TSTP Solution File: NUM701+4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM701+4 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 13:30:57 EDT 2022
% Result : Timeout 300.10s 300.40s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM701+4 : TPTP v8.1.0. Released v7.3.0.
% 0.12/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Wed Jul 6 00:56:12 EDT 2022
% 0.14/0.36 % CPUTime :
% 1.02/1.35 ============================== Prover9 ===============================
% 1.02/1.35 Prover9 (32) version 2009-11A, November 2009.
% 1.02/1.35 Process 15489 was started by sandbox on n029.cluster.edu,
% 1.02/1.35 Wed Jul 6 00:56:13 2022
% 1.02/1.35 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_15335_n029.cluster.edu".
% 1.02/1.35 ============================== end of head ===========================
% 1.02/1.35
% 1.02/1.35 ============================== INPUT =================================
% 1.02/1.35
% 1.02/1.35 % Reading from file /tmp/Prover9_15335_n029.cluster.edu
% 1.02/1.35
% 1.02/1.35 set(prolog_style_variables).
% 1.02/1.35 set(auto2).
% 1.02/1.35 % set(auto2) -> set(auto).
% 1.02/1.35 % set(auto) -> set(auto_inference).
% 1.02/1.35 % set(auto) -> set(auto_setup).
% 1.02/1.35 % set(auto_setup) -> set(predicate_elim).
% 1.02/1.35 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.02/1.35 % set(auto) -> set(auto_limits).
% 1.02/1.35 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.02/1.35 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.02/1.35 % set(auto) -> set(auto_denials).
% 1.02/1.35 % set(auto) -> set(auto_process).
% 1.02/1.35 % set(auto2) -> assign(new_constants, 1).
% 1.02/1.35 % set(auto2) -> assign(fold_denial_max, 3).
% 1.02/1.35 % set(auto2) -> assign(max_weight, "200.000").
% 1.02/1.35 % set(auto2) -> assign(max_hours, 1).
% 1.02/1.35 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.02/1.35 % set(auto2) -> assign(max_seconds, 0).
% 1.02/1.35 % set(auto2) -> assign(max_minutes, 5).
% 1.02/1.35 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.02/1.35 % set(auto2) -> set(sort_initial_sos).
% 1.02/1.35 % set(auto2) -> assign(sos_limit, -1).
% 1.02/1.35 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.02/1.35 % set(auto2) -> assign(max_megs, 400).
% 1.02/1.35 % set(auto2) -> assign(stats, some).
% 1.02/1.35 % set(auto2) -> clear(echo_input).
% 1.02/1.35 % set(auto2) -> set(quiet).
% 1.02/1.35 % set(auto2) -> clear(print_initial_clauses).
% 1.02/1.35 % set(auto2) -> clear(print_given).
% 1.02/1.35 assign(lrs_ticks,-1).
% 1.02/1.35 assign(sos_limit,10000).
% 1.02/1.35 assign(order,kbo).
% 1.02/1.35 set(lex_order_vars).
% 1.02/1.35 clear(print_given).
% 1.02/1.35
% 1.02/1.35 % formulas(sos). % not echoed (595 formulas)
% 1.02/1.35
% 1.02/1.35 ============================== end of input ==========================
% 1.02/1.35
% 1.02/1.35 % From the command line: assign(max_seconds, 300).
% 1.02/1.35
% 1.02/1.35 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.02/1.35
% 1.02/1.35 % Formulas that are not ordinary clauses:
% 1.02/1.35 1 (all B_1 all B_2 gg_bool(scratc173580189_amone(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__51566__4158_ONUM701__thf__4__p_Obnd__amone) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 2 (all B_1 all B_2 gg_bool(scratc1211721328_d_and(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__51566__4158_ONUM701__thf__4__p_Obnd__d__and) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 3 (all B_1 gg_bool(scratc1319186508_d_not(B_1))) # label(gsy_c_Scratch__tptp__translate__51566__4158_ONUM701__thf__4__p_Obnd__d__not) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 4 (all B_1 all B_2 all B_3 gg_bool(scratc999158392nd_ec3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__51566__4158_ONUM701__thf__4__p_Obnd__ec3) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 5 (all B_1 all B_2 gg_TPTP_ind(scratc999158457nd_ect(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__51566__4158_ONUM701__thf__4__p_Obnd__ect) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 6 (all B_1 gg_TPTP_ind(scratc1000011243nd_eps(B_1))) # label(gsy_c_Scratch__tptp__translate__51566__4158_ONUM701__thf__4__p_Obnd__eps) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 7 (all B_1 all B_2 gg_TPTP_ind(scratc1032926050nd_ind(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__51566__4158_ONUM701__thf__4__p_Obnd__ind) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 8 (all B_1 all B_2 gg_bool(scratc1647792109d_l_ec(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__51566__4158_ONUM701__thf__4__p_Obnd__l__ec) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 9 (all B_1 all B_2 all B_3 gg_bool(scratc1082757427nd_or3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__51566__4158_ONUM701__thf__4__p_Obnd__or3) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 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].
% 1.02/1.35 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].
% 1.02/1.35 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].
% 1.02/1.35 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].
% 1.02/1.35 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].
% 1.02/1.35 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].
% 1.02/1.35 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].
% 1.02/1.35 17 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1015484224lessis,X),Xa)) <-> pp(aa_bool_bool(scratc1648448114d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,X),Xa))))) # label(fact_def__lessis) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 18 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1149467836moreis,X),Xa)) <-> pp(aa_bool_bool(scratc1648448114d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,X),Xa))))) # label(fact_def__moreis) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 19 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1582421952_prop1,X),Xa)) <-> pp(scratc1082757427nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,X),Xa))))) # label(fact_def__d__29__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 20 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1346324005n_some,aa_TPT43085870d_bool(scratc1576049029ffprop(Xa),X))))) # label(fact_def__iii) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 21 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1346324005n_some,aa_TPT43085870d_bool(scratc1576049029ffprop(X),Xa))))) # label(fact_def__d__29__ii) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 22 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1576049029ffprop(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,X),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Xa),Xb))))) # label(fact_def__diffprop) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 23 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc994059777_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1073905595nd_nis,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(X),Xb))))) # label(fact_def__d__28__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 24 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc405697602_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1073905595nd_nis,Xa),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(X),Xa))))) # label(fact_def__d__27__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 25 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1964819075_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Xa),X))))) # label(fact_def__d__26__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 26 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1376456900_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(X),Xa)),Xb)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(X),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Xa),Xb)))))) # label(fact_def__d__25__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 27 (all X scratc1780158637d_n_pl(X) = aa_TPT1424761345TP_ind(scratc787753868bnd_ap,aa_TPTP_ind_TPTP_ind(scratc518143991d_plus,X))) # label(fact_def__n__pl) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 28 (all X aa_TPTP_ind_TPTP_ind(scratc518143991d_plus,X) = scratc1032926050nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1119834816d_d_Pi,scratc1073380804nd_nat),aTP_Lamm_ac),aa_TPT43085870d_bool(scratc788094726_prop2,X))) # label(fact_def__plus) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 29 (all X aa_TPTP_ind_TPTP_ind(scratc671431742d_24_g,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc258290270_Sigma,scratc1073380804nd_nat),aTP_Lamm_ad(X))) # label(fact_def__d__24__g) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 30 (all X (pp(aa_TPTP_ind_bool(scratc1842758836_prop4,X)) <-> pp(aa_fun171081125l_bool(scratc602499363l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1119834816d_d_Pi,scratc1073380804nd_nat),aTP_Lamm_ac)),aa_TPT43085870d_bool(scratc788094726_prop2,X))))) # label(fact_def__prop4) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 31 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1842758835_prop3(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,X),Xb)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,Xa),Xb))))) # label(fact_def__prop3) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 32 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788094726_prop2,X),Xa)) <-> pp(scratc1211721328_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,Xa),scratc995610432nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,X)),aa_TPTP_ind_bool(scratc788094725_prop1,Xa))))) # label(fact_def__d__24__prop2) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 33 (all X (pp(aa_TPTP_ind_bool(scratc788094725_prop1,X)) <-> pp(aa_fun171081125l_bool(scratc636695152_n_all,aa_TPT43085870d_bool(aTP_Lamm_ae,X))))) # label(fact_def__d__24__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 34 (all X (pp(aa_TPTP_ind_bool(scratc199732550_prop1,X)) <-> pp(aa_bool_bool(scratc1648448114d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,X),scratc995610432nd_n_1)),aa_fun171081125l_bool(scratc1346324005n_some,aa_TPT43085870d_bool(aTP_Lamm_af,X)))))) # label(fact_def__d__23__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 35 (all X (pp(aa_TPTP_ind_bool(scratc1758854023_prop1,X)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1073905595nd_nis,aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,X)),X)))) # label(fact_def__d__22__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 36 (all X (pp(aa_TPTP_ind_bool(scratc1857481971_cond2,X)) <-> pp(aa_fun171081125l_bool(scratc636695152_n_all,aa_TPT43085870d_bool(aTP_Lamm_ag,X))))) # label(fact_def__cond2) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 37 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1073905595nd_nis,X),Xa)) <-> pp(scratc1319186508_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,X),Xa))))) # label(fact_def__nis) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 38 (all X all Xa all Xb all Xc all Xd scratc479080452indeq2(X,Xa,Xb,Xc,Xd) = aa_TPT1424761345TP_ind(scratc1389280174_indeq(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1485073154d_11_i(X,Xa,Xb),Xc),Xd))) # label(fact_def__indeq2) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 39 (all X all Xa all Xb scratc1485073154d_11_i(X,Xa,Xb) = scratc1389280174_indeq(X,Xa,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1119834816d_d_Pi,X),aTP_Lamm_ai(Xb)))) # label(fact_def__d__11__i) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 40 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc695570603fixfu2(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_an(X),Xa),Xb),Xc))))) # label(fact_def__fixfu2) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 41 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1389280174_indeq(X,Xa,Xb),Xc),Xd) = scratc1032926050nd_ind(Xb,aa_TPT43085870d_bool(scratc1842758834_prop2(X,Xa,Xb,Xc),Xd))) # label(fact_def__indeq) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 42 (all X all Xa all Xb all Xc all Xd all Xe (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1842758834_prop2(X,Xa,Xb,Xc),Xd),Xe)) <-> pp(aa_fun171081125l_bool(scratc602499363l_some(X),aa_TPT43085870d_bool(scratc1335417352_prop1(X,Xa,Xb,Xc,Xd),Xe))))) # label(fact_def__prop2) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 43 (all X all Xa all Xb all Xc all Xd all Xe all Xf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1335417352_prop1(X,Xa,Xb,Xc,Xd),Xe),Xf)) <-> pp(scratc1211721328_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc579384320d_esti(X),Xf),aa_TPTP_ind_TPTP_ind(scratc1137596027_ecect(X,Xa),Xd)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc113555442d_e_is(Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,Xc),Xf)),Xe))))) # label(fact_def__d__10__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 44 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc675397959_fixfu(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ap(X),Xa),Xb),Xc))))) # label(fact_def__fixfu) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 45 (all X all Xa scratc1137596027_ecect(X,Xa) = scratc113555437d_e_in(aa_TPTP_ind_TPTP_ind(scratc1713851400_power,X),scratc1709711304d_anec(X,Xa))) # label(fact_def__ecect) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 46 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1092395252ectelt(X,Xa),Xb) = aa_TPTP_ind_TPTP_ind(scratc1207597129ectset(X,Xa),aa_TPTP_ind_TPTP_ind(scratc1138186418_ecelt(X,Xa),Xb))) # label(fact_def__ectelt) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 47 (all X all Xa scratc1207597129ectset(X,Xa) = scratc1082954289nd_out(aa_TPTP_ind_TPTP_ind(scratc1713851400_power,X),scratc1709711304d_anec(X,Xa))) # label(fact_def__ectset) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 48 (all X all Xa scratc999158457nd_ect(X,Xa) = aa_fun1431113780TP_ind(scratc1095469879_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1713851400_power,X)),scratc1709711304d_anec(X,Xa))) # label(fact_def__ect) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 49 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc1709711304d_anec(X,Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc602499363l_some(X),aa_TPT43085870d_bool(scratc999158453nd_ecp(X,Xa),Xb))))) # label(fact_def__anec) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 50 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc999158453nd_ecp(X,Xa),Xb),Xc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc113555442d_e_is(aa_TPTP_ind_TPTP_ind(scratc1713851400_power,X)),Xb),aa_TPTP_ind_TPTP_ind(scratc1138186418_ecelt(X,Xa),Xc))))) # label(fact_def__ecp) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 51 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1138186418_ecelt(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc1095469879_d_Sep(X),aa_TPT43085870d_bool(Xa,Xb))) # label(fact_def__ecelt) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 52 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1313714475unmore(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc1095469879_d_Sep(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ar(X),Xa),Xb))) # label(fact_def__unmore) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 