TSTP Solution File: NUM702+4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM702+4 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 13:30:58 EDT 2022
% Result : Timeout 300.06s 300.42s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM702+4 : TPTP v8.1.0. Released v7.3.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jul 8 01:42:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.08/1.42 ============================== Prover9 ===============================
% 1.08/1.42 Prover9 (32) version 2009-11A, November 2009.
% 1.08/1.42 Process 5774 was started by sandbox on n025.cluster.edu,
% 1.08/1.42 Fri Jul 8 01:42:45 2022
% 1.08/1.42 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_5621_n025.cluster.edu".
% 1.08/1.42 ============================== end of head ===========================
% 1.08/1.42
% 1.08/1.42 ============================== INPUT =================================
% 1.08/1.42
% 1.08/1.42 % Reading from file /tmp/Prover9_5621_n025.cluster.edu
% 1.08/1.42
% 1.08/1.42 set(prolog_style_variables).
% 1.08/1.42 set(auto2).
% 1.08/1.42 % set(auto2) -> set(auto).
% 1.08/1.42 % set(auto) -> set(auto_inference).
% 1.08/1.42 % set(auto) -> set(auto_setup).
% 1.08/1.42 % set(auto_setup) -> set(predicate_elim).
% 1.08/1.42 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.08/1.42 % set(auto) -> set(auto_limits).
% 1.08/1.42 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.08/1.42 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.08/1.42 % set(auto) -> set(auto_denials).
% 1.08/1.42 % set(auto) -> set(auto_process).
% 1.08/1.42 % set(auto2) -> assign(new_constants, 1).
% 1.08/1.42 % set(auto2) -> assign(fold_denial_max, 3).
% 1.08/1.42 % set(auto2) -> assign(max_weight, "200.000").
% 1.08/1.42 % set(auto2) -> assign(max_hours, 1).
% 1.08/1.42 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.08/1.42 % set(auto2) -> assign(max_seconds, 0).
% 1.08/1.42 % set(auto2) -> assign(max_minutes, 5).
% 1.08/1.42 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.08/1.42 % set(auto2) -> set(sort_initial_sos).
% 1.08/1.42 % set(auto2) -> assign(sos_limit, -1).
% 1.08/1.42 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.08/1.42 % set(auto2) -> assign(max_megs, 400).
% 1.08/1.42 % set(auto2) -> assign(stats, some).
% 1.08/1.42 % set(auto2) -> clear(echo_input).
% 1.08/1.42 % set(auto2) -> set(quiet).
% 1.08/1.42 % set(auto2) -> clear(print_initial_clauses).
% 1.08/1.42 % set(auto2) -> clear(print_given).
% 1.08/1.42 assign(lrs_ticks,-1).
% 1.08/1.42 assign(sos_limit,10000).
% 1.08/1.42 assign(order,kbo).
% 1.08/1.42 set(lex_order_vars).
% 1.08/1.42 clear(print_given).
% 1.08/1.42
% 1.08/1.42 % formulas(sos). % not echoed (598 formulas)
% 1.08/1.42
% 1.08/1.42 ============================== end of input ==========================
% 1.08/1.42
% 1.08/1.42 % From the command line: assign(max_seconds, 300).
% 1.08/1.42
% 1.08/1.42 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.08/1.42
% 1.08/1.42 % Formulas that are not ordinary clauses:
% 1.08/1.42 1 (all B_1 all B_2 gg_bool(scratc1581925715_amone(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__51767__4802_ONUM702__thf__4__p_Obnd__amone) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 2 (all B_1 all B_2 gg_bool(scratc375860794_d_and(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__51767__4802_ONUM702__thf__4__p_Obnd__d__and) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 3 (all B_1 gg_bool(scratc483325974_d_not(B_1))) # label(gsy_c_Scratch__tptp__translate__51767__4802_ONUM702__thf__4__p_Obnd__d__not) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 4 (all B_1 all B_2 all B_3 gg_bool(scratc489722670nd_ec3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__51767__4802_ONUM702__thf__4__p_Obnd__ec3) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 5 (all B_1 all B_2 gg_TPTP_ind(scratc489722735nd_ect(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__51767__4802_ONUM702__thf__4__p_Obnd__ect) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 6 (all B_1 gg_TPTP_ind(scratc490575521nd_eps(B_1))) # label(gsy_c_Scratch__tptp__translate__51767__4802_ONUM702__thf__4__p_Obnd__eps) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 7 (all B_1 all B_2 gg_TPTP_ind(scratc523490328nd_ind(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__51767__4802_ONUM702__thf__4__p_Obnd__ind) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 8 (all B_1 all B_2 gg_bool(scratc908653987d_l_ec(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__51767__4802_ONUM702__thf__4__p_Obnd__l__ec) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 9 (all B_1 all B_2 all B_3 gg_bool(scratc573321705nd_or3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__51767__4802_ONUM702__thf__4__p_Obnd__or3) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 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].
% 1.08/1.42 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].
% 1.08/1.42 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].
% 1.08/1.42 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].
% 1.08/1.42 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].
% 1.08/1.42 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].
% 1.08/1.42 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].
% 1.08/1.42 17 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc179623690lessis,X),Xa)) <-> pp(aa_bool_bool(scratc909309992d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,X),Xa))))) # label(fact_def__lessis) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 18 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc313607302moreis,X),Xa)) <-> pp(aa_bool_bool(scratc909309992d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,X),Xa))))) # label(fact_def__moreis) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 19 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1984254090_prop1,X),Xa)) <-> pp(scratc573321705nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,X),Xa))))) # label(fact_def__d__29__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 20 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1431138523n_some,aa_TPT43085870d_bool(scratc1193483343ffprop(Xa),X))))) # label(fact_def__iii) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 21 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1431138523n_some,aa_TPT43085870d_bool(scratc1193483343ffprop(X),Xa))))) # label(fact_def__d__29__ii) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 22 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1193483343ffprop(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,X),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Xa),Xb))))) # label(fact_def__diffprop) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 23 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1395891915_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc564469873nd_nis,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(X),Xb))))) # label(fact_def__d__28__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 24 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc807529740_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc564469873nd_nis,Xa),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(X),Xa))))) # label(fact_def__d__27__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 25 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc219167565_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Xa),X))))) # label(fact_def__d__26__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 26 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1778289038_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(X),Xa)),Xb)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(X),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Xa),Xb)))))) # label(fact_def__d__25__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 27 (all X scratc1041020515d_n_pl(X) = aa_TPT1424761345TP_ind(scratc1712323926bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1184746689d_plus,X))) # label(fact_def__n__pl) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 28 (all X aa_TPTP_ind_TPTP_ind(scratc1184746689d_plus,X) = scratc523490328nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc380696694d_d_Pi,scratc563945082nd_nat),aTP_Lamm_ac),aa_TPT43085870d_bool(scratc1189926864_prop2,X))) # label(fact_def__plus) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 29 (all X aa_TPTP_ind_TPTP_ind(scratc288866056d_24_g,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2023208232_Sigma,scratc563945082nd_nat),aTP_Lamm_ad(X))) # label(fact_def__d__24__g) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 30 (all X (pp(aa_TPTP_ind_bool(scratc1103620714_prop4,X)) <-> pp(aa_fun171081125l_bool(scratc687313881l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc380696694d_d_Pi,scratc563945082nd_nat),aTP_Lamm_ac)),aa_TPT43085870d_bool(scratc1189926864_prop2,X))))) # label(fact_def__prop4) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 31 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1103620713_prop3(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1712323926bnd_ap,X),Xb)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1712323926bnd_ap,Xa),Xb))))) # label(fact_def__prop3) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 32 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1189926864_prop2,X),Xa)) <-> pp(scratc375860794_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1712323926bnd_ap,Xa),scratc1662213130nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,X)),aa_TPTP_ind_bool(scratc1189926863_prop1,Xa))))) # label(fact_def__d__24__prop2) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 33 (all X (pp(aa_TPTP_ind_bool(scratc1189926863_prop1,X)) <-> pp(aa_fun171081125l_bool(scratc1948318266_n_all,aa_TPT43085870d_bool(aTP_Lamm_ae,X))))) # label(fact_def__d__24__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 34 (all X (pp(aa_TPTP_ind_bool(scratc601564688_prop1,X)) <-> pp(aa_bool_bool(scratc909309992d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,X),scratc1662213130nd_n_1)),aa_fun171081125l_bool(scratc1431138523n_some,aa_TPT43085870d_bool(aTP_Lamm_af,X)))))) # label(fact_def__d__23__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 35 (all X (pp(aa_TPTP_ind_bool(scratc13202513_prop1,X)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc564469873nd_nis,aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,X)),X)))) # label(fact_def__d__22__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 36 (all X (pp(aa_TPTP_ind_bool(scratc1118343849_cond2,X)) <-> pp(aa_fun171081125l_bool(scratc1948318266_n_all,aa_TPT43085870d_bool(aTP_Lamm_ag,X))))) # label(fact_def__cond2) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 37 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc564469873nd_nis,X),Xa)) <-> pp(scratc483325974_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,X),Xa))))) # label(fact_def__nis) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 38 (all X all Xa all Xb all Xc all Xd scratc1790703566indeq2(X,Xa,Xb,Xc,Xd) = aa_TPT1424761345TP_ind(scratc650142052_indeq(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1102507468d_11_i(X,Xa,Xb),Xc),Xd))) # label(fact_def__indeq2) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 39 (all X all Xa all Xb scratc1102507468d_11_i(X,Xa,Xb) = scratc650142052_indeq(X,Xa,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc380696694d_d_Pi,X),aTP_Lamm_ai(Xb)))) # label(fact_def__d__11__i) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 40 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2007193717fixfu2(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_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].
% 1.08/1.42 41 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc650142052_indeq(X,Xa,Xb),Xc),Xd) = scratc523490328nd_ind(Xb,aa_TPT43085870d_bool(scratc1103620712_prop2(X,Xa,Xb,Xc),Xd))) # label(fact_def__indeq) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 42 (all X all Xa all Xb all Xc all Xd all Xe (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1103620712_prop2(X,Xa,Xb,Xc),Xd),Xe)) <-> pp(aa_fun171081125l_bool(scratc687313881l_some(X),aa_TPT43085870d_bool(scratc1737249490_prop1(X,Xa,Xb,Xc,Xd),Xe))))) # label(fact_def__prop2) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 43 (all X all Xa all Xb all Xc all Xd all Xe all Xf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1737249490_prop1(X,Xa,Xb,Xc,Xd),Xe),Xf)) <-> pp(scratc375860794_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1245987018d_esti(X),Xf),aa_TPTP_ind_TPTP_ind(scratc398457905_ecect(X,Xa),Xd)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1521900968d_e_is(Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1712323926bnd_ap,Xc),Xf)),Xe))))) # label(fact_def__d__10__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 44 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2083743485_fixfu(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_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].
