TSTP Solution File: NUM652+4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM652+4 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n007.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 13:30:03 EDT 2022
% Result : Timeout 300.03s 300.41s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM652+4 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.10/0.32 % Computer : n007.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 600
% 0.10/0.32 % DateTime : Tue Jul 5 02:02:27 EDT 2022
% 0.10/0.32 % CPUTime :
% 1.07/1.39 ============================== Prover9 ===============================
% 1.07/1.39 Prover9 (32) version 2009-11A, November 2009.
% 1.07/1.39 Process 18074 was started by sandbox on n007.cluster.edu,
% 1.07/1.39 Tue Jul 5 02:02:28 2022
% 1.07/1.39 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_17921_n007.cluster.edu".
% 1.07/1.39 ============================== end of head ===========================
% 1.07/1.39
% 1.07/1.39 ============================== INPUT =================================
% 1.07/1.39
% 1.07/1.39 % Reading from file /tmp/Prover9_17921_n007.cluster.edu
% 1.07/1.39
% 1.07/1.39 set(prolog_style_variables).
% 1.07/1.39 set(auto2).
% 1.07/1.39 % set(auto2) -> set(auto).
% 1.07/1.39 % set(auto) -> set(auto_inference).
% 1.07/1.39 % set(auto) -> set(auto_setup).
% 1.07/1.39 % set(auto_setup) -> set(predicate_elim).
% 1.07/1.39 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.07/1.39 % set(auto) -> set(auto_limits).
% 1.07/1.39 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.07/1.39 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.07/1.39 % set(auto) -> set(auto_denials).
% 1.07/1.39 % set(auto) -> set(auto_process).
% 1.07/1.39 % set(auto2) -> assign(new_constants, 1).
% 1.07/1.39 % set(auto2) -> assign(fold_denial_max, 3).
% 1.07/1.39 % set(auto2) -> assign(max_weight, "200.000").
% 1.07/1.39 % set(auto2) -> assign(max_hours, 1).
% 1.07/1.39 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.07/1.39 % set(auto2) -> assign(max_seconds, 0).
% 1.07/1.39 % set(auto2) -> assign(max_minutes, 5).
% 1.07/1.39 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.07/1.39 % set(auto2) -> set(sort_initial_sos).
% 1.07/1.39 % set(auto2) -> assign(sos_limit, -1).
% 1.07/1.39 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.07/1.39 % set(auto2) -> assign(max_megs, 400).
% 1.07/1.39 % set(auto2) -> assign(stats, some).
% 1.07/1.39 % set(auto2) -> clear(echo_input).
% 1.07/1.39 % set(auto2) -> set(quiet).
% 1.07/1.39 % set(auto2) -> clear(print_initial_clauses).
% 1.07/1.39 % set(auto2) -> clear(print_given).
% 1.07/1.39 assign(lrs_ticks,-1).
% 1.07/1.39 assign(sos_limit,10000).
% 1.07/1.39 assign(order,kbo).
% 1.07/1.39 set(lex_order_vars).
% 1.07/1.39 clear(print_given).
% 1.07/1.39
% 1.07/1.39 % formulas(sos). % not echoed (391 formulas)
% 1.07/1.39
% 1.07/1.39 ============================== end of input ==========================
% 1.07/1.39
% 1.07/1.39 % From the command line: assign(max_seconds, 300).
% 1.07/1.39
% 1.07/1.39 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.07/1.39
% 1.07/1.39 % Formulas that are not ordinary clauses:
% 1.07/1.39 1 (all B_1 all B_2 gg_bool(scratc530322608_amone(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__42582__9795_ONUM652__thf__4__p_Obnd__amone) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 2 (all B_1 all B_2 gg_bool(scratc2028353053_d_and(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__42582__9795_ONUM652__thf__4__p_Obnd__d__and) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 3 (all B_1 gg_bool(scratc2135818233_d_not(B_1))) # label(gsy_c_Scratch__tptp__translate__42582__9795_ONUM652__thf__4__p_Obnd__d__not) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 4 (all B_1 all B_2 all B_3 gg_bool(scratc257261835nd_ec3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__42582__9795_ONUM652__thf__4__p_Obnd__ec3) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 5 (all B_1 all B_2 gg_TPTP_ind(scratc257261900nd_ect(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__42582__9795_ONUM652__thf__4__p_Obnd__ect) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 6 (all B_1 gg_TPTP_ind(scratc258114686nd_eps(B_1))) # label(gsy_c_Scratch__tptp__translate__42582__9795_ONUM652__thf__4__p_Obnd__eps) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 7 (all B_1 all B_2 gg_TPTP_ind(scratc291029493nd_ind(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__42582__9795_ONUM652__thf__4__p_Obnd__ind) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 8 (all B_1 all B_2 gg_bool(scratc2004534528d_l_ec(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__42582__9795_ONUM652__thf__4__p_Obnd__l__ec) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 9 (all B_1 all B_2 all B_3 gg_bool(scratc340860870nd_or3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__42582__9795_ONUM652__thf__4__p_Obnd__or3) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 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].
% 1.07/1.39 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].
% 1.07/1.39 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].
% 1.07/1.39 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].
% 1.07/1.39 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].
% 1.07/1.39 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].
% 1.07/1.39 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].
% 1.07/1.39 17 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1832115949lessis,X),Xa)) <-> pp(aa_bool_bool(scratc2005190533d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc290701503nd_iii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,X),Xa))))) # label(fact_def__lessis) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 18 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1966099561moreis,X),Xa)) <-> pp(aa_bool_bool(scratc2005190533d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1835086145_29_ii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,X),Xa))))) # label(fact_def__moreis) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 19 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1054561261_prop1,X),Xa)) <-> pp(scratc340860870nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1835086145_29_ii,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc290701503nd_iii,X),Xa))))) # label(fact_def__d__29__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 20 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc290701503nd_iii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc443769272n_some,aa_TPT43085870d_bool(scratc1012294322ffprop(Xa),X))))) # label(fact_def__iii) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 21 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1835086145_29_ii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc443769272n_some,aa_TPT43085870d_bool(scratc1012294322ffprop(X),Xa))))) # label(fact_def__d__29__ii) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 22 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1012294322ffprop(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,X),aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(Xa),Xb))))) # label(fact_def__diffprop) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 23 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc466199086_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc332009038nd_nis,aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(X),Xb))))) # label(fact_def__d__28__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 24 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2025320559_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc332009038nd_nis,Xa),aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(X),Xa))))) # label(fact_def__d__27__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 25 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1436958384_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(Xa),X))))) # label(fact_def__d__26__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 26 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc848596209_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(X),Xa)),Xb)),aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(X),aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(Xa),Xb)))))) # label(fact_def__d__25__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 27 (all X scratc2136901056d_n_pl(X) = aa_TPT1424761345TP_ind(scratc2063648825bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1267815972d_plus,X))) # label(fact_def__n__pl) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 28 (all X aa_TPTP_ind_TPTP_ind(scratc1267815972d_plus,X) = scratc291029493nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1476577235d_d_Pi,scratc331484247nd_nat),aTP_Lamm_ac),aa_TPT43085870d_bool(scratc260234035_prop2,X))) # label(fact_def__plus) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 29 (all X aa_TPTP_ind_TPTP_ind(scratc107677035d_24_g,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1842019211_Sigma,scratc331484247nd_nat),aTP_Lamm_ad(X))) # label(fact_def__d__24__g) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 30 (all X (pp(aa_TPTP_ind_bool(scratc52017607_prop4,X)) <-> pp(aa_fun171081125l_bool(scratc1847428278l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1476577235d_d_Pi,scratc331484247nd_nat),aTP_Lamm_ac)),aa_TPT43085870d_bool(scratc260234035_prop2,X))))) # label(fact_def__prop4) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 31 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52017606_prop3(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2063648825bnd_ap,X),Xb)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2063648825bnd_ap,Xa),Xb))))) # label(fact_def__prop3) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 32 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc260234035_prop2,X),Xa)) <-> pp(scratc2028353053_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2063648825bnd_ap,Xa),scratc1745282413nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,X)),aa_TPTP_ind_bool(scratc260234034_prop1,Xa))))) # label(fact_def__d__24__prop2) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 33 (all X (pp(aa_TPTP_ind_bool(scratc260234034_prop1,X)) <-> pp(aa_fun171081125l_bool(scratc1453326877_n_all,aa_TPT43085870d_bool(aTP_Lamm_ae,X))))) # label(fact_def__d__24__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 34 (all X (pp(aa_TPTP_ind_bool(scratc1819355507_prop1,X)) <-> pp(aa_bool_bool(scratc2005190533d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,X),scratc1745282413nd_n_1)),aa_fun171081125l_bool(scratc443769272n_some,aa_TPT43085870d_bool(aTP_Lamm_af,X)))))) # label(fact_def__d__23__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 35 (all X (pp(aa_TPTP_ind_bool(scratc1230993332_prop1,X)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc332009038nd_nis,aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,X)),X)))) # label(fact_def__d__22__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 36 (all X (pp(aa_TPTP_ind_bool(scratc66740742_cond2,X)) <-> pp(aa_fun171081125l_bool(scratc1453326877_n_all,aa_TPT43085870d_bool(aTP_Lamm_ag,X))))) # label(fact_def__cond2) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 37 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc332009038nd_nis,X),Xa)) <-> pp(scratc2135818233_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,X),Xa))))) # label(fact_def__nis) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 38 (all X all Xa all Xb all Xc all Xd scratc1295712177indeq2(X,Xa,Xb,Xc,Xd) = aa_TPT1424761345TP_ind(scratc1746022593_indeq(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc921318447d_11_i(X,Xa,Xb),Xc),Xd))) # label(fact_def__indeq2) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 39 (all X all Xa all Xb scratc921318447d_11_i(X,Xa,Xb) = scratc1746022593_indeq(X,Xa,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1476577235d_d_Pi,X),aTP_Lamm_ai(Xb)))) # label(fact_def__d__11__i) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 40 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1512202328fixfu2(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc589283822all_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].
