TSTP Solution File: NUM712+4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM712+4 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 13:31:07 EDT 2022
% Result : Timeout 300.03s 300.29s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : NUM712+4 : TPTP v8.1.0. Released v7.3.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.33 % Computer : n018.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Wed Jul 6 07:08:08 EDT 2022
% 0.11/0.33 % CPUTime :
% 1.07/1.38 ============================== Prover9 ===============================
% 1.07/1.38 Prover9 (32) version 2009-11A, November 2009.
% 1.07/1.38 Process 423 was started by sandbox on n018.cluster.edu,
% 1.07/1.38 Wed Jul 6 07:08:09 2022
% 1.07/1.38 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_32738_n018.cluster.edu".
% 1.07/1.38 ============================== end of head ===========================
% 1.07/1.38
% 1.07/1.38 ============================== INPUT =================================
% 1.07/1.38
% 1.07/1.38 % Reading from file /tmp/Prover9_32738_n018.cluster.edu
% 1.07/1.38
% 1.07/1.38 set(prolog_style_variables).
% 1.07/1.38 set(auto2).
% 1.07/1.38 % set(auto2) -> set(auto).
% 1.07/1.38 % set(auto) -> set(auto_inference).
% 1.07/1.38 % set(auto) -> set(auto_setup).
% 1.07/1.38 % set(auto_setup) -> set(predicate_elim).
% 1.07/1.38 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.07/1.38 % set(auto) -> set(auto_limits).
% 1.07/1.38 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.07/1.38 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.07/1.38 % set(auto) -> set(auto_denials).
% 1.07/1.38 % set(auto) -> set(auto_process).
% 1.07/1.38 % set(auto2) -> assign(new_constants, 1).
% 1.07/1.38 % set(auto2) -> assign(fold_denial_max, 3).
% 1.07/1.38 % set(auto2) -> assign(max_weight, "200.000").
% 1.07/1.38 % set(auto2) -> assign(max_hours, 1).
% 1.07/1.38 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.07/1.38 % set(auto2) -> assign(max_seconds, 0).
% 1.07/1.38 % set(auto2) -> assign(max_minutes, 5).
% 1.07/1.38 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.07/1.38 % set(auto2) -> set(sort_initial_sos).
% 1.07/1.38 % set(auto2) -> assign(sos_limit, -1).
% 1.07/1.38 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.07/1.38 % set(auto2) -> assign(max_megs, 400).
% 1.07/1.38 % set(auto2) -> assign(stats, some).
% 1.07/1.38 % set(auto2) -> clear(echo_input).
% 1.07/1.38 % set(auto2) -> set(quiet).
% 1.07/1.38 % set(auto2) -> clear(print_initial_clauses).
% 1.07/1.38 % set(auto2) -> clear(print_given).
% 1.07/1.38 assign(lrs_ticks,-1).
% 1.07/1.38 assign(sos_limit,10000).
% 1.07/1.38 assign(order,kbo).
% 1.07/1.38 set(lex_order_vars).
% 1.07/1.38 clear(print_given).
% 1.07/1.38
% 1.07/1.38 % formulas(sos). % not echoed (654 formulas)
% 1.07/1.38
% 1.07/1.38 ============================== end of input ==========================
% 1.07/1.38
% 1.07/1.38 % From the command line: assign(max_seconds, 300).
% 1.07/1.38
% 1.07/1.38 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.07/1.38
% 1.07/1.38 % Formulas that are not ordinary clauses:
% 1.07/1.38 1 (all B_1 all B_2 gg_bool(scratc920260971_amone(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__53843__10784_ONUM712__thf__4__p_Obnd__amone) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 2 (all B_1 all B_2 gg_bool(scratc769812514_d_and(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__53843__10784_ONUM712__thf__4__p_Obnd__d__and) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 3 (all B_1 gg_bool(scratc877277694_d_not(B_1))) # label(gsy_c_Scratch__tptp__translate__53843__10784_ONUM712__thf__4__p_Obnd__d__not) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 4 (all B_1 all B_2 all B_3 gg_bool(scratc698018630nd_ec3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__53843__10784_ONUM712__thf__4__p_Obnd__ec3) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 5 (all B_1 all B_2 gg_TPTP_ind(scratc698018695nd_ect(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__53843__10784_ONUM712__thf__4__p_Obnd__ect) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 6 (all B_1 gg_TPTP_ind(scratc698871481nd_eps(B_1))) # label(gsy_c_Scratch__tptp__translate__53843__10784_ONUM712__thf__4__p_Obnd__eps) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 7 (all B_1 all B_2 gg_TPTP_ind(scratc731786288nd_ind(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__53843__10784_ONUM712__thf__4__p_Obnd__ind) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 8 (all B_1 all B_2 gg_bool(scratc246989243d_l_ec(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__53843__10784_ONUM712__thf__4__p_Obnd__l__ec) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 9 (all B_1 all B_2 all B_3 gg_bool(scratc781617665nd_or3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__53843__10784_ONUM712__thf__4__p_Obnd__or3) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 10 (all B_1 all B_2 gg_bool(aa_bool_bool(B_1,B_2))) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 11 (all B_1 all B_2 gg_bool(aa_TPTP_ind_bool(B_1,B_2))) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 12 (all B_1 all B_2 gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2))) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 13 (all B_1 all B_2 gg_bool(aa_fun171081125l_bool(B_1,B_2))) # label(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__HOL__Obool) # label(hypothesis) # label(non_clause). [assumption].
