TSTP Solution File: NUM684+4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM684+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 13:30:37 EDT 2022
% Result : Timeout 300.03s 300.32s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM684+4 : TPTP v8.1.0. Released v7.3.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jul 7 12:20:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.04/1.34 ============================== Prover9 ===============================
% 1.04/1.34 Prover9 (32) version 2009-11A, November 2009.
% 1.04/1.34 Process 12257 was started by sandbox on n021.cluster.edu,
% 1.04/1.34 Thu Jul 7 12:20:05 2022
% 1.04/1.34 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_12090_n021.cluster.edu".
% 1.04/1.34 ============================== end of head ===========================
% 1.04/1.34
% 1.04/1.34 ============================== INPUT =================================
% 1.04/1.34
% 1.04/1.34 % Reading from file /tmp/Prover9_12090_n021.cluster.edu
% 1.04/1.34
% 1.04/1.34 set(prolog_style_variables).
% 1.04/1.34 set(auto2).
% 1.04/1.34 % set(auto2) -> set(auto).
% 1.04/1.34 % set(auto) -> set(auto_inference).
% 1.04/1.34 % set(auto) -> set(auto_setup).
% 1.04/1.34 % set(auto_setup) -> set(predicate_elim).
% 1.04/1.34 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.04/1.34 % set(auto) -> set(auto_limits).
% 1.04/1.34 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.04/1.34 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.04/1.34 % set(auto) -> set(auto_denials).
% 1.04/1.34 % set(auto) -> set(auto_process).
% 1.04/1.34 % set(auto2) -> assign(new_constants, 1).
% 1.04/1.34 % set(auto2) -> assign(fold_denial_max, 3).
% 1.04/1.34 % set(auto2) -> assign(max_weight, "200.000").
% 1.04/1.34 % set(auto2) -> assign(max_hours, 1).
% 1.04/1.34 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.04/1.34 % set(auto2) -> assign(max_seconds, 0).
% 1.04/1.34 % set(auto2) -> assign(max_minutes, 5).
% 1.04/1.34 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.04/1.34 % set(auto2) -> set(sort_initial_sos).
% 1.04/1.34 % set(auto2) -> assign(sos_limit, -1).
% 1.04/1.34 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.04/1.34 % set(auto2) -> assign(max_megs, 400).
% 1.04/1.34 % set(auto2) -> assign(stats, some).
% 1.04/1.34 % set(auto2) -> clear(echo_input).
% 1.04/1.34 % set(auto2) -> set(quiet).
% 1.04/1.34 % set(auto2) -> clear(print_initial_clauses).
% 1.04/1.34 % set(auto2) -> clear(print_given).
% 1.04/1.34 assign(lrs_ticks,-1).
% 1.04/1.34 assign(sos_limit,10000).
% 1.04/1.34 assign(order,kbo).
% 1.04/1.34 set(lex_order_vars).
% 1.04/1.34 clear(print_given).
% 1.04/1.34
% 1.04/1.34 % formulas(sos). % not echoed (526 formulas)
% 1.04/1.34
% 1.04/1.34 ============================== end of input ==========================
% 1.04/1.34
% 1.04/1.34 % From the command line: assign(max_seconds, 300).
% 1.04/1.34
% 1.04/1.34 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.04/1.34
% 1.04/1.34 % Formulas that are not ordinary clauses:
% 1.04/1.34 1 (all B_1 all B_2 gg_bool(scratc193618603_amone(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__48274__6815_ONUM684__thf__4__p_Obnd__amone) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 2 (all B_1 all B_2 gg_bool(scratc1451648738_d_and(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__48274__6815_ONUM684__thf__4__p_Obnd__d__and) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 3 (all B_1 gg_bool(scratc1559113918_d_not(B_1))) # label(gsy_c_Scratch__tptp__translate__48274__6815_ONUM684__thf__4__p_Obnd__d__not) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 4 (all B_1 all B_2 all B_3 gg_bool(scratc1009769606nd_ec3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__48274__6815_ONUM684__thf__4__p_Obnd__ec3) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 5 (all B_1 all B_2 gg_TPTP_ind(scratc1009769671nd_ect(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__48274__6815_ONUM684__thf__4__p_Obnd__ect) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 6 (all B_1 gg_TPTP_ind(scratc1010622457nd_eps(B_1))) # label(gsy_c_Scratch__tptp__translate__48274__6815_ONUM684__thf__4__p_Obnd__eps) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 7 (all B_1 all B_2 gg_TPTP_ind(scratc1043537264nd_ind(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__48274__6815_ONUM684__thf__4__p_Obnd__ind) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 8 (all B_1 all B_2 gg_bool(scratc1667830523d_l_ec(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__48274__6815_ONUM684__thf__4__p_Obnd__l__ec) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 9 (all B_1 all B_2 all B_3 gg_bool(scratc1093368641nd_or3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__48274__6815_ONUM684__thf__4__p_Obnd__or3) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 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].
% 1.04/1.34 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].
% 1.04/1.35 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].
% 1.04/1.35 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].
% 1.04/1.35 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].
% 1.04/1.35 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].
% 1.04/1.35 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].
% 1.04/1.35 17 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1255411634lessis,X),Xa)) <-> pp(aa_bool_bool(scratc1668486528d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1043209274nd_iii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,X),Xa))))) # label(fact_def__lessis) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 18 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1389395246moreis,X),Xa)) <-> pp(aa_bool_bool(scratc1668486528d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1554228284_29_ii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,X),Xa))))) # label(fact_def__moreis) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 19 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc138218802_prop1,X),Xa)) <-> pp(scratc1093368641nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1554228284_29_ii,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1043209274nd_iii,X),Xa))))) # label(fact_def__d__29__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 20 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1043209274nd_iii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1436836403n_some,aa_TPT43085870d_bool(scratc1306558711ffprop(Xa),X))))) # label(fact_def__iii) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 21 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1554228284_29_ii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1436836403n_some,aa_TPT43085870d_bool(scratc1306558711ffprop(X),Xa))))) # label(fact_def__d__29__ii) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 22 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1306558711ffprop(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,X),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Xa),Xb))))) # label(fact_def__diffprop) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 23 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1697340275_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1084516809nd_nis,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(X),Xb))))) # label(fact_def__d__28__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 24 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1108978100_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1084516809nd_nis,Xa),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(X),Xa))))) # label(fact_def__d__27__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 25 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc520615925_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Xa),X))))) # label(fact_def__d__26__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 26 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2079737398_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(X),Xa)),Xb)),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(X),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Xa),Xb)))))) # label(fact_def__d__25__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 27 (all X scratc1800197051d_n_pl(X) = aa_TPT1424761345TP_ind(scratc535879166bnd_ap,aa_TPTP_ind_TPTP_ind(scratc818469225d_plus,X))) # label(fact_def__n__pl) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 28 (all X aa_TPTP_ind_TPTP_ind(scratc818469225d_plus,X) = scratc1043537264nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1139873230d_d_Pi,scratc1083992018nd_nat),aTP_Lamm_ad),aa_TPT43085870d_bool(scratc1491375224_prop2,X))) # label(fact_def__plus) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 29 (all X aa_TPTP_ind_TPTP_ind(scratc401941424d_24_g,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2136283600_Sigma,scratc1083992018nd_nat),aTP_Lamm_ae(X))) # label(fact_def__d__24__g) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 30 (all X (pp(aa_TPTP_ind_bool(scratc1862797250_prop4,X)) <-> pp(aa_fun171081125l_bool(scratc693011761l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1139873230d_d_Pi,scratc1083992018nd_nat),aTP_Lamm_ad)),aa_TPT43085870d_bool(scratc1491375224_prop2,X))))) # label(fact_def__prop4) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 31 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1862797249_prop3(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,X),Xb)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,Xa),Xb))))) # label(fact_def__prop3) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 32 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1491375224_prop2,X),Xa)) <-> pp(scratc1451648738_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,Xa),scratc1295935666nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,X)),aa_TPTP_ind_bool(scratc1491375223_prop1,Xa))))) # label(fact_def__d__24__prop2) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 33 (all X (pp(aa_TPTP_ind_bool(scratc1491375223_prop1,X)) <-> pp(aa_fun171081125l_bool(scratc876622562_n_all,aa_TPT43085870d_bool(aTP_Lamm_af,X))))) # label(fact_def__d__24__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 34 (all X (pp(aa_TPTP_ind_bool(scratc903013048_prop1,X)) <-> pp(aa_bool_bool(scratc1668486528d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,X),scratc1295935666nd_n_1)),aa_fun171081125l_bool(scratc1436836403n_some,aa_TPT43085870d_bool(aTP_Lamm_ag,X)))))) # label(fact_def__d__23__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 35 (all X (pp(aa_TPTP_ind_bool(scratc314650873_prop1,X)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1084516809nd_nis,aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,X)),X)))) # label(fact_def__d__22__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 36 (all X (pp(aa_TPTP_ind_bool(scratc1877520385_cond2,X)) <-> pp(aa_fun171081125l_bool(scratc876622562_n_all,aa_TPT43085870d_bool(aTP_Lamm_ah,X))))) # label(fact_def__cond2) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 37 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1084516809nd_nis,X),Xa)) <-> pp(scratc1559113918_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,X),Xa))))) # label(fact_def__nis) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 38 (all X all Xa all Xb all Xc all Xd scratc719007862indeq2(X,Xa,Xb,Xc,Xd) = aa_TPT1424761345TP_ind(scratc1409318588_indeq(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1215582836d_11_i(X,Xa,Xb),Xc),Xd))) # label(fact_def__indeq2) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 39 (all X all Xa all Xb scratc1215582836d_11_i(X,Xa,Xb) = scratc1409318588_indeq(X,Xa,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1139873230d_d_Pi,X),aTP_Lamm_aj(Xb)))) # label(fact_def__d__11__i) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 40 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc935498013fixfu2(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ao(X),Xa),Xb),Xc))))) # label(fact_def__fixfu2) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 41 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1409318588_indeq(X,Xa,Xb),Xc),Xd) = scratc1043537264nd_ind(Xb,aa_TPT43085870d_bool(scratc1862797248_prop2(X,Xa,Xb,Xc),Xd))) # label(fact_def__indeq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 42 (all X all Xa all Xb all Xc all Xd all Xe (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1862797248_prop2(X,Xa,Xb,Xc),Xd),Xe)) <-> pp(aa_fun171081125l_bool(scratc693011761l_some(X),aa_TPT43085870d_bool(scratc2038697850_prop1(X,Xa,Xb,Xc,Xd),Xe))))) # label(fact_def__prop2) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 43 (all X all Xa all Xb all Xc all Xd all Xe all