TSTP Solution File: NUM699+4 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM699+4 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 13:30:55 EDT 2022
% Result : Timeout 300.04s 300.30s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM699+4 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jul 7 15:16:09 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.09/1.40 ============================== Prover9 ===============================
% 1.09/1.40 Prover9 (32) version 2009-11A, November 2009.
% 1.09/1.40 Process 7864 was started by sandbox2 on n011.cluster.edu,
% 1.09/1.40 Thu Jul 7 15:16:10 2022
% 1.09/1.40 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_7710_n011.cluster.edu".
% 1.09/1.40 ============================== end of head ===========================
% 1.09/1.40
% 1.09/1.40 ============================== INPUT =================================
% 1.09/1.40
% 1.09/1.40 % Reading from file /tmp/Prover9_7710_n011.cluster.edu
% 1.09/1.40
% 1.09/1.40 set(prolog_style_variables).
% 1.09/1.40 set(auto2).
% 1.09/1.40 % set(auto2) -> set(auto).
% 1.09/1.40 % set(auto) -> set(auto_inference).
% 1.09/1.40 % set(auto) -> set(auto_setup).
% 1.09/1.40 % set(auto_setup) -> set(predicate_elim).
% 1.09/1.40 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.09/1.40 % set(auto) -> set(auto_limits).
% 1.09/1.40 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.09/1.40 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.09/1.40 % set(auto) -> set(auto_denials).
% 1.09/1.40 % set(auto) -> set(auto_process).
% 1.09/1.40 % set(auto2) -> assign(new_constants, 1).
% 1.09/1.40 % set(auto2) -> assign(fold_denial_max, 3).
% 1.09/1.40 % set(auto2) -> assign(max_weight, "200.000").
% 1.09/1.40 % set(auto2) -> assign(max_hours, 1).
% 1.09/1.40 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.09/1.40 % set(auto2) -> assign(max_seconds, 0).
% 1.09/1.40 % set(auto2) -> assign(max_minutes, 5).
% 1.09/1.40 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.09/1.40 % set(auto2) -> set(sort_initial_sos).
% 1.09/1.40 % set(auto2) -> assign(sos_limit, -1).
% 1.09/1.40 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.09/1.40 % set(auto2) -> assign(max_megs, 400).
% 1.09/1.40 % set(auto2) -> assign(stats, some).
% 1.09/1.40 % set(auto2) -> clear(echo_input).
% 1.09/1.40 % set(auto2) -> set(quiet).
% 1.09/1.40 % set(auto2) -> clear(print_initial_clauses).
% 1.09/1.40 % set(auto2) -> clear(print_given).
% 1.09/1.40 assign(lrs_ticks,-1).
% 1.09/1.40 assign(sos_limit,10000).
% 1.09/1.40 assign(order,kbo).
% 1.09/1.40 set(lex_order_vars).
% 1.09/1.40 clear(print_given).
% 1.09/1.40
% 1.09/1.40 % formulas(sos). % not echoed (589 formulas)
% 1.09/1.40
% 1.09/1.40 ============================== end of input ==========================
% 1.09/1.40
% 1.09/1.40 % From the command line: assign(max_seconds, 300).
% 1.09/1.40
% 1.09/1.40 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.09/1.40
% 1.09/1.40 % Formulas that are not ordinary clauses:
% 1.09/1.40 1 (all B_1 all B_2 gg_bool(scratc219602158_amone(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__51156__28358_ONUM699__thf__4__p_Obnd__amone) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.40 2 (all B_1 all B_2 gg_bool(scratc844856671_d_and(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__51156__28358_ONUM699__thf__4__p_Obnd__d__and) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.40 3 (all B_1 gg_bool(scratc952321851_d_not(B_1))) # label(gsy_c_Scratch__tptp__translate__51156__28358_ONUM699__thf__4__p_Obnd__d__not) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.40 4 (all B_1 all B_2 all B_3 gg_bool(scratc1729890377nd_ec3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__51156__28358_ONUM699__thf__4__p_Obnd__ec3) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.40 5 (all B_1 all B_2 gg_TPTP_ind(scratc1729890442nd_ect(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__51156__28358_ONUM699__thf__4__p_Obnd__ect) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.40 6 (all B_1 gg_TPTP_ind(scratc1730743228nd_eps(B_1))) # label(gsy_c_Scratch__tptp__translate__51156__28358_ONUM699__thf__4__p_Obnd__eps) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.40 7 (all B_1 all B_2 gg_TPTP_ind(scratc1763658035nd_ind(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__51156__28358_ONUM699__thf__4__p_Obnd__ind) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.40 8 (all B_1 all B_2 gg_bool(scratc1693814078d_l_ec(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__51156__28358_ONUM699__thf__4__p_Obnd__l__ec) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.40 9 (all B_1 all B_2 all B_3 gg_bool(scratc1813489412nd_or3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__51156__28358_ONUM699__thf__4__p_Obnd__or3) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.40 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].
% 1.09/1.40 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].
% 1.09/1.40 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].
% 1.09/1.40 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].
% 1.09/1.40 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].
% 1.09/1.40 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].
% 1.09/1.40 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].
% 1.09/1.40 17 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,X),Xa)) <-> pp(aa_bool_bool(scratc1694470083d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,X),Xa))))) # label(fact_def__lessis) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.40 18 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,X),Xa)) <-> pp(aa_bool_bool(scratc1694470083d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,X),Xa))))) # label(fact_def__moreis) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.40 19 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc403150895_prop1,X),Xa)) <-> pp(scratc1813489412nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,X),Xa))))) # label(fact_def__d__29__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.40 20 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc93448950n_some,aa_TPT43085870d_bool(scratc572008692ffprop(Xa),X))))) # label(fact_def__iii) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.40 21 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc93448950n_some,aa_TPT43085870d_bool(scratc572008692ffprop(X),Xa))))) # label(fact_def__d__29__ii) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.40 22 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc572008692ffprop(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,X),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Xa),Xb))))) # label(fact_def__diffprop) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.40 23 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1962272368_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1804637580nd_nis,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(X),Xb))))) # label(fact_def__d__28__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.40 24 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1373910193_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1804637580nd_nis,Xa),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(X),Xa))))) # label(fact_def__d__27__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.40 25 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc785548018_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Xa),X))))) # label(fact_def__d__26__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.40 26 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc197185843_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(X),Xa)),Xb)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(X),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Xa),Xb)))))) # label(fact_def__d__25__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.40 27 (all X scratc1826180606d_n_pl(X) = aa_TPT1424761345TP_ind(scratc669946235bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1823120998d_plus,X))) # label(fact_def__n__pl) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.40 28 (all X aa_TPTP_ind_TPTP_ind(scratc1823120998d_plus,X) = scratc1763658035nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1165856785d_d_Pi,scratc1804112789nd_nat),aTP_Lamm_ac),aa_TPT43085870d_bool(scratc1756307317_prop2,X))) # label(fact_def__plus) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.40 29 (all X aa_TPTP_ind_TPTP_ind(scratc1814875053d_24_g,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1401733581_Sigma,scratc1804112789nd_nat),aTP_Lamm_ad(X))) # label(fact_def__d__24__g) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.40 30 (all X (pp(aa_TPTP_ind_bool(scratc1888780805_prop4,X)) <-> pp(aa_fun171081125l_bool(scratc1497107956l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1165856785d_d_Pi,scratc1804112789nd_nat),aTP_Lamm_ac)),aa_TPT43085870d_bool(scratc1756307317_prop2,X))))) # label(fact_def__prop4) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.40 31 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1888780804_prop3(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc669946235bnd_ap,X),Xb)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc669946235bnd_ap,Xa),Xb))))) # label(fact_def__prop3) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.40 32 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1756307317_prop2,X),Xa)) <-> pp(scratc844856671_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc669946235bnd_ap,Xa),scratc153103791nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,X)),aa_TPTP_ind_bool(scratc1756307316_prop1,Xa))))) # label(fact_def__d__24__prop2) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.40 33 (all X (pp(aa_TPTP_ind_bool(scratc1756307316_prop1,X)) <-> pp(aa_fun171081125l_bool(scratc269830495_n_all,aa_TPT43085870d_bool(aTP_Lamm_ae,X))))) # label(fact_def__d__24__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.40 34 (all X (pp(aa_TPTP_ind_bool(scratc1167945141_prop1,X)) <-> pp(aa_bool_bool(scratc1694470083d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,X),scratc153103791nd_n_1)),aa_fun171081125l_bool(scratc93448950n_some,aa_TPT43085870d_bool(aTP_Lamm_af,X)))))) # label(fact_def__d__23__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.40 35 (all X (pp(aa_TPTP_ind_bool(scratc579582966_prop1,X)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1804637580nd_nis,aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,X)),X)))) # label(fact_def__d__22__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.40 36 (all X (pp(aa_TPTP_ind_bool(scratc1903503940_cond2,X)) <-> pp(aa_fun171081125l_bool(scratc269830495_n_all,aa_TPT43085870d_bool(aTP_Lamm_ag,X))))) # label(fact_def__cond2) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.40 37 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1804637580nd_nis,X),Xa)) <-> pp(scratc952321851_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,X),Xa))))) # label(fact_def__nis) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.40 38 (all X all Xa all Xb all Xc all Xd scratc112215795indeq2(X,Xa,Xb,Xc,Xd) = aa_TPT1424761345TP_ind(scratc1435302143_indeq(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc481032817d_11_i(X,Xa,Xb),Xc),Xd))) # label(fact_def__indeq2) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.40 39 (all X all Xa all Xb scratc481032817d_11_i(X,Xa,Xb) = scratc1435302143_indeq(X,Xa,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1165856785d_d_Pi,X),aTP_Lamm_ai(Xb)))) # label(fact_def__d__11__i) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 40 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc328705946fixfu2(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc238963500all_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].
% 1.09/1.41 41 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1435302143_indeq(X,Xa,Xb),Xc),Xd) = scratc1763658035nd_ind(Xb,aa_TPT43085870d_bool(scratc1888780803_prop2(X,Xa,Xb,Xc),Xd))) # label(fact_def__indeq) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 42 (all X all Xa all Xb all Xc all Xd all Xe (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1888780803_prop2(X,Xa,Xb,Xc),Xd),Xe)) <-> pp(aa_fun171081125l_bool(scratc1497107956l_some(X),aa_TPT43085870d_bool(scratc156146295_prop1(X,Xa,Xb,Xc,Xd),Xe))))) # label(fact_def__prop2) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 43 (all X all Xa all Xb all Xc all Xd all Xe all Xf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc156146295_prop1(X,Xa,Xb,Xc,Xd),Xe),Xf)) <-> pp(scratc844856671_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1884361327d_esti(X),Xf),aa_TPTP_ind_TPTP_ind(scratc1183617996_ecect(X,Xa),Xd)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc159577411d_e_is(Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc669946235bnd_ap,Xc),Xf)),Xe))))) # label(fact_def__d__10__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 44 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc721419928_fixfu(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc238963500all_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].