53 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1477213322etprop(X,Xa),Xb),Xc)) <-> pp(scratc1211721328_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc579384320d_esti(X),Xc),Xa),scratc1319186508_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc579384320d_esti(X),Xc),Xb)))))) # label(fact_def__nissetprop) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 54 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1986571770t_disj(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc966702820nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_as(X),Xa),Xb))))) # label(fact_def__st__disj) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 55 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511826763d_incl(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc966702820nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_at(X),Xa),Xb))))) # label(fact_def__incl) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 56 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc579747069nempty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc602499363l_some(X),aa_TPT43085870d_bool(aTP_Lamm_au(X),Xa))))) # label(fact_def__nonempty) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 57 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc445525168_empty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),scratc1074299184nd_non(X,aa_TPT43085870d_bool(aTP_Lamm_au(X),Xa)))))) # label(fact_def__empty) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 58 (all X scratc579384320d_esti(X) = scratc788278658bnd_in) # label(fact_def__esti) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 59 (all X all Xa (scratc2042726899d_r_ec(X,Xa) <-> (pp(X) -> pp(scratc1319186508_d_not(Xa))))) # label(fact_def__r__ec) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 60 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc2134154777hangef(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc258290270_Sigma,X),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_av(X),Xb),Xc),Xd))) # label(fact_def__changef) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 61 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1075623926wissel(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc258290270_Sigma,X),scratc1416583009sel_wb(X,Xa,Xb))) # label(fact_def__wissel) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 62 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1416583009sel_wb(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc1033319645nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc113555442d_e_is(X),Xc),Xb),X,Xa),aa_TPTP_ind_TPTP_ind(scratc1416583008sel_wa(X,Xa,Xb),Xc))) # label(fact_def__wissel__wb) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 63 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1416583008sel_wa(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc1033319645nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc113555442d_e_is(X),Xc),Xa),X,Xb),Xc)) # label(fact_def__wissel__wa) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 64 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1033319645nd_ite(X,Xa,Xb),Xc) = scratc1032926050nd_ind(Xa,aa_TPT43085870d_bool(scratc1842758833_prop1(X,Xa,Xb),Xc))) # label(fact_def__ite) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 65 (all X all Xa all Xb all Xc all Xd (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1842758833_prop1(X,Xa,Xb),Xc),Xd)) <-> pp(scratc1211721328_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1032860463nd_imp,X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc113555442d_e_is(Xa),Xd),Xb)),aa_bool_bool(aa_boo1142376798l_bool(scratc1032860463nd_imp,scratc1319186508_d_not(X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc113555442d_e_is(Xa),Xd),Xc)))))) # label(fact_def__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 66 (all X all Xa scratc1834839857second(X,Xa) = scratc1842365239_proj1) # label(fact_def__second) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 67 (all X all Xa scratc626681715_first(X,Xa) = scratc1842365238_proj0) # label(fact_def__first) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 68 (all X all Xa scratc1611966689d_pair(X,Xa) = scratc426480247d_pair) # label(fact_def__d__pair) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 69 (all X all Xa scratc1082954289nd_out(X,Xa) = scratc736222471d_soft(aa_fun1431113780TP_ind(scratc1095469879_d_Sep(X),Xa),X,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc258290270_Sigma,aa_fun1431113780TP_ind(scratc1095469879_d_Sep(X),Xa)),scratc113555437d_e_in(X,Xa)))) # label(fact_def__out) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 70 (all X all Xa all Xb (gg_TPTP_ind(Xb) -> aa_TPTP_ind_TPTP_ind(scratc113555437d_e_in(X,Xa),Xb) = Xb)) # label(fact_def__e__in) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 71 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc816886592_inj_h(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc258290270_Sigma,X),aa_TPT1424761345TP_ind(aTP_Lamm_aw(Xc),Xd))) # label(fact_def__inj__h) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 72 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1513073138d_invf(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc258290270_Sigma,Xa),scratc736222471d_soft(X,Xa,Xb))) # label(fact_def__invf) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 73 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc992286664ective(X),Xa),Xb)) <-> pp(scratc1211721328_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc808567434ective(X),Xa),Xb),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1012958617ective(X),Xa),Xb))))) # label(fact_def__bijective) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 74 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1012958617ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc966702820nd_all(Xa),aa_TPT43085870d_bool(scratc584039646_image(X,Xa),Xb))))) # label(fact_def__surjective) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 75 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc2120195827nverse(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc258290270_Sigma,Xa),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ax(X),Xa),Xb))) # label(fact_def__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 76 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc736222471d_soft(X,Xa,Xb),Xc) = scratc1032926050nd_ind(X,aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(Xa),Xb),Xc))) # label(fact_def__soft) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 77 (all X all Xa scratc1516809669d_tofs(X,Xa) = scratc787753868bnd_ap) # label(fact_def__tofs) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 78 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc584039646_image(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc602499363l_some(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(Xa),Xb),Xc))))) # label(fact_def__image) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 79 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc808567434ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc966702820nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ba(X),Xa),Xb))))) # label(fact_def__injective) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 80 (all X all Xa scratc1032926050nd_ind(X,Xa) = scratc1000011243nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bb(X),Xa))) # label(fact_def__ind) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 81 (all X all Xa (pp(aa_fun171081125l_bool(scratc1082495081nd_one(X),Xa)) <-> pp(scratc1211721328_d_and(scratc173580189_amone(X,Xa),aa_fun171081125l_bool(scratc602499363l_some(X),Xa))))) # label(fact_def__one) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 82 (all X all Xa (pp(scratc173580189_amone(X,Xa)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),aa_fun1584354236d_bool(aTP_Lamm_bd(X),Xa))))) # label(fact_def__amone) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 83 (all X scratc113555442d_e_is(X) = fequal_TPTP_ind) # label(fact_def__e__is) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 84 (all X all Xa all Xb (scratc619726709_orec3(X,Xa,Xb) <-> pp(scratc1211721328_d_and(scratc1082757427nd_or3(X,Xa,Xb),scratc999158392nd_ec3(X,Xa,Xb))))) # label(fact_def__orec3) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 85 (all X all Xa all Xb (pp(scratc999158392nd_ec3(X,Xa,Xb)) <-> scratc1709645657d_and3(scratc1647792109d_l_ec(X,Xa),scratc1647792109d_l_ec(Xa,Xb),scratc1647792109d_l_ec(Xb,X)))) # label(fact_def__ec3) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 86 (all X all Xa all Xb (scratc1709645657d_and3(X,Xa,Xb) <-> pp(scratc1211721328_d_and(X,scratc1211721328_d_and(Xa,Xb))))) # label(fact_def__and3) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 87 (all X all Xa all Xb (pp(scratc1082757427nd_or3(X,Xa,Xb)) <-> pp(aa_bool_bool(scratc1648448114d_l_or(X),aa_bool_bool(scratc1648448114d_l_or(Xa),Xb))))) # label(fact_def__or3) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 88 (all X all Xa (pp(aa_fun171081125l_bool(scratc602499363l_some(X),Xa)) <-> pp(scratc1319186508_d_not(aa_fun171081125l_bool(scratc1491838555all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),scratc1074299184nd_non(X,Xa)))))) # label(fact_def__l__some) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 89 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc1074299184nd_non(X,Xa),Xb)) <-> pp(scratc1319186508_d_not(aa_TPTP_ind_bool(Xa,Xb))))) # label(fact_def__non) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 90 (all X scratc966702820nd_all(X) = scratc1491838555all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X))) # label(fact_def__all) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 91 (all X all Xa (scratc2105862778_l_iff(X,Xa) <-> pp(scratc1211721328_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1032860463nd_imp,X),Xa),aa_bool_bool(aa_boo1142376798l_bool(scratc1032860463nd_imp,Xa),X))))) # label(fact_def__l__iff) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 92 (all X all Xa (scratc1933559870d_orec(X,Xa) <-> pp(scratc1211721328_d_and(aa_bool_bool(scratc1648448114d_l_or(X),Xa),scratc1647792109d_l_ec(X,Xa))))) # label(fact_def__orec) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 93 (all X scratc1648448114d_l_or(X) = aa_boo1142376798l_bool(scratc1032860463nd_imp,scratc1319186508_d_not(X))) # label(fact_def__l__or) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 94 (all X all Xa (pp(scratc1211721328_d_and(X,Xa)) <-> pp(scratc1319186508_d_not(scratc1647792109d_l_ec(X,Xa))))) # label(fact_def__d__and) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 95 (all X all Xa (pp(scratc1647792109d_l_ec(X,Xa)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1032860463nd_imp,X),scratc1319186508_d_not(Xa))))) # label(fact_def__l__ec) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 96 scratc837794826bvious <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1032860463nd_imp,fFalse),fFalse)) # label(fact_def__obvious) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 97 (all X (scratc1147996737nd_wel(X) <-> pp(scratc1319186508_d_not(scratc1319186508_d_not(X))))) # label(fact_def__wel) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 98 (all X (pp(scratc1319186508_d_not(X)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1032860463nd_imp,X),fFalse)))) # label(fact_def__d__not) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 99 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1119834816d_d_Pi,X),Xa) = aa_fun1431113780TP_ind(scratc1095469879_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1713851400_power,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc258290270_Sigma,X),aTP_Lamm_be(Xa)))),aa_fun1913827119d_bool(aTP_Lamm_bf(X),Xa))) # label(fact_def__d__Pi) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.35 100 (all X (gg_TPTP_ind(X) -> (pp(aa_TPTP_ind_bool(scratc431214457pair_p,X)) <-> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc426480247d_pair,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,X),scratc294152082ptyset)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,X),aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,scratc294152082ptyset))) = X))) # label(fact_def__pair__p) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 101 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc2040673896eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bg,Xa)),scratc1842365239_proj1)) # label(fact_def__ap) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 102 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc208387580etprod(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc258290270_Sigma,X),aTP_Lamm_ai(Xa))) # label(fact_def__setprod) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 103 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc258290270_Sigma,X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc659592634munion,X),aTP_Lamm_bh(Xa))) # label(fact_def__d__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 104 (all X aa_TPTP_ind_TPTP_ind(scratc1842365239_proj1,X) = aa_fun277296641TP_ind(scratc2040673896eplSep(X,aTP_Lamm_bi),scratc1112583274_d_Unj)) # label(fact_def__proj1) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 105 (all X aa_TPTP_ind_TPTP_ind(scratc1842365238_proj0,X) = aa_fun277296641TP_ind(scratc2040673896eplSep(X,aTP_Lamm_bj),scratc1112583274_d_Unj)) # label(fact_def__proj0) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 106 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc426480247d_pair,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1653449733nunion(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2021159852d_repl,X),scratc1341302098d_Inj0)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2021159852d_repl,Xa),scratc1341302099d_Inj1))) # label(fact_def__pair) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 107 (all X aa_TPTP_ind_TPTP_ind(scratc1341302098d_Inj0,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2021159852d_repl,X),scratc1341302099d_Inj1)) # label(fact_def__d__Inj0) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 108 (all X (pp(aa_TPTP_ind_bool(scratc2110909932_nat_p,X)) <-> (all X1 (pp(aa_TPTP_ind_bool(X1,scratc294152082ptyset)) -> ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(X1,X2)) -> pp(aa_TPTP_ind_bool(X1,aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,X2)))))) -> pp(aa_TPTP_ind_bool(X1,X))))))) # label(fact_def__nat__p) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 109 (all X aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1653449733nunion(X),aa_TPTP_ind_TPTP_ind(scratc516194422d_Sing,X))) # label(fact_def__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 110 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1768437476In_rec(X),Xa) = scratc1000011243nd_eps(aa_TPT43085870d_bool(scratc869862563_rec_G(X),Xa))) # label(fact_def__d__In__rec) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 111 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc869862563_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(scratc788278658bnd_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].
% 1.02/1.36 112 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1569735275tminus(X),Xa) = aa_fun1431113780TP_ind(scratc1095469879_d_Sep(X),aa_TPT43085870d_bool(aTP_Lamm_bm,Xa))) # label(fact_def__setminus) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 113 (all X all Xa scratc2040673896eplSep(X,Xa) = aa_TPT494704832TP_ind(scratc2021159852d_repl,aa_fun1431113780TP_ind(scratc1095469879_d_Sep(X),Xa))) # label(fact_def__d__ReplSep) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 114 (all X all Xa aa_fun1431113780TP_ind(scratc1095469879_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc788278650bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc788278658bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2021159852d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bn(X),Xa))),scratc294152082ptyset)) # label(fact_def__d__Sep) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 115 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc659592634munion,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc73629618_union,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2021159852d_repl,X),Xa))) # label(fact_def__famunion) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 116 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1653449733nunion(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc73629618_union,aa_TPTP_ind_TPTP_ind(scratc152776648_UPair(X),Xa))) # label(fact_def__binunion) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 117 (all X aa_TPTP_ind_TPTP_ind(scratc516194422d_Sing,X) = aa_TPTP_ind_TPTP_ind(scratc152776648_UPair(X),X)) # label(fact_def__d__Sing) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 118 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc152776648_UPair(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2021159852d_repl,aa_TPTP_ind_TPTP_ind(scratc1713851400_power,aa_TPTP_ind_TPTP_ind(scratc1713851400_power,scratc294152082ptyset))),aa_TPT1424761345TP_ind(aTP_Lamm_bo(X),Xa))) # label(fact_def__d__UPair) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 119 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1071806422nd_nIn,X),Xa)) <-> -pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X),Xa)))) # label(fact_def__nIn) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 120 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc788278650bnd_if(X,Xa),Xb) = scratc1000011243nd_eps(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bp(X),Xa),Xb))) # label(fact_def__if) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 121 (all X (pp(aa_TPTP_ind_bool(scratc1168386463closed,X)) <-> pp(aa_TPTP_ind_bool(scratc1889046068closed,X)) & pp(aa_TPTP_ind_bool(scratc2053779082closed,X)) & pp(aa_TPTP_ind_bool(scratc1009598658closed,X)))) # label(fact_def__d__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 122 (all X (pp(aa_TPTP_ind_bool(scratc1009598658closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X1),X)) -> (all X2 ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X3),X1)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,aa_TPTP_ind_TPTP_ind(X2,X3)),X))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2021159852d_repl,X1),X2)),X))))))))) # label(fact_def__d__Repl__closed) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 123 (all X (pp(aa_TPTP_ind_bool(scratc2053779082closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,aa_TPTP_ind_TPTP_ind(scratc1713851400_power,X1)),X))))))) # label(fact_def__d__Power__closed) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 124 (all X (pp(aa_TPTP_ind_bool(scratc1889046068closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,aa_TPTP_ind_TPTP_ind(scratc73629618_union,X1)),X))))))) # label(fact_def__d__Union__closed) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 125 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc614545304d_Subq,X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X2),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X2),Xa))))))) # label(fact_def__d__Subq) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 126 (all X all Xa (pp(aa_fun171081125l_bool(scratc1491838555all_of(X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (scratc76782078_is_of(X2,X) -> pp(aa_TPTP_ind_bool(Xa,X2))))))) # label(fact_def__all__of) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 127 (all X all Xa (scratc76782078_is_of(X,Xa) <-> pp(aa_TPTP_ind_bool(Xa,X)))) # label(fact_def__is__of) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 128 (all X0 pp(aa_fun171081125l_bool(scratc1491838555all_of(aa_TPT43085870d_bool(aTP_Lamm_ju,X0)),aa_TPT43085870d_bool(aTP_Lamm_jw,X0)))) # label(fact_isseti) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 129 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1491838555all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_jx(X0),X12)))) # label(fact_estie) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 130 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1491838555all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_jy(X0),X12)))) # label(fact_estii) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 131 (all X0 all X12 scratc76782078_is_of(aa_fun1431113780TP_ind(scratc1095469879_d_Sep(X0),X12),aa_TPT43085870d_bool(aTP_Lamm_ju,X0))) # label(fact_setof__p) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 132 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1491838555all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_ka(X0),X12)))) # label(fact_secondis1) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 133 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1491838555all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_kc(X0),X12)))) # label(fact_firstis1) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 134 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1491838555all_of(aa_TPT43085870d_bool(aTP_Lamm_kd(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_ke(X0),X12)))) # label(fact_pairis1) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 135 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1491838555all_of(aa_TPT43085870d_bool(aTP_Lamm_kd(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_kf(X0),X12)))) # label(fact_second__p) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 136 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1491838555all_of(aa_TPT43085870d_bool(aTP_Lamm_kd(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_kg(X0),X12)))) # label(fact_first__p) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 137 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1491838555all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_ki(X0),X12)))) # label(fact_e__pair__p) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 138 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1491838555all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_kj(X0),X12)))) # label(fact_otax2) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 139 (all X0 all X12 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc808567434ective(aa_fun1431113780TP_ind(scratc1095469879_d_Sep(X0),X12)),X0),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc258290270_Sigma,aa_fun1431113780TP_ind(scratc1095469879_d_Sep(X0),X12)),scratc113555437d_e_in(X0,X12))))) # label(fact_otax1) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 140 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1491838555all_of(aa_fun1584354236d_bool(aTP_Lamm_kk(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_kl(X0),X12)))) # label(fact_e__inp) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 141 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1491838555all_of(aa_fun1584354236d_bool(aTP_Lamm_kk(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_km(X0),X12)))) # label(fact_e__in__p) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 142 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1491838555all_of(aa_TPT43085870d_bool(aTP_Lamm_kn(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_kq(X0),X12)))) # label(fact_e__fisi) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 143 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc1082495081nd_one(X0),X12)) -> pp(aa_TPTP_ind_bool(X12,scratc1032926050nd_ind(X0,X12))))) # label(fact_oneax) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 144 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc1082495081nd_one(X0),X12)) -> scratc76782078_is_of(scratc1032926050nd_ind(X0,X12),aa_TPT43085870d_bool(aTP_Lamm_aj,X0)))) # label(fact_ind__p) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 145 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1491838555all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_ks(X0),X12)))) # label(fact_e__isp) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 146 (all X0 pp(aa_fun171081125l_bool(scratc1491838555all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_kt,X0)))) # label(fact_refis) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 147 (all X0 (scratc1147996737nd_wel(X0) -> pp(X0))) # label(fact_l__et) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 148 (all X0 all X12 all X22 all X32 (pp(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc788278650bnd_if(X0,X22),X32))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X12),X22))))) # label(fact_k__If__In__then__E) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 149 (all X0 all X12 all X22 ((pp(X0) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X12),X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,aa_TPTP_ind_TPTP_ind(scratc788278650bnd_if(X0,X12),scratc294152082ptyset)),aa_TPTP_ind_TPTP_ind(scratc788278650bnd_if(X0,X22),aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,scratc294152082ptyset)))))) # label(fact_k__If__In__01) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 150 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X33),X0)) -> aa_TPTP_ind_TPTP_ind(X12,X33) = aa_TPTP_ind_TPTP_ind(X22,X33)))) -> aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc258290270_Sigma,X0),X12) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc258290270_Sigma,X0),X22))) # label(fact_xi__ext) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 151 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1119834816d_d_Pi,X0),X12))) -> (all X32 (gg_TPTP_ind(X32) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X32),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1119834816d_d_Pi,X0),X12))) -> ((all X42 (gg_TPTP_ind(X42) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X42),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,X22),X42) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,X32),X42)))) -> X22 = X32))))))) # label(fact_k__Pi__ext) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 152 (all X0 all X12 all X22 all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1119834816d_d_Pi,X0),X12))) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X32),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,X22),X32)),aa_TPTP_ind_TPTP_ind(X12,X32)))))) # label(fact_ap__Pi) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 153 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X33),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,aa_TPTP_ind_TPTP_ind(X22,X33)),aa_TPTP_ind_TPTP_ind(X12,X33)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc258290270_Sigma,X0),X22)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1119834816d_d_Pi,X0),X12))))) # label(fact_lam__Pi) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 154 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X22),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc258290270_Sigma,X0),X12)),X22) = aa_TPTP_ind_TPTP_ind(X12,X22))) # label(fact_beta) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 155 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc258290270_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,aa_TPTP_ind_TPTP_ind(scratc1842365239_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1842365238_proj0,X22)))))) # label(fact_proj1__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 156 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc258290270_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,aa_TPTP_ind_TPTP_ind(scratc1842365238_proj0,X22)),X0)))) # label(fact_proj0__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 157 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc258290270_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc426480247d_pair,aa_TPTP_ind_TPTP_ind(scratc1842365238_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1842365239_proj1,X22)) = X22))) # label(fact_proj__Sigma__eta) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 158 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc258290270_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc426480247d_pair,aa_TPTP_ind_TPTP_ind(scratc1842365238_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1842365239_proj1,X22)) = X22 & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,aa_TPTP_ind_TPTP_ind(scratc1842365238_proj0,X22)),X0)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,aa_TPTP_ind_TPTP_ind(scratc1842365239_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1842365238_proj0,X22))))))) # label(fact_k__Sigma__eta__proj0__proj1) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 159 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X22),X0)) -> (all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X32),aa_TPTP_ind_TPTP_ind(X12,X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc426480247d_pair,X22),X32)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc258290270_Sigma,X0),X12))))))) # label(fact_pair__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 160 (all X0 all X12 (gg_TPTP_ind(X12) -> aa_TPTP_ind_TPTP_ind(scratc1842365239_proj1,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc426480247d_pair,X0),X12)) = X12)) # label(fact_proj1__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 161 (all X0 all X12 (gg_TPTP_ind(X0) -> aa_TPTP_ind_TPTP_ind(scratc1842365238_proj0,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc426480247d_pair,X0),X12)) = X0)) # label(fact_proj0__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 162 (all X0 (pp(aa_TPTP_ind_bool(scratc2110909932_nat_p,X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X0),scratc1012020452_omega)))) # label(fact_nat__p__omega) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 163 (all X0 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X0),scratc1012020452_omega)) -> pp(aa_TPTP_ind_bool(scratc2110909932_nat_p,X0)))) # label(fact_omega__nat__p) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 164 (all X0 (gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(scratc2110909932_nat_p,X0)) -> X0 = scratc294152082ptyset | (exists X13 (gg_TPTP_ind(X13) & pp(aa_TPTP_ind_bool(scratc2110909932_nat_p,X13)) & X0 = aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,X13)))))) # label(fact_nat__inv) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 165 (all X0 (pp(aa_TPTP_ind_bool(X0,scratc294152082ptyset)) -> ((all X13 (gg_TPTP_ind(X13) -> (pp(aa_TPTP_ind_bool(scratc2110909932_nat_p,X13)) -> (pp(aa_TPTP_ind_bool(X0,X13)) -> pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,X13))))))) -> (all X12 (pp(aa_TPTP_ind_bool(scratc2110909932_nat_p,X12)) -> pp(aa_TPTP_ind_bool(X0,X12))))))) # label(fact_nat__ind) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 166 (all X0 (pp(aa_TPTP_ind_bool(scratc2110909932_nat_p,X0)) -> pp(aa_TPTP_ind_bool(scratc2110909932_nat_p,aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,X0))))) # label(fact_nat__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 167 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,X0) = aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,X12) -> X0 = X12))) # label(fact_ordsucc__inj) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 168 (all X0 aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,X0) != scratc294152082ptyset) # label(fact_neq__ordsucc__0) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 169 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X22),aa_fun1431113780TP_ind(scratc1095469879_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(X12,X22)))) # label(fact_k__SepE2) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 170 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X22),aa_fun1431113780TP_ind(scratc1095469879_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X22),X0)))) # label(fact_k__SepE1) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 171 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X22),X0)) -> (pp(aa_TPTP_ind_bool(X12,X22)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X22),aa_fun1431113780TP_ind(scratc1095469879_d_Sep(X0),X12)))))) # label(fact_k__SepI) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 172 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc1713851400_power,X0)))) # label(fact_k__Self__In__Power) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 173 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc614545304d_Subq,X12),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1713851400_power,X0))))) # label(fact_k__PowerI) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 174 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1713851400_power,X0))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc614545304d_Subq,X12),X0)))) # label(fact_k__PowerE) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 175 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> aa_TPTP_ind_TPTP_ind(scratc788278650bnd_if(X0,X12),X22) = X12 | aa_TPTP_ind_TPTP_ind(scratc788278650bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__or) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 176 (all X0 all X12 all X22 (gg_TPTP_ind(X12) -> (pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc788278650bnd_if(X0,X12),X22) = X12))) # label(fact_if__i__1) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 177 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (-pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc788278650bnd_if(X0,X12),X22) = X22))) # label(fact_if__i__0) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 178 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> pp(X0) & aa_TPTP_ind_TPTP_ind(scratc788278650bnd_if(X0,X12),X22) = X12 | -pp(X0) & aa_TPTP_ind_TPTP_ind(scratc788278650bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__correct) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 179 (all X0 pp(aa_TPTP_ind_bool(scratc1168386463closed,aa_TPTP_ind_TPTP_ind(scratc396483066univof,X0)))) # label(fact_k__UnivOf__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 180 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc396483066univof,X0)))) # label(fact_k__UnivOf__In) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 181 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2021159852d_repl,X0),X12))) <-> (exists X3 (gg_TPTP_ind(X3) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X3),X0)) & X22 = aa_TPTP_ind_TPTP_ind(X12,X3)))))) # label(fact_k__ReplEq) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 182 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1713851400_power,X0))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc614545304d_Subq,X12),X0)))) # label(fact_k__PowerEq) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 183 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc73629618_union,X0))) <-> (exists X2 (gg_TPTP_ind(X2) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X12),X2)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X2),X0)))))) # label(fact_k__UnionEq) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 184 -(exists X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X0),scratc294152082ptyset))) # label(fact_k__EmptyAx) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 185 (all X0 ((all X13 (gg_TPTP_ind(X13) -> ((all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_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].