Xf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2038697850_prop1(X,Xa,Xb,Xc,Xd),Xe),Xf)) <-> pp(scratc1451648738_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc879709554d_esti(X),Xf),aa_TPTP_ind_TPTP_ind(scratc1157634441_ecect(X,Xa),Xd)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc133593856d_e_is(Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,Xc),Xf)),Xe))))) # label(fact_def__d__10__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 44 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc695436373_fixfu(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_aq(X),Xa),Xb),Xc))))) # label(fact_def__fixfu) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 45 (all X all Xa scratc1157634441_ecect(X,Xa) = scratc133593851d_e_in(aa_TPTP_ind_TPTP_ind(scratc1733889814_power,X),scratc2010036538d_anec(X,Xa))) # label(fact_def__ecect) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 46 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1332322662ectelt(X,Xa),Xb) = aa_TPTP_ind_TPTP_ind(scratc1447524539ectset(X,Xa),aa_TPTP_ind_TPTP_ind(scratc1158224832_ecelt(X,Xa),Xb))) # label(fact_def__ectelt) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 47 (all X all Xa scratc1447524539ectset(X,Xa) = scratc1093565503nd_out(aa_TPTP_ind_TPTP_ind(scratc1733889814_power,X),scratc2010036538d_anec(X,Xa))) # label(fact_def__ectset) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 48 (all X all Xa scratc1009769671nd_ect(X,Xa) = aa_fun1431113780TP_ind(scratc1335397289_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1733889814_power,X)),scratc2010036538d_anec(X,Xa))) # label(fact_def__ect) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 49 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc2010036538d_anec(X,Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc693011761l_some(X),aa_TPT43085870d_bool(scratc1009769667nd_ecp(X,Xa),Xb))))) # label(fact_def__anec) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 50 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1009769667nd_ecp(X,Xa),Xb),Xc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc133593856d_e_is(aa_TPTP_ind_TPTP_ind(scratc1733889814_power,X)),Xb),aa_TPTP_ind_TPTP_ind(scratc1158224832_ecelt(X,Xa),Xc))))) # label(fact_def__ecp) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 51 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1158224832_ecelt(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc1335397289_d_Sep(X),aa_TPT43085870d_bool(Xa,Xb))) # label(fact_def__ecelt) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 52 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1553641885unmore(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc1335397289_d_Sep(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_as(X),Xa),Xb))) # label(fact_def__unmore) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 53 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc949734140etprop(X,Xa),Xb),Xc)) <-> pp(scratc1451648738_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc879709554d_esti(X),Xc),Xa),scratc1559113918_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc879709554d_esti(X),Xc),Xb)))))) # label(fact_def__nissetprop) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 54 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1717081452t_disj(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc977314034nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_at(X),Xa),Xb))))) # label(fact_def__st__disj) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 55 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1812151997d_incl(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc977314034nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_au(X),Xa),Xb))))) # label(fact_def__incl) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 56 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc310256751nempty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc693011761l_some(X),aa_TPT43085870d_bool(aTP_Lamm_av(X),Xa))))) # label(fact_def__nonempty) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 57 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc465563582_empty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X)),scratc1084910398nd_non(X,aa_TPT43085870d_bool(aTP_Lamm_av(X),Xa)))))) # label(fact_def__empty) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 58 (all X scratc879709554d_esti(X) = scratc536403956bnd_in) # label(fact_def__esti) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 59 (all X all Xa (scratc2062765313d_r_ec(X,Xa) <-> (pp(X) -> pp(scratc1559113918_d_not(Xa))))) # label(fact_def__r__ec) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 60 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc77183527hangef(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2136283600_Sigma,X),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_aw(X),Xb),Xc),Xd))) # label(fact_def__changef) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 61 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1315551336wissel(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2136283600_Sigma,X),scratc889103827sel_wb(X,Xa,Xb))) # label(fact_def__wissel) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 62 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc889103827sel_wb(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc1043930859nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc133593856d_e_is(X),Xc),Xb),X,Xa),aa_TPTP_ind_TPTP_ind(scratc889103826sel_wa(X,Xa,Xb),Xc))) # label(fact_def__wissel__wb) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 63 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc889103826sel_wa(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc1043930859nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc133593856d_e_is(X),Xc),Xa),X,Xb),Xc)) # label(fact_def__wissel__wa) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 64 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1043930859nd_ite(X,Xa,Xb),Xc) = scratc1043537264nd_ind(Xa,aa_TPT43085870d_bool(scratc1862797247_prop1(X,Xa,Xb),Xc))) # label(fact_def__ite) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 65 (all X all Xa all Xb all Xc all Xd (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1862797247_prop1(X,Xa,Xb),Xc),Xd)) <-> pp(scratc1451648738_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1043471677nd_imp,X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc133593856d_e_is(Xa),Xd),Xb)),aa_bool_bool(aa_boo1142376798l_bool(scratc1043471677nd_imp,scratc1559113918_d_not(X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc133593856d_e_is(Xa),Xd),Xc)))))) # label(fact_def__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 66 (all X all Xa scratc2074767267second(X,Xa) = scratc1862403653_proj1) # label(fact_def__second) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 67 (all X all Xa scratc646720129_first(X,Xa) = scratc1862403652_proj0) # label(fact_def__first) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 68 (all X all Xa scratc1702479087d_pair(X,Xa) = scratc726805481d_pair) # label(fact_def__d__pair) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 69 (all X all Xa scratc1093565503nd_out(X,Xa) = scratc1036547705d_soft(aa_fun1431113780TP_ind(scratc1335397289_d_Sep(X),Xa),X,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2136283600_Sigma,aa_fun1431113780TP_ind(scratc1335397289_d_Sep(X),Xa)),scratc133593851d_e_in(X,Xa)))) # label(fact_def__out) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 70 (all X all Xa all Xb (gg_TPTP_ind(Xb) -> aa_TPTP_ind_TPTP_ind(scratc133593851d_e_in(X,Xa),Xb) = Xb)) # label(fact_def__e__in) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 71 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc1056814002_inj_h(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2136283600_Sigma,X),aa_TPT1424761345TP_ind(aTP_Lamm_ax(Xc),Xd))) # label(fact_def__inj__h) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 72 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1813398372d_invf(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2136283600_Sigma,Xa),scratc1036547705d_soft(X,Xa,Xb))) # label(fact_def__invf) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 73 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782306518ective(X),Xa),Xb)) <-> pp(scratc1451648738_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc598587288ective(X),Xa),Xb),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc485479435ective(X),Xa),Xb))))) # label(fact_def__bijective) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 74 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc485479435ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc977314034nd_all(Xa),aa_TPT43085870d_bool(scratc604078060_image(X,Xa),Xb))))) # label(fact_def__surjective) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 75 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc63224577nverse(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2136283600_Sigma,Xa),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ay(X),Xa),Xb))) # label(fact_def__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 76 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1036547705d_soft(X,Xa,Xb),Xc) = scratc1043537264nd_ind(X,aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_az(Xa),Xb),Xc))) # label(fact_def__soft) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 77 (all X all Xa scratc1817134903d_tofs(X,Xa) = scratc535879166bnd_ap) # label(fact_def__tofs) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 78 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc604078060_image(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc693011761l_some(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_az(Xa),Xb),Xc))))) # label(fact_def__image) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 79 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc598587288ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc977314034nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bb(X),Xa),Xb))))) # label(fact_def__injective) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 80 (all X all Xa scratc1043537264nd_ind(X,Xa) = scratc1010622457nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bc(X),Xa))) # label(fact_def__ind) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 81 (all X all Xa (pp(aa_fun171081125l_bool(scratc1093106295nd_one(X),Xa)) <-> pp(scratc1451648738_d_and(scratc193618603_amone(X,Xa),aa_fun171081125l_bool(scratc693011761l_some(X),Xa))))) # label(fact_def__one) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 82 (all X all Xa (pp(scratc193618603_amone(X,Xa)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X)),aa_fun1584354236d_bool(aTP_Lamm_be(X),Xa))))) # label(fact_def__amone) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 83 (all X scratc133593856d_e_is(X) = fequal_TPTP_ind) # label(fact_def__e__is) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 84 (all X all Xa all Xb (scratc639765123_orec3(X,Xa,Xb) <-> pp(scratc1451648738_d_and(scratc1093368641nd_or3(X,Xa,Xb),scratc1009769606nd_ec3(X,Xa,Xb))))) # label(fact_def__orec3) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 85 (all X all Xa all Xb (pp(scratc1009769606nd_ec3(X,Xa,Xb)) <-> scratc2009970891d_and3(scratc1667830523d_l_ec(X,Xa),scratc1667830523d_l_ec(Xa,Xb),scratc1667830523d_l_ec(Xb,X)))) # label(fact_def__ec3) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 86 (all X all Xa all Xb (scratc2009970891d_and3(X,Xa,Xb) <-> pp(scratc1451648738_d_and(X,scratc1451648738_d_and(Xa,Xb))))) # label(fact_def__and3) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 87 (all X all Xa all Xb (pp(scratc1093368641nd_or3(X,Xa,Xb)) <-> pp(aa_bool_bool(scratc1668486528d_l_or(X),aa_bool_bool(scratc1668486528d_l_or(Xa),Xb))))) # label(fact_def__or3) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 88 (all X all Xa (pp(aa_fun171081125l_bool(scratc693011761l_some(X),Xa)) <-> pp(scratc1559113918_d_not(aa_fun171081125l_bool(scratc1582350953all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X)),scratc1084910398nd_non(X,Xa)))))) # label(fact_def__l__some) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 89 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc1084910398nd_non(X,Xa),Xb)) <-> pp(scratc1559113918_d_not(aa_TPTP_ind_bool(Xa,Xb))))) # label(fact_def__non) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 90 (all X scratc977314034nd_all(X) = scratc1582350953all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X))) # label(fact_def__all) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 91 (all X all Xa (scratc198306540_l_iff(X,Xa) <-> pp(scratc1451648738_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1043471677nd_imp,X),Xa),aa_bool_bool(aa_boo1142376798l_bool(scratc1043471677nd_imp,Xa),X))))) # label(fact_def__l__iff) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 