% 1.09/1.41 45 (all X all Xa scratc1183617996_ecect(X,Xa) = scratc159577406d_e_in(aa_TPTP_ind_TPTP_ind(scratc1759873369_power,X),scratc867204663d_anec(X,Xa))) # label(fact_def__ecect) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 46 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc725530595ectelt(X,Xa),Xb) = aa_TPTP_ind_TPTP_ind(scratc840732472ectset(X,Xa),aa_TPTP_ind_TPTP_ind(scratc1184208387_ecelt(X,Xa),Xb))) # label(fact_def__ectelt) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 47 (all X all Xa scratc840732472ectset(X,Xa) = scratc1813686274nd_out(aa_TPTP_ind_TPTP_ind(scratc1759873369_power,X),scratc867204663d_anec(X,Xa))) # label(fact_def__ectset) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 48 (all X all Xa scratc1729890442nd_ect(X,Xa) = aa_fun1431113780TP_ind(scratc728605222_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1759873369_power,X)),scratc867204663d_anec(X,Xa))) # label(fact_def__ect) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 49 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc867204663d_anec(X,Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1497107956l_some(X),aa_TPT43085870d_bool(scratc1729890438nd_ecp(X,Xa),Xb))))) # label(fact_def__anec) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 50 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1729890438nd_ecp(X,Xa),Xb),Xc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc159577411d_e_is(aa_TPTP_ind_TPTP_ind(scratc1759873369_power,X)),Xb),aa_TPTP_ind_TPTP_ind(scratc1184208387_ecelt(X,Xa),Xc))))) # label(fact_def__ecp) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 51 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1184208387_ecelt(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc728605222_d_Sep(X),aa_TPT43085870d_bool(Xa,Xb))) # label(fact_def__ecelt) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 52 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc946849818unmore(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc728605222_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].
% 1.09/1.41 53 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc436552825etprop(X,Xa),Xb),Xc)) <-> pp(scratc844856671_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1884361327d_esti(X),Xc),Xa),scratc952321851_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1884361327d_esti(X),Xc),Xb)))))) # label(fact_def__nissetprop) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 54 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc982531433t_disj(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1697434805nd_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].
% 1.09/1.41 55 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc669320122d_incl(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1697434805nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_at(X),Xa),Xb))))) # label(fact_def__incl) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 56 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1723190380nempty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1497107956l_some(X),aa_TPT43085870d_bool(aTP_Lamm_au(X),Xa))))) # label(fact_def__nonempty) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 57 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc491547137_empty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),scratc1805031169nd_non(X,aa_TPT43085870d_bool(aTP_Lamm_au(X),Xa)))))) # label(fact_def__empty) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 58 (all X scratc1884361327d_esti(X) = scratc670471025bnd_in) # label(fact_def__esti) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 59 (all X all Xa (scratc2088748868d_r_ec(X,Xa) <-> (pp(X) -> pp(scratc952321851_d_not(Xa))))) # label(fact_def__r__ec) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 60 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc881279722hangef(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1401733581_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].
% 1.09/1.41 61 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc708759269wissel(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1401733581_Sigma,X),scratc375922512sel_wb(X,Xa,Xb))) # label(fact_def__wissel) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 62 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc375922512sel_wb(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc1764051630nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc159577411d_e_is(X),Xc),Xb),X,Xa),aa_TPTP_ind_TPTP_ind(scratc375922511sel_wa(X,Xa,Xb),Xc))) # label(fact_def__wissel__wb) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 63 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc375922511sel_wa(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc1764051630nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc159577411d_e_is(X),Xc),Xa),X,Xb),Xc)) # label(fact_def__wissel__wa) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 64 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1764051630nd_ite(X,Xa,Xb),Xc) = scratc1763658035nd_ind(Xa,aa_TPT43085870d_bool(scratc1888780802_prop1(X,Xa,Xb),Xc))) # label(fact_def__ite) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 65 (all X all Xa all Xb all Xc all Xd (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1888780802_prop1(X,Xa,Xb),Xc),Xd)) <-> pp(scratc844856671_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1763592448nd_imp,X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc159577411d_e_is(Xa),Xd),Xb)),aa_bool_bool(aa_boo1142376798l_bool(scratc1763592448nd_imp,scratc952321851_d_not(X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc159577411d_e_is(Xa),Xd),Xc)))))) # label(fact_def__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 66 (all X all Xa scratc1467975200second(X,Xa) = scratc1888387208_proj1) # label(fact_def__second) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 67 (all X all Xa scratc672703684_first(X,Xa) = scratc1888387207_proj0) # label(fact_def__first) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 68 (all X all Xa scratc359091634d_pair(X,Xa) = scratc1731457254d_pair) # label(fact_def__d__pair) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 69 (all X all Xa scratc1813686274nd_out(X,Xa) = scratc2041199478d_soft(aa_fun1431113780TP_ind(scratc728605222_d_Sep(X),Xa),X,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1401733581_Sigma,aa_fun1431113780TP_ind(scratc728605222_d_Sep(X),Xa)),scratc159577406d_e_in(X,Xa)))) # label(fact_def__out) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 70 (all X all Xa all Xb (gg_TPTP_ind(Xb) -> aa_TPTP_ind_TPTP_ind(scratc159577406d_e_in(X,Xa),Xb) = Xb)) # label(fact_def__e__in) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 71 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc450021935_inj_h(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1401733581_Sigma,X),aa_TPT1424761345TP_ind(aTP_Lamm_aw(Xc),Xd))) # label(fact_def__inj__h) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 72 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc670566497d_invf(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1401733581_Sigma,Xa),scratc2041199478d_soft(X,Xa,Xb))) # label(fact_def__invf) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 73 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc273703961ective(X),Xa),Xb)) <-> pp(scratc844856671_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc89984731ective(X),Xa),Xb),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2119781768ective(X),Xa),Xb))))) # label(fact_def__bijective) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 74 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2119781768ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1697434805nd_all(Xa),aa_TPT43085870d_bool(scratc630061615_image(X,Xa),Xb))))) # label(fact_def__surjective) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 75 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc867320772nverse(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1401733581_Sigma,Xa),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ax(X),Xa),Xb))) # label(fact_def__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 76 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc2041199478d_soft(X,Xa,Xb),Xc) = scratc1763658035nd_ind(X,aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(Xa),Xb),Xc))) # label(fact_def__soft) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 77 (all X all Xa scratc674303028d_tofs(X,Xa) = scratc669946235bnd_ap) # label(fact_def__tofs) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 78 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc630061615_image(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1497107956l_some(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(Xa),Xb),Xc))))) # label(fact_def__image) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 79 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc89984731ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1697434805nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ba(X),Xa),Xb))))) # label(fact_def__injective) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 80 (all X all Xa scratc1763658035nd_ind(X,Xa) = scratc1730743228nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bb(X),Xa))) # label(fact_def__ind) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 81 (all X all Xa (pp(aa_fun171081125l_bool(scratc1813227066nd_one(X),Xa)) <-> pp(scratc844856671_d_and(scratc219602158_amone(X,Xa),aa_fun171081125l_bool(scratc1497107956l_some(X),Xa))))) # label(fact_def__one) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 82 (all X all Xa (pp(scratc219602158_amone(X,Xa)) <-> pp(aa_fun171081125l_bool(scratc238963500all_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].
% 1.09/1.41 83 (all X scratc159577411d_e_is(X) = fequal_TPTP_ind) # label(fact_def__e__is) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 84 (all X all Xa all Xb (scratc665748678_orec3(X,Xa,Xb) <-> pp(scratc844856671_d_and(scratc1813489412nd_or3(X,Xa,Xb),scratc1729890377nd_ec3(X,Xa,Xb))))) # label(fact_def__orec3) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 85 (all X all Xa all Xb (pp(scratc1729890377nd_ec3(X,Xa,Xb)) <-> scratc867139016d_and3(scratc1693814078d_l_ec(X,Xa),scratc1693814078d_l_ec(Xa,Xb),scratc1693814078d_l_ec(Xb,X)))) # label(fact_def__ec3) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 86 (all X all Xa all Xb (scratc867139016d_and3(X,Xa,Xb) <-> pp(scratc844856671_d_and(X,scratc844856671_d_and(Xa,Xb))))) # label(fact_def__and3) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 87 (all X all Xa all Xb (pp(scratc1813489412nd_or3(X,Xa,Xb)) <-> pp(aa_bool_bool(scratc1694470083d_l_or(X),aa_bool_bool(scratc1694470083d_l_or(Xa),Xb))))) # label(fact_def__or3) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 88 (all X all Xa (pp(aa_fun171081125l_bool(scratc1497107956l_some(X),Xa)) <-> pp(scratc952321851_d_not(aa_fun171081125l_bool(scratc238963500all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),scratc1805031169nd_non(X,Xa)))))) # label(fact_def__l__some) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 89 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc1805031169nd_non(X,Xa),Xb)) <-> pp(scratc952321851_d_not(aa_TPTP_ind_bool(Xa,Xb))))) # label(fact_def__non) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 90 (all X scratc1697434805nd_all(X) = scratc238963500all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X))) # label(fact_def__all) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 91 (all X all Xa (scratc1738998121_l_iff(X,Xa) <-> pp(scratc844856671_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1763592448nd_imp,X),Xa),aa_bool_bool(aa_boo1142376798l_bool(scratc1763592448nd_imp,Xa),X))))) # label(fact_def__l__iff) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 92 (all X all Xa (scratc1091053229d_orec(X,Xa) <-> pp(scratc844856671_d_and(aa_bool_bool(scratc1694470083d_l_or(X),Xa),scratc1693814078d_l_ec(X,Xa))))) # label(fact_def__orec) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 93 (all X scratc1694470083d_l_or(X) = aa_boo1142376798l_bool(scratc1763592448nd_imp,scratc952321851_d_not(X))) # label(fact_def__l__or) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 94 (all X all Xa (pp(scratc844856671_d_and(X,Xa)) <-> pp(scratc952321851_d_not(scratc1693814078d_l_ec(X,Xa))))) # label(fact_def__d__and) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 95 (all X all Xa (pp(scratc1693814078d_l_ec(X,Xa)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1763592448nd_imp,X),scratc952321851_d_not(Xa))))) # label(fact_def__l__ec) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 96 scratc1732403419bvious <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1763592448nd_imp,fFalse),fFalse)) # label(fact_def__obvious) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 97 (all X (scratc1878728722nd_wel(X) <-> pp(scratc952321851_d_not(scratc952321851_d_not(X))))) # label(fact_def__wel) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 98 (all X (pp(scratc952321851_d_not(X)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1763592448nd_imp,X),fFalse)))) # label(fact_def__d__not) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 99 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1165856785d_d_Pi,X),Xa) = aa_fun1431113780TP_ind(scratc728605222_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1759873369_power,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1401733581_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].