% 1.07/1.39 41 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1746022593_indeq(X,Xa,Xb),Xc),Xd) = scratc291029493nd_ind(Xb,aa_TPT43085870d_bool(scratc52017605_prop2(X,Xa,Xb,Xc),Xd))) # label(fact_def__indeq) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 42 (all X all Xa all Xb all Xc all Xd all Xe (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52017605_prop2(X,Xa,Xb,Xc),Xd),Xe)) <-> pp(aa_fun171081125l_bool(scratc1847428278l_some(X),aa_TPT43085870d_bool(scratc807556661_prop1(X,Xa,Xb,Xc,Xd),Xe))))) # label(fact_def__prop2) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 43 (all X all Xa all Xb all Xc all Xd all Xe all Xf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc807556661_prop1(X,Xa,Xb,Xc,Xd),Xe),Xf)) <-> pp(scratc2028353053_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1329056301d_esti(X),Xf),aa_TPTP_ind_TPTP_ind(scratc1494338446_ecect(X,Xa),Xd)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc470297861d_e_is(Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2063648825bnd_ap,Xc),Xf)),Xe))))) # label(fact_def__d__10__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 44 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1032140378_fixfu(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc589283822all_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].
% 1.07/1.39 45 (all X all Xa scratc1494338446_ecect(X,Xa) = scratc470297856d_e_in(aa_TPTP_ind_TPTP_ind(scratc2070593819_power,X),scratc311899637d_anec(X,Xa))) # label(fact_def__ecect) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 46 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1909026977ectelt(X,Xa),Xb) = aa_TPTP_ind_TPTP_ind(scratc2024228854ectset(X,Xa),aa_TPTP_ind_TPTP_ind(scratc1494928837_ecelt(X,Xa),Xb))) # label(fact_def__ectelt) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 47 (all X all Xa scratc2024228854ectset(X,Xa) = scratc341057732nd_out(aa_TPTP_ind_TPTP_ind(scratc2070593819_power,X),scratc311899637d_anec(X,Xa))) # label(fact_def__ectset) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 48 (all X all Xa scratc257261900nd_ect(X,Xa) = aa_fun1431113780TP_ind(scratc1912101604_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2070593819_power,X)),scratc311899637d_anec(X,Xa))) # label(fact_def__ect) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 49 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc311899637d_anec(X,Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1847428278l_some(X),aa_TPT43085870d_bool(scratc257261896nd_ecp(X,Xa),Xb))))) # label(fact_def__anec) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 50 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc257261896nd_ecp(X,Xa),Xb),Xc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc470297861d_e_is(aa_TPTP_ind_TPTP_ind(scratc2070593819_power,X)),Xb),aa_TPTP_ind_TPTP_ind(scratc1494928837_ecelt(X,Xa),Xc))))) # label(fact_def__ecp) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 51 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1494928837_ecelt(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc1912101604_d_Sep(X),aa_TPT43085870d_bool(Xa,Xb))) # label(fact_def__ecelt) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 52 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc2130346200unmore(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc1912101604_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].
% 1.07/1.39 53 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682341687etprop(X,Xa),Xb),Xc)) <-> pp(scratc2028353053_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1329056301d_esti(X),Xc),Xa),scratc2135818233_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1329056301d_esti(X),Xc),Xb)))))) # label(fact_def__nissetprop) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 54 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1422817063t_disj(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc224806263nd_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].
% 1.07/1.39 55 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc114015096d_incl(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc224806263nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_at(X),Xa),Xb))))) # label(fact_def__incl) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 56 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc15992362nempty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1847428278l_some(X),aa_TPT43085870d_bool(aTP_Lamm_au(X),Xa))))) # label(fact_def__nonempty) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 57 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc802267587_empty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),scratc332402627nd_non(X,aa_TPT43085870d_bool(aTP_Lamm_au(X),Xa)))))) # label(fact_def__empty) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 58 (all X scratc1329056301d_esti(X) = scratc2064173615bnd_in) # label(fact_def__esti) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 59 (all X all Xa (scratc251985670d_r_ec(X,Xa) <-> (pp(X) -> pp(scratc2135818233_d_not(Xa))))) # label(fact_def__r__ec) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 60 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc1231600044hangef(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1842019211_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].
% 1.07/1.39 61 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1892255651wissel(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1842019211_Sigma,X),scratc1621711374sel_wb(X,Xa,Xb))) # label(fact_def__wissel) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 62 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1621711374sel_wb(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc291423088nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc470297861d_e_is(X),Xc),Xb),X,Xa),aa_TPTP_ind_TPTP_ind(scratc1621711373sel_wa(X,Xa,Xb),Xc))) # label(fact_def__wissel__wb) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 63 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1621711373sel_wa(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc291423088nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc470297861d_e_is(X),Xc),Xa),X,Xb),Xc)) # label(fact_def__wissel__wa) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 64 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc291423088nd_ite(X,Xa,Xb),Xc) = scratc291029493nd_ind(Xa,aa_TPT43085870d_bool(scratc52017604_prop1(X,Xa,Xb),Xc))) # label(fact_def__ite) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 65 (all X all Xa all Xb all Xc all Xd (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc52017604_prop1(X,Xa,Xb),Xc),Xd)) <-> pp(scratc2028353053_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc290963906nd_imp,X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc470297861d_e_is(Xa),Xd),Xb)),aa_bool_bool(aa_boo1142376798l_bool(scratc290963906nd_imp,scratc2135818233_d_not(X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc470297861d_e_is(Xa),Xd),Xc)))))) # label(fact_def__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 66 (all X all Xa scratc503987934second(X,Xa) = scratc51624010_proj1) # label(fact_def__second) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 67 (all X all Xa scratc983424134_first(X,Xa) = scratc51624009_proj0) # label(fact_def__first) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 68 (all X all Xa scratc709411956d_pair(X,Xa) = scratc1176152228d_pair) # label(fact_def__d__pair) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 69 (all X all Xa scratc341057732nd_out(X,Xa) = scratc1485894452d_soft(aa_fun1431113780TP_ind(scratc1912101604_d_Sep(X),Xa),X,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1842019211_Sigma,aa_fun1431113780TP_ind(scratc1912101604_d_Sep(X),Xa)),scratc470297856d_e_in(X,Xa)))) # label(fact_def__out) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 70 (all X all Xa all Xb (gg_TPTP_ind(Xb) -> aa_TPTP_ind_TPTP_ind(scratc470297856d_e_in(X,Xa),Xb) = Xb)) # label(fact_def__e__in) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 71 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc1633518317_inj_h(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1842019211_Sigma,X),aa_TPT1424761345TP_ind(aTP_Lamm_aw(Xc),Xd))) # label(fact_def__inj__h) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 72 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc115261471d_invf(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1842019211_Sigma,Xa),scratc1485894452d_soft(X,Xa,Xb))) # label(fact_def__invf) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 73 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1063164379ective(X),Xa),Xb)) <-> pp(scratc2028353053_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc879445149ective(X),Xa),Xb),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1218086982ective(X),Xa),Xb))))) # label(fact_def__bijective) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 74 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1218086982ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc224806263nd_all(Xa),aa_TPT43085870d_bool(scratc940782065_image(X,Xa),Xb))))) # label(fact_def__surjective) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 75 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1217641094nverse(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1842019211_Sigma,Xa),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ax(X),Xa),Xb))) # label(fact_def__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 76 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1485894452d_soft(X,Xa,Xb),Xc) = scratc291029493nd_ind(X,aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(Xa),Xb),Xc))) # label(fact_def__soft) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 77 (all X all Xa scratc118998002d_tofs(X,Xa) = scratc2063648825bnd_ap) # label(fact_def__tofs) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 78 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc940782065_image(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1847428278l_some(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(Xa),Xb),Xc))))) # label(fact_def__image) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 79 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc879445149ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc224806263nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ba(X),Xa),Xb))))) # label(fact_def__injective) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 80 (all X all Xa scratc291029493nd_ind(X,Xa) = scratc258114686nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bb(X),Xa))) # label(fact_def__ind) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 81 (all X all Xa (pp(aa_fun171081125l_bool(scratc340598524nd_one(X),Xa)) <-> pp(scratc2028353053_d_and(scratc530322608_amone(X,Xa),aa_fun171081125l_bool(scratc1847428278l_some(X),Xa))))) # label(fact_def__one) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 82 (all X all Xa (pp(scratc530322608_amone(X,Xa)) <-> pp(aa_fun171081125l_bool(scratc589283822all_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].