% 1.07/1.38 14 (all B_1 all B_2 gg_TPTP_ind(aa_fun1431113780TP_ind(B_1,B_2))) # label(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 15 (all B_1 all B_2 gg_TPTP_ind(aa_fun277296641TP_ind(B_1,B_2))) # label(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__TPTP____Interpret__Oind_J_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 16 (all B_1 gg_bool(fEx_TPTP_ind(B_1))) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 17 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1634323825_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(scratc379618174d_n_ts(aa_TPTP_ind_TPTP_ind(scratc379618174d_n_ts(X),Xa)),Xb)),aa_TPTP_ind_TPTP_ind(scratc379618174d_n_ts(X),aa_TPTP_ind_TPTP_ind(scratc379618174d_n_ts(Xa),Xb)))))) # label(fact_def__d__431__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 18 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1045961650_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(scratc379618174d_n_ts(X),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Xa),Xb))),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(aa_TPTP_ind_TPTP_ind(scratc379618174d_n_ts(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc379618174d_n_ts(X),Xb)))))) # label(fact_def__d__430__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 19 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc652057960_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(scratc379618174d_n_ts(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc379618174d_n_ts(Xa),X))))) # label(fact_def__d__429__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 20 (all X scratc379618174d_n_ts(X) = aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,aa_TPTP_ind_TPTP_ind(scratc105167447_times,X))) # label(fact_def__n__ts) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 21 (all X aa_TPTP_ind_TPTP_ind(scratc105167447_times,X) = scratc731786288nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1866515598d_d_Pi,scratc772241042nd_nat),aTP_Lamm_ad),aa_TPT43085870d_bool(scratc63695786_prop2,X))) # label(fact_def__times) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 22 (all X aa_TPTP_ind_TPTP_ind(scratc756739298_428_g,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc105151248_Sigma,scratc772241042nd_nat),aTP_Lamm_ae(X))) # label(fact_def__d__428__g) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 23 (all X (pp(aa_TPTP_ind_bool(scratc63695788_prop4,X)) <-> pp(aa_fun171081125l_bool(scratc707974129l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1866515598d_d_Pi,scratc772241042nd_nat),aTP_Lamm_ad)),aa_TPT43085870d_bool(scratc63695786_prop2,X))))) # label(fact_def__d__428__prop4) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 24 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc63695786_prop2,X),Xa)) <-> pp(scratc769812514_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,Xa),scratc1230440946nd_n_1)),X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc63695785_prop1,X),Xa))))) # label(fact_def__d__428__prop2) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 25 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc63695785_prop1,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc194786338_n_all,aa_TPT43085870d_bool(aTP_Lamm_ag(X),Xa))))) # label(fact_def__d__428__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 26 (all X all Xa (pp(aa_TPTP_ind_bool(scratc764504323nd_min(X),Xa)) <-> pp(scratc769812514_d_and(aa_TPTP_ind_bool(scratc379093365d_n_lb(X),Xa),aa_TPTP_ind_bool(X,Xa))))) # label(fact_def__min) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 27 (all X all Xa (pp(aa_TPTP_ind_bool(scratc379093365d_n_lb(X),Xa)) <-> pp(aa_fun171081125l_bool(scratc194786338_n_all,aa_TPT43085870d_bool(scratc1247703976lbprop(X),Xa))))) # label(fact_def__n__lb) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 28 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1247703976lbprop(X),Xa),Xb)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc731720701nd_imp,aa_TPTP_ind_bool(X,Xb)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc573575410lessis,Xa),Xb))))) # label(fact_def__lbprop) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 29 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc573575410lessis,X),Xa)) <-> pp(aa_bool_bool(scratc247645248d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,X),Xa))))) # label(fact_def__lessis) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 30 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc707559022moreis,X),Xa)) <-> pp(aa_bool_bool(scratc247645248d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,X),Xa))))) # label(fact_def__moreis) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 31 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1262694002_prop1,X),Xa)) <-> pp(scratc781617665nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,X),Xa))))) # label(fact_def__d__29__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 32 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1451798771n_some,aa_TPT43085870d_bool(scratc1422910007ffprop(Xa),X))))) # label(fact_def__iii) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 33 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1451798771n_some,aa_TPT43085870d_bool(scratc1422910007ffprop(X),Xa))))) # label(fact_def__d__29__ii) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 34 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1422910007ffprop(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,X),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Xa),Xb))))) # label(fact_def__diffprop) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 35 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc674331827_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc772765833nd_nis,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(X),Xb))))) # label(fact_def__d__28__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 36 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc85969652_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc772765833nd_nis,Xa),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(X),Xa))))) # label(fact_def__d__27__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 37 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1645091125_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Xa),X))))) # label(fact_def__d__26__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 38 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1056728950_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(X),Xa)),Xb)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(X),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Xa),Xb)))))) # label(fact_def__d__25__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 39 (all X scratc379355771d_n_pl(X) = aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,aa_TPTP_ind_TPTP_ind(scratc752974505d_plus,X))) # label(fact_def__n__pl) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 40 (all X aa_TPTP_ind_TPTP_ind(scratc752974505d_plus,X) = scratc731786288nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1866515598d_d_Pi,scratc772241042nd_nat),aTP_Lamm_ad),aa_TPT43085870d_bool(scratc468366776_prop2,X))) # label(fact_def__plus) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 41 (all X aa_TPTP_ind_TPTP_ind(scratc518292720d_24_g,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc105151248_Sigma,scratc772241042nd_nat),aTP_Lamm_ah(X))) # label(fact_def__d__24__g) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 42 (all X (pp(aa_TPTP_ind_bool(scratc441955970_prop4,X)) <-> pp(aa_fun171081125l_bool(scratc707974129l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1866515598d_d_Pi,scratc772241042nd_nat),aTP_Lamm_ad)),aa_TPT43085870d_bool(scratc468366776_prop2,X))))) # label(fact_def__prop4) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 43 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441955969_prop3(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,X),Xb)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,Xa),Xb))))) # label(fact_def__prop3) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 44 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc468366776_prop2,X),Xa)) <-> pp(scratc769812514_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,Xa),scratc1230440946nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,X)),aa_TPTP_ind_bool(scratc468366775_prop1,Xa))))) # label(fact_def__d__24__prop2) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 45 (all X (pp(aa_TPTP_ind_bool(scratc468366775_prop1,X)) <-> pp(aa_fun171081125l_bool(scratc194786338_n_all,aa_TPT43085870d_bool(aTP_Lamm_ai,X))))) # label(fact_def__d__24__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 46 (all X (pp(aa_TPTP_ind_bool(scratc2027488248_prop1,X)) <-> pp(aa_bool_bool(scratc247645248d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,X),scratc1230440946nd_n_1)),aa_fun171081125l_bool(scratc1451798771n_some,aa_TPT43085870d_bool(aTP_Lamm_aj,X)))))) # label(fact_def__d__23__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 