% 1.09/1.41 100 (all X (gg_TPTP_ind(X) -> (pp(aa_TPTP_ind_bool(scratc1325823050pair_p,X)) <-> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1731457254d_pair,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc669946235bnd_ap,X),scratc1437595393ptyset)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc669946235bnd_ap,X),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,scratc1437595393ptyset))) = X))) # label(fact_def__pair__p) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 101 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc669946235bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc1000013399eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bg,Xa)),scratc1888387208_proj1)) # label(fact_def__ap) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 102 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1102996173etprod(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1401733581_Sigma,X),aTP_Lamm_ai(Xa))) # label(fact_def__setprod) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 103 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1401733581_Sigma,X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1803035945munion,X),aTP_Lamm_bh(Xa))) # label(fact_def__d__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 104 (all X aa_TPTP_ind_TPTP_ind(scratc1888387208_proj1,X) = aa_fun277296641TP_ind(scratc1000013399eplSep(X,aTP_Lamm_bi),scratc745718617_d_Unj)) # label(fact_def__proj1) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 105 (all X aa_TPTP_ind_TPTP_ind(scratc1888387207_proj0,X) = aa_fun277296641TP_ind(scratc1000013399eplSep(X,aTP_Lamm_bj),scratc745718617_d_Unj)) # label(fact_def__proj0) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 106 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1731457254d_pair,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc649409396nunion(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1178653211d_repl,X),scratc88427043d_Inj0)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1178653211d_repl,Xa),scratc88427044d_Inj1))) # label(fact_def__pair) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 107 (all X aa_TPTP_ind_TPTP_ind(scratc88427043d_Inj0,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1178653211d_repl,X),scratc88427044d_Inj1)) # label(fact_def__d__Inj0) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 108 (all X (pp(aa_TPTP_ind_bool(scratc1744045275_nat_p,X)) <-> (all X1 (pp(aa_TPTP_ind_bool(X1,scratc1437595393ptyset)) -> ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(X1,X2)) -> pp(aa_TPTP_ind_bool(X1,aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,X2)))))) -> pp(aa_TPTP_ind_bool(X1,X))))))) # label(fact_def__nat__p) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 109 (all X aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc649409396nunion(X),aa_TPTP_ind_TPTP_ind(scratc1410803015d_Sing,X))) # label(fact_def__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 110 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc727776979In_rec(X),Xa) = scratc1730743228nd_eps(aa_TPT43085870d_bool(scratc671246324_rec_G(X),Xa))) # label(fact_def__d__In__rec) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 111 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc671246324_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(scratc670471025bnd_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].
% 1.09/1.41 112 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc565694938tminus(X),Xa) = aa_fun1431113780TP_ind(scratc728605222_d_Sep(X),aa_TPT43085870d_bool(aTP_Lamm_bm,Xa))) # label(fact_def__setminus) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 113 (all X all Xa scratc1000013399eplSep(X,Xa) = aa_TPT494704832TP_ind(scratc1178653211d_repl,aa_fun1431113780TP_ind(scratc728605222_d_Sep(X),Xa))) # label(fact_def__d__ReplSep) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 114 (all X all Xa aa_fun1431113780TP_ind(scratc728605222_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc670471017bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc670471025bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1178653211d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bn(X),Xa))),scratc1437595393ptyset)) # label(fact_def__d__Sep) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 115 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1803035945munion,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc119651587_union,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1178653211d_repl,X),Xa))) # label(fact_def__famunion) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 116 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc649409396nunion(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc119651587_union,aa_TPTP_ind_TPTP_ind(scratc1296219959_UPair(X),Xa))) # label(fact_def__binunion) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 117 (all X aa_TPTP_ind_TPTP_ind(scratc1410803015d_Sing,X) = aa_TPTP_ind_TPTP_ind(scratc1296219959_UPair(X),X)) # label(fact_def__d__Sing) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 118 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1296219959_UPair(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1178653211d_repl,aa_TPTP_ind_TPTP_ind(scratc1759873369_power,aa_TPTP_ind_TPTP_ind(scratc1759873369_power,scratc1437595393ptyset))),aa_TPT1424761345TP_ind(aTP_Lamm_bo(X),Xa))) # label(fact_def__d__UPair) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 119 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1802538407nd_nIn,X),Xa)) <-> -pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X),Xa)))) # label(fact_def__nIn) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 120 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc670471017bnd_if(X,Xa),Xb) = scratc1730743228nd_eps(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bp(X),Xa),Xb))) # label(fact_def__if) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 121 (all X (pp(aa_TPTP_ind_bool(scratc969770224closed,X)) <-> pp(aa_TPTP_ind_bool(scratc269189027closed,X)) & pp(aa_TPTP_ind_bool(scratc433922041closed,X)) & pp(aa_TPTP_ind_bool(scratc591135635closed,X)))) # label(fact_def__d__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 122 (all X (pp(aa_TPTP_ind_bool(scratc591135635closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X1),X)) -> (all X2 ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X3),X1)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,aa_TPTP_ind_TPTP_ind(X2,X3)),X))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1178653211d_repl,X1),X2)),X))))))))) # label(fact_def__d__Repl__closed) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 123 (all X (pp(aa_TPTP_ind_bool(scratc433922041closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,aa_TPTP_ind_TPTP_ind(scratc1759873369_power,X1)),X))))))) # label(fact_def__d__Power__closed) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 124 (all X (pp(aa_TPTP_ind_bool(scratc269189027closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,aa_TPTP_ind_TPTP_ind(scratc119651587_union,X1)),X))))))) # label(fact_def__d__Union__closed) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 125 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1509153897d_Subq,X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X2),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X2),Xa))))))) # label(fact_def__d__Subq) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 126 (all X all Xa (pp(aa_fun171081125l_bool(scratc238963500all_of(X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (scratc1857401069_is_of(X2,X) -> pp(aa_TPTP_ind_bool(Xa,X2))))))) # label(fact_def__all__of) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 127 (all X all Xa (scratc1857401069_is_of(X,Xa) <-> pp(aa_TPTP_ind_bool(Xa,X)))) # label(fact_def__is__of) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 128 (all X0 pp(aa_fun171081125l_bool(scratc238963500all_of(aa_TPT43085870d_bool(aTP_Lamm_jq,X0)),aa_TPT43085870d_bool(aTP_Lamm_js,X0)))) # label(fact_isseti) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 129 (all X0 all X12 pp(aa_fun171081125l_bool(scratc238963500all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_jt(X0),X12)))) # label(fact_estie) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 130 (all X0 all X12 pp(aa_fun171081125l_bool(scratc238963500all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_ju(X0),X12)))) # label(fact_estii) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 131 (all X0 all X12 scratc1857401069_is_of(aa_fun1431113780TP_ind(scratc728605222_d_Sep(X0),X12),aa_TPT43085870d_bool(aTP_Lamm_jq,X0))) # label(fact_setof__p) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 132 (all X0 all X12 pp(aa_fun171081125l_bool(scratc238963500all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_jw(X0),X12)))) # label(fact_secondis1) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 133 (all X0 all X12 pp(aa_fun171081125l_bool(scratc238963500all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_jy(X0),X12)))) # label(fact_firstis1) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 134 (all X0 all X12 pp(aa_fun171081125l_bool(scratc238963500all_of(aa_TPT43085870d_bool(aTP_Lamm_jz(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_ka(X0),X12)))) # label(fact_pairis1) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 135 (all X0 all X12 pp(aa_fun171081125l_bool(scratc238963500all_of(aa_TPT43085870d_bool(aTP_Lamm_jz(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_kb(X0),X12)))) # label(fact_second__p) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 136 (all X0 all X12 pp(aa_fun171081125l_bool(scratc238963500all_of(aa_TPT43085870d_bool(aTP_Lamm_jz(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_kc(X0),X12)))) # label(fact_first__p) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 137 (all X0 all X12 pp(aa_fun171081125l_bool(scratc238963500all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_ke(X0),X12)))) # label(fact_e__pair__p) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 138 (all X0 all X12 pp(aa_fun171081125l_bool(scratc238963500all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_kf(X0),X12)))) # label(fact_otax2) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 139 (all X0 all X12 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc89984731ective(aa_fun1431113780TP_ind(scratc728605222_d_Sep(X0),X12)),X0),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1401733581_Sigma,aa_fun1431113780TP_ind(scratc728605222_d_Sep(X0),X12)),scratc159577406d_e_in(X0,X12))))) # label(fact_otax1) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 140 (all X0 all X12 pp(aa_fun171081125l_bool(scratc238963500all_of(aa_fun1584354236d_bool(aTP_Lamm_kg(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_kh(X0),X12)))) # label(fact_e__inp) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 141 (all X0 all X12 pp(aa_fun171081125l_bool(scratc238963500all_of(aa_fun1584354236d_bool(aTP_Lamm_kg(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_ki(X0),X12)))) # label(fact_e__in__p) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 142 (all X0 all X12 pp(aa_fun171081125l_bool(scratc238963500all_of(aa_TPT43085870d_bool(aTP_Lamm_kj(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_km(X0),X12)))) # label(fact_e__fisi) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 143 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc1813227066nd_one(X0),X12)) -> pp(aa_TPTP_ind_bool(X12,scratc1763658035nd_ind(X0,X12))))) # label(fact_oneax) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 144 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc1813227066nd_one(X0),X12)) -> scratc1857401069_is_of(scratc1763658035nd_ind(X0,X12),aa_TPT43085870d_bool(aTP_Lamm_aj,X0)))) # label(fact_ind__p) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 145 (all X0 all X12 pp(aa_fun171081125l_bool(scratc238963500all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_ko(X0),X12)))) # label(fact_e__isp) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 146 (all X0 pp(aa_fun171081125l_bool(scratc238963500all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_kp,X0)))) # label(fact_refis) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 147 (all X0 (scratc1878728722nd_wel(X0) -> pp(X0))) # label(fact_l__et) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 148 (all X0 all X12 all X22 all X32 (pp(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc670471017bnd_if(X0,X22),X32))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X12),X22))))) # label(fact_k__If__In__then__E) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 149 (all X0 all X12 all X22 ((pp(X0) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X12),X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,aa_TPTP_ind_TPTP_ind(scratc670471017bnd_if(X0,X12),scratc1437595393ptyset)),aa_TPTP_ind_TPTP_ind(scratc670471017bnd_if(X0,X22),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,scratc1437595393ptyset)))))) # label(fact_k__If__In__01) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 150 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X33),X0)) -> aa_TPTP_ind_TPTP_ind(X12,X33) = aa_TPTP_ind_TPTP_ind(X22,X33)))) -> aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1401733581_Sigma,X0),X12) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1401733581_Sigma,X0),X22))) # label(fact_xi__ext) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 151 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1165856785d_d_Pi,X0),X12))) -> (all X32 (gg_TPTP_ind(X32) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X32),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1165856785d_d_Pi,X0),X12))) -> ((all X42 (gg_TPTP_ind(X42) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X42),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc669946235bnd_ap,X22),X42) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc669946235bnd_ap,X32),X42)))) -> X22 = X32))))))) # label(fact_k__Pi__ext) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 152 (all X0 all X12 all X22 all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1165856785d_d_Pi,X0),X12))) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X32),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc669946235bnd_ap,X22),X32)),aa_TPTP_ind_TPTP_ind(X12,X32)))))) # label(fact_ap__Pi) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 153 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X33),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,aa_TPTP_ind_TPTP_ind(X22,X33)),aa_TPTP_ind_TPTP_ind(X12,X33)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1401733581_Sigma,X0),X22)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1165856785d_d_Pi,X0),X12))))) # label(fact_lam__Pi) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 154 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X22),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc669946235bnd_ap,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1401733581_Sigma,X0),X12)),X22) = aa_TPTP_ind_TPTP_ind(X12,X22))) # label(fact_beta) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 155 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1401733581_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,aa_TPTP_ind_TPTP_ind(scratc1888387208_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1888387207_proj0,X22)))))) # label(fact_proj1__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 156 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1401733581_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,aa_TPTP_ind_TPTP_ind(scratc1888387207_proj0,X22)),X0)))) # label(fact_proj0__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 157 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1401733581_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1731457254d_pair,aa_TPTP_ind_TPTP_ind(scratc1888387207_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1888387208_proj1,X22)) = X22))) # label(fact_proj__Sigma__eta) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 158 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1401733581_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1731457254d_pair,aa_TPTP_ind_TPTP_ind(scratc1888387207_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1888387208_proj1,X22)) = X22 & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,aa_TPTP_ind_TPTP_ind(scratc1888387207_proj0,X22)),X0)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,aa_TPTP_ind_TPTP_ind(scratc1888387208_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1888387207_proj0,X22))))))) # label(fact_k__Sigma__eta__proj0__proj1) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 159 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X22),X0)) -> (all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X32),aa_TPTP_ind_TPTP_ind(X12,X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1731457254d_pair,X22),X32)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1401733581_Sigma,X0),X12))))))) # label(fact_pair__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 160 (all X0 all X12 (gg_TPTP_ind(X12) -> aa_TPTP_ind_TPTP_ind(scratc1888387208_proj1,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1731457254d_pair,X0),X12)) = X12)) # label(fact_proj1__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 161 (all X0 all X12 (gg_TPTP_ind(X0) -> aa_TPTP_ind_TPTP_ind(scratc1888387207_proj0,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1731457254d_pair,X0),X12)) = X0)) # label(fact_proj0__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 162 (all X0 (pp(aa_TPTP_ind_bool(scratc1744045275_nat_p,X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X0),scratc1058042421_omega)))) # label(fact_nat__p__omega) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 163 (all X0 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X0),scratc1058042421_omega)) -> pp(aa_TPTP_ind_bool(scratc1744045275_nat_p,X0)))) # label(fact_omega__nat__p) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 164 (all X0 (gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(scratc1744045275_nat_p,X0)) -> X0 = scratc1437595393ptyset | (exists X13 (gg_TPTP_ind(X13) & pp(aa_TPTP_ind_bool(scratc1744045275_nat_p,X13)) & X0 = aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,X13)))))) # label(fact_nat__inv) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.41 165 (all X0 (pp(aa_TPTP_ind_bool(X0,scratc1437595393ptyset)) -> ((all X13 (gg_TPTP_ind(X13) -> (pp(aa_TPTP_ind_bool(scratc1744045275_nat_p,X13)) -> (pp(aa_TPTP_ind_bool(X0,X13)) -> pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,X13))))))) -> (all X12 (pp(aa_TPTP_ind_bool(scratc1744045275_nat_p,X12)) -> pp(aa_TPTP_ind_bool(X0,X12))))))) # label(fact_nat__ind) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 166 (all X0 (pp(aa_TPTP_ind_bool(scratc1744045275_nat_p,X0)) -> pp(aa_TPTP_ind_bool(scratc1744045275_nat_p,aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,X0))))) # label(fact_nat__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 167 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,X0) = aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,X12) -> X0 = X12))) # label(fact_ordsucc__inj) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 168 (all X0 aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,X0) != scratc1437595393ptyset) # label(fact_neq__ordsucc__0) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 169 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X22),aa_fun1431113780TP_ind(scratc728605222_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(X12,X22)))) # label(fact_k__SepE2) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 170 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X22),aa_fun1431113780TP_ind(scratc728605222_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X22),X0)))) # label(fact_k__SepE1) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 171 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X22),X0)) -> (pp(aa_TPTP_ind_bool(X12,X22)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X22),aa_fun1431113780TP_ind(scratc728605222_d_Sep(X0),X12)))))) # label(fact_k__SepI) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 172 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc1759873369_power,X0)))) # label(fact_k__Self__In__Power) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 173 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1509153897d_Subq,X12),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1759873369_power,X0))))) # label(fact_k__PowerI) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 174 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1759873369_power,X0))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1509153897d_Subq,X12),X0)))) # label(fact_k__PowerE) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 175 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> aa_TPTP_ind_TPTP_ind(scratc670471017bnd_if(X0,X12),X22) = X12 | aa_TPTP_ind_TPTP_ind(scratc670471017bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__or) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 176 (all X0 all X12 all X22 (gg_TPTP_ind(X12) -> (pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc670471017bnd_if(X0,X12),X22) = X12))) # label(fact_if__i__1) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 177 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (-pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc670471017bnd_if(X0,X12),X22) = X22))) # label(fact_if__i__0) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 178 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> pp(X0) & aa_TPTP_ind_TPTP_ind(scratc670471017bnd_if(X0,X12),X22) = X12 | -pp(X0) & aa_TPTP_ind_TPTP_ind(scratc670471017bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__correct) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 179 (all X0 pp(aa_TPTP_ind_bool(scratc969770224closed,aa_TPTP_ind_TPTP_ind(scratc29618409univof,X0)))) # label(fact_k__UnivOf__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 180 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc29618409univof,X0)))) # label(fact_k__UnivOf__In) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 181 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1178653211d_repl,X0),X12))) <-> (exists X3 (gg_TPTP_ind(X3) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X3),X0)) & X22 = aa_TPTP_ind_TPTP_ind(X12,X3)))))) # label(fact_k__ReplEq) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 182 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1759873369_power,X0))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1509153897d_Subq,X12),X0)))) # label(fact_k__PowerEq) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 183 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc119651587_union,X0))) <-> (exists X2 (gg_TPTP_ind(X2) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X12),X2)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X2),X0)))))) # label(fact_k__UnionEq) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 184 -(exists X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,X0),scratc1437595393ptyset))) # label(fact_k__EmptyAx) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 185 (all X0 ((all X13 (gg_TPTP_ind(X13) -> ((all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_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].