% 1.07/1.39 83 (all X scratc470297861d_e_is(X) = fequal_TPTP_ind) # label(fact_def__e__is) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 84 (all X all Xa all Xb (scratc976469128_orec3(X,Xa,Xb) <-> pp(scratc2028353053_d_and(scratc340860870nd_or3(X,Xa,Xb),scratc257261835nd_ec3(X,Xa,Xb))))) # label(fact_def__orec3) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 85 (all X all Xa all Xb (pp(scratc257261835nd_ec3(X,Xa,Xb)) <-> scratc311833990d_and3(scratc2004534528d_l_ec(X,Xa),scratc2004534528d_l_ec(Xa,Xb),scratc2004534528d_l_ec(Xb,X)))) # label(fact_def__ec3) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 86 (all X all Xa all Xb (scratc311833990d_and3(X,Xa,Xb) <-> pp(scratc2028353053_d_and(X,scratc2028353053_d_and(Xa,Xb))))) # label(fact_def__and3) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 87 (all X all Xa all Xb (pp(scratc340860870nd_or3(X,Xa,Xb)) <-> pp(aa_bool_bool(scratc2005190533d_l_or(X),aa_bool_bool(scratc2005190533d_l_or(Xa),Xb))))) # label(fact_def__or3) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 88 (all X all Xa (pp(aa_fun171081125l_bool(scratc1847428278l_some(X),Xa)) <-> pp(scratc2135818233_d_not(aa_fun171081125l_bool(scratc589283822all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),scratc332402627nd_non(X,Xa)))))) # label(fact_def__l__some) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 89 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc332402627nd_non(X,Xa),Xb)) <-> pp(scratc2135818233_d_not(aa_TPTP_ind_bool(Xa,Xb))))) # label(fact_def__non) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 90 (all X scratc224806263nd_all(X) = scratc589283822all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X))) # label(fact_def__all) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 91 (all X all Xa (scratc775010855_l_iff(X,Xa) <-> pp(scratc2028353053_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc290963906nd_imp,X),Xa),aa_bool_bool(aa_boo1142376798l_bool(scratc290963906nd_imp,Xa),X))))) # label(fact_def__l__iff) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 92 (all X all Xa (scratc535748203d_orec(X,Xa) <-> pp(scratc2028353053_d_and(aa_bool_bool(scratc2005190533d_l_or(X),Xa),scratc2004534528d_l_ec(X,Xa))))) # label(fact_def__orec) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 93 (all X scratc2005190533d_l_or(X) = aa_boo1142376798l_bool(scratc290963906nd_imp,scratc2135818233_d_not(X))) # label(fact_def__l__or) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 94 (all X all Xa (pp(scratc2028353053_d_and(X,Xa)) <-> pp(scratc2135818233_d_not(scratc2004534528d_l_ec(X,Xa))))) # label(fact_def__d__and) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 95 (all X all Xa (pp(scratc2004534528d_l_ec(X,Xa)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc290963906nd_imp,X),scratc2135818233_d_not(Xa))))) # label(fact_def__l__ec) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 96 scratc2082723741bvious <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc290963906nd_imp,fFalse),fFalse)) # label(fact_def__obvious) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 97 (all X (scratc406100180nd_wel(X) <-> pp(scratc2135818233_d_not(scratc2135818233_d_not(X))))) # label(fact_def__wel) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 98 (all X (pp(scratc2135818233_d_not(X)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc290963906nd_imp,X),fFalse)))) # label(fact_def__d__not) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 99 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1476577235d_d_Pi,X),Xa) = aa_fun1431113780TP_ind(scratc1912101604_d_Sep(aa_TPTP_ind_TPTP_ind(scratc2070593819_power,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1842019211_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].
% 1.07/1.39 100 (all X (gg_TPTP_ind(X) -> (pp(aa_TPTP_ind_bool(scratc1676143372pair_p,X)) <-> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1176152228d_pair,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2063648825bnd_ap,X),scratc1877881023ptyset)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2063648825bnd_ap,X),aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,scratc1877881023ptyset))) = X))) # label(fact_def__pair__p) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 101 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2063648825bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc98318613eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bg,Xa)),scratc51624010_proj1)) # label(fact_def__ap) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 102 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1453316495etprod(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1842019211_Sigma,X),aTP_Lamm_ai(Xa))) # label(fact_def__setprod) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 103 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1842019211_Sigma,X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc95837927munion,X),aTP_Lamm_bh(Xa))) # label(fact_def__d__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 104 (all X aa_TPTP_ind_TPTP_ind(scratc51624010_proj1,X) = aa_fun277296641TP_ind(scratc98318613eplSep(X,aTP_Lamm_bi),scratc1929214999_d_Unj)) # label(fact_def__proj1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 105 (all X aa_TPTP_ind_TPTP_ind(scratc51624009_proj0,X) = aa_fun277296641TP_ind(scratc98318613eplSep(X,aTP_Lamm_bj),scratc1929214999_d_Unj)) # label(fact_def__proj0) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 106 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1176152228d_pair,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1089695026nunion(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc623348185d_repl,X),scratc438747365d_Inj0)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc623348185d_repl,Xa),scratc438747366d_Inj1))) # label(fact_def__pair) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 107 (all X aa_TPTP_ind_TPTP_ind(scratc438747365d_Inj0,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc623348185d_repl,X),scratc438747366d_Inj1)) # label(fact_def__d__Inj0) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 108 (all X (pp(aa_TPTP_ind_bool(scratc780058009_nat_p,X)) <-> (all X1 (pp(aa_TPTP_ind_bool(X1,scratc1877881023ptyset)) -> ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(X1,X2)) -> pp(aa_TPTP_ind_bool(X1,aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,X2)))))) -> pp(aa_TPTP_ind_bool(X1,X))))))) # label(fact_def__nat__p) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 109 (all X aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1089695026nunion(X),aa_TPTP_ind_TPTP_ind(scratc1761123337d_Sing,X))) # label(fact_def__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 110 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1973565841In_rec(X),Xa) = scratc258114686nd_eps(aa_TPT43085870d_bool(scratc1910217654_rec_G(X),Xa))) # label(fact_def__d__In__rec) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 111 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1910217654_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(scratc2064173615bnd_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].
% 1.07/1.39 112 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1005980568tminus(X),Xa) = aa_fun1431113780TP_ind(scratc1912101604_d_Sep(X),aa_TPT43085870d_bool(aTP_Lamm_bm,Xa))) # label(fact_def__setminus) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 113 (all X all Xa scratc98318613eplSep(X,Xa) = aa_TPT494704832TP_ind(scratc623348185d_repl,aa_fun1431113780TP_ind(scratc1912101604_d_Sep(X),Xa))) # label(fact_def__d__ReplSep) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 114 (all X all Xa aa_fun1431113780TP_ind(scratc1912101604_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc2064173607bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc2064173615bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc623348185d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bn(X),Xa))),scratc1877881023ptyset)) # label(fact_def__d__Sep) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 115 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc95837927munion,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc430372037_union,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc623348185d_repl,X),Xa))) # label(fact_def__famunion) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 116 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1089695026nunion(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc430372037_union,aa_TPTP_ind_TPTP_ind(scratc1736505589_UPair(X),Xa))) # label(fact_def__binunion) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 117 (all X aa_TPTP_ind_TPTP_ind(scratc1761123337d_Sing,X) = aa_TPTP_ind_TPTP_ind(scratc1736505589_UPair(X),X)) # label(fact_def__d__Sing) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 118 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1736505589_UPair(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc623348185d_repl,aa_TPTP_ind_TPTP_ind(scratc2070593819_power,aa_TPTP_ind_TPTP_ind(scratc2070593819_power,scratc1877881023ptyset))),aa_TPT1424761345TP_ind(aTP_Lamm_bo(X),Xa))) # label(fact_def__d__UPair) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 119 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc329909865nd_nIn,X),Xa)) <-> -pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X),Xa)))) # label(fact_def__nIn) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 120 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc2064173607bnd_if(X,Xa),Xb) = scratc258114686nd_eps(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bp(X),Xa),Xb))) # label(fact_def__if) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 121 (all X (pp(aa_TPTP_ind_bool(scratc61257906closed,X)) <-> pp(aa_TPTP_ind_bool(scratc380812641closed,X)) & pp(aa_TPTP_ind_bool(scratc545545655closed,X)) & pp(aa_TPTP_ind_bool(scratc221476437closed,X)))) # label(fact_def__d__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 122 (all X (pp(aa_TPTP_ind_bool(scratc221476437closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X1),X)) -> (all X2 ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X3),X1)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,aa_TPTP_ind_TPTP_ind(X2,X3)),X))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc623348185d_repl,X1),X2)),X))))))))) # label(fact_def__d__Repl__closed) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 123 (all X (pp(aa_TPTP_ind_bool(scratc545545655closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,aa_TPTP_ind_TPTP_ind(scratc2070593819_power,X1)),X))))))) # label(fact_def__d__Power__closed) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 124 (all X (pp(aa_TPTP_ind_bool(scratc380812641closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,aa_TPTP_ind_TPTP_ind(scratc430372037_union,X1)),X))))))) # label(fact_def__d__Union__closed) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 125 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1859474219d_Subq,X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X2),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X2),Xa))))))) # label(fact_def__d__Subq) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 126 (all X all Xa (pp(aa_fun171081125l_bool(scratc589283822all_of(X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (scratc893413803_is_of(X2,X) -> pp(aa_TPTP_ind_bool(Xa,X2))))))) # label(fact_def__all__of) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 127 (all X all Xa (scratc893413803_is_of(X,Xa) <-> pp(aa_TPTP_ind_bool(Xa,X)))) # label(fact_def__is__of) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 128 (all X0 pp(aa_fun171081125l_bool(scratc589283822all_of(aa_TPT43085870d_bool(aTP_Lamm_eb,X0)),aa_TPT43085870d_bool(aTP_Lamm_ed,X0)))) # label(fact_isseti) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 129 (all X0 all X12 pp(aa_fun171081125l_bool(scratc589283822all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_ee(X0),X12)))) # label(fact_estie) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 130 (all X0 all X12 pp(aa_fun171081125l_bool(scratc589283822all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_ef(X0),X12)))) # label(fact_estii) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 131 (all X0 all X12 scratc893413803_is_of(aa_fun1431113780TP_ind(scratc1912101604_d_Sep(X0),X12),aa_TPT43085870d_bool(aTP_Lamm_eb,X0))) # label(fact_setof__p) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 132 (all X0 all X12 pp(aa_fun171081125l_bool(scratc589283822all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_eh(X0),X12)))) # label(fact_secondis1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 133 (all X0 all X12 pp(aa_fun171081125l_bool(scratc589283822all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_ej(X0),X12)))) # label(fact_firstis1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 134 (all X0 all X12 pp(aa_fun171081125l_bool(scratc589283822all_of(aa_TPT43085870d_bool(aTP_Lamm_ek(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_el(X0),X12)))) # label(fact_pairis1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 135 (all X0 all X12 pp(aa_fun171081125l_bool(scratc589283822all_of(aa_TPT43085870d_bool(aTP_Lamm_ek(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_em(X0),X12)))) # label(fact_second__p) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 136 (all X0 all X12 pp(aa_fun171081125l_bool(scratc589283822all_of(aa_TPT43085870d_bool(aTP_Lamm_ek(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_en(X0),X12)))) # label(fact_first__p) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 