TSTP Solution File: NUM698+4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM698+4 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 13:30:51 EDT 2022
% Result : Timeout 300.01s 300.34s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM698+4 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jul 5 20:44:03 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.05/1.37 ============================== Prover9 ===============================
% 1.05/1.37 Prover9 (32) version 2009-11A, November 2009.
% 1.05/1.37 Process 22143 was started by sandbox on n021.cluster.edu,
% 1.05/1.37 Tue Jul 5 20:44:04 2022
% 1.05/1.37 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_21973_n021.cluster.edu".
% 1.05/1.37 ============================== end of head ===========================
% 1.05/1.37
% 1.05/1.37 ============================== INPUT =================================
% 1.05/1.37
% 1.05/1.37 % Reading from file /tmp/Prover9_21973_n021.cluster.edu
% 1.05/1.37
% 1.05/1.37 set(prolog_style_variables).
% 1.05/1.37 set(auto2).
% 1.05/1.37 % set(auto2) -> set(auto).
% 1.05/1.37 % set(auto) -> set(auto_inference).
% 1.05/1.37 % set(auto) -> set(auto_setup).
% 1.05/1.37 % set(auto_setup) -> set(predicate_elim).
% 1.05/1.37 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.05/1.37 % set(auto) -> set(auto_limits).
% 1.05/1.37 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.05/1.37 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.05/1.37 % set(auto) -> set(auto_denials).
% 1.05/1.37 % set(auto) -> set(auto_process).
% 1.05/1.37 % set(auto2) -> assign(new_constants, 1).
% 1.05/1.37 % set(auto2) -> assign(fold_denial_max, 3).
% 1.05/1.37 % set(auto2) -> assign(max_weight, "200.000").
% 1.05/1.37 % set(auto2) -> assign(max_hours, 1).
% 1.05/1.37 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.05/1.37 % set(auto2) -> assign(max_seconds, 0).
% 1.05/1.37 % set(auto2) -> assign(max_minutes, 5).
% 1.05/1.37 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.05/1.37 % set(auto2) -> set(sort_initial_sos).
% 1.05/1.37 % set(auto2) -> assign(sos_limit, -1).
% 1.05/1.37 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.05/1.37 % set(auto2) -> assign(max_megs, 400).
% 1.05/1.37 % set(auto2) -> assign(stats, some).
% 1.05/1.37 % set(auto2) -> clear(echo_input).
% 1.05/1.37 % set(auto2) -> set(quiet).
% 1.05/1.37 % set(auto2) -> clear(print_initial_clauses).
% 1.05/1.37 % set(auto2) -> clear(print_given).
% 1.05/1.37 assign(lrs_ticks,-1).
% 1.05/1.37 assign(sos_limit,10000).
% 1.05/1.37 assign(order,kbo).
% 1.05/1.37 set(lex_order_vars).
% 1.05/1.37 clear(print_given).
% 1.05/1.37
% 1.05/1.37 % formulas(sos). % not echoed (586 formulas)
% 1.05/1.37
% 1.05/1.37 ============================== end of input ==========================
% 1.05/1.37
% 1.05/1.37 % From the command line: assign(max_seconds, 300).
% 1.05/1.37
% 1.05/1.37 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.05/1.37
% 1.05/1.37 % Formulas that are not ordinary clauses:
% 1.05/1.37 1 (all B_1 all B_2 gg_bool(scratc1652025587_amone(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__50955__26514_ONUM698__thf__4__p_Obnd__amone) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 2 (all B_1 all B_2 gg_bool(scratc1094873754_d_and(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__50955__26514_ONUM698__thf__4__p_Obnd__d__and) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 3 (all B_1 gg_bool(scratc1202338934_d_not(B_1))) # label(gsy_c_Scratch__tptp__translate__50955__26514_ONUM698__thf__4__p_Obnd__d__not) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 4 (all B_1 all B_2 all B_3 gg_bool(scratc1478362830nd_ec3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__50955__26514_ONUM698__thf__4__p_Obnd__ec3) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 5 (all B_1 all B_2 gg_TPTP_ind(scratc1478362895nd_ect(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__50955__26514_ONUM698__thf__4__p_Obnd__ect) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 6 (all B_1 gg_TPTP_ind(scratc1479215681nd_eps(B_1))) # label(gsy_c_Scratch__tptp__translate__50955__26514_ONUM698__thf__4__p_Obnd__eps) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 7 (all B_1 all B_2 gg_TPTP_ind(scratc1512130488nd_ind(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__50955__26514_ONUM698__thf__4__p_Obnd__ind) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 8 (all B_1 all B_2 gg_bool(scratc978753859d_l_ec(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__50955__26514_ONUM698__thf__4__p_Obnd__l__ec) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 9 (all B_1 all B_2 all B_3 gg_bool(scratc1561961865nd_or3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__50955__26514_ONUM698__thf__4__p_Obnd__or3) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 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].
% 1.05/1.37 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].
% 1.05/1.37 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].
% 1.05/1.37 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].
% 1.05/1.37 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].
% 1.05/1.37 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].
% 1.05/1.37 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].
% 1.05/1.37 17 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc898636650lessis,X),Xa)) <-> pp(aa_bool_bool(scratc979409864d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,X),Xa))))) # label(fact_def__lessis) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 18 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032620262moreis,X),Xa)) <-> pp(aa_bool_bool(scratc979409864d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,X),Xa))))) # label(fact_def__moreis) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 19 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1611924714_prop1,X),Xa)) <-> pp(scratc1561961865nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,X),Xa))))) # label(fact_def__d__29__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 20 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc631456891n_some,aa_TPT43085870d_bool(scratc1608659119ffprop(Xa),X))))) # label(fact_def__iii) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 21 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc631456891n_some,aa_TPT43085870d_bool(scratc1608659119ffprop(X),Xa))))) # label(fact_def__d__29__ii) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 22 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1608659119ffprop(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,X),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Xa),Xb))))) # label(fact_def__diffprop) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 23 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1023562539_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1553110033nd_nis,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(X),Xb))))) # label(fact_def__d__28__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 24 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc435200364_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1553110033nd_nis,Xa),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(X),Xa))))) # label(fact_def__d__27__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 25 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1994321837_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Xa),X))))) # label(fact_def__d__26__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 26 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1405959662_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(X),Xa)),Xb)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(X),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Xa),Xb)))))) # label(fact_def__d__25__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 27 (all X scratc1111120387d_n_pl(X) = aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,aa_TPTP_ind_TPTP_ind(scratc984432929d_plus,X))) # label(fact_def__n__pl) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 28 (all X aa_TPTP_ind_TPTP_ind(scratc984432929d_plus,X) = scratc1512130488nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc450796566d_d_Pi,scratc1552585242nd_nat),aTP_Lamm_ac),aa_TPT43085870d_bool(scratc817597488_prop2,X))) # label(fact_def__plus) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 29 (all X aa_TPTP_ind_TPTP_ind(scratc704041832d_24_g,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc290900360_Sigma,scratc1552585242nd_nat),aTP_Lamm_ad(X))) # label(fact_def__d__24__g) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 30 (all X (pp(aa_TPTP_ind_bool(scratc1173720586_prop4,X)) <-> pp(aa_fun171081125l_bool(scratc2035115897l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc450796566d_d_Pi,scratc1552585242nd_nat),aTP_Lamm_ac)),aa_TPT43085870d_bool(scratc817597488_prop2,X))))) # label(fact_def__prop4) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 31 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1173720585_prop3(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,X),Xb)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,Xa),Xb))))) # label(fact_def__prop3) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 32 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc817597488_prop2,X),Xa)) <-> pp(scratc1094873754_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,Xa),scratc1461899370nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,X)),aa_TPTP_ind_bool(scratc817597487_prop1,Xa))))) # label(fact_def__d__24__prop2) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 33 (all X (pp(aa_TPTP_ind_bool(scratc817597487_prop1,X)) <-> pp(aa_fun171081125l_bool(scratc519847578_n_all,aa_TPT43085870d_bool(aTP_Lamm_ae,X))))) # label(fact_def__d__24__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 34 (all X (pp(aa_TPTP_ind_bool(scratc229235312_prop1,X)) <-> pp(aa_bool_bool(scratc979409864d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,X),scratc1461899370nd_n_1)),aa_fun171081125l_bool(scratc631456891n_some,aa_TPT43085870d_bool(aTP_Lamm_af,X)))))) # label(fact_def__d__23__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 35 (all X (pp(aa_TPTP_ind_bool(scratc1788356785_prop1,X)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1553110033nd_nis,aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,X)),X)))) # label(fact_def__d__22__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 36 (all X (pp(aa_TPTP_ind_bool(scratc1188443721_cond2,X)) <-> pp(aa_fun171081125l_bool(scratc519847578_n_all,aa_TPT43085870d_bool(aTP_Lamm_ag,X))))) # label(fact_def__cond2) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 37 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1553110033nd_nis,X),Xa)) <-> pp(scratc1202338934_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,X),Xa))))) # label(fact_def__nis) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 38 (all X all Xa all Xb all Xc all Xd scratc362232878indeq2(X,Xa,Xb,Xc,Xd) = aa_TPT1424761345TP_ind(scratc720241924_indeq(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1517683244d_11_i(X,Xa,Xb),Xc),Xd))) # label(fact_def__indeq2) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 39 (all X all Xa all Xb scratc1517683244d_11_i(X,Xa,Xb) = scratc720241924_indeq(X,Xa,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc450796566d_d_Pi,X),aTP_Lamm_ai(Xb)))) # label(fact_def__d__11__i) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 40 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc578723029fixfu2(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_an(X),Xa),Xb),Xc))))) # label(fact_def__fixfu2) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 41 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc720241924_indeq(X,Xa,Xb),Xc),Xd) = scratc1512130488nd_ind(Xb,aa_TPT43085870d_bool(scratc1173720584_prop2(X,Xa,Xb,Xc),Xd))) # label(fact_def__indeq) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 42 (all X all Xa all Xb all Xc all Xd all Xe (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1173720584_prop2(X,Xa,Xb,Xc),Xd),Xe)) <-> pp(aa_fun171081125l_bool(scratc2035115897l_some(X),aa_TPT43085870d_bool(scratc1364920114_prop1(X,Xa,Xb,Xc,Xd),Xe))))) # label(fact_def__prop2) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 43 (all X all Xa all Xb all Xc all Xd all Xe all Xf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1364920114_prop1(X,Xa,Xb,Xc,Xd),Xe),Xf)) <-> pp(scratc1094873754_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045673258d_esti(X),Xf),aa_TPTP_ind_TPTP_ind(scratc468557777_ecect(X,Xa),Xd)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1592000840d_e_is(Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,Xc),Xf)),Xe))))) # label(fact_def__d__10__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 44 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6359709_fixfu(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ap(X),Xa),Xb),Xc))))) # label(fact_def__fixfu) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 45 (all X all Xa scratc468557777_ecect(X,Xa) = scratc1592000835d_e_in(aa_TPTP_ind_TPTP_ind(scratc1044813150_power,X),scratc28516594d_anec(X,Xa))) # label(fact_def__ecect) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 46 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc975547678ectelt(X,Xa),Xb) = aa_TPTP_ind_TPTP_ind(scratc1090749555ectset(X,Xa),aa_TPTP_ind_TPTP_ind(scratc469148168_ecelt(X,Xa),Xb))) # label(fact_def__ectelt) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 47 (all X all Xa scratc1090749555ectset(X,Xa) = scratc1562158727nd_out(aa_TPTP_ind_TPTP_ind(scratc1044813150_power,X),scratc28516594d_anec(X,Xa))) # label(fact_def__ectset) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 48 (all X all Xa scratc1478362895nd_ect(X,Xa) = aa_fun1431113780TP_ind(scratc978622305_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1044813150_power,X)),scratc28516594d_anec(X,Xa))) # label(fact_def__ect) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 49 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc28516594d_anec(X,Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc2035115897l_some(X),aa_TPT43085870d_bool(scratc1478362891nd_ecp(X,Xa),Xb))))) # label(fact_def__anec) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 50 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1478362891nd_ecp(X,Xa),Xb),Xc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1592000840d_e_is(aa_TPTP_ind_TPTP_ind(scratc1044813150_power,X)),Xb),aa_TPTP_ind_TPTP_ind(scratc469148168_ecelt(X,Xa),Xc))))) # label(fact_def__ecp) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 51 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc469148168_ecelt(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc978622305_d_Sep(X),aa_TPT43085870d_bool(Xa,Xb))) # label(fact_def__ecelt) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 52 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1196866901unmore(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc978622305_d_Sep(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ar(X),Xa),Xb))) # label(fact_def__unmore) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 