92 (all X all Xa (scratc86401456d_orec(X,Xa) <-> pp(scratc1451648738_d_and(aa_bool_bool(scratc1668486528d_l_or(X),Xa),scratc1667830523d_l_ec(X,Xa))))) # label(fact_def__orec) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 93 (all X scratc1668486528d_l_or(X) = aa_boo1142376798l_bool(scratc1043471677nd_imp,scratc1559113918_d_not(X))) # label(fact_def__l__or) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 94 (all X all Xa (pp(scratc1451648738_d_and(X,Xa)) <-> pp(scratc1559113918_d_not(scratc1667830523d_l_ec(X,Xa))))) # label(fact_def__d__and) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 95 (all X all Xa (pp(scratc1667830523d_l_ec(X,Xa)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1043471677nd_imp,X),scratc1559113918_d_not(Xa))))) # label(fact_def__l__ec) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 96 scratc928307224bvious <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1043471677nd_imp,fFalse),fFalse)) # label(fact_def__obvious) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 97 (all X (scratc1158607951nd_wel(X) <-> pp(scratc1559113918_d_not(scratc1559113918_d_not(X))))) # label(fact_def__wel) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 98 (all X (pp(scratc1559113918_d_not(X)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1043471677nd_imp,X),fFalse)))) # label(fact_def__d__not) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 99 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1139873230d_d_Pi,X),Xa) = aa_fun1431113780TP_ind(scratc1335397289_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1733889814_power,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2136283600_Sigma,X),aTP_Lamm_bf(Xa)))),aa_fun1913827119d_bool(aTP_Lamm_bg(X),Xa))) # label(fact_def__d__Pi) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 100 (all X (gg_TPTP_ind(X) -> (pp(aa_TPTP_ind_bool(scratc521726855pair_p,X)) <-> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc726805481d_pair,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,X),scratc24661764ptyset)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,X),aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,scratc24661764ptyset))) = X))) # label(fact_def__pair__p) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 101 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc1513194714eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bh,Xa)),scratc1862403653_proj1)) # label(fact_def__ap) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 102 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc298899978etprod(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2136283600_Sigma,X),aTP_Lamm_aj(Xa))) # label(fact_def__setprod) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 103 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2136283600_Sigma,X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc390102316munion,X),aTP_Lamm_bi(Xa))) # label(fact_def__d__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 104 (all X aa_TPTP_ind_TPTP_ind(scratc1862403653_proj1,X) = aa_fun277296641TP_ind(scratc1513194714eplSep(X,aTP_Lamm_bj),scratc1352510684_d_Unj)) # label(fact_def__proj1) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 105 (all X aa_TPTP_ind_TPTP_ind(scratc1862403652_proj0,X) = aa_fun277296641TP_ind(scratc1513194714eplSep(X,aTP_Lamm_bk),scratc1352510684_d_Unj)) # label(fact_def__proj0) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 106 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc726805481d_pair,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1383959415nunion(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc174001438d_repl,X),scratc1431814496d_Inj0)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc174001438d_repl,Xa),scratc1431814497d_Inj1))) # label(fact_def__pair) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 107 (all X aa_TPTP_ind_TPTP_ind(scratc1431814496d_Inj0,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc174001438d_repl,X),scratc1431814497d_Inj1)) # label(fact_def__d__Inj0) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 108 (all X (pp(aa_TPTP_ind_bool(scratc203353694_nat_p,X)) <-> (all X1 (pp(aa_TPTP_ind_bool(X1,scratc24661764ptyset)) -> ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(X1,X2)) -> pp(aa_TPTP_ind_bool(X1,aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,X2)))))) -> pp(aa_TPTP_ind_bool(X1,X))))))) # label(fact_def__nat__p) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 109 (all X aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1383959415nunion(X),aa_TPTP_ind_TPTP_ind(scratc606706820d_Sing,X))) # label(fact_def__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 110 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1240958294In_rec(X),Xa) = scratc1010622457nd_eps(aa_TPT43085870d_bool(scratc976040881_rec_G(X),Xa))) # label(fact_def__d__In__rec) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 111 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc976040881_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(scratc536403956bnd_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].
% 1.04/1.35 112 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1300244957tminus(X),Xa) = aa_fun1431113780TP_ind(scratc1335397289_d_Sep(X),aa_TPT43085870d_bool(aTP_Lamm_bn,Xa))) # label(fact_def__setminus) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 113 (all X all Xa scratc1513194714eplSep(X,Xa) = aa_TPT494704832TP_ind(scratc174001438d_repl,aa_fun1431113780TP_ind(scratc1335397289_d_Sep(X),Xa))) # label(fact_def__d__ReplSep) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 114 (all X all Xa aa_fun1431113780TP_ind(scratc1335397289_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc536403948bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc536403956bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc174001438d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bo(X),Xa))),scratc24661764ptyset)) # label(fact_def__d__Sep) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 115 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc390102316munion,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc93668032_union,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc174001438d_repl,X),Xa))) # label(fact_def__famunion) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 116 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1383959415nunion(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc93668032_union,aa_TPTP_ind_TPTP_ind(scratc2030769978_UPair(X),Xa))) # label(fact_def__binunion) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 117 (all X aa_TPTP_ind_TPTP_ind(scratc606706820d_Sing,X) = aa_TPTP_ind_TPTP_ind(scratc2030769978_UPair(X),X)) # label(fact_def__d__Sing) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 118 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc2030769978_UPair(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc174001438d_repl,aa_TPTP_ind_TPTP_ind(scratc1733889814_power,aa_TPTP_ind_TPTP_ind(scratc1733889814_power,scratc24661764ptyset))),aa_TPT1424761345TP_ind(aTP_Lamm_bp(X),Xa))) # label(fact_def__d__UPair) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 119 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1082417636nd_nIn,X),Xa)) <-> -pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X),Xa)))) # label(fact_def__nIn) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 120 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc536403948bnd_if(X,Xa),Xb) = scratc1010622457nd_eps(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bq(X),Xa),Xb))) # label(fact_def__if) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 121 (all X (pp(aa_TPTP_ind_bool(scratc1274564781closed,X)) <-> pp(aa_TPTP_ind_bool(scratc2121339302closed,X)) & pp(aa_TPTP_ind_bool(scratc138588668closed,X)) & pp(aa_TPTP_ind_bool(scratc331530448closed,X)))) # label(fact_def__d__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 122 (all X (pp(aa_TPTP_ind_bool(scratc331530448closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X1),X)) -> (all X2 ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X3),X1)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,aa_TPTP_ind_TPTP_ind(X2,X3)),X))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc174001438d_repl,X1),X2)),X))))))))) # label(fact_def__d__Repl__closed) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 123 (all X (pp(aa_TPTP_ind_bool(scratc138588668closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,aa_TPTP_ind_TPTP_ind(scratc1733889814_power,X1)),X))))))) # label(fact_def__d__Power__closed) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 124 (all X (pp(aa_TPTP_ind_bool(scratc2121339302closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,aa_TPTP_ind_TPTP_ind(scratc93668032_union,X1)),X))))))) # label(fact_def__d__Union__closed) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 125 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc705057702d_Subq,X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X2),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X2),Xa))))))) # label(fact_def__d__Subq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 126 (all X all Xa (pp(aa_fun171081125l_bool(scratc1582350953all_of(X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (scratc316709488_is_of(X2,X) -> pp(aa_TPTP_ind_bool(Xa,X2))))))) # label(fact_def__all__of) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 127 (all X all Xa (scratc316709488_is_of(X,Xa) <-> pp(aa_TPTP_ind_bool(Xa,X)))) # label(fact_def__is__of) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 128 (all X0 pp(aa_fun171081125l_bool(scratc1582350953all_of(aa_TPT43085870d_bool(aTP_Lamm_hw,X0)),aa_TPT43085870d_bool(aTP_Lamm_hy,X0)))) # label(fact_isseti) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 129 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1582350953all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X0)),aa_fun1584354236d_bool(aTP_Lamm_hz(X0),X12)))) # label(fact_estie) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 130 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1582350953all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X0)),aa_fun1584354236d_bool(aTP_Lamm_ia(X0),X12)))) # label(fact_estii) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 131 (all X0 all X12 scratc316709488_is_of(aa_fun1431113780TP_ind(scratc1335397289_d_Sep(X0),X12),aa_TPT43085870d_bool(aTP_Lamm_hw,X0))) # label(fact_setof__p) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 132 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1582350953all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X0)),aa_TPT43085870d_bool(aTP_Lamm_ic(X0),X12)))) # label(fact_secondis1) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 133 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1582350953all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X0)),aa_TPT43085870d_bool(aTP_Lamm_ie(X0),X12)))) # label(fact_firstis1) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 134 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1582350953all_of(aa_TPT43085870d_bool(aTP_Lamm_if(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_ig(X0),X12)))) # label(fact_pairis1) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 135 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1582350953all_of(aa_TPT43085870d_bool(aTP_Lamm_if(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_ih(X0),X12)))) # label(fact_second__p) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 136 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1582350953all_of(aa_TPT43085870d_bool(aTP_Lamm_if(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_ii(X0),X12)))) # label(fact_first__p) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 137 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1582350953all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X0)),aa_TPT43085870d_bool(aTP_Lamm_ik(X0),X12)))) # label(fact_e__pair__p) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 138 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1582350953all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X0)),aa_fun1584354236d_bool(aTP_Lamm_il(X0),X12)))) # label(fact_otax2) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 139 (all X0 all X12 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc598587288ective(aa_fun1431113780TP_ind(scratc1335397289_d_Sep(X0),X12)),X0),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2136283600_Sigma,aa_fun1431113780TP_ind(scratc1335397289_d_Sep(X0),X12)),scratc133593851d_e_in(X0,X12))))) # label(fact_otax1) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 