137 (all X0 all X12 pp(aa_fun171081125l_bool(scratc589283822all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_ep(X0),X12)))) # label(fact_e__pair__p) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 138 (all X0 all X12 pp(aa_fun171081125l_bool(scratc589283822all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_eq(X0),X12)))) # label(fact_otax2) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 139 (all X0 all X12 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc879445149ective(aa_fun1431113780TP_ind(scratc1912101604_d_Sep(X0),X12)),X0),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1842019211_Sigma,aa_fun1431113780TP_ind(scratc1912101604_d_Sep(X0),X12)),scratc470297856d_e_in(X0,X12))))) # label(fact_otax1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 140 (all X0 all X12 pp(aa_fun171081125l_bool(scratc589283822all_of(aa_fun1584354236d_bool(aTP_Lamm_er(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_es(X0),X12)))) # label(fact_e__inp) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 141 (all X0 all X12 pp(aa_fun171081125l_bool(scratc589283822all_of(aa_fun1584354236d_bool(aTP_Lamm_er(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_et(X0),X12)))) # label(fact_e__in__p) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 142 (all X0 all X12 pp(aa_fun171081125l_bool(scratc589283822all_of(aa_TPT43085870d_bool(aTP_Lamm_eu(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_ex(X0),X12)))) # label(fact_e__fisi) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 143 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc340598524nd_one(X0),X12)) -> pp(aa_TPTP_ind_bool(X12,scratc291029493nd_ind(X0,X12))))) # label(fact_oneax) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 144 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc340598524nd_one(X0),X12)) -> scratc893413803_is_of(scratc291029493nd_ind(X0,X12),aa_TPT43085870d_bool(aTP_Lamm_aj,X0)))) # label(fact_ind__p) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 145 (all X0 all X12 pp(aa_fun171081125l_bool(scratc589283822all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_ez(X0),X12)))) # label(fact_e__isp) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 146 (all X0 pp(aa_fun171081125l_bool(scratc589283822all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_fa,X0)))) # label(fact_refis) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 147 (all X0 (scratc406100180nd_wel(X0) -> pp(X0))) # label(fact_l__et) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 148 (all X0 all X12 all X22 all X32 (pp(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc2064173607bnd_if(X0,X22),X32))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X12),X22))))) # label(fact_k__If__In__then__E) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 149 (all X0 all X12 all X22 ((pp(X0) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X12),X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,aa_TPTP_ind_TPTP_ind(scratc2064173607bnd_if(X0,X12),scratc1877881023ptyset)),aa_TPTP_ind_TPTP_ind(scratc2064173607bnd_if(X0,X22),aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,scratc1877881023ptyset)))))) # label(fact_k__If__In__01) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 150 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X33),X0)) -> aa_TPTP_ind_TPTP_ind(X12,X33) = aa_TPTP_ind_TPTP_ind(X22,X33)))) -> aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1842019211_Sigma,X0),X12) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1842019211_Sigma,X0),X22))) # label(fact_xi__ext) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 151 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1476577235d_d_Pi,X0),X12))) -> (all X32 (gg_TPTP_ind(X32) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X32),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1476577235d_d_Pi,X0),X12))) -> ((all X42 (gg_TPTP_ind(X42) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X42),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2063648825bnd_ap,X22),X42) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2063648825bnd_ap,X32),X42)))) -> X22 = X32))))))) # label(fact_k__Pi__ext) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 152 (all X0 all X12 all X22 all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1476577235d_d_Pi,X0),X12))) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X32),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2063648825bnd_ap,X22),X32)),aa_TPTP_ind_TPTP_ind(X12,X32)))))) # label(fact_ap__Pi) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 153 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X33),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,aa_TPTP_ind_TPTP_ind(X22,X33)),aa_TPTP_ind_TPTP_ind(X12,X33)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1842019211_Sigma,X0),X22)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1476577235d_d_Pi,X0),X12))))) # label(fact_lam__Pi) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 154 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X22),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2063648825bnd_ap,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1842019211_Sigma,X0),X12)),X22) = aa_TPTP_ind_TPTP_ind(X12,X22))) # label(fact_beta) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 155 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1842019211_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,aa_TPTP_ind_TPTP_ind(scratc51624010_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc51624009_proj0,X22)))))) # label(fact_proj1__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 156 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1842019211_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,aa_TPTP_ind_TPTP_ind(scratc51624009_proj0,X22)),X0)))) # label(fact_proj0__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 157 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1842019211_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1176152228d_pair,aa_TPTP_ind_TPTP_ind(scratc51624009_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc51624010_proj1,X22)) = X22))) # label(fact_proj__Sigma__eta) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 158 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1842019211_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1176152228d_pair,aa_TPTP_ind_TPTP_ind(scratc51624009_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc51624010_proj1,X22)) = X22 & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,aa_TPTP_ind_TPTP_ind(scratc51624009_proj0,X22)),X0)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,aa_TPTP_ind_TPTP_ind(scratc51624010_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc51624009_proj0,X22))))))) # label(fact_k__Sigma__eta__proj0__proj1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 159 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X22),X0)) -> (all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X32),aa_TPTP_ind_TPTP_ind(X12,X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1176152228d_pair,X22),X32)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1842019211_Sigma,X0),X12))))))) # label(fact_pair__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 160 (all X0 all X12 (gg_TPTP_ind(X12) -> aa_TPTP_ind_TPTP_ind(scratc51624010_proj1,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1176152228d_pair,X0),X12)) = X12)) # label(fact_proj1__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 161 (all X0 all X12 (gg_TPTP_ind(X0) -> aa_TPTP_ind_TPTP_ind(scratc51624009_proj0,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1176152228d_pair,X0),X12)) = X0)) # label(fact_proj0__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 162 (all X0 (pp(aa_TPTP_ind_bool(scratc780058009_nat_p,X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X0),scratc1368762871_omega)))) # label(fact_nat__p__omega) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 163 (all X0 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X0),scratc1368762871_omega)) -> pp(aa_TPTP_ind_bool(scratc780058009_nat_p,X0)))) # label(fact_omega__nat__p) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 164 (all X0 (gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(scratc780058009_nat_p,X0)) -> X0 = scratc1877881023ptyset | (exists X13 (gg_TPTP_ind(X13) & pp(aa_TPTP_ind_bool(scratc780058009_nat_p,X13)) & X0 = aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,X13)))))) # label(fact_nat__inv) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 165 (all X0 (pp(aa_TPTP_ind_bool(X0,scratc1877881023ptyset)) -> ((all X13 (gg_TPTP_ind(X13) -> (pp(aa_TPTP_ind_bool(scratc780058009_nat_p,X13)) -> (pp(aa_TPTP_ind_bool(X0,X13)) -> pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,X13))))))) -> (all X12 (pp(aa_TPTP_ind_bool(scratc780058009_nat_p,X12)) -> pp(aa_TPTP_ind_bool(X0,X12))))))) # label(fact_nat__ind) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 166 (all X0 (pp(aa_TPTP_ind_bool(scratc780058009_nat_p,X0)) -> pp(aa_TPTP_ind_bool(scratc780058009_nat_p,aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,X0))))) # label(fact_nat__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 167 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,X0) = aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,X12) -> X0 = X12))) # label(fact_ordsucc__inj) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 168 (all X0 aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,X0) != scratc1877881023ptyset) # label(fact_neq__ordsucc__0) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 169 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X22),aa_fun1431113780TP_ind(scratc1912101604_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(X12,X22)))) # label(fact_k__SepE2) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 170 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X22),aa_fun1431113780TP_ind(scratc1912101604_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X22),X0)))) # label(fact_k__SepE1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 171 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X22),X0)) -> (pp(aa_TPTP_ind_bool(X12,X22)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X22),aa_fun1431113780TP_ind(scratc1912101604_d_Sep(X0),X12)))))) # label(fact_k__SepI) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 172 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc2070593819_power,X0)))) # label(fact_k__Self__In__Power) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 173 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1859474219d_Subq,X12),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc2070593819_power,X0))))) # label(fact_k__PowerI) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 174 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc2070593819_power,X0))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1859474219d_Subq,X12),X0)))) # label(fact_k__PowerE) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 175 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> aa_TPTP_ind_TPTP_ind(scratc2064173607bnd_if(X0,X12),X22) = X12 | aa_TPTP_ind_TPTP_ind(scratc2064173607bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__or) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 176 (all X0 all X12 all X22 (gg_TPTP_ind(X12) -> (pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc2064173607bnd_if(X0,X12),X22) = X12))) # label(fact_if__i__1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 177 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (-pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc2064173607bnd_if(X0,X12),X22) = X22))) # label(fact_if__i__0) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 178 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> pp(X0) & aa_TPTP_ind_TPTP_ind(scratc2064173607bnd_if(X0,X12),X22) = X12 | -pp(X0) & aa_TPTP_ind_TPTP_ind(scratc2064173607bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__correct) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 179 (all X0 pp(aa_TPTP_ind_bool(scratc61257906closed,aa_TPTP_ind_TPTP_ind(scratc1213114791univof,X0)))) # label(fact_k__UnivOf__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 180 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc1213114791univof,X0)))) # label(fact_k__UnivOf__In) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 181 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc623348185d_repl,X0),X12))) <-> (exists X3 (gg_TPTP_ind(X3) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X3),X0)) & X22 = aa_TPTP_ind_TPTP_ind(X12,X3)))))) # label(fact_k__ReplEq) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 182 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc2070593819_power,X0))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1859474219d_Subq,X12),X0)))) # label(fact_k__PowerEq) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 183 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc430372037_union,X0))) <-> (exists X2 (gg_TPTP_ind(X2) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X12),X2)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X2),X0)))))) # label(fact_k__UnionEq) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 184 -(exists X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,X0),scratc1877881023ptyset))) # label(fact_k__EmptyAx) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 185 (all X0 ((all X13 (gg_TPTP_ind(X13) -> ((all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_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].
% 1.07/1.40 186 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1859474219d_Subq,X0),X12)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1859474219d_Subq,X12),X0)) -> X0 = X12)))) # label(fact_set__ext) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 187 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dq,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc332009038nd_nis,Uu),scratc1745282413nd_n_1)) -> pp(aa_fun171081125l_bool(scratc443769272n_some,aa_TPT43085870d_bool(aTP_Lamm_af,Uu)))))) # label(fact_ATP_Olambda__1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 188 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dp,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc332009038nd_nis,Uu),scratc1745282413nd_n_1)) -> pp(aa_fun171081125l_bool(scratc1569119138_n_one,aa_TPT43085870d_bool(aTP_Lamm_af,Uu)))))) # label(fact_ATP_Olambda__2) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 189 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dm,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(Uu),scratc1745282413nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,Uu))))) # label(fact_ATP_Olambda__3) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 190 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dj,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(scratc1745282413nd_n_1),Uu)),aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,Uu))))) # label(fact_ATP_Olambda__4) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 191 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_do,Uu)) <-> pp(aa_fun171081125l_bool(scratc340598524nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1476577235d_d_Pi,scratc331484247nd_nat),aTP_Lamm_ac)),aa_TPT43085870d_bool(aTP_Lamm_dn,Uu))))) # label(fact_ATP_Olambda__5) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 192 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dw,Uu)) <-> (pp(aa_TPTP_ind_bool(scratc66740741_cond1,Uu)) -> (pp(aa_TPTP_ind_bool(scratc66740742_cond2,Uu)) -> pp(aa_fun171081125l_bool(scratc589283822all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dv,Uu))))))) # label(fact_ATP_Olambda__6) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 193 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dg,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(Uu),scratc1745282413nd_n_1))))) # label(fact_ATP_Olambda__7) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 194 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dd,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(scratc1745282413nd_n_1),Uu))))) # label(fact_ATP_Olambda__8) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 195 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dr,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc332009038nd_nis,aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__9) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 196 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ea,Uu)) <-> scratc893413803_is_of(aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,Uu),aTP_Lamm_a))) # label(fact_ATP_Olambda__10) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 197 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dz,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc332009038nd_nis,aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,Uu)),scratc1745282413nd_n_1)))) # label(fact_ATP_Olambda__11) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 198 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_du,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,Uu),aa_TPTP_ind_TPTP_ind(scratc2070593819_power,scratc331484247nd_nat))))) # label(fact_ATP_Olambda__12) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 199 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_a,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,Uu),scratc331484247nd_nat)))) # label(fact_ATP_Olambda__13) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 200 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dy,Uu)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dx,Uu))))) # label(fact_ATP_Olambda__14) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 201 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dt,Uu)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ds,Uu))))) # label(fact_ATP_Olambda__15) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 202 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dl,Uu)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dk,Uu))))) # label(fact_ATP_Olambda__16) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 203 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_di,Uu)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dh,Uu))))) # label(fact_ATP_Olambda__17) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 204 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_df,Uu)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_de,Uu))))) # label(fact_ATP_Olambda__18) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 205 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dc,Uu)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_db,Uu))))) # label(fact_ATP_Olambda__19) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 206 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_da,Uu)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cz,Uu))))) # label(fact_ATP_Olambda__20) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 207 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cx,Uu)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cw,Uu))))) # label(fact_ATP_Olambda__21) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 208 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cv,Uu)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cu,Uu))))) # label(fact_ATP_Olambda__22) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 209 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ct,Uu)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cs,Uu))))) # label(fact_ATP_Olambda__23) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 210 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cq,Uu)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cp,Uu))))) # label(fact_ATP_Olambda__24) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 211 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cn,Uu)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cm,Uu))))) # label(fact_ATP_Olambda__25) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 212 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cl,Uu)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ck,Uu))))) # label(fact_ATP_Olambda__26) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 213 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ch,Uu)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cg,Uu))))) # label(fact_ATP_Olambda__27) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 214 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cf,Uu)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ce,Uu))))) # label(fact_ATP_Olambda__28) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 215 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cd,Uu)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cc,Uu))))) # label(fact_ATP_Olambda__29) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 216 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cb,Uu)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ca,Uu))))) # label(fact_ATP_Olambda__30) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 217 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bz,Uu)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_by,Uu))))) # label(fact_ATP_Olambda__31) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 218 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bw,Uu))))) # label(fact_ATP_Olambda__32) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 219 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bv,Uu)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bu,Uu))))) # label(fact_ATP_Olambda__33) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 220 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bt,Uu)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bs,Uu))))) # label(fact_ATP_Olambda__34) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 221 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_br,Uu)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bq,Uu))))) # label(fact_ATP_Olambda__35) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 222 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ab,Uu)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,Uu))))) # label(fact_ATP_Olambda__36) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 223 (all Uu aa_TPT494704832TP_ind(aTP_Lamm_bk,Uu) = aa_TPT494704832TP_ind(scratc623348185d_repl,aa_TPTP_ind_TPTP_ind(scratc1005980568tminus(Uu),aa_TPTP_ind_TPTP_ind(scratc1761123337d_Sing,scratc1877881023ptyset)))) # label(fact_ATP_Olambda__37) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 224 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_ah,Uu)) <-> Uu != scratc1877881023ptyset))) # label(fact_ATP_Olambda__38) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 225 (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(scratc438747366d_Inj1,X2) = Uu))))) # label(fact_ATP_Olambda__39) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 226 (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(scratc438747365d_Inj0,X2) = Uu))))) # label(fact_ATP_Olambda__40) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 227 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cc,Uu),Uua)) <-> scratc976469128_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1835086145_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc290701503nd_iii,Uu),Uua)))) # label(fact_ATP_Olambda__41) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 228 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ca,Uu),Uua)) <-> pp(scratc340860870nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1835086145_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc290701503nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__42) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 229 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_by,Uu),Uua)) <-> pp(scratc257261835nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1835086145_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc290701503nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__43) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 230 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ck,Uu),Uua)) <-> scratc976469128_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc443769272n_some,aa_TPT43085870d_bool(aTP_Lamm_ci(Uu),Uua)),aa_fun171081125l_bool(scratc443769272n_some,aa_TPT43085870d_bool(aTP_Lamm_cj(Uu),Uua))))) # label(fact_ATP_Olambda__44) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 231 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cg,Uu),Uua)) <-> pp(scratc340860870nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc443769272n_some,aa_TPT43085870d_bool(scratc1012294322ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc443769272n_some,aa_TPT43085870d_bool(scratc1012294322ffprop(Uua),Uu)))))) # label(fact_ATP_Olambda__45) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 232 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ce,Uu),Uua)) <-> pp(scratc257261835nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc443769272n_some,aa_TPT43085870d_bool(scratc1012294322ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc443769272n_some,aa_TPT43085870d_bool(scratc1012294322ffprop(Uua),Uu)))))) # label(fact_ATP_Olambda__46) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 233 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fa,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc470297861d_e_is(Uu),Uua),Uua)))) # label(fact_ATP_Olambda__47) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 234 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dn,Uu),Uua)) <-> pp(scratc2028353053_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2063648825bnd_ap,Uua),scratc1745282413nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,Uu)),aa_fun171081125l_bool(scratc1453326877_n_all,aa_TPT43085870d_bool(aTP_Lamm_ae,Uua)))))) # label(fact_ATP_Olambda__48) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 235 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dx,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__49) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 236 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dh,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__50) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 237 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dk,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__51) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 238 (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(scratc2136441870d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2063648825bnd_ap,Uu),aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2063648825bnd_ap,Uu),Uua)))))) # label(fact_ATP_Olambda__52) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 239 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ds,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc332009038nd_nis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc332009038nd_nis,aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,Uua)))))) # label(fact_ATP_Olambda__53) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 240 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ag,Uu),Uua)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc290963906nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441865d_n_in,Uua),Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441865d_n_in,aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,Uua)),Uu))))) # label(fact_ATP_Olambda__54) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 241 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cw,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(Uua),Uu))))) # label(fact_ATP_Olambda__55) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 242 (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(scratc1835086145_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc290701503nd_iii,Uua),Uu))))) # label(fact_ATP_Olambda__56) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 243 (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(scratc1966099561moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1832115949lessis,Uua),Uu))))) # label(fact_ATP_Olambda__57) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 244 (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(scratc1832115949lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1966099561moreis,Uua),Uu))))) # label(fact_ATP_Olambda__58) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 245 (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(scratc290701503nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1835086145_29_ii,Uua),Uu))))) # label(fact_ATP_Olambda__59) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 246 (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(scratc1966099561moreis,Uu),Uua)) -> pp(scratc2135818233_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc290701503nd_iii,Uu),Uua)))))) # label(fact_ATP_Olambda__60) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 247 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bh(Uu),Uua) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc623348185d_repl,aa_TPTP_ind_TPTP_ind(Uu,Uua)),aa_TPT1424761345TP_ind(scratc1176152228d_pair,Uua))) # label(fact_ATP_Olambda__61) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 248 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ed,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aa_TPT43085870d_bool(aTP_Lamm_eb,Uu)),aa_TPT43085870d_bool(aTP_Lamm_ec(Uu),Uua))))) # label(fact_ATP_Olambda__62) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 249 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_db,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,Uu)),Uua))))) # label(fact_ATP_Olambda__63) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 250 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_de,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,Uua)))))) # label(fact_ATP_Olambda__64) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 251 (all Uu all Uua aa_fun277296641TP_ind(aa_TPT494704832TP_ind(aTP_Lamm_bl,Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1089695026nunion(aa_TPTP_ind_TPTP_ind(scratc1761123337d_Sing,scratc1877881023ptyset)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc623348185d_repl,Uu),Uua))) # label(fact_ATP_Olambda__65) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 252 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cu,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc332009038nd_nis,Uua),aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__66) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 253 (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(scratc2136441870d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,Uua))))) # label(fact_ATP_Olambda__67) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 254 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eb,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,Uua),aa_TPTP_ind_TPTP_ind(scratc2070593819_power,Uu))))) # label(fact_ATP_Olambda__68) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 255 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dv,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441865d_n_in,Uua),Uu)))) # label(fact_ATP_Olambda__69) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 256 (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(scratc329909865nd_nIn,Uua),Uu)))) # label(fact_ATP_Olambda__70) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 257 (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(scratc2064173615bnd_in,Uua),Uu)))) # label(fact_ATP_Olambda__71) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 258 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cz,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cy(Uu),Uua))))) # label(fact_ATP_Olambda__72) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 259 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cs,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cr(Uu),Uua))))) # label(fact_ATP_Olambda__73) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 260 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cp,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_co(Uu),Uua))))) # label(fact_ATP_Olambda__74) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 261 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cm,Uu),Uua)) <-> pp(scratc530322608_amone(scratc331484247nd_nat,aa_TPT43085870d_bool(aTP_Lamm_ci(Uu),Uua))))) # label(fact_ATP_Olambda__75) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 262 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_ad(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1819393401rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2063648825bnd_ap,Uu),Uua))) # label(fact_ATP_Olambda__76) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 263 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_be(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc430372037_union,aa_TPTP_ind_TPTP_ind(Uu,Uua))) # label(fact_ATP_Olambda__77) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 264 (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(scratc1176152228d_pair,Uu),X3)))))) # label(fact_ATP_Olambda__78) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 265 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_el(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc470297861d_e_is(aa_TPTP_ind_TPTP_ind(scratc1453316495etprod(Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc709411956d_pair(Uu,Uua),aa_TPTP_ind_TPTP_ind(scratc983424134_first(Uu,Uua),Uub)),aa_TPTP_ind_TPTP_ind(scratc503987934second(Uu,Uua),Uub))),Uub)))) # label(fact_ATP_Olambda__79) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 266 (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(scratc2064173607bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,scratc1877881023ptyset),Uub),Uu),Uua)) # label(fact_ATP_Olambda__80) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 267 (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(scratc2064173607bnd_if(aa_TPTP_ind_bool(Uua,Uub),Uub),scratc258114686nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bb(Uu),Uua)))) # label(fact_ATP_Olambda__81) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 268 (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(scratc1329056301d_esti(Uu),Uub),Uua)))) # label(fact_ATP_Olambda__82) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 269 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ee(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1329056301d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc1912101604_d_Sep(Uu),Uua))) -> pp(aa_TPTP_ind_bool(Uua,Uub))))) # label(fact_ATP_Olambda__83) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 270 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ec(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc114015096d_incl(Uu),Uua),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc114015096d_incl(Uu),Uub),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc470297861d_e_is(aa_TPTP_ind_TPTP_ind(scratc2070593819_power,Uu)),Uua),Uub)))))) # label(fact_ATP_Olambda__84) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 271 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_em(Uu),Uua),Uub)) <-> scratc893413803_is_of(aa_TPTP_ind_TPTP_ind(scratc503987934second(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)))) # label(fact_ATP_Olambda__85) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 272 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_en(Uu),Uua),Uub)) <-> scratc893413803_is_of(aa_TPTP_ind_TPTP_ind(scratc983424134_first(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)))) # label(fact_ATP_Olambda__86) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 273 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_et(Uu),Uua),Uub)) <-> scratc893413803_is_of(aa_TPTP_ind_TPTP_ind(scratc470297856d_e_in(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)))) # label(fact_ATP_Olambda__87) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 274 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ex(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aa_TPT43085870d_bool(aTP_Lamm_eu(Uu),Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ew(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__88) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 275 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_co(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(Uu),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,Uua),Uub))))) # label(fact_ATP_Olambda__89) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 276 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cy(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__90) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 277 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cr(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc332009038nd_nis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc332009038nd_nis,aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(Uu),Uub)))))) # label(fact_ATP_Olambda__91) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 278 (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(scratc2064173615bnd_in,Uub),Uu)) & pp(aa_TPTP_ind_bool(Uua,Uub)))) # label(fact_ATP_Olambda__92) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 279 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_eq(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc940782065_image(aa_fun1431113780TP_ind(scratc1912101604_d_Sep(Uu),Uua),Uu),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1842019211_Sigma,aa_fun1431113780TP_ind(scratc1912101604_d_Sep(Uu),Uua)),scratc470297856d_e_in(Uu,Uua))),Uub))))) # label(fact_ATP_Olambda__93) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 280 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ef(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1329056301d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc1912101604_d_Sep(Uu),Uua)))))) # label(fact_ATP_Olambda__94) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 281 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ez(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_ey(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__95) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 282 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bd(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bc(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__96) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 283 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ep(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_eo(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__97) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 284 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ej(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ei(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__98) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 285 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eh(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc589283822all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_eg(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__99) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 286 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eu(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,Uub),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1476577235d_d_Pi,Uu),aTP_Lamm_ai(Uua)))))) # label(fact_ATP_Olambda__100) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 287 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ci(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(Uua),Uub))))) # label(fact_ATP_Olambda__101) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 288 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cj(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2136441870d_n_is,Uua),aa_TPTP_ind_TPTP_ind(scratc2136901056d_n_pl(Uu),Uub))))) # label(fact_ATP_Olambda__102) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 289 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ek(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,Uub),aa_TPTP_ind_TPTP_ind(scratc1453316495etprod(Uu),Uua))))) # label(fact_ATP_Olambda__103) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 290 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_er(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,Uub),aa_fun1431113780TP_ind(scratc1912101604_d_Sep(Uu),Uua))))) # label(fact_ATP_Olambda__104) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 291 (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(scratc2063648825bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2063648825bnd_ap,Uu),Uub))) # label(fact_ATP_Olambda__105) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 292 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_es(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(Uua,aa_TPTP_ind_TPTP_ind(scratc470297856d_e_in(Uu,Uua),Uub))))) # label(fact_ATP_Olambda__106) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 293 (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(scratc2064173615bnd_in,X3),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064173615bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2063648825bnd_ap,Uub),X3)),aa_TPTP_ind_TPTP_ind(Uua,X3)))))))) # label(fact_ATP_Olambda__107) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 294 (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(scratc2064173607bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc940782065_image(Uu,Uua),Uub),Uuc),aa_TPTP_ind_TPTP_ind(scratc1485894452d_soft(Uu,Uua,Uub),Uuc)),scratc1877881023ptyset)) # label(fact_ATP_Olambda__108) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 295 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ei(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc470297861d_e_is(Uu),aa_TPTP_ind_TPTP_ind(scratc983424134_first(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc709411956d_pair(Uu,Uua),Uub),Uuc))),Uub)))) # label(fact_ATP_Olambda__109) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 296 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_eg(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc470297861d_e_is(Uua),aa_TPTP_ind_TPTP_ind(scratc503987934second(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc709411956d_pair(Uu,Uua),Uub),Uuc))),Uuc)))) # label(fact_ATP_Olambda__110) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 297 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ev(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc470297861d_e_is(Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2063648825bnd_ap,Uua),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2063648825bnd_ap,Uub),Uuc))))) # label(fact_ATP_Olambda__111) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 298 (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(scratc1329056301d_esti(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2063648825bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__112) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 299 (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(scratc470297861d_e_is(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2063648825bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__113) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 300 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_eo(Uu),Uua),Uub),Uuc)) <-> scratc893413803_is_of(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc709411956d_pair(Uu,Uua),Uub),Uuc),aa_TPT43085870d_bool(aTP_Lamm_ek(Uu),Uua)))) # label(fact_ATP_Olambda__114) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 301 (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(scratc2004534528d_l_ec(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1329056301d_esti(Uu),Uuc),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1329056301d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__115) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 302 (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(scratc290963906nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1329056301d_esti(Uu),Uuc),Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1329056301d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__116) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 303 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ew(Uu),Uua),Uub),Uuc)) <-> (pp(aa_fun171081125l_bool(scratc589283822all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ev(Uua),Uub),Uuc))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc470297861d_e_is(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1476577235d_d_Pi,Uu),aTP_Lamm_ai(Uua))),Uub),Uuc))))) # label(fact_ATP_Olambda__117) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 304 (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__118) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 305 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_ey(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc470297861d_e_is(Uu),Uub),Uuc)) -> pp(aa_TPTP_ind_bool(Uua,Uuc)))))) # label(fact_ATP_Olambda__119) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 306 (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(scratc470297861d_e_is(Uu),Uub),Uuc)))))) # label(fact_ATP_Olambda__120) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 307 (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(scratc224806263nd_all(Uu),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_az(Uu),Uua),Uub),Uuc))))) # label(fact_ATP_Olambda__121) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 308 (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(scratc1847428278l_some(Uua),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aq(Uu),Uub),Uuc))))) # label(fact_ATP_Olambda__122) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 309 (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(scratc290963906nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc470297861d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2063648825bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2063648825bnd_ap,Uub),Uud))),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc470297861d_e_is(Uu),Uuc),Uud))))) # label(fact_ATP_Olambda__123) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 310 (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(scratc470297861d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2063648825bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2063648825bnd_ap,Uub),Uud)))))) # label(fact_ATP_Olambda__124) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 311 (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(scratc589283822all_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__125) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 312 (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(scratc589283822all_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__126) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 313 (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(scratc2063648825bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2063648825bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1892255651wissel(Uu,Uub),Uuc)),Uud))) # label(fact_ATP_Olambda__127) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 314 (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(scratc589283822all_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__128) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 315 (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(scratc470297861d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2063648825bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2063648825bnd_ap,Uub),Uuc)),Uue)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2063648825bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2063648825bnd_ap,Uub),Uud)),Uuf))))))) # label(fact_ATP_Olambda__129) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.42 316 (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(scratc589283822all_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__130) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.42 317 (all Uu all Uua (gg_TPTP_ind(Uu) -> aa_TPTP_ind_TPTP_ind(aTP_Lamm_ai(Uu),Uua) = Uu)) # label(fact_ATP_Olambda__131) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.42 318 (all Uu aa_TPTP_ind_TPTP_ind(aTP_Lamm_ac,Uu) = scratc331484247nd_nat) # label(fact_ATP_Olambda__132) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.42 319 (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].
% 1.07/1.42 320 (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].
% 1.07/1.42 321 (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].
% 1.07/1.42 322 (all P (gg_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.42 323 (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].
% 1.07/1.42 324 (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].
% 1.07/1.42 325 (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].
% 1.07/1.42 326 (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].
% 1.07/1.42 327 (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].
% 1.07/1.42 328 (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].
% 1.07/1.42 329 (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].
% 1.07/1.42 330 (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].
% 1.07/1.42 331 (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].
% 1.07/1.42
% 1.07/1.42 ============================== end of process non-clausal formulas ===
% 1.07/1.42
% 1.07/1.42 ============================== PROCESS INITIAL CLAUSES ===============
% 1.07/1.42
% 1.07/1.42 ============================== PREDICATE ELIMINATION =================
% 1.07/1.42 332 -gg_bool(A) | A = fTrue | A = fFalse # label(help_fFalse_1_1_T) # label(axiom). [clausify(322)].
% 1.07/1.42 333 gg_bool(undefined_bool(bool)) # label(gsy_c_HOL_Oundefined_001t__HOL__Obool) # label(axiom). [assumption].
% 1.07/1.46 334 gg_bool(scratc530322608_amone(A,B)) # label(gsy_c_Scratch__tptp__translate__42582__9795_ONUM652__thf__4__p_Obnd__amone) # label(axiom). [clausify(1)].
% 1.07/1.46 335 gg_bool(scratc2028353053_d_and(A,B)) # label(gsy_c_Scratch__tptp__translate__42582__9795_ONUM652__thf__4__p_Obnd__d__and) # label(axiom). [clausify(2)].
% 1.07/1.46 336 gg_bool(scratc2135818233_d_not(A)) # label(gsy_c_Scratch__tptp__translate__42582__9795_ONUM652__thf__4__p_Obnd__d__not) # label(axiom). [clausify(3)].
% 1.07/1.46 337 gg_bool(scratc257261835nd_ec3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__42582__9795_ONUM652__thf__4__p_Obnd__ec3) # label(axiom). [clausify(4)].
% 1.07/1.46 338 gg_bool(scratc2004534528d_l_ec(A,B)) # label(gsy_c_Scratch__tptp__translate__42582__9795_ONUM652__thf__4__p_Obnd__l__ec) # label(axiom). [clausify(8)].
% 1.07/1.46 339 gg_bool(scratc340860870nd_or3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__42582__9795_ONUM652__thf__4__p_Obnd__or3) # label(axiom). [clausify(9)].
% 1.07/1.46 340 gg_bool(aa_bool_bool(A,B)) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom). [clausify(10)].
% 1.07/1.46 341 gg_bool(aa_TPTP_ind_bool(A,B)) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom). [clausify(11)].
% 1.07/1.46 342 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)].
% 1.07/1.46 343 gg_bool(fEx_TPTP_ind(A)) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom). [clausify(16)].
% 1.07/1.46 344 gg_bool(fFalse) # label(gsy_c_fFalse) # label(axiom). [assumption].
% 1.07/1.46 345 gg_bool(fTrue) # label(gsy_c_fTrue) # label(axiom). [assumption].
% 1.07/1.46 Derived: undefined_bool(bool) = fTrue | undefined_bool(bool) = fFalse. [resolve(332,a,333,a)].
% 1.07/1.46 Derived: scratc530322608_amone(A,B) = fTrue | scratc530322608_amone(A,B) = fFalse. [resolve(332,a,334,a)].
% 1.07/1.46 Derived: scratc2028353053_d_and(A,B) = fTrue | scratc2028353053_d_and(A,B) = fFalse. [resolve(332,a,335,a)].
% 1.07/1.46 Derived: scratc2135818233_d_not(A) = fTrue | scratc2135818233_d_not(A) = fFalse. [resolve(332,a,336,a)].
% 1.07/1.46 Derived: scratc257261835nd_ec3(A,B,C) = fTrue | scratc257261835nd_ec3(A,B,C) = fFalse. [resolve(332,a,337,a)].
% 1.07/1.46 Derived: scratc2004534528d_l_ec(A,B) = fTrue | scratc2004534528d_l_ec(A,B) = fFalse. [resolve(332,a,338,a)].
% 1.07/1.46 Derived: scratc340860870nd_or3(A,B,C) = fTrue | scratc340860870nd_or3(A,B,C) = fFalse. [resolve(332,a,339,a)].
% 1.07/1.46 Derived: aa_bool_bool(A,B) = fTrue | aa_bool_bool(A,B) = fFalse. [resolve(332,a,340,a)].
% 1.07/1.46 Derived: aa_TPTP_ind_bool(A,B) = fTrue | aa_TPTP_ind_bool(A,B) = fFalse. [resolve(332,a,341,a)].
% 1.07/1.46 Derived: aa_fun171081125l_bool(A,B) = fTrue | aa_fun171081125l_bool(A,B) = fFalse. [resolve(332,a,342,a)].
% 1.07/1.46 Derived: fEx_TPTP_ind(A) = fTrue | fEx_TPTP_ind(A) = fFalse. [resolve(332,a,343,a)].
% 1.07/1.46 Derived: fFalse = fTrue | fFalse = fFalse. [resolve(332,a,344,a)].
% 1.07/1.46 Derived: fTrue = fTrue | fTrue = fFalse. [resolve(332,a,345,a)].
% 1.07/1.46 346 scratc251985670d_r_ec(A,B) | pp(A) # label(fact_def__r__ec) # label(axiom). [clausify(59)].
% 1.07/1.46 347 -scratc251985670d_r_ec(A,B) | -pp(A) | pp(scratc2135818233_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(59)].
% 1.07/1.46 348 scratc251985670d_r_ec(A,B) | -pp(scratc2135818233_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(59)].
% 1.07/1.46 349 scratc775010855_l_iff(A,B) | -pp(scratc2028353053_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc290963906nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc290963906nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(91)].
% 1.07/1.46 350 -scratc775010855_l_iff(A,B) | pp(scratc2028353053_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc290963906nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc290963906nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(91)].
% 1.07/1.46 351 scratc535748203d_orec(A,B) | -pp(scratc2028353053_d_and(aa_bool_bool(scratc2005190533d_l_or(A),B),scratc2004534528d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(92)].
% 1.07/1.46 352 -scratc535748203d_orec(A,B) | pp(scratc2028353053_d_and(aa_bool_bool(scratc2005190533d_l_or(A),B),scratc2004534528d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(92)].
% 1.52/1.81 353 scratc406100180nd_wel(A) | -pp(scratc2135818233_d_not(scratc2135818233_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(97)].
% 1.52/1.81 354 -scratc406100180nd_wel(A) | pp(scratc2135818233_d_not(scratc2135818233_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(97)].
% 1.52/1.81 355 -scratc406100180nd_wel(A) | pp(A) # label(fact_l__et) # label(axiom). [clausify(147)].
% 1.52/1.81 Derived: pp(A) | -pp(scratc2135818233_d_not(scratc2135818233_d_not(A))). [resolve(355,a,353,a)].
% 1.52/1.81
% 1.52/1.81 ============================== end predicate elimination =============
% 1.52/1.81
% 1.52/1.81 Auto_denials: (non-Horn, no changes).
% 1.52/1.81
% 1.52/1.81 Term ordering decisions:
% 1.52/1.81 Function symbol KB weights: scratc2064173615bnd_in=1. aTP_Lamm_a=1. scratc2136441870d_n_is=1. scratc1819393401rdsucc=1. scratc2063648825bnd_ap=1. aTP_Lamm_aj=1. scratc1877881023ptyset=1. scratc1842019211_Sigma=1. scratc332009038nd_nis=1. scratc1745282413nd_n_1=1. fFalse=1. scratc1476577235d_d_Pi=1. scratc2070593819_power=1. scratc331484247nd_nat=1. scratc443769272n_some=1. scratc780058009_nat_p=1. scratc290701503nd_iii=1. scratc290963906nd_imp=1. scratc623348185d_repl=1. fTrue=1. scratc1835086145_29_ii=1. scratc1176152228d_pair=1. scratc1859474219d_Subq=1. scratc221476437closed=1. scratc430372037_union=1. scratc51624009_proj0=1. aTP_Lamm_af=1. scratc1966099561moreis=1. scratc2136441865d_n_in=1. scratc51624010_proj1=1. scratc1453326877_n_all=1. aTP_Lamm_ac=1. aTP_Lamm_ae=1. aTP_Lamm_eb=1. scratc1832115949lessis=1. scratc380812641closed=1. scratc545545655closed=1. aTP_Lamm_aa=1. aTP_Lamm_bq=1. aTP_Lamm_bs=1. aTP_Lamm_bu=1. aTP_Lamm_bw=1. aTP_Lamm_ds=1. aTP_Lamm_dw=1. aTP_Lamm_dx=1. scratc1368762871_omega=1. scratc260234035_prop2=1. scratc438747366d_Inj1=1. scratc61257906closed=1. aTP_Lamm_ag=1. aTP_Lamm_bg=1. aTP_Lamm_bi=1. aTP_Lamm_bj=1. aTP_Lamm_by=1. aTP_Lamm_ca=1. aTP_Lamm_cc=1. aTP_Lamm_ce=1. aTP_Lamm_cg=1. aTP_Lamm_ck=1. aTP_Lamm_cm=1. aTP_Lamm_cp=1. aTP_Lamm_cs=1. aTP_Lamm_cu=1. aTP_Lamm_cw=1. aTP_Lamm_cz=1. aTP_Lamm_db=1. aTP_Lamm_de=1. aTP_Lamm_dh=1. aTP_Lamm_dk=1. aTP_Lamm_dn=1. aTP_Lamm_dp=1. aTP_Lamm_dq=1. aTP_Lamm_dv=1. fconj=1. fimplies=1. scratc1761123337d_Sing=1. scratc260234034_prop1=1. scratc438747365d_Inj0=1. scratc66740742_cond2=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_cd=1. aTP_Lamm_cf=1. aTP_Lamm_ch=1. aTP_Lamm_cl=1. aTP_Lamm_cn=1. aTP_Lamm_cq=1. aTP_Lamm_ct=1. aTP_Lamm_cv=1. aTP_Lamm_cx=1. aTP_Lamm_da=1. aTP_Lamm_dc=1. aTP_Lamm_dd=1. aTP_Lamm_df=1. aTP_Lamm_dg=1. aTP_Lamm_di=1. aTP_Lamm_dj=1. aTP_Lamm_dl=1. aTP_Lamm_dm=1. aTP_Lamm_do=1. aTP_Lamm_dr=1. aTP_Lamm_dt=1. aTP_Lamm_du=1. aTP_Lamm_dy=1. aTP_Lamm_dz=1. aTP_Lamm_ea=1. aTP_Lamm_ed=1. aTP_Lamm_fa=1. fequal_TPTP_ind=1. scratc1213114791univof=1. scratc1569119138_n_one=1. scratc1929214999_d_Unj=1. scratc329909865nd_nIn=1. scratc66740741_cond1=1. aTP_Lamm_ab=1. aTP_Lamm_ah=1. aTP_Lamm_bk=1. aTP_Lamm_bl=1. bool=1. scratc1054561261_prop1=1. scratc1230993332_prop1=1. scratc1267815972d_plus=1. scratc1436958384_prop1=1. scratc15992362nempty=1. scratc1676143372pair_p=1. scratc1819355507_prop1=1. scratc2025320559_prop1=1. scratc52017607_prop4=1. scratc802267587_empty=1. scratc95837927munion=1. scratc107677035d_24_g=1. scratc1333142593d_i1_s=1. tPTP_ind=1. aa_TPTP_ind_bool=1. aa_TPT43085870d_bool=1. aa_TPTP_ind_TPTP_ind=1. aa_fun171081125l_bool=1. aa_TPT1424761345TP_ind=1. aa_TPT60673477d_bool=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. scratc2028353053_d_and=1. aa_TPT1123896796d_bool=1. scratc2064173607bnd_if=1. scratc2004534528d_l_ec=1. aa_fun1212484691d_bool=1. aa_TPT985247859d_bool=1. scratc470297856d_e_in=1. scratc709411956d_pair=1. aa_fun987228051d_bool=1. scratc291029493nd_ind=1. scratc530322608_amone=1. scratc503987934second=1. scratc940782065_image=1. scratc983424134_first=1. aa_TPT125613450d_bool=1. scratc332402627nd_non=1. aa_fun1913827119d_bool=1. scratc311899637d_anec=1. aa_TPT1791839040TP_ind=1. aa_fun1107270209d_bool=1. aa_fun845057962d_bool=1. scratc1494928837_ecelt=1. scratc257261896nd_ecp=1. scratc98318613eplSep=1. scratc1494338446_ecect=1. aa_TPT1781712639TP_ind=1. aa_TPT2142672771l_bool=1. aa_fun1235454963TP_ind=1. cOMBB_658106424TP_ind=1. cOMBS_2003118649l_bool=1. scratc1032140378_fixfu=1. scratc1512202328fixfu2=1. scratc1682341687etprop=1. scratc1892255651wissel=1. scratc2024228854ectset=1. scratc257261900nd_ect=1. scratc341057732nd_out=1. scratc115261471d_invf=1. scratc118998002d_tofs=1. scratc1217641094nverse=1. scratc1909026977ectelt=1. scratc2130346200unmore=1. f1=1. f12=1. f13=1. f20=1. f24=1. scratc589283822all_of=1. scratc2136901056d_n_pl=1. scratc470297861d_e_is=1. scratc1912101604_d_Sep=1. scratc1329056301d_esti=1. scratc2135818233_d_not=1. scratc1847428278l_some=1. scratc1012294322ffprop=1. scratc224806263nd_all=1. scratc2005190533d_l_or=1. scratc1910217654_rec_G=1. aTP_Lamm_ai=1. aTP_Lamm_ek=1. scratc340598524nd_one=1. aTP_Lamm_ak=1. aTP_Lamm_au=1. aTP_Lamm_bc=1. aTP_Lamm_bp=1. aTP_Lamm_ci=1. aTP_Lamm_ec=1. aTP_Lamm_ey=1. scratc114015096d_incl=1. aTP_Lamm_ao=1. aTP_Lamm_ay=1. aTP_Lamm_bb=1. aTP_Lamm_bf=1. aTP_Lamm_co=1. aTP_Lamm_cr=1. aTP_Lamm_eu=1. aTP_Lamm_ew=1. scratc1453316495etprod=1. scratc258114686nd_eps=1. scratc879445149ective=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_cj=1. aTP_Lamm_cy=1. aTP_Lamm_ee=1. aTP_Lamm_ef=1. aTP_Lamm_eg=1. aTP_Lamm_ei=1. aTP_Lamm_eo=1. aTP_Lamm_eq=1. aTP_Lamm_er=1. aTP_Lamm_ev=1. fEx_TPTP_ind=1. scratc1089695026nunion=1. scratc1218086982ective=1. aTP_Lamm_ar=1. aTP_Lamm_eh=1. aTP_Lamm_ej=1. aTP_Lamm_el=1. aTP_Lamm_em=1. aTP_Lamm_en=1. aTP_Lamm_ep=1. aTP_Lamm_es=1. aTP_Lamm_et=1. aTP_Lamm_ex=1. aTP_Lamm_ez=1. scratc1736505589_UPair=1. scratc1973565841In_rec=1. aTP_Lamm_ad=1. aTP_Lamm_av=1. aTP_Lamm_aw=1. aTP_Lamm_ax=1. aTP_Lamm_be=1. aTP_Lamm_bh=1. aTP_Lamm_bn=1. aTP_Lamm_bo=1. cOMBC_1555011498d_bool=1. scratc1005980568tminus=1. scratc1063164379ective=1. scratc1422817063t_disj=1. scratc466199086_prop1=1. scratc52017606_prop3=1. scratc848596209_prop1=1. undefined_bool=1. undefined_TPTP_ind=1. f2=1. f8=1. f9=1. f10=1. f11=1. f17=1. f18=1. f21=1. f22=1. f23=1. scratc340860870nd_or3=1. scratc257261835nd_ec3=1. scratc1485894452d_soft=1. scratc1746022593_indeq=1. scratc291423088nd_ite=1. scratc52017604_prop1=1. scratc1621711373sel_wa=1. scratc1621711374sel_wb=1. scratc921318447d_11_i=1. f5=1. f7=1. f14=1. f16=1. f19=1. f25=1. scratc52017605_prop2=1. scratc1231600044hangef=1. scratc1633518317_inj_h=1. f3=1. f4=1. f15=1. scratc807556661_prop1=1. scratc1295712177indeq2=1. f6=1.
% 5.34/5.64
% 5.34/5.64 ============================== end of process initial clauses ========
% 5.34/5.64
% 5.34/5.64 ============================== CLAUSES FOR SEARCH ====================
% 5.34/5.64
% 5.34/5.64 ============================== end of clauses for search =============
% 5.34/5.64
% 5.34/5.64 ============================== SEARCH ================================
% 5.34/5.64
% 5.34/5.64 % Starting search at 0.46 seconds.
% 5.34/5.64
% 5.34/5.64 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 41 (0.00 of 1.63 sec).
% 5.34/5.64
% 5.34/5.64 Low Water (keep): wt=54.000, iters=3709
% 5.34/5.64
% 5.34/5.64 Low Water (keep): wt=41.000, iters=3530
% 5.34/5.64
% 5.34/5.64 Low Water (keep): wt=39.000, iters=3531
% 5.34/5.64
% 5.34/5.64 Low Water (keep): wt=37.000, iters=3464
% 5.34/5.64
% 5.34/5.64 Low Water (keep): wt=36.000, iters=3430
% 5.34/5.64
% 5.34/5.64 Low Water (keep): wt=34.000, iters=3360
% 5.34/5.64
% 5.34/5.64 Low Water (keep): wt=33.000, iters=3342
% 5.34/5.64
% 5.34/5.64 Low Water (keep): wt=32.000, iters=3353
% 5.34/5.64
% 5.34/5.64 Low Water (keep): wt=31.000, iters=3350
% 5.34/5.64
% 5.34/5.64 Low Water (keep): wt=30.000, iters=3353
% 5.34/5.64
% 5.34/5.64 Low Water (keep): wt=29.000, iters=3336
% 5.34/5.64
% 5.34/5.64 Low Water (keep): wt=28.000, iters=3423
% 5.34/5.64
% 5.34/5.64 Low Water (keep): wt=26.000, iters=3334
% 5.34/5.64
% 5.34/5.64 Low Water (keep): wt=25.000, iters=3421
% 5.34/5.64
% 5.34/5.64 Low Water (keep): wt=24.000, iters=3368
% 5.34/5.64
% 5.34/5.64 Low Water (keep): wt=23.000, iters=3350
% 5.34/5.64
% 5.34/5.64 Low Water (keep): wt=22.000, iters=3396
% 5.34/5.64
% 5.34/5.64 Low Water (keep): wt=21.000, iters=3422
% 5.34/5.64
% 5.34/5.64 Low Water (keep): wt=20.000, iters=3333
% 5.34/5.64
% 5.34/5.64 Low Water (keep): wt=19.000, iters=3347
% 5.34/5.64
% 5.34/5.64 Low Water (keep): wt=18.000, iters=3336
% 5.34/5.64
% 5.34/5.64 Low Water (keep): wt=17.000, iters=3336
% 5.34/5.64
% 5.34/5.64 Low Water (keep): wt=16.000, iters=3335
% 5.34/5.64
% 5.34/5.64 Low Water (keep): wt=15.000, iters=3470
% 5.34/5.64
% 5.34/5.64 Low Water (keep): wt=14.000, itersCputime limit exceeded (core dumped)
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