% 1.09/1.42 186 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1509153897d_Subq,X0),X12)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1509153897d_Subq,X12),X0)) -> X0 = X12)))) # label(fact_set__ext) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 187 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jf,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1804637580nd_nis,Uu),scratc153103791nd_n_1)) -> pp(aa_fun171081125l_bool(scratc93448950n_some,aa_TPT43085870d_bool(aTP_Lamm_af,Uu)))))) # label(fact_ATP_Olambda__1) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 188 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_je,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1804637580nd_nis,Uu),scratc153103791nd_n_1)) -> pp(aa_fun171081125l_bool(scratc385622756_n_one,aa_TPT43085870d_bool(aTP_Lamm_af,Uu)))))) # label(fact_ATP_Olambda__2) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 189 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jb,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),scratc153103791nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,Uu))))) # label(fact_ATP_Olambda__3) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 190 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_iy,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(scratc153103791nd_n_1),Uu)),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,Uu))))) # label(fact_ATP_Olambda__4) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 191 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jd,Uu)) <-> pp(aa_fun171081125l_bool(scratc1813227066nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1165856785d_d_Pi,scratc1804112789nd_nat),aTP_Lamm_ac)),aa_TPT43085870d_bool(aTP_Lamm_jc,Uu))))) # label(fact_ATP_Olambda__5) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 192 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jl,Uu)) <-> (pp(aa_TPTP_ind_bool(scratc1903503939_cond1,Uu)) -> (pp(aa_TPTP_ind_bool(scratc1903503940_cond2,Uu)) -> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jk,Uu))))))) # label(fact_ATP_Olambda__6) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 193 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_iv,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),scratc153103791nd_n_1))))) # label(fact_ATP_Olambda__7) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 194 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_is,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(scratc153103791nd_n_1),Uu))))) # label(fact_ATP_Olambda__8) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 195 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fs,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__9) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 196 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jg,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1804637580nd_nis,aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__10) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 197 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jp,Uu)) <-> scratc1857401069_is_of(aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,Uu),aTP_Lamm_a))) # label(fact_ATP_Olambda__11) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 198 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,Uu)),scratc153103791nd_n_1)))) # label(fact_ATP_Olambda__12) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 199 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jo,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1804637580nd_nis,aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,Uu)),scratc153103791nd_n_1)))) # label(fact_ATP_Olambda__13) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 200 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fr,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,Uu))))) # label(fact_ATP_Olambda__14) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 201 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jj,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,Uu),aa_TPTP_ind_TPTP_ind(scratc1759873369_power,scratc1804112789nd_nat))))) # label(fact_ATP_Olambda__15) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 202 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_by,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,Uu),scratc153103791nd_n_1)))) # label(fact_ATP_Olambda__16) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 203 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_a,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,Uu),scratc1804112789nd_nat)))) # label(fact_ATP_Olambda__17) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 204 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jn,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jm,Uu))))) # label(fact_ATP_Olambda__18) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 205 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ji,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jh,Uu))))) # label(fact_ATP_Olambda__19) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 206 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ja,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_iz,Uu))))) # label(fact_ATP_Olambda__20) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 207 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ix,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_iw,Uu))))) # label(fact_ATP_Olambda__21) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 208 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_iu,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_it,Uu))))) # label(fact_ATP_Olambda__22) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 209 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ir,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_iq,Uu))))) # label(fact_ATP_Olambda__23) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 210 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ip,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_io,Uu))))) # label(fact_ATP_Olambda__24) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 211 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_im,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_il,Uu))))) # label(fact_ATP_Olambda__25) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 212 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ik,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ij,Uu))))) # label(fact_ATP_Olambda__26) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 213 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ii,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ih,Uu))))) # label(fact_ATP_Olambda__27) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 214 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_if,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ie,Uu))))) # label(fact_ATP_Olambda__28) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 215 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ic,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ib,Uu))))) # label(fact_ATP_Olambda__29) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 216 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ia,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hz,Uu))))) # label(fact_ATP_Olambda__30) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 217 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hw,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hv,Uu))))) # label(fact_ATP_Olambda__31) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 218 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hu,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ht,Uu))))) # label(fact_ATP_Olambda__32) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 219 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hs,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hr,Uu))))) # label(fact_ATP_Olambda__33) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 220 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hq,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hp,Uu))))) # label(fact_ATP_Olambda__34) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 221 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ho,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hn,Uu))))) # label(fact_ATP_Olambda__35) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 222 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hm,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hl,Uu))))) # label(fact_ATP_Olambda__36) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 223 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hk,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hj,Uu))))) # label(fact_ATP_Olambda__37) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 224 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hi,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hh,Uu))))) # label(fact_ATP_Olambda__38) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 225 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hg,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hf,Uu))))) # label(fact_ATP_Olambda__39) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 226 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_he,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hd,Uu))))) # label(fact_ATP_Olambda__40) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 227 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hc,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hb,Uu))))) # label(fact_ATP_Olambda__41) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 228 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ha,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gz,Uu))))) # label(fact_ATP_Olambda__42) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 229 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gy,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,Uu))))) # label(fact_ATP_Olambda__43) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 230 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gw,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gv,Uu))))) # label(fact_ATP_Olambda__44) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 231 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gu,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gt,Uu))))) # label(fact_ATP_Olambda__45) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 232 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gs,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gr,Uu))))) # label(fact_ATP_Olambda__46) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 233 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gq,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gp,Uu))))) # label(fact_ATP_Olambda__47) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 234 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_go,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gn,Uu))))) # label(fact_ATP_Olambda__48) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 235 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gl,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gk,Uu))))) # label(fact_ATP_Olambda__49) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 236 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gi,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gh,Uu))))) # label(fact_ATP_Olambda__50) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 237 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gf,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ge,Uu))))) # label(fact_ATP_Olambda__51) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 238 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gc,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gb,Uu))))) # label(fact_ATP_Olambda__52) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 239 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fz,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fy,Uu))))) # label(fact_ATP_Olambda__53) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 240 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fw,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fv,Uu))))) # label(fact_ATP_Olambda__54) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 241 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fu,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ft,Uu))))) # label(fact_ATP_Olambda__55) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 242 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fq,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fp,Uu))))) # label(fact_ATP_Olambda__56) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 243 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fn,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fm,Uu))))) # label(fact_ATP_Olambda__57) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 244 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fk,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fj,Uu))))) # label(fact_ATP_Olambda__58) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 245 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fh,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fg,Uu))))) # label(fact_ATP_Olambda__59) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 246 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fe,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fd,Uu))))) # label(fact_ATP_Olambda__60) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 247 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fb,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fa,Uu))))) # label(fact_ATP_Olambda__61) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 248 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ey,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ex,Uu))))) # label(fact_ATP_Olambda__62) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 249 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_eu,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_et,Uu))))) # label(fact_ATP_Olambda__63) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 250 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_eq,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ep,Uu))))) # label(fact_ATP_Olambda__64) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 251 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_em,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_el,Uu))))) # label(fact_ATP_Olambda__65) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 252 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ei,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eh,Uu))))) # label(fact_ATP_Olambda__66) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 253 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ef,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ee,Uu))))) # label(fact_ATP_Olambda__67) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 254 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ec,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eb,Uu))))) # label(fact_ATP_Olambda__68) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 255 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dz,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dy,Uu))))) # label(fact_ATP_Olambda__69) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 256 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dw,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dv,Uu))))) # label(fact_ATP_Olambda__70) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 257 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dt,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ds,Uu))))) # label(fact_ATP_Olambda__71) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 258 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dq,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dp,Uu))))) # label(fact_ATP_Olambda__72) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 259 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dn,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dm,Uu))))) # label(fact_ATP_Olambda__73) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 260 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dk,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dj,Uu))))) # label(fact_ATP_Olambda__74) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 261 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dh,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dg,Uu))))) # label(fact_ATP_Olambda__75) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 262 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_de,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dd,Uu))))) # label(fact_ATP_Olambda__76) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 263 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_da,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cz,Uu))))) # label(fact_ATP_Olambda__77) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 264 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cw,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cv,Uu))))) # label(fact_ATP_Olambda__78) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 265 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cs,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cr,Uu))))) # label(fact_ATP_Olambda__79) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 266 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_co,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cn,Uu))))) # label(fact_ATP_Olambda__80) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 267 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ck,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cj,Uu))))) # label(fact_ATP_Olambda__81) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 268 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cg,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cf,Uu))))) # label(fact_ATP_Olambda__82) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 269 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cc,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cb,Uu))))) # label(fact_ATP_Olambda__83) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 270 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bv,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bu,Uu))))) # label(fact_ATP_Olambda__84) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 271 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bt,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bs,Uu))))) # label(fact_ATP_Olambda__85) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 272 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_br,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bq,Uu))))) # label(fact_ATP_Olambda__86) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 273 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ab,Uu)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,Uu))))) # label(fact_ATP_Olambda__87) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 274 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bw,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,scratc153103791nd_n_1),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,Uu))))) # label(fact_ATP_Olambda__88) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 275 (all Uu aa_TPT494704832TP_ind(aTP_Lamm_bk,Uu) = aa_TPT494704832TP_ind(scratc1178653211d_repl,aa_TPTP_ind_TPTP_ind(scratc565694938tminus(Uu),aa_TPTP_ind_TPTP_ind(scratc1410803015d_Sing,scratc1437595393ptyset)))) # label(fact_ATP_Olambda__89) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 276 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_ah,Uu)) <-> Uu != scratc1437595393ptyset))) # label(fact_ATP_Olambda__90) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 277 (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(scratc88427044d_Inj1,X2) = Uu))))) # label(fact_ATP_Olambda__91) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 278 (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(scratc88427043d_Inj0,X2) = Uu))))) # label(fact_ATP_Olambda__92) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 279 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hr,Uu),Uua)) <-> scratc665748678_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,Uu),Uua)))) # label(fact_ATP_Olambda__93) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 280 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hp,Uu),Uua)) <-> pp(scratc1813489412nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__94) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 281 