTP_ind(X5,X6)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(X3,X4),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(X,X4),X5)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(X3,Xa),Xb)))))) # label(fact_def__d__In__rec__G) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 112 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1461260569tminus(X),Xa) = aa_fun1431113780TP_ind(scratc423121125_d_Sep(X),aa_TPT43085870d_bool(aTP_Lamm_bo,Xa))) # label(fact_def__setminus) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 113 (all X all Xa scratc1968344598eplSep(X,Xa) = aa_TPT494704832TP_ind(scratc2098507866d_repl,aa_fun1431113780TP_ind(scratc423121125_d_Sep(X),Xa))) # label(fact_def__d__ReplSep) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 114 (all X all Xa aa_fun1431113780TP_ind(scratc423121125_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc2085839144bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc2085839152bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2098507866d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bp(X),Xa))),scratc185677376ptyset)) # label(fact_def__d__Sep) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 115 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc551117928munion,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1669623428_union,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2098507866d_repl,X),Xa))) # label(fact_def__famunion) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 116 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1544975027nunion(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1669623428_union,aa_TPTP_ind_TPTP_ind(scratc44301942_UPair(X),Xa))) # label(fact_def__binunion) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 117 (all X aa_TPTP_ind_TPTP_ind(scratc129443400d_Sing,X) = aa_TPTP_ind_TPTP_ind(scratc44301942_UPair(X),X)) # label(fact_def__d__Sing) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 118 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc44301942_UPair(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2098507866d_repl,aa_TPTP_ind_TPTP_ind(scratc1162361562_power,aa_TPTP_ind_TPTP_ind(scratc1162361562_power,scratc185677376ptyset))),aa_TPT1424761345TP_ind(aTP_Lamm_bq(X),Xa))) # label(fact_def__d__UPair) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 119 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2080780200nd_nIn,X),Xa)) <-> -pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X),Xa)))) # label(fact_def__nIn) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 120 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc2085839144bnd_if(X,Xa),Xb) = scratc2008985021nd_eps(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_br(X),Xa),Xb))) # label(fact_def__if) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 121 (all X (pp(aa_TPTP_ind_bool(scratc2122773617closed,X)) <-> pp(aa_TPTP_ind_bool(scratc210010338closed,X)) & pp(aa_TPTP_ind_bool(scratc374743352closed,X)) & pp(aa_TPTP_ind_bool(scratc62112404closed,X)))) # label(fact_def__d__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 122 (all X (pp(aa_TPTP_ind_bool(scratc62112404closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X1),X)) -> (all X2 ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X3),X1)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,aa_TPTP_ind_TPTP_ind(X2,X3)),X))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2098507866d_repl,X1),X2)),X))))))))) # label(fact_def__d__Repl__closed) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 123 (all X (pp(aa_TPTP_ind_bool(scratc374743352closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,aa_TPTP_ind_TPTP_ind(scratc1162361562_power,X1)),X))))))) # label(fact_def__d__Power__closed) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 124 (all X (pp(aa_TPTP_ind_bool(scratc210010338closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,aa_TPTP_ind_TPTP_ind(scratc1669623428_union,X1)),X))))))) # label(fact_def__d__Union__closed) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 125 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc227794282d_Subq,X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X2),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X2),Xa))))))) # label(fact_def__d__Subq) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 126 (all X all Xa (pp(aa_fun171081125l_bool(scratc1105087533all_of(X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (scratc1551916972_is_of(X2,X) -> pp(aa_TPTP_ind_bool(Xa,X2))))))) # label(fact_def__all__of) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 127 (all X all Xa (scratc1551916972_is_of(X,Xa) <-> pp(aa_TPTP_ind_bool(Xa,X)))) # label(fact_def__is__of) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 128 (all X0 pp(aa_fun171081125l_bool(scratc1105087533all_of(aa_TPT43085870d_bool(aTP_Lamm_id,X0)),aa_TPT43085870d_bool(aTP_Lamm_if,X0)))) # label(fact_isseti) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 129 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1105087533all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X0)),aa_fun1584354236d_bool(aTP_Lamm_ig(X0),X12)))) # label(fact_estie) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 130 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1105087533all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X0)),aa_fun1584354236d_bool(aTP_Lamm_ih(X0),X12)))) # label(fact_estii) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 131 (all X0 all X12 scratc1551916972_is_of(aa_fun1431113780TP_ind(scratc423121125_d_Sep(X0),X12),aa_TPT43085870d_bool(aTP_Lamm_id,X0))) # label(fact_setof__p) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 132 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1105087533all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X0)),aa_TPT43085870d_bool(aTP_Lamm_ij(X0),X12)))) # label(fact_secondis1) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 133 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1105087533all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X0)),aa_TPT43085870d_bool(aTP_Lamm_il(X0),X12)))) # label(fact_firstis1) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 134 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1105087533all_of(aa_TPT43085870d_bool(aTP_Lamm_im(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_in(X0),X12)))) # label(fact_pairis1) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 135 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1105087533all_of(aa_TPT43085870d_bool(aTP_Lamm_im(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_io(X0),X12)))) # label(fact_second__p) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 136 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1105087533all_of(aa_TPT43085870d_bool(aTP_Lamm_im(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_ip(X0),X12)))) # label(fact_first__p) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 137 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1105087533all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X0)),aa_TPT43085870d_bool(aTP_Lamm_ir(X0),X12)))) # label(fact_e__pair__p) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 138 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1105087533all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X0)),aa_fun1584354236d_bool(aTP_Lamm_is(X0),X12)))) # label(fact_otax2) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 139 (all X0 all X12 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1737138012ective(aa_fun1431113780TP_ind(scratc423121125_d_Sep(X0),X12)),X0),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc149815564_Sigma,aa_fun1431113780TP_ind(scratc423121125_d_Sep(X0),X12)),scratc1709549247d_e_in(X0,X12))))) # label(fact_otax1) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 140 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1105087533all_of(aa_fun1584354236d_bool(aTP_Lamm_it(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_iu(X0),X12)))) # label(fact_e__inp) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 141 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1105087533all_of(aa_fun1584354236d_bool(aTP_Lamm_it(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_iv(X0),X12)))) # label(fact_e__in__p) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 142 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1105087533all_of(aa_TPT43085870d_bool(aTP_Lamm_iw(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_iz(X0),X12)))) # label(fact_e__fisi) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 143 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc2091468859nd_one(X0),X12)) -> pp(aa_TPTP_ind_bool(X12,scratc2041899828nd_ind(X0,X12))))) # label(fact_oneax) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 144 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc2091468859nd_one(X0),X12)) -> scratc1551916972_is_of(scratc2041899828nd_ind(X0,X12),aa_TPT43085870d_bool(aTP_Lamm_al,X0)))) # label(fact_ind__p) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 145 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1105087533all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X0)),aa_fun1584354236d_bool(aTP_Lamm_jb(X0),X12)))) # label(fact_e__isp) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 146 (all X0 pp(aa_fun171081125l_bool(scratc1105087533all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X0)),aa_TPT43085870d_bool(aTP_Lamm_jc,X0)))) # label(fact_refis) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 147 (all X0 (scratc9486867nd_wel(X0) -> pp(X0))) # label(fact_l__et) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 148 (all X0 all X12 all X22 all X32 (pp(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc2085839144bnd_if(X0,X22),X32))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X12),X22))))) # label(fact_k__If__In__then__E) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 149 (all X0 all X12 all X22 ((pp(X0) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X12),X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,aa_TPTP_ind_TPTP_ind(scratc2085839144bnd_if(X0,X12),scratc185677376ptyset)),aa_TPTP_ind_TPTP_ind(scratc2085839144bnd_if(X0,X22),aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,scratc185677376ptyset)))))) # label(fact_k__If__In__01) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 150 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X33),X0)) -> aa_TPTP_ind_TPTP_ind(X12,X33) = aa_TPTP_ind_TPTP_ind(X22,X33)))) -> aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc149815564_Sigma,X0),X12) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc149815564_Sigma,X0),X22))) # label(fact_xi__ext) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 151 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc568344978d_d_Pi,X0),X12))) -> (all X32 (gg_TPTP_ind(X32) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X32),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc568344978d_d_Pi,X0),X12))) -> ((all X42 (gg_TPTP_ind(X42) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X42),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,X22),X42) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,X32),X42)))) -> X22 = X32))))))) # label(fact_k__Pi__ext) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 152 (all X0 all X12 all X22 all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc568344978d_d_Pi,X0),X12))) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X32),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,X22),X32)),aa_TPTP_ind_TPTP_ind(X12,X32)))))) # label(fact_ap__Pi) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 153 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X33),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,aa_TPTP_ind_TPTP_ind(X22,X33)),aa_TPTP_ind_TPTP_ind(X12,X33)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc149815564_Sigma,X0),X22)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc568344978d_d_Pi,X0),X12))))) # label(fact_lam__Pi) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 154 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X22),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc149815564_Sigma,X0),X12)),X22) = aa_TPTP_ind_TPTP_ind(X12,X22))) # label(fact_beta) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 155 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc149815564_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,aa_TPTP_ind_TPTP_ind(scratc1290875401_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1290875400_proj0,X22)))))) # label(fact_proj1__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 156 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc149815564_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,aa_TPTP_ind_TPTP_ind(scratc1290875400_proj0,X22)),X0)))) # label(fact_proj0__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 157 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc149815564_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc503828261d_pair,aa_TPTP_ind_TPTP_ind(scratc1290875400_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1290875401_proj1,X22)) = X22))) # label(fact_proj__Sigma__eta) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 158 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc149815564_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc503828261d_pair,aa_TPTP_ind_TPTP_ind(scratc1290875400_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1290875401_proj1,X22)) = X22 & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,aa_TPTP_ind_TPTP_ind(scratc1290875400_proj0,X22)),X0)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,aa_TPTP_ind_TPTP_ind(scratc1290875401_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1290875400_proj0,X22))))))) # label(fact_k__Sigma__eta__proj0__proj1) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 159 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X22),X0)) -> (all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X32),aa_TPTP_ind_TPTP_ind(X12,X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc503828261d_pair,X22),X32)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc149815564_Sigma,X0),X12))))))) # label(fact_pair__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 