53 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1632706228etprop(X,Xa),Xb),Xc)) <-> pp(scratc1094873754_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045673258d_esti(X),Xc),Xa),scratc1202338934_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045673258d_esti(X),Xc),Xb)))))) # label(fact_def__nissetprop) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 54 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2019181860t_disj(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1445907258nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_as(X),Xa),Xb))))) # label(fact_def__st__disj) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 55 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1978115701d_incl(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1445907258nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_at(X),Xa),Xb))))) # label(fact_def__incl) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 56 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc612357159nempty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc2035115897l_some(X),aa_TPT43085870d_bool(aTP_Lamm_au(X),Xa))))) # label(fact_def__nonempty) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 57 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1923970566_empty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),scratc1553503622nd_non(X,aa_TPT43085870d_bool(aTP_Lamm_au(X),Xa)))))) # label(fact_def__empty) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 58 (all X scratc1045673258d_esti(X) = scratc1718854572bnd_in) # label(fact_def__esti) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 59 (all X all Xa (scratc1373688649d_r_ec(X,Xa) <-> (pp(X) -> pp(scratc1202338934_d_not(Xa))))) # label(fact_def__r__ec) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 60 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc1419287663hangef(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc290900360_Sigma,X),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_av(X),Xb),Xc),Xd))) # label(fact_def__changef) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 61 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc958776352wissel(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc290900360_Sigma,X),scratc1572075915sel_wb(X,Xa,Xb))) # label(fact_def__wissel) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 62 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1572075915sel_wb(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc1512524083nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1592000840d_e_is(X),Xc),Xb),X,Xa),aa_TPTP_ind_TPTP_ind(scratc1572075914sel_wa(X,Xa,Xb),Xc))) # label(fact_def__wissel__wb) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 63 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1572075914sel_wa(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc1512524083nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1592000840d_e_is(X),Xc),Xa),X,Xb),Xc)) # label(fact_def__wissel__wa) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 64 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1512524083nd_ite(X,Xa,Xb),Xc) = scratc1512130488nd_ind(Xa,aa_TPT43085870d_bool(scratc1173720583_prop1(X,Xa,Xb),Xc))) # label(fact_def__ite) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 65 (all X all Xa all Xb all Xc all Xd (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1173720583_prop1(X,Xa,Xb),Xc),Xd)) <-> pp(scratc1094873754_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1512064901nd_imp,X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1592000840d_e_is(Xa),Xd),Xb)),aa_bool_bool(aa_boo1142376798l_bool(scratc1512064901nd_imp,scratc1202338934_d_not(X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1592000840d_e_is(Xa),Xd),Xc)))))) # label(fact_def__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 66 (all X all Xa scratc1717992283second(X,Xa) = scratc1173326989_proj1) # label(fact_def__second) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 67 (all X all Xa scratc2105127113_first(X,Xa) = scratc1173326988_proj0) # label(fact_def__first) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 68 (all X all Xa scratc897099575d_pair(X,Xa) = scratc892769185d_pair) # label(fact_def__d__pair) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 69 (all X all Xa scratc1562158727nd_out(X,Xa) = scratc1202511409d_soft(aa_fun1431113780TP_ind(scratc978622305_d_Sep(X),Xa),X,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc290900360_Sigma,aa_fun1431113780TP_ind(scratc978622305_d_Sep(X),Xa)),scratc1592000835d_e_in(X,Xa)))) # label(fact_def__out) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 70 (all X all Xa all Xb (gg_TPTP_ind(Xb) -> aa_TPTP_ind_TPTP_ind(scratc1592000835d_e_in(X,Xa),Xb) = Xb)) # label(fact_def__e__in) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 71 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc700039018_inj_h(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc290900360_Sigma,X),aa_TPT1424761345TP_ind(aTP_Lamm_aw(Xc),Xd))) # label(fact_def__inj__h) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 72 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1979362076d_invf(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc290900360_Sigma,Xa),scratc1202511409d_soft(X,Xa,Xb))) # label(fact_def__invf) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 73 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1287867166ective(X),Xa),Xb)) <-> pp(scratc1094873754_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1104147936ective(X),Xa),Xb),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1168451523ective(X),Xa),Xb))))) # label(fact_def__bijective) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 74 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1168451523ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1445907258nd_all(Xa),aa_TPT43085870d_bool(scratc2062485044_image(X,Xa),Xb))))) # label(fact_def__surjective) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 75 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1405328713nverse(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc290900360_Sigma,Xa),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ax(X),Xa),Xb))) # label(fact_def__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 76 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1202511409d_soft(X,Xa,Xb),Xc) = scratc1512130488nd_ind(X,aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(Xa),Xb),Xc))) # label(fact_def__soft) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 77 (all X all Xa scratc1983098607d_tofs(X,Xa) = scratc1718329782bnd_ap) # label(fact_def__tofs) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 78 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2062485044_image(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc2035115897l_some(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(Xa),Xb),Xc))))) # label(fact_def__image) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 79 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1104147936ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1445907258nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ba(X),Xa),Xb))))) # label(fact_def__injective) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 80 (all X all Xa scratc1512130488nd_ind(X,Xa) = scratc1479215681nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bb(X),Xa))) # label(fact_def__ind) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 81 (all X all Xa (pp(aa_fun171081125l_bool(scratc1561699519nd_one(X),Xa)) <-> pp(scratc1094873754_d_and(scratc1652025587_amone(X,Xa),aa_fun171081125l_bool(scratc2035115897l_some(X),Xa))))) # label(fact_def__one) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.37 82 (all X all Xa (pp(scratc1652025587_amone(X,Xa)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),aa_fun1584354236d_bool(aTP_Lamm_bd(X),Xa))))) # label(fact_def__amone) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 83 (all X scratc1592000840d_e_is(X) = fequal_TPTP_ind) # label(fact_def__e__is) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 84 (all X all Xa all Xb (scratc2098172107_orec3(X,Xa,Xb) <-> pp(scratc1094873754_d_and(scratc1561961865nd_or3(X,Xa,Xb),scratc1478362830nd_ec3(X,Xa,Xb))))) # label(fact_def__orec3) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 85 (all X all Xa all Xb (pp(scratc1478362830nd_ec3(X,Xa,Xb)) <-> scratc28450947d_and3(scratc978753859d_l_ec(X,Xa),scratc978753859d_l_ec(Xa,Xb),scratc978753859d_l_ec(Xb,X)))) # label(fact_def__ec3) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 86 (all X all Xa all Xb (scratc28450947d_and3(X,Xa,Xb) <-> pp(scratc1094873754_d_and(X,scratc1094873754_d_and(Xa,Xb))))) # label(fact_def__and3) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 87 (all X all Xa all Xb (pp(scratc1561961865nd_or3(X,Xa,Xb)) <-> pp(aa_bool_bool(scratc979409864d_l_or(X),aa_bool_bool(scratc979409864d_l_or(Xa),Xb))))) # label(fact_def__or3) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 88 (all X all Xa (pp(aa_fun171081125l_bool(scratc2035115897l_some(X),Xa)) <-> pp(scratc1202338934_d_not(aa_fun171081125l_bool(scratc776971441all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),scratc1553503622nd_non(X,Xa)))))) # label(fact_def__l__some) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 89 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc1553503622nd_non(X,Xa),Xb)) <-> pp(scratc1202338934_d_not(aa_TPTP_ind_bool(Xa,Xb))))) # label(fact_def__non) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 90 (all X scratc1445907258nd_all(X) = scratc776971441all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X))) # label(fact_def__all) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 91 (all X all Xa (scratc1989015204_l_iff(X,Xa) <-> pp(scratc1094873754_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1512064901nd_imp,X),Xa),aa_bool_bool(aa_boo1142376798l_bool(scratc1512064901nd_imp,Xa),X))))) # label(fact_def__l__iff) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 92 (all X all Xa (scratc252365160d_orec(X,Xa) <-> pp(scratc1094873754_d_and(aa_bool_bool(scratc979409864d_l_or(X),Xa),scratc978753859d_l_ec(X,Xa))))) # label(fact_def__orec) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 93 (all X scratc979409864d_l_or(X) = aa_boo1142376798l_bool(scratc1512064901nd_imp,scratc1202338934_d_not(X))) # label(fact_def__l__or) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 94 (all X all Xa (pp(scratc1094873754_d_and(X,Xa)) <-> pp(scratc1202338934_d_not(scratc978753859d_l_ec(X,Xa))))) # label(fact_def__d__and) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 95 (all X all Xa (pp(scratc978753859d_l_ec(X,Xa)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1512064901nd_imp,X),scratc1202338934_d_not(Xa))))) # label(fact_def__l__ec) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 96 scratc122927712bvious <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1512064901nd_imp,fFalse),fFalse)) # label(fact_def__obvious) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 97 (all X (scratc1627201175nd_wel(X) <-> pp(scratc1202338934_d_not(scratc1202338934_d_not(X))))) # label(fact_def__wel) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 98 (all X (pp(scratc1202338934_d_not(X)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1512064901nd_imp,X),fFalse)))) # label(fact_def__d__not) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 99 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc450796566d_d_Pi,X),Xa) = aa_fun1431113780TP_ind(scratc978622305_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1044813150_power,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc290900360_Sigma,X),aTP_Lamm_be(Xa)))),aa_fun1913827119d_bool(aTP_Lamm_bf(X),Xa))) # label(fact_def__d__Pi) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 100 (all X (gg_TPTP_ind(X) -> (pp(aa_TPTP_ind_bool(scratc1863830991pair_p,X)) <-> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc892769185d_pair,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,X),scratc326762172ptyset)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,X),aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,scratc326762172ptyset))) = X))) # label(fact_def__pair__p) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 101 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc48683154eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bg,Xa)),scratc1173326989_proj1)) # label(fact_def__ap) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 102 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1641004114etprod(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc290900360_Sigma,X),aTP_Lamm_ai(Xa))) # label(fact_def__setprod) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 103 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc290900360_Sigma,X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc692202724munion,X),aTP_Lamm_bh(Xa))) # label(fact_def__d__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 104 (all X aa_TPTP_ind_TPTP_ind(scratc1173326989_proj1,X) = aa_fun277296641TP_ind(scratc48683154eplSep(X,aTP_Lamm_bi),scratc995735700_d_Unj)) # label(fact_def__proj1) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 105 (all X aa_TPTP_ind_TPTP_ind(scratc1173326988_proj0,X) = aa_fun277296641TP_ind(scratc48683154eplSep(X,aTP_Lamm_bj),scratc995735700_d_Unj)) # label(fact_def__proj0) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 106 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc892769185d_pair,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1686059823nunion(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc339965142d_repl,X),scratc626434984d_Inj0)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc339965142d_repl,Xa),scratc626434985d_Inj1))) # label(fact_def__pair) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 107 (all X aa_TPTP_ind_TPTP_ind(scratc626434984d_Inj0,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc339965142d_repl,X),scratc626434985d_Inj1)) # label(fact_def__d__Inj0) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 108 (all X (pp(aa_TPTP_ind_bool(scratc1994062358_nat_p,X)) <-> (all X1 (pp(aa_TPTP_ind_bool(X1,scratc326762172ptyset)) -> ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(X1,X2)) -> pp(aa_TPTP_ind_bool(X1,aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,X2)))))) -> pp(aa_TPTP_ind_bool(X1,X))))))) # label(fact_def__nat__p) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 109 (all X aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1686059823nunion(X),aa_TPTP_ind_TPTP_ind(scratc1948810956d_Sing,X))) # label(fact_def__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 110 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1923930382In_rec(X),Xa) = scratc1479215681nd_eps(aa_TPT43085870d_bool(scratc1338780153_rec_G(X),Xa))) # label(fact_def__d__In__rec) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 111 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1338780153_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(scratc1718854572bnd_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].
% 1.05/1.38 112 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1602345365tminus(X),Xa) = aa_fun1431113780TP_ind(scratc978622305_d_Sep(X),aa_TPT43085870d_bool(aTP_Lamm_bm,Xa))) # label(fact_def__setminus) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 113 (all X all Xa scratc48683154eplSep(X,Xa) = aa_TPT494704832TP_ind(scratc339965142d_repl,aa_fun1431113780TP_ind(scratc978622305_d_Sep(X),Xa))) # label(fact_def__d__ReplSep) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 114 (all X all Xa aa_fun1431113780TP_ind(scratc978622305_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1718854564bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1718854572bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc339965142d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bn(X),Xa))),scratc326762172ptyset)) # label(fact_def__d__Sep) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 115 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc692202724munion,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1552075016_union,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc339965142d_repl,X),Xa))) # label(fact_def__famunion) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 116 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1686059823nunion(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1552075016_union,aa_TPTP_ind_TPTP_ind(scratc185386738_UPair(X),Xa))) # label(fact_def__binunion) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 117 (all X aa_TPTP_ind_TPTP_ind(scratc1948810956d_Sing,X) = aa_TPTP_ind_TPTP_ind(scratc185386738_UPair(X),X)) # label(fact_def__d__Sing) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 118 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc185386738_UPair(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc339965142d_repl,aa_TPTP_ind_TPTP_ind(scratc1044813150_power,aa_TPTP_ind_TPTP_ind(scratc1044813150_power,scratc326762172ptyset))),aa_TPT1424761345TP_ind(aTP_Lamm_bo(X),Xa))) # label(fact_def__d__UPair) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 119 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1551010860nd_nIn,X),Xa)) <-> -pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X),Xa)))) # label(fact_def__nIn) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 120 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1718854564bnd_if(X,Xa),Xb) = scratc1479215681nd_eps(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bp(X),Xa),Xb))) # label(fact_def__if) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 121 (all X (pp(aa_TPTP_ind_bool(scratc1637304053closed,X)) <-> pp(aa_TPTP_ind_bool(scratc567628126closed,X)) & pp(aa_TPTP_ind_bool(scratc732361140closed,X)) & pp(aa_TPTP_ind_bool(scratc12260120closed,X)))) # label(fact_def__d__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 122 (all X (pp(aa_TPTP_ind_bool(scratc12260120closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X1),X)) -> (all X2 ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X3),X1)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,aa_TPTP_ind_TPTP_ind(X2,X3)),X))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc339965142d_repl,X1),X2)),X))))))))) # label(fact_def__d__Repl__closed) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 123 (all X (pp(aa_TPTP_ind_bool(scratc732361140closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,aa_TPTP_ind_TPTP_ind(scratc1044813150_power,X1)),X))))))) # label(fact_def__d__Power__closed) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 124 (all X (pp(aa_TPTP_ind_bool(scratc567628126closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,aa_TPTP_ind_TPTP_ind(scratc1552075016_union,X1)),X))))))) # label(fact_def__d__Union__closed) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 125 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2047161838d_Subq,X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X2),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X2),Xa))))))) # label(fact_def__d__Subq) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 126 (all X all Xa (pp(aa_fun171081125l_bool(scratc776971441all_of(X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (scratc2107418152_is_of(X2,X) -> pp(aa_TPTP_ind_bool(Xa,X2))))))) # label(fact_def__all__of) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 127 (all X all Xa (scratc2107418152_is_of(X,Xa) <-> pp(aa_TPTP_ind_bool(Xa,X)))) # label(fact_def__is__of) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 128 (all X0 pp(aa_fun171081125l_bool(scratc776971441all_of(aa_TPT43085870d_bool(aTP_Lamm_jo,X0)),aa_TPT43085870d_bool(aTP_Lamm_jq,X0)))) # label(fact_isseti) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 129 (all X0 all X12 pp(aa_fun171081125l_bool(scratc776971441all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_jr(X0),X12)))) # label(fact_estie) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 130 (all X0 all X12 pp(aa_fun171081125l_bool(scratc776971441all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_js(X0),X12)))) # label(fact_estii) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 131 (all X0 all X12 scratc2107418152_is_of(aa_fun1431113780TP_ind(scratc978622305_d_Sep(X0),X12),aa_TPT43085870d_bool(aTP_Lamm_jo,X0))) # label(fact_setof__p) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 132 (all X0 all X12 pp(aa_fun171081125l_bool(scratc776971441all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_ju(X0),X12)))) # label(fact_secondis1) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 133 (all X0 all X12 pp(aa_fun171081125l_bool(scratc776971441all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_jw(X0),X12)))) # label(fact_firstis1) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 134 (all X0 all X12 pp(aa_fun171081125l_bool(scratc776971441all_of(aa_TPT43085870d_bool(aTP_Lamm_jx(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_jy(X0),X12)))) # label(fact_pairis1) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 135 (all X0 all X12 pp(aa_fun171081125l_bool(scratc776971441all_of(aa_TPT43085870d_bool(aTP_Lamm_jx(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_jz(X0),X12)))) # label(fact_second__p) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 136 (all X0 all X12 pp(aa_fun171081125l_bool(scratc776971441all_of(aa_TPT43085870d_bool(aTP_Lamm_jx(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_ka(X0),X12)))) # label(fact_first__p) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 137 (all X0 all X12 pp(aa_fun171081125l_bool(scratc776971441all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_kc(X0),X12)))) # label(fact_e__pair__p) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 138 (all X0 all X12 pp(aa_fun171081125l_bool(scratc776971441all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_kd(X0),X12)))) # label(fact_otax2) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 139 (all X0 all X12 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1104147936ective(aa_fun1431113780TP_ind(scratc978622305_d_Sep(X0),X12)),X0),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc290900360_Sigma,aa_fun1431113780TP_ind(scratc978622305_d_Sep(X0),X12)),scratc1592000835d_e_in(X0,X12))))) # label(fact_otax1) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 140 (all X0 all X12 pp(aa_fun171081125l_bool(scratc776971441all_of(aa_fun1584354236d_bool(aTP_Lamm_ke(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_kf(X0),X12)))) # label(fact_e__inp) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 141 (all X0 all X12 pp(aa_fun171081125l_bool(scratc776971441all_of(aa_fun1584354236d_bool(aTP_Lamm_ke(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_kg(X0),X12)))) # label(fact_e__in__p) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 142 (all X0 all X12 pp(aa_fun171081125l_bool(scratc776971441all_of(aa_TPT43085870d_bool(aTP_Lamm_kh(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_kk(X0),X12)))) # label(fact_e__fisi) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 143 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc1561699519nd_one(X0),X12)) -> pp(aa_TPTP_ind_bool(X12,scratc1512130488nd_ind(X0,X12))))) # label(fact_oneax) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 144 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc1561699519nd_one(X0),X12)) -> scratc2107418152_is_of(scratc1512130488nd_ind(X0,X12),aa_TPT43085870d_bool(aTP_Lamm_aj,X0)))) # label(fact_ind__p) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 145 (all X0 all X12 pp(aa_fun171081125l_bool(scratc776971441all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_km(X0),X12)))) # label(fact_e__isp) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 146 (all X0 pp(aa_fun171081125l_bool(scratc776971441all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_kn,X0)))) # label(fact_refis) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 147 (all X0 (scratc1627201175nd_wel(X0) -> pp(X0))) # label(fact_l__et) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 148 (all X0 all X12 all X22 all X32 (pp(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1718854564bnd_if(X0,X22),X32))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X12),X22))))) # label(fact_k__If__In__then__E) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 149 (all X0 all X12 all X22 ((pp(X0) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X12),X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,aa_TPTP_ind_TPTP_ind(scratc1718854564bnd_if(X0,X12),scratc326762172ptyset)),aa_TPTP_ind_TPTP_ind(scratc1718854564bnd_if(X0,X22),aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,scratc326762172ptyset)))))) # label(fact_k__If__In__01) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 150 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X33),X0)) -> aa_TPTP_ind_TPTP_ind(X12,X33) = aa_TPTP_ind_TPTP_ind(X22,X33)))) -> aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc290900360_Sigma,X0),X12) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc290900360_Sigma,X0),X22))) # label(fact_xi__ext) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 151 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc450796566d_d_Pi,X0),X12))) -> (all X32 (gg_TPTP_ind(X32) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X32),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc450796566d_d_Pi,X0),X12))) -> ((all X42 (gg_TPTP_ind(X42) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X42),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,X22),X42) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,X32),X42)))) -> X22 = X32))))))) # label(fact_k__Pi__ext) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 152 (all X0 all X12 all X22 all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc450796566d_d_Pi,X0),X12))) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X32),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,X22),X32)),aa_TPTP_ind_TPTP_ind(X12,X32)))))) # label(fact_ap__Pi) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 153 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X33),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,aa_TPTP_ind_TPTP_ind(X22,X33)),aa_TPTP_ind_TPTP_ind(X12,X33)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc290900360_Sigma,X0),X22)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc450796566d_d_Pi,X0),X12))))) # label(fact_lam__Pi) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 154 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X22),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc290900360_Sigma,X0),X12)),X22) = aa_TPTP_ind_TPTP_ind(X12,X22))) # label(fact_beta) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 155 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc290900360_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,aa_TPTP_ind_TPTP_ind(scratc1173326989_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1173326988_proj0,X22)))))) # label(fact_proj1__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 156 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc290900360_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,aa_TPTP_ind_TPTP_ind(scratc1173326988_proj0,X22)),X0)))) # label(fact_proj0__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 157 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc290900360_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc892769185d_pair,aa_TPTP_ind_TPTP_ind(scratc1173326988_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1173326989_proj1,X22)) = X22))) # label(fact_proj__Sigma__eta) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 158 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc290900360_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc892769185d_pair,aa_TPTP_ind_TPTP_ind(scratc1173326988_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1173326989_proj1,X22)) = X22 & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,aa_TPTP_ind_TPTP_ind(scratc1173326988_proj0,X22)),X0)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,aa_TPTP_ind_TPTP_ind(scratc1173326989_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1173326988_proj0,X22))))))) # label(fact_k__Sigma__eta__proj0__proj1) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 159 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X22),X0)) -> (all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X32),aa_TPTP_ind_TPTP_ind(X12,X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc892769185d_pair,X22),X32)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc290900360_Sigma,X0),X12))))))) # label(fact_pair__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 160 (all X0 all X12 (gg_TPTP_ind(X12) -> aa_TPTP_ind_TPTP_ind(scratc1173326989_proj1,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc892769185d_pair,X0),X12)) = X12)) # label(fact_proj1__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 161 (all X0 all X12 (gg_TPTP_ind(X0) -> aa_TPTP_ind_TPTP_ind(scratc1173326988_proj0,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc892769185d_pair,X0),X12)) = X0)) # label(fact_proj0__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 162 (all X0 (pp(aa_TPTP_ind_bool(scratc1994062358_nat_p,X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X0),scratc342982202_omega)))) # label(fact_nat__p__omega) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 163 (all X0 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X0),scratc342982202_omega)) -> pp(aa_TPTP_ind_bool(scratc1994062358_nat_p,X0)))) # label(fact_omega__nat__p) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 164 (all X0 (gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(scratc1994062358_nat_p,X0)) -> X0 = scratc326762172ptyset | (exists X13 (gg_TPTP_ind(X13) & pp(aa_TPTP_ind_bool(scratc1994062358_nat_p,X13)) & X0 = aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,X13)))))) # label(fact_nat__inv) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 165 (all X0 (pp(aa_TPTP_ind_bool(X0,scratc326762172ptyset)) -> ((all X13 (gg_TPTP_ind(X13) -> (pp(aa_TPTP_ind_bool(scratc1994062358_nat_p,X13)) -> (pp(aa_TPTP_ind_bool(X0,X13)) -> pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,X13))))))) -> (all X12 (pp(aa_TPTP_ind_bool(scratc1994062358_nat_p,X12)) -> pp(aa_TPTP_ind_bool(X0,X12))))))) # label(fact_nat__ind) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 166 (all X0 (pp(aa_TPTP_ind_bool(scratc1994062358_nat_p,X0)) -> pp(aa_TPTP_ind_bool(scratc1994062358_nat_p,aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,X0))))) # label(fact_nat__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 167 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,X0) = aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,X12) -> X0 = X12))) # label(fact_ordsucc__inj) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 168 (all X0 aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,X0) != scratc326762172ptyset) # label(fact_neq__ordsucc__0) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 169 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X22),aa_fun1431113780TP_ind(scratc978622305_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(X12,X22)))) # label(fact_k__SepE2) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 170 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X22),aa_fun1431113780TP_ind(scratc978622305_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X22),X0)))) # label(fact_k__SepE1) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 171 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X22),X0)) -> (pp(aa_TPTP_ind_bool(X12,X22)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X22),aa_fun1431113780TP_ind(scratc978622305_d_Sep(X0),X12)))))) # label(fact_k__SepI) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 172 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc1044813150_power,X0)))) # label(fact_k__Self__In__Power) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 173 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2047161838d_Subq,X12),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1044813150_power,X0))))) # label(fact_k__PowerI) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 174 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1044813150_power,X0))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2047161838d_Subq,X12),X0)))) # label(fact_k__PowerE) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 175 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> aa_TPTP_ind_TPTP_ind(scratc1718854564bnd_if(X0,X12),X22) = X12 | aa_TPTP_ind_TPTP_ind(scratc1718854564bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__or) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 176 (all X0 all X12 all X22 (gg_TPTP_ind(X12) -> (pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc1718854564bnd_if(X0,X12),X22) = X12))) # label(fact_if__i__1) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 177 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (-pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc1718854564bnd_if(X0,X12),X22) = X22))) # label(fact_if__i__0) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 178 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> pp(X0) & aa_TPTP_ind_TPTP_ind(scratc1718854564bnd_if(X0,X12),X22) = X12 | -pp(X0) & aa_TPTP_ind_TPTP_ind(scratc1718854564bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__correct) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 179 (all X0 pp(aa_TPTP_ind_bool(scratc1637304053closed,aa_TPTP_ind_TPTP_ind(scratc279635492univof,X0)))) # label(fact_k__UnivOf__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 180 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc279635492univof,X0)))) # label(fact_k__UnivOf__In) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 181 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc339965142d_repl,X0),X12))) <-> (exists X3 (gg_TPTP_ind(X3) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X3),X0)) & X22 = aa_TPTP_ind_TPTP_ind(X12,X3)))))) # label(fact_k__ReplEq) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 182 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1044813150_power,X0))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2047161838d_Subq,X12),X0)))) # label(fact_k__PowerEq) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 183 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1552075016_union,X0))) <-> (exists X2 (gg_TPTP_ind(X2) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X12),X2)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X2),X0)))))) # label(fact_k__UnionEq) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 184 -(exists X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X0),scratc326762172ptyset))) # label(fact_k__EmptyAx) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 185 (all X0 ((all X13 (gg_TPTP_ind(X13) -> ((all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_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].