47 (all X (pp(aa_TPTP_ind_bool(scratc1439126073_prop1,X)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc772765833nd_nis,aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,X)),X)))) # label(fact_def__d__22__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 48 (all X (pp(aa_TPTP_ind_bool(scratc456679105_cond2,X)) <-> pp(aa_fun171081125l_bool(scratc194786338_n_all,aa_TPT43085870d_bool(aTP_Lamm_ak,X))))) # label(fact_def__cond2) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 49 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc772765833nd_nis,X),Xa)) <-> pp(scratc877277694_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,X),Xa))))) # label(fact_def__nis) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 50 (all X all Xa all Xb all Xc all Xd scratc37171638indeq2(X,Xa,Xb,Xc,Xd) = aa_TPT1424761345TP_ind(scratc2135960956_indeq(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1331934132d_11_i(X,Xa,Xb),Xc),Xd))) # label(fact_def__indeq2) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 51 (all X all Xa all Xb scratc1331934132d_11_i(X,Xa,Xb) = scratc2135960956_indeq(X,Xa,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1866515598d_d_Pi,X),aTP_Lamm_am(Xb)))) # label(fact_def__d__11__i) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.38 52 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc253661789fixfu2(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aa_TPT43085870d_bool(aTP_Lamm_an,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ar(X),Xa),Xb),Xc))))) # label(fact_def__fixfu2) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 53 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2135960956_indeq(X,Xa,Xb),Xc),Xd) = scratc731786288nd_ind(Xb,aa_TPT43085870d_bool(scratc441955968_prop2(X,Xa,Xb,Xc),Xd))) # label(fact_def__indeq) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 54 (all X all Xa all Xb all Xc all Xd all Xe (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441955968_prop2(X,Xa,Xb,Xc),Xd),Xe)) <-> pp(aa_fun171081125l_bool(scratc707974129l_some(X),aa_TPT43085870d_bool(scratc1015689402_prop1(X,Xa,Xb,Xc,Xd),Xe))))) # label(fact_def__prop2) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 55 (all X all Xa all Xb all Xc all Xd all Xe all Xf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1015689402_prop1(X,Xa,Xb,Xc,Xd),Xe),Xf)) <-> pp(scratc769812514_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc814214834d_esti(X),Xf),aa_TPTP_ind_TPTP_ind(scratc1884276809_ecect(X,Xa),Xd)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc860236224d_e_is(Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,Xc),Xf)),Xe))))) # label(fact_def__d__10__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 56 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1422078741_fixfu(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aa_TPT43085870d_bool(aTP_Lamm_an,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_at(X),Xa),Xb),Xc))))) # label(fact_def__fixfu) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 57 (all X all Xa scratc1884276809_ecect(X,Xa) = scratc860236219d_e_in(aa_TPTP_ind_TPTP_ind(scratc313048534_power,X),scratc1944541818d_anec(X,Xa))) # label(fact_def__ecect) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 58 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc650486438ectelt(X,Xa),Xb) = aa_TPTP_ind_TPTP_ind(scratc765688315ectset(X,Xa),aa_TPTP_ind_TPTP_ind(scratc1884867200_ecelt(X,Xa),Xb))) # label(fact_def__ectelt) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 59 (all X all Xa scratc765688315ectset(X,Xa) = scratc781814527nd_out(aa_TPTP_ind_TPTP_ind(scratc313048534_power,X),scratc1944541818d_anec(X,Xa))) # label(fact_def__ectset) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 60 (all X all Xa scratc698018695nd_ect(X,Xa) = aa_fun1431113780TP_ind(scratc653561065_d_Sep(aa_TPTP_ind_TPTP_ind(scratc313048534_power,X)),scratc1944541818d_anec(X,Xa))) # label(fact_def__ect) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 61 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc1944541818d_anec(X,Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc707974129l_some(X),aa_TPT43085870d_bool(scratc698018691nd_ecp(X,Xa),Xb))))) # label(fact_def__anec) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 62 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc698018691nd_ecp(X,Xa),Xb),Xc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc860236224d_e_is(aa_TPTP_ind_TPTP_ind(scratc313048534_power,X)),Xb),aa_TPTP_ind_TPTP_ind(scratc1884867200_ecelt(X,Xa),Xc))))) # label(fact_def__ecp) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 63 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1884867200_ecelt(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc653561065_d_Sep(X),aa_TPT43085870d_bool(Xa,Xb))) # label(fact_def__ecelt) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 64 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc871805661unmore(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc653561065_d_Sep(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_av(X),Xa),Xb))) # label(fact_def__unmore) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 65 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc460229692etprop(X,Xa),Xb),Xc)) <-> pp(scratc769812514_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc814214834d_esti(X),Xc),Xa),scratc877277694_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc814214834d_esti(X),Xc),Xb)))))) # label(fact_def__nissetprop) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 66 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1833432748t_disj(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc665563058nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aw(X),Xa),Xb))))) # label(fact_def__st__disj) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 67 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1746657277d_incl(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc665563058nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ax(X),Xa),Xb))))) # label(fact_def__incl) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 68 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc426608047nempty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc707974129l_some(X),aa_TPT43085870d_bool(aTP_Lamm_ay(X),Xa))))) # label(fact_def__nonempty) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 69 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1192205950_empty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aa_TPT43085870d_bool(aTP_Lamm_an,X)),scratc773159422nd_non(X,aa_TPT43085870d_bool(aTP_Lamm_ay(X),Xa)))))) # label(fact_def__empty) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 70 (all X scratc814214834d_esti(X) = scratc1025384756bnd_in) # label(fact_def__esti) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 71 (all X all Xa (scratc641924033d_r_ec(X,Xa) <-> (pp(X) -> pp(scratc877277694_d_not(Xa))))) # label(fact_def__r__ec) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 72 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc92145895hangef(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc105151248_Sigma,X),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_az(X),Xb),Xc),Xd))) # label(fact_def__changef) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 73 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc633715112wissel(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc105151248_Sigma,X),scratc399599379sel_wb(X,Xa,Xb))) # label(fact_def__wissel) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 74 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc399599379sel_wb(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc732179883nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc860236224d_e_is(X),Xc),Xb),X,Xa),aa_TPTP_ind_TPTP_ind(scratc399599378sel_wa(X,Xa,Xb),Xc))) # label(fact_def__wissel__wb) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 75 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc399599378sel_wa(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc732179883nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc860236224d_e_is(X),Xc),Xa),X,Xb),Xc)) # label(fact_def__wissel__wa) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 76 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc732179883nd_ite(X,Xa,Xb),Xc) = scratc731786288nd_ind(Xa,aa_TPT43085870d_bool(scratc441955967_prop1(X,Xa,Xb),Xc))) # label(fact_def__ite) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 77 (all X all Xa all Xb all Xc all Xd (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc441955967_prop1(X,Xa,Xb),Xc),Xd)) <-> pp(scratc769812514_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc731720701nd_imp,X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc860236224d_e_is(Xa),Xd),Xb)),aa_bool_bool(aa_boo1142376798l_bool(scratc731720701nd_imp,scratc877277694_d_not(X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc860236224d_e_is(Xa),Xd),Xc)))))) # label(fact_def__prop1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 