140 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1582350953all_of(aa_fun1584354236d_bool(aTP_Lamm_im(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_in(X0),X12)))) # label(fact_e__inp) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 141 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1582350953all_of(aa_fun1584354236d_bool(aTP_Lamm_im(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_io(X0),X12)))) # label(fact_e__in__p) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 142 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1582350953all_of(aa_TPT43085870d_bool(aTP_Lamm_ip(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_is(X0),X12)))) # label(fact_e__fisi) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 143 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc1093106295nd_one(X0),X12)) -> pp(aa_TPTP_ind_bool(X12,scratc1043537264nd_ind(X0,X12))))) # label(fact_oneax) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 144 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc1093106295nd_one(X0),X12)) -> scratc316709488_is_of(scratc1043537264nd_ind(X0,X12),aa_TPT43085870d_bool(aTP_Lamm_ak,X0)))) # label(fact_ind__p) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 145 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1582350953all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X0)),aa_fun1584354236d_bool(aTP_Lamm_iu(X0),X12)))) # label(fact_e__isp) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 146 (all X0 pp(aa_fun171081125l_bool(scratc1582350953all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X0)),aa_TPT43085870d_bool(aTP_Lamm_iv,X0)))) # label(fact_refis) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 147 (all X0 (scratc1158607951nd_wel(X0) -> pp(X0))) # label(fact_l__et) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 148 (all X0 all X12 all X22 all X32 (pp(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc536403948bnd_if(X0,X22),X32))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X12),X22))))) # label(fact_k__If__In__then__E) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 149 (all X0 all X12 all X22 ((pp(X0) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X12),X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,aa_TPTP_ind_TPTP_ind(scratc536403948bnd_if(X0,X12),scratc24661764ptyset)),aa_TPTP_ind_TPTP_ind(scratc536403948bnd_if(X0,X22),aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,scratc24661764ptyset)))))) # label(fact_k__If__In__01) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 150 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X33),X0)) -> aa_TPTP_ind_TPTP_ind(X12,X33) = aa_TPTP_ind_TPTP_ind(X22,X33)))) -> aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2136283600_Sigma,X0),X12) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2136283600_Sigma,X0),X22))) # label(fact_xi__ext) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 151 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1139873230d_d_Pi,X0),X12))) -> (all X32 (gg_TPTP_ind(X32) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X32),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1139873230d_d_Pi,X0),X12))) -> ((all X42 (gg_TPTP_ind(X42) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X42),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,X22),X42) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,X32),X42)))) -> X22 = X32))))))) # label(fact_k__Pi__ext) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 152 (all X0 all X12 all X22 all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1139873230d_d_Pi,X0),X12))) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X32),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,X22),X32)),aa_TPTP_ind_TPTP_ind(X12,X32)))))) # label(fact_ap__Pi) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 153 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X33),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,aa_TPTP_ind_TPTP_ind(X22,X33)),aa_TPTP_ind_TPTP_ind(X12,X33)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2136283600_Sigma,X0),X22)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1139873230d_d_Pi,X0),X12))))) # label(fact_lam__Pi) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 154 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X22),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2136283600_Sigma,X0),X12)),X22) = aa_TPTP_ind_TPTP_ind(X12,X22))) # label(fact_beta) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 155 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2136283600_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,aa_TPTP_ind_TPTP_ind(scratc1862403653_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1862403652_proj0,X22)))))) # label(fact_proj1__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 156 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2136283600_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,aa_TPTP_ind_TPTP_ind(scratc1862403652_proj0,X22)),X0)))) # label(fact_proj0__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 157 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2136283600_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc726805481d_pair,aa_TPTP_ind_TPTP_ind(scratc1862403652_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1862403653_proj1,X22)) = X22))) # label(fact_proj__Sigma__eta) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 158 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2136283600_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc726805481d_pair,aa_TPTP_ind_TPTP_ind(scratc1862403652_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1862403653_proj1,X22)) = X22 & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,aa_TPTP_ind_TPTP_ind(scratc1862403652_proj0,X22)),X0)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,aa_TPTP_ind_TPTP_ind(scratc1862403653_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1862403652_proj0,X22))))))) # label(fact_k__Sigma__eta__proj0__proj1) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 159 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X22),X0)) -> (all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X32),aa_TPTP_ind_TPTP_ind(X12,X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc726805481d_pair,X22),X32)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2136283600_Sigma,X0),X12))))))) # label(fact_pair__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 160 (all X0 all X12 (gg_TPTP_ind(X12) -> aa_TPTP_ind_TPTP_ind(scratc1862403653_proj1,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc726805481d_pair,X0),X12)) = X12)) # label(fact_proj1__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 161 (all X0 all X12 (gg_TPTP_ind(X0) -> aa_TPTP_ind_TPTP_ind(scratc1862403652_proj0,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc726805481d_pair,X0),X12)) = X0)) # label(fact_proj0__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 162 (all X0 (pp(aa_TPTP_ind_bool(scratc203353694_nat_p,X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X0),scratc1032058866_omega)))) # label(fact_nat__p__omega) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 163 (all X0 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X0),scratc1032058866_omega)) -> pp(aa_TPTP_ind_bool(scratc203353694_nat_p,X0)))) # label(fact_omega__nat__p) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 164 (all X0 (gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(scratc203353694_nat_p,X0)) -> X0 = scratc24661764ptyset | (exists X13 (gg_TPTP_ind(X13) & pp(aa_TPTP_ind_bool(scratc203353694_nat_p,X13)) & X0 = aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,X13)))))) # label(fact_nat__inv) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 165 (all X0 (pp(aa_TPTP_ind_bool(X0,scratc24661764ptyset)) -> ((all X13 (gg_TPTP_ind(X13) -> (pp(aa_TPTP_ind_bool(scratc203353694_nat_p,X13)) -> (pp(aa_TPTP_ind_bool(X0,X13)) -> pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,X13))))))) -> (all X12 (pp(aa_TPTP_ind_bool(scratc203353694_nat_p,X12)) -> pp(aa_TPTP_ind_bool(X0,X12))))))) # label(fact_nat__ind) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 166 (all X0 (pp(aa_TPTP_ind_bool(scratc203353694_nat_p,X0)) -> pp(aa_TPTP_ind_bool(scratc203353694_nat_p,aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,X0))))) # label(fact_nat__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 167 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,X0) = aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,X12) -> X0 = X12))) # label(fact_ordsucc__inj) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 168 (all X0 aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,X0) != scratc24661764ptyset) # label(fact_neq__ordsucc__0) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 169 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X22),aa_fun1431113780TP_ind(scratc1335397289_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(X12,X22)))) # label(fact_k__SepE2) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 170 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X22),aa_fun1431113780TP_ind(scratc1335397289_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X22),X0)))) # label(fact_k__SepE1) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 171 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X22),X0)) -> (pp(aa_TPTP_ind_bool(X12,X22)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X22),aa_fun1431113780TP_ind(scratc1335397289_d_Sep(X0),X12)))))) # label(fact_k__SepI) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 172 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc1733889814_power,X0)))) # label(fact_k__Self__In__Power) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 173 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc705057702d_Subq,X12),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1733889814_power,X0))))) # label(fact_k__PowerI) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 174 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1733889814_power,X0))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc705057702d_Subq,X12),X0)))) # label(fact_k__PowerE) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 175 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> aa_TPTP_ind_TPTP_ind(scratc536403948bnd_if(X0,X12),X22) = X12 | aa_TPTP_ind_TPTP_ind(scratc536403948bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__or) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 176 (all X0 all X12 all X22 (gg_TPTP_ind(X12) -> (pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc536403948bnd_if(X0,X12),X22) = X12))) # label(fact_if__i__1) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 177 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (-pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc536403948bnd_if(X0,X12),X22) = X22))) # label(fact_if__i__0) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 178 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> pp(X0) & aa_TPTP_ind_TPTP_ind(scratc536403948bnd_if(X0,X12),X22) = X12 | -pp(X0) & aa_TPTP_ind_TPTP_ind(scratc536403948bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__correct) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 179 (all X0 pp(aa_TPTP_ind_bool(scratc1274564781closed,aa_TPTP_ind_TPTP_ind(scratc636410476univof,X0)))) # label(fact_k__UnivOf__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 180 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc636410476univof,X0)))) # label(fact_k__UnivOf__In) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 181 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc174001438d_repl,X0),X12))) <-> (exists X3 (gg_TPTP_ind(X3) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X3),X0)) & X22 = aa_TPTP_ind_TPTP_ind(X12,X3)))))) # label(fact_k__ReplEq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 182 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1733889814_power,X0))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc705057702d_Subq,X12),X0)))) # label(fact_k__PowerEq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 183 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc93668032_union,X0))) <-> (exists X2 (gg_TPTP_ind(X2) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X12),X2)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X2),X0)))))) # label(fact_k__UnionEq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 184 -(exists X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X0),scratc24661764ptyset))) # label(fact_k__EmptyAx) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 185 (all X0 ((all X13 (gg_TPTP_ind(X13) -> ((all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_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].
% 1.04/1.36 186 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc705057702d_Subq,X0),X12)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc705057702d_Subq,X12),X0)) -> X0 = X12)))) # label(fact_set__ext) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 187 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hl,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1084516809nd_nis,Uu),scratc1295935666nd_n_1)) -> pp(aa_fun171081125l_bool(scratc1436836403n_some,aa_TPT43085870d_bool(aTP_Lamm_ag,Uu)))))) # label(fact_ATP_Olambda__1) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 188 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hk,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1084516809nd_nis,Uu),scratc1295935666nd_n_1)) -> pp(aa_fun171081125l_bool(scratc992414823_n_one,aa_TPT43085870d_bool(aTP_Lamm_ag,Uu)))))) # label(fact_ATP_Olambda__2) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 189 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hh,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uu),scratc1295935666nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,Uu))))) # label(fact_ATP_Olambda__3) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 190 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_he,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(scratc1295935666nd_n_1),Uu)),aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,Uu))))) # label(fact_ATP_Olambda__4) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 191 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hj,Uu)) <-> pp(aa_fun171081125l_bool(scratc1093106295nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1139873230d_d_Pi,scratc1083992018nd_nat),aTP_Lamm_ad)),aa_TPT43085870d_bool(aTP_Lamm_hi,Uu))))) # label(fact_ATP_Olambda__5) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 192 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hr,Uu)) <-> (pp(aa_TPTP_ind_bool(scratc1877520384_cond1,Uu)) -> (pp(aa_TPTP_ind_bool(scratc1877520385_cond2,Uu)) -> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hq,Uu))))))) # label(fact_ATP_Olambda__6) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 193 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hb,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uu),scratc1295935666nd_n_1))))) # label(fact_ATP_Olambda__7) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 194 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gy,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(scratc1295935666nd_n_1),Uu))))) # label(fact_ATP_Olambda__8) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 195 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dy,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1554228284_29_ii,aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__9) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 196 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hm,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1084516809nd_nis,aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__10) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 197 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hv,Uu)) <-> scratc316709488_is_of(aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,Uu),aTP_Lamm_a))) # label(fact_ATP_Olambda__11) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 198 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hu,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1084516809nd_nis,aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,Uu)),scratc1295935666nd_n_1)))) # label(fact_ATP_Olambda__12) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 199 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dx,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1043209274nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,Uu))))) # label(fact_ATP_Olambda__13) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 200 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hp,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,Uu),aa_TPTP_ind_TPTP_ind(scratc1733889814_power,scratc1083992018nd_nat))))) # label(fact_ATP_Olambda__14) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 201 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_a,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,Uu),scratc1083992018nd_nat)))) # label(fact_ATP_Olambda__15) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 202 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ht,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hs,Uu))))) # label(fact_ATP_Olambda__16) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 203 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ho,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hn,Uu))))) # label(fact_ATP_Olambda__17) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 204 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hg,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hf,Uu))))) # label(fact_ATP_Olambda__18) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 205 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hd,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hc,Uu))))) # label(fact_ATP_Olambda__19) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 206 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ha,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gz,Uu))))) # label(fact_ATP_Olambda__20) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 207 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gx,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gw,Uu))))) # label(fact_ATP_Olambda__21) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 208 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gv,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gu,Uu))))) # label(fact_ATP_Olambda__22) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 209 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gs,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gr,Uu))))) # label(fact_ATP_Olambda__23) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 210 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gq,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gp,Uu))))) # label(fact_ATP_Olambda__24) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 211 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_go,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gn,Uu))))) # label(fact_ATP_Olambda__25) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 212 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gl,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gk,Uu))))) # label(fact_ATP_Olambda__26) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 213 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gi,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gh,Uu))))) # label(fact_ATP_Olambda__27) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 214 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gg,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gf,Uu))))) # label(fact_ATP_Olambda__28) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 215 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gc,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gb,Uu))))) # label(fact_ATP_Olambda__29) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 216 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ga,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fz,Uu))))) # label(fact_ATP_Olambda__30) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 217 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fy,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fx,Uu))))) # label(fact_ATP_Olambda__31) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 218 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fw,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fv,Uu))))) # label(fact_ATP_Olambda__32) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 219 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fu,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ft,Uu))))) # label(fact_ATP_Olambda__33) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 220 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fs,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fr,Uu))))) # label(fact_ATP_Olambda__34) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 221 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fq,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fp,Uu))))) # label(fact_ATP_Olambda__35) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 222 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fo,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fn,Uu))))) # label(fact_ATP_Olambda__36) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 223 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fm,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fl,Uu))))) # label(fact_ATP_Olambda__37) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 224 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fk,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fj,Uu))))) # label(fact_ATP_Olambda__38) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 225 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fi,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fh,Uu))))) # label(fact_ATP_Olambda__39) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 226 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fg,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ff,Uu))))) # label(fact_ATP_Olambda__40) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 227 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fe,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fd,Uu))))) # label(fact_ATP_Olambda__41) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 228 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fc,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fb,Uu))))) # label(fact_ATP_Olambda__42) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 229 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fa,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ez,Uu))))) # label(fact_ATP_Olambda__43) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 230 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ey,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ex,Uu))))) # label(fact_ATP_Olambda__44) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 231 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ew,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ev,Uu))))) # label(fact_ATP_Olambda__45) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 232 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_eu,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_et,Uu))))) # label(fact_ATP_Olambda__46) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 233 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_er,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eq,Uu))))) # label(fact_ATP_Olambda__47) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 234 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_eo,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_en,Uu))))) # label(fact_ATP_Olambda__48) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 235 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_el,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ek,Uu))))) # label(fact_ATP_Olambda__49) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 236 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ei,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eh,Uu))))) # label(fact_ATP_Olambda__50) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 237 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ef,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ee,Uu))))) # label(fact_ATP_Olambda__51) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 238 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ec,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eb,Uu))))) # label(fact_ATP_Olambda__52) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 239 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ea,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dz,Uu))))) # label(fact_ATP_Olambda__53) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 240 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dw,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dv,Uu))))) # label(fact_ATP_Olambda__54) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 241 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dt,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ds,Uu))))) # label(fact_ATP_Olambda__55) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 242 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dq,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dp,Uu))))) # label(fact_ATP_Olambda__56) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 243 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dn,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dm,Uu))))) # label(fact_ATP_Olambda__57) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 244 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dk,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dj,Uu))))) # label(fact_ATP_Olambda__58) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 245 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dh,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dg,Uu))))) # label(fact_ATP_Olambda__59) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 246 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_de,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dd,Uu))))) # label(fact_ATP_Olambda__60) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 247 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_da,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cz,Uu))))) # label(fact_ATP_Olambda__61) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 248 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cw,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cv,Uu))))) # label(fact_ATP_Olambda__62) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 249 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cs,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cr,Uu))))) # label(fact_ATP_Olambda__63) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 250 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_co,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cn,Uu))))) # label(fact_ATP_Olambda__64) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 251 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cl,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ck,Uu))))) # label(fact_ATP_Olambda__65) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 252 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ci,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ch,Uu))))) # label(fact_ATP_Olambda__66) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 253 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cf,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ce,Uu))))) # label(fact_ATP_Olambda__67) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 254 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cc,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cb,Uu))))) # label(fact_ATP_Olambda__68) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 255 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bz,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_by,Uu))))) # label(fact_ATP_Olambda__69) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 256 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bw,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bv,Uu))))) # label(fact_ATP_Olambda__70) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 257 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bt,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bs,Uu))))) # label(fact_ATP_Olambda__71) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 258 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ac,Uu)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ab,Uu))))) # label(fact_ATP_Olambda__72) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 259 (all Uu aa_TPT494704832TP_ind(aTP_Lamm_bl,Uu) = aa_TPT494704832TP_ind(scratc174001438d_repl,aa_TPTP_ind_TPTP_ind(scratc1300244957tminus(Uu),aa_TPTP_ind_TPTP_ind(scratc606706820d_Sing,scratc24661764ptyset)))) # label(fact_ATP_Olambda__73) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 260 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_ai,Uu)) <-> Uu != scratc24661764ptyset))) # label(fact_ATP_Olambda__74) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 261 (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(scratc1431814497d_Inj1,X2) = Uu))))) # label(fact_ATP_Olambda__75) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 262 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_bk,Uu)) <-> (exists X2 (gg_TPTP_ind(X2) & aa_TPTP_ind_TPTP_ind(scratc1431814496d_Inj0,X2) = Uu))))) # label(fact_ATP_Olambda__76) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 263 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fx,Uu),Uua)) <-> scratc639765123_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1554228284_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1043209274nd_iii,Uu),Uua)))) # label(fact_ATP_Olambda__77) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 264 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fv,Uu),Uua)) <-> pp(scratc1093368641nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1554228284_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1043209274nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__78) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 265 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ft,Uu),Uua)) <-> pp(scratc1009769606nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1554228284_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1043209274nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__79) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 266 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gf,Uu),Uua)) <-> scratc639765123_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1436836403n_some,aa_TPT43085870d_bool(aTP_Lamm_gd(Uu),Uua)),aa_fun171081125l_bool(scratc1436836403n_some,aa_TPT43085870d_bool(aTP_Lamm_ge(Uu),Uua))))) # label(fact_ATP_Olambda__80) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 267 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gb,Uu),Uua)) <-> pp(scratc1093368641nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1436836403n_some,aa_TPT43085870d_bool(scratc1306558711ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc1436836403n_some,aa_TPT43085870d_bool(scratc1306558711ffprop(Uua),Uu)))))) # label(fact_ATP_Olambda__81) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 268 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fz,Uu),Uua)) <-> pp(scratc1009769606nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1436836403n_some,aa_TPT43085870d_bool(scratc1306558711ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc1436836403n_some,aa_TPT43085870d_bool(scratc1306558711ffprop(Uua),Uu)))))) # label(fact_ATP_Olambda__82) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 269 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iv,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc133593856d_e_is(Uu),Uua),Uua)))) # label(fact_ATP_Olambda__83) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 270 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hi,Uu),Uua)) <-> pp(scratc1451648738_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,Uua),scratc1295935666nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,Uu)),aa_fun171081125l_bool(scratc876622562_n_all,aa_TPT43085870d_bool(aTP_Lamm_af,Uua)))))) # label(fact_ATP_Olambda__84) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 271 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hs,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__85) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 272 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hc,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__86) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 273 (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(scratc1799737865d_n_is,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__87) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 274 (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(scratc1799737865d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,Uu),aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,Uu),Uua)))))) # label(fact_ATP_Olambda__88) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 275 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hn,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1084516809nd_nis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1084516809nd_nis,aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,Uua)))))) # label(fact_ATP_Olambda__89) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 276 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ah,Uu),Uua)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1043471677nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737860d_n_in,Uua),Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737860d_n_in,aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,Uua)),Uu))))) # label(fact_ATP_Olambda__90) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 277 (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(scratc1799737865d_n_is,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uua),Uu))))) # label(fact_ATP_Olambda__91) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 278 (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(scratc1554228284_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1043209274nd_iii,Uua),Uu))))) # label(fact_ATP_Olambda__92) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 279 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fn,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1389395246moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1255411634lessis,Uua),Uu))))) # label(fact_ATP_Olambda__93) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 280 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fl,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1255411634lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1389395246moreis,Uua),Uu))))) # label(fact_ATP_Olambda__94) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 281 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fp,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1043209274nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1554228284_29_ii,Uua),Uu))))) # label(fact_ATP_Olambda__95) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 282 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fb,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1554228284_29_ii,Uu),Uua)) -> pp(scratc1559113918_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1255411634lessis,Uu),Uua)))))) # label(fact_ATP_Olambda__96) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 283 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fj,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1389395246moreis,Uu),Uua)) -> pp(scratc1559113918_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1043209274nd_iii,Uu),Uua)))))) # label(fact_ATP_Olambda__97) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.36 284 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fh,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1255411634lessis,Uu),Uua)) -> pp(scratc1559113918_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1554228284_29_ii,Uu),Uua)))))) # label(fact_ATP_Olambda__98) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 285 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ez,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1043209274nd_iii,Uu),Uua)) -> pp(scratc1559113918_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1389395246moreis,Uu),Uua)))))) # label(fact_ATP_Olambda__99) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 286 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eb,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1554228284_29_ii,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uu),Uua)),Uu)))) # label(fact_ATP_Olambda__100) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 287 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bi(Uu),Uua) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc174001438d_repl,aa_TPTP_ind_TPTP_ind(Uu,Uua)),aa_TPT1424761345TP_ind(scratc726805481d_pair,Uua))) # label(fact_ATP_Olambda__101) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 288 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hy,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aa_TPT43085870d_bool(aTP_Lamm_hw,Uu)),aa_TPT43085870d_bool(aTP_Lamm_hx(Uu),Uua))))) # label(fact_ATP_Olambda__102) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 289 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gw,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,Uu)),Uua))))) # label(fact_ATP_Olambda__103) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 290 (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(scratc1799737865d_n_is,aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,Uua)))))) # label(fact_ATP_Olambda__104) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 291 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ff,Uu),Uua)) <-> (pp(scratc1559113918_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1554228284_29_ii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1255411634lessis,Uu),Uua))))) # label(fact_ATP_Olambda__105) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 292 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ex,Uu),Uua)) <-> (pp(scratc1559113918_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1389395246moreis,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1043209274nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__106) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 293 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ev,Uu),Uua)) <-> (pp(scratc1559113918_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1255411634lessis,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1554228284_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__107) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 294 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fd,Uu),Uua)) <-> (pp(scratc1559113918_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1043209274nd_iii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1389395246moreis,Uu),Uua))))) # label(fact_ATP_Olambda__108) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 295 (all Uu all Uua aa_fun277296641TP_ind(aa_TPT494704832TP_ind(aTP_Lamm_bm,Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1383959415nunion(aa_TPTP_ind_TPTP_ind(scratc606706820d_Sing,scratc24661764ptyset)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc174001438d_repl,Uu),Uua))) # label(fact_ATP_Olambda__109) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 296 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gp,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1084516809nd_nis,Uua),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__110) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 297 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dz,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1043209274nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__111) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 298 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ag,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,Uua))))) # label(fact_ATP_Olambda__112) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 299 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hw,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,Uua),aa_TPTP_ind_TPTP_ind(scratc1733889814_power,Uu))))) # label(fact_ATP_Olambda__113) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 300 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hq,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737860d_n_in,Uua),Uu)))) # label(fact_ATP_Olambda__114) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 301 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bn,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1082417636nd_nIn,Uua),Uu)))) # label(fact_ATP_Olambda__115) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 302 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ak,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,Uua),Uu)))) # label(fact_ATP_Olambda__116) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 303 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gu,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gt(Uu),Uua))))) # label(fact_ATP_Olambda__117) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 304 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gn,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gm(Uu),Uua))))) # label(fact_ATP_Olambda__118) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 305 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gk,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gj(Uu),Uua))))) # label(fact_ATP_Olambda__119) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 306 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_et,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_es(Uu),Uua))))) # label(fact_ATP_Olambda__120) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 307 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eq,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ep(Uu),Uua))))) # label(fact_ATP_Olambda__121) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 308 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_en,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_em(Uu),Uua))))) # label(fact_ATP_Olambda__122) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 309 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ek,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ej(Uu),Uua))))) # label(fact_ATP_Olambda__123) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 310 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eh,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eg(Uu),Uua))))) # label(fact_ATP_Olambda__124) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 311 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ee,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ed(Uu),Uua))))) # label(fact_ATP_Olambda__125) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 312 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dv,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_du(Uu),Uua))))) # label(fact_ATP_Olambda__126) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 313 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ds,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dr(Uu),Uua))))) # label(fact_ATP_Olambda__127) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 314 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dp,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_do(Uu),Uua))))) # label(fact_ATP_Olambda__128) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 315 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dm,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dl(Uu),Uua))))) # label(fact_ATP_Olambda__129) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 316 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dj,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_di(Uu),Uua))))) # label(fact_ATP_Olambda__130) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 317 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dg,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_df(Uu),Uua))))) # label(fact_ATP_Olambda__131) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 318 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dd,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dc(Uu),Uua))))) # label(fact_ATP_Olambda__132) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 319 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cz,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cy(Uu),Uua))))) # label(fact_ATP_Olambda__133) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 320 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cv,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cu(Uu),Uua))))) # label(fact_ATP_Olambda__134) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 321 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cr,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cq(Uu),Uua))))) # label(fact_ATP_Olambda__135) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 322 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cn,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cm(Uu),Uua))))) # label(fact_ATP_Olambda__136) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 323 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ck,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cj(Uu),Uua))))) # label(fact_ATP_Olambda__137) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 324 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ch,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cg(Uu),Uua))))) # label(fact_ATP_Olambda__138) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 325 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ce,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cd(Uu),Uua))))) # label(fact_ATP_Olambda__139) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 326 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cb,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ca(Uu),Uua))))) # label(fact_ATP_Olambda__140) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 327 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_by,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bx(Uu),Uua))))) # label(fact_ATP_Olambda__141) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 328 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bv,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bu(Uu),Uua))))) # label(fact_ATP_Olambda__142) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 329 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bs,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_br(Uu),Uua))))) # label(fact_ATP_Olambda__143) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 330 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ab,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa(Uu),Uua))))) # label(fact_ATP_Olambda__144) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 331 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gh,Uu),Uua)) <-> pp(scratc193618603_amone(scratc1083992018nd_nat,aa_TPT43085870d_bool(aTP_Lamm_gd(Uu),Uua))))) # label(fact_ATP_Olambda__145) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 332 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_ae(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc664976884rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,Uu),Uua))) # label(fact_ATP_Olambda__146) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 333 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bf(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc93668032_union,aa_TPTP_ind_TPTP_ind(Uu,Uua))) # label(fact_ATP_Olambda__147) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 334 (all Uu all Uua (gg_TPTP_ind(Uua) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bh,Uu),Uua)) <-> (exists X3 (gg_TPTP_ind(X3) & Uua = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc726805481d_pair,Uu),X3)))))) # label(fact_ATP_Olambda__148) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 335 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ig(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc133593856d_e_is(aa_TPTP_ind_TPTP_ind(scratc298899978etprod(Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1702479087d_pair(Uu,Uua),aa_TPTP_ind_TPTP_ind(scratc646720129_first(Uu,Uua),Uub)),aa_TPTP_ind_TPTP_ind(scratc2074767267second(Uu,Uua),Uub))),Uub)))) # label(fact_ATP_Olambda__149) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 336 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_bp(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc536403948bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,scratc24661764ptyset),Uub),Uu),Uua)) # label(fact_ATP_Olambda__150) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 337 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_fun1235454963TP_ind(aTP_Lamm_bo(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc536403948bnd_if(aa_TPTP_ind_bool(Uua,Uub),Uub),scratc1010622457nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bc(Uu),Uua)))) # label(fact_ATP_Olambda__151) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 338 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_av(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc879709554d_esti(Uu),Uub),Uua)))) # label(fact_ATP_Olambda__152) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 339 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_hz(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc879709554d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc1335397289_d_Sep(Uu),Uua))) -> pp(aa_TPTP_ind_bool(Uua,Uub))))) # label(fact_ATP_Olambda__153) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 340 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hx(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1812151997d_incl(Uu),Uua),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1812151997d_incl(Uu),Uub),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc133593856d_e_is(aa_TPTP_ind_TPTP_ind(scratc1733889814_power,Uu)),Uua),Uub)))))) # label(fact_ATP_Olambda__154) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 341 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ih(Uu),Uua),Uub)) <-> scratc316709488_is_of(aa_TPTP_ind_TPTP_ind(scratc2074767267second(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_ak,Uua)))) # label(fact_ATP_Olambda__155) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 342 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ii(Uu),Uua),Uub)) <-> scratc316709488_is_of(aa_TPTP_ind_TPTP_ind(scratc646720129_first(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_ak,Uu)))) # label(fact_ATP_Olambda__156) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 343 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_io(Uu),Uua),Uub)) <-> scratc316709488_is_of(aa_TPTP_ind_TPTP_ind(scratc133593851d_e_in(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_ak,Uu)))) # label(fact_ATP_Olambda__157) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 344 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_is(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aa_TPT43085870d_bool(aTP_Lamm_ip(Uu),Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ir(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__158) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 345 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ca(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1554228284_29_ii,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1554228284_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__159) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 346 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_br(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1554228284_29_ii,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1554228284_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__160) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 347 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gj(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uu),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,Uua),Uub))))) # label(fact_ATP_Olambda__161) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 348 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bx(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__162) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 349 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__163) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 350 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bu(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1043209274nd_iii,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1043209274nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__164) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 351 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gt(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__165) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 352 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_du(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1554228284_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1554228284_29_ii,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__166) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 353 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dl(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1554228284_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1554228284_29_ii,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__167) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 354 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eg(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1554228284_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1389395246moreis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1554228284_29_ii,Uu),Uub)))))) # label(fact_ATP_Olambda__168) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 355 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cm(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1389395246moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1389395246moreis,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__169) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 356 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cj(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1389395246moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1389395246moreis,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__170) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 357 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ej(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1389395246moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1554228284_29_ii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1554228284_29_ii,Uu),Uub)))))) # label(fact_ATP_Olambda__171) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 358 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cg(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1255411634lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1255411634lessis,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__172) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 359 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cd(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1255411634lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1255411634lessis,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__173) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 360 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ed(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1255411634lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1255411634lessis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1255411634lessis,Uu),Uub)))))) # label(fact_ATP_Olambda__174) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 361 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ep(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1255411634lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1043209274nd_iii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1043209274nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__175) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 362 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dr(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__176) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 363 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_di(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__177) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 364 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gm(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1084516809nd_nis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1084516809nd_nis,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uu),Uub)))))) # label(fact_ATP_Olambda__178) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 365 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_do(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1043209274nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1043209274nd_iii,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__179) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 366 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_df(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1043209274nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1043209274nd_iii,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__180) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 367 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_em(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1043209274nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1255411634lessis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1043209274nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__181) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 368 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_es(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1043209274nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1043209274nd_iii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1043209274nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__182) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 369 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bc(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,Uub),Uu)) & pp(aa_TPTP_ind_bool(Uua,Uub)))) # label(fact_ATP_Olambda__183) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 370 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_il(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc604078060_image(aa_fun1431113780TP_ind(scratc1335397289_d_Sep(Uu),Uua),Uu),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2136283600_Sigma,aa_fun1431113780TP_ind(scratc1335397289_d_Sep(Uu),Uua)),scratc133593851d_e_in(Uu,Uua))),Uub))))) # label(fact_ATP_Olambda__184) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 371 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ia(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc879709554d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc1335397289_d_Sep(Uu),Uua)))))) # label(fact_ATP_Olambda__185) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 372 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_iu(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_it(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__186) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 373 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_be(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bd(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__187) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 374 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ik(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ij(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__188) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 375 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ie(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_id(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__189) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 376 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ic(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ib(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__190) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 377 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ip(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,Uub),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1139873230d_d_Pi,Uu),aTP_Lamm_aj(Uua)))))) # label(fact_ATP_Olambda__191) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 378 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gd(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uua),Uub))))) # label(fact_ATP_Olambda__192) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 379 (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(scratc1799737865d_n_is,Uua),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uu),Uub))))) # label(fact_ATP_Olambda__193) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 380 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_if(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,Uub),aa_TPTP_ind_TPTP_ind(scratc298899978etprod(Uu),Uua))))) # label(fact_ATP_Olambda__194) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 381 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_im(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,Uub),aa_fun1431113780TP_ind(scratc1335397289_d_Sep(Uu),Uua))))) # label(fact_ATP_Olambda__195) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 382 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_ax(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,Uu),Uub))) # label(fact_ATP_Olambda__196) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 383 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dc(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_db(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__197) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 384 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cy(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cx(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__198) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 385 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cu(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ct(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__199) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 386 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cq(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cp(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__200) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 387 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_in(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(Uua,aa_TPTP_ind_TPTP_ind(scratc133593851d_e_in(Uu,Uua),Uub))))) # label(fact_ATP_Olambda__201) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 388 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1913827119d_bool(aTP_Lamm_bg(Uu),Uua),Uub)) <-> (all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,X3),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc536403956bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,Uub),X3)),aa_TPTP_ind_TPTP_ind(Uua,X3)))))))) # label(fact_ATP_Olambda__202) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 389 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ay(Uu),Uua),Uub),Uuc) = aa_TPTP_ind_TPTP_ind(scratc536403948bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc604078060_image(Uu,Uua),Uub),Uuc),aa_TPTP_ind_TPTP_ind(scratc1036547705d_soft(Uu,Uua,Uub),Uuc)),scratc24661764ptyset)) # label(fact_ATP_Olambda__203) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 390 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_id(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc133593856d_e_is(Uu),aa_TPTP_ind_TPTP_ind(scratc646720129_first(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1702479087d_pair(Uu,Uua),Uub),Uuc))),Uub)))) # label(fact_ATP_Olambda__204) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 391 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ib(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc133593856d_e_is(Uua),aa_TPTP_ind_TPTP_ind(scratc2074767267second(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1702479087d_pair(Uu,Uua),Uub),Uuc))),Uuc)))) # label(fact_ATP_Olambda__205) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 392 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_iq(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc133593856d_e_is(Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,Uua),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,Uub),Uuc))))) # label(fact_ATP_Olambda__206) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 393 (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_TPTP_ind_bool(aa_TPT43085870d_bool(scratc879709554d_esti(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__207) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 394 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_az(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc133593856d_e_is(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__208) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 395 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ij(Uu),Uua),Uub),Uuc)) <-> scratc316709488_is_of(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1702479087d_pair(Uu,Uua),Uub),Uuc),aa_TPT43085870d_bool(aTP_Lamm_if(Uu),Uua)))) # label(fact_ATP_Olambda__209) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 396 (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(scratc1667830523d_l_ec(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc879709554d_esti(Uu),Uuc),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc879709554d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__210) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 397 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_au(Uu),Uua),Uub),Uuc)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1043471677nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc879709554d_esti(Uu),Uuc),Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc879709554d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__211) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 398 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ir(Uu),Uua),Uub),Uuc)) <-> (pp(aa_fun171081125l_bool(scratc1582350953all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_iq(Uua),Uub),Uuc))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc133593856d_e_is(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1139873230d_d_Pi,Uu),aTP_Lamm_aj(Uua))),Uub),Uuc))))) # label(fact_ATP_Olambda__212) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 399 (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_bq(Uu),Uua),Uub),Uuc)) <-> pp(Uu) & Uuc = Uua | -pp(Uu) & Uuc = Uub))) # label(fact_ATP_Olambda__213) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 400 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_db(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1554228284_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1554228284_29_ii,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__214) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.37 401 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cx(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1554228284_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1554228284_29_ii,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uuc),Uua))))))) # label(fact_ATP_Olambda__215) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.38 402 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ct(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1043209274nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1043209274nd_iii,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__216) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.38 403 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cp(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1799737865d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1043209274nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1043209274nd_iii,aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1800197051d_n_pl(Uuc),Uua))))))) # label(fact_ATP_Olambda__217) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.38 404 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_it(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc133593856d_e_is(Uu),Uub),Uuc)) -> pp(aa_TPTP_ind_bool(Uua,Uuc)))))) # label(fact_ATP_Olambda__218) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.38 405 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bd(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(scratc133593856d_e_is(Uu),Uub),Uuc)))))) # label(fact_ATP_Olambda__219) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.38 406 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bb(Uu),Uua),Uub),Uuc)) <-> pp(aa_fun171081125l_bool(scratc977314034nd_all(Uu),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_ba(Uu),Uua),Uub),Uuc))))) # label(fact_ATP_Olambda__220) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.38 407 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_as(Uu),Uua),Uub),Uuc)) <-> pp(aa_fun171081125l_bool(scratc693011761l_some(Uua),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ar(Uu),Uub),Uuc))))) # label(fact_ATP_Olambda__221) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.38 408 (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_ba(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1043471677nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc133593856d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,Uub),Uud))),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc133593856d_e_is(Uu),Uuc),Uud))))) # label(fact_ATP_Olambda__222) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.38 409 (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_ap(Uu),Uua),Uub),Uuc),Uud)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc133593856d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,Uub),Uud)))))) # label(fact_ATP_Olambda__223) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.38 410 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ao(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_an(Uu),Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__224) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.38 411 (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_aq(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_ap(Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__225) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.38 412 (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_aw(Uu),Uua),Uub),Uuc),Uud) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1315551336wissel(Uu,Uub),Uuc)),Uud))) # label(fact_ATP_Olambda__226) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.38 413 (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_an(Uu),Uua),Uub),Uuc),Uud),Uue)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_am(Uu),Uua),Uub),Uuc),Uud),Uue))))) # label(fact_ATP_Olambda__227) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.38 414 (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_al(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(scratc133593856d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,Uub),Uuc)),Uue)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc535879166bnd_ap,Uub),Uud)),Uuf))))))) # label(fact_ATP_Olambda__228) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.38 415 (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_am(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)) <-> pp(aa_fun171081125l_bool(scratc1582350953all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_al(Uua),Uub),Uuc),Uud),Uue),Uuf))))) # label(fact_ATP_Olambda__229) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.38 416 (all Uu all Uua (gg_TPTP_ind(Uu) -> aa_TPTP_ind_TPTP_ind(aTP_Lamm_aj(Uu),Uua) = Uu)) # label(fact_ATP_Olambda__230) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.38 417 (all Uu aa_TPTP_ind_TPTP_ind(aTP_Lamm_ad,Uu) = scratc1083992018nd_nat) # label(fact_ATP_Olambda__231) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.38 418 (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].
% 1.04/1.38 419 (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].
% 1.04/1.38 420 (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].
% 1.04/1.38 421 (all P (gg_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.38 422 (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].
% 1.04/1.41 423 (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].
% 1.04/1.41 424 (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].
% 1.04/1.41 425 (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].
% 1.04/1.41 426 (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].
% 1.04/1.41 427 (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].
% 1.04/1.41 428 (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].
% 1.04/1.41 429 (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].
% 1.04/1.41 430 (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].
% 1.04/1.41
% 1.04/1.41 ============================== end of process non-clausal formulas ===
% 1.04/1.41
% 1.04/1.41 ============================== PROCESS INITIAL CLAUSES ===============
% 1.04/1.41
% 1.04/1.41 ============================== PREDICATE ELIMINATION =================
% 1.04/1.41 431 -gg_bool(A) | A = fTrue | A = fFalse # label(help_fFalse_1_1_T) # label(axiom). [clausify(421)].
% 1.04/1.41 432 gg_bool(undefined_bool(bool)) # label(gsy_c_HOL_Oundefined_001t__HOL__Obool) # label(axiom). [assumption].
% 1.04/1.41 433 gg_bool(scratc193618603_amone(A,B)) # label(gsy_c_Scratch__tptp__translate__48274__6815_ONUM684__thf__4__p_Obnd__amone) # label(axiom). [clausify(1)].
% 1.04/1.41 434 gg_bool(scratc1451648738_d_and(A,B)) # label(gsy_c_Scratch__tptp__translate__48274__6815_ONUM684__thf__4__p_Obnd__d__and) # label(axiom). [clausify(2)].
% 1.04/1.41 435 gg_bool(scratc1559113918_d_not(A)) # label(gsy_c_Scratch__tptp__translate__48274__6815_ONUM684__thf__4__p_Obnd__d__not) # label(axiom). [clausify(3)].
% 1.04/1.41 436 gg_bool(scratc1009769606nd_ec3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__48274__6815_ONUM684__thf__4__p_Obnd__ec3) # label(axiom). [clausify(4)].
% 1.04/1.41 437 gg_bool(scratc1667830523d_l_ec(A,B)) # label(gsy_c_Scratch__tptp__translate__48274__6815_ONUM684__thf__4__p_Obnd__l__ec) # label(axiom). [clausify(8)].
% 1.04/1.41 438 gg_bool(scratc1093368641nd_or3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__48274__6815_ONUM684__thf__4__p_Obnd__or3) # label(axiom). [clausify(9)].
% 1.04/1.41 439 gg_bool(aa_bool_bool(A,B)) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom). [clausify(10)].
% 1.04/1.41 440 gg_bool(aa_TPTP_ind_bool(A,B)) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom). [clausify(11)].
% 1.04/1.41 441 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)].
% 1.04/1.41 442 gg_bool(fEx_TPTP_ind(A)) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom). [clausify(16)].
% 1.04/1.41 443 gg_bool(fFalse) # label(gsy_c_fFalse) # label(axiom). [assumption].
% 1.04/1.41 444 gg_bool(fTrue) # label(gsy_c_fTrue) # label(axiom). [assumption].
% 1.04/1.41 Derived: undefined_bool(bool) = fTrue | undefined_bool(bool) = fFalse. [resolve(431,a,432,a)].
% 1.61/1.89 Derived: scratc193618603_amone(A,B) = fTrue | scratc193618603_amone(A,B) = fFalse. [resolve(431,a,433,a)].
% 1.61/1.89 Derived: scratc1451648738_d_and(A,B) = fTrue | scratc1451648738_d_and(A,B) = fFalse. [resolve(431,a,434,a)].
% 1.61/1.89 Derived: scratc1559113918_d_not(A) = fTrue | scratc1559113918_d_not(A) = fFalse. [resolve(431,a,435,a)].
% 1.61/1.89 Derived: scratc1009769606nd_ec3(A,B,C) = fTrue | scratc1009769606nd_ec3(A,B,C) = fFalse. [resolve(431,a,436,a)].
% 1.61/1.89 Derived: scratc1667830523d_l_ec(A,B) = fTrue | scratc1667830523d_l_ec(A,B) = fFalse. [resolve(431,a,437,a)].
% 1.61/1.89 Derived: scratc1093368641nd_or3(A,B,C) = fTrue | scratc1093368641nd_or3(A,B,C) = fFalse. [resolve(431,a,438,a)].
% 1.61/1.89 Derived: aa_bool_bool(A,B) = fTrue | aa_bool_bool(A,B) = fFalse. [resolve(431,a,439,a)].
% 1.61/1.89 Derived: aa_TPTP_ind_bool(A,B) = fTrue | aa_TPTP_ind_bool(A,B) = fFalse. [resolve(431,a,440,a)].
% 1.61/1.89 Derived: aa_fun171081125l_bool(A,B) = fTrue | aa_fun171081125l_bool(A,B) = fFalse. [resolve(431,a,441,a)].