160 (all X0 all X12 (gg_TPTP_ind(X12) -> aa_TPTP_ind_TPTP_ind(scratc1290875401_proj1,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc503828261d_pair,X0),X12)) = X12)) # label(fact_proj1__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 161 (all X0 all X12 (gg_TPTP_ind(X0) -> aa_TPTP_ind_TPTP_ind(scratc1290875400_proj0,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc503828261d_pair,X0),X12)) = X0)) # label(fact_proj0__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 162 (all X0 (pp(aa_TPTP_ind_bool(scratc1438561178_nat_p,X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X0),scratc460530614_omega)))) # label(fact_nat__p__omega) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 163 (all X0 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X0),scratc460530614_omega)) -> pp(aa_TPTP_ind_bool(scratc1438561178_nat_p,X0)))) # label(fact_omega__nat__p) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 164 (all X0 (gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(scratc1438561178_nat_p,X0)) -> X0 = scratc185677376ptyset | (exists X13 (gg_TPTP_ind(X13) & pp(aa_TPTP_ind_bool(scratc1438561178_nat_p,X13)) & X0 = aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,X13)))))) # label(fact_nat__inv) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.33 165 (all X0 (pp(aa_TPTP_ind_bool(X0,scratc185677376ptyset)) -> ((all X13 (gg_TPTP_ind(X13) -> (pp(aa_TPTP_ind_bool(scratc1438561178_nat_p,X13)) -> (pp(aa_TPTP_ind_bool(X0,X13)) -> pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,X13))))))) -> (all X12 (pp(aa_TPTP_ind_bool(scratc1438561178_nat_p,X12)) -> pp(aa_TPTP_ind_bool(X0,X12))))))) # label(fact_nat__ind) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 166 (all X0 (pp(aa_TPTP_ind_bool(scratc1438561178_nat_p,X0)) -> pp(aa_TPTP_ind_bool(scratc1438561178_nat_p,aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,X0))))) # label(fact_nat__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 167 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,X0) = aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,X12) -> X0 = X12))) # label(fact_ordsucc__inj) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 168 (all X0 aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,X0) != scratc185677376ptyset) # label(fact_neq__ordsucc__0) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 169 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X22),aa_fun1431113780TP_ind(scratc423121125_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(X12,X22)))) # label(fact_k__SepE2) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 170 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X22),aa_fun1431113780TP_ind(scratc423121125_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X22),X0)))) # label(fact_k__SepE1) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 171 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X22),X0)) -> (pp(aa_TPTP_ind_bool(X12,X22)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X22),aa_fun1431113780TP_ind(scratc423121125_d_Sep(X0),X12)))))) # label(fact_k__SepI) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 172 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc1162361562_power,X0)))) # label(fact_k__Self__In__Power) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 173 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc227794282d_Subq,X12),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1162361562_power,X0))))) # label(fact_k__PowerI) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 174 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1162361562_power,X0))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc227794282d_Subq,X12),X0)))) # label(fact_k__PowerE) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 175 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> aa_TPTP_ind_TPTP_ind(scratc2085839144bnd_if(X0,X12),X22) = X12 | aa_TPTP_ind_TPTP_ind(scratc2085839144bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__or) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 176 (all X0 all X12 all X22 (gg_TPTP_ind(X12) -> (pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc2085839144bnd_if(X0,X12),X22) = X12))) # label(fact_if__i__1) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 177 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (-pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc2085839144bnd_if(X0,X12),X22) = X22))) # label(fact_if__i__0) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 178 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> pp(X0) & aa_TPTP_ind_TPTP_ind(scratc2085839144bnd_if(X0,X12),X22) = X12 | -pp(X0) & aa_TPTP_ind_TPTP_ind(scratc2085839144bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__correct) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 179 (all X0 pp(aa_TPTP_ind_bool(scratc2122773617closed,aa_TPTP_ind_TPTP_ind(scratc1871617960univof,X0)))) # label(fact_k__UnivOf__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 180 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc1871617960univof,X0)))) # label(fact_k__UnivOf__In) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 181 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2098507866d_repl,X0),X12))) <-> (exists X3 (gg_TPTP_ind(X3) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X3),X0)) & X22 = aa_TPTP_ind_TPTP_ind(X12,X3)))))) # label(fact_k__ReplEq) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 182 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1162361562_power,X0))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc227794282d_Subq,X12),X0)))) # label(fact_k__PowerEq) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 183 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1669623428_union,X0))) <-> (exists X2 (gg_TPTP_ind(X2) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X12),X2)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X2),X0)))))) # label(fact_k__UnionEq) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 184 -(exists X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X0),scratc185677376ptyset))) # label(fact_k__EmptyAx) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 185 (all X0 ((all X13 (gg_TPTP_ind(X13) -> ((all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X22),X13)) -> pp(aa_TPTP_ind_bool(X0,X22)))) -> pp(aa_TPTP_ind_bool(X0,X13))))) -> (all X14 pp(aa_TPTP_ind_bool(X0,X14))))) # label(fact_k__In__ind) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 186 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc227794282d_Subq,X0),X12)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc227794282d_Subq,X12),X0)) -> X0 = X12)))) # label(fact_set__ext) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 187 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hs,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2082879373nd_nis,Uu),scratc1072958446nd_n_1)) -> pp(aa_fun171081125l_bool(scratc959572983n_some,aa_TPT43085870d_bool(aTP_Lamm_ah,Uu)))))) # label(fact_ATP_Olambda__1) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 188 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hr,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2082879373nd_nis,Uu),scratc1072958446nd_n_1)) -> pp(aa_fun171081125l_bool(scratc80138659_n_one,aa_TPT43085870d_bool(aTP_Lamm_ah,Uu)))))) # label(fact_ATP_Olambda__2) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 189 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ho,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uu),scratc1072958446nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,Uu))))) # label(fact_ATP_Olambda__3) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 190 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hl,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(scratc1072958446nd_n_1),Uu)),aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,Uu))))) # label(fact_ATP_Olambda__4) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 191 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hq,Uu)) <-> pp(aa_fun171081125l_bool(scratc2091468859nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc568344978d_d_Pi,scratc2082354582nd_nat),aTP_Lamm_ae)),aa_TPT43085870d_bool(aTP_Lamm_hp,Uu))))) # label(fact_ATP_Olambda__5) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 192 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hy,Uu)) <-> (pp(aa_TPTP_ind_bool(scratc1305992132_cond1,Uu)) -> (pp(aa_TPTP_ind_bool(scratc1305992133_cond2,Uu)) -> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hx,Uu))))))) # label(fact_ATP_Olambda__6) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 193 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hi,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uu),scratc1072958446nd_n_1))))) # label(fact_ATP_Olambda__7) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 194 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hf,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(scratc1072958446nd_n_1),Uu))))) # label(fact_ATP_Olambda__8) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 195 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ef,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__9) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 196 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ht,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2082879373nd_nis,aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__10) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 197 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ic,Uu)) <-> scratc1551916972_is_of(aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,Uu),aTP_Lamm_a))) # label(fact_ATP_Olambda__11) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 198 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ib,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2082879373nd_nis,aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,Uu)),scratc1072958446nd_n_1)))) # label(fact_ATP_Olambda__12) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 199 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ee,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,Uu))))) # label(fact_ATP_Olambda__13) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 200 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hw,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,Uu),aa_TPTP_ind_TPTP_ind(scratc1162361562_power,scratc2082354582nd_nat))))) # label(fact_ATP_Olambda__14) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 201 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_a,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,Uu),scratc2082354582nd_nat)))) # label(fact_ATP_Olambda__15) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 202 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ia,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hz,Uu))))) # label(fact_ATP_Olambda__16) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 203 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hv,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hu,Uu))))) # label(fact_ATP_Olambda__17) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 204 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hn,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hm,Uu))))) # label(fact_ATP_Olambda__18) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 205 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hk,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hj,Uu))))) # label(fact_ATP_Olambda__19) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 206 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hh,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hg,Uu))))) # label(fact_ATP_Olambda__20) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 207 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_he,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hd,Uu))))) # label(fact_ATP_Olambda__21) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 208 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hc,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hb,Uu))))) # label(fact_ATP_Olambda__22) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 209 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gz,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gy,Uu))))) # label(fact_ATP_Olambda__23) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 210 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gx,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gw,Uu))))) # label(fact_ATP_Olambda__24) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 211 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gv,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gu,Uu))))) # label(fact_ATP_Olambda__25) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 212 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gs,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gr,Uu))))) # label(fact_ATP_Olambda__26) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 213 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gp,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_go,Uu))))) # label(fact_ATP_Olambda__27) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 214 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gn,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gm,Uu))))) # label(fact_ATP_Olambda__28) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 215 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gj,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gi,Uu))))) # label(fact_ATP_Olambda__29) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 216 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gh,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gg,Uu))))) # label(fact_ATP_Olambda__30) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 217 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gf,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ge,Uu))))) # label(fact_ATP_Olambda__31) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 218 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gd,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gc,Uu))))) # label(fact_ATP_Olambda__32) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 219 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gb,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ga,Uu))))) # label(fact_ATP_Olambda__33) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 220 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fz,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fy,Uu))))) # label(fact_ATP_Olambda__34) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 221 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fx,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fw,Uu))))) # label(fact_ATP_Olambda__35) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 222 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fv,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fu,Uu))))) # label(fact_ATP_Olambda__36) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 223 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ft,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fs,Uu))))) # label(fact_ATP_Olambda__37) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 224 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fr,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fq,Uu))))) # label(fact_ATP_Olambda__38) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 225 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fp,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fo,Uu))))) # label(fact_ATP_Olambda__39) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 226 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fn,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fm,Uu))))) # label(fact_ATP_Olambda__40) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 227 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fl,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fk,Uu))))) # label(fact_ATP_Olambda__41) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 228 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fj,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fi,Uu))))) # label(fact_ATP_Olambda__42) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 229 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fh,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fg,Uu))))) # label(fact_ATP_Olambda__43) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 230 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ff,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fe,Uu))))) # label(fact_ATP_Olambda__44) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 231 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fd,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fc,Uu))))) # label(fact_ATP_Olambda__45) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 232 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fb,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fa,Uu))))) # label(fact_ATP_Olambda__46) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 233 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ey,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ex,Uu))))) # label(fact_ATP_Olambda__47) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 234 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ev,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eu,Uu))))) # label(fact_ATP_Olambda__48) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 235 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_es,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_er,Uu))))) # label(fact_ATP_Olambda__49) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 236 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ep,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eo,Uu))))) # label(fact_ATP_Olambda__50) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 237 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_em,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_el,Uu))))) # label(fact_ATP_Olambda__51) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 238 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ej,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ei,Uu))))) # label(fact_ATP_Olambda__52) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 239 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_eh,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eg,Uu))))) # label(fact_ATP_Olambda__53) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 240 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ed,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ec,Uu))))) # label(fact_ATP_Olambda__54) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 241 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ea,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dz,Uu))))) # label(fact_ATP_Olambda__55) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 242 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dx,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dw,Uu))))) # label(fact_ATP_Olambda__56) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 243 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_du,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dt,Uu))))) # label(fact_ATP_Olambda__57) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 244 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dr,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dq,Uu))))) # label(fact_ATP_Olambda__58) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 245 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_do,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dn,Uu))))) # label(fact_ATP_Olambda__59) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 246 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dl,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dk,Uu))))) # label(fact_ATP_Olambda__60) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 247 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dh,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dg,Uu))))) # label(fact_ATP_Olambda__61) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 248 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dd,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dc,Uu))))) # label(fact_ATP_Olambda__62) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 249 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cz,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cy,Uu))))) # label(fact_ATP_Olambda__63) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 250 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cv,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cu,Uu))))) # label(fact_ATP_Olambda__64) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 251 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cs,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cr,Uu))))) # label(fact_ATP_Olambda__65) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 252 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cp,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_co,Uu))))) # label(fact_ATP_Olambda__66) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 253 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cm,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cl,Uu))))) # label(fact_ATP_Olambda__67) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 254 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cj,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ci,Uu))))) # label(fact_ATP_Olambda__68) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 255 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cg,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cf,Uu))))) # label(fact_ATP_Olambda__69) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 256 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cd,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cc,Uu))))) # label(fact_ATP_Olambda__70) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 257 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ca,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bz,Uu))))) # label(fact_ATP_Olambda__71) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 258 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bw,Uu))))) # label(fact_ATP_Olambda__72) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 259 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bt,Uu))))) # label(fact_ATP_Olambda__73) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 260 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ad,Uu)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ac,Uu))))) # label(fact_ATP_Olambda__74) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 261 (all Uu aa_TPT494704832TP_ind(aTP_Lamm_bm,Uu) = aa_TPT494704832TP_ind(scratc2098507866d_repl,aa_TPTP_ind_TPTP_ind(scratc1461260569tminus(Uu),aa_TPTP_ind_TPTP_ind(scratc129443400d_Sing,scratc185677376ptyset)))) # label(fact_ATP_Olambda__75) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 262 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_aj,Uu)) <-> Uu != scratc185677376ptyset))) # label(fact_ATP_Olambda__76) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 263 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_bk,Uu)) <-> (exists X2 (gg_TPTP_ind(X2) & aa_TPTP_ind_TPTP_ind(scratc954551077d_Inj1,X2) = Uu))))) # label(fact_ATP_Olambda__77) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 264 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_bl,Uu)) <-> (exists X2 (gg_TPTP_ind(X2) & aa_TPTP_ind_TPTP_ind(scratc954551076d_Inj0,X2) = Uu))))) # label(fact_ATP_Olambda__78) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 265 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ge,Uu),Uua)) <-> scratc68236871_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,Uu),Uua)))) # label(fact_ATP_Olambda__79) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 266 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gc,Uu),Uua)) <-> pp(scratc2091731205nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__80) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 267 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ga,Uu),Uua)) <-> pp(scratc2008132170nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__81) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 268 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gm,Uu),Uua)) <-> scratc68236871_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc959572983n_some,aa_TPT43085870d_bool(aTP_Lamm_gk(Uu),Uua)),aa_fun171081125l_bool(scratc959572983n_some,aa_TPT43085870d_bool(aTP_Lamm_gl(Uu),Uua))))) # label(fact_ATP_Olambda__82) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 269 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gi,Uu),Uua)) <-> pp(scratc2091731205nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc959572983n_some,aa_TPT43085870d_bool(scratc1467574323ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc959572983n_some,aa_TPT43085870d_bool(scratc1467574323ffprop(Uua),Uu)))))) # label(fact_ATP_Olambda__83) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 270 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gg,Uu),Uua)) <-> pp(scratc2008132170nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc959572983n_some,aa_TPT43085870d_bool(scratc1467574323ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc959572983n_some,aa_TPT43085870d_bool(scratc1467574323ffprop(Uua),Uu)))))) # label(fact_ATP_Olambda__84) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 271 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jc,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1709549252d_e_is(Uu),Uua),Uua)))) # label(fact_ATP_Olambda__85) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 272 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hp,Uu),Uua)) <-> pp(scratc539372574_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,Uua),scratc1072958446nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,Uu)),aa_fun171081125l_bool(scratc2111830046_n_all,aa_TPT43085870d_bool(aTP_Lamm_ag,Uua)))))) # label(fact_ATP_Olambda__86) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 273 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hz,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__87) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 274 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hj,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__88) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 275 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hm,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__89) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 276 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ag,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,Uu),aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,Uu),Uua)))))) # label(fact_ATP_Olambda__90) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 277 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hu,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2082879373nd_nis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2082879373nd_nis,aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,Uua)))))) # label(fact_ATP_Olambda__91) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 278 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ai,Uu),Uua)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc2041834241nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209608d_n_in,Uua),Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209608d_n_in,aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,Uua)),Uu))))) # label(fact_ATP_Olambda__92) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 279 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gy,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uua),Uu))))) # label(fact_ATP_Olambda__93) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 280 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fy,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,Uua),Uu))))) # label(fact_ATP_Olambda__94) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 281 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fu,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc477119082moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc343135470lessis,Uua),Uu))))) # label(fact_ATP_Olambda__95) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 282 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fs,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc343135470lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc477119082moreis,Uua),Uu))))) # label(fact_ATP_Olambda__96) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 283 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fw,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,Uua),Uu))))) # label(fact_ATP_Olambda__97) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 284 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fi,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,Uu),Uua)) -> pp(scratc646837754_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc343135470lessis,Uu),Uua)))))) # label(fact_ATP_Olambda__98) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 285 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fq,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc477119082moreis,Uu),Uua)) -> pp(scratc646837754_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,Uu),Uua)))))) # label(fact_ATP_Olambda__99) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 286 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fo,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc343135470lessis,Uu),Uua)) -> pp(scratc646837754_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,Uu),Uua)))))) # label(fact_ATP_Olambda__100) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 287 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fg,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,Uu),Uua)) -> pp(scratc646837754_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc477119082moreis,Uu),Uua)))))) # label(fact_ATP_Olambda__101) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 288 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ei,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uu),Uua)),Uu)))) # label(fact_ATP_Olambda__102) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 289 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bj(Uu),Uua) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2098507866d_repl,aa_TPTP_ind_TPTP_ind(Uu,Uua)),aa_TPT1424761345TP_ind(scratc503828261d_pair,Uua))) # label(fact_ATP_Olambda__103) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 290 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_if,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aa_TPT43085870d_bool(aTP_Lamm_id,Uu)),aa_TPT43085870d_bool(aTP_Lamm_ie(Uu),Uua))))) # label(fact_ATP_Olambda__104) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 291 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hd,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,Uu)),Uua))))) # label(fact_ATP_Olambda__105) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 292 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hg,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,Uua)))))) # label(fact_ATP_Olambda__106) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 293 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fm,Uu),Uua)) <-> (pp(scratc646837754_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc343135470lessis,Uu),Uua))))) # label(fact_ATP_Olambda__107) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 294 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fe,Uu),Uua)) <-> (pp(scratc646837754_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc477119082moreis,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__108) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 295 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fc,Uu),Uua)) <-> (pp(scratc646837754_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc343135470lessis,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__109) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 296 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fk,Uu),Uua)) <-> (pp(scratc646837754_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc477119082moreis,Uu),Uua))))) # label(fact_ATP_Olambda__110) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 297 (all Uu all Uua aa_fun277296641TP_ind(aa_TPT494704832TP_ind(aTP_Lamm_bn,Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1544975027nunion(aa_TPTP_ind_TPTP_ind(scratc129443400d_Sing,scratc185677376ptyset)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2098507866d_repl,Uu),Uua))) # label(fact_ATP_Olambda__111) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 298 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gw,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2082879373nd_nis,Uua),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__112) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 299 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eg,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__113) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 300 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ah,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,Uua))))) # label(fact_ATP_Olambda__114) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 301 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_id,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,Uua),aa_TPTP_ind_TPTP_ind(scratc1162361562_power,Uu))))) # label(fact_ATP_Olambda__115) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 302 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hx,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209608d_n_in,Uua),Uu)))) # label(fact_ATP_Olambda__116) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 303 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bo,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2080780200nd_nIn,Uua),Uu)))) # label(fact_ATP_Olambda__117) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 304 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_al,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,Uua),Uu)))) # label(fact_ATP_Olambda__118) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 305 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hb,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ha(Uu),Uua))))) # label(fact_ATP_Olambda__119) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 306 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gu,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gt(Uu),Uua))))) # label(fact_ATP_Olambda__120) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 307 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gr,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gq(Uu),Uua))))) # label(fact_ATP_Olambda__121) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 308 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fa,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ez(Uu),Uua))))) # label(fact_ATP_Olambda__122) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 309 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ex,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ew(Uu),Uua))))) # label(fact_ATP_Olambda__123) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 310 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eu,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_et(Uu),Uua))))) # label(fact_ATP_Olambda__124) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 311 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_er,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eq(Uu),Uua))))) # label(fact_ATP_Olambda__125) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 312 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eo,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_en(Uu),Uua))))) # label(fact_ATP_Olambda__126) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 313 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_el,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ek(Uu),Uua))))) # label(fact_ATP_Olambda__127) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 314 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ec,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eb(Uu),Uua))))) # label(fact_ATP_Olambda__128) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 315 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dz,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dy(Uu),Uua))))) # label(fact_ATP_Olambda__129) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 316 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dw,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dv(Uu),Uua))))) # label(fact_ATP_Olambda__130) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 317 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dt,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ds(Uu),Uua))))) # label(fact_ATP_Olambda__131) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 318 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dq,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dp(Uu),Uua))))) # label(fact_ATP_Olambda__132) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 319 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dn,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dm(Uu),Uua))))) # label(fact_ATP_Olambda__133) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 320 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dk,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dj(Uu),Uua))))) # label(fact_ATP_Olambda__134) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 321 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dg,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_df(Uu),Uua))))) # label(fact_ATP_Olambda__135) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 322 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dc,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_db(Uu),Uua))))) # label(fact_ATP_Olambda__136) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 323 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cy,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cx(Uu),Uua))))) # label(fact_ATP_Olambda__137) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 324 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cu,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ct(Uu),Uua))))) # label(fact_ATP_Olambda__138) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.34 325 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cr,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cq(Uu),Uua))))) # label(fact_ATP_Olambda__139) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 326 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_co,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cn(Uu),Uua))))) # label(fact_ATP_Olambda__140) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 327 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cl,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ck(Uu),Uua))))) # label(fact_ATP_Olambda__141) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 328 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ci,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ch(Uu),Uua))))) # label(fact_ATP_Olambda__142) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 329 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cf,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ce(Uu),Uua))))) # label(fact_ATP_Olambda__143) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 330 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cc,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cb(Uu),Uua))))) # label(fact_ATP_Olambda__144) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 331 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bz,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_by(Uu),Uua))))) # label(fact_ATP_Olambda__145) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 332 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bw,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bv(Uu),Uua))))) # label(fact_ATP_Olambda__146) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 333 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bt,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bs(Uu),Uua))))) # label(fact_ATP_Olambda__147) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 334 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ac,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ab(Uu),Uua))))) # label(fact_ATP_Olambda__148) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 335 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_go,Uu),Uua)) <-> pp(scratc1769573999_amone(scratc2082354582nd_nat,aa_TPT43085870d_bool(aTP_Lamm_gk(Uu),Uua))))) # label(fact_ATP_Olambda__149) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 336 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_af(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc187713464rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,Uu),Uua))) # label(fact_ATP_Olambda__150) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 337 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bg(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1669623428_union,aa_TPTP_ind_TPTP_ind(Uu,Uua))) # label(fact_ATP_Olambda__151) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 338 (all Uu all Uua (gg_TPTP_ind(Uua) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bi,Uu),Uua)) <-> (exists X3 (gg_TPTP_ind(X3) & Uua = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc503828261d_pair,Uu),X3)))))) # label(fact_ATP_Olambda__152) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 339 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_in(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1709549252d_e_is(aa_TPTP_ind_TPTP_ind(scratc1969120206etprod(Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1225215667d_pair(Uu,Uua),aa_TPTP_ind_TPTP_ind(scratc75191877_first(Uu,Uua),Uub)),aa_TPTP_ind_TPTP_ind(scratc1162491103second(Uu,Uua),Uub))),Uub)))) # label(fact_ATP_Olambda__153) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 340 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_bq(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc2085839144bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,scratc185677376ptyset),Uub),Uu),Uua)) # label(fact_ATP_Olambda__154) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 341 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_fun1235454963TP_ind(aTP_Lamm_bp(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc2085839144bnd_if(aa_TPTP_ind_bool(Uua,Uub),Uub),scratc2008985021nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bd(Uu),Uua)))) # label(fact_ATP_Olambda__155) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 342 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aw(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc656732334d_esti(Uu),Uub),Uua)))) # label(fact_ATP_Olambda__156) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 343 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ig(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc656732334d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc423121125_d_Sep(Uu),Uua))) -> pp(aa_TPTP_ind_bool(Uua,Uub))))) # label(fact_ATP_Olambda__157) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 344 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ie(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1589174777d_incl(Uu),Uua),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1589174777d_incl(Uu),Uub),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1709549252d_e_is(aa_TPTP_ind_TPTP_ind(scratc1162361562_power,Uu)),Uua),Uub)))))) # label(fact_ATP_Olambda__158) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 345 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_io(Uu),Uua),Uub)) <-> scratc1551916972_is_of(aa_TPTP_ind_TPTP_ind(scratc1162491103second(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_al,Uua)))) # label(fact_ATP_Olambda__159) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 346 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ip(Uu),Uua),Uub)) <-> scratc1551916972_is_of(aa_TPTP_ind_TPTP_ind(scratc75191877_first(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_al,Uu)))) # label(fact_ATP_Olambda__160) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 347 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_iv(Uu),Uua),Uub)) <-> scratc1551916972_is_of(aa_TPTP_ind_TPTP_ind(scratc1709549247d_e_in(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_al,Uu)))) # label(fact_ATP_Olambda__161) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 348 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iz(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aa_TPT43085870d_bool(aTP_Lamm_iw(Uu),Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_iy(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__162) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 349 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ch(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__163) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 350 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_by(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__164) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 351 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gq(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uu),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,Uua),Uub))))) # label(fact_ATP_Olambda__165) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 352 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ce(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__166) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 353 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bv(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__167) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 354 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cb(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__168) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 355 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bs(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__169) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 356 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ha(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__170) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 357 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eb(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__171) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 358 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ds(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__172) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 359 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_en(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc477119082moreis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,Uu),Uub)))))) # label(fact_ATP_Olambda__173) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 360 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ct(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc477119082moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc477119082moreis,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__174) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 361 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cq(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc477119082moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc477119082moreis,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__175) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 362 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eq(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc477119082moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,Uu),Uub)))))) # label(fact_ATP_Olambda__176) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 363 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cn(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc343135470lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc343135470lessis,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__177) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 364 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ck(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc343135470lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc343135470lessis,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__178) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 365 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ek(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc343135470lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc343135470lessis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc343135470lessis,Uu),Uub)))))) # label(fact_ATP_Olambda__179) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 366 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ew(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc343135470lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__180) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 367 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dy(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__181) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 368 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dp(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__182) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 369 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gt(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2082879373nd_nis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2082879373nd_nis,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uu),Uub)))))) # label(fact_ATP_Olambda__183) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 370 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dv(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__184) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 371 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dm(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__185) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 372 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_et(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc343135470lessis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__186) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 373 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ez(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__187) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 374 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bd(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,Uub),Uu)) & pp(aa_TPTP_ind_bool(Uua,Uub)))) # label(fact_ATP_Olambda__188) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 375 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_is(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc32549808_image(aa_fun1431113780TP_ind(scratc423121125_d_Sep(Uu),Uua),Uu),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc149815564_Sigma,aa_fun1431113780TP_ind(scratc423121125_d_Sep(Uu),Uua)),scratc1709549247d_e_in(Uu,Uua))),Uub))))) # label(fact_ATP_Olambda__189) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 376 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ih(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc656732334d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc423121125_d_Sep(Uu),Uua)))))) # label(fact_ATP_Olambda__190) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 377 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_jb(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aa_TPT43085870d_bool(aTP_Lamm_al,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_ja(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__191) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 378 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bf(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aa_TPT43085870d_bool(aTP_Lamm_al,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_be(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__192) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 379 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ir(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aa_TPT43085870d_bool(aTP_Lamm_al,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_iq(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__193) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 380 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_il(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aa_TPT43085870d_bool(aTP_Lamm_al,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ik(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__194) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 381 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ij(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aa_TPT43085870d_bool(aTP_Lamm_al,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ii(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__195) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 382 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iw(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,Uub),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc568344978d_d_Pi,Uu),aTP_Lamm_ak(Uua)))))) # label(fact_ATP_Olambda__196) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 383 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gk(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uua),Uub))))) # label(fact_ATP_Olambda__197) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 384 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gl(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,Uua),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uu),Uub))))) # label(fact_ATP_Olambda__198) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 385 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_im(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,Uub),aa_TPTP_ind_TPTP_ind(scratc1969120206etprod(Uu),Uua))))) # label(fact_ATP_Olambda__199) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 386 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_it(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,Uub),aa_fun1431113780TP_ind(scratc423121125_d_Sep(Uu),Uua))))) # label(fact_ATP_Olambda__200) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 387 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_ay(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,Uu),Uub))) # label(fact_ATP_Olambda__201) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 388 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dj(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_di(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__202) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 389 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_df(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_de(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__203) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 390 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_db(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_da(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__204) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 391 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cx(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cw(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__205) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 392 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ab(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aa(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__206) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 393 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_iu(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(Uua,aa_TPTP_ind_TPTP_ind(scratc1709549247d_e_in(Uu,Uua),Uub))))) # label(fact_ATP_Olambda__207) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 394 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1913827119d_bool(aTP_Lamm_bh(Uu),Uua),Uub)) <-> (all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,X3),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085839152bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,Uub),X3)),aa_TPTP_ind_TPTP_ind(Uua,X3)))))))) # label(fact_ATP_Olambda__208) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 395 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_az(Uu),Uua),Uub),Uuc) = aa_TPTP_ind_TPTP_ind(scratc2085839144bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc32549808_image(Uu,Uua),Uub),Uuc),aa_TPTP_ind_TPTP_ind(scratc813570485d_soft(Uu,Uua,Uub),Uuc)),scratc185677376ptyset)) # label(fact_ATP_Olambda__209) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 396 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ik(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1709549252d_e_is(Uu),aa_TPTP_ind_TPTP_ind(scratc75191877_first(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1225215667d_pair(Uu,Uua),Uub),Uuc))),Uub)))) # label(fact_ATP_Olambda__210) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 397 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ii(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1709549252d_e_is(Uua),aa_TPTP_ind_TPTP_ind(scratc1162491103second(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1225215667d_pair(Uu,Uua),Uub),Uuc))),Uuc)))) # label(fact_ATP_Olambda__211) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 398 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ix(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1709549252d_e_is(Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,Uua),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,Uub),Uuc))))) # label(fact_ATP_Olambda__212) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 399 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_as(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc656732334d_esti(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__213) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 400 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ba(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1709549252d_e_is(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__214) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 401 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_iq(Uu),Uua),Uub),Uuc)) <-> scratc1551916972_is_of(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1225215667d_pair(Uu,Uua),Uub),Uuc),aa_TPT43085870d_bool(aTP_Lamm_im(Uu),Uua)))) # label(fact_ATP_Olambda__215) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 402 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_au(Uu),Uua),Uub),Uuc)) <-> pp(scratc1096302271d_l_ec(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc656732334d_esti(Uu),Uuc),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc656732334d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__216) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 403 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_av(Uu),Uua),Uub),Uuc)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc2041834241nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc656732334d_esti(Uu),Uuc),Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc656732334d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__217) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 404 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_iy(Uu),Uua),Uub),Uuc)) <-> (pp(aa_fun171081125l_bool(scratc1105087533all_of(aa_TPT43085870d_bool(aTP_Lamm_al,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ix(Uua),Uub),Uuc))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1709549252d_e_is(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc568344978d_d_Pi,Uu),aTP_Lamm_ak(Uua))),Uub),Uuc))))) # label(fact_ATP_Olambda__218) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 405 (all Uu all Uua all Uub all Uuc (gg_TPTP_ind(Uua) & gg_TPTP_ind(Uub) & gg_TPTP_ind(Uuc) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_br(Uu),Uua),Uub),Uuc)) <-> pp(Uu) & Uuc = Uua | -pp(Uu) & Uuc = Uub))) # label(fact_ATP_Olambda__219) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 406 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aa(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__220) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 407 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_di(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__221) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 408 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_de(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc545295360_29_ii,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uuc),Uua))))))) # label(fact_ATP_Olambda__222) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 409 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_da(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__223) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 410 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cw(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1228209613d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2041571838nd_iii,aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1228668799d_n_pl(Uuc),Uua))))))) # label(fact_ATP_Olambda__224) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 411 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_ja(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1709549252d_e_is(Uu),Uub),Uuc)) -> pp(aa_TPTP_ind_bool(Uua,Uuc)))))) # label(fact_ATP_Olambda__225) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 412 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_be(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(Uua,Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1709549252d_e_is(Uu),Uub),Uuc)))))) # label(fact_ATP_Olambda__226) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 413 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bc(Uu),Uua),Uub),Uuc)) <-> pp(aa_fun171081125l_bool(scratc1975676598nd_all(Uu),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_bb(Uu),Uua),Uub),Uuc))))) # label(fact_ATP_Olambda__227) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 414 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_at(Uu),Uua),Uub),Uuc)) <-> pp(aa_fun171081125l_bool(scratc215748341l_some(Uua),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_as(Uu),Uub),Uuc))))) # label(fact_ATP_Olambda__228) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 415 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_bb(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc2041834241nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1709549252d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,Uub),Uud))),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1709549252d_e_is(Uu),Uuc),Uud))))) # label(fact_ATP_Olambda__229) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 416 (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_aq(Uu),Uua),Uub),Uuc),Uud)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1709549252d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,Uub),Uud)))))) # label(fact_ATP_Olambda__230) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 417 (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(scratc1105087533all_of(aa_TPT43085870d_bool(aTP_Lamm_al,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_ao(Uu),Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__231) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 418 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ar(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aa_TPT43085870d_bool(aTP_Lamm_al,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_aq(Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__232) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 419 (all Uu all Uua all Uub all Uuc all Uud aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_ax(Uu),Uua),Uub),Uuc),Uud) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,aa_TPTP_ind_TPTP_ind(scratc403275172wissel(Uu,Uub),Uuc)),Uud))) # label(fact_ATP_Olambda__233) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 420 (all Uu all Uua all Uub all Uuc all Uud all Uue (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_ao(Uu),Uua),Uub),Uuc),Uud),Uue)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aa_TPT43085870d_bool(aTP_Lamm_al,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_an(Uu),Uua),Uub),Uuc),Uud),Uue))))) # label(fact_ATP_Olambda__234) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 421 (all Uu all Uua all Uub all Uuc all Uud all Uue all Uuf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_am(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uue),Uuf)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1709549252d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,Uub),Uuc)),Uue)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2085314362bnd_ap,Uub),Uud)),Uuf))))))) # label(fact_ATP_Olambda__235) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 422 (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_an(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)) <-> pp(aa_fun171081125l_bool(scratc1105087533all_of(aa_TPT43085870d_bool(aTP_Lamm_al,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_am(Uua),Uub),Uuc),Uud),Uue),Uuf))))) # label(fact_ATP_Olambda__236) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 423 (all Uu all Uua (gg_TPTP_ind(Uu) -> aa_TPTP_ind_TPTP_ind(aTP_Lamm_ak(Uu),Uua) = Uu)) # label(fact_ATP_Olambda__237) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 424 (all Uu aa_TPTP_ind_TPTP_ind(aTP_Lamm_ae,Uu) = scratc2082354582nd_nat) # label(fact_ATP_Olambda__238) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 425 (all P all Q (-pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)) | pp(Q))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 426 (all P all Q (-pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)) | pp(P))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 427 (all P all Q (-pp(P) | -pp(Q) | pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 428 (all P (gg_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 429 (all P all Q (-pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) | -pp(P) | pp(Q))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 430 (all Q all P (-pp(Q) | pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)))) # label(help_fimplies_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 431 (all P all Q (pp(P) | pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)))) # label(help_fimplies_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 432 (all P all X7 (-pp(aa_TPTP_ind_bool(P,X7)) | pp(fEx_TPTP_ind(P)))) # label(help_fEx_1_1_fEx_001t__TPTP____Interpret__Oind_U) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 433 (all X7 all Y (X7 != Y | pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)))) # label(help_fequal_2_1_fequal_001t__TPTP____Interpret__Oind_T) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 434 (all X7 all Y (gg_TPTP_ind(X7) & gg_TPTP_ind(Y) -> -pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) | X7 = Y)) # label(help_fequal_1_1_fequal_001t__TPTP____Interpret__Oind_T) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 435 (all P all Q all R aa_TPTP_ind_bool(cOMBS_2003118649l_bool(P,Q),R) = aa_bool_bool(aa_TPT2142672771l_bool(P,R),aa_TPTP_ind_bool(Q,R))) # label(help_COMBS_1_1_COMBS_001t__TPTP____Interpret__Oind_001t__HOL__Obool_001t__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 436 (all P all Q all R aa_TPTP_ind_bool(aa_TPT43085870d_bool(cOMBC_1555011498d_bool(P),Q),R) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind_001t__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.35 437 (all P all Q all R aa_TPT2142672771l_bool(cOMBB_658106424TP_ind(P,Q),R) = aa_boo1142376798l_bool(P,aa_TPTP_ind_bool(Q,R))) # label(help_COMBB_1_1_COMBB_001t__HOL__Obool_001t__fun_It__HOL__Obool_Mt__HOL__Obool_J_001t__TPTP____Interpret__Oind_U) # label(axiom) # label(non_clause). [assumption].
% 1.00/1.42
% 1.00/1.42 ============================== end of process non-clausal formulas ===
% 1.00/1.42
% 1.00/1.42 ============================== PROCESS INITIAL CLAUSES ===============
% 1.00/1.42
% 1.00/1.42 ============================== PREDICATE ELIMINATION =================
% 1.00/1.42 438 -gg_bool(A) | A = fTrue | A = fFalse # label(help_fFalse_1_1_T) # label(axiom). [clausify(428)].
% 1.00/1.42 439 gg_bool(undefined_bool(bool)) # label(gsy_c_HOL_Oundefined_001t__HOL__Obool) # label(axiom). [assumption].
% 1.00/1.42 440 gg_bool(scratc1769573999_amone(A,B)) # label(gsy_c_Scratch__tptp__translate__48475__25370_ONUM686__thf__4__p_Obnd__amone) # label(axiom). [clausify(1)].
% 1.00/1.42 441 gg_bool(scratc539372574_d_and(A,B)) # label(gsy_c_Scratch__tptp__translate__48475__25370_ONUM686__thf__4__p_Obnd__d__and) # label(axiom). [clausify(2)].
% 1.00/1.42 442 gg_bool(scratc646837754_d_not(A)) # label(gsy_c_Scratch__tptp__translate__48475__25370_ONUM686__thf__4__p_Obnd__d__not) # label(axiom). [clausify(3)].
% 1.00/1.42 443 gg_bool(scratc2008132170nd_ec3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__48475__25370_ONUM686__thf__4__p_Obnd__ec3) # label(axiom). [clausify(4)].
% 1.00/1.42 444 gg_bool(scratc1096302271d_l_ec(A,B)) # label(gsy_c_Scratch__tptp__translate__48475__25370_ONUM686__thf__4__p_Obnd__l__ec) # label(axiom). [clausify(8)].
% 1.00/1.42 445 gg_bool(scratc2091731205nd_or3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__48475__25370_ONUM686__thf__4__p_Obnd__or3) # label(axiom). [clausify(9)].
% 1.00/1.42 446 gg_bool(aa_bool_bool(A,B)) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom). [clausify(10)].
% 1.00/1.42 447 gg_bool(aa_TPTP_ind_bool(A,B)) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom). [clausify(11)].
% 1.00/1.42 448 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(13)].
% 1.00/1.42 449 gg_bool(fEx_TPTP_ind(A)) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom). [clausify(16)].
% 1.00/1.42 450 gg_bool(fFalse) # label(gsy_c_fFalse) # label(axiom). [assumption].
% 1.00/1.42 451 gg_bool(fTrue) # label(gsy_c_fTrue) # label(axiom). [assumption].
% 1.00/1.42 Derived: undefined_bool(bool) = fTrue | undefined_bool(bool) = fFalse. [resolve(438,a,439,a)].
% 1.00/1.42 Derived: scratc1769573999_amone(A,B) = fTrue | scratc1769573999_amone(A,B) = fFalse. [resolve(438,a,440,a)].
% 1.00/1.42 Derived: scratc539372574_d_and(A,B) = fTrue | scratc539372574_d_and(A,B) = fFalse. [resolve(438,a,441,a)].
% 1.00/1.42 Derived: scratc646837754_d_not(A) = fTrue | scratc646837754_d_not(A) = fFalse. [resolve(438,a,442,a)].
% 1.00/1.42 Derived: scratc2008132170nd_ec3(A,B,C) = fTrue | scratc2008132170nd_ec3(A,B,C) = fFalse. [resolve(438,a,443,a)].
% 1.00/1.42 Derived: scratc1096302271d_l_ec(A,B) = fTrue | scratc1096302271d_l_ec(A,B) = fFalse. [resolve(438,a,444,a)].
% 1.00/1.42 Derived: scratc2091731205nd_or3(A,B,C) = fTrue | scratc2091731205nd_or3(A,B,C) = fFalse. [resolve(438,a,445,a)].
% 1.00/1.42 Derived: aa_bool_bool(A,B) = fTrue | aa_bool_bool(A,B) = fFalse. [resolve(438,a,446,a)].
% 1.00/1.42 Derived: aa_TPTP_ind_bool(A,B) = fTrue | aa_TPTP_ind_bool(A,B) = fFalse. [resolve(438,a,447,a)].
% 1.00/1.42 Derived: aa_fun171081125l_bool(A,B) = fTrue | aa_fun171081125l_bool(A,B) = fFalse. [resolve(438,a,448,a)].
% 1.00/1.42 Derived: fEx_TPTP_ind(A) = fTrue | fEx_TPTP_ind(A) = fFalse. [resolve(438,a,449,a)].
% 1.00/1.42 Derived: fFalse = fTrue | fFalse = fFalse. [resolve(438,a,450,a)].
% 1.00/1.42 Derived: fTrue = fTrue | fTrue = fFalse. [resolve(438,a,451,a)].
% 1.00/1.42 452 scratc1491237061d_r_ec(A,B) | pp(A) # label(fact_def__r__ec) # label(axiom). [clausify(59)].
% 1.00/1.42 453 -scratc1491237061d_r_ec(A,B) | -pp(A) | pp(scratc646837754_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(59)].
% 1.00/1.42 454 scratc1491237061d_r_ec(A,B) | -pp(scratc646837754_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(59)].
% 1.00/1.42 455 scratc1433514024_l_iff(A,B) | -pp(scratc539372574_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc2041834241nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc2041834241nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(91)].
% 1.57/1.88 456 -scratc1433514024_l_iff(A,B) | pp(scratc539372574_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc2041834241nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc2041834241nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(91)].
% 1.57/1.88 457 scratc2010907884d_orec(A,B) | -pp(scratc539372574_d_and(aa_bool_bool(scratc1096958276d_l_or(A),B),scratc1096302271d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(92)].
% 1.57/1.88 458 -scratc2010907884d_orec(A,B) | pp(scratc539372574_d_and(aa_bool_bool(scratc1096958276d_l_or(A),B),scratc1096302271d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(92)].
% 1.57/1.88 459 scratc9486867nd_wel(A) | -pp(scratc646837754_d_not(scratc646837754_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(97)].
% 1.57/1.88 460 -scratc9486867nd_wel(A) | pp(scratc646837754_d_not(scratc646837754_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(97)].
% 1.57/1.88 461 -scratc9486867nd_wel(A) | pp(A) # label(fact_l__et) # label(axiom). [clausify(147)].
% 1.57/1.88 Derived: pp(A) | -pp(scratc646837754_d_not(scratc646837754_d_not(A))). [resolve(461,a,459,a)].
% 1.57/1.88
% 1.57/1.88 ============================== end predicate elimination =============
% 1.57/1.88
% 1.57/1.88 Auto_denials: (non-Horn, no changes).
% 1.57/1.88
% 1.57/1.88 Term ordering decisions:
% 1.57/1.88 Function symbol KB weights: aTP_Lamm_a=1. scratc2085839152bnd_in=1. scratc1228209613d_n_is=1. scratc187713464rdsucc=1. scratc2041571838nd_iii=1. scratc545295360_29_ii=1. scratc2085314362bnd_ap=1. aTP_Lamm_al=1. scratc185677376ptyset=1. scratc343135470lessis=1. scratc149815564_Sigma=1. scratc2082879373nd_nis=1. scratc477119082moreis=1. scratc1072958446nd_n_1=1. fFalse=1. scratc1162361562_power=1. scratc1438561178_nat_p=1. scratc2082354582nd_nat=1. scratc568344978d_d_Pi=1. scratc959572983n_some=1. scratc2041834241nd_imp=1. scratc2098507866d_repl=1. fTrue=1. scratc503828261d_pair=1. scratc227794282d_Subq=1. scratc1290875400_proj0=1. scratc1669623428_union=1. scratc62112404closed=1. aTP_Lamm_ah=1. scratc1228209608d_n_in=1. scratc1290875401_proj1=1. scratc2111830046_n_all=1. aTP_Lamm_ae=1. aTP_Lamm_ag=1. aTP_Lamm_id=1. scratc210010338closed=1. scratc374743352closed=1. aTP_Lamm_fc=1. aTP_Lamm_fe=1. aTP_Lamm_fg=1. aTP_Lamm_fi=1. aTP_Lamm_fk=1. aTP_Lamm_fm=1. aTP_Lamm_fo=1. aTP_Lamm_fq=1. aTP_Lamm_fs=1. aTP_Lamm_fu=1. aTP_Lamm_fw=1. aTP_Lamm_fy=1. aTP_Lamm_hu=1. aTP_Lamm_hy=1. aTP_Lamm_hz=1. scratc2122773617closed=1. scratc2140979124_prop2=1. scratc460530614_omega=1. scratc954551077d_Inj1=1. aTP_Lamm_ac=1. aTP_Lamm_ai=1. aTP_Lamm_bi=1. aTP_Lamm_bk=1. aTP_Lamm_bl=1. aTP_Lamm_bt=1. aTP_Lamm_bw=1. aTP_Lamm_bz=1. aTP_Lamm_cc=1. aTP_Lamm_cf=1. aTP_Lamm_ci=1. aTP_Lamm_cl=1. aTP_Lamm_co=1. aTP_Lamm_cr=1. aTP_Lamm_cu=1. aTP_Lamm_cy=1. aTP_Lamm_dc=1. aTP_Lamm_dg=1. aTP_Lamm_dk=1. aTP_Lamm_dn=1. aTP_Lamm_dq=1. aTP_Lamm_dt=1. aTP_Lamm_dw=1. aTP_Lamm_dz=1. aTP_Lamm_ec=1. aTP_Lamm_eg=1. aTP_Lamm_ei=1. aTP_Lamm_el=1. aTP_Lamm_eo=1. aTP_Lamm_er=1. aTP_Lamm_eu=1. aTP_Lamm_ex=1. aTP_Lamm_fa=1. aTP_Lamm_ga=1. aTP_Lamm_gc=1. aTP_Lamm_ge=1. aTP_Lamm_gg=1. aTP_Lamm_gi=1. aTP_Lamm_gm=1. aTP_Lamm_go=1. aTP_Lamm_gr=1. aTP_Lamm_gu=1. aTP_Lamm_gw=1. aTP_Lamm_gy=1. aTP_Lamm_hb=1. aTP_Lamm_hd=1. aTP_Lamm_hg=1. aTP_Lamm_hj=1. aTP_Lamm_hm=1. aTP_Lamm_hp=1. aTP_Lamm_hr=1. aTP_Lamm_hs=1. aTP_Lamm_hx=1. fconj=1. fimplies=1. scratc129443400d_Sing=1. scratc1305992133_cond2=1. scratc2140979123_prop1=1. scratc954551076d_Inj0=1. aTP_Lamm_bo=1. aTP_Lamm_bu=1. aTP_Lamm_bx=1. aTP_Lamm_ca=1. aTP_Lamm_cd=1. aTP_Lamm_cg=1. aTP_Lamm_cj=1. aTP_Lamm_cm=1. aTP_Lamm_cp=1. aTP_Lamm_cs=1. aTP_Lamm_cv=1. aTP_Lamm_cz=1. aTP_Lamm_dd=1. aTP_Lamm_dh=1. aTP_Lamm_dl=1. aTP_Lamm_do=1. aTP_Lamm_dr=1. aTP_Lamm_du=1. aTP_Lamm_dx=1. aTP_Lamm_ea=1. aTP_Lamm_ed=1. aTP_Lamm_ee=1. aTP_Lamm_ef=1. aTP_Lamm_eh=1. aTP_Lamm_ej=1. aTP_Lamm_em=1. aTP_Lamm_ep=1. aTP_Lamm_es=1. aTP_Lamm_ev=1. aTP_Lamm_ey=1. aTP_Lamm_fb=1. aTP_Lamm_fd=1. aTP_Lamm_ff=1. aTP_Lamm_fh=1. aTP_Lamm_fj=1. aTP_Lamm_fl=1. aTP_Lamm_fn=1. aTP_Lamm_fp=1. aTP_Lamm_fr=1. aTP_Lamm_ft=1. aTP_Lamm_fv=1. aTP_Lamm_fx=1. aTP_Lamm_fz=1. aTP_Lamm_gb=1. aTP_Lamm_gd=1. aTP_Lamm_gf=1. aTP_Lamm_gh=1. aTP_Lamm_gj=1. aTP_Lamm_gn=1. aTP_Lamm_gp=1. aTP_Lamm_gs=1. aTP_Lamm_gv=1. aTP_Lamm_gx=1. aTP_Lamm_gz=1. aTP_Lamm_hc=1. aTP_Lamm_he=1. aTP_Lamm_hf=1. aTP_Lamm_hh=1. aTP_Lamm_hi=1. aTP_Lamm_hk=1. aTP_Lamm_hl=1. aTP_Lamm_hn=1. aTP_Lamm_ho=1. aTP_Lamm_hq=1. aTP_Lamm_ht=1. aTP_Lamm_hv=1. aTP_Lamm_hw=1. aTP_Lamm_ia=1. aTP_Lamm_ib=1. aTP_Lamm_ic=1. aTP_Lamm_if=1. aTP_Lamm_jc=1. fequal_TPTP_ind=1. scratc1305992132_cond1=1. scratc1871617960univof=1. scratc2080780200nd_nIn=1. scratc440234520_d_Unj=1. scratc80138659_n_one=1. aTP_Lamm_ad=1. aTP_Lamm_aj=1. aTP_Lamm_bm=1. aTP_Lamm_bn=1. bool=1. scratc1170219825_prop1=1. scratc1291268998_prop4=1. scratc1552616948_prop1=1. scratc1758582000_prop1=1. scratc2041518978_empty=1. scratc44463435pair_p=1. scratc471272363nempty=1. scratc551117928munion=1. scratc595492005d_plus=1. scratc787822702_prop1=1. scratc964254773_prop1=1. scratc424910336d_i1_s=1. scratc562957036d_24_g=1. tPTP_ind=1. aa_TPT43085870d_bool=1. aa_TPTP_ind_bool=1. aa_TPTP_ind_TPTP_ind=1. aa_fun171081125l_bool=1. aa_TPT60673477d_bool=1. aa_TPT1424761345TP_ind=1. aa_fun277296641TP_ind=1. aa_TPT494704832TP_ind=1. aa_bool_bool=1. aa_fun1584354236d_bool=1. aa_fun1431113780TP_ind=1. aa_boo1142376798l_bool=1. scratc539372574_d_and=1. aa_TPT1123896796d_bool=1. scratc2085839144bnd_if=1. scratc1096302271d_l_ec=1. aa_fun1212484691d_bool=1. aa_TPT985247859d_bool=1. scratc1709549247d_e_in=1. scratc1225215667d_pair=1. aa_fun987228051d_bool=1. scratc1769573999_amone=1. scratc2041899828nd_ind=1. scratc1162491103second=1. scratc32549808_image=1. scratc75191877_first=1. aa_TPT125613450d_bool=1. scratc2083272962nd_non=1. aa_fun1913827119d_bool=1. scratc1787059318d_anec=1. aa_TPT1791839040TP_ind=1. aa_fun1107270209d_bool=1. aa_fun845057962d_bool=1. scratc1968344598eplSep=1. scratc2008132231nd_ecp=1. scratc586696580_ecelt=1. scratc586106189_ecect=1. aa_TPT1781712639TP_ind=1. aa_TPT2142672771l_bool=1. aa_fun1235454963TP_ind=1. cOMBB_658106424TP_ind=1. cOMBS_2003118649l_bool=1. scratc123908121_fixfu=1. scratc1404884024etprop=1. scratc2008132235nd_ect=1. scratc2091928067nd_out=1. scratc23221849fixfu2=1. scratc403275172wissel=1. scratc535248375ectset=1. scratc1590421152d_invf=1. scratc1594157683d_tofs=1. scratc1733444805nverse=1. scratc420046498ectelt=1. scratc641365721unmore=1. f1=1. f12=1. f13=1. f20=1. f24=1. scratc1105087533all_of=1. scratc1228668799d_n_pl=1. scratc1709549252d_e_is=1. scratc646837754_d_not=1. scratc423121125_d_Sep=1. scratc656732334d_esti=1. scratc215748341l_some=1. scratc1467574323ffprop=1. scratc1975676598nd_all=1. scratc1096958276d_l_or=1. scratc1824249717_rec_G=1. aTP_Lamm_ak=1. aTP_Lamm_im=1. scratc2091468859nd_one=1. aTP_Lamm_aa=1. aTP_Lamm_am=1. aTP_Lamm_aw=1. aTP_Lamm_be=1. aTP_Lamm_br=1. aTP_Lamm_cw=1. aTP_Lamm_da=1. aTP_Lamm_de=1. aTP_Lamm_di=1. aTP_Lamm_ek=1. aTP_Lamm_en=1. aTP_Lamm_eq=1. aTP_Lamm_et=1. aTP_Lamm_ew=1. aTP_Lamm_ez=1. aTP_Lamm_gk=1. aTP_Lamm_ie=1. aTP_Lamm_ja=1. scratc1589174777d_incl=1. aTP_Lamm_aq=1. aTP_Lamm_ba=1. aTP_Lamm_bd=1. aTP_Lamm_bh=1. aTP_Lamm_bs=1. aTP_Lamm_bv=1. aTP_Lamm_by=1. aTP_Lamm_cb=1. aTP_Lamm_ce=1. aTP_Lamm_ch=1. aTP_Lamm_ck=1. aTP_Lamm_cn=1. aTP_Lamm_cq=1. aTP_Lamm_ct=1. aTP_Lamm_dm=1. aTP_Lamm_dp=1. aTP_Lamm_ds=1. aTP_Lamm_dv=1. aTP_Lamm_dy=1. aTP_Lamm_eb=1. aTP_Lamm_gq=1. aTP_Lamm_gt=1. aTP_Lamm_iw=1. aTP_Lamm_iy=1. scratc1737138012ective=1. scratc1969120206etprod=1. scratc2008985021nd_eps=1. aTP_Lamm_ab=1. aTP_Lamm_an=1. aTP_Lamm_ao=1. aTP_Lamm_ap=1. aTP_Lamm_ar=1. aTP_Lamm_as=1. aTP_Lamm_au=1. aTP_Lamm_av=1. aTP_Lamm_bb=1. aTP_Lamm_bc=1. aTP_Lamm_bf=1. aTP_Lamm_cx=1. aTP_Lamm_db=1. aTP_Lamm_df=1. aTP_Lamm_dj=1. aTP_Lamm_gl=1. aTP_Lamm_ha=1. aTP_Lamm_ig=1. aTP_Lamm_ih=1. aTP_Lamm_ii=1. aTP_Lamm_ik=1. aTP_Lamm_iq=1. aTP_Lamm_is=1. aTP_Lamm_it=1. aTP_Lamm_ix=1. fEx_TPTP_ind=1. scratc1544975027nunion=1. scratc940629319ective=1. aTP_Lamm_at=1. aTP_Lamm_ij=1. aTP_Lamm_il=1. aTP_Lamm_in=1. aTP_Lamm_io=1. aTP_Lamm_ip=1. aTP_Lamm_ir=1. aTP_Lamm_iu=1. aTP_Lamm_iv=1. aTP_Lamm_iz=1. aTP_Lamm_jb=1. scratc1696108178In_rec=1. scratc44301942_UPair=1. aTP_Lamm_af=1. aTP_Lamm_ax=1.Cputime limit exceeded (core dumped)
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