% 1.05/1.38 186 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2047161838d_Subq,X0),X12)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2047161838d_Subq,X12),X0)) -> X0 = X12)))) # label(fact_set__ext) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 187 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jd,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1553110033nd_nis,Uu),scratc1461899370nd_n_1)) -> pp(aa_fun171081125l_bool(scratc631456891n_some,aa_TPT43085870d_bool(aTP_Lamm_af,Uu)))))) # label(fact_ATP_Olambda__1) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 188 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jc,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1553110033nd_nis,Uu),scratc1461899370nd_n_1)) -> pp(aa_fun171081125l_bool(scratc635639839_n_one,aa_TPT43085870d_bool(aTP_Lamm_af,Uu)))))) # label(fact_ATP_Olambda__2) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 189 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_iz,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),scratc1461899370nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,Uu))))) # label(fact_ATP_Olambda__3) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 190 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_iw,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(scratc1461899370nd_n_1),Uu)),aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,Uu))))) # label(fact_ATP_Olambda__4) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 191 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jb,Uu)) <-> pp(aa_fun171081125l_bool(scratc1561699519nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc450796566d_d_Pi,scratc1552585242nd_nat),aTP_Lamm_ac)),aa_TPT43085870d_bool(aTP_Lamm_ja,Uu))))) # label(fact_ATP_Olambda__5) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 192 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jj,Uu)) <-> (pp(aa_TPTP_ind_bool(scratc1188443720_cond1,Uu)) -> (pp(aa_TPTP_ind_bool(scratc1188443721_cond2,Uu)) -> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ji,Uu))))))) # label(fact_ATP_Olambda__6) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 193 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_it,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),scratc1461899370nd_n_1))))) # label(fact_ATP_Olambda__7) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 194 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_iq,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(scratc1461899370nd_n_1),Uu))))) # label(fact_ATP_Olambda__8) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 195 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fq,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__9) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 196 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_je,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1553110033nd_nis,aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__10) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 197 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jn,Uu)) <-> scratc2107418152_is_of(aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,Uu),aTP_Lamm_a))) # label(fact_ATP_Olambda__11) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 198 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bv,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,Uu)),scratc1461899370nd_n_1)))) # label(fact_ATP_Olambda__12) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 199 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jm,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1553110033nd_nis,aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,Uu)),scratc1461899370nd_n_1)))) # label(fact_ATP_Olambda__13) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 200 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fp,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,Uu))))) # label(fact_ATP_Olambda__14) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 201 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jh,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,Uu),aa_TPTP_ind_TPTP_ind(scratc1044813150_power,scratc1552585242nd_nat))))) # label(fact_ATP_Olambda__15) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 202 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bw,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032620262moreis,Uu),scratc1461899370nd_n_1)))) # label(fact_ATP_Olambda__16) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 203 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_a,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,Uu),scratc1552585242nd_nat)))) # label(fact_ATP_Olambda__17) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 204 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jl,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jk,Uu))))) # label(fact_ATP_Olambda__18) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 205 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jg,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jf,Uu))))) # label(fact_ATP_Olambda__19) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 206 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_iy,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ix,Uu))))) # label(fact_ATP_Olambda__20) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 207 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_iv,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_iu,Uu))))) # label(fact_ATP_Olambda__21) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 208 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_is,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ir,Uu))))) # label(fact_ATP_Olambda__22) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 209 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ip,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_io,Uu))))) # label(fact_ATP_Olambda__23) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 210 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_in,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_im,Uu))))) # label(fact_ATP_Olambda__24) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 211 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ik,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ij,Uu))))) # label(fact_ATP_Olambda__25) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 212 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ii,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ih,Uu))))) # label(fact_ATP_Olambda__26) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 213 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ig,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_if,Uu))))) # label(fact_ATP_Olambda__27) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 214 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_id,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ic,Uu))))) # label(fact_ATP_Olambda__28) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 215 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ia,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hz,Uu))))) # label(fact_ATP_Olambda__29) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 216 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hy,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hx,Uu))))) # label(fact_ATP_Olambda__30) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 217 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hu,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ht,Uu))))) # label(fact_ATP_Olambda__31) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 218 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hs,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hr,Uu))))) # label(fact_ATP_Olambda__32) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 219 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hq,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hp,Uu))))) # label(fact_ATP_Olambda__33) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 220 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ho,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hn,Uu))))) # label(fact_ATP_Olambda__34) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 221 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hm,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hl,Uu))))) # label(fact_ATP_Olambda__35) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 222 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hk,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hj,Uu))))) # label(fact_ATP_Olambda__36) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 223 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hi,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hh,Uu))))) # label(fact_ATP_Olambda__37) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 224 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hg,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hf,Uu))))) # label(fact_ATP_Olambda__38) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 225 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_he,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hd,Uu))))) # label(fact_ATP_Olambda__39) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 226 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hc,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hb,Uu))))) # label(fact_ATP_Olambda__40) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 227 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ha,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gz,Uu))))) # label(fact_ATP_Olambda__41) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.38 228 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gy,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,Uu))))) # label(fact_ATP_Olambda__42) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 229 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gw,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gv,Uu))))) # label(fact_ATP_Olambda__43) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 230 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gu,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gt,Uu))))) # label(fact_ATP_Olambda__44) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 231 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gs,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gr,Uu))))) # label(fact_ATP_Olambda__45) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 232 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gq,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gp,Uu))))) # label(fact_ATP_Olambda__46) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 233 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_go,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gn,Uu))))) # label(fact_ATP_Olambda__47) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 234 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gm,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gl,Uu))))) # label(fact_ATP_Olambda__48) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 235 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gj,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gi,Uu))))) # label(fact_ATP_Olambda__49) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 236 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gg,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gf,Uu))))) # label(fact_ATP_Olambda__50) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 237 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gd,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gc,Uu))))) # label(fact_ATP_Olambda__51) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 238 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ga,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fz,Uu))))) # label(fact_ATP_Olambda__52) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 239 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fx,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fw,Uu))))) # label(fact_ATP_Olambda__53) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 240 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fu,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ft,Uu))))) # label(fact_ATP_Olambda__54) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 241 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fs,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fr,Uu))))) # label(fact_ATP_Olambda__55) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 242 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fo,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fn,Uu))))) # label(fact_ATP_Olambda__56) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 243 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fl,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fk,Uu))))) # label(fact_ATP_Olambda__57) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 244 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fi,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fh,Uu))))) # label(fact_ATP_Olambda__58) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 245 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ff,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fe,Uu))))) # label(fact_ATP_Olambda__59) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 246 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fc,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fb,Uu))))) # label(fact_ATP_Olambda__60) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 247 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ez,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ey,Uu))))) # label(fact_ATP_Olambda__61) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 248 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ew,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ev,Uu))))) # label(fact_ATP_Olambda__62) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 249 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_es,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_er,Uu))))) # label(fact_ATP_Olambda__63) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 250 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_eo,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_en,Uu))))) # label(fact_ATP_Olambda__64) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 251 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ek,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ej,Uu))))) # label(fact_ATP_Olambda__65) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 252 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_eg,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ef,Uu))))) # label(fact_ATP_Olambda__66) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 253 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ed,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ec,Uu))))) # label(fact_ATP_Olambda__67) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 254 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ea,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dz,Uu))))) # label(fact_ATP_Olambda__68) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 255 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dx,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dw,Uu))))) # label(fact_ATP_Olambda__69) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 256 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_du,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dt,Uu))))) # label(fact_ATP_Olambda__70) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 257 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dr,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dq,Uu))))) # label(fact_ATP_Olambda__71) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 258 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_do,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dn,Uu))))) # label(fact_ATP_Olambda__72) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 259 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dl,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dk,Uu))))) # label(fact_ATP_Olambda__73) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 260 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_di,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dh,Uu))))) # label(fact_ATP_Olambda__74) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 261 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_df,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_de,Uu))))) # label(fact_ATP_Olambda__75) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 262 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dc,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_db,Uu))))) # label(fact_ATP_Olambda__76) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 263 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cy,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cx,Uu))))) # label(fact_ATP_Olambda__77) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 264 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cu,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ct,Uu))))) # label(fact_ATP_Olambda__78) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 265 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cq,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cp,Uu))))) # label(fact_ATP_Olambda__79) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 266 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cm,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cl,Uu))))) # label(fact_ATP_Olambda__80) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 267 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ci,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ch,Uu))))) # label(fact_ATP_Olambda__81) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 268 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ce,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cd,Uu))))) # label(fact_ATP_Olambda__82) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 269 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ca,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bz,Uu))))) # label(fact_ATP_Olambda__83) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 270 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bt,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bs,Uu))))) # label(fact_ATP_Olambda__84) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 271 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_br,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bq,Uu))))) # label(fact_ATP_Olambda__85) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 272 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ab,Uu)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,Uu))))) # label(fact_ATP_Olambda__86) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 273 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,scratc1461899370nd_n_1),aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,Uu))))) # label(fact_ATP_Olambda__87) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 274 (all Uu aa_TPT494704832TP_ind(aTP_Lamm_bk,Uu) = aa_TPT494704832TP_ind(scratc339965142d_repl,aa_TPTP_ind_TPTP_ind(scratc1602345365tminus(Uu),aa_TPTP_ind_TPTP_ind(scratc1948810956d_Sing,scratc326762172ptyset)))) # label(fact_ATP_Olambda__88) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 275 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_ah,Uu)) <-> Uu != scratc326762172ptyset))) # label(fact_ATP_Olambda__89) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 276 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_bi,Uu)) <-> (exists X2 (gg_TPTP_ind(X2) & aa_TPTP_ind_TPTP_ind(scratc626434985d_Inj1,X2) = Uu))))) # label(fact_ATP_Olambda__90) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 277 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_bj,Uu)) <-> (exists X2 (gg_TPTP_ind(X2) & aa_TPTP_ind_TPTP_ind(scratc626434984d_Inj0,X2) = Uu))))) # label(fact_ATP_Olambda__91) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 278 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hp,Uu),Uua)) <-> scratc2098172107_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,Uu),Uua)))) # label(fact_ATP_Olambda__92) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 279 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hn,Uu),Uua)) <-> pp(scratc1561961865nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__93) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 280 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hl,Uu),Uua)) <-> pp(scratc1478362830nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__94) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 281 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hx,Uu),Uua)) <-> scratc2098172107_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc631456891n_some,aa_TPT43085870d_bool(aTP_Lamm_hv(Uu),Uua)),aa_fun171081125l_bool(scratc631456891n_some,aa_TPT43085870d_bool(aTP_Lamm_hw(Uu),Uua))))) # label(fact_ATP_Olambda__95) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 282 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ht,Uu),Uua)) <-> pp(scratc1561961865nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc631456891n_some,aa_TPT43085870d_bool(scratc1608659119ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc631456891n_some,aa_TPT43085870d_bool(scratc1608659119ffprop(Uua),Uu)))))) # label(fact_ATP_Olambda__96) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 283 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hr,Uu),Uua)) <-> pp(scratc1478362830nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc631456891n_some,aa_TPT43085870d_bool(scratc1608659119ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc631456891n_some,aa_TPT43085870d_bool(scratc1608659119ffprop(Uua),Uu)))))) # label(fact_ATP_Olambda__97) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 284 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kn,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1592000840d_e_is(Uu),Uua),Uua)))) # label(fact_ATP_Olambda__98) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 285 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ja,Uu),Uua)) <-> pp(scratc1094873754_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,Uua),scratc1461899370nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,Uu)),aa_fun171081125l_bool(scratc519847578_n_all,aa_TPT43085870d_bool(aTP_Lamm_ae,Uua)))))) # label(fact_ATP_Olambda__99) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 286 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jk,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__100) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 287 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iu,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__101) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 288 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ix,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__102) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 289 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ae,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,Uu),aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,Uu),Uua)))))) # label(fact_ATP_Olambda__103) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 290 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc898636650lessis,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uua),scratc1461899370nd_n_1)),Uu))))) # label(fact_ATP_Olambda__104) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 291 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jf,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1553110033nd_nis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1553110033nd_nis,aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,Uua)))))) # label(fact_ATP_Olambda__105) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 292 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ag,Uu),Uua)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1512064901nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661196d_n_in,Uua),Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661196d_n_in,aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,Uua)),Uu))))) # label(fact_ATP_Olambda__106) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 293 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bs,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032620262moreis,Uua),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),scratc1461899370nd_n_1)))))) # label(fact_ATP_Olambda__107) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 294 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bq,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032620262moreis,Uua),aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,Uu)))))) # label(fact_ATP_Olambda__108) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 295 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ij,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uua),Uu))))) # label(fact_ATP_Olambda__109) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 296 (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(scratc2059788932_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,Uua),Uu))))) # label(fact_ATP_Olambda__110) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 297 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hf,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032620262moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc898636650lessis,Uua),Uu))))) # label(fact_ATP_Olambda__111) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 298 (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(scratc898636650lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032620262moreis,Uua),Uu))))) # label(fact_ATP_Olambda__112) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 299 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hh,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,Uua),Uu))))) # label(fact_ATP_Olambda__113) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 300 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gt,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,Uu),Uua)) -> pp(scratc1202338934_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc898636650lessis,Uu),Uua)))))) # label(fact_ATP_Olambda__114) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 301 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hb,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032620262moreis,Uu),Uua)) -> pp(scratc1202338934_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,Uu),Uua)))))) # label(fact_ATP_Olambda__115) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 302 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gz,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc898636650lessis,Uu),Uua)) -> pp(scratc1202338934_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,Uu),Uua)))))) # label(fact_ATP_Olambda__116) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 303 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gr,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,Uu),Uua)) -> pp(scratc1202338934_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032620262moreis,Uu),Uua)))))) # label(fact_ATP_Olambda__117) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 304 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ft,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uua)),Uu)))) # label(fact_ATP_Olambda__118) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 305 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bh(Uu),Uua) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc339965142d_repl,aa_TPTP_ind_TPTP_ind(Uu,Uua)),aa_TPT1424761345TP_ind(scratc892769185d_pair,Uua))) # label(fact_ATP_Olambda__119) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 306 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jq,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aa_TPT43085870d_bool(aTP_Lamm_jo,Uu)),aa_TPT43085870d_bool(aTP_Lamm_jp(Uu),Uua))))) # label(fact_ATP_Olambda__120) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 307 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_io,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,Uu)),Uua))))) # label(fact_ATP_Olambda__121) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 308 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ir,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,Uua)))))) # label(fact_ATP_Olambda__122) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 309 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,Uu),Uua)) <-> (pp(scratc1202338934_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc898636650lessis,Uu),Uua))))) # label(fact_ATP_Olambda__123) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 310 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gp,Uu),Uua)) <-> (pp(scratc1202338934_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032620262moreis,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__124) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 311 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gn,Uu),Uua)) <-> (pp(scratc1202338934_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc898636650lessis,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__125) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 312 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gv,Uu),Uua)) <-> (pp(scratc1202338934_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032620262moreis,Uu),Uua))))) # label(fact_ATP_Olambda__126) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 313 (all Uu all Uua aa_fun277296641TP_ind(aa_TPT494704832TP_ind(aTP_Lamm_bl,Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1686059823nunion(aa_TPTP_ind_TPTP_ind(scratc1948810956d_Sing,scratc326762172ptyset)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc339965142d_repl,Uu),Uua))) # label(fact_ATP_Olambda__127) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 314 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ih,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1553110033nd_nis,Uua),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__128) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 315 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fr,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__129) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 316 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_af,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,Uua))))) # label(fact_ATP_Olambda__130) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 317 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jo,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,Uua),aa_TPTP_ind_TPTP_ind(scratc1044813150_power,Uu))))) # label(fact_ATP_Olambda__131) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 318 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ji,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661196d_n_in,Uua),Uu)))) # label(fact_ATP_Olambda__132) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 319 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bm,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1551010860nd_nIn,Uua),Uu)))) # label(fact_ATP_Olambda__133) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 320 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,Uua),Uu)))) # label(fact_ATP_Olambda__134) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 321 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_im,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_il(Uu),Uua))))) # label(fact_ATP_Olambda__135) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 322 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_if,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ie(Uu),Uua))))) # label(fact_ATP_Olambda__136) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 323 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ic,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ib(Uu),Uua))))) # label(fact_ATP_Olambda__137) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 324 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gl,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gk(Uu),Uua))))) # label(fact_ATP_Olambda__138) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 325 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gi,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gh(Uu),Uua))))) # label(fact_ATP_Olambda__139) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 326 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gf,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ge(Uu),Uua))))) # label(fact_ATP_Olambda__140) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 327 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gc,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gb(Uu),Uua))))) # label(fact_ATP_Olambda__141) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 328 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fz,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fy(Uu),Uua))))) # label(fact_ATP_Olambda__142) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 329 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fw,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fv(Uu),Uua))))) # label(fact_ATP_Olambda__143) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 330 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fn,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fm(Uu),Uua))))) # label(fact_ATP_Olambda__144) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 331 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fk,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fj(Uu),Uua))))) # label(fact_ATP_Olambda__145) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 332 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fh,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fg(Uu),Uua))))) # label(fact_ATP_Olambda__146) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 333 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fe,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fd(Uu),Uua))))) # label(fact_ATP_Olambda__147) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 334 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fb,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fa(Uu),Uua))))) # label(fact_ATP_Olambda__148) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 335 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ey,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ex(Uu),Uua))))) # label(fact_ATP_Olambda__149) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 336 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ev,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eu(Uu),Uua))))) # label(fact_ATP_Olambda__150) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 337 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_er,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eq(Uu),Uua))))) # label(fact_ATP_Olambda__151) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 338 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_en,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_em(Uu),Uua))))) # label(fact_ATP_Olambda__152) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 339 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ej,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ei(Uu),Uua))))) # label(fact_ATP_Olambda__153) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 340 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ef,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ee(Uu),Uua))))) # label(fact_ATP_Olambda__154) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 341 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ec,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eb(Uu),Uua))))) # label(fact_ATP_Olambda__155) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 342 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dz,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dy(Uu),Uua))))) # label(fact_ATP_Olambda__156) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 343 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dw,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dv(Uu),Uua))))) # label(fact_ATP_Olambda__157) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 344 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dt,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ds(Uu),Uua))))) # label(fact_ATP_Olambda__158) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 345 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dq,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dp(Uu),Uua))))) # label(fact_ATP_Olambda__159) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 346 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dn,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dm(Uu),Uua))))) # label(fact_ATP_Olambda__160) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 347 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dk,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dj(Uu),Uua))))) # label(fact_ATP_Olambda__161) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 348 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dh,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dg(Uu),Uua))))) # label(fact_ATP_Olambda__162) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 349 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_de,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dd(Uu),Uua))))) # label(fact_ATP_Olambda__163) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 350 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_db,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_da(Uu),Uua))))) # label(fact_ATP_Olambda__164) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 351 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cx,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cw(Uu),Uua))))) # label(fact_ATP_Olambda__165) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 352 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ct,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cs(Uu),Uua))))) # label(fact_ATP_Olambda__166) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 353 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cp,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_co(Uu),Uua))))) # label(fact_ATP_Olambda__167) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 354 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cl,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ck(Uu),Uua))))) # label(fact_ATP_Olambda__168) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 355 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ch,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cg(Uu),Uua))))) # label(fact_ATP_Olambda__169) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 356 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cd,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cc(Uu),Uua))))) # label(fact_ATP_Olambda__170) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 357 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bz,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_by(Uu),Uua))))) # label(fact_ATP_Olambda__171) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 358 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hz,Uu),Uua)) <-> pp(scratc1652025587_amone(scratc1552585242nd_nat,aa_TPT43085870d_bool(aTP_Lamm_hv(Uu),Uua))))) # label(fact_ATP_Olambda__172) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 359 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_ad(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc2007081020rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,Uu),Uua))) # label(fact_ATP_Olambda__173) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 360 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_be(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1552075016_union,aa_TPTP_ind_TPTP_ind(Uu,Uua))) # label(fact_ATP_Olambda__174) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 361 (all Uu all Uua (gg_TPTP_ind(Uua) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bg,Uu),Uua)) <-> (exists X3 (gg_TPTP_ind(X3) & Uua = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc892769185d_pair,Uu),X3)))))) # label(fact_ATP_Olambda__175) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 362 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jy(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1592000840d_e_is(aa_TPTP_ind_TPTP_ind(scratc1641004114etprod(Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc897099575d_pair(Uu,Uua),aa_TPTP_ind_TPTP_ind(scratc2105127113_first(Uu,Uua),Uub)),aa_TPTP_ind_TPTP_ind(scratc1717992283second(Uu,Uua),Uub))),Uub)))) # label(fact_ATP_Olambda__176) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 363 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_bo(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc1718854564bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,scratc326762172ptyset),Uub),Uu),Uua)) # label(fact_ATP_Olambda__177) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 364 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_fun1235454963TP_ind(aTP_Lamm_bn(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc1718854564bnd_if(aa_TPTP_ind_bool(Uua,Uub),Uub),scratc1479215681nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bb(Uu),Uua)))) # label(fact_ATP_Olambda__178) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 365 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_au(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045673258d_esti(Uu),Uub),Uua)))) # label(fact_ATP_Olambda__179) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 366 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_jr(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045673258d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc978622305_d_Sep(Uu),Uua))) -> pp(aa_TPTP_ind_bool(Uua,Uub))))) # label(fact_ATP_Olambda__180) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 367 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jp(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1978115701d_incl(Uu),Uua),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1978115701d_incl(Uu),Uub),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1592000840d_e_is(aa_TPTP_ind_TPTP_ind(scratc1044813150_power,Uu)),Uua),Uub)))))) # label(fact_ATP_Olambda__181) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.39 368 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jz(Uu),Uua),Uub)) <-> scratc2107418152_is_of(aa_TPTP_ind_TPTP_ind(scratc1717992283second(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)))) # label(fact_ATP_Olambda__182) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 369 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ka(Uu),Uua),Uub)) <-> scratc2107418152_is_of(aa_TPTP_ind_TPTP_ind(scratc2105127113_first(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)))) # label(fact_ATP_Olambda__183) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 370 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_kg(Uu),Uua),Uub)) <-> scratc2107418152_is_of(aa_TPTP_ind_TPTP_ind(scratc1592000835d_e_in(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)))) # label(fact_ATP_Olambda__184) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 371 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kk(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aa_TPT43085870d_bool(aTP_Lamm_kh(Uu),Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kj(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__185) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 372 (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(scratc2059788932_29_ii,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__186) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 373 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dj(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__187) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 374 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ib(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,Uua),Uub))))) # label(fact_ATP_Olambda__188) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 375 (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(scratc1110661201d_n_is,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__189) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 376 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dg(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__190) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 377 (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(scratc1511802498nd_iii,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__191) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 378 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dd(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__192) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 379 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_il(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__193) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 380 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fm(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__194) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 381 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fd(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__195) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 382 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fy(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032620262moreis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,Uu),Uub)))))) # label(fact_ATP_Olambda__196) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 383 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ee(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032620262moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032620262moreis,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__197) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 384 (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(scratc1032620262moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032620262moreis,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__198) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 385 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gb(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032620262moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,Uu),Uub)))))) # label(fact_ATP_Olambda__199) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 386 (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(scratc898636650lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc898636650lessis,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__200) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 387 (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(scratc898636650lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc898636650lessis,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__201) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 388 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fv(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc898636650lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc898636650lessis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc898636650lessis,Uu),Uub)))))) # label(fact_ATP_Olambda__202) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 389 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gh(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc898636650lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__203) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 390 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fj(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__204) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 391 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fa(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__205) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 392 (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(scratc1553110033nd_nis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1553110033nd_nis,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uub)))))) # label(fact_ATP_Olambda__206) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 393 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fg(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__207) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 394 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ex(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__208) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 395 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ge(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc898636650lessis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__209) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 396 (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(scratc1511802498nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__210) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 397 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bb(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,Uub),Uu)) & pp(aa_TPTP_ind_bool(Uua,Uub)))) # label(fact_ATP_Olambda__211) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 398 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_kd(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2062485044_image(aa_fun1431113780TP_ind(scratc978622305_d_Sep(Uu),Uua),Uu),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc290900360_Sigma,aa_fun1431113780TP_ind(scratc978622305_d_Sep(Uu),Uua)),scratc1592000835d_e_in(Uu,Uua))),Uub))))) # label(fact_ATP_Olambda__212) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 399 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_js(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045673258d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc978622305_d_Sep(Uu),Uua)))))) # label(fact_ATP_Olambda__213) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 400 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_km(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_kl(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__214) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 401 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bd(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bc(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__215) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 402 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kc(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kb(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__216) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 403 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jw(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jv(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__217) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 404 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ju(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jt(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__218) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 405 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kh(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,Uub),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc450796566d_d_Pi,Uu),aTP_Lamm_ai(Uua)))))) # label(fact_ATP_Olambda__219) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 406 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hv(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uua),Uub))))) # label(fact_ATP_Olambda__220) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 407 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hw(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,Uua),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uub))))) # label(fact_ATP_Olambda__221) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 408 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jx(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,Uub),aa_TPTP_ind_TPTP_ind(scratc1641004114etprod(Uu),Uua))))) # label(fact_ATP_Olambda__222) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 409 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ke(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,Uub),aa_fun1431113780TP_ind(scratc978622305_d_Sep(Uu),Uua))))) # label(fact_ATP_Olambda__223) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 410 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_aw(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,Uu),Uub))) # label(fact_ATP_Olambda__224) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 411 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eu(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_et(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__225) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 412 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eq(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ep(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__226) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 413 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_em(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_el(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__227) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 414 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ei(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_eh(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__228) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 415 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_da(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cz(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__229) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 416 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cw(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cv(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__230) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 417 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cs(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cr(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__231) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 418 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_co(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cn(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__232) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 419 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ck(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cj(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__233) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 420 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cg(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cf(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__234) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 421 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cc(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cb(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__235) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 422 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_by(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bx(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__236) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 423 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_kf(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(Uua,aa_TPTP_ind_TPTP_ind(scratc1592000835d_e_in(Uu,Uua),Uub))))) # label(fact_ATP_Olambda__237) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 424 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1913827119d_bool(aTP_Lamm_bf(Uu),Uua),Uub)) <-> (all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,X3),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1718854572bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,Uub),X3)),aa_TPTP_ind_TPTP_ind(Uua,X3)))))))) # label(fact_ATP_Olambda__238) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 425 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ax(Uu),Uua),Uub),Uuc) = aa_TPTP_ind_TPTP_ind(scratc1718854564bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2062485044_image(Uu,Uua),Uub),Uuc),aa_TPTP_ind_TPTP_ind(scratc1202511409d_soft(Uu,Uua,Uub),Uuc)),scratc326762172ptyset)) # label(fact_ATP_Olambda__239) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 426 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jv(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1592000840d_e_is(Uu),aa_TPTP_ind_TPTP_ind(scratc2105127113_first(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc897099575d_pair(Uu,Uua),Uub),Uuc))),Uub)))) # label(fact_ATP_Olambda__240) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 427 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jt(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1592000840d_e_is(Uua),aa_TPTP_ind_TPTP_ind(scratc1717992283second(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc897099575d_pair(Uu,Uua),Uub),Uuc))),Uuc)))) # label(fact_ATP_Olambda__241) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 428 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ki(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1592000840d_e_is(Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,Uua),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,Uub),Uuc))))) # label(fact_ATP_Olambda__242) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 429 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aq(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045673258d_esti(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__243) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 430 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1592000840d_e_is(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__244) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 431 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kb(Uu),Uua),Uub),Uuc)) <-> scratc2107418152_is_of(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc897099575d_pair(Uu,Uua),Uub),Uuc),aa_TPT43085870d_bool(aTP_Lamm_jx(Uu),Uua)))) # label(fact_ATP_Olambda__245) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 432 (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(scratc978753859d_l_ec(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045673258d_esti(Uu),Uuc),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045673258d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__246) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 433 (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_bool_bool(aa_boo1142376798l_bool(scratc1512064901nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045673258d_esti(Uu),Uuc),Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045673258d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__247) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 434 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kj(Uu),Uua),Uub),Uuc)) <-> (pp(aa_fun171081125l_bool(scratc776971441all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ki(Uua),Uub),Uuc))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1592000840d_e_is(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc450796566d_d_Pi,Uu),aTP_Lamm_ai(Uua))),Uub),Uuc))))) # label(fact_ATP_Olambda__248) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 435 (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_bp(Uu),Uua),Uub),Uuc)) <-> pp(Uu) & Uuc = Uua | -pp(Uu) & Uuc = Uub))) # label(fact_ATP_Olambda__249) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 436 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cz(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__250) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 437 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cn(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032620262moreis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__251) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 438 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cr(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032620262moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__252) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 439 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cb(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032620262moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032620262moreis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032620262moreis,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__253) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 440 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bx(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc898636650lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc898636650lessis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc898636650lessis,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__254) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 441 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cj(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc898636650lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__255) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 442 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_et(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__256) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 443 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ep(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2059788932_29_ii,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uuc),Uua))))))) # label(fact_ATP_Olambda__257) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 444 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_el(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__258) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 445 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_eh(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1110661201d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uuc),Uua))))))) # label(fact_ATP_Olambda__259) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 446 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cf(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc898636650lessis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__260) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 447 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cv(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511802498nd_iii,aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1111120387d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__261) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 448 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_kl(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1592000840d_e_is(Uu),Uub),Uuc)) -> pp(aa_TPTP_ind_bool(Uua,Uuc)))))) # label(fact_ATP_Olambda__262) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 449 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bc(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(scratc1592000840d_e_is(Uu),Uub),Uuc)))))) # label(fact_ATP_Olambda__263) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 450 (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_fun171081125l_bool(scratc1445907258nd_all(Uu),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_az(Uu),Uua),Uub),Uuc))))) # label(fact_ATP_Olambda__264) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 451 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ar(Uu),Uua),Uub),Uuc)) <-> pp(aa_fun171081125l_bool(scratc2035115897l_some(Uua),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aq(Uu),Uub),Uuc))))) # label(fact_ATP_Olambda__265) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 452 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_az(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1512064901nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1592000840d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,Uub),Uud))),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1592000840d_e_is(Uu),Uuc),Uud))))) # label(fact_ATP_Olambda__266) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 453 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_ao(Uu),Uua),Uub),Uuc),Uud)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1592000840d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,Uub),Uud)))))) # label(fact_ATP_Olambda__267) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 454 (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_an(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_am(Uu),Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__268) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 455 (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(scratc776971441all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_ao(Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__269) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 456 (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_av(Uu),Uua),Uub),Uuc),Uud) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,aa_TPTP_ind_TPTP_ind(scratc958776352wissel(Uu,Uub),Uuc)),Uud))) # label(fact_ATP_Olambda__270) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 457 (all Uu all Uua all Uub all Uuc all Uud all Uue (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_am(Uu),Uua),Uub),Uuc),Uud),Uue)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_al(Uu),Uua),Uub),Uuc),Uud),Uue))))) # label(fact_ATP_Olambda__271) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 458 (all Uu all Uua all Uub all Uuc all Uud all Uue all Uuf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_ak(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uue),Uuf)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1592000840d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,Uub),Uuc)),Uue)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1718329782bnd_ap,Uub),Uud)),Uuf))))))) # label(fact_ATP_Olambda__272) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 459 (all Uu all Uua all Uub all Uuc all Uud all Uue all Uuf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_al(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)) <-> pp(aa_fun171081125l_bool(scratc776971441all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_ak(Uua),Uub),Uuc),Uud),Uue),Uuf))))) # label(fact_ATP_Olambda__273) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 460 (all Uu all Uua (gg_TPTP_ind(Uu) -> aa_TPTP_ind_TPTP_ind(aTP_Lamm_ai(Uu),Uua) = Uu)) # label(fact_ATP_Olambda__274) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 461 (all Uu aa_TPTP_ind_TPTP_ind(aTP_Lamm_ac,Uu) = scratc1552585242nd_nat) # label(fact_ATP_Olambda__275) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 462 (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].
% 1.05/1.40 463 (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].
% 1.05/1.40 464 (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].
% 1.05/1.40 465 (all P (gg_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.05/1.40 466 (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].
% 1.05/1.40 467 (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].
% 1.05/1.40 468 (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].
% 1.05/1.40 469 (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].
% 1.05/1.40 470 (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].
% 1.05/1.40 471 (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].
% 1.05/1.40 472 (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].
% 1.05/1.40 473 (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].
% 1.05/1.40 474 (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].
% 1.05/1.48
% 1.05/1.48 ============================== end of process non-clausal formulas ===
% 1.05/1.48
% 1.05/1.48 ============================== PROCESS INITIAL CLAUSES ===============
% 1.05/1.48
% 1.05/1.48 ============================== PREDICATE ELIMINATION =================
% 1.05/1.48 475 -gg_bool(A) | A = fTrue | A = fFalse # label(help_fFalse_1_1_T) # label(axiom). [clausify(465)].
% 1.05/1.48 476 gg_bool(undefined_bool(bool)) # label(gsy_c_HOL_Oundefined_001t__HOL__Obool) # label(axiom). [assumption].
% 1.05/1.48 477 gg_bool(scratc1652025587_amone(A,B)) # label(gsy_c_Scratch__tptp__translate__50955__26514_ONUM698__thf__4__p_Obnd__amone) # label(axiom). [clausify(1)].
% 1.05/1.48 478 gg_bool(scratc1094873754_d_and(A,B)) # label(gsy_c_Scratch__tptp__translate__50955__26514_ONUM698__thf__4__p_Obnd__d__and) # label(axiom). [clausify(2)].
% 1.05/1.48 479 gg_bool(scratc1202338934_d_not(A)) # label(gsy_c_Scratch__tptp__translate__50955__26514_ONUM698__thf__4__p_Obnd__d__not) # label(axiom). [clausify(3)].
% 1.05/1.48 480 gg_bool(scratc1478362830nd_ec3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__50955__26514_ONUM698__thf__4__p_Obnd__ec3) # label(axiom). [clausify(4)].
% 1.05/1.48 481 gg_bool(scratc978753859d_l_ec(A,B)) # label(gsy_c_Scratch__tptp__translate__50955__26514_ONUM698__thf__4__p_Obnd__l__ec) # label(axiom). [clausify(8)].
% 1.05/1.48 482 gg_bool(scratc1561961865nd_or3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__50955__26514_ONUM698__thf__4__p_Obnd__or3) # label(axiom). [clausify(9)].
% 1.05/1.48 483 gg_bool(aa_bool_bool(A,B)) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom). [clausify(10)].
% 1.05/1.48 484 gg_bool(aa_TPTP_ind_bool(A,B)) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom). [clausify(11)].
% 1.05/1.48 485 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)].
% 1.05/1.48 486 gg_bool(fEx_TPTP_ind(A)) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom). [clausify(16)].
% 1.05/1.48 487 gg_bool(fFalse) # label(gsy_c_fFalse) # label(axiom). [assumption].
% 1.05/1.48 488 gg_bool(fTrue) # label(gsy_c_fTrue) # label(axiom). [assumption].
% 1.05/1.48 Derived: undefined_bool(bool) = fTrue | undefined_bool(bool) = fFalse. [resolve(475,a,476,a)].
% 1.05/1.48 Derived: scratc1652025587_amone(A,B) = fTrue | scratc1652025587_amone(A,B) = fFalse. [resolve(475,a,477,a)].
% 1.05/1.48 Derived: scratc1094873754_d_and(A,B) = fTrue | scratc1094873754_d_and(A,B) = fFalse. [resolve(475,a,478,a)].
% 1.05/1.48 Derived: scratc1202338934_d_not(A) = fTrue | scratc1202338934_d_not(A) = fFalse. [resolve(475,a,479,a)].
% 1.05/1.48 Derived: scratc1478362830nd_ec3(A,B,C) = fTrue | scratc1478362830nd_ec3(A,B,C) = fFalse. [resolve(475,a,480,a)].
% 1.05/1.48 Derived: scratc978753859d_l_ec(A,B) = fTrue | scratc978753859d_l_ec(A,B) = fFalse. [resolve(475,a,481,a)].
% 1.05/1.48 Derived: scratc1561961865nd_or3(A,B,C) = fTrue | scratc1561961865nd_or3(A,B,C) = fFalse. [resolve(475,a,482,a)].
% 1.05/1.48 Derived: aa_bool_bool(A,B) = fTrue | aa_bool_bool(A,B) = fFalse. [resolve(475,a,483,a)].
% 1.05/1.48 Derived: aa_TPTP_ind_bool(A,B) = fTrue | aa_TPTP_ind_bool(A,B) = fFalse. [resolve(475,a,484,a)].
% 1.05/1.48 Derived: aa_fun171081125l_bool(A,B) = fTrue | aa_fun171081125l_bool(A,B) = fFalse. [resolve(475,a,485,a)].
% 1.05/1.48 Derived: fEx_TPTP_ind(A) = fTrue | fEx_TPTP_ind(A) = fFalse. [resolve(475,a,486,a)].
% 1.05/1.48 Derived: fFalse = fTrue | fFalse = fFalse. [resolve(475,a,487,a)].
% 1.05/1.48 Derived: fTrue = fTrue | fTrue = fFalse. [resolve(475,a,488,a)].
% 1.05/1.48 489 scratc1373688649d_r_ec(A,B) | pp(A) # label(fact_def__r__ec) # label(axiom). [clausify(59)].
% 1.05/1.48 490 -scratc1373688649d_r_ec(A,B) | -pp(A) | pp(scratc1202338934_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(59)].
% 1.05/1.48 491 scratc1373688649d_r_ec(A,B) | -pp(scratc1202338934_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(59)].
% 1.05/1.48 492 scratc1989015204_l_iff(A,B) | -pp(scratc1094873754_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1512064901nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc1512064901nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(91)].
% 1.74/1.99 493 -scratc1989015204_l_iff(A,B) | pp(scratc1094873754_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1512064901nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc1512064901nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(91)].
% 1.74/1.99 494 scratc252365160d_orec(A,B) | -pp(scratc1094873754_d_and(aa_bool_bool(scratc979409864d_l_or(A),B),scratc978753859d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(92)].
% 1.74/1.99 495 -scratc252365160d_orec(A,B) | pp(scratc1094873754_d_and(aa_bool_bool(scratc979409864d_l_or(A),B),scratc978753859d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(92)].
% 1.74/1.99 496 scratc1627201175nd_wel(A) | -pp(scratc1202338934_d_not(scratc1202338934_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(97)].
% 1.74/1.99 497 -scratc1627201175nd_wel(A) | pp(scratc1202338934_d_not(scratc1202338934_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(97)].
% 1.74/1.99 498 -scratc1627201175nd_wel(A) | pp(A) # label(fact_l__et) # label(axiom). [clausify(147)].
% 1.74/1.99 Derived: pp(A) | -pp(scratc1202338934_d_not(scratc1202338934_d_not(A))). [resolve(498,a,496,a)].
% 1.74/1.99
% 1.74/1.99 ============================== end predicate elimination =============
% 1.74/1.99
% 1.74/1.99 Auto_denials: (non-Horn, no changes).
% 1.74/1.99
% 1.74/1.99 Term ordering decisions:
% 1.74/1.99 Function symbol KB weights: aTP_Lamm_a=1. scratc1718854572bnd_in=1. scratc1110661201d_n_is=1. scratc1511802498nd_iii=1. scratc2059788932_29_ii=1. scratc2007081020rdsucc=1. scratc1718329782bnd_ap=1. aTP_Lamm_aj=1. scratc898636650lessis=1. scratc1032620262moreis=1. scratc1461899370nd_n_1=1. scratc326762172ptyset=1. scratc290900360_Sigma=1. scratc1553110033nd_nis=1. fFalse=1. scratc1044813150_power=1. scratc1552585242nd_nat=1. scratc1994062358_nat_p=1. scratc450796566d_d_Pi=1. scratc631456891n_some=1. scratc1512064901nd_imp=1. scratc339965142d_repl=1. fTrue=1. scratc892769185d_pair=1. scratc2047161838d_Subq=1. scratc1173326988_proj0=1. scratc12260120closed=1. scratc1552075016_union=1. aTP_Lamm_af=1. scratc1110661196d_n_in=1. scratc1173326989_proj1=1. scratc519847578_n_all=1. aTP_Lamm_ac=1. aTP_Lamm_ae=1. aTP_Lamm_jo=1. scratc567628126closed=1. scratc732361140closed=1. aTP_Lamm_aa=1. aTP_Lamm_bq=1. aTP_Lamm_bs=1. aTP_Lamm_gn=1. aTP_Lamm_gp=1. aTP_Lamm_gr=1. aTP_Lamm_gt=1. aTP_Lamm_gv=1. aTP_Lamm_gx=1. aTP_Lamm_gz=1. aTP_Lamm_hb=1. aTP_Lamm_hd=1. aTP_Lamm_hf=1. aTP_Lamm_hh=1. aTP_Lamm_hj=1. aTP_Lamm_jf=1. aTP_Lamm_jj=1. aTP_Lamm_jk=1. scratc1637304053closed=1. scratc342982202_omega=1. scratc626434985d_Inj1=1. scratc817597488_prop2=1. aTP_Lamm_ag=1. aTP_Lamm_bg=1. aTP_Lamm_bi=1. aTP_Lamm_bj=1. aTP_Lamm_bz=1. aTP_Lamm_cd=1. aTP_Lamm_ch=1. aTP_Lamm_cl=1. aTP_Lamm_cp=1. aTP_Lamm_ct=1. aTP_Lamm_cx=1. aTP_Lamm_db=1. aTP_Lamm_de=1. aTP_Lamm_dh=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_ef=1. aTP_Lamm_ej=1. aTP_Lamm_en=1. aTP_Lamm_er=1. aTP_Lamm_ev=1. aTP_Lamm_ey=1. aTP_Lamm_fb=1. aTP_Lamm_fe=1. aTP_Lamm_fh=1. aTP_Lamm_fk=1. aTP_Lamm_fn=1. aTP_Lamm_fr=1. aTP_Lamm_ft=1. aTP_Lamm_fw=1. aTP_Lamm_fz=1. aTP_Lamm_gc=1. aTP_Lamm_gf=1. aTP_Lamm_gi=1. aTP_Lamm_gl=1. aTP_Lamm_hl=1. aTP_Lamm_hn=1. aTP_Lamm_hp=1. aTP_Lamm_hr=1. aTP_Lamm_ht=1. aTP_Lamm_hx=1. aTP_Lamm_hz=1. aTP_Lamm_ic=1. aTP_Lamm_if=1. aTP_Lamm_ih=1. aTP_Lamm_ij=1. aTP_Lamm_im=1. aTP_Lamm_io=1. aTP_Lamm_ir=1. aTP_Lamm_iu=1. aTP_Lamm_ix=1. aTP_Lamm_ja=1. aTP_Lamm_jc=1. aTP_Lamm_jd=1. aTP_Lamm_ji=1. fconj=1. fimplies=1. scratc1188443721_cond2=1. scratc1948810956d_Sing=1. scratc626434984d_Inj0=1. scratc817597487_prop1=1. aTP_Lamm_bm=1. aTP_Lamm_br=1. aTP_Lamm_bt=1. aTP_Lamm_bu=1. aTP_Lamm_bv=1. aTP_Lamm_bw=1. aTP_Lamm_ca=1. aTP_Lamm_ce=1. aTP_Lamm_ci=1. aTP_Lamm_cm=1. aTP_Lamm_cq=1. aTP_Lamm_cu=1. aTP_Lamm_cy=1. aTP_Lamm_dc=1. aTP_Lamm_df=1. aTP_Lamm_di=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_eg=1. aTP_Lamm_ek=1. aTP_Lamm_eo=1. aTP_Lamm_es=1. aTP_Lamm_ew=1. aTP_Lamm_ez=1. aTP_Lamm_fc=1. aTP_Lamm_ff=1. aTP_Lamm_fi=1. aTP_Lamm_fl=1. aTP_Lamm_fo=1. aTP_Lamm_fp=1. aTP_Lamm_fq=1. aTP_Lamm_fs=1. aTP_Lamm_fu=1. aTP_Lamm_fx=1. aTP_Lamm_ga=1. aTP_Lamm_gd=1. aTP_Lamm_gg=1. aTP_Lamm_gj=1. aTP_Lamm_gm=1. aTP_Lamm_go=1. aTP_Lamm_gq=1. aTP_Lamm_gs=1. aTP_Lamm_gu=1. aTP_Lamm_gw=1. aTP_Lamm_gy=1. aTP_Lamm_ha=1. aTP_Lamm_hc=1. aTP_Lamm_he=1. aTP_Lamm_hg=1. aTP_Lamm_hi=1. aTP_Lamm_hk=1. aTP_Lamm_hm=1. aTP_Lamm_ho=1. aTP_Lamm_hq=1. aTP_Lamm_hs=1. aTP_Lamm_hu=1. aTP_Lamm_hy=1. aTP_Lamm_ia=1. aTP_Lamm_id=1. aTP_Lamm_ig=1. aTP_Lamm_ii=1. aTP_Lamm_ik=1. aTP_Lamm_in=1. aTP_Lamm_ip=1. aTP_Lamm_iq=1. aTP_Lamm_is=1. aTP_Lamm_it=1. aTP_Lamm_iv=1. aTP_Lamm_iw=1. aTP_Lamm_iy=1. aTP_Lamm_iz=1. aTP_Lamm_jb=1. aTP_Lamm_je=1. aTP_Lamm_jg=1. aTP_Lamm_jh=1. aTP_Lamm_jl=1. aTP_Lamm_jm=1. aTP_Lamm_jn=1. aTP_Lamm_jq=1. aTP_Lamm_kn=1. fequal_TPTP_ind=1. scratc1188443720_cond1=1. scratc1551010860nd_nIn=1. scratc279635492univof=1. scratc635639839_n_one=1. scratc995735700_d_Unj=1. aTP_Lamm_ab=1. aTP_Lamm_ah=1. aTP_Lamm_bk=1. aTP_Lamm_bl=1. bool=1. scratc1173720586_prop4=1. scratc1611924714_prop1=1. scratc1788356785_prop1=1. scratc1863830991pair_p=1. scratc1923970566_empty=1. scratc1994321837_prop1=1. scratc229235312_prop1=1. scratc435200364_prop1=1. scratc612357159nempty=1. scratc692202724munion=1. scratc984432929d_plus=1. scratc307361924d_i1_s=1. scratc704041832d_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. scratc1094873754_d_and=1. aa_TPT1123896796d_bool=1. scratc1718854564bnd_if=1. scratc978753859d_l_ec=1. aa_fun1212484691d_bool=1. aa_TPT985247859d_bool=1. scratc1592000835d_e_in=1. scratc897099575d_pair=1. aa_fun987228051d_bool=1. scratc1512130488nd_ind=1. scratc1652025587_amone=1. scratc1717992283second=1. scratc2062485044_image=1. scratc2105127113_first=1. aa_TPT125613450d_bool=1. scratc1553503622nd_non=1. aa_fun1913827119d_bool=1. scratc28516594d_anec=1. aa_TPT1791839040TP_ind=1. aa_fun1107270209d_bool=1. aa_fun845057962d_bool=1. scratc1478362891nd_ecp=1. scratc469148168_ecelt=1. scratc48683154eplSep=1. scratc468557777_ecect=1. aa_TPT1781712639TP_ind=1. aa_TPT2142672771l_bool=1. aa_fun1235454963TP_ind=1. cOMBB_658106424TP_ind=1. cOMBS_2003118649l_bool=1. scratc1090749555ectset=1. scratc1478362895nd_ect=1. scratc1562158727nd_out=1. scratc1632706228etprop=1. scratc578723029fixfu2=1. scratc6359709_fixfu=1. scratc958776352wissel=1. scratc1196866901unmore=1. scratc1405328713nverse=1. scratc1979362076d_invf=1. scratc1983098607d_tofs=1. scratc975547678ectelt=1. f1=1. f12=1. f13=1. f20=1. f24=1. scratc776971441all_of=1. scratc1111120387d_n_pl=1. scratc1592000840d_e_is=1. scratc1202338934_d_not=1. scratc978622305_d_Sep=1. scratc1045673258d_esti=1. scratc2035115897l_some=1. scratc1608659119ffprop=1. scratc1445907258nd_all=1. scratc979409864d_l_or=1. scratc1338780153_rec_G=1. aTP_Lamm_ai=1. aTP_Lamm_jx=1. scratc1561699519nd_one=1. aTP_Lamm_ak=1. aTP_Lamm_au=1. aTP_Lamm_bc=1. aTP_Lamm_bp=1. aTP_Lamm_bx=1. aTP_Lamm_cb=1. aTP_Lamm_cf=1. aTP_Lamm_cj=1. aTP_Lamm_cn=1. aTP_Lamm_cr=1. aTP_Lamm_cv=1. aTP_Lamm_cz=1. aTP_Lamm_eh=1. aTP_Lamm_el=1. aTP_Lamm_ep=1. aTP_Lamm_et=1. aTP_Lamm_fv=1. aTP_Lamm_fy=1. aTP_Lamm_gb=1. aTP_Lamm_ge=1. aTP_Lamm_gh=1. aTP_Lamm_gk=1. aTP_Lamm_hv=1. aTP_Lamm_jp=1. aTP_Lamm_kl=1. scratc1978115701d_incl=1. aTP_Lamm_ao=1. aTP_Lamm_ay=1. aTP_Lamm_bb=1. aTP_Lamm_bf=1. aTP_Lamm_dd=1. aTP_Lamm_dg=1. aTP_Lamm_dj=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_ee=1. aTP_Lamm_ex=1. aTP_Lamm_fa=1. aTP_Lamm_fd=1. aTP_Lamm_fg=1. aTP_Lamm_fj=1. aTP_Lamm_fm=1. aTP_Lamm_ib=1. aTP_Lamm_ie=1. aTP_Lamm_kh=1. aTP_Lamm_kj=1. scratc1104147936ective=1. scratc1479215681nd_eps=1. scratc1641004114etprod=1. aTP_Lamm_al=1. aTP_Lamm_am=1. aTP_Lamm_an=1. aTP_Lamm_ap=1. aTP_Lamm_aq=1. aTP_Lamm_as=1. aTP_Lamm_at=1. aTP_Lamm_az=1. aTP_Lamm_ba=1. aTP_Lamm_bd=1. aTP_Lamm_by=1. aTP_Lamm_cc=1. aTP_Lamm_cg=1. aTP_Lamm_ck=1. aTP_Cputime limit exceeded (core dumped)
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