% 1.61/1.89 Derived: fEx_TPTP_ind(A) = fTrue | fEx_TPTP_ind(A) = fFalse. [resolve(431,a,442,a)].
% 1.61/1.89 Derived: fFalse = fTrue | fFalse = fFalse. [resolve(431,a,443,a)].
% 1.61/1.89 Derived: fTrue = fTrue | fTrue = fFalse. [resolve(431,a,444,a)].
% 1.61/1.89 445 scratc2062765313d_r_ec(A,B) | pp(A) # label(fact_def__r__ec) # label(axiom). [clausify(59)].
% 1.61/1.89 446 -scratc2062765313d_r_ec(A,B) | -pp(A) | pp(scratc1559113918_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(59)].
% 1.61/1.89 447 scratc2062765313d_r_ec(A,B) | -pp(scratc1559113918_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(59)].
% 1.61/1.89 448 scratc198306540_l_iff(A,B) | -pp(scratc1451648738_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1043471677nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc1043471677nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(91)].
% 1.61/1.89 449 -scratc198306540_l_iff(A,B) | pp(scratc1451648738_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1043471677nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc1043471677nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(91)].
% 1.61/1.89 450 scratc86401456d_orec(A,B) | -pp(scratc1451648738_d_and(aa_bool_bool(scratc1668486528d_l_or(A),B),scratc1667830523d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(92)].
% 1.61/1.89 451 -scratc86401456d_orec(A,B) | pp(scratc1451648738_d_and(aa_bool_bool(scratc1668486528d_l_or(A),B),scratc1667830523d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(92)].
% 1.61/1.89 452 scratc1158607951nd_wel(A) | -pp(scratc1559113918_d_not(scratc1559113918_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(97)].
% 1.61/1.89 453 -scratc1158607951nd_wel(A) | pp(scratc1559113918_d_not(scratc1559113918_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(97)].
% 1.61/1.89 454 -scratc1158607951nd_wel(A) | pp(A) # label(fact_l__et) # label(axiom). [clausify(147)].
% 1.61/1.89 Derived: pp(A) | -pp(scratc1559113918_d_not(scratc1559113918_d_not(A))). [resolve(454,a,452,a)].
% 1.61/1.89
% 1.61/1.89 ============================== end predicate elimination =============
% 1.61/1.89
% 1.61/1.89 Auto_denials: (non-Horn, no changes).
% 1.61/1.89
% 1.61/1.89 Term ordering decisions:
% 1.61/1.89 Function symbol KB weights: aTP_Lamm_a=1. scratc536403956bnd_in=1. scratc1799737865d_n_is=1. scratc664976884rdsucc=1. scratc1043209274nd_iii=1. scratc1554228284_29_ii=1. scratc535879166bnd_ap=1. aTP_Lamm_ak=1. scratc1255411634lessis=1. scratc24661764ptyset=1. scratc2136283600_Sigma=1. scratc1084516809nd_nis=1. scratc1389395246moreis=1. scratc1295935666nd_n_1=1. fFalse=1. scratc1083992018nd_nat=1. scratc1139873230d_d_Pi=1. scratc1436836403n_some=1. scratc1733889814_power=1. scratc203353694_nat_p=1. scratc1043471677nd_imp=1. scratc174001438d_repl=1. fTrue=1. scratc726805481d_pair=1. scratc705057702d_Subq=1. scratc1862403652_proj0=1. scratc331530448closed=1. scratc93668032_union=1. aTP_Lamm_ag=1. scratc1799737860d_n_in=1. scratc1862403653_proj1=1. scratc876622562_n_all=1. aTP_Lamm_ad=1. aTP_Lamm_af=1. aTP_Lamm_hw=1. scratc138588668closed=1. scratc2121339302closed=1. aTP_Lamm_ev=1. aTP_Lamm_ex=1. aTP_Lamm_ez=1. aTP_Lamm_fb=1. aTP_Lamm_fd=1. aTP_Lamm_ff=1. aTP_Lamm_fh=1. aTP_Lamm_fj=1. aTP_Lamm_fl=1. aTP_Lamm_fn=1. aTP_Lamm_fp=1. aTP_Lamm_fr=1. aTP_Lamm_hn=1. aTP_Lamm_hr=1. aTP_Lamm_hs=1. scratc1032058866_omega=1. scratc1274564781closed=1. scratc1431814497d_Inj1=1. scratc1491375224_prop2=1. aTP_Lamm_ab=1. aTP_Lamm_ah=1. aTP_Lamm_bh=1. aTP_Lamm_bj=1. aTP_Lamm_bk=1. aTP_Lamm_bs=1. aTP_Lamm_bv=1. aTP_Lamm_by=1. aTP_Lamm_cb=1. aTP_Lamm_ce=1. aTP_Lamm_ch=1. aTP_Lamm_ck=1. aTP_Lamm_cn=1. aTP_Lamm_cr=1. aTP_Lamm_cv=1. aTP_Lamm_cz=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_dz=1. aTP_Lamm_eb=1. aTP_Lamm_ee=1. aTP_Lamm_eh=1. aTP_Lamm_ek=1. aTP_Lamm_en=1. aTP_Lamm_eq=1. aTP_Lamm_et=1. aTP_Lamm_ft=1. aTP_Lamm_fv=1. aTP_Lamm_fx=1. aTP_Lamm_fz=1. aTP_Lamm_gb=1. aTP_Lamm_gf=1. aTP_Lamm_gh=1. aTP_Lamm_gk=1. aTP_Lamm_gn=1. aTP_Lamm_gp=1. aTP_Lamm_gr=1. aTP_Lamm_gu=1. aTP_Lamm_gw=1. aTP_Lamm_gz=1. aTP_Lamm_hc=1. aTP_Lamm_hf=1. aTP_Lamm_hi=1. aTP_Lamm_hk=1. aTP_Lamm_hl=1. aTP_Lamm_hq=1. fconj=1. fimplies=1. scratc1431814496d_Inj0=1. scratc1491375223_prop1=1. scratc1877520385_cond2=1. scratc606706820d_Sing=1. aTP_Lamm_bn=1. aTP_Lamm_bt=1. aTP_Lamm_bw=1. aTP_Lamm_bz=1. aTP_Lamm_cc=1. aTP_Lamm_cf=1. aTP_Lamm_ci=1. aTP_Lamm_cl=1. aTP_Lamm_co=1. aTP_Lamm_cs=1. aTP_Lamm_cw=1. aTP_Lamm_da=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_dx=1. aTP_Lamm_dy=1. aTP_Lamm_ea=1. aTP_Lamm_ec=1. aTP_Lamm_ef=1. aTP_Lamm_ei=1. aTP_Lamm_el=1. aTP_Lamm_eo=1. aTP_Lamm_er=1. aTP_Lamm_eu=1. aTP_Lamm_ew=1. aTP_Lamm_ey=1. aTP_Lamm_fa=1. aTP_Lamm_fc=1. aTP_Lamm_fe=1. aTP_Lamm_fg=1. aTP_Lamm_fi=1. aTP_Lamm_fk=1. aTP_Lamm_fm=1. aTP_Lamm_fo=1. aTP_Lamm_fq=1. aTP_Lamm_fs=1. aTP_Lamm_fu=1. aTP_Lamm_fw=1. aTP_Lamm_fy=1. aTP_Lamm_ga=1. aTP_Lamm_gc=1. aTP_Lamm_gg=1. aTP_Lamm_gi=1. aTP_Lamm_gl=1. aTP_Lamm_go=1. aTP_Lamm_gq=1. aTP_Lamm_gs=1. aTP_Lamm_gv=1. aTP_Lamm_gx=1. aTP_Lamm_gy=1. aTP_Lamm_ha=1. aTP_Lamm_hb=1. aTP_Lamm_hd=1. aTP_Lamm_he=1. aTP_Lamm_hg=1. aTP_Lamm_hh=1. aTP_Lamm_hj=1. aTP_Lamm_hm=1. aTP_Lamm_ho=1. aTP_Lamm_hp=1. aTP_Lamm_ht=1. aTP_Lamm_hu=1. aTP_Lamm_hv=1. aTP_Lamm_hy=1. aTP_Lamm_iv=1. fequal_TPTP_ind=1. scratc1082417636nd_nIn=1. scratc1352510684_d_Unj=1. scratc1877520384_cond1=1. scratc636410476univof=1. scratc992414823_n_one=1. aTP_Lamm_ac=1. aTP_Lamm_ai=1. aTP_Lamm_bl=1. aTP_Lamm_bm=1. bool=1. scratc1108978100_prop1=1. scratc138218802_prop1=1. scratc1862797250_prop4=1. scratc310256751nempty=1. scratc314650873_prop1=1. scratc390102316munion=1. scratc465563582_empty=1. scratc520615925_prop1=1. scratc521726855pair_p=1. scratc818469225d_plus=1. scratc903013048_prop1=1. scratc401941424d_24_g=1. scratc996438588d_i1_s=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. scratc1451648738_d_and=1. aa_TPT1123896796d_bool=1. scratc536403948bnd_if=1. scratc1667830523d_l_ec=1. aa_fun1212484691d_bool=1. aa_TPT985247859d_bool=1. scratc133593851d_e_in=1. scratc1702479087d_pair=1. aa_fun987228051d_bool=1. scratc1043537264nd_ind=1. scratc193618603_amone=1. scratc2074767267second=1. scratc604078060_image=1. scratc646720129_first=1. aa_TPT125613450d_bool=1. scratc1084910398nd_non=1. aa_fun1913827119d_bool=1. scratc2010036538d_anec=1. aa_TPT1791839040TP_ind=1. aa_fun1107270209d_bool=1. aa_fun845057962d_bool=1. scratc1009769667nd_ecp=1. scratc1158224832_ecelt=1. scratc1513194714eplSep=1. scratc1157634441_ecect=1. aa_TPT1781712639TP_ind=1. aa_TPT2142672771l_bool=1. aa_fun1235454963TP_ind=1. cOMBB_658106424TP_ind=1. cOMBS_2003118649l_bool=1. scratc1009769671nd_ect=1. scratc1093565503nd_out=1. scratc1315551336wissel=1. scratc1447524539ectset=1. scratc695436373_fixfu=1. scratc935498013fixfu2=1. scratc949734140etprop=1. scratc1332322662ectelt=1. scratc1553641885unmore=1. scratc1813398372d_invf=1. scratc1817134903d_tofs=1. scratc63224577nverse=1. f1=1. f12=1. f13=1. f20=1. f24=1. scratc1582350953all_of=1. scratc1800197051d_n_pl=1. scratc133Cputime limit exceeded (core dumped)
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