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hn,Uu),Uua)) <-> pp(scratc1729890377nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__95) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 282 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hz,Uu),Uua)) <-> scratc665748678_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc93448950n_some,aa_TPT43085870d_bool(aTP_Lamm_hx(Uu),Uua)),aa_fun171081125l_bool(scratc93448950n_some,aa_TPT43085870d_bool(aTP_Lamm_hy(Uu),Uua))))) # label(fact_ATP_Olambda__96) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 283 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hv,Uu),Uua)) <-> pp(scratc1813489412nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc93448950n_some,aa_TPT43085870d_bool(scratc572008692ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc93448950n_some,aa_TPT43085870d_bool(scratc572008692ffprop(Uua),Uu)))))) # label(fact_ATP_Olambda__97) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 284 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ht,Uu),Uua)) <-> pp(scratc1729890377nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc93448950n_some,aa_TPT43085870d_bool(scratc572008692ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc93448950n_some,aa_TPT43085870d_bool(scratc572008692ffprop(Uua),Uu)))))) # label(fact_ATP_Olambda__98) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 285 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kp,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc159577411d_e_is(Uu),Uua),Uua)))) # label(fact_ATP_Olambda__99) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 286 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jc,Uu),Uua)) <-> pp(scratc844856671_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc669946235bnd_ap,Uua),scratc153103791nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,Uu)),aa_fun171081125l_bool(scratc269830495_n_all,aa_TPT43085870d_bool(aTP_Lamm_ae,Uua)))))) # label(fact_ATP_Olambda__100) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 287 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jm,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__101) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 288 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iw,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__102) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 289 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iz,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__103) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 290 (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(scratc1825721420d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc669946235bnd_ap,Uu),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc669946235bnd_ap,Uu),Uua)))))) # label(fact_ATP_Olambda__104) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 291 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bq,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uua),scratc153103791nd_n_1)),Uu))))) # label(fact_ATP_Olambda__105) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 292 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jh,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1804637580nd_nis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1804637580nd_nis,aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,Uua)))))) # label(fact_ATP_Olambda__106) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 293 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ag,Uu),Uua)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1763592448nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721415d_n_in,Uua),Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721415d_n_in,aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,Uua)),Uu))))) # label(fact_ATP_Olambda__107) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 294 (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(scratc1763330045nd_iii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,Uua)),Uu))))) # label(fact_ATP_Olambda__108) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 295 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bu,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,Uua),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),scratc153103791nd_n_1)))))) # label(fact_ATP_Olambda__109) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 296 (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(scratc1045625727_29_ii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,Uua),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,Uu)))))) # label(fact_ATP_Olambda__110) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 297 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_il,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uua),Uu))))) # label(fact_ATP_Olambda__111) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 298 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hl,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,Uua),Uu))))) # label(fact_ATP_Olambda__112) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 299 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hh,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,Uua),Uu))))) # label(fact_ATP_Olambda__113) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 300 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hf,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,Uua),Uu))))) # label(fact_ATP_Olambda__114) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 301 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hj,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,Uua),Uu))))) # label(fact_ATP_Olambda__115) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 302 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gv,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,Uu),Uua)) -> pp(scratc952321851_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,Uu),Uua)))))) # label(fact_ATP_Olambda__116) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 303 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hd,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,Uu),Uua)) -> pp(scratc952321851_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,Uu),Uua)))))) # label(fact_ATP_Olambda__117) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 304 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hb,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,Uu),Uua)) -> pp(scratc952321851_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,Uu),Uua)))))) # label(fact_ATP_Olambda__118) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 305 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gt,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,Uu),Uua)) -> pp(scratc952321851_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,Uu),Uua)))))) # label(fact_ATP_Olambda__119) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 306 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fv,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uua)),Uu)))) # label(fact_ATP_Olambda__120) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 307 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bh(Uu),Uua) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1178653211d_repl,aa_TPTP_ind_TPTP_ind(Uu,Uua)),aa_TPT1424761345TP_ind(scratc1731457254d_pair,Uua))) # label(fact_ATP_Olambda__121) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 308 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_js,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aa_TPT43085870d_bool(aTP_Lamm_jq,Uu)),aa_TPT43085870d_bool(aTP_Lamm_jr(Uu),Uua))))) # label(fact_ATP_Olambda__122) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 309 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iq,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,Uu)),Uua))))) # label(fact_ATP_Olambda__123) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 310 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_it,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,Uua)))))) # label(fact_ATP_Olambda__124) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 311 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gz,Uu),Uua)) <-> (pp(scratc952321851_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,Uu),Uua))))) # label(fact_ATP_Olambda__125) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 312 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gr,Uu),Uua)) <-> (pp(scratc952321851_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__126) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 313 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gp,Uu),Uua)) <-> (pp(scratc952321851_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__127) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 314 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,Uu),Uua)) <-> (pp(scratc952321851_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,Uu),Uua))))) # label(fact_ATP_Olambda__128) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 315 (all Uu all Uua aa_fun277296641TP_ind(aa_TPT494704832TP_ind(aTP_Lamm_bl,Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc649409396nunion(aa_TPTP_ind_TPTP_ind(scratc1410803015d_Sing,scratc1437595393ptyset)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1178653211d_repl,Uu),Uua))) # label(fact_ATP_Olambda__129) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 316 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ij,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1804637580nd_nis,Uua),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__130) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 317 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ft,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__131) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 318 (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(scratc1825721420d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,Uua))))) # label(fact_ATP_Olambda__132) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 319 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jq,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,Uua),aa_TPTP_ind_TPTP_ind(scratc1759873369_power,Uu))))) # label(fact_ATP_Olambda__133) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 320 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jk,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721415d_n_in,Uua),Uu)))) # label(fact_ATP_Olambda__134) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 321 (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(scratc1802538407nd_nIn,Uua),Uu)))) # label(fact_ATP_Olambda__135) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 322 (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(scratc670471025bnd_in,Uua),Uu)))) # label(fact_ATP_Olambda__136) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 323 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_io,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_in(Uu),Uua))))) # label(fact_ATP_Olambda__137) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 324 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ih,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ig(Uu),Uua))))) # label(fact_ATP_Olambda__138) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 325 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ie,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_id(Uu),Uua))))) # label(fact_ATP_Olambda__139) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.42 326 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gn,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gm(Uu),Uua))))) # label(fact_ATP_Olambda__140) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 327 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gk,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gj(Uu),Uua))))) # label(fact_ATP_Olambda__141) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 328 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gh,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gg(Uu),Uua))))) # label(fact_ATP_Olambda__142) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 329 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ge,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gd(Uu),Uua))))) # label(fact_ATP_Olambda__143) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 330 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gb,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ga(Uu),Uua))))) # label(fact_ATP_Olambda__144) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 331 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fy,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fx(Uu),Uua))))) # label(fact_ATP_Olambda__145) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 332 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fp,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fo(Uu),Uua))))) # label(fact_ATP_Olambda__146) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 333 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fm,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fl(Uu),Uua))))) # label(fact_ATP_Olambda__147) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 334 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fj,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fi(Uu),Uua))))) # label(fact_ATP_Olambda__148) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 335 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fg,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ff(Uu),Uua))))) # label(fact_ATP_Olambda__149) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 336 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fd,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fc(Uu),Uua))))) # label(fact_ATP_Olambda__150) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 337 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fa,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ez(Uu),Uua))))) # label(fact_ATP_Olambda__151) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 338 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ex,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ew(Uu),Uua))))) # label(fact_ATP_Olambda__152) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 339 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_et,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_es(Uu),Uua))))) # label(fact_ATP_Olambda__153) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 340 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ep,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eo(Uu),Uua))))) # label(fact_ATP_Olambda__154) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 341 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_el,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ek(Uu),Uua))))) # label(fact_ATP_Olambda__155) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 342 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eh,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eg(Uu),Uua))))) # label(fact_ATP_Olambda__156) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 343 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ee,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ed(Uu),Uua))))) # label(fact_ATP_Olambda__157) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 344 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eb,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ea(Uu),Uua))))) # label(fact_ATP_Olambda__158) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 345 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dy,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dx(Uu),Uua))))) # label(fact_ATP_Olambda__159) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 346 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dv,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_du(Uu),Uua))))) # label(fact_ATP_Olambda__160) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 347 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ds,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dr(Uu),Uua))))) # label(fact_ATP_Olambda__161) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 348 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dp,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_do(Uu),Uua))))) # label(fact_ATP_Olambda__162) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 349 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dm,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dl(Uu),Uua))))) # label(fact_ATP_Olambda__163) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 350 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dj,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_di(Uu),Uua))))) # label(fact_ATP_Olambda__164) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 351 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dg,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_df(Uu),Uua))))) # label(fact_ATP_Olambda__165) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 352 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dd,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dc(Uu),Uua))))) # label(fact_ATP_Olambda__166) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 353 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cz,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cy(Uu),Uua))))) # label(fact_ATP_Olambda__167) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 354 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cv,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cu(Uu),Uua))))) # label(fact_ATP_Olambda__168) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 355 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cr,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cq(Uu),Uua))))) # label(fact_ATP_Olambda__169) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 356 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cn,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cm(Uu),Uua))))) # label(fact_ATP_Olambda__170) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 357 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cj,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ci(Uu),Uua))))) # label(fact_ATP_Olambda__171) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 358 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cf,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ce(Uu),Uua))))) # label(fact_ATP_Olambda__172) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 359 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cb,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ca(Uu),Uua))))) # label(fact_ATP_Olambda__173) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 360 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ib,Uu),Uua)) <-> pp(scratc219602158_amone(scratc1804112789nd_nat,aa_TPT43085870d_bool(aTP_Lamm_hx(Uu),Uua))))) # label(fact_ATP_Olambda__174) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 361 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_ad(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1469073079rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc669946235bnd_ap,Uu),Uua))) # label(fact_ATP_Olambda__175) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 362 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_be(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc119651587_union,aa_TPTP_ind_TPTP_ind(Uu,Uua))) # label(fact_ATP_Olambda__176) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 363 (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(scratc1731457254d_pair,Uu),X3)))))) # label(fact_ATP_Olambda__177) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 364 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ka(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc159577411d_e_is(aa_TPTP_ind_TPTP_ind(scratc1102996173etprod(Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc359091634d_pair(Uu,Uua),aa_TPTP_ind_TPTP_ind(scratc672703684_first(Uu,Uua),Uub)),aa_TPTP_ind_TPTP_ind(scratc1467975200second(Uu,Uua),Uub))),Uub)))) # label(fact_ATP_Olambda__178) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 365 (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(scratc670471017bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,scratc1437595393ptyset),Uub),Uu),Uua)) # label(fact_ATP_Olambda__179) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 366 (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(scratc670471017bnd_if(aa_TPTP_ind_bool(Uua,Uub),Uub),scratc1730743228nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bb(Uu),Uua)))) # label(fact_ATP_Olambda__180) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 367 (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(scratc1884361327d_esti(Uu),Uub),Uua)))) # label(fact_ATP_Olambda__181) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 368 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_jt(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1884361327d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc728605222_d_Sep(Uu),Uua))) -> pp(aa_TPTP_ind_bool(Uua,Uub))))) # label(fact_ATP_Olambda__182) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 369 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jr(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc669320122d_incl(Uu),Uua),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc669320122d_incl(Uu),Uub),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc159577411d_e_is(aa_TPTP_ind_TPTP_ind(scratc1759873369_power,Uu)),Uua),Uub)))))) # label(fact_ATP_Olambda__183) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 370 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kb(Uu),Uua),Uub)) <-> scratc1857401069_is_of(aa_TPTP_ind_TPTP_ind(scratc1467975200second(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)))) # label(fact_ATP_Olambda__184) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 371 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kc(Uu),Uua),Uub)) <-> scratc1857401069_is_of(aa_TPTP_ind_TPTP_ind(scratc672703684_first(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)))) # label(fact_ATP_Olambda__185) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 