78 (all X all Xa scratc1392931043second(X,Xa) = scratc441562373_proj1) # label(fact_def__second) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 79 (all X all Xa scratc1373362497_first(X,Xa) = scratc441562372_proj0) # label(fact_def__first) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 80 (all X all Xa scratc1717441455d_pair(X,Xa) = scratc661310761d_pair) # label(fact_def__d__pair) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 81 (all X all Xa scratc781814527nd_out(X,Xa) = scratc971052985d_soft(aa_fun1431113780TP_ind(scratc653561065_d_Sep(X),Xa),X,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc105151248_Sigma,aa_fun1431113780TP_ind(scratc653561065_d_Sep(X),Xa)),scratc860236219d_e_in(X,Xa)))) # label(fact_def__out) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 82 (all X all Xa all Xb (gg_TPTP_ind(Xb) -> aa_TPTP_ind_TPTP_ind(scratc860236219d_e_in(X,Xa),Xb) = Xb)) # label(fact_def__e__in) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 83 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc374977778_inj_h(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc105151248_Sigma,X),aa_TPT1424761345TP_ind(aTP_Lamm_ba(Xc),Xd))) # label(fact_def__inj__h) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 84 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1747903652d_invf(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc105151248_Sigma,Xa),scratc971052985d_soft(X,Xa,Xb))) # label(fact_def__invf) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 85 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1154087830ective(X),Xa),Xb)) <-> pp(scratc769812514_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc970368600ective(X),Xa),Xb),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2143458635ective(X),Xa),Xb))))) # label(fact_def__bijective) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 86 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2143458635ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc665563058nd_all(Xa),aa_TPT43085870d_bool(scratc1330720428_image(X,Xa),Xb))))) # label(fact_def__surjective) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 87 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc78186945nverse(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc105151248_Sigma,Xa),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_bb(X),Xa),Xb))) # label(fact_def__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 88 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc971052985d_soft(X,Xa,Xb),Xc) = scratc731786288nd_ind(X,aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bc(Xa),Xb),Xc))) # label(fact_def__soft) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 89 (all X all Xa scratc1751640183d_tofs(X,Xa) = scratc1024859966bnd_ap) # label(fact_def__tofs) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 90 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1330720428_image(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc707974129l_some(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bc(Xa),Xb),Xc))))) # label(fact_def__image) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 91 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc970368600ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc665563058nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_be(X),Xa),Xb))))) # label(fact_def__injective) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 92 (all X all Xa scratc731786288nd_ind(X,Xa) = scratc698871481nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bf(X),Xa))) # label(fact_def__ind) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 93 (all X all Xa (pp(aa_fun171081125l_bool(scratc781355319nd_one(X),Xa)) <-> pp(scratc769812514_d_and(scratc920260971_amone(X,Xa),aa_fun171081125l_bool(scratc707974129l_some(X),Xa))))) # label(fact_def__one) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 94 (all X all Xa (pp(scratc920260971_amone(X,Xa)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aa_TPT43085870d_bool(aTP_Lamm_an,X)),aa_fun1584354236d_bool(aTP_Lamm_bh(X),Xa))))) # label(fact_def__amone) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 95 (all X scratc860236224d_e_is(X) = fequal_TPTP_ind) # label(fact_def__e__is) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 96 (all X all Xa all Xb (scratc1366407491_orec3(X,Xa,Xb) <-> pp(scratc769812514_d_and(scratc781617665nd_or3(X,Xa,Xb),scratc698018630nd_ec3(X,Xa,Xb))))) # label(fact_def__orec3) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 97 (all X all Xa all Xb (pp(scratc698018630nd_ec3(X,Xa,Xb)) <-> scratc1944476171d_and3(scratc246989243d_l_ec(X,Xa),scratc246989243d_l_ec(Xa,Xb),scratc246989243d_l_ec(Xb,X)))) # label(fact_def__ec3) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 98 (all X all Xa all Xb (scratc1944476171d_and3(X,Xa,Xb) <-> pp(scratc769812514_d_and(X,scratc769812514_d_and(Xa,Xb))))) # label(fact_def__and3) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 99 (all X all Xa all Xb (pp(scratc781617665nd_or3(X,Xa,Xb)) <-> pp(aa_bool_bool(scratc247645248d_l_or(X),aa_bool_bool(scratc247645248d_l_or(Xa),Xb))))) # label(fact_def__or3) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 100 (all X all Xa (pp(aa_fun171081125l_bool(scratc707974129l_some(X),Xa)) <-> pp(scratc877277694_d_not(aa_fun171081125l_bool(scratc1597313321all_of(aa_TPT43085870d_bool(aTP_Lamm_an,X)),scratc773159422nd_non(X,Xa)))))) # label(fact_def__l__some) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 101 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc773159422nd_non(X,Xa),Xb)) <-> pp(scratc877277694_d_not(aa_TPTP_ind_bool(Xa,Xb))))) # label(fact_def__non) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 102 (all X scratc665563058nd_all(X) = scratc1597313321all_of(aa_TPT43085870d_bool(aTP_Lamm_an,X))) # label(fact_def__all) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 103 (all X all Xa (scratc1663953964_l_iff(X,Xa) <-> pp(scratc769812514_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc731720701nd_imp,X),Xa),aa_bool_bool(aa_boo1142376798l_bool(scratc731720701nd_imp,Xa),X))))) # label(fact_def__l__iff) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 104 (all X all Xa (scratc20906736d_orec(X,Xa) <-> pp(scratc769812514_d_and(aa_bool_bool(scratc247645248d_l_or(X),Xa),scratc246989243d_l_ec(X,Xa))))) # label(fact_def__orec) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 105 (all X scratc247645248d_l_or(X) = aa_boo1142376798l_bool(scratc731720701nd_imp,scratc877277694_d_not(X))) # label(fact_def__l__or) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 106 (all X all Xa (pp(scratc769812514_d_and(X,Xa)) <-> pp(scratc877277694_d_not(scratc246989243d_l_ec(X,Xa))))) # label(fact_def__d__and) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 107 (all X all Xa (pp(scratc246989243d_l_ec(X,Xa)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc731720701nd_imp,X),scratc877277694_d_not(Xa))))) # label(fact_def__l__ec) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 108 scratc943269592bvious <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc731720701nd_imp,fFalse),fFalse)) # label(fact_def__obvious) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 109 (all X (scratc846856975nd_wel(X) <-> pp(scratc877277694_d_not(scratc877277694_d_not(X))))) # label(fact_def__wel) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 110 (all X (pp(scratc877277694_d_not(X)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc731720701nd_imp,X),fFalse)))) # label(fact_def__d__not) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 111 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1866515598d_d_Pi,X),Xa) = aa_fun1431113780TP_ind(scratc653561065_d_Sep(aa_TPTP_ind_TPTP_ind(scratc313048534_power,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc105151248_Sigma,X),aTP_Lamm_bi(Xa)))),aa_fun1913827119d_bool(aTP_Lamm_bj(X),Xa))) # label(fact_def__d__Pi) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 112 (all X (gg_TPTP_ind(X) -> (pp(aa_TPTP_ind_bool(scratc536689223pair_p,X)) <-> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc661310761d_pair,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,X),scratc141013060ptyset)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,X),aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,scratc141013060ptyset))) = X))) # label(fact_def__pair__p) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 113 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc1023690266eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bk,Xa)),scratc441562373_proj1)) # label(fact_def__ap) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 114 