% 1.08/1.42 45 (all X all Xa scratc398457905_ecect(X,Xa) = scratc1521900963d_e_in(aa_TPTP_ind_TPTP_ind(scratc974713278_power,X),scratc228830354d_anec(X,Xa))) # label(fact_def__ecect) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 46 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc256534718ectelt(X,Xa),Xb) = aa_TPTP_ind_TPTP_ind(scratc371736595ectset(X,Xa),aa_TPTP_ind_TPTP_ind(scratc399048296_ecelt(X,Xa),Xb))) # label(fact_def__ectelt) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 47 (all X all Xa scratc371736595ectset(X,Xa) = scratc573518567nd_out(aa_TPTP_ind_TPTP_ind(scratc974713278_power,X),scratc228830354d_anec(X,Xa))) # label(fact_def__ectset) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 48 (all X all Xa scratc489722735nd_ect(X,Xa) = aa_fun1431113780TP_ind(scratc259609345_d_Sep(aa_TPTP_ind_TPTP_ind(scratc974713278_power,X)),scratc228830354d_anec(X,Xa))) # label(fact_def__ect) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 49 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc228830354d_anec(X,Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc687313881l_some(X),aa_TPT43085870d_bool(scratc489722731nd_ecp(X,Xa),Xb))))) # label(fact_def__anec) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 50 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc489722731nd_ecp(X,Xa),Xb),Xc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1521900968d_e_is(aa_TPTP_ind_TPTP_ind(scratc974713278_power,X)),Xb),aa_TPTP_ind_TPTP_ind(scratc399048296_ecelt(X,Xa),Xc))))) # label(fact_def__ecp) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 51 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc399048296_ecelt(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc259609345_d_Sep(X),aa_TPT43085870d_bool(Xa,Xb))) # label(fact_def__ecelt) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 52 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc477853941unmore(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc259609345_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].
% 1.08/1.42 53 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc798374484etprop(X,Xa),Xb),Xc)) <-> pp(scratc375860794_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1245987018d_esti(X),Xc),Xa),scratc483325974_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1245987018d_esti(X),Xc),Xb)))))) # label(fact_def__nissetprop) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 54 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1604006084t_disj(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc457267098nd_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].
% 1.08/1.42 55 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc30945813d_incl(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc457267098nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_at(X),Xa),Xb))))) # label(fact_def__incl) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 56 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc197181383nempty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc687313881l_some(X),aa_TPT43085870d_bool(aTP_Lamm_au(X),Xa))))) # label(fact_def__nonempty) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 57 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1853870694_empty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),scratc564863462nd_non(X,aa_TPT43085870d_bool(aTP_Lamm_au(X),Xa)))))) # label(fact_def__empty) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 58 (all X scratc1245987018d_esti(X) = scratc1712848716bnd_in) # label(fact_def__esti) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 59 (all X all Xa (scratc1303588777d_r_ec(X,Xa) <-> (pp(X) -> pp(scratc483325974_d_not(Xa))))) # label(fact_def__r__ec) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 60 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc71485647hangef(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2023208232_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].
% 1.08/1.42 61 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc239763392wissel(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2023208232_Sigma,X),scratc737744171sel_wb(X,Xa,Xb))) # label(fact_def__wissel) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 62 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc737744171sel_wb(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc523883923nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1521900968d_e_is(X),Xc),Xb),X,Xa),aa_TPTP_ind_TPTP_ind(scratc737744170sel_wa(X,Xa,Xb),Xc))) # label(fact_def__wissel__wb) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 63 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc737744170sel_wa(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc523883923nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1521900968d_e_is(X),Xc),Xa),X,Xb),Xc)) # label(fact_def__wissel__wa) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 64 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc523883923nd_ite(X,Xa,Xb),Xc) = scratc523490328nd_ind(Xa,aa_TPT43085870d_bool(scratc1103620711_prop1(X,Xa,Xb),Xc))) # label(fact_def__ite) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 65 (all X all Xa all Xb all Xc all Xd (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1103620711_prop1(X,Xa,Xb),Xc),Xd)) <-> pp(scratc375860794_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc523424741nd_imp,X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1521900968d_e_is(Xa),Xd),Xb)),aa_bool_bool(aa_boo1142376798l_bool(scratc523424741nd_imp,scratc483325974_d_not(X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1521900968d_e_is(Xa),Xd),Xc)))))) # label(fact_def__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 66 (all X all Xa scratc998979323second(X,Xa) = scratc1103227117_proj1) # label(fact_def__second) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 67 (all X all Xa scratc2035027241_first(X,Xa) = scratc1103227116_proj0) # label(fact_def__first) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 68 (all X all Xa scratc1696781207d_pair(X,Xa) = scratc1093082945d_pair) # label(fact_def__d__pair) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 69 (all X all Xa scratc573518567nd_out(X,Xa) = scratc1402825169d_soft(aa_fun1431113780TP_ind(scratc259609345_d_Sep(X),Xa),X,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2023208232_Sigma,aa_fun1431113780TP_ind(scratc259609345_d_Sep(X),Xa)),scratc1521900963d_e_in(X,Xa)))) # label(fact_def__out) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 70 (all X all Xa all Xb (gg_TPTP_ind(Xb) -> aa_TPTP_ind_TPTP_ind(scratc1521900963d_e_in(X,Xa),Xb) = Xb)) # label(fact_def__e__in) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 71 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc2128509706_inj_h(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2023208232_Sigma,X),aa_TPT1424761345TP_ind(aTP_Lamm_aw(Xc),Xd))) # label(fact_def__inj__h) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 72 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc32192188d_invf(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2023208232_Sigma,Xa),scratc1402825169d_soft(X,Xa,Xb))) # label(fact_def__invf) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 73 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc559761278ective(X),Xa),Xb)) <-> pp(scratc375860794_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc376042048ective(X),Xa),Xb),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc334119779ective(X),Xa),Xb))))) # label(fact_def__bijective) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 74 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc334119779ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc457267098nd_all(Xa),aa_TPT43085870d_bool(scratc1992385172_image(X,Xa),Xb))))) # label(fact_def__surjective) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 75 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc57526697nverse(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2023208232_Sigma,Xa),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ax(X),Xa),Xb))) # label(fact_def__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 76 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1402825169d_soft(X,Xa,Xb),Xc) = scratc523490328nd_ind(X,aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(Xa),Xb),Xc))) # label(fact_def__soft) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 77 (all X all Xa scratc35928719d_tofs(X,Xa) = scratc1712323926bnd_ap) # label(fact_def__tofs) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 78 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1992385172_image(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc687313881l_some(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(Xa),Xb),Xc))))) # label(fact_def__image) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 79 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc376042048ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc457267098nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ba(X),Xa),Xb))))) # label(fact_def__injective) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 80 (all X all Xa scratc523490328nd_ind(X,Xa) = scratc490575521nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bb(X),Xa))) # label(fact_def__ind) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 81 (all X all Xa (pp(aa_fun171081125l_bool(scratc573059359nd_one(X),Xa)) <-> pp(scratc375860794_d_and(scratc1581925715_amone(X,Xa),aa_fun171081125l_bool(scratc687313881l_some(X),Xa))))) # label(fact_def__one) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 82 (all X all Xa (pp(scratc1581925715_amone(X,Xa)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_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].
% 1.08/1.42 83 (all X scratc1521900968d_e_is(X) = fequal_TPTP_ind) # label(fact_def__e__is) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 84 (all X all Xa all Xb (scratc2028072235_orec3(X,Xa,Xb) <-> pp(scratc375860794_d_and(scratc573321705nd_or3(X,Xa,Xb),scratc489722670nd_ec3(X,Xa,Xb))))) # label(fact_def__orec3) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 85 (all X all Xa all Xb (pp(scratc489722670nd_ec3(X,Xa,Xb)) <-> scratc228764707d_and3(scratc908653987d_l_ec(X,Xa),scratc908653987d_l_ec(Xa,Xb),scratc908653987d_l_ec(Xb,X)))) # label(fact_def__ec3) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 86 (all X all Xa all Xb (scratc228764707d_and3(X,Xa,Xb) <-> pp(scratc375860794_d_and(X,scratc375860794_d_and(Xa,Xb))))) # label(fact_def__and3) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 87 (all X all Xa all Xb (pp(scratc573321705nd_or3(X,Xa,Xb)) <-> pp(aa_bool_bool(scratc909309992d_l_or(X),aa_bool_bool(scratc909309992d_l_or(Xa),Xb))))) # label(fact_def__or3) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 88 (all X all Xa (pp(aa_fun171081125l_bool(scratc687313881l_some(X),Xa)) <-> pp(scratc483325974_d_not(aa_fun171081125l_bool(scratc1576653073all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),scratc564863462nd_non(X,Xa)))))) # label(fact_def__l__some) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 89 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc564863462nd_non(X,Xa),Xb)) <-> pp(scratc483325974_d_not(aa_TPTP_ind_bool(Xa,Xb))))) # label(fact_def__non) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 90 (all X scratc457267098nd_all(X) = scratc1576653073all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X))) # label(fact_def__all) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 91 (all X all Xa (scratc1270002244_l_iff(X,Xa) <-> pp(scratc375860794_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc523424741nd_imp,X),Xa),aa_bool_bool(aa_boo1142376798l_bool(scratc523424741nd_imp,Xa),X))))) # label(fact_def__l__iff) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 92 (all X all Xa (scratc452678920d_orec(X,Xa) <-> pp(scratc375860794_d_and(aa_bool_bool(scratc909309992d_l_or(X),Xa),scratc908653987d_l_ec(X,Xa))))) # label(fact_def__orec) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 93 (all X scratc909309992d_l_or(X) = aa_boo1142376798l_bool(scratc523424741nd_imp,scratc483325974_d_not(X))) # label(fact_def__l__or) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 94 (all X all Xa (pp(scratc375860794_d_and(X,Xa)) <-> pp(scratc483325974_d_not(scratc908653987d_l_ec(X,Xa))))) # label(fact_def__d__and) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 95 (all X all Xa (pp(scratc908653987d_l_ec(X,Xa)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc523424741nd_imp,X),scratc483325974_d_not(Xa))))) # label(fact_def__l__ec) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 96 scratc922609344bvious <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc523424741nd_imp,fFalse),fFalse)) # label(fact_def__obvious) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 97 (all X (scratc638561015nd_wel(X) <-> pp(scratc483325974_d_not(scratc483325974_d_not(X))))) # label(fact_def__wel) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 98 (all X (pp(scratc483325974_d_not(X)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc523424741nd_imp,X),fFalse)))) # label(fact_def__d__not) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 99 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc380696694d_d_Pi,X),Xa) = aa_fun1431113780TP_ind(scratc259609345_d_Sep(aa_TPTP_ind_TPTP_ind(scratc974713278_power,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2023208232_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].
% 1.08/1.42 100 (all X (gg_TPTP_ind(X) -> (pp(aa_TPTP_ind_bool(scratc516028975pair_p,X)) <-> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1093082945d_pair,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1712323926bnd_ap,X),scratc2059070044ptyset)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1712323926bnd_ap,X),aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,scratc2059070044ptyset))) = X))) # label(fact_def__pair__p) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 101 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1712323926bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc1361835058eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bg,Xa)),scratc1103227117_proj1)) # label(fact_def__ap) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 102 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc293202098etprod(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2023208232_Sigma,X),aTP_Lamm_ai(Xa))) # label(fact_def__setprod) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 103 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2023208232_Sigma,X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc277026948munion,X),aTP_Lamm_bh(Xa))) # label(fact_def__d__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 104 (all X aa_TPTP_ind_TPTP_ind(scratc1103227117_proj1,X) = aa_fun277296641TP_ind(scratc1361835058eplSep(X,aTP_Lamm_bi),scratc276722740_d_Unj)) # label(fact_def__proj1) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 105 (all X aa_TPTP_ind_TPTP_ind(scratc1103227116_proj0,X) = aa_fun277296641TP_ind(scratc1361835058eplSep(X,aTP_Lamm_bj),scratc276722740_d_Unj)) # label(fact_def__proj0) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 106 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1093082945d_pair,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1270884047nunion(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc540278902d_repl,X),scratc1426116616d_Inj0)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc540278902d_repl,Xa),scratc1426116617d_Inj1))) # label(fact_def__pair) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 107 (all X aa_TPTP_ind_TPTP_ind(scratc1426116616d_Inj0,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc540278902d_repl,X),scratc1426116617d_Inj1)) # label(fact_def__d__Inj0) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 108 (all X (pp(aa_TPTP_ind_bool(scratc1275049398_nat_p,X)) <-> (all X1 (pp(aa_TPTP_ind_bool(X1,scratc2059070044ptyset)) -> ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(X1,X2)) -> pp(aa_TPTP_ind_bool(X1,aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,X2)))))) -> pp(aa_TPTP_ind_bool(X1,X))))))) # label(fact_def__nat__p) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 109 (all X aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1270884047nunion(X),aa_TPTP_ind_TPTP_ind(scratc601008940d_Sing,X))) # label(fact_def__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 110 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1089598638In_rec(X),Xa) = scratc490575521nd_eps(aa_TPT43085870d_bool(scratc294504025_rec_G(X),Xa))) # label(fact_def__d__In__rec) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 111 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc294504025_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(scratc1712848716bnd_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].
% 1.08/1.42 112 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1187169589tminus(X),Xa) = aa_fun1431113780TP_ind(scratc259609345_d_Sep(X),aa_TPT43085870d_bool(aTP_Lamm_bm,Xa))) # label(fact_def__setminus) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 113 (all X all Xa scratc1361835058eplSep(X,Xa) = aa_TPT494704832TP_ind(scratc540278902d_repl,aa_fun1431113780TP_ind(scratc259609345_d_Sep(X),Xa))) # label(fact_def__d__ReplSep) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 114 (all X all Xa aa_fun1431113780TP_ind(scratc259609345_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1712848708bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1712848716bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc540278902d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bn(X),Xa))),scratc2059070044ptyset)) # label(fact_def__d__Sep) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 115 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc277026948munion,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1481975144_union,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc540278902d_repl,X),Xa))) # label(fact_def__famunion) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 116 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1270884047nunion(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1481975144_union,aa_TPTP_ind_TPTP_ind(scratc1917694610_UPair(X),Xa))) # label(fact_def__binunion) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 117 (all X aa_TPTP_ind_TPTP_ind(scratc601008940d_Sing,X) = aa_TPTP_ind_TPTP_ind(scratc1917694610_UPair(X),X)) # label(fact_def__d__Sing) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 118 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1917694610_UPair(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc540278902d_repl,aa_TPTP_ind_TPTP_ind(scratc974713278_power,aa_TPTP_ind_TPTP_ind(scratc974713278_power,scratc2059070044ptyset))),aa_TPT1424761345TP_ind(aTP_Lamm_bo(X),Xa))) # label(fact_def__d__UPair) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 119 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc562370700nd_nIn,X),Xa)) <-> -pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X),Xa)))) # label(fact_def__nIn) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 120 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1712848708bnd_if(X,Xa),Xb) = scratc490575521nd_eps(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bp(X),Xa),Xb))) # label(fact_def__if) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 121 (all X (pp(aa_TPTP_ind_bool(scratc593027925closed,X)) <-> pp(aa_TPTP_ind_bool(scratc446102782closed,X)) & pp(aa_TPTP_ind_bool(scratc610835796closed,X)) & pp(aa_TPTP_ind_bool(scratc1924431736closed,X)))) # label(fact_def__d__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 122 (all X (pp(aa_TPTP_ind_bool(scratc1924431736closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X1),X)) -> (all X2 ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X3),X1)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,aa_TPTP_ind_TPTP_ind(X2,X3)),X))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc540278902d_repl,X1),X2)),X))))))))) # label(fact_def__d__Repl__closed) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 123 (all X (pp(aa_TPTP_ind_bool(scratc610835796closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,aa_TPTP_ind_TPTP_ind(scratc974713278_power,X1)),X))))))) # label(fact_def__d__Power__closed) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 124 (all X (pp(aa_TPTP_ind_bool(scratc446102782closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,aa_TPTP_ind_TPTP_ind(scratc1481975144_union,X1)),X))))))) # label(fact_def__d__Union__closed) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 125 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc699359822d_Subq,X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X2),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X2),Xa))))))) # label(fact_def__d__Subq) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 126 (all X all Xa (pp(aa_fun171081125l_bool(scratc1576653073all_of(X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (scratc1388405192_is_of(X2,X) -> pp(aa_TPTP_ind_bool(Xa,X2))))))) # label(fact_def__all__of) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 127 (all X all Xa (scratc1388405192_is_of(X,Xa) <-> pp(aa_TPTP_ind_bool(Xa,X)))) # label(fact_def__is__of) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 128 (all X0 pp(aa_fun171081125l_bool(scratc1576653073all_of(aa_TPT43085870d_bool(aTP_Lamm_jw,X0)),aa_TPT43085870d_bool(aTP_Lamm_jy,X0)))) # label(fact_isseti) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 129 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1576653073all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_jz(X0),X12)))) # label(fact_estie) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 130 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1576653073all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_ka(X0),X12)))) # label(fact_estii) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 131 (all X0 all X12 scratc1388405192_is_of(aa_fun1431113780TP_ind(scratc259609345_d_Sep(X0),X12),aa_TPT43085870d_bool(aTP_Lamm_jw,X0))) # label(fact_setof__p) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 132 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1576653073all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_kc(X0),X12)))) # label(fact_secondis1) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 133 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1576653073all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_ke(X0),X12)))) # label(fact_firstis1) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 134 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1576653073all_of(aa_TPT43085870d_bool(aTP_Lamm_kf(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_kg(X0),X12)))) # label(fact_pairis1) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 135 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1576653073all_of(aa_TPT43085870d_bool(aTP_Lamm_kf(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_kh(X0),X12)))) # label(fact_second__p) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 136 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1576653073all_of(aa_TPT43085870d_bool(aTP_Lamm_kf(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_ki(X0),X12)))) # label(fact_first__p) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 137 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1576653073all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_kk(X0),X12)))) # label(fact_e__pair__p) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 138 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1576653073all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_kl(X0),X12)))) # label(fact_otax2) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 139 (all X0 all X12 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc376042048ective(aa_fun1431113780TP_ind(scratc259609345_d_Sep(X0),X12)),X0),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2023208232_Sigma,aa_fun1431113780TP_ind(scratc259609345_d_Sep(X0),X12)),scratc1521900963d_e_in(X0,X12))))) # label(fact_otax1) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 140 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1576653073all_of(aa_fun1584354236d_bool(aTP_Lamm_km(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_kn(X0),X12)))) # label(fact_e__inp) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 141 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1576653073all_of(aa_fun1584354236d_bool(aTP_Lamm_km(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_ko(X0),X12)))) # label(fact_e__in__p) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 142 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1576653073all_of(aa_TPT43085870d_bool(aTP_Lamm_kp(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_ks(X0),X12)))) # label(fact_e__fisi) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 143 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc573059359nd_one(X0),X12)) -> pp(aa_TPTP_ind_bool(X12,scratc523490328nd_ind(X0,X12))))) # label(fact_oneax) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 144 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc573059359nd_one(X0),X12)) -> scratc1388405192_is_of(scratc523490328nd_ind(X0,X12),aa_TPT43085870d_bool(aTP_Lamm_aj,X0)))) # label(fact_ind__p) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.42 145 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1576653073all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_ku(X0),X12)))) # label(fact_e__isp) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 146 (all X0 pp(aa_fun171081125l_bool(scratc1576653073all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_kv,X0)))) # label(fact_refis) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 147 (all X0 (scratc638561015nd_wel(X0) -> pp(X0))) # label(fact_l__et) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 148 (all X0 all X12 all X22 all X32 (pp(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1712848708bnd_if(X0,X22),X32))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X12),X22))))) # label(fact_k__If__In__then__E) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 149 (all X0 all X12 all X22 ((pp(X0) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X12),X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,aa_TPTP_ind_TPTP_ind(scratc1712848708bnd_if(X0,X12),scratc2059070044ptyset)),aa_TPTP_ind_TPTP_ind(scratc1712848708bnd_if(X0,X22),aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,scratc2059070044ptyset)))))) # label(fact_k__If__In__01) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 150 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X33),X0)) -> aa_TPTP_ind_TPTP_ind(X12,X33) = aa_TPTP_ind_TPTP_ind(X22,X33)))) -> aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2023208232_Sigma,X0),X12) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2023208232_Sigma,X0),X22))) # label(fact_xi__ext) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 151 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc380696694d_d_Pi,X0),X12))) -> (all X32 (gg_TPTP_ind(X32) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X32),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc380696694d_d_Pi,X0),X12))) -> ((all X42 (gg_TPTP_ind(X42) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X42),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1712323926bnd_ap,X22),X42) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1712323926bnd_ap,X32),X42)))) -> X22 = X32))))))) # label(fact_k__Pi__ext) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 152 (all X0 all X12 all X22 all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc380696694d_d_Pi,X0),X12))) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X32),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1712323926bnd_ap,X22),X32)),aa_TPTP_ind_TPTP_ind(X12,X32)))))) # label(fact_ap__Pi) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 153 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X33),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,aa_TPTP_ind_TPTP_ind(X22,X33)),aa_TPTP_ind_TPTP_ind(X12,X33)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2023208232_Sigma,X0),X22)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc380696694d_d_Pi,X0),X12))))) # label(fact_lam__Pi) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 154 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X22),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1712323926bnd_ap,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2023208232_Sigma,X0),X12)),X22) = aa_TPTP_ind_TPTP_ind(X12,X22))) # label(fact_beta) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 155 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2023208232_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,aa_TPTP_ind_TPTP_ind(scratc1103227117_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1103227116_proj0,X22)))))) # label(fact_proj1__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 156 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2023208232_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,aa_TPTP_ind_TPTP_ind(scratc1103227116_proj0,X22)),X0)))) # label(fact_proj0__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 157 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2023208232_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1093082945d_pair,aa_TPTP_ind_TPTP_ind(scratc1103227116_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1103227117_proj1,X22)) = X22))) # label(fact_proj__Sigma__eta) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 158 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2023208232_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1093082945d_pair,aa_TPTP_ind_TPTP_ind(scratc1103227116_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1103227117_proj1,X22)) = X22 & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,aa_TPTP_ind_TPTP_ind(scratc1103227116_proj0,X22)),X0)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,aa_TPTP_ind_TPTP_ind(scratc1103227117_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1103227116_proj0,X22))))))) # label(fact_k__Sigma__eta__proj0__proj1) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 159 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X22),X0)) -> (all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X32),aa_TPTP_ind_TPTP_ind(X12,X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1093082945d_pair,X22),X32)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2023208232_Sigma,X0),X12))))))) # label(fact_pair__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 160 (all X0 all X12 (gg_TPTP_ind(X12) -> aa_TPTP_ind_TPTP_ind(scratc1103227117_proj1,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1093082945d_pair,X0),X12)) = X12)) # label(fact_proj1__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 161 (all X0 all X12 (gg_TPTP_ind(X0) -> aa_TPTP_ind_TPTP_ind(scratc1103227116_proj0,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1093082945d_pair,X0),X12)) = X0)) # label(fact_proj0__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 162 (all X0 (pp(aa_TPTP_ind_bool(scratc1275049398_nat_p,X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X0),scratc272882330_omega)))) # label(fact_nat__p__omega) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 163 (all X0 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X0),scratc272882330_omega)) -> pp(aa_TPTP_ind_bool(scratc1275049398_nat_p,X0)))) # label(fact_omega__nat__p) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 164 (all X0 (gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(scratc1275049398_nat_p,X0)) -> X0 = scratc2059070044ptyset | (exists X13 (gg_TPTP_ind(X13) & pp(aa_TPTP_ind_bool(scratc1275049398_nat_p,X13)) & X0 = aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,X13)))))) # label(fact_nat__inv) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 165 (all X0 (pp(aa_TPTP_ind_bool(X0,scratc2059070044ptyset)) -> ((all X13 (gg_TPTP_ind(X13) -> (pp(aa_TPTP_ind_bool(scratc1275049398_nat_p,X13)) -> (pp(aa_TPTP_ind_bool(X0,X13)) -> pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,X13))))))) -> (all X12 (pp(aa_TPTP_ind_bool(scratc1275049398_nat_p,X12)) -> pp(aa_TPTP_ind_bool(X0,X12))))))) # label(fact_nat__ind) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 166 (all X0 (pp(aa_TPTP_ind_bool(scratc1275049398_nat_p,X0)) -> pp(aa_TPTP_ind_bool(scratc1275049398_nat_p,aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,X0))))) # label(fact_nat__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 167 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,X0) = aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,X12) -> X0 = X12))) # label(fact_ordsucc__inj) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 168 (all X0 aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,X0) != scratc2059070044ptyset) # label(fact_neq__ordsucc__0) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 169 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X22),aa_fun1431113780TP_ind(scratc259609345_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(X12,X22)))) # label(fact_k__SepE2) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 170 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X22),aa_fun1431113780TP_ind(scratc259609345_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X22),X0)))) # label(fact_k__SepE1) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 171 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X22),X0)) -> (pp(aa_TPTP_ind_bool(X12,X22)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X22),aa_fun1431113780TP_ind(scratc259609345_d_Sep(X0),X12)))))) # label(fact_k__SepI) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 172 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc974713278_power,X0)))) # label(fact_k__Self__In__Power) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 173 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc699359822d_Subq,X12),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc974713278_power,X0))))) # label(fact_k__PowerI) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 174 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc974713278_power,X0))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc699359822d_Subq,X12),X0)))) # label(fact_k__PowerE) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 175 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> aa_TPTP_ind_TPTP_ind(scratc1712848708bnd_if(X0,X12),X22) = X12 | aa_TPTP_ind_TPTP_ind(scratc1712848708bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__or) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 176 (all X0 all X12 all X22 (gg_TPTP_ind(X12) -> (pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc1712848708bnd_if(X0,X12),X22) = X12))) # label(fact_if__i__1) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 177 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (-pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc1712848708bnd_if(X0,X12),X22) = X22))) # label(fact_if__i__0) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 178 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> pp(X0) & aa_TPTP_ind_TPTP_ind(scratc1712848708bnd_if(X0,X12),X22) = X12 | -pp(X0) & aa_TPTP_ind_TPTP_ind(scratc1712848708bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__correct) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 179 (all X0 pp(aa_TPTP_ind_bool(scratc593027925closed,aa_TPTP_ind_TPTP_ind(scratc1708106180univof,X0)))) # label(fact_k__UnivOf__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 180 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc1708106180univof,X0)))) # label(fact_k__UnivOf__In) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 181 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc540278902d_repl,X0),X12))) <-> (exists X3 (gg_TPTP_ind(X3) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X3),X0)) & X22 = aa_TPTP_ind_TPTP_ind(X12,X3)))))) # label(fact_k__ReplEq) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 182 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc974713278_power,X0))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc699359822d_Subq,X12),X0)))) # label(fact_k__PowerEq) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 183 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1481975144_union,X0))) <-> (exists X2 (gg_TPTP_ind(X2) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X12),X2)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X2),X0)))))) # label(fact_k__UnionEq) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 184 -(exists X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,X0),scratc2059070044ptyset))) # label(fact_k__EmptyAx) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 185 (all X0 ((all X13 (gg_TPTP_ind(X13) -> ((all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_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].
% 1.08/1.43 186 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc699359822d_Subq,X0),X12)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc699359822d_Subq,X12),X0)) -> X0 = X12)))) # label(fact_set__ext) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 187 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jl,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc564469873nd_nis,Uu),scratc1662213130nd_n_1)) -> pp(aa_fun171081125l_bool(scratc1431138523n_some,aa_TPT43085870d_bool(aTP_Lamm_af,Uu)))))) # label(fact_ATP_Olambda__1) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 188 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jk,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc564469873nd_nis,Uu),scratc1662213130nd_n_1)) -> pp(aa_fun171081125l_bool(scratc2064110527_n_one,aa_TPT43085870d_bool(aTP_Lamm_af,Uu)))))) # label(fact_ATP_Olambda__2) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 189 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jh,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),scratc1662213130nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,Uu))))) # label(fact_ATP_Olambda__3) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 190 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_je,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(scratc1662213130nd_n_1),Uu)),aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,Uu))))) # label(fact_ATP_Olambda__4) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 191 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jj,Uu)) <-> pp(aa_fun171081125l_bool(scratc573059359nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc380696694d_d_Pi,scratc563945082nd_nat),aTP_Lamm_ac)),aa_TPT43085870d_bool(aTP_Lamm_ji,Uu))))) # label(fact_ATP_Olambda__5) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 192 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jr,Uu)) <-> (pp(aa_TPTP_ind_bool(scratc1118343848_cond1,Uu)) -> (pp(aa_TPTP_ind_bool(scratc1118343849_cond2,Uu)) -> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jq,Uu))))))) # label(fact_ATP_Olambda__6) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 193 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jb,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),scratc1662213130nd_n_1))))) # label(fact_ATP_Olambda__7) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 194 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_iy,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(scratc1662213130nd_n_1),Uu))))) # label(fact_ATP_Olambda__8) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 195 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fy,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__9) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 196 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jm,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc564469873nd_nis,aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__10) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 197 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jv,Uu)) <-> scratc1388405192_is_of(aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,Uu),aTP_Lamm_a))) # label(fact_ATP_Olambda__11) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 198 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cd,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,Uu)),scratc1662213130nd_n_1)))) # label(fact_ATP_Olambda__12) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 199 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ju,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc564469873nd_nis,aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,Uu)),scratc1662213130nd_n_1)))) # label(fact_ATP_Olambda__13) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 200 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fx,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,Uu))))) # label(fact_ATP_Olambda__14) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 201 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jp,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,Uu),aa_TPTP_ind_TPTP_ind(scratc974713278_power,scratc563945082nd_nat))))) # label(fact_ATP_Olambda__15) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 202 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ce,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc313607302moreis,Uu),scratc1662213130nd_n_1)))) # label(fact_ATP_Olambda__16) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 203 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_a,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,Uu),scratc563945082nd_nat)))) # label(fact_ATP_Olambda__17) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 204 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jt,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_js,Uu))))) # label(fact_ATP_Olambda__18) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 205 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jo,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jn,Uu))))) # label(fact_ATP_Olambda__19) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 206 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jg,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jf,Uu))))) # label(fact_ATP_Olambda__20) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 207 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jd,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jc,Uu))))) # label(fact_ATP_Olambda__21) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 208 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ja,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_iz,Uu))))) # label(fact_ATP_Olambda__22) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 209 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ix,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_iw,Uu))))) # label(fact_ATP_Olambda__23) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 210 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_iv,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_iu,Uu))))) # label(fact_ATP_Olambda__24) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 211 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_is,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ir,Uu))))) # label(fact_ATP_Olambda__25) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 212 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_iq,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ip,Uu))))) # label(fact_ATP_Olambda__26) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 213 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_io,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_in,Uu))))) # label(fact_ATP_Olambda__27) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 214 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_il,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ik,Uu))))) # label(fact_ATP_Olambda__28) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 215 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ii,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ih,Uu))))) # label(fact_ATP_Olambda__29) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 216 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ig,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_if,Uu))))) # label(fact_ATP_Olambda__30) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 217 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ic,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ib,Uu))))) # label(fact_ATP_Olambda__31) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 218 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ia,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hz,Uu))))) # label(fact_ATP_Olambda__32) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 219 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hy,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hx,Uu))))) # label(fact_ATP_Olambda__33) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 220 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hw,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hv,Uu))))) # label(fact_ATP_Olambda__34) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 221 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hu,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ht,Uu))))) # label(fact_ATP_Olambda__35) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 222 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hs,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hr,Uu))))) # label(fact_ATP_Olambda__36) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 223 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hq,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hp,Uu))))) # label(fact_ATP_Olambda__37) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 224 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ho,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hn,Uu))))) # label(fact_ATP_Olambda__38) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 225 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hm,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hl,Uu))))) # label(fact_ATP_Olambda__39) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 226 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hk,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hj,Uu))))) # label(fact_ATP_Olambda__40) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 227 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hi,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hh,Uu))))) # label(fact_ATP_Olambda__41) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 228 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hg,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hf,Uu))))) # label(fact_ATP_Olambda__42) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 229 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_he,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hd,Uu))))) # label(fact_ATP_Olambda__43) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 230 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hc,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hb,Uu))))) # label(fact_ATP_Olambda__44) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 231 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ha,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gz,Uu))))) # label(fact_ATP_Olambda__45) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 232 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gy,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,Uu))))) # label(fact_ATP_Olambda__46) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 233 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gw,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gv,Uu))))) # label(fact_ATP_Olambda__47) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 234 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gu,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gt,Uu))))) # label(fact_ATP_Olambda__48) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 235 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gr,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gq,Uu))))) # label(fact_ATP_Olambda__49) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 236 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_go,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gn,Uu))))) # label(fact_ATP_Olambda__50) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 237 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gl,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gk,Uu))))) # label(fact_ATP_Olambda__51) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 238 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gi,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gh,Uu))))) # label(fact_ATP_Olambda__52) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 239 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gf,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ge,Uu))))) # label(fact_ATP_Olambda__53) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 240 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gc,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gb,Uu))))) # label(fact_ATP_Olambda__54) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 241 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ga,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fz,Uu))))) # label(fact_ATP_Olambda__55) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 242 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fw,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fv,Uu))))) # label(fact_ATP_Olambda__56) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 243 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ft,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fs,Uu))))) # label(fact_ATP_Olambda__57) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 244 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fq,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fp,Uu))))) # label(fact_ATP_Olambda__58) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 245 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fn,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fm,Uu))))) # label(fact_ATP_Olambda__59) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 246 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fk,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fj,Uu))))) # label(fact_ATP_Olambda__60) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 247 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fh,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fg,Uu))))) # label(fact_ATP_Olambda__61) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 248 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fe,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fd,Uu))))) # label(fact_ATP_Olambda__62) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 249 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fa,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ez,Uu))))) # label(fact_ATP_Olambda__63) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 250 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ew,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ev,Uu))))) # label(fact_ATP_Olambda__64) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 251 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_es,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_er,Uu))))) # label(fact_ATP_Olambda__65) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 252 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_eo,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_en,Uu))))) # label(fact_ATP_Olambda__66) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 253 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_el,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ek,Uu))))) # label(fact_ATP_Olambda__67) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 254 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ei,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eh,Uu))))) # label(fact_ATP_Olambda__68) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 255 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ef,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ee,Uu))))) # label(fact_ATP_Olambda__69) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 256 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ec,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eb,Uu))))) # label(fact_ATP_Olambda__70) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 257 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dz,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dy,Uu))))) # label(fact_ATP_Olambda__71) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 258 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dw,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dv,Uu))))) # label(fact_ATP_Olambda__72) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 259 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dt,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ds,Uu))))) # label(fact_ATP_Olambda__73) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 260 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dq,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dp,Uu))))) # label(fact_ATP_Olambda__74) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 261 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dn,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dm,Uu))))) # label(fact_ATP_Olambda__75) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 262 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dk,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dj,Uu))))) # label(fact_ATP_Olambda__76) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 263 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dg,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_df,Uu))))) # label(fact_ATP_Olambda__77) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 264 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dc,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_db,Uu))))) # label(fact_ATP_Olambda__78) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 265 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cy,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cx,Uu))))) # label(fact_ATP_Olambda__79) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 266 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cu,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ct,Uu))))) # label(fact_ATP_Olambda__80) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 267 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cq,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cp,Uu))))) # label(fact_ATP_Olambda__81) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 268 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cm,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cl,Uu))))) # label(fact_ATP_Olambda__82) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 269 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ci,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ch,Uu))))) # label(fact_ATP_Olambda__83) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 270 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cb,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ca,Uu))))) # label(fact_ATP_Olambda__84) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 271 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bz,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_by,Uu))))) # label(fact_ATP_Olambda__85) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 272 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bw,Uu))))) # label(fact_ATP_Olambda__86) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 273 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bv,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bu,Uu))))) # label(fact_ATP_Olambda__87) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 274 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bt,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bs,Uu))))) # label(fact_ATP_Olambda__88) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 275 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_br,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bq,Uu))))) # label(fact_ATP_Olambda__89) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 276 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ab,Uu)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,Uu))))) # label(fact_ATP_Olambda__90) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 277 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cc,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,scratc1662213130nd_n_1),aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,Uu))))) # label(fact_ATP_Olambda__91) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 278 (all Uu aa_TPT494704832TP_ind(aTP_Lamm_bk,Uu) = aa_TPT494704832TP_ind(scratc540278902d_repl,aa_TPTP_ind_TPTP_ind(scratc1187169589tminus(Uu),aa_TPTP_ind_TPTP_ind(scratc601008940d_Sing,scratc2059070044ptyset)))) # label(fact_ATP_Olambda__92) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 279 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_ah,Uu)) <-> Uu != scratc2059070044ptyset))) # label(fact_ATP_Olambda__93) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 280 (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(scratc1426116617d_Inj1,X2) = Uu))))) # label(fact_ATP_Olambda__94) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 281 (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(scratc1426116616d_Inj0,X2) = Uu))))) # label(fact_ATP_Olambda__95) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 282 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hx,Uu),Uua)) <-> scratc2028072235_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,Uu),Uua)))) # label(fact_ATP_Olambda__96) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 283 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hv,Uu),Uua)) <-> pp(scratc573321705nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__97) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 284 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ht,Uu),Uua)) <-> pp(scratc489722670nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__98) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 285 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_if,Uu),Uua)) <-> scratc2028072235_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1431138523n_some,aa_TPT43085870d_bool(aTP_Lamm_id(Uu),Uua)),aa_fun171081125l_bool(scratc1431138523n_some,aa_TPT43085870d_bool(aTP_Lamm_ie(Uu),Uua))))) # label(fact_ATP_Olambda__99) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 286 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ib,Uu),Uua)) <-> pp(scratc573321705nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1431138523n_some,aa_TPT43085870d_bool(scratc1193483343ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc1431138523n_some,aa_TPT43085870d_bool(scratc1193483343ffprop(Uua),Uu)))))) # label(fact_ATP_Olambda__100) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 287 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hz,Uu),Uua)) <-> pp(scratc489722670nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1431138523n_some,aa_TPT43085870d_bool(scratc1193483343ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc1431138523n_some,aa_TPT43085870d_bool(scratc1193483343ffprop(Uua),Uu)))))) # label(fact_ATP_Olambda__101) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 288 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kv,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1521900968d_e_is(Uu),Uua),Uua)))) # label(fact_ATP_Olambda__102) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 289 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ji,Uu),Uua)) <-> pp(scratc375860794_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1712323926bnd_ap,Uua),scratc1662213130nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,Uu)),aa_fun171081125l_bool(scratc1948318266_n_all,aa_TPT43085870d_bool(aTP_Lamm_ae,Uua)))))) # label(fact_ATP_Olambda__103) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 290 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uua),scratc1662213130nd_n_1)),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc313607302moreis,Uua),Uu))))) # label(fact_ATP_Olambda__104) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 291 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_js,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__105) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 292 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jc,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__106) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 293 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bs,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,Uua),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),scratc1662213130nd_n_1))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc179623690lessis,Uua),Uu))))) # label(fact_ATP_Olambda__107) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 294 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bq,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,Uua),aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,Uu))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc179623690lessis,Uua),Uu))))) # label(fact_ATP_Olambda__108) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 295 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jf,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__109) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 296 (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(scratc1040561329d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1712323926bnd_ap,Uu),aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1712323926bnd_ap,Uu),Uua)))))) # label(fact_ATP_Olambda__110) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 297 (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(scratc523162338nd_iii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc179623690lessis,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uua),scratc1662213130nd_n_1)),Uu))))) # label(fact_ATP_Olambda__111) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 298 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jn,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc564469873nd_nis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc564469873nd_nis,aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,Uua)))))) # label(fact_ATP_Olambda__112) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 299 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ag,Uu),Uua)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc523424741nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561324d_n_in,Uua),Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561324d_n_in,aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,Uua)),Uu))))) # label(fact_ATP_Olambda__113) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.43 300 (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(scratc523162338nd_iii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc179623690lessis,aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,Uua)),Uu))))) # label(fact_ATP_Olambda__114) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 301 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ca,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc313607302moreis,Uua),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),scratc1662213130nd_n_1)))))) # label(fact_ATP_Olambda__115) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 302 (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(scratc1331683044_29_ii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc313607302moreis,Uua),aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,Uu)))))) # label(fact_ATP_Olambda__116) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 303 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ir,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uua),Uu))))) # label(fact_ATP_Olambda__117) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 304 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hr,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,Uua),Uu))))) # label(fact_ATP_Olambda__118) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 305 (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(scratc313607302moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc179623690lessis,Uua),Uu))))) # label(fact_ATP_Olambda__119) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 306 (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(scratc179623690lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc313607302moreis,Uua),Uu))))) # label(fact_ATP_Olambda__120) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 307 (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(scratc523162338nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,Uua),Uu))))) # label(fact_ATP_Olambda__121) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 308 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hb,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,Uu),Uua)) -> pp(scratc483325974_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc179623690lessis,Uu),Uua)))))) # label(fact_ATP_Olambda__122) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 309 (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(scratc313607302moreis,Uu),Uua)) -> pp(scratc483325974_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,Uu),Uua)))))) # label(fact_ATP_Olambda__123) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 310 (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(scratc179623690lessis,Uu),Uua)) -> pp(scratc483325974_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,Uu),Uua)))))) # label(fact_ATP_Olambda__124) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 311 (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(scratc523162338nd_iii,Uu),Uua)) -> pp(scratc483325974_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc313607302moreis,Uu),Uua)))))) # label(fact_ATP_Olambda__125) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 312 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gb,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uua)),Uu)))) # label(fact_ATP_Olambda__126) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 313 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bh(Uu),Uua) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc540278902d_repl,aa_TPTP_ind_TPTP_ind(Uu,Uua)),aa_TPT1424761345TP_ind(scratc1093082945d_pair,Uua))) # label(fact_ATP_Olambda__127) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 314 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jy,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aa_TPT43085870d_bool(aTP_Lamm_jw,Uu)),aa_TPT43085870d_bool(aTP_Lamm_jx(Uu),Uua))))) # label(fact_ATP_Olambda__128) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 315 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iw,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,Uu)),Uua))))) # label(fact_ATP_Olambda__129) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 316 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iz,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,Uua)))))) # label(fact_ATP_Olambda__130) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 317 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hf,Uu),Uua)) <-> (pp(scratc483325974_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc179623690lessis,Uu),Uua))))) # label(fact_ATP_Olambda__131) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 318 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,Uu),Uua)) <-> (pp(scratc483325974_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc313607302moreis,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__132) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 319 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gv,Uu),Uua)) <-> (pp(scratc483325974_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc179623690lessis,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__133) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 320 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hd,Uu),Uua)) <-> (pp(scratc483325974_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc313607302moreis,Uu),Uua))))) # label(fact_ATP_Olambda__134) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 321 (all Uu all Uua aa_fun277296641TP_ind(aa_TPT494704832TP_ind(aTP_Lamm_bl,Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1270884047nunion(aa_TPTP_ind_TPTP_ind(scratc601008940d_Sing,scratc2059070044ptyset)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc540278902d_repl,Uu),Uua))) # label(fact_ATP_Olambda__135) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 322 (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(scratc564469873nd_nis,Uua),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__136) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 323 (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(scratc523162338nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__137) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 324 (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(scratc1040561329d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,Uua))))) # label(fact_ATP_Olambda__138) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 325 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jw,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,Uua),aa_TPTP_ind_TPTP_ind(scratc974713278_power,Uu))))) # label(fact_ATP_Olambda__139) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 326 (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(scratc1040561324d_n_in,Uua),Uu)))) # label(fact_ATP_Olambda__140) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 327 (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(scratc562370700nd_nIn,Uua),Uu)))) # label(fact_ATP_Olambda__141) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 328 (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(scratc1712848716bnd_in,Uua),Uu)))) # label(fact_ATP_Olambda__142) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 329 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iu,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_it(Uu),Uua))))) # label(fact_ATP_Olambda__143) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 330 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_in,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_im(Uu),Uua))))) # label(fact_ATP_Olambda__144) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 331 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ik,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ij(Uu),Uua))))) # label(fact_ATP_Olambda__145) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 332 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gt,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gs(Uu),Uua))))) # label(fact_ATP_Olambda__146) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 333 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gq,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gp(Uu),Uua))))) # label(fact_ATP_Olambda__147) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 334 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gn,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gm(Uu),Uua))))) # label(fact_ATP_Olambda__148) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 335 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gk,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gj(Uu),Uua))))) # label(fact_ATP_Olambda__149) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 336 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gh,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gg(Uu),Uua))))) # label(fact_ATP_Olambda__150) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 337 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ge,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gd(Uu),Uua))))) # label(fact_ATP_Olambda__151) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 338 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fv,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fu(Uu),Uua))))) # label(fact_ATP_Olambda__152) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 339 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fs,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fr(Uu),Uua))))) # label(fact_ATP_Olambda__153) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 340 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fp,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fo(Uu),Uua))))) # label(fact_ATP_Olambda__154) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 341 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fm,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fl(Uu),Uua))))) # label(fact_ATP_Olambda__155) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 342 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fj,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fi(Uu),Uua))))) # label(fact_ATP_Olambda__156) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 343 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fg,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ff(Uu),Uua))))) # label(fact_ATP_Olambda__157) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 344 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fd,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fc(Uu),Uua))))) # label(fact_ATP_Olambda__158) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 345 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ez,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ey(Uu),Uua))))) # label(fact_ATP_Olambda__159) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 346 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ev,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eu(Uu),Uua))))) # label(fact_ATP_Olambda__160) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 347 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_er,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eq(Uu),Uua))))) # label(fact_ATP_Olambda__161) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 348 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_en,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_em(Uu),Uua))))) # label(fact_ATP_Olambda__162) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 349 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ek,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ej(Uu),Uua))))) # label(fact_ATP_Olambda__163) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 350 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eh,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eg(Uu),Uua))))) # label(fact_ATP_Olambda__164) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 351 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ee,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ed(Uu),Uua))))) # label(fact_ATP_Olambda__165) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 352 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eb,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ea(Uu),Uua))))) # label(fact_ATP_Olambda__166) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 353 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dy,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dx(Uu),Uua))))) # label(fact_ATP_Olambda__167) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 354 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dv,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_du(Uu),Uua))))) # label(fact_ATP_Olambda__168) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 355 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ds,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dr(Uu),Uua))))) # label(fact_ATP_Olambda__169) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 356 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dp,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_do(Uu),Uua))))) # label(fact_ATP_Olambda__170) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 357 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dm,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dl(Uu),Uua))))) # label(fact_ATP_Olambda__171) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 358 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dj,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_di(Uu),Uua))))) # label(fact_ATP_Olambda__172) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 359 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_df,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_de(Uu),Uua))))) # label(fact_ATP_Olambda__173) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 360 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_db,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_da(Uu),Uua))))) # label(fact_ATP_Olambda__174) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 361 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cx,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cw(Uu),Uua))))) # label(fact_ATP_Olambda__175) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 362 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ct,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cs(Uu),Uua))))) # label(fact_ATP_Olambda__176) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 363 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cp,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_co(Uu),Uua))))) # label(fact_ATP_Olambda__177) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 364 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cl,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ck(Uu),Uua))))) # label(fact_ATP_Olambda__178) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 365 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ch,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cg(Uu),Uua))))) # label(fact_ATP_Olambda__179) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 366 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ih,Uu),Uua)) <-> pp(scratc1581925715_amone(scratc563945082nd_nat,aa_TPT43085870d_bool(aTP_Lamm_id(Uu),Uua))))) # label(fact_ATP_Olambda__180) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 367 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_ad(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc659279004rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1712323926bnd_ap,Uu),Uua))) # label(fact_ATP_Olambda__181) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 368 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_be(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1481975144_union,aa_TPTP_ind_TPTP_ind(Uu,Uua))) # label(fact_ATP_Olambda__182) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 369 (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(scratc1093082945d_pair,Uu),X3)))))) # label(fact_ATP_Olambda__183) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 370 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kg(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1521900968d_e_is(aa_TPTP_ind_TPTP_ind(scratc293202098etprod(Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1696781207d_pair(Uu,Uua),aa_TPTP_ind_TPTP_ind(scratc2035027241_first(Uu,Uua),Uub)),aa_TPTP_ind_TPTP_ind(scratc998979323second(Uu,Uua),Uub))),Uub)))) # label(fact_ATP_Olambda__184) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 371 (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(scratc1712848708bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,scratc2059070044ptyset),Uub),Uu),Uua)) # label(fact_ATP_Olambda__185) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 372 (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(scratc1712848708bnd_if(aa_TPTP_ind_bool(Uua,Uub),Uub),scratc490575521nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bb(Uu),Uua)))) # label(fact_ATP_Olambda__186) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 373 (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(scratc1245987018d_esti(Uu),Uub),Uua)))) # label(fact_ATP_Olambda__187) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 374 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_jz(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1245987018d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc259609345_d_Sep(Uu),Uua))) -> pp(aa_TPTP_ind_bool(Uua,Uub))))) # label(fact_ATP_Olambda__188) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 375 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jx(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc30945813d_incl(Uu),Uua),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc30945813d_incl(Uu),Uub),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1521900968d_e_is(aa_TPTP_ind_TPTP_ind(scratc974713278_power,Uu)),Uua),Uub)))))) # label(fact_ATP_Olambda__189) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 376 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kh(Uu),Uua),Uub)) <-> scratc1388405192_is_of(aa_TPTP_ind_TPTP_ind(scratc998979323second(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)))) # label(fact_ATP_Olambda__190) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 377 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ki(Uu),Uua),Uub)) <-> scratc1388405192_is_of(aa_TPTP_ind_TPTP_ind(scratc2035027241_first(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)))) # label(fact_ATP_Olambda__191) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 378 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ko(Uu),Uua),Uub)) <-> scratc1388405192_is_of(aa_TPTP_ind_TPTP_ind(scratc1521900963d_e_in(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)))) # label(fact_ATP_Olambda__192) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 379 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ks(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aa_TPT43085870d_bool(aTP_Lamm_kp(Uu),Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kr(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__193) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 380 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ea(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__194) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 381 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dr(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__195) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 382 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ij(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,Uua),Uub))))) # label(fact_ATP_Olambda__196) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 383 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dx(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__197) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 384 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_do(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__198) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 385 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_du(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__199) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 386 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dl(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__200) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 387 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_it(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__201) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 388 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fu(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__202) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 389 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fl(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__203) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 390 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gg(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc313607302moreis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,Uu),Uub)))))) # label(fact_ATP_Olambda__204) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 391 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_em(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc313607302moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc313607302moreis,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__205) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 392 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ej(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc313607302moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc313607302moreis,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__206) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 393 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gj(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc313607302moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,Uu),Uub)))))) # label(fact_ATP_Olambda__207) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 394 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eg(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc179623690lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc179623690lessis,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__208) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 395 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ed(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc179623690lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc179623690lessis,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__209) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 396 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gd(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc179623690lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc179623690lessis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc179623690lessis,Uu),Uub)))))) # label(fact_ATP_Olambda__210) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 397 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gp(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc179623690lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__211) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 398 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fr(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__212) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 399 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fi(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__213) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 400 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_im(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc564469873nd_nis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc564469873nd_nis,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uub)))))) # label(fact_ATP_Olambda__214) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 401 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fo(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__215) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 402 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ff(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__216) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 403 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gm(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc179623690lessis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__217) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 404 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gs(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__218) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 405 (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(scratc1712848716bnd_in,Uub),Uu)) & pp(aa_TPTP_ind_bool(Uua,Uub)))) # label(fact_ATP_Olambda__219) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 406 (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,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1992385172_image(aa_fun1431113780TP_ind(scratc259609345_d_Sep(Uu),Uua),Uu),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2023208232_Sigma,aa_fun1431113780TP_ind(scratc259609345_d_Sep(Uu),Uua)),scratc1521900963d_e_in(Uu,Uua))),Uub))))) # label(fact_ATP_Olambda__220) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 407 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ka(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1245987018d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc259609345_d_Sep(Uu),Uua)))))) # label(fact_ATP_Olambda__221) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 408 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ku(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_kt(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__222) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 409 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bd(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bc(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__223) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 410 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kk(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kj(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__224) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 411 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ke(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kd(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__225) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 412 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kc(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kb(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__226) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 413 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kp(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,Uub),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc380696694d_d_Pi,Uu),aTP_Lamm_ai(Uua)))))) # label(fact_ATP_Olambda__227) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 414 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_id(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uua),Uub))))) # label(fact_ATP_Olambda__228) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 415 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ie(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,Uua),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uub))))) # label(fact_ATP_Olambda__229) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 416 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kf(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,Uub),aa_TPTP_ind_TPTP_ind(scratc293202098etprod(Uu),Uua))))) # label(fact_ATP_Olambda__230) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 417 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_km(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,Uub),aa_fun1431113780TP_ind(scratc259609345_d_Sep(Uu),Uua))))) # label(fact_ATP_Olambda__231) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 418 (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(scratc1712323926bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1712323926bnd_ap,Uu),Uub))) # label(fact_ATP_Olambda__232) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 419 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fc(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fb(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__233) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 420 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ey(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ex(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__234) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 421 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eu(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_et(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__235) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 422 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eq(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ep(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__236) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 423 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_di(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dh(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__237) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 424 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_de(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dd(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__238) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 425 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_da(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cz(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__239) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 426 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cw(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cv(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__240) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 427 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cs(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cr(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__241) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 428 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_co(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cn(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__242) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 429 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ck(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cj(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__243) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 430 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cg(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1576653073all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cf(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__244) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 431 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_kn(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(Uua,aa_TPTP_ind_TPTP_ind(scratc1521900963d_e_in(Uu,Uua),Uub))))) # label(fact_ATP_Olambda__245) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 432 (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(scratc1712848716bnd_in,X3),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1712848716bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1712323926bnd_ap,Uub),X3)),aa_TPTP_ind_TPTP_ind(Uua,X3)))))))) # label(fact_ATP_Olambda__246) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 433 (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(scratc1712848708bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1992385172_image(Uu,Uua),Uub),Uuc),aa_TPTP_ind_TPTP_ind(scratc1402825169d_soft(Uu,Uua,Uub),Uuc)),scratc2059070044ptyset)) # label(fact_ATP_Olambda__247) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 434 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kd(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1521900968d_e_is(Uu),aa_TPTP_ind_TPTP_ind(scratc2035027241_first(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1696781207d_pair(Uu,Uua),Uub),Uuc))),Uub)))) # label(fact_ATP_Olambda__248) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 435 (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(scratc1521900968d_e_is(Uua),aa_TPTP_ind_TPTP_ind(scratc998979323second(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1696781207d_pair(Uu,Uua),Uub),Uuc))),Uuc)))) # label(fact_ATP_Olambda__249) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 436 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kq(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1521900968d_e_is(Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1712323926bnd_ap,Uua),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1712323926bnd_ap,Uub),Uuc))))) # label(fact_ATP_Olambda__250) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 437 (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(scratc1245987018d_esti(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1712323926bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__251) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 438 (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(scratc1521900968d_e_is(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1712323926bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__252) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 439 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kj(Uu),Uua),Uub),Uuc)) <-> scratc1388405192_is_of(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1696781207d_pair(Uu,Uua),Uub),Uuc),aa_TPT43085870d_bool(aTP_Lamm_kf(Uu),Uua)))) # label(fact_ATP_Olambda__253) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 440 (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(scratc908653987d_l_ec(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1245987018d_esti(Uu),Uuc),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1245987018d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__254) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 441 (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(scratc523424741nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1245987018d_esti(Uu),Uuc),Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1245987018d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__255) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 442 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kr(Uu),Uua),Uub),Uuc)) <-> (pp(aa_fun171081125l_bool(scratc1576653073all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kq(Uua),Uub),Uuc))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1521900968d_e_is(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc380696694d_d_Pi,Uu),aTP_Lamm_ai(Uua))),Uub),Uuc))))) # label(fact_ATP_Olambda__256) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 443 (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__257) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 444 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dh(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__258) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 445 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cv(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc313607302moreis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__259) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 446 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cz(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc313607302moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__260) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 447 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cj(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc313607302moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc313607302moreis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc313607302moreis,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__261) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 448 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cf(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc179623690lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc179623690lessis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc179623690lessis,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__262) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 449 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cr(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc179623690lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__263) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 450 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fb(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__264) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 451 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ex(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1331683044_29_ii,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uuc),Uua))))))) # label(fact_ATP_Olambda__265) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 452 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_et(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__266) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 453 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ep(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1040561329d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uuc),Uua))))))) # label(fact_ATP_Olambda__267) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 454 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cn(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc179623690lessis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__268) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 455 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dd(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc523162338nd_iii,aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1041020515d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__269) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 456 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_kt(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1521900968d_e_is(Uu),Uub),Uuc)) -> pp(aa_TPTP_ind_bool(Uua,Uuc)))))) # label(fact_ATP_Olambda__270) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 457 (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(scratc1521900968d_e_is(Uu),Uub),Uuc)))))) # label(fact_ATP_Olambda__271) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 458 (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(scratc457267098nd_all(Uu),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_az(Uu),Uua),Uub),Uuc))))) # label(fact_ATP_Olambda__272) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 459 (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(scratc687313881l_some(Uua),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aq(Uu),Uub),Uuc))))) # label(fact_ATP_Olambda__273) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 460 (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(scratc523424741nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1521900968d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1712323926bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1712323926bnd_ap,Uub),Uud))),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1521900968d_e_is(Uu),Uuc),Uud))))) # label(fact_ATP_Olambda__274) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 461 (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(scratc1521900968d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1712323926bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1712323926bnd_ap,Uub),Uud)))))) # label(fact_ATP_Olambda__275) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 462 (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(scratc1576653073all_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__276) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 463 (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(scratc1576653073all_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__277) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 464 (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(scratc1712323926bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1712323926bnd_ap,aa_TPTP_ind_TPTP_ind(scratc239763392wissel(Uu,Uub),Uuc)),Uud))) # label(fact_ATP_Olambda__278) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 465 (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(scratc1576653073all_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__279) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 466 (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(scratc1521900968d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1712323926bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1712323926bnd_ap,Uub),Uuc)),Uue)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1712323926bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1712323926bnd_ap,Uub),Uud)),Uuf))))))) # label(fact_ATP_Olambda__280) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 467 (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(scratc1576653073all_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__281) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 468 (all Uu all Uua (gg_TPTP_ind(Uu) -> aa_TPTP_ind_TPTP_ind(aTP_Lamm_ai(Uu),Uua) = Uu)) # label(fact_ATP_Olambda__282) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.44 469 (all Uu aa_TPTP_ind_TPTP_ind(aTP_Lamm_ac,Uu) = scratc563945082nd_nat) # label(fact_ATP_Olambda__283) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.47 470 (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].
% 1.08/1.47 471 (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].
% 1.08/1.47 472 (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].
% 1.08/1.47 473 (all P (gg_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.47 474 (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].
% 1.08/1.47 475 (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].
% 1.08/1.47 476 (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].
% 1.08/1.47 477 (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].
% 1.08/1.47 478 (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].
% 1.08/1.47 479 (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].
% 1.08/1.47 480 (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].
% 1.08/1.47 481 (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].
% 1.08/1.47 482 (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].
% 1.08/1.47
% 1.08/1.47 ============================== end of process non-clausal formulas ===
% 1.08/1.47
% 1.08/1.47 ============================== PROCESS INITIAL CLAUSES ===============
% 1.08/1.47
% 1.08/1.47 ============================== PREDICATE ELIMINATION =================
% 1.08/1.47 483 -gg_bool(A) | A = fTrue | A = fFalse # label(help_fFalse_1_1_T) # label(axiom). [clausify(473)].
% 1.08/1.47 484 gg_bool(undefined_bool(bool)) # label(gsy_c_HOL_Oundefined_001t__HOL__Obool) # label(axiom). [assumption].
% 1.08/1.47 485 gg_bool(scratc1581925715_amone(A,B)) # label(gsy_c_Scratch__tptp__translate__51767__4802_ONUM702__thf__4__p_Obnd__amone) # label(axiom). [clausify(1)].
% 1.08/1.47 486 gg_bool(scratc375860794_d_and(A,B)) # label(gsy_c_Scratch__tptp__translate__51767__4802_ONUM702__thf__4__p_Obnd__d__and) # label(axiom). [clausify(2)].
% 1.08/1.47 487 gg_bool(scratc483325974_d_not(A)) # label(gsy_c_Scratch__tptp__translate__51767__4802_ONUM702__thf__4__p_Obnd__d__not) # label(axiom). [clausify(3)].
% 1.08/1.47 488 gg_bool(scratc489722670nd_ec3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__51767__4802_ONUM702__thf__4__p_Obnd__ec3) # label(axiom). [clausify(4)].
% 1.08/1.47 489 gg_bool(scratc908653987d_l_ec(A,B)) # label(gsy_c_Scratch__tptp__translate__51767__4802_ONUM702__thf__4__p_Obnd__l__ec) # label(axiom). [clausify(8)].
% 1.08/1.47 490 gg_bool(scratc573321705nd_or3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__51767__4802_ONUM702__thf__4__p_Obnd__or3) # label(axiom). [clausify(9)].
% 1.08/1.47 491 gg_bool(aa_bool_bool(A,B)) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom). [clausify(10)].
% 1.73/2.03 492 gg_bool(aa_TPTP_ind_bool(A,B)) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom). [clausify(11)].
% 1.73/2.03 493 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)].
% 1.73/2.03 494 gg_bool(fEx_TPTP_ind(A)) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom). [clausify(16)].
% 1.73/2.03 495 gg_bool(fFalse) # label(gsy_c_fFalse) # label(axiom). [assumption].
% 1.73/2.03 496 gg_bool(fTrue) # label(gsy_c_fTrue) # label(axiom). [assumption].
% 1.73/2.03 Derived: undefined_bool(bool) = fTrue | undefined_bool(bool) = fFalse. [resolve(483,a,484,a)].
% 1.73/2.03 Derived: scratc1581925715_amone(A,B) = fTrue | scratc1581925715_amone(A,B) = fFalse. [resolve(483,a,485,a)].
% 1.73/2.03 Derived: scratc375860794_d_and(A,B) = fTrue | scratc375860794_d_and(A,B) = fFalse. [resolve(483,a,486,a)].
% 1.73/2.03 Derived: scratc483325974_d_not(A) = fTrue | scratc483325974_d_not(A) = fFalse. [resolve(483,a,487,a)].
% 1.73/2.03 Derived: scratc489722670nd_ec3(A,B,C) = fTrue | scratc489722670nd_ec3(A,B,C) = fFalse. [resolve(483,a,488,a)].
% 1.73/2.03 Derived: scratc908653987d_l_ec(A,B) = fTrue | scratc908653987d_l_ec(A,B) = fFalse. [resolve(483,a,489,a)].
% 1.73/2.03 Derived: scratc573321705nd_or3(A,B,C) = fTrue | scratc573321705nd_or3(A,B,C) = fFalse. [resolve(483,a,490,a)].
% 1.73/2.03 Derived: aa_bool_bool(A,B) = fTrue | aa_bool_bool(A,B) = fFalse. [resolve(483,a,491,a)].
% 1.73/2.03 Derived: aa_TPTP_ind_bool(A,B) = fTrue | aa_TPTP_ind_bool(A,B) = fFalse. [resolve(483,a,492,a)].
% 1.73/2.03 Derived: aa_fun171081125l_bool(A,B) = fTrue | aa_fun171081125l_bool(A,B) = fFalse. [resolve(483,a,493,a)].
% 1.73/2.03 Derived: fEx_TPTP_ind(A) = fTrue | fEx_TPTP_ind(A) = fFalse. [resolve(483,a,494,a)].
% 1.73/2.03 Derived: fFalse = fTrue | fFalse = fFalse. [resolve(483,a,495,a)].
% 1.73/2.03 Derived: fTrue = fTrue | fTrue = fFalse. [resolve(483,a,496,a)].
% 1.73/2.03 497 scratc1303588777d_r_ec(A,B) | pp(A) # label(fact_def__r__ec) # label(axiom). [clausify(59)].
% 1.73/2.03 498 -scratc1303588777d_r_ec(A,B) | -pp(A) | pp(scratc483325974_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(59)].
% 1.73/2.03 499 scratc1303588777d_r_ec(A,B) | -pp(scratc483325974_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(59)].
% 1.73/2.03 500 scratc1270002244_l_iff(A,B) | -pp(scratc375860794_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc523424741nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc523424741nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(91)].
% 1.73/2.03 501 -scratc1270002244_l_iff(A,B) | pp(scratc375860794_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc523424741nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc523424741nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(91)].
% 1.73/2.03 502 scratc452678920d_orec(A,B) | -pp(scratc375860794_d_and(aa_bool_bool(scratc909309992d_l_or(A),B),scratc908653987d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(92)].
% 1.73/2.03 503 -scratc452678920d_orec(A,B) | pp(scratc375860794_d_and(aa_bool_bool(scratc909309992d_l_or(A),B),scratc908653987d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(92)].
% 1.73/2.03 504 scratc638561015nd_wel(A) | -pp(scratc483325974_d_not(scratc483325974_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(97)].
% 1.73/2.03 505 -scratc638561015nd_wel(A) | pp(scratc483325974_d_not(scratc483325974_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(97)].
% 1.73/2.03 506 -scratc638561015nd_wel(A) | pp(A) # label(fact_l__et) # label(axiom). [clausify(147)].
% 1.73/2.03 Derived: pp(A) | -pp(scratc483325974_d_not(scratc483325974_d_not(A))). [resolve(506,a,504,a)].
% 1.73/2.03
% 1.73/2.03 ============================== end predicate elimination =============
% 1.73/2.03
% 1.73/2.03 Auto_denials: (non-Horn, no changes).
% 1.73/2.03
% 1.73/2.03 Term ordering decisions:
% 1.73/2.03 Function symbol KB weights: aTP_Lamm_a=1. scratc1712848716bnd_in=1. scratc1040561329d_n_is=1. scratc523162338nd_iii=1. scratc1331683044_29_ii=1. scratc659279004rdsucc=1. scratc1712323926bnd_ap=1. scratc179623690lessis=1. aTP_Lamm_aj=1. scratc313607302moreis=1. scratc1662213130nd_n_1=1. scratc2059070044ptyset=1. scratc2023208232_Sigma=1. scratc564469873nd_nis=1. fFalse=1. scratc1275049398_nat_p=1. scratc1431138523n_some=1. scratc380696694d_d_Pi=1. scratc563945082nd_nat=1. scratc974713278_power=1. scratc523424741nd_imp=1. scratc540278902d_repl=1. fTrue=1. scratc1093082945d_pair=1. scratc699359822d_Subq=1. scratc1103227116_proj0=1. scratc1481975144_union=1. scratc1924431736closed=1. aTP_Lamm_af=1. scratc1040561324d_n_in=1. scratc1103227117_proj1=1. scratc1948318266_n_all=1. aTP_Lamm_ac=1. aTP_Lamm_ae=1. aTP_Lamm_jw=1. scratc446102782closed=1. scratc610835796closed=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_ca=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_hr=1. aTP_Lamm_jn=1. aTP_Lamm_jr=1. aTP_Lamm_js=1. scratc1189926864_prop2=1. scratc1426116617d_Inj1=1. scratc272882330_omega=1. scratc593027925closed=1. aTP_Lamm_ag=1. aTP_Lamm_bg=1. aTP_Lamm_bi=1. aTP_Lamm_bj=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_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_en=1. aTP_Lamm_er=1. aTP_Lamm_ev=1. aTP_Lamm_ez=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_fv=1. aTP_Lamm_fz=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_gt=1. aTP_Lamm_ht=1. aTP_Lamm_hv=1. aTP_Lamm_hx=1. aTP_Lamm_hz=1. aTP_Lamm_ib=1. aTP_Lamm_if=1. aTP_Lamm_ih=1. aTP_Lamm_ik=1. aTP_Lamm_in=1. aTP_Lamm_ip=1. aTP_Lamm_ir=1. aTP_Lamm_iu=1. aTP_Lamm_iw=1. aTP_Lamm_iz=1. aTP_Lamm_jc=1. aTP_Lamm_jf=1. aTP_Lamm_ji=1. aTP_Lamm_jk=1. aTP_Lamm_jl=1. aTP_Lamm_jq=1. fconj=1. fimplies=1. scratc1118343849_cond2=1. scratc1189926863_prop1=1. scratc1426116616d_Inj0=1. scratc601008940d_Sing=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_cb=1. aTP_Lamm_cc=1. aTP_Lamm_cd=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_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_eo=1. aTP_Lamm_es=1. aTP_Lamm_ew=1. aTP_Lamm_fa=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_fw=1. aTP_Lamm_fx=1. aTP_Lamm_fy=1. aTP_Lamm_ga=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_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_ic=1. aTP_Lamm_ig=1. aTP_Lamm_ii=1. aTP_Lamm_il=1. aTP_Lamm_io=1. aTP_Lamm_iq=1. aTP_Lamm_is=1. aTP_Lamm_iv=1. aTP_Lamm_ix=1. aTP_Lamm_iy=1. aTP_Lamm_ja=1. aTP_Lamm_jb=1. aTP_Lamm_jd=1. aTP_Lamm_je=1. aTP_Lamm_jg=1. aTP_Lamm_jh=1. aTP_Lamm_jj=1. aTP_Lamm_jm=1. aTP_Lamm_jo=1. aTP_Lamm_jp=1. aTP_Lamm_jt=1. aTP_Lamm_ju=1. aTP_Lamm_jv=1. aTP_Lamm_jy=1. aTP_Lamm_kv=1. fequal_TPTP_ind=1. scratc1118343848_cond1=1. scratc1708106180univof=1. scratc2064110527_n_one=1. scratc276722740_d_Unj=1. scratc562370700nd_nIn=1. aTP_Lamm_ab=1. aTP_Lamm_ah=1. aTP_Lamm_bk=1. aTP_Lamm_bl=1. bool=1. scratc1103620714_prop4=1. scratc1184746689d_plus=1. scratc13202513_prop1=1. scratc1853870694_empty=1. scratc197181383nempty=1. scratc1984254090_prop1=1. scratc219167565_prop1=1. scratc277026948munion=1. scratc516028975pair_p=1. scratc601564688_prop1=1. scratc807529740_prop1=1. scratc237262052d_i1_s=1. scratc288866056d_24_g=1. tPTP_ind=1. aa_TPT43085870d_bool=1. aa_TPTP_ind_bool=1. aa_TPTP_ind_TPTP_ind=1. aa_fun171081125l_bool=1. aa_TPT60673477d_bool=1. aa_TPT1424761345TP_ind=1. aa_fun277296641TP_ind=1. aa_TPT494704832TP_ind=1. aa_bool_bool=1. aa_fun1584354236d_bool=1. aa_fun1431113780TP_ind=1. aa_boo1142376798l_bool=1. scratc375860794_d_and=1. aa_TPT1123896796d_bool=1. scratc1712848708bnd_if=1. scratc908653987d_l_ec=1. aa_fun1212484691d_bool=1. aa_TPT985247859d_bool=1. scratc1521900963d_e_in=1. scratc1696781207d_pair=1. aa_fun987228051d_bool=1. scratc1581925715_amone=1. scratc523490328nd_ind=1. scratc1992385172_image=1. scratc2035027241_first=1. scratc998979323second=1. aa_TPT125613450d_bool=1. scratc564863462nd_non=1. aa_fun1913827119d_bool=1. scratc228830354d_anec=1. aa_TPT1791839040TP_ind=1. aa_fun1107270209d_bool=1. aa_fun845057962d_bool=1. scratc1361835058eplSep=1. scratc399048296_ecelt=1. scratc489722731nd_ecp=1. scratc398457905_ecect=1. aa_TPT1781712639TP_ind=1. aa_TPT2142672771l_bool=1. aa_fun1235454963TP_ind=1. cOMBB_658106424TP_ind=1. cOMBS_2003118649l_bool=1. scratc2007193717fixfu2=1. scratc2083743485_fixfu=1. scratc239763392wissel=1. scratc371736595ectset=1. scratc489722735nd_ect=1. scratc573518567nd_out=1. scratc798374484etprop=1. scratc256534718ectelt=1. scratc32192188d_invf=1. scratc35928719d_tofs=1. scratc477853941unmore=1. scratc57526697nverse=1. f1=1. f12=1. f13=1. f20=1. f24=1. scratc1576653073all_of=1. scratc1041020515d_n_pl=1. scratc1521900968d_e_is=1. scratc483325974_d_not=1. scratc259609345_d_Sep=1. scratc1245987018d_esti=1. scratc687313881l_some=1. scratc1193483343ffprop=1. scratc457267098nd_all=1. scratc909309992d_l_or=1. scratc294504025_rec_G=1. aTP_Lamm_ai=1. aTP_Lamm_kf=1. scratc573059359nd_one=1. aTP_Lamm_ak=1. aTP_Lamm_au=1. aTP_Lamm_bc=1. aTP_Lamm_bp=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_ep=1. aTP_Lamm_et=1. aTP_Lamm_ex=1. aTP_Lamm_fb=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_id=1. aTP_Lamm_jx=1. aTP_Lamm_kt=1. scratc30945813d_incl=1. aTP_Lamm_ao=1. aTP_Lamm_ay=1. aTP_Lamm_bb=1. aTP_Lamm_bf=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_ff=1. aTP_Lamm_fi=1. aTP_Lamm_fl=1. aTP_Lamm_fo=1. aTP_Lamm_fr=1. aTP_Lamm_fu=1. aTP_Lamm_ij=1. aTP_Lamm_im=1. aTP_Lamm_kp=1. aTP_Lamm_kr=1. scratc293202098etprod=1. scratc376042048ective=1. scratc490575521nd_eps=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_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_eq=1. aTP_Lamm_eu=1. aTP_Lamm_ey=1. aTP_Lamm_fc=1. aTP_Lamm_ie=1. aTP_Lamm_it=1. aTP_Lamm_jz=1. aTP_Lamm_ka=1. aTP_Lamm_kb=1. aTP_Lamm_kd=1. aTP_Lamm_kj=1. aTP_Lamm_kl=1. aTP_Lamm_km=1. aTP_Lamm_kq=1. fEx_TPTP_ind=1. scratc1270884047nunion=1. scratc334119779ective=1. aTP_Lamm_ar=1. aTP_Lamm_kc=1. aTP_Lamm_ke=1. aTP_Lamm_kg=1. aTP_Lamm_kh=1. aTP_Lamm_ki=1. aTP_Lamm_kk=1. aTP_Lamm_kn=1. aTP_Lamm_ko=1. aTP_Lamm_ks=1. aTP_Lamm_ku=1. scratc1089598638In_rec=1. scratc1917694610_UPair=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. scratc1103620713_prop3=1. scratc1187169589tminus=1. scratc1395891915_prop1=1. scratc1604006084t_disj=1. scratc1778289038_prop1=1. scratc559761278ective=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. scratc573321705nd_or3=1. scratc489722670nd_ec3=1. scratc1402825169d_soft=1. scratc1103620711_prop1=1. scratc523883923nd_ite=1. scratc650142052_indeq=1. scratc1102507468d_11_i=1. scratc737744170sel_wa=1. scratc737744171sel_wb=1. f5=1. f7=1. f14=1. f16=1. f19=1. f25=1. scratc1103620712_prop2=1. scratc2128509706_inj_h=1. scratc71485647hangef=1. f3=1. f4=1. f15=1. scratc1737249490_prop1=1. scratc1790703566indeq2=1. f6=1.
% 1.73/2.03
% 1.73/2.03 ============================== end of process initial clauses ========
% 1.73/2.03
% 1.73/2.03 ============================== CLAUSES FOR SEARCH ====================
% 1.73/2.03
% 1.73/2.03 ============================== end of clauses for search =============
% 1.73/2.03
% 1.73/2.03 =================Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------