372 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ki(Uu),Uua),Uub)) <-> scratc1857401069_is_of(aa_TPTP_ind_TPTP_ind(scratc159577406d_e_in(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)))) # label(fact_ATP_Olambda__186) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 373 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_km(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aa_TPT43085870d_bool(aTP_Lamm_kj(Uu),Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kl(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__187) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 374 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_du(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__188) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 375 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dl(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__189) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 376 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_id(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,Uua),Uub))))) # label(fact_ATP_Olambda__190) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 377 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dr(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__191) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 378 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_di(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__192) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 379 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_do(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__193) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 380 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_df(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__194) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 381 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_in(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__195) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 382 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fo(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__196) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 383 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ff(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__197) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 384 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ga(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,Uu),Uub)))))) # label(fact_ATP_Olambda__198) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 385 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eg(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__199) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 386 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ed(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__200) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 387 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gd(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,Uu),Uub)))))) # label(fact_ATP_Olambda__201) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 388 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ea(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__202) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 389 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dx(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__203) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 390 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fx(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,Uu),Uub)))))) # label(fact_ATP_Olambda__204) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 391 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gj(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__205) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 392 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fl(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__206) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 393 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fc(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__207) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 394 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ig(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1804637580nd_nis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1804637580nd_nis,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uub)))))) # label(fact_ATP_Olambda__208) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 395 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fi(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__209) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 396 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ez(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__210) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 397 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gg(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__211) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 398 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gm(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__212) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 399 (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(scratc670471025bnd_in,Uub),Uu)) & pp(aa_TPTP_ind_bool(Uua,Uub)))) # label(fact_ATP_Olambda__213) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 400 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_kf(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc630061615_image(aa_fun1431113780TP_ind(scratc728605222_d_Sep(Uu),Uua),Uu),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1401733581_Sigma,aa_fun1431113780TP_ind(scratc728605222_d_Sep(Uu),Uua)),scratc159577406d_e_in(Uu,Uua))),Uub))))) # label(fact_ATP_Olambda__214) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 401 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ju(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1884361327d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc728605222_d_Sep(Uu),Uua)))))) # label(fact_ATP_Olambda__215) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 402 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ko(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_kn(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__216) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 403 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bd(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bc(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__217) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 404 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ke(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kd(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__218) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 405 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jy(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jx(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__219) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 406 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jw(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jv(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__220) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 407 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kj(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,Uub),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1165856785d_d_Pi,Uu),aTP_Lamm_ai(Uua)))))) # label(fact_ATP_Olambda__221) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 408 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hx(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uua),Uub))))) # label(fact_ATP_Olambda__222) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 409 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hy(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,Uua),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uub))))) # label(fact_ATP_Olambda__223) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 410 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jz(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,Uub),aa_TPTP_ind_TPTP_ind(scratc1102996173etprod(Uu),Uua))))) # label(fact_ATP_Olambda__224) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 411 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_kg(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,Uub),aa_fun1431113780TP_ind(scratc728605222_d_Sep(Uu),Uua))))) # label(fact_ATP_Olambda__225) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 412 (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(scratc669946235bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc669946235bnd_ap,Uu),Uub))) # label(fact_ATP_Olambda__226) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 413 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ew(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ev(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__227) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 414 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_es(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_er(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__228) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 415 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eo(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_en(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__229) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 416 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ek(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ej(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__230) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 417 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dc(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_db(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__231) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 418 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cy(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cx(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__232) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 419 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cu(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ct(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__233) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 420 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cq(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cp(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__234) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 421 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cm(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cl(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__235) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 422 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ci(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ch(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__236) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 423 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ce(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cd(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__237) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 424 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ca(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc238963500all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bz(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__238) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 425 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_kh(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(Uua,aa_TPTP_ind_TPTP_ind(scratc159577406d_e_in(Uu,Uua),Uub))))) # label(fact_ATP_Olambda__239) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 426 (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(scratc670471025bnd_in,X3),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670471025bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc669946235bnd_ap,Uub),X3)),aa_TPTP_ind_TPTP_ind(Uua,X3)))))))) # label(fact_ATP_Olambda__240) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 427 (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(scratc670471017bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc630061615_image(Uu,Uua),Uub),Uuc),aa_TPTP_ind_TPTP_ind(scratc2041199478d_soft(Uu,Uua,Uub),Uuc)),scratc1437595393ptyset)) # label(fact_ATP_Olambda__241) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 428 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jx(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc159577411d_e_is(Uu),aa_TPTP_ind_TPTP_ind(scratc672703684_first(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc359091634d_pair(Uu,Uua),Uub),Uuc))),Uub)))) # label(fact_ATP_Olambda__242) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 429 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_jv(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc159577411d_e_is(Uua),aa_TPTP_ind_TPTP_ind(scratc1467975200second(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc359091634d_pair(Uu,Uua),Uub),Uuc))),Uuc)))) # label(fact_ATP_Olambda__243) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 430 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kk(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc159577411d_e_is(Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc669946235bnd_ap,Uua),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc669946235bnd_ap,Uub),Uuc))))) # label(fact_ATP_Olambda__244) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 431 (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(scratc1884361327d_esti(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc669946235bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__245) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 432 (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(scratc159577411d_e_is(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc669946235bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__246) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 433 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kd(Uu),Uua),Uub),Uuc)) <-> scratc1857401069_is_of(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc359091634d_pair(Uu,Uua),Uub),Uuc),aa_TPT43085870d_bool(aTP_Lamm_jz(Uu),Uua)))) # label(fact_ATP_Olambda__247) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 434 (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(scratc1693814078d_l_ec(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1884361327d_esti(Uu),Uuc),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1884361327d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__248) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 435 (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(scratc1763592448nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1884361327d_esti(Uu),Uuc),Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1884361327d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__249) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 436 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kl(Uu),Uua),Uub),Uuc)) <-> (pp(aa_fun171081125l_bool(scratc238963500all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_kk(Uua),Uub),Uuc))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc159577411d_e_is(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1165856785d_d_Pi,Uu),aTP_Lamm_ai(Uua))),Uub),Uuc))))) # label(fact_ATP_Olambda__250) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 437 (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__251) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 438 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_db(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__252) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 439 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cp(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__253) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 440 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ct(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__254) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 441 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cd(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc782603179moreis,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__255) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 442 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bz(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__256) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 443 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cl(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__257) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 444 (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(scratc1825721420d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__258) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 445 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_er(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045625727_29_ii,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uuc),Uua))))))) # label(fact_ATP_Olambda__259) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 446 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_en(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__260) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 447 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ej(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1825721420d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uuc),Uua))))))) # label(fact_ATP_Olambda__261) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 448 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ch(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc648619567lessis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__262) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 449 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cx(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1763330045nd_iii,aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc1826180606d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__263) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 450 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_kn(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc159577411d_e_is(Uu),Uub),Uuc)) -> pp(aa_TPTP_ind_bool(Uua,Uuc)))))) # label(fact_ATP_Olambda__264) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 451 (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(scratc159577411d_e_is(Uu),Uub),Uuc)))))) # label(fact_ATP_Olambda__265) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 452 (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(scratc1697434805nd_all(Uu),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_az(Uu),Uua),Uub),Uuc))))) # label(fact_ATP_Olambda__266) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 453 (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(scratc1497107956l_some(Uua),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aq(Uu),Uub),Uuc))))) # label(fact_ATP_Olambda__267) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 454 (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(scratc1763592448nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc159577411d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc669946235bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc669946235bnd_ap,Uub),Uud))),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc159577411d_e_is(Uu),Uuc),Uud))))) # label(fact_ATP_Olambda__268) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 455 (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(scratc159577411d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc669946235bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc669946235bnd_ap,Uub),Uud)))))) # label(fact_ATP_Olambda__269) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 456 (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(scratc238963500all_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__270) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 457 (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(scratc238963500all_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__271) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 458 (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(scratc669946235bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc669946235bnd_ap,aa_TPTP_ind_TPTP_ind(scratc708759269wissel(Uu,Uub),Uuc)),Uud))) # label(fact_ATP_Olambda__272) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 459 (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(scratc238963500all_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__273) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 460 (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(scratc159577411d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc669946235bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc669946235bnd_ap,Uub),Uuc)),Uue)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc669946235bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc669946235bnd_ap,Uub),Uud)),Uuf))))))) # label(fact_ATP_Olambda__274) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 461 (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(scratc238963500all_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__275) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 462 (all Uu all Uua (gg_TPTP_ind(Uu) -> aa_TPTP_ind_TPTP_ind(aTP_Lamm_ai(Uu),Uua) = Uu)) # label(fact_ATP_Olambda__276) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 463 (all Uu aa_TPTP_ind_TPTP_ind(aTP_Lamm_ac,Uu) = scratc1804112789nd_nat) # label(fact_ATP_Olambda__277) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 464 (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].
% 1.09/1.43 465 (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].
% 1.09/1.43 466 (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].
% 1.09/1.43 467 (all P (gg_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.43 468 (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].
% 1.09/1.43 469 (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].
% 1.09/1.43 470 (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].
% 1.09/1.43 471 (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].
% 1.09/1.43 472 (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].
% 1.09/1.43 473 (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].
% 1.09/1.43 474 (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].
% 1.09/1.47 475 (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].
% 1.09/1.47 476 (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].
% 1.09/1.47
% 1.09/1.47 ============================== end of process non-clausal formulas ===
% 1.09/1.47
% 1.09/1.47 ============================== PROCESS INITIAL CLAUSES ===============
% 1.09/1.47
% 1.09/1.47 ============================== PREDICATE ELIMINATION =================
% 1.09/1.47 477 -gg_bool(A) | A = fTrue | A = fFalse # label(help_fFalse_1_1_T) # label(axiom). [clausify(467)].
% 1.09/1.47 478 gg_bool(undefined_bool(bool)) # label(gsy_c_HOL_Oundefined_001t__HOL__Obool) # label(axiom). [assumption].
% 1.09/1.47 479 gg_bool(scratc219602158_amone(A,B)) # label(gsy_c_Scratch__tptp__translate__51156__28358_ONUM699__thf__4__p_Obnd__amone) # label(axiom). [clausify(1)].
% 1.09/1.47 480 gg_bool(scratc844856671_d_and(A,B)) # label(gsy_c_Scratch__tptp__translate__51156__28358_ONUM699__thf__4__p_Obnd__d__and) # label(axiom). [clausify(2)].
% 1.09/1.47 481 gg_bool(scratc952321851_d_not(A)) # label(gsy_c_Scratch__tptp__translate__51156__28358_ONUM699__thf__4__p_Obnd__d__not) # label(axiom). [clausify(3)].
% 1.09/1.47 482 gg_bool(scratc1729890377nd_ec3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__51156__28358_ONUM699__thf__4__p_Obnd__ec3) # label(axiom). [clausify(4)].
% 1.09/1.47 483 gg_bool(scratc1693814078d_l_ec(A,B)) # label(gsy_c_Scratch__tptp__translate__51156__28358_ONUM699__thf__4__p_Obnd__l__ec) # label(axiom). [clausify(8)].
% 1.09/1.47 484 gg_bool(scratc1813489412nd_or3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__51156__28358_ONUM699__thf__4__p_Obnd__or3) # label(axiom). [clausify(9)].
% 1.09/1.47 485 gg_bool(aa_bool_bool(A,B)) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom). [clausify(10)].
% 1.09/1.47 486 gg_bool(aa_TPTP_ind_bool(A,B)) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom). [clausify(11)].
% 1.09/1.47 487 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)].
% 1.09/1.47 488 gg_bool(fEx_TPTP_ind(A)) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom). [clausify(16)].
% 1.09/1.47 489 gg_bool(fFalse) # label(gsy_c_fFalse) # label(axiom). [assumption].
% 1.09/1.47 490 gg_bool(fTrue) # label(gsy_c_fTrue) # label(axiom). [assumption].
% 1.09/1.47 Derived: undefined_bool(bool) = fTrue | undefined_bool(bool) = fFalse. [resolve(477,a,478,a)].
% 1.09/1.47 Derived: scratc219602158_amone(A,B) = fTrue | scratc219602158_amone(A,B) = fFalse. [resolve(477,a,479,a)].
% 1.09/1.47 Derived: scratc844856671_d_and(A,B) = fTrue | scratc844856671_d_and(A,B) = fFalse. [resolve(477,a,480,a)].
% 1.09/1.47 Derived: scratc952321851_d_not(A) = fTrue | scratc952321851_d_not(A) = fFalse. [resolve(477,a,481,a)].
% 1.09/1.47 Derived: scratc1729890377nd_ec3(A,B,C) = fTrue | scratc1729890377nd_ec3(A,B,C) = fFalse. [resolve(477,a,482,a)].
% 1.09/1.47 Derived: scratc1693814078d_l_ec(A,B) = fTrue | scratc1693814078d_l_ec(A,B) = fFalse. [resolve(477,a,483,a)].
% 1.09/1.47 Derived: scratc1813489412nd_or3(A,B,C) = fTrue | scratc1813489412nd_or3(A,B,C) = fFalse. [resolve(477,a,484,a)].
% 1.09/1.47 Derived: aa_bool_bool(A,B) = fTrue | aa_bool_bool(A,B) = fFalse. [resolve(477,a,485,a)].
% 1.09/1.47 Derived: aa_TPTP_ind_bool(A,B) = fTrue | aa_TPTP_ind_bool(A,B) = fFalse. [resolve(477,a,486,a)].
% 1.09/1.47 Derived: aa_fun171081125l_bool(A,B) = fTrue | aa_fun171081125l_bool(A,B) = fFalse. [resolve(477,a,487,a)].
% 1.09/1.47 Derived: fEx_TPTP_ind(A) = fTrue | fEx_TPTP_ind(A) = fFalse. [resolve(477,a,488,a)].
% 1.09/1.47 Derived: fFalse = fTrue | fFalse = fFalse. [resolve(477,a,489,a)].
% 1.09/1.47 Derived: fTrue = fTrue | fTrue = fFalse. [resolve(477,a,490,a)].
% 1.09/1.47 491 scratc2088748868d_r_ec(A,B) | pp(A) # label(fact_def__r__ec) # label(axiom). [clausify(59)].
% 1.09/1.47 492 -scratc2088748868d_r_ec(A,B) | -pp(A) | pp(scratc952321851_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(59)].
% 1.75/2.04 493 scratc2088748868d_r_ec(A,B) | -pp(scratc952321851_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(59)].
% 1.75/2.04 494 scratc1738998121_l_iff(A,B) | -pp(scratc844856671_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1763592448nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc1763592448nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(91)].
% 1.75/2.04 495 -scratc1738998121_l_iff(A,B) | pp(scratc844856671_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1763592448nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc1763592448nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(91)].
% 1.75/2.04 496 scratc1091053229d_orec(A,B) | -pp(scratc844856671_d_and(aa_bool_bool(scratc1694470083d_l_or(A),B),scratc1693814078d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(92)].
% 1.75/2.04 497 -scratc1091053229d_orec(A,B) | pp(scratc844856671_d_and(aa_bool_bool(scratc1694470083d_l_or(A),B),scratc1693814078d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(92)].
% 1.75/2.04 498 scratc1878728722nd_wel(A) | -pp(scratc952321851_d_not(scratc952321851_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(97)].
% 1.75/2.04 499 -scratc1878728722nd_wel(A) | pp(scratc952321851_d_not(scratc952321851_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(97)].
% 1.75/2.04 500 -scratc1878728722nd_wel(A) | pp(A) # label(fact_l__et) # label(axiom). [clausify(147)].
% 1.75/2.04 Derived: pp(A) | -pp(scratc952321851_d_not(scratc952321851_d_not(A))). [resolve(500,a,498,a)].
% 1.75/2.04
% 1.75/2.04 ============================== end predicate elimination =============
% 1.75/2.04
% 1.75/2.04 Auto_denials: (non-Horn, no changes).
% 1.75/2.04
% 1.75/2.04 Term ordering decisions:
% 1.75/2.04 Function symbol KB weights: aTP_Lamm_a=1. scratc670471025bnd_in=1. scratc1825721420d_n_is=1. scratc1763330045nd_iii=1. scratc1045625727_29_ii=1. scratc1469073079rdsucc=1. scratc669946235bnd_ap=1. aTP_Lamm_aj=1. scratc648619567lessis=1. scratc782603179moreis=1. scratc153103791nd_n_1=1. scratc1437595393ptyset=1. scratc1401733581_Sigma=1. scratc1804637580nd_nis=1. fFalse=1. scratc1165856785d_d_Pi=1. scratc1744045275_nat_p=1. scratc1759873369_power=1. scratc1804112789nd_nat=1. scratc93448950n_some=1. scratc1178653211d_repl=1. scratc1763592448nd_imp=1. fTrue=1. scratc1731457254d_pair=1. scratc1509153897d_Subq=1. scratc119651587_union=1. scratc1888387207_proj0=1. scratc591135635closed=1. aTP_Lamm_af=1. scratc1825721415d_n_in=1. scratc1888387208_proj1=1. scratc269830495_n_all=1. aTP_Lamm_ac=1. aTP_Lamm_ae=1. aTP_Lamm_jq=1. scratc269189027closed=1. scratc433922041closed=1. aTP_Lamm_aa=1. aTP_Lamm_bq=1. aTP_Lamm_bs=1. aTP_Lamm_bu=1. aTP_Lamm_gp=1. aTP_Lamm_gr=1. aTP_Lamm_gt=1. aTP_Lamm_gv=1. aTP_Lamm_gx=1. aTP_Lamm_gz=1. aTP_Lamm_hb=1. aTP_Lamm_hd=1. aTP_Lamm_hf=1. aTP_Lamm_hh=1. aTP_Lamm_hj=1. aTP_Lamm_hl=1. aTP_Lamm_jh=1. aTP_Lamm_jl=1. aTP_Lamm_jm=1. scratc1058042421_omega=1. scratc1756307317_prop2=1. scratc88427044d_Inj1=1. scratc969770224closed=1. aTP_Lamm_ag=1. aTP_Lamm_bg=1. aTP_Lamm_bi=1. aTP_Lamm_bj=1. aTP_Lamm_cb=1. aTP_Lamm_cf=1. aTP_Lamm_cj=1. aTP_Lamm_cn=1. aTP_Lamm_cr=1. aTP_Lamm_cv=1. aTP_Lamm_cz=1. aTP_Lamm_dd=1. aTP_Lamm_dg=1. aTP_Lamm_dj=1. aTP_Lamm_dm=1. aTP_Lamm_dp=1. aTP_Lamm_ds=1. aTP_Lamm_dv=1. aTP_Lamm_dy=1. aTP_Lamm_eb=1. aTP_Lamm_ee=1. aTP_Lamm_eh=1. aTP_Lamm_el=1. aTP_Lamm_ep=1. aTP_Lamm_et=1. aTP_Lamm_ex=1. aTP_Lamm_fa=1. aTP_Lamm_fd=1. aTP_Lamm_fg=1. aTP_Lamm_fj=1. aTP_Lamm_fm=1. aTP_Lamm_fp=1. aTP_Lamm_ft=1. aTP_Lamm_fv=1. aTP_Lamm_fy=1. aTP_Lamm_gb=1. aTP_Lamm_ge=1. aTP_Lamm_gh=1. aTP_Lamm_gk=1. aTP_Lamm_gn=1. aTP_Lamm_hn=1. aTP_Lamm_hp=1. aTP_Lamm_hr=1. aTP_Lamm_ht=1. aTP_Lamm_hv=1. aTP_Lamm_hz=1. aTP_Lamm_ib=1. aTP_Lamm_ie=1. aTP_Lamm_ih=1. aTP_Lamm_ij=1. aTP_Lamm_il=1. aTP_Lamm_io=1. aTP_Lamm_iq=1. aTP_Lamm_it=1. aTP_Lamm_iw=1. aTP_Lamm_iz=1. aTP_Lamm_jc=1. aTP_Lamm_je=1. aTP_Lamm_jf=1. aTP_Lamm_jk=1. fconj=1. fimplies=1. scratc1410803015d_Sing=1. scratc1756307316_prop1=1. scratc1903503940_cond2=1. scratc88427043d_Inj0=1. aTP_Lamm_bm=1. aTP_Lamm_br=1. aTP_Lamm_bt=1. aTP_Lamm_bv=1. aTP_Lamm_bw=1. aTP_Lamm_bx=1. aTP_Lamm_by=1. aTP_Lamm_cc=1. aTP_Lamm_cg=1. aTP_Lamm_ck=1. aTP_Lamm_co=1. aTP_Lamm_cs=1. aTP_Lamm_cw=1. aTP_Lamm_da=1. aTP_Lamm_de=1. aTP_Lamm_dh=1. aTP_Lamm_dk=1. aTP_Lamm_dn=1. aTP_Lamm_dq=1. aTP_Lamm_dt=1. aTP_Lamm_dw=1. aTP_Lamm_dz=1. aTP_Lamm_ec=1. aTP_Lamm_ef=1. aTP_Lamm_ei=1. aTP_Lamm_em=1. aTP_Lamm_eq=1. aTP_Lamm_eu=1. aTP_Lamm_ey=1. aTP_Lamm_fb=1. aTP_Lamm_fe=1. aTP_Lamm_fh=1. aTP_Lamm_fk=1. aTP_Lamm_fn=1. aTP_Lamm_fq=1. aTP_Lamm_fr=1. aTP_Lamm_fs=1. aTP_Lamm_fu=1. aTP_Lamm_fw=1. aTP_Lamm_fz=1. aTP_Lamm_gc=1. aTP_Lamm_gf=1. aTP_Lamm_gi=1. aTP_Lamm_gl=1. aTP_Lamm_go=1. aTP_Lamm_gq=1. aTP_Lamm_gs=1. aTP_Lamm_gu=1. aTP_Lamm_gw=1. aTP_Lamm_gy=1. aTP_Lamm_ha=1. aTP_Lamm_hc=1. aTP_Lamm_he=1. aTP_Lamm_hg=1. aTP_Lamm_hi=1. aTP_Lamm_hk=1. aTP_Lamm_hm=1. aTP_Lamm_ho=1. aTP_Lamm_hq=1. aTP_Lamm_hs=1. aTP_Lamm_hu=1. aTP_Lamm_hw=1. aTP_Lamm_ia=1. aTP_Lamm_ic=1. aTP_Lamm_if=1. aTP_Lamm_ii=1. aTP_Lamm_ik=1. aTP_Lamm_im=1. aTP_Lamm_ip=1. aTP_Lamm_ir=1. aTP_Lamm_is=1. aTP_Lamm_iu=1. aTP_Lamm_iv=1. aTP_Lamm_ix=1. aTP_Lamm_iy=1. aTP_Lamm_ja=1. aTP_Lamm_jb=1. aTP_Lamm_jd=1. aTP_Lamm_jg=1. aTP_Lamm_ji=1. aTP_Lamm_jj=1. aTP_Lamm_jn=1. aTP_Lamm_jo=1. aTP_Lamm_jp=1. aTP_Lamm_js=1. aTP_Lamm_kp=1. fequal_TPTP_ind=1. scratc1802538407nd_nIn=1. scratc1903503939_cond1=1. scratc29618409univof=1. scratc385622756_n_one=1. scratc745718617_d_Unj=1. aTP_Lamm_ab=1. aTP_Lamm_ah=1. aTP_Lamm_bk=1. aTP_Lamm_bl=1. bool=1. scratc1167945141_prop1=1. scratc1325823050pair_p=1. scratc1373910193_prop1=1. scratc1723190380nempty=1. scratc1803035945munion=1. scratc1823120998d_plus=1. scratc1888780805_prop4=1. scratc403150895_prop1=1. scratc491547137_empty=1. scratc579582966_prop1=1. scratc785548018_prop1=1. scratc1022422143d_i1_s=1. scratc1814875053d_24_g=1. tPTP_ind=1. aa_TPT43085870d_bool=1. aa_TPTP_ind_bool=1. aa_TPTP_ind_TPTP_ind=1. aa_fun171081125l_bool=1. aa_TPT60673477d_bool=1. aa_TPT1424761345TP_ind=1. aa_fun277296641TP_ind=1. aa_TPT494704832TP_ind=1. aa_bool_bool=1. aa_fun1584354236d_bool=1. aa_fun1431113780TP_ind=1. aa_boo1142376798l_bool=1. scratc844856671_d_and=1. aa_TPT1123896796d_bool=1. scratc670471017bnd_if=1. scratc1693814078d_l_ec=1. aa_fun1212484691d_bool=1. aa_TPT985247859d_bool=1. scratc159577406d_e_in=1. scratc359091634d_pair=1. aa_fun987228051d_bool=1. scratc1763658035nd_ind=1. scratc219602158_amone=1. scratc1467975200second=1. scratc630061615_image=1. scratc672703684_first=1. aa_TPT125613450d_bool=1. scratc1805031169nd_non=1. aa_fun1913827119d_bool=1. scratc867204663d_anec=1. aa_TPT1791839040TP_ind=1. aa_fun1107270209d_bool=1. aa_fun845057962d_bool=1. scratc1000013399eplSep=1. scratc1184208387_ecelt=1. scratc1729890438nd_ecp=1. scratc1183617996_ecect=1. aa_TPT1781712639TP_ind=1. aa_TPT2142672771l_bool=1. aa_fun1235454963TP_ind=1. cOMBB_658106424TP_ind=1. cOMBS_2003118649l_bool=1. scratc1729890442nd_ect=1. scratc1813686274nd_out=1. scratc328705946fixfu2=1. scratc436552825etprop=1. scratc708759269wissel=1. scratc721419928_fixfu=1. scratc840732472ectset=1. scratc670566497d_invf=1. scratc674303028d_tofs=1. scratc725530595ectelt=1. scratc867320772nverse=1. scratc946849818unmore=1. f1=1. f12=1. f13=1. f20=1. f24=1. scratc238963500all_of=1. scratc1826180606d_n_pl=1. scratc159577411d_e_is=1. scratc952321851_d_not=1. scratc728605222_d_Sep=1. scratc1884361327d_esti=1. scratc1497107956l_some=1. scratc572008692ffprop=1. scratc1697434805nd_all=1. scratc1694470083d_l_or=1. scratc671246324_rec_G=1. aTP_Lamm_ai=1. aTP_Lamm_jz=1. scratc1813227066nd_one=1. aTP_Lamm_ak=1. aTP_Lamm_au=1. aTP_Lamm_bc=1. aTP_Lamm_bp=1. aTP_Lamm_bz=1. aTP_Lamm_cd=1. aTP_Lamm_ch=1. aTP_Lamm_cl=1. aTP_Lamm_cp=1. aTP_Lamm_ct=1. aTP_Lamm_cx=1. aTP_Lamm_db=1. aTP_Lamm_ej=1. aTP_Lamm_en=1. aTP_Lamm_er=1. aTP_Lamm_ev=1. aTP_Lamm_fx=1. aTP_Lamm_ga=1. aTP_Lamm_gd=1. aTP_Lamm_gg=1. aTP_Lamm_gj=1. aTP_Lamm_gm=1. aTP_Lamm_hx=1. aTP_Lamm_jr=1. aTP_Lamm_kn=1. scratc669320122d_incl=1. aTP_Lamm_ao=1. aTP_Lamm_ay=1. aTP_Lamm_bb=1. aTP_Lamm_bf=1. aTP_Lamm_df=1. aTP_Lamm_di=1. aTP_Lamm_dl=1. aTP_Lamm_do=1. aTP_Lamm_dr=1. aTP_Lamm_du=1. aTP_Lamm_dx=1. aTP_Lamm_ea=1. aTP_Lamm_ed=1. aTP_Lamm_eg=1. Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------