% 1.02/1.36 186 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc614545304d_Subq,X0),X12)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc614545304d_Subq,X12),X0)) -> X0 = X12)))) # label(fact_set__ext) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 187 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jj,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1073905595nd_nis,Uu),scratc995610432nd_n_1)) -> pp(aa_fun171081125l_bool(scratc1346324005n_some,aa_TPT43085870d_bool(aTP_Lamm_af,Uu)))))) # label(fact_ATP_Olambda__1) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 188 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ji,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1073905595nd_nis,Uu),scratc995610432nd_n_1)) -> pp(aa_fun171081125l_bool(scratc752487413_n_one,aa_TPT43085870d_bool(aTP_Lamm_af,Uu)))))) # label(fact_ATP_Olambda__2) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 189 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jf,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),scratc995610432nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,Uu))))) # label(fact_ATP_Olambda__3) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 190 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jc,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(scratc995610432nd_n_1),Uu)),aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,Uu))))) # label(fact_ATP_Olambda__4) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 191 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jh,Uu)) <-> pp(aa_fun171081125l_bool(scratc1082495081nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1119834816d_d_Pi,scratc1073380804nd_nat),aTP_Lamm_ac)),aa_TPT43085870d_bool(aTP_Lamm_jg,Uu))))) # label(fact_ATP_Olambda__5) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 192 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jp,Uu)) <-> (pp(aa_TPTP_ind_bool(scratc1857481970_cond1,Uu)) -> (pp(aa_TPTP_ind_bool(scratc1857481971_cond2,Uu)) -> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jo,Uu))))))) # label(fact_ATP_Olambda__6) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 193 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_iz,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),scratc995610432nd_n_1))))) # label(fact_ATP_Olambda__7) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 194 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_iw,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(scratc995610432nd_n_1),Uu))))) # label(fact_ATP_Olambda__8) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 195 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fw,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__9) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 196 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jk,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1073905595nd_nis,aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__10) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 197 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jt,Uu)) <-> scratc76782078_is_of(aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,Uu),aTP_Lamm_a))) # label(fact_ATP_Olambda__11) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 198 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cb,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,Uu)),scratc995610432nd_n_1)))) # label(fact_ATP_Olambda__12) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 199 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_js,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1073905595nd_nis,aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,Uu)),scratc995610432nd_n_1)))) # label(fact_ATP_Olambda__13) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 200 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fv,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,Uu))))) # label(fact_ATP_Olambda__14) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 201 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jn,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,Uu),aa_TPTP_ind_TPTP_ind(scratc1713851400_power,scratc1073380804nd_nat))))) # label(fact_ATP_Olambda__15) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 202 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cc,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1149467836moreis,Uu),scratc995610432nd_n_1)))) # label(fact_ATP_Olambda__16) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 203 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_a,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,Uu),scratc1073380804nd_nat)))) # label(fact_ATP_Olambda__17) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 204 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jr,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jq,Uu))))) # label(fact_ATP_Olambda__18) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 205 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jm,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jl,Uu))))) # label(fact_ATP_Olambda__19) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 206 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_je,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jd,Uu))))) # label(fact_ATP_Olambda__20) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 207 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jb,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ja,Uu))))) # label(fact_ATP_Olambda__21) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 208 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_iy,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ix,Uu))))) # label(fact_ATP_Olambda__22) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 209 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_iv,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_iu,Uu))))) # label(fact_ATP_Olambda__23) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 210 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_it,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_is,Uu))))) # label(fact_ATP_Olambda__24) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 211 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_iq,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ip,Uu))))) # label(fact_ATP_Olambda__25) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 212 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_io,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_in,Uu))))) # label(fact_ATP_Olambda__26) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 213 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_im,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_il,Uu))))) # label(fact_ATP_Olambda__27) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 214 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ij,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ii,Uu))))) # label(fact_ATP_Olambda__28) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 215 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ig,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_if,Uu))))) # label(fact_ATP_Olambda__29) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 216 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ie,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_id,Uu))))) # label(fact_ATP_Olambda__30) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 217 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ia,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hz,Uu))))) # label(fact_ATP_Olambda__31) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 218 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hy,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hx,Uu))))) # label(fact_ATP_Olambda__32) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 219 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hw,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hv,Uu))))) # label(fact_ATP_Olambda__33) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 220 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hu,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ht,Uu))))) # label(fact_ATP_Olambda__34) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 221 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hs,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hr,Uu))))) # label(fact_ATP_Olambda__35) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 222 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hq,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hp,Uu))))) # label(fact_ATP_Olambda__36) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 223 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ho,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hn,Uu))))) # label(fact_ATP_Olambda__37) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 224 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hm,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hl,Uu))))) # label(fact_ATP_Olambda__38) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 225 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hk,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hj,Uu))))) # label(fact_ATP_Olambda__39) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 226 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hi,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hh,Uu))))) # label(fact_ATP_Olambda__40) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 227 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hg,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hf,Uu))))) # label(fact_ATP_Olambda__41) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.36 228 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_he,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hd,Uu))))) # label(fact_ATP_Olambda__42) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 229 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hc,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hb,Uu))))) # label(fact_ATP_Olambda__43) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 230 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ha,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gz,Uu))))) # label(fact_ATP_Olambda__44) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 231 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gy,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,Uu))))) # label(fact_ATP_Olambda__45) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 232 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gw,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gv,Uu))))) # label(fact_ATP_Olambda__46) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 233 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gu,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gt,Uu))))) # label(fact_ATP_Olambda__47) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 234 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gs,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gr,Uu))))) # label(fact_ATP_Olambda__48) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 235 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gp,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_go,Uu))))) # label(fact_ATP_Olambda__49) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 236 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gm,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gl,Uu))))) # label(fact_ATP_Olambda__50) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 237 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gj,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gi,Uu))))) # label(fact_ATP_Olambda__51) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 238 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gg,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gf,Uu))))) # label(fact_ATP_Olambda__52) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 239 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gd,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gc,Uu))))) # label(fact_ATP_Olambda__53) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 240 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ga,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fz,Uu))))) # label(fact_ATP_Olambda__54) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 241 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fy,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fx,Uu))))) # label(fact_ATP_Olambda__55) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 242 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fu,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ft,Uu))))) # label(fact_ATP_Olambda__56) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 243 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fr,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fq,Uu))))) # label(fact_ATP_Olambda__57) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 244 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fo,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fn,Uu))))) # label(fact_ATP_Olambda__58) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 245 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fl,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fk,Uu))))) # label(fact_ATP_Olambda__59) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 246 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fi,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fh,Uu))))) # label(fact_ATP_Olambda__60) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 247 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ff,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fe,Uu))))) # label(fact_ATP_Olambda__61) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 248 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fc,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fb,Uu))))) # label(fact_ATP_Olambda__62) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 249 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ey,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ex,Uu))))) # label(fact_ATP_Olambda__63) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 250 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_eu,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_et,Uu))))) # label(fact_ATP_Olambda__64) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 251 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_eq,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ep,Uu))))) # label(fact_ATP_Olambda__65) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 252 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_em,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_el,Uu))))) # label(fact_ATP_Olambda__66) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 253 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ej,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ei,Uu))))) # label(fact_ATP_Olambda__67) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 254 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_eg,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ef,Uu))))) # label(fact_ATP_Olambda__68) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 255 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ed,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ec,Uu))))) # label(fact_ATP_Olambda__69) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 256 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ea,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dz,Uu))))) # label(fact_ATP_Olambda__70) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 257 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dx,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dw,Uu))))) # label(fact_ATP_Olambda__71) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 258 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_du,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dt,Uu))))) # label(fact_ATP_Olambda__72) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 259 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dr,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dq,Uu))))) # label(fact_ATP_Olambda__73) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 260 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_do,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dn,Uu))))) # label(fact_ATP_Olambda__74) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 261 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dl,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dk,Uu))))) # label(fact_ATP_Olambda__75) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 262 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_di,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dh,Uu))))) # label(fact_ATP_Olambda__76) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 263 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_de,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dd,Uu))))) # label(fact_ATP_Olambda__77) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 264 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_da,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cz,Uu))))) # label(fact_ATP_Olambda__78) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 265 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cw,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cv,Uu))))) # label(fact_ATP_Olambda__79) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 266 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cs,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cr,Uu))))) # label(fact_ATP_Olambda__80) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 267 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_co,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cn,Uu))))) # label(fact_ATP_Olambda__81) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 268 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ck,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cj,Uu))))) # label(fact_ATP_Olambda__82) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 269 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cg,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cf,Uu))))) # label(fact_ATP_Olambda__83) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 270 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bz,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_by,Uu))))) # label(fact_ATP_Olambda__84) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 271 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bw,Uu))))) # label(fact_ATP_Olambda__85) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 272 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bv,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bu,Uu))))) # label(fact_ATP_Olambda__86) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 273 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bt,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bs,Uu))))) # label(fact_ATP_Olambda__87) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 274 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_br,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bq,Uu))))) # label(fact_ATP_Olambda__88) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 275 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ab,Uu)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,Uu))))) # label(fact_ATP_Olambda__89) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 276 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ca,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,scratc995610432nd_n_1),aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,Uu))))) # label(fact_ATP_Olambda__90) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 277 (all Uu aa_TPT494704832TP_ind(aTP_Lamm_bk,Uu) = aa_TPT494704832TP_ind(scratc2021159852d_repl,aa_TPTP_ind_TPTP_ind(scratc1569735275tminus(Uu),aa_TPTP_ind_TPTP_ind(scratc516194422d_Sing,scratc294152082ptyset)))) # label(fact_ATP_Olambda__91) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 278 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_ah,Uu)) <-> Uu != scratc294152082ptyset))) # label(fact_ATP_Olambda__92) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 279 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_bi,Uu)) <-> (exists X2 (gg_TPTP_ind(X2) & aa_TPTP_ind_TPTP_ind(scratc1341302099d_Inj1,X2) = Uu))))) # label(fact_ATP_Olambda__93) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 280 (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(scratc1341302098d_Inj0,X2) = Uu))))) # label(fact_ATP_Olambda__94) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 281 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hv,Uu),Uua)) <-> scratc619726709_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,Uu),Uua)))) # label(fact_ATP_Olambda__95) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 282 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ht,Uu),Uua)) <-> pp(scratc1082757427nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__96) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 283 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hr,Uu),Uua)) <-> pp(scratc999158392nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__97) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 284 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_id,Uu),Uua)) <-> scratc619726709_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1346324005n_some,aa_TPT43085870d_bool(aTP_Lamm_ib(Uu),Uua)),aa_fun171081125l_bool(scratc1346324005n_some,aa_TPT43085870d_bool(aTP_Lamm_ic(Uu),Uua))))) # label(fact_ATP_Olambda__98) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 285 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hz,Uu),Uua)) <-> pp(scratc1082757427nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1346324005n_some,aa_TPT43085870d_bool(scratc1576049029ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc1346324005n_some,aa_TPT43085870d_bool(scratc1576049029ffprop(Uua),Uu)))))) # label(fact_ATP_Olambda__99) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 286 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hx,Uu),Uua)) <-> pp(scratc999158392nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1346324005n_some,aa_TPT43085870d_bool(scratc1576049029ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc1346324005n_some,aa_TPT43085870d_bool(scratc1576049029ffprop(Uua),Uu)))))) # label(fact_ATP_Olambda__100) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 287 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kt,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc113555442d_e_is(Uu),Uua),Uua)))) # label(fact_ATP_Olambda__101) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 288 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jg,Uu),Uua)) <-> pp(scratc1211721328_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,Uua),scratc995610432nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,Uu)),aa_fun171081125l_bool(scratc636695152_n_all,aa_TPT43085870d_bool(aTP_Lamm_ae,Uua)))))) # label(fact_ATP_Olambda__102) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 289 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jq,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__103) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 290 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ja,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__104) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 291 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bq,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,Uua),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),scratc995610432nd_n_1))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1015484224lessis,Uua),Uu))))) # label(fact_ATP_Olambda__105) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 292 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,Uua),aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,Uu))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1015484224lessis,Uua),Uu))))) # label(fact_ATP_Olambda__106) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 293 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jd,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__107) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 294 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ae,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,Uu),aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,Uu),Uua)))))) # label(fact_ATP_Olambda__108) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 295 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bu,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1015484224lessis,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uua),scratc995610432nd_n_1)),Uu))))) # label(fact_ATP_Olambda__109) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 296 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jl,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1073905595nd_nis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1073905595nd_nis,aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,Uua)))))) # label(fact_ATP_Olambda__110) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 297 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ag,Uu),Uua)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1032860463nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699446d_n_in,Uua),Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699446d_n_in,aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,Uua)),Uu))))) # label(fact_ATP_Olambda__111) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 298 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bs,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1015484224lessis,aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,Uua)),Uu))))) # label(fact_ATP_Olambda__112) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 299 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_by,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1149467836moreis,Uua),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),scratc995610432nd_n_1)))))) # label(fact_ATP_Olambda__113) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 300 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bw,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1149467836moreis,Uua),aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,Uu)))))) # label(fact_ATP_Olambda__114) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 301 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ip,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uua),Uu))))) # label(fact_ATP_Olambda__115) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 302 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hp,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,Uua),Uu))))) # label(fact_ATP_Olambda__116) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 303 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hl,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1149467836moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1015484224lessis,Uua),Uu))))) # label(fact_ATP_Olambda__117) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 304 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hj,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1015484224lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1149467836moreis,Uua),Uu))))) # label(fact_ATP_Olambda__118) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 305 (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(scratc1032598060nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,Uua),Uu))))) # label(fact_ATP_Olambda__119) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 306 (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(scratc1764208430_29_ii,Uu),Uua)) -> pp(scratc1319186508_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1015484224lessis,Uu),Uua)))))) # label(fact_ATP_Olambda__120) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 307 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hh,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1149467836moreis,Uu),Uua)) -> pp(scratc1319186508_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,Uu),Uua)))))) # label(fact_ATP_Olambda__121) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 308 (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(scratc1015484224lessis,Uu),Uua)) -> pp(scratc1319186508_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,Uu),Uua)))))) # label(fact_ATP_Olambda__122) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 309 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,Uu),Uua)) -> pp(scratc1319186508_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1149467836moreis,Uu),Uua)))))) # label(fact_ATP_Olambda__123) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 310 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fz,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uua)),Uu)))) # label(fact_ATP_Olambda__124) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 311 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bh(Uu),Uua) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2021159852d_repl,aa_TPTP_ind_TPTP_ind(Uu,Uua)),aa_TPT1424761345TP_ind(scratc426480247d_pair,Uua))) # label(fact_ATP_Olambda__125) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 312 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jw,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aa_TPT43085870d_bool(aTP_Lamm_ju,Uu)),aa_TPT43085870d_bool(aTP_Lamm_jv(Uu),Uua))))) # label(fact_ATP_Olambda__126) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 313 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iu,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,Uu)),Uua))))) # label(fact_ATP_Olambda__127) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 314 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ix,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,Uua)))))) # label(fact_ATP_Olambda__128) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 315 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hd,Uu),Uua)) <-> (pp(scratc1319186508_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1015484224lessis,Uu),Uua))))) # label(fact_ATP_Olambda__129) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 316 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gv,Uu),Uua)) <-> (pp(scratc1319186508_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1149467836moreis,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__130) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 317 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gt,Uu),Uua)) <-> (pp(scratc1319186508_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1015484224lessis,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__131) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 318 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hb,Uu),Uua)) <-> (pp(scratc1319186508_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1149467836moreis,Uu),Uua))))) # label(fact_ATP_Olambda__132) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 319 (all Uu all Uua aa_fun277296641TP_ind(aa_TPT494704832TP_ind(aTP_Lamm_bl,Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1653449733nunion(aa_TPTP_ind_TPTP_ind(scratc516194422d_Sing,scratc294152082ptyset)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2021159852d_repl,Uu),Uua))) # label(fact_ATP_Olambda__133) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 320 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_in,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1073905595nd_nis,Uua),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__134) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 321 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fx,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__135) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 322 (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(scratc1779699451d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,Uua))))) # label(fact_ATP_Olambda__136) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 323 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ju,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,Uua),aa_TPTP_ind_TPTP_ind(scratc1713851400_power,Uu))))) # label(fact_ATP_Olambda__137) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 324 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jo,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699446d_n_in,Uua),Uu)))) # label(fact_ATP_Olambda__138) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 325 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bm,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1071806422nd_nIn,Uua),Uu)))) # label(fact_ATP_Olambda__139) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 326 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,Uua),Uu)))) # label(fact_ATP_Olambda__140) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 327 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_is,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ir(Uu),Uua))))) # label(fact_ATP_Olambda__141) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 328 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_il,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ik(Uu),Uua))))) # label(fact_ATP_Olambda__142) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 329 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ii,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ih(Uu),Uua))))) # label(fact_ATP_Olambda__143) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 330 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gr,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gq(Uu),Uua))))) # label(fact_ATP_Olambda__144) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 331 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_go,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gn(Uu),Uua))))) # label(fact_ATP_Olambda__145) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 332 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gl,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gk(Uu),Uua))))) # label(fact_ATP_Olambda__146) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 333 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gi,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gh(Uu),Uua))))) # label(fact_ATP_Olambda__147) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 334 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gf,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ge(Uu),Uua))))) # label(fact_ATP_Olambda__148) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 335 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gc,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gb(Uu),Uua))))) # label(fact_ATP_Olambda__149) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 336 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ft,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fs(Uu),Uua))))) # label(fact_ATP_Olambda__150) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 337 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fq,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fp(Uu),Uua))))) # label(fact_ATP_Olambda__151) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 338 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fn,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fm(Uu),Uua))))) # label(fact_ATP_Olambda__152) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 339 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fk,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fj(Uu),Uua))))) # label(fact_ATP_Olambda__153) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 340 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fh,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fg(Uu),Uua))))) # label(fact_ATP_Olambda__154) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 341 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fe,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fd(Uu),Uua))))) # label(fact_ATP_Olambda__155) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 342 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fb,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fa(Uu),Uua))))) # label(fact_ATP_Olambda__156) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 343 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ex,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ew(Uu),Uua))))) # label(fact_ATP_Olambda__157) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 344 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_et,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_es(Uu),Uua))))) # label(fact_ATP_Olambda__158) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 345 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ep,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eo(Uu),Uua))))) # label(fact_ATP_Olambda__159) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 346 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_el,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ek(Uu),Uua))))) # label(fact_ATP_Olambda__160) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 347 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ei,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eh(Uu),Uua))))) # label(fact_ATP_Olambda__161) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 348 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ef,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ee(Uu),Uua))))) # label(fact_ATP_Olambda__162) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 349 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ec,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eb(Uu),Uua))))) # label(fact_ATP_Olambda__163) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 350 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dz,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dy(Uu),Uua))))) # label(fact_ATP_Olambda__164) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 351 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dw,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dv(Uu),Uua))))) # label(fact_ATP_Olambda__165) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 352 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dt,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ds(Uu),Uua))))) # label(fact_ATP_Olambda__166) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 353 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dq,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dp(Uu),Uua))))) # label(fact_ATP_Olambda__167) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 354 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dn,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dm(Uu),Uua))))) # label(fact_ATP_Olambda__168) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 355 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dk,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dj(Uu),Uua))))) # label(fact_ATP_Olambda__169) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 356 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dh,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dg(Uu),Uua))))) # label(fact_ATP_Olambda__170) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 357 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dd,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dc(Uu),Uua))))) # label(fact_ATP_Olambda__171) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 358 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cz,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cy(Uu),Uua))))) # label(fact_ATP_Olambda__172) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 359 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cv,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cu(Uu),Uua))))) # label(fact_ATP_Olambda__173) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 360 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cr,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cq(Uu),Uua))))) # label(fact_ATP_Olambda__174) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 361 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cn,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cm(Uu),Uua))))) # label(fact_ATP_Olambda__175) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 362 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cj,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ci(Uu),Uua))))) # label(fact_ATP_Olambda__176) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 363 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cf,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ce(Uu),Uua))))) # label(fact_ATP_Olambda__177) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 364 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_if,Uu),Uua)) <-> pp(scratc173580189_amone(scratc1073380804nd_nat,aa_TPT43085870d_bool(aTP_Lamm_ib(Uu),Uua))))) # label(fact_ATP_Olambda__178) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 365 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_ad(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc574464486rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,Uu),Uua))) # label(fact_ATP_Olambda__179) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 366 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_be(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc73629618_union,aa_TPTP_ind_TPTP_ind(Uu,Uua))) # label(fact_ATP_Olambda__180) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 367 (all Uu all Uua (gg_TPTP_ind(Uua) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bg,Uu),Uua)) <-> (exists X3 (gg_TPTP_ind(X3) & Uua = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc426480247d_pair,Uu),X3)))))) # label(fact_ATP_Olambda__181) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 368 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ke(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc113555442d_e_is(aa_TPTP_ind_TPTP_ind(scratc208387580etprod(Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1611966689d_pair(Uu,Uua),aa_TPTP_ind_TPTP_ind(scratc626681715_first(Uu,Uua),Uub)),aa_TPTP_ind_TPTP_ind(scratc1834839857second(Uu,Uua),Uub))),Uub)))) # label(fact_ATP_Olambda__182) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 369 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_bo(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc788278650bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,scratc294152082ptyset),Uub),Uu),Uua)) # label(fact_ATP_Olambda__183) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 370 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_fun1235454963TP_ind(aTP_Lamm_bn(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc788278650bnd_if(aa_TPTP_ind_bool(Uua,Uub),Uub),scratc1000011243nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bb(Uu),Uua)))) # label(fact_ATP_Olambda__184) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 371 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_au(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc579384320d_esti(Uu),Uub),Uua)))) # label(fact_ATP_Olambda__185) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 372 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_jx(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc579384320d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc1095469879_d_Sep(Uu),Uua))) -> pp(aa_TPTP_ind_bool(Uua,Uub))))) # label(fact_ATP_Olambda__186) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 373 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jv(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511826763d_incl(Uu),Uua),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1511826763d_incl(Uu),Uub),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc113555442d_e_is(aa_TPTP_ind_TPTP_ind(scratc1713851400_power,Uu)),Uua),Uub)))))) # label(fact_ATP_Olambda__187) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 374 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kf(Uu),Uua),Uub)) <-> scratc76782078_is_of(aa_TPTP_ind_TPTP_ind(scratc1834839857second(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)))) # label(fact_ATP_Olambda__188) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 375 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kg(Uu),Uua),Uub)) <-> scratc76782078_is_of(aa_TPTP_ind_TPTP_ind(scratc626681715_first(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)))) # label(fact_ATP_Olambda__189) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 376 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_km(Uu),Uua),Uub)) <-> scratc76782078_is_of(aa_TPTP_ind_TPTP_ind(scratc113555437d_e_in(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)))) # label(fact_ATP_Olambda__190) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 377 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kq(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aa_TPT43085870d_bool(aTP_Lamm_kn(Uu),Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kp(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__191) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 378 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dy(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__192) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 379 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dp(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__193) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.37 380 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ih(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,Uua),Uub))))) # label(fact_ATP_Olambda__194) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 381 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dv(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__195) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 382 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dm(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__196) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 383 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ds(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__197) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 384 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dj(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__198) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 385 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ir(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__199) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 386 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fs(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__200) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 387 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fj(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__201) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 388 (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(scratc1764208430_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1149467836moreis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,Uu),Uub)))))) # label(fact_ATP_Olambda__202) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 389 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ek(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1149467836moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1149467836moreis,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__203) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 390 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eh(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1149467836moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1149467836moreis,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__204) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 391 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gh(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1149467836moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,Uu),Uub)))))) # label(fact_ATP_Olambda__205) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 392 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ee(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1015484224lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1015484224lessis,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__206) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 393 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eb(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1015484224lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1015484224lessis,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__207) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 394 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gb(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1015484224lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1015484224lessis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1015484224lessis,Uu),Uub)))))) # label(fact_ATP_Olambda__208) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 395 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gn(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1015484224lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__209) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 396 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fp(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__210) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 397 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fg(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__211) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 398 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ik(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1073905595nd_nis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1073905595nd_nis,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uub)))))) # label(fact_ATP_Olambda__212) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 399 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fm(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__213) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 400 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fd(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__214) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 401 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gk(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1015484224lessis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__215) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 402 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gq(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__216) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 403 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bb(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,Uub),Uu)) & pp(aa_TPTP_ind_bool(Uua,Uub)))) # label(fact_ATP_Olambda__217) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 404 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_kj(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc584039646_image(aa_fun1431113780TP_ind(scratc1095469879_d_Sep(Uu),Uua),Uu),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc258290270_Sigma,aa_fun1431113780TP_ind(scratc1095469879_d_Sep(Uu),Uua)),scratc113555437d_e_in(Uu,Uua))),Uub))))) # label(fact_ATP_Olambda__218) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 405 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_jy(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc579384320d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc1095469879_d_Sep(Uu),Uua)))))) # label(fact_ATP_Olambda__219) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 406 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ks(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_kr(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__220) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 407 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bd(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bc(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__221) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 408 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ki(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kh(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__222) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 409 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kc(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kb(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__223) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 410 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ka(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jz(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__224) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 411 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kn(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,Uub),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1119834816d_d_Pi,Uu),aTP_Lamm_ai(Uua)))))) # label(fact_ATP_Olambda__225) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 412 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ib(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uua),Uub))))) # label(fact_ATP_Olambda__226) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 413 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ic(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,Uua),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uub))))) # label(fact_ATP_Olambda__227) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 414 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kd(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,Uub),aa_TPTP_ind_TPTP_ind(scratc208387580etprod(Uu),Uua))))) # label(fact_ATP_Olambda__228) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 415 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_kk(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,Uub),aa_fun1431113780TP_ind(scratc1095469879_d_Sep(Uu),Uua))))) # label(fact_ATP_Olambda__229) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 416 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_aw(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,Uu),Uub))) # label(fact_ATP_Olambda__230) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 417 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fa(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ez(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__231) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 418 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ew(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ev(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__232) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 419 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_es(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_er(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__233) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 420 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eo(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_en(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__234) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 421 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dg(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_df(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__235) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 422 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dc(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_db(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__236) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 423 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cy(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cx(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__237) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 424 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cu(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ct(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__238) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 425 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cq(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cp(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__239) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 426 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cm(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cl(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__240) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 427 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ci(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ch(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__241) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 428 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ce(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cd(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__242) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 429 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_kl(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(Uua,aa_TPTP_ind_TPTP_ind(scratc113555437d_e_in(Uu,Uua),Uub))))) # label(fact_ATP_Olambda__243) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 430 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1913827119d_bool(aTP_Lamm_bf(Uu),Uua),Uub)) <-> (all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,X3),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc788278658bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,Uub),X3)),aa_TPTP_ind_TPTP_ind(Uua,X3)))))))) # label(fact_ATP_Olambda__244) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 431 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ax(Uu),Uua),Uub),Uuc) = aa_TPTP_ind_TPTP_ind(scratc788278650bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc584039646_image(Uu,Uua),Uub),Uuc),aa_TPTP_ind_TPTP_ind(scratc736222471d_soft(Uu,Uua,Uub),Uuc)),scratc294152082ptyset)) # label(fact_ATP_Olambda__245) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 432 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kb(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc113555442d_e_is(Uu),aa_TPTP_ind_TPTP_ind(scratc626681715_first(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1611966689d_pair(Uu,Uua),Uub),Uuc))),Uub)))) # label(fact_ATP_Olambda__246) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 433 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jz(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc113555442d_e_is(Uua),aa_TPTP_ind_TPTP_ind(scratc1834839857second(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1611966689d_pair(Uu,Uua),Uub),Uuc))),Uuc)))) # label(fact_ATP_Olambda__247) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 434 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ko(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc113555442d_e_is(Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,Uua),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,Uub),Uuc))))) # label(fact_ATP_Olambda__248) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 435 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aq(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc579384320d_esti(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__249) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 436 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc113555442d_e_is(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__250) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 437 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kh(Uu),Uua),Uub),Uuc)) <-> scratc76782078_is_of(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1611966689d_pair(Uu,Uua),Uub),Uuc),aa_TPT43085870d_bool(aTP_Lamm_kd(Uu),Uua)))) # label(fact_ATP_Olambda__251) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 438 (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(scratc1647792109d_l_ec(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc579384320d_esti(Uu),Uuc),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc579384320d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__252) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 439 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_at(Uu),Uua),Uub),Uuc)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1032860463nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc579384320d_esti(Uu),Uuc),Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc579384320d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__253) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 440 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kp(Uu),Uua),Uub),Uuc)) <-> (pp(aa_fun171081125l_bool(scratc1491838555all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ko(Uua),Uub),Uuc))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc113555442d_e_is(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1119834816d_d_Pi,Uu),aTP_Lamm_ai(Uua))),Uub),Uuc))))) # label(fact_ATP_Olambda__254) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 441 (all Uu all Uua all Uub all Uuc (gg_TPTP_ind(Uua) & gg_TPTP_ind(Uub) & gg_TPTP_ind(Uuc) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bp(Uu),Uua),Uub),Uuc)) <-> pp(Uu) & Uuc = Uua | -pp(Uu) & Uuc = Uub))) # label(fact_ATP_Olambda__255) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 442 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_df(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__256) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 443 (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(scratc1764208430_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1149467836moreis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__257) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 444 (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(scratc1149467836moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__258) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 445 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ch(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1149467836moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1149467836moreis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1149467836moreis,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__259) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 446 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cd(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1015484224lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1015484224lessis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1015484224lessis,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__260) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 447 (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(scratc1015484224lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__261) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 448 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ez(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__262) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 449 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ev(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1764208430_29_ii,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uuc),Uua))))))) # label(fact_ATP_Olambda__263) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 450 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_er(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__264) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 451 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_en(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1779699451d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uuc),Uua))))))) # label(fact_ATP_Olambda__265) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 452 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cl(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1015484224lessis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__266) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 453 (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(scratc1032598060nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032598060nd_iii,aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1780158637d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__267) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 454 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_kr(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc113555442d_e_is(Uu),Uub),Uuc)) -> pp(aa_TPTP_ind_bool(Uua,Uuc)))))) # label(fact_ATP_Olambda__268) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 455 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bc(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(Uua,Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc113555442d_e_is(Uu),Uub),Uuc)))))) # label(fact_ATP_Olambda__269) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 456 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ba(Uu),Uua),Uub),Uuc)) <-> pp(aa_fun171081125l_bool(scratc966702820nd_all(Uu),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_az(Uu),Uua),Uub),Uuc))))) # label(fact_ATP_Olambda__270) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 457 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ar(Uu),Uua),Uub),Uuc)) <-> pp(aa_fun171081125l_bool(scratc602499363l_some(Uua),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aq(Uu),Uub),Uuc))))) # label(fact_ATP_Olambda__271) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 458 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_az(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1032860463nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc113555442d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,Uub),Uud))),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc113555442d_e_is(Uu),Uuc),Uud))))) # label(fact_ATP_Olambda__272) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 459 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_ao(Uu),Uua),Uub),Uuc),Uud)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc113555442d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,Uub),Uud)))))) # label(fact_ATP_Olambda__273) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 460 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_an(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_am(Uu),Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__274) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 461 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ap(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_ao(Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__275) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 462 (all Uu all Uua all Uub all Uuc all Uud aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_av(Uu),Uua),Uub),Uuc),Uud) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1075623926wissel(Uu,Uub),Uuc)),Uud))) # label(fact_ATP_Olambda__276) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 463 (all Uu all Uua all Uub all Uuc all Uud all Uue (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_am(Uu),Uua),Uub),Uuc),Uud),Uue)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_al(Uu),Uua),Uub),Uuc),Uud),Uue))))) # label(fact_ATP_Olambda__277) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 464 (all Uu all Uua all Uub all Uuc all Uud all Uue all Uuf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_ak(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uue),Uuf)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc113555442d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,Uub),Uuc)),Uue)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc787753868bnd_ap,Uub),Uud)),Uuf))))))) # label(fact_ATP_Olambda__278) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 465 (all Uu all Uua all Uub all Uuc all Uud all Uue all Uuf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_al(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)) <-> pp(aa_fun171081125l_bool(scratc1491838555all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_ak(Uua),Uub),Uuc),Uud),Uue),Uuf))))) # label(fact_ATP_Olambda__279) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 466 (all Uu all Uua (gg_TPTP_ind(Uu) -> aa_TPTP_ind_TPTP_ind(aTP_Lamm_ai(Uu),Uua) = Uu)) # label(fact_ATP_Olambda__280) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 467 (all Uu aa_TPTP_ind_TPTP_ind(aTP_Lamm_ac,Uu) = scratc1073380804nd_nat) # label(fact_ATP_Olambda__281) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.38 468 (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].
% 1.02/1.38 469 (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].
% 1.02/1.38 470 (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].
% 1.02/1.38 471 (all P (gg_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.42 472 (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].
% 1.02/1.42 473 (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].
% 1.02/1.42 474 (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].
% 1.02/1.42 475 (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].
% 1.02/1.42 476 (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].
% 1.02/1.42 477 (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].
% 1.02/1.42 478 (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].
% 1.02/1.42 479 (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].
% 1.02/1.42 480 (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].
% 1.02/1.42
% 1.02/1.42 ============================== end of process non-clausal formulas ===
% 1.02/1.42
% 1.02/1.42 ============================== PROCESS INITIAL CLAUSES ===============
% 1.02/1.42
% 1.02/1.42 ============================== PREDICATE ELIMINATION =================
% 1.02/1.42 481 -gg_bool(A) | A = fTrue | A = fFalse # label(help_fFalse_1_1_T) # label(axiom). [clausify(471)].
% 1.02/1.42 482 gg_bool(undefined_bool(bool)) # label(gsy_c_HOL_Oundefined_001t__HOL__Obool) # label(axiom). [assumption].
% 1.02/1.42 483 gg_bool(scratc173580189_amone(A,B)) # label(gsy_c_Scratch__tptp__translate__51566__4158_ONUM701__thf__4__p_Obnd__amone) # label(axiom). [clausify(1)].
% 1.02/1.42 484 gg_bool(scratc1211721328_d_and(A,B)) # label(gsy_c_Scratch__tptp__translate__51566__4158_ONUM701__thf__4__p_Obnd__d__and) # label(axiom). [clausify(2)].
% 1.02/1.42 485 gg_bool(scratc1319186508_d_not(A)) # label(gsy_c_Scratch__tptp__translate__51566__4158_ONUM701__thf__4__p_Obnd__d__not) # label(axiom). [clausify(3)].
% 1.02/1.42 486 gg_bool(scratc999158392nd_ec3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__51566__4158_ONUM701__thf__4__p_Obnd__ec3) # label(axiom). [clausify(4)].
% 1.02/1.42 487 gg_bool(scratc1647792109d_l_ec(A,B)) # label(gsy_c_Scratch__tptp__translate__51566__4158_ONUM701__thf__4__p_Obnd__l__ec) # label(axiom). [clausify(8)].
% 1.02/1.42 488 gg_bool(scratc1082757427nd_or3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__51566__4158_ONUM701__thf__4__p_Obnd__or3) # label(axiom). [clausify(9)].
% 1.02/1.42 489 gg_bool(aa_bool_bool(A,B)) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom). [clausify(10)].
% 1.02/1.42 490 gg_bool(aa_TPTP_ind_bool(A,B)) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom). [clausify(11)].
% 1.02/1.42 491 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)].
% 1.02/1.42 492 gg_bool(fEx_TPTP_ind(A)) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom). [clausify(16)].
% 1.02/1.42 493 gg_bool(fFalse) # label(gsy_c_fFalse) # label(axiom). [assumption].
% 1.02/1.42 494 gg_bool(fTrue) # label(gsy_c_fTrue) # label(axiom). [assumption].
% 1.74/1.98 Derived: undefined_bool(bool) = fTrue | undefined_bool(bool) = fFalse. [resolve(481,a,482,a)].
% 1.74/1.98 Derived: scratc173580189_amone(A,B) = fTrue | scratc173580189_amone(A,B) = fFalse. [resolve(481,a,483,a)].
% 1.74/1.98 Derived: scratc1211721328_d_and(A,B) = fTrue | scratc1211721328_d_and(A,B) = fFalse. [resolve(481,a,484,a)].
% 1.74/1.98 Derived: scratc1319186508_d_not(A) = fTrue | scratc1319186508_d_not(A) = fFalse. [resolve(481,a,485,a)].
% 1.74/1.98 Derived: scratc999158392nd_ec3(A,B,C) = fTrue | scratc999158392nd_ec3(A,B,C) = fFalse. [resolve(481,a,486,a)].
% 1.74/1.98 Derived: scratc1647792109d_l_ec(A,B) = fTrue | scratc1647792109d_l_ec(A,B) = fFalse. [resolve(481,a,487,a)].
% 1.74/1.98 Derived: scratc1082757427nd_or3(A,B,C) = fTrue | scratc1082757427nd_or3(A,B,C) = fFalse. [resolve(481,a,488,a)].
% 1.74/1.98 Derived: aa_bool_bool(A,B) = fTrue | aa_bool_bool(A,B) = fFalse. [resolve(481,a,489,a)].
% 1.74/1.98 Derived: aa_TPTP_ind_bool(A,B) = fTrue | aa_TPTP_ind_bool(A,B) = fFalse. [resolve(481,a,490,a)].
% 1.74/1.98 Derived: aa_fun171081125l_bool(A,B) = fTrue | aa_fun171081125l_bool(A,B) = fFalse. [resolve(481,a,491,a)].
% 1.74/1.98 Derived: fEx_TPTP_ind(A) = fTrue | fEx_TPTP_ind(A) = fFalse. [resolve(481,a,492,a)].
% 1.74/1.98 Derived: fFalse = fTrue | fFalse = fFalse. [resolve(481,a,493,a)].
% 1.74/1.98 Derived: fTrue = fTrue | fTrue = fFalse. [resolve(481,a,494,a)].
% 1.74/1.98 495 scratc2042726899d_r_ec(A,B) | pp(A) # label(fact_def__r__ec) # label(axiom). [clausify(59)].
% 1.74/1.98 496 -scratc2042726899d_r_ec(A,B) | -pp(A) | pp(scratc1319186508_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(59)].
% 1.74/1.98 497 scratc2042726899d_r_ec(A,B) | -pp(scratc1319186508_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(59)].
% 1.74/1.98 498 scratc2105862778_l_iff(A,B) | -pp(scratc1211721328_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1032860463nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc1032860463nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(91)].
% 1.74/1.98 499 -scratc2105862778_l_iff(A,B) | pp(scratc1211721328_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1032860463nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc1032860463nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(91)].
% 1.74/1.98 500 scratc1933559870d_orec(A,B) | -pp(scratc1211721328_d_and(aa_bool_bool(scratc1648448114d_l_or(A),B),scratc1647792109d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(92)].
% 1.74/1.98 501 -scratc1933559870d_orec(A,B) | pp(scratc1211721328_d_and(aa_bool_bool(scratc1648448114d_l_or(A),B),scratc1647792109d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(92)].
% 1.74/1.98 502 scratc1147996737nd_wel(A) | -pp(scratc1319186508_d_not(scratc1319186508_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(97)].
% 1.74/1.98 503 -scratc1147996737nd_wel(A) | pp(scratc1319186508_d_not(scratc1319186508_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(97)].
% 1.74/1.98 504 -scratc1147996737nd_wel(A) | pp(A) # label(fact_l__et) # label(axiom). [clausify(147)].
% 1.74/1.98 Derived: pp(A) | -pp(scratc1319186508_d_not(scratc1319186508_d_not(A))). [resolve(504,a,502,a)].
% 1.74/1.98
% 1.74/1.98 ============================== end predicate elimination =============
% 1.74/1.98
% 1.74/1.98 Auto_denials: (non-Horn, no changes).
% 1.74/1.98
% 1.74/1.98 Term ordering decisions:
% 1.74/1.98 Function symbol KB weights: aTP_Lamm_a=1. scratc788278658bnd_in=1. scratc1779699451d_n_is=1. scratc1032598060nd_iii=1. scratc574464486rdsucc=1. scratc1764208430_29_ii=1. scratc787753868bnd_ap=1. scratc1015484224lessis=1. aTP_Lamm_aj=1. scratc1149467836moreis=1. scratc995610432nd_n_1=1. scratc294152082ptyset=1. scratc258290270_Sigma=1. scratc1073905595nd_nis=1. fFalse=1. scratc1073380804nd_nat=1. scratc1119834816d_d_Pi=1. scratc1346324005n_some=1. scratc1713851400_power=1. scratc2110909932_nat_p=1. scratc1032860463nd_imp=1. scratc2021159852d_repl=1. fTrue=1. scratc426480247d_pair=1. scratc614545304d_Subq=1. scratc1009598658closed=1. scratc1842365238_proj0=1. scratc73629618_union=1. aTP_Lamm_af=1. scratc1779699446d_n_in=1. scratc1842365239_proj1=1. scratc636695152_n_all=1. aTP_Lamm_ac=1. aTP_Lamm_ae=1. aTP_Lamm_ju=1. scratc1889046068closed=1. scratc2053779082closed=1. aTP_Lamm_aa=1. aTP_Lamm_bq=1. aTP_Lamm_bs=1. aTP_Lamm_bu=1. aTP_Lamm_bw=1. aTP_Lamm_by=1. aTP_Lamm_gt=1. aTP_Lamm_gv=1. aTP_Lamm_gx=1. aTP_Lamm_gz=1. aTP_Lamm_hb=1. aTP_Lamm_hd=1. aTP_Lamm_hf=1. aTP_Lamm_hh=1. aTP_Lamm_hj=1. aTP_Lamm_hl=1. aTP_Lamm_hn=1. aTP_Lamm_hp=1. aTP_Lamm_jl=1. aTP_Lamm_jp=1. aTP_Lamm_jq=1. scratc1012020452_omega=1. scratc1168386463closed=1. scratc1341302099d_Inj1=1. scratc788094726_prop2=1. aTP_Lamm_ag=1. aTP_Lamm_bg=1. aTP_Lamm_bi=1. aTP_Lamm_bj=1. aTP_Lamm_cf=1. aTP_Lamm_cj=1. aTP_Lamm_cn=1. aTP_Lamm_cr=1. aTP_Lamm_cv=1. aTP_Lamm_cz=1. aTP_Lamm_dd=1. aTP_Lamm_dh=1. aTP_Lamm_dk=1. aTP_Lamm_dn=1. aTP_Lamm_dq=1. aTP_Lamm_dt=1. aTP_Lamm_dw=1. aTP_Lamm_dz=1. aTP_Lamm_ec=1. aTP_Lamm_ef=1. aTP_Lamm_ei=1. aTP_Lamm_el=1. aTP_Lamm_ep=1. aTP_Lamm_et=1. aTP_Lamm_ex=1. aTP_Lamm_fb=1. aTP_Lamm_fe=1. aTP_Lamm_fh=1. aTP_Lamm_fk=1. aTP_Lamm_fn=1. aTP_Lamm_fq=1. aTP_Lamm_ft=1. aTP_Lamm_fx=1. aTP_Lamm_fz=1. aTP_Lamm_gc=1. aTP_Lamm_gf=1. aTP_Lamm_gi=1. aTP_Lamm_gl=1. aTP_Lamm_go=1. aTP_Lamm_gr=1. aTP_Lamm_hr=1. aTP_Lamm_ht=1. aTP_Lamm_hv=1. aTP_Lamm_hx=1. aTP_Lamm_hz=1. aTP_Lamm_id=1. aTP_Lamm_if=1. aTP_Lamm_ii=1. aTP_Lamm_il=1. aTP_Lamm_in=1. aTP_Lamm_ip=1. aTP_Lamm_is=1. aTP_Lamm_iu=1. aTP_Lamm_ix=1. aTP_Lamm_ja=1. aTP_Lamm_jd=1. aTP_Lamm_jg=1. aTP_Lamm_ji=1. aTP_Lamm_jj=1. aTP_Lamm_jo=1. fconj=1. fimplies=1. scratc1341302098d_Inj0=1. scratc1857481971_cond2=1. scratc516194422d_Sing=1. scratc788094725_prop1=1. aTP_Lamm_bm=1. aTP_Lamm_br=1. aTP_Lamm_bt=1. aTP_Lamm_bv=1. aTP_Lamm_bx=1. aTP_Lamm_bz=1. aTP_Lamm_ca=1. aTP_Lamm_cb=1. aTP_Lamm_cc=1. aTP_Lamm_cg=1. aTP_Lamm_ck=1. aTP_Lamm_co=1. aTP_Lamm_cs=1. aTP_Lamm_cw=1. aTP_Lamm_da=1. aTP_Lamm_de=1. aTP_Lamm_di=1. aTP_Lamm_dl=1. aTP_Lamm_do=1. aTP_Lamm_dr=1. aTP_Lamm_du=1. aTP_Lamm_dx=1. aTP_Lamm_ea=1. aTP_Lamm_ed=1. aTP_Lamm_eg=1. aTP_Lamm_ej=1. aTP_Lamm_em=1. aTP_Lamm_eq=1. aTP_Lamm_eu=1. aTP_Lamm_ey=1. aTP_Lamm_fc=1. aTP_Lamm_ff=1. aTP_Lamm_fi=1. aTP_Lamm_fl=1. aTP_Lamm_fo=1. aTP_Lamm_fr=1. aTP_Lamm_fu=1. aTP_Lamm_fv=1. aTP_Lamm_fw=1. aTP_Lamm_fy=1. aTP_Lamm_ga=1. aTP_Lamm_gd=1. aTP_Lamm_gg=1. aTP_Lamm_gj=1. aTP_Lamm_gm=1. aTP_Lamm_gp=1. aTP_Lamm_gs=1. aTP_Lamm_gu=1. aTP_Lamm_gw=1. aTP_Lamm_gy=1. aTP_Lamm_ha=1. aTP_Lamm_hc=1. aTP_Lamm_he=1. aTP_Lamm_hg=1. aTP_Lamm_hi=1. aTP_Lamm_hk=1. aTP_Lamm_hm=1. aTP_Lamm_ho=1. aTP_Lamm_hq=1. aTP_Lamm_hs=1. aTP_Lamm_hu=1. aTP_Lamm_hw=1. aTP_Lamm_hy=1. aTP_Lamm_ia=1. aTP_Lamm_ie=1. aTP_Lamm_ig=1. aTP_Lamm_ij=1. aTP_Lamm_im=1. aTP_Lamm_io=1. aTP_Lamm_iq=1. aTP_Lamm_it=1. aTP_Lamm_iv=1. aTP_Lamm_iw=1. aTP_Lamm_iy=1. aTP_Lamm_iz=1. aTP_Lamm_jb=1. aTP_Lamm_jc=1. aTP_Lamm_je=1. aTP_Lamm_jf=1. aTP_Lamm_jh=1. aTP_Lamm_jk=1. aTP_Lamm_jm=1. aTP_Lamm_jn=1. aTP_Lamm_jr=1. aTP_Lamm_js=1. aTP_Lamm_jt=1. aTP_Lamm_jw=1. aTP_Lamm_kt=1. fequal_TPTP_ind=1. scratc1071806422nd_nIn=1. scratc1112583274_d_Unj=1. scratc1857481970_cond1=1. scratc396483066univof=1. scratc752487413_n_one=1. aTP_Lamm_ab=1. aTP_Lamm_ah=1. aTP_Lamm_bk=1. aTP_Lamm_bl=1. bool=1. scratc1582421952_prop1=1. scratc1758854023_prop1=1. scratc1842758836_prop4=1. scratc1964819075_prop1=1. scratc199732550_prop1=1. scratc405697602_prop1=1. scratc431214457pair_p=1. scratc445525168_empty=1. scratc518143991d_plus=1. scratc579747069nempty=1. scratc659592634munion=1. scratc671431742d_24_g=1. scratc976400174d_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. scratc1211721328_d_and=1. aa_TPT1123896796d_bool=1. scratc788278650bnd_if=1. scratc1647792109d_l_ec=1. aa_fun1212484691d_bool=1. aa_TPT985247859d_bool=1. scratc113555437d_e_in=1. scratc1611966689d_pair=1. aa_fun987228051d_bool=1. scratc1032926050nd_ind=1. scratc173580189_amone=1. scratc1834839857second=1. scratc584039646_image=1. scratc626681715_first=1. aa_TPT125613450d_bool=1. scratc1074299184nd_non=1. aa_fun1913827119d_bool=1. scratc1709711304d_anec=1. aa_TPT1791839040TP_ind=1. aa_fun1107270209d_bool=1. aa_fun845057962d_bool=1. scratc1138186418_ecelt=1. scratc2040673896eplSep=1. scratc999158453nd_ecp=1. scratc1137596027_ecect=1. aa_TPT1781712639TP_ind=1. aa_TPT2142672771l_bool=1. aa_fun1235454963TP_ind=1. cOMBB_658106424TP_ind=1. cOMBS_2003118649l_bool=1. scratc1075623926wissel=1. scratc1082954289nd_out=1. scratc1207597129ectset=1. scratc1477213322etprop=1. scratc675397959_fixfu=1. scratc695570603fixfu2=1. scratc999158457nd_ect=1. scratc1092395252ectelt=1. scratc1313714475unmore=1. scratc1513073138d_invf=1. scratc1516809669d_tofs=1. scratc2120195827nverse=1. f1=1. f12=1. f13=1. f20=1. f24=1. scratc1491838555all_of=1. scratc1780158637d_n_pl=1. scratc113555442d_e_is=1. scratc1319186508_d_not=1. scratc1095469879_d_Sep=1. scratc579384320d_esti=1. scratc602499363l_some=1. scratc1576049029ffprop=1. scratc966702820nd_all=1. scratc1648448114d_l_or=1. scratc869862563_rec_G=1. aTP_Lamm_ai=1. aTP_Lamm_kd=1. scratc1082495081nd_one=1. aTP_Lamm_ak=1. aTP_Lamm_au=1. aTP_Lamm_bc=1. aTP_Lamm_bp=1. aTP_Lamm_cd=1. aTP_Lamm_ch=1. aTP_Lamm_cl=1. aTP_Lamm_cp=1. aTP_Lamm_ct=1. aTP_Lamm_cx=1. aTP_Lamm_db=1. aTP_Lamm_df=1. aTP_Lamm_en=1. aTP_Lamm_er=1. aTP_Lamm_ev=1. aTP_Lamm_ez=1. aTP_Lamm_gb=1. aTP_Lamm_ge=1. aTP_Lamm_gh=1. aTP_Lamm_gk=1. aTP_Lamm_gn=1. aTP_Lamm_gq=1. aTP_Lamm_ib=1. aTP_Lamm_jv=1. aTP_Lamm_kr=1. scratc1511826763d_incl=1. aTP_Lamm_ao=1. aTP_Lamm_ay=1. aTP_Lamm_bb=1. aTP_Lamm_bf=1. aTP_Lamm_dj=1. aTP_Lamm_dm=1. aTP_Lamm_dp=1. aTP_Lamm_ds=1. aTP_Lamm_dv=1. aTP_Lamm_dy=1. aTP_Lamm_eb=1. aTP_Lamm_ee=1. aTP_Lamm_eh=1. aTP_Lamm_ek=1. aTP_Lamm_fd=1. aTP_Lamm_fg=1. aTP_Lamm_fj=1. aTP_Lamm_fm=1. aTP_Lamm_fp=1. aTP_Lamm_fs=1. aTP_Lamm_ih=1. aTP_Lamm_ik=1. aTP_Lamm_kn=1. aTP_Lamm_kp=1. scratc1000011243nd_eps=1. scratc208387580etprod=1. scratc808567434ective=1. aTP_Lamm_al=1. aTP_Lamm_am=1. aTP_Lamm_an=1. aTP_Lamm_ap=1. aTP_Lamm_aq=1. aTP_Lamm_as=1. aTP_Lamm_at=1. aTP_Lamm_az=1. aTP_Lamm_ba=1. aTP_Lamm_bd=1. aTP_Lamm_ce=1. aTP_Lamm_ci=1. aTP_Lamm_cm=1. aTP_Lamm_cq=1. aTP_Lamm_cu=1. aTP_Lamm_cy=1. aTP_Lamm_dc=1. aTP_Lamm_dg=1. aTP_Lamm_eo=1. aTP_Lamm_es=1. aTP_Lamm_ew=1. aTP_Lamm_fa=1. aTP_Lamm_ic=1. aTP_Lamm_ir=1. aTP_Lamm_jx=1. aTP_Lamm_jy=1. aTP_Lamm_jz=1. aTP_Lamm_kb=1. aTP_Lamm_kh=1. aTP_Lamm_kj=1. aTP_Lamm_kk=1. aTP_Lamm_ko=1. fEx_TPTP_ind=1. scratc1012958617ective=1. scratc1653449733nunion=1. aTP_Lamm_ar=1. aTP_Lamm_ka=1. aTP_Lamm_kc=1. aTP_Lamm_ke=1. aTP_Lamm_kf=1. aTP_Lamm_kg=1. aTP_Lamm_ki=1. aTP_Lamm_kl=1. aTP_Lamm_km=1. aTP_Lamm_kq=1. aTP_Lamm_ks=1. scratc152776648_UPair=1. scratc1768437476In_rec=1. aTP_Lamm_ad=1. aTP_Lamm_av=1. aTP_Lamm_aw=1. aTP_Lamm_ax=1. aTP_Lamm_be=1. aTP_Lamm_bh=1. aTP_Lamm_bn=1. aTP_Lamm_bo=1. cOMBC_1555011498d_bool=1. scratc1376456900_prop1=1. scratc1569735275tminus=1. scratc1842758835_prop3=1. scratc1986571770t_disj=1. scratc992286664ective=1. scratc994059777_prop1=1. undefined_bool=1. undefined_TPTP_ind=1. f2=1. f8=1. f9=1. f10=1. f11=1. f17=1. f18=1. f21=1. f22=1. f23=1. scratc1082757427nd_or3=1. scratc999158392nd_ec3=1. scratc736222471d_soft=1. scratc1033319645nd_ite=1. scratc1389280174_indeq=1. scratc1842758833_prop1=1. scratc1416583008sel_wa=1. scratc1416583009sel_wb=1. scratc1485073154d_11_i=1. f5=1. f7=1. f14=1. f16=1. f19=1. f25=1. scratc1842758834_prop2=1. scratc2134154777hangef=1. scratc816886592_inj_h=1. f3=1. f4=1. f15=1. scratc1335417352_prop1=1. scratc479080452indeq2=1. f6=1.
% 2.87/3.19
% 2.87/3.19 ============================== end of process initial clauses ========
% 2.87/3.19
% 2.87/3.19 ============================== CLAUSES FOR SEARCH ====================
% 2.87/3.19
% 2.87/3.19 ============================== end of clauses for search =============
% 2.87/3.19
% 2.87/3.19 ============================== SEARCH ================================
% 2.87/3.19
% 2.87/3.19 % Starting search at 0.71 seconds.
% 2.87/3.19
% 2.87/3.19 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 64 (0.00 of 1.04 sec).
% 2.87/3.19
% 2.87/3.19 Low Water (keep): wt=36.000, iters=3353
% 2.87/3.19
% 2.87/3.19 Low Water (keep): wt=35.000, iters=3337
% 2.87/3.19
% 2.87/3.19 Low Water (keep): wt=34.000, iters=3338
% 2.87/3.19
% 2.87/3.19 Low Water (keep): wt=32.000, iters=3354
% 2.87/3.19
% 2.87/3.19 Low Water (keep): wt=31.000, iters=3434
% 2.87/3.19
% 2.87/3.19 Low Water (keep): wt=30.000, iters=3343
% 2.87/3.19
% 2.87/3.19 Low Water (keep): wt=29.000, iters=3765
% 2.87/3.19
% 2.87/3.19 Low Water (keep): wt=27.000, iters=3547
% 2.87/3.19
% 2.87/3.19 Low Water (keep): wt=24.000, iters=3389
% 2.87/3.19
% 2.87/3.19 Low Water (keCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------