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc313862346etprod(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc105151248_Sigma,X),aTP_Lamm_am(Xa))) # label(fact_def__setprod) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 115 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc105151248_Sigma,X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc506453612munion,X),aTP_Lamm_bl(Xa))) # label(fact_def__d__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 116 (all X aa_TPTP_ind_TPTP_ind(scratc441562373_proj1,X) = aa_fun277296641TP_ind(scratc1023690266eplSep(X,aTP_Lamm_bm),scratc670674460_d_Unj)) # label(fact_def__proj1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 117 (all X aa_TPTP_ind_TPTP_ind(scratc441562372_proj0,X) = aa_fun277296641TP_ind(scratc1023690266eplSep(X,aTP_Lamm_bn),scratc670674460_d_Unj)) # label(fact_def__proj0) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 118 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc661310761d_pair,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1500310711nunion(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc108506718d_repl,X),scratc1446776864d_Inj0)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc108506718d_repl,Xa),scratc1446776865d_Inj1))) # label(fact_def__pair) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 119 (all X aa_TPTP_ind_TPTP_ind(scratc1446776864d_Inj0,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc108506718d_repl,X),scratc1446776865d_Inj1)) # label(fact_def__d__Inj0) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 120 (all X (pp(aa_TPTP_ind_bool(scratc1669001118_nat_p,X)) <-> (all X1 (pp(aa_TPTP_ind_bool(X1,scratc141013060ptyset)) -> ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(X1,X2)) -> pp(aa_TPTP_ind_bool(X1,aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,X2)))))) -> pp(aa_TPTP_ind_bool(X1,X))))))) # label(fact_def__nat__p) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 121 (all X aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1500310711nunion(X),aa_TPTP_ind_TPTP_ind(scratc621669188d_Sing,X))) # label(fact_def__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 122 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc751453846In_rec(X),Xa) = scratc698871481nd_eps(aa_TPT43085870d_bool(scratc1508860529_rec_G(X),Xa))) # label(fact_def__d__In__rec) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 123 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1508860529_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(scratc1025384756bnd_in,X6),X4)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(X3,X6),aa_TPTP_ind_TPTP_ind(X5,X6)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(X3,X4),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(X,X4),X5)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(X3,Xa),Xb)))))) # label(fact_def__d__In__rec__G) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 124 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1416596253tminus(X),Xa) = aa_fun1431113780TP_ind(scratc653561065_d_Sep(X),aa_TPT43085870d_bool(aTP_Lamm_bq,Xa))) # label(fact_def__setminus) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 125 (all X all Xa scratc1023690266eplSep(X,Xa) = aa_TPT494704832TP_ind(scratc108506718d_repl,aa_fun1431113780TP_ind(scratc653561065_d_Sep(X),Xa))) # label(fact_def__d__ReplSep) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 126 (all X all Xa aa_fun1431113780TP_ind(scratc653561065_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1025384748bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1025384756bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc108506718d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_br(X),Xa))),scratc141013060ptyset)) # label(fact_def__d__Sep) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 127 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc506453612munion,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc820310400_union,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc108506718d_repl,X),Xa))) # label(fact_def__famunion) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 128 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1500310711nunion(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc820310400_union,aa_TPTP_ind_TPTP_ind(scratc2147121274_UPair(X),Xa))) # label(fact_def__binunion) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 129 (all X aa_TPTP_ind_TPTP_ind(scratc621669188d_Sing,X) = aa_TPTP_ind_TPTP_ind(scratc2147121274_UPair(X),X)) # label(fact_def__d__Sing) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 130 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc2147121274_UPair(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc108506718d_repl,aa_TPTP_ind_TPTP_ind(scratc313048534_power,aa_TPTP_ind_TPTP_ind(scratc313048534_power,scratc141013060ptyset))),aa_TPT1424761345TP_ind(aTP_Lamm_bs(X),Xa))) # label(fact_def__d__UPair) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 131 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc770666660nd_nIn,X),Xa)) <-> -pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X),Xa)))) # label(fact_def__nIn) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 132 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1025384748bnd_if(X,Xa),Xb) = scratc698871481nd_eps(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bt(X),Xa),Xb))) # label(fact_def__if) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 133 (all X (pp(aa_TPTP_ind_bool(scratc1807384429closed,X)) <-> pp(aa_TPTP_ind_bool(scratc1858990822closed,X)) & pp(aa_TPTP_ind_bool(scratc2023723836closed,X)) & pp(aa_TPTP_ind_bool(scratc2010746768closed,X)))) # label(fact_def__d__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 134 (all X (pp(aa_TPTP_ind_bool(scratc2010746768closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X1),X)) -> (all X2 ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X3),X1)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,aa_TPTP_ind_TPTP_ind(X2,X3)),X))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc108506718d_repl,X1),X2)),X))))))))) # label(fact_def__d__Repl__closed) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 135 (all X (pp(aa_TPTP_ind_bool(scratc2023723836closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,aa_TPTP_ind_TPTP_ind(scratc313048534_power,X1)),X))))))) # label(fact_def__d__Power__closed) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 136 (all X (pp(aa_TPTP_ind_bool(scratc1858990822closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,aa_TPTP_ind_TPTP_ind(scratc820310400_union,X1)),X))))))) # label(fact_def__d__Union__closed) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 137 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc720020070d_Subq,X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X2),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X2),Xa))))))) # label(fact_def__d__Subq) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 138 (all X all Xa (pp(aa_fun171081125l_bool(scratc1597313321all_of(X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (scratc1782356912_is_of(X2,X) -> pp(aa_TPTP_ind_bool(Xa,X2))))))) # label(fact_def__all__of) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 139 (all X all Xa (scratc1782356912_is_of(X,Xa) <-> pp(aa_TPTP_ind_bool(Xa,X)))) # label(fact_def__is__of) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 140 (all X0 (pp(aa_fun171081125l_bool(scratc1451798771n_some,X0)) -> pp(aa_fun171081125l_bool(scratc310578599_n_one,scratc764504323nd_min(X0))))) # label(fact_satz27a) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 141 (all X0 (pp(aa_fun171081125l_bool(scratc1451798771n_some,X0)) -> pp(aa_fun171081125l_bool(scratc1451798771n_some,scratc764504323nd_min(X0))))) # label(fact_satz27) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 142 (all X0 pp(aa_fun171081125l_bool(scratc1597313321all_of(aa_TPT43085870d_bool(aTP_Lamm_kx,X0)),aa_TPT43085870d_bool(aTP_Lamm_kz,X0)))) # label(fact_isseti) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 143 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1597313321all_of(aa_TPT43085870d_bool(aTP_Lamm_an,X0)),aa_fun1584354236d_bool(aTP_Lamm_la(X0),X12)))) # label(fact_estie) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 144 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1597313321all_of(aa_TPT43085870d_bool(aTP_Lamm_an,X0)),aa_fun1584354236d_bool(aTP_Lamm_lb(X0),X12)))) # label(fact_estii) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 145 (all X0 all X12 scratc1782356912_is_of(aa_fun1431113780TP_ind(scratc653561065_d_Sep(X0),X12),aa_TPT43085870d_bool(aTP_Lamm_kx,X0))) # label(fact_setof__p) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 146 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1597313321all_of(aa_TPT43085870d_bool(aTP_Lamm_an,X0)),aa_TPT43085870d_bool(aTP_Lamm_ld(X0),X12)))) # label(fact_secondis1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 147 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1597313321all_of(aa_TPT43085870d_bool(aTP_Lamm_an,X0)),aa_TPT43085870d_bool(aTP_Lamm_lf(X0),X12)))) # label(fact_firstis1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 148 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1597313321all_of(aa_TPT43085870d_bool(aTP_Lamm_lg(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_lh(X0),X12)))) # label(fact_pairis1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 149 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1597313321all_of(aa_TPT43085870d_bool(aTP_Lamm_lg(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_li(X0),X12)))) # label(fact_second__p) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 150 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1597313321all_of(aa_TPT43085870d_bool(aTP_Lamm_lg(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_lj(X0),X12)))) # label(fact_first__p) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 151 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1597313321all_of(aa_TPT43085870d_bool(aTP_Lamm_an,X0)),aa_TPT43085870d_bool(aTP_Lamm_ll(X0),X12)))) # label(fact_e__pair__p) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 152 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1597313321all_of(aa_TPT43085870d_bool(aTP_Lamm_an,X0)),aa_fun1584354236d_bool(aTP_Lamm_lm(X0),X12)))) # label(fact_otax2) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 153 (all X0 all X12 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc970368600ective(aa_fun1431113780TP_ind(scratc653561065_d_Sep(X0),X12)),X0),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc105151248_Sigma,aa_fun1431113780TP_ind(scratc653561065_d_Sep(X0),X12)),scratc860236219d_e_in(X0,X12))))) # label(fact_otax1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 154 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1597313321all_of(aa_fun1584354236d_bool(aTP_Lamm_ln(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_lo(X0),X12)))) # label(fact_e__inp) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 155 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1597313321all_of(aa_fun1584354236d_bool(aTP_Lamm_ln(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_lp(X0),X12)))) # label(fact_e__in__p) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 156 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1597313321all_of(aa_TPT43085870d_bool(aTP_Lamm_lq(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_lt(X0),X12)))) # label(fact_e__fisi) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 157 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc781355319nd_one(X0),X12)) -> pp(aa_TPTP_ind_bool(X12,scratc731786288nd_ind(X0,X12))))) # label(fact_oneax) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 158 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc781355319nd_one(X0),X12)) -> scratc1782356912_is_of(scratc731786288nd_ind(X0,X12),aa_TPT43085870d_bool(aTP_Lamm_an,X0)))) # label(fact_ind__p) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 159 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1597313321all_of(aa_TPT43085870d_bool(aTP_Lamm_an,X0)),aa_fun1584354236d_bool(aTP_Lamm_lv(X0),X12)))) # label(fact_e__isp) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 160 (all X0 pp(aa_fun171081125l_bool(scratc1597313321all_of(aa_TPT43085870d_bool(aTP_Lamm_an,X0)),aa_TPT43085870d_bool(aTP_Lamm_lw,X0)))) # label(fact_refis) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 161 (all X0 (scratc846856975nd_wel(X0) -> pp(X0))) # label(fact_l__et) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 162 (all X0 all X12 all X22 all X32 (pp(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1025384748bnd_if(X0,X22),X32))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X12),X22))))) # label(fact_k__If__In__then__E) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 163 (all X0 all X12 all X22 ((pp(X0) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X12),X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,aa_TPTP_ind_TPTP_ind(scratc1025384748bnd_if(X0,X12),scratc141013060ptyset)),aa_TPTP_ind_TPTP_ind(scratc1025384748bnd_if(X0,X22),aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,scratc141013060ptyset)))))) # label(fact_k__If__In__01) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 164 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X33),X0)) -> aa_TPTP_ind_TPTP_ind(X12,X33) = aa_TPTP_ind_TPTP_ind(X22,X33)))) -> aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc105151248_Sigma,X0),X12) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc105151248_Sigma,X0),X22))) # label(fact_xi__ext) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 165 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1866515598d_d_Pi,X0),X12))) -> (all X32 (gg_TPTP_ind(X32) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X32),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1866515598d_d_Pi,X0),X12))) -> ((all X42 (gg_TPTP_ind(X42) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X42),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,X22),X42) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,X32),X42)))) -> X22 = X32))))))) # label(fact_k__Pi__ext) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 166 (all X0 all X12 all X22 all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1866515598d_d_Pi,X0),X12))) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X32),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,X22),X32)),aa_TPTP_ind_TPTP_ind(X12,X32)))))) # label(fact_ap__Pi) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 167 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X33),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,aa_TPTP_ind_TPTP_ind(X22,X33)),aa_TPTP_ind_TPTP_ind(X12,X33)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc105151248_Sigma,X0),X22)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1866515598d_d_Pi,X0),X12))))) # label(fact_lam__Pi) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 168 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X22),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc105151248_Sigma,X0),X12)),X22) = aa_TPTP_ind_TPTP_ind(X12,X22))) # label(fact_beta) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 169 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc105151248_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,aa_TPTP_ind_TPTP_ind(scratc441562373_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc441562372_proj0,X22)))))) # label(fact_proj1__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 170 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc105151248_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,aa_TPTP_ind_TPTP_ind(scratc441562372_proj0,X22)),X0)))) # label(fact_proj0__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 171 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc105151248_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc661310761d_pair,aa_TPTP_ind_TPTP_ind(scratc441562372_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc441562373_proj1,X22)) = X22))) # label(fact_proj__Sigma__eta) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 172 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc105151248_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc661310761d_pair,aa_TPTP_ind_TPTP_ind(scratc441562372_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc441562373_proj1,X22)) = X22 & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,aa_TPTP_ind_TPTP_ind(scratc441562372_proj0,X22)),X0)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,aa_TPTP_ind_TPTP_ind(scratc441562373_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc441562372_proj0,X22))))))) # label(fact_k__Sigma__eta__proj0__proj1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 173 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X22),X0)) -> (all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X32),aa_TPTP_ind_TPTP_ind(X12,X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc661310761d_pair,X22),X32)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc105151248_Sigma,X0),X12))))))) # label(fact_pair__Sigma) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 174 (all X0 all X12 (gg_TPTP_ind(X12) -> aa_TPTP_ind_TPTP_ind(scratc441562373_proj1,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc661310761d_pair,X0),X12)) = X12)) # label(fact_proj1__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 175 (all X0 all X12 (gg_TPTP_ind(X0) -> aa_TPTP_ind_TPTP_ind(scratc441562372_proj0,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc661310761d_pair,X0),X12)) = X0)) # label(fact_proj0__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 176 (all X0 (pp(aa_TPTP_ind_bool(scratc1669001118_nat_p,X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X0),scratc1758701234_omega)))) # label(fact_nat__p__omega) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 177 (all X0 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X0),scratc1758701234_omega)) -> pp(aa_TPTP_ind_bool(scratc1669001118_nat_p,X0)))) # label(fact_omega__nat__p) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 178 (all X0 (gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(scratc1669001118_nat_p,X0)) -> X0 = scratc141013060ptyset | (exists X13 (gg_TPTP_ind(X13) & pp(aa_TPTP_ind_bool(scratc1669001118_nat_p,X13)) & X0 = aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,X13)))))) # label(fact_nat__inv) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 179 (all X0 (pp(aa_TPTP_ind_bool(X0,scratc141013060ptyset)) -> ((all X13 (gg_TPTP_ind(X13) -> (pp(aa_TPTP_ind_bool(scratc1669001118_nat_p,X13)) -> (pp(aa_TPTP_ind_bool(X0,X13)) -> pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,X13))))))) -> (all X12 (pp(aa_TPTP_ind_bool(scratc1669001118_nat_p,X12)) -> pp(aa_TPTP_ind_bool(X0,X12))))))) # label(fact_nat__ind) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 180 (all X0 (pp(aa_TPTP_ind_bool(scratc1669001118_nat_p,X0)) -> pp(aa_TPTP_ind_bool(scratc1669001118_nat_p,aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,X0))))) # label(fact_nat__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 181 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,X0) = aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,X12) -> X0 = X12))) # label(fact_ordsucc__inj) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 182 (all X0 aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,X0) != scratc141013060ptyset) # label(fact_neq__ordsucc__0) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.39 183 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X22),aa_fun1431113780TP_ind(scratc653561065_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(X12,X22)))) # label(fact_k__SepE2) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 184 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X22),aa_fun1431113780TP_ind(scratc653561065_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X22),X0)))) # label(fact_k__SepE1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 185 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X22),X0)) -> (pp(aa_TPTP_ind_bool(X12,X22)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X22),aa_fun1431113780TP_ind(scratc653561065_d_Sep(X0),X12)))))) # label(fact_k__SepI) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 186 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc313048534_power,X0)))) # label(fact_k__Self__In__Power) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 187 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc720020070d_Subq,X12),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc313048534_power,X0))))) # label(fact_k__PowerI) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 188 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc313048534_power,X0))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc720020070d_Subq,X12),X0)))) # label(fact_k__PowerE) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 189 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> aa_TPTP_ind_TPTP_ind(scratc1025384748bnd_if(X0,X12),X22) = X12 | aa_TPTP_ind_TPTP_ind(scratc1025384748bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__or) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 190 (all X0 all X12 all X22 (gg_TPTP_ind(X12) -> (pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc1025384748bnd_if(X0,X12),X22) = X12))) # label(fact_if__i__1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 191 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (-pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc1025384748bnd_if(X0,X12),X22) = X22))) # label(fact_if__i__0) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 192 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> pp(X0) & aa_TPTP_ind_TPTP_ind(scratc1025384748bnd_if(X0,X12),X22) = X12 | -pp(X0) & aa_TPTP_ind_TPTP_ind(scratc1025384748bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__correct) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 193 (all X0 pp(aa_TPTP_ind_bool(scratc1807384429closed,aa_TPTP_ind_TPTP_ind(scratc2102057900univof,X0)))) # label(fact_k__UnivOf__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 194 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc2102057900univof,X0)))) # label(fact_k__UnivOf__In) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 195 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc108506718d_repl,X0),X12))) <-> (exists X3 (gg_TPTP_ind(X3) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X3),X0)) & X22 = aa_TPTP_ind_TPTP_ind(X12,X3)))))) # label(fact_k__ReplEq) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 196 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc313048534_power,X0))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc720020070d_Subq,X12),X0)))) # label(fact_k__PowerEq) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 197 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc820310400_union,X0))) <-> (exists X2 (gg_TPTP_ind(X2) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X12),X2)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X2),X0)))))) # label(fact_k__UnionEq) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 198 -(exists X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X0),scratc141013060ptyset))) # label(fact_k__EmptyAx) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 199 (all X0 ((all X13 (gg_TPTP_ind(X13) -> ((all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X22),X13)) -> pp(aa_TPTP_ind_bool(X0,X22)))) -> pp(aa_TPTP_ind_bool(X0,X13))))) -> (all X14 pp(aa_TPTP_ind_bool(X0,X14))))) # label(fact_k__In__ind) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 200 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc720020070d_Subq,X0),X12)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc720020070d_Subq,X12),X0)) -> X0 = X12)))) # label(fact_set__ext) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 201 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_km,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc772765833nd_nis,Uu),scratc1230440946nd_n_1)) -> pp(aa_fun171081125l_bool(scratc1451798771n_some,aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)))))) # label(fact_ATP_Olambda__1) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 202 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_kl,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc772765833nd_nis,Uu),scratc1230440946nd_n_1)) -> pp(aa_fun171081125l_bool(scratc310578599_n_one,aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)))))) # label(fact_ATP_Olambda__2) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 203 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ki,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),scratc1230440946nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uu))))) # label(fact_ATP_Olambda__3) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 204 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ck,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(scratc379618174d_n_ts(Uu),scratc1230440946nd_n_1)),Uu)))) # label(fact_ATP_Olambda__4) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 205 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_kf,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(scratc1230440946nd_n_1),Uu)),aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uu))))) # label(fact_ATP_Olambda__5) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 206 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ch,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(scratc379618174d_n_ts(scratc1230440946nd_n_1),Uu)),Uu)))) # label(fact_ATP_Olambda__6) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 207 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_kk,Uu)) <-> pp(aa_fun171081125l_bool(scratc781355319nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1866515598d_d_Pi,scratc772241042nd_nat),aTP_Lamm_ad)),aa_TPT43085870d_bool(aTP_Lamm_kj,Uu))))) # label(fact_ATP_Olambda__7) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 208 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cm,Uu)) <-> pp(aa_fun171081125l_bool(scratc781355319nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1866515598d_d_Pi,scratc772241042nd_nat),aTP_Lamm_ad)),aa_TPT43085870d_bool(aTP_Lamm_cl,Uu))))) # label(fact_ATP_Olambda__8) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 209 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ks,Uu)) <-> (pp(aa_TPTP_ind_bool(scratc456679104_cond1,Uu)) -> (pp(aa_TPTP_ind_bool(scratc456679105_cond2,Uu)) -> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_kr,Uu))))))) # label(fact_ATP_Olambda__9) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 210 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_kc,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),scratc1230440946nd_n_1))))) # label(fact_ATP_Olambda__10) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 211 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jz,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(scratc1230440946nd_n_1),Uu))))) # label(fact_ATP_Olambda__11) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 212 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gz,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__12) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 213 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_kn,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc772765833nd_nis,aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__13) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 214 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_kw,Uu)) <-> scratc1782356912_is_of(aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uu),aTP_Lamm_a))) # label(fact_ATP_Olambda__14) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 215 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_de,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uu)),scratc1230440946nd_n_1)))) # label(fact_ATP_Olambda__15) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 216 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_kv,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc772765833nd_nis,aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uu)),scratc1230440946nd_n_1)))) # label(fact_ATP_Olambda__16) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 217 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ce,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc379618174d_n_ts(Uu),scratc1230440946nd_n_1))))) # label(fact_ATP_Olambda__17) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 218 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cb,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc379618174d_n_ts(scratc1230440946nd_n_1),Uu))))) # label(fact_ATP_Olambda__18) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 219 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gy,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uu))))) # label(fact_ATP_Olambda__19) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 220 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_kq,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,Uu),aa_TPTP_ind_TPTP_ind(scratc313048534_power,scratc772241042nd_nat))))) # label(fact_ATP_Olambda__20) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 221 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_df,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc707559022moreis,Uu),scratc1230440946nd_n_1)))) # label(fact_ATP_Olambda__21) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 222 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_a,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,Uu),scratc772241042nd_nat)))) # label(fact_ATP_Olambda__22) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 223 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ku,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_kt,Uu))))) # label(fact_ATP_Olambda__23) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 224 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_kp,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ko,Uu))))) # label(fact_ATP_Olambda__24) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 225 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_kh,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_kg,Uu))))) # label(fact_ATP_Olambda__25) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 226 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ke,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_kd,Uu))))) # label(fact_ATP_Olambda__26) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 227 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_kb,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ka,Uu))))) # label(fact_ATP_Olambda__27) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 228 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jy,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jx,Uu))))) # label(fact_ATP_Olambda__28) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 229 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jw,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jv,Uu))))) # label(fact_ATP_Olambda__29) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 230 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jt,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_js,Uu))))) # label(fact_ATP_Olambda__30) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 231 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jr,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jq,Uu))))) # label(fact_ATP_Olambda__31) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 232 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jp,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jo,Uu))))) # label(fact_ATP_Olambda__32) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 233 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jm,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jl,Uu))))) # label(fact_ATP_Olambda__33) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 234 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jj,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ji,Uu))))) # label(fact_ATP_Olambda__34) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 235 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jh,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jg,Uu))))) # label(fact_ATP_Olambda__35) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 236 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jd,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jc,Uu))))) # label(fact_ATP_Olambda__36) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 237 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_jb,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ja,Uu))))) # label(fact_ATP_Olambda__37) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 238 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_iz,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_iy,Uu))))) # label(fact_ATP_Olambda__38) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 239 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ix,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_iw,Uu))))) # label(fact_ATP_Olambda__39) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 240 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_iv,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_iu,Uu))))) # label(fact_ATP_Olambda__40) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 241 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_it,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_is,Uu))))) # label(fact_ATP_Olambda__41) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 242 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ir,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_iq,Uu))))) # label(fact_ATP_Olambda__42) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 243 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ip,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_io,Uu))))) # label(fact_ATP_Olambda__43) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 244 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_in,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_im,Uu))))) # label(fact_ATP_Olambda__44) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 245 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_il,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ik,Uu))))) # label(fact_ATP_Olambda__45) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 246 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ij,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ii,Uu))))) # label(fact_ATP_Olambda__46) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 247 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ih,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ig,Uu))))) # label(fact_ATP_Olambda__47) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 248 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_if,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ie,Uu))))) # label(fact_ATP_Olambda__48) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 249 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_id,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ic,Uu))))) # label(fact_ATP_Olambda__49) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 250 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ib,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ia,Uu))))) # label(fact_ATP_Olambda__50) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 251 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hz,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hy,Uu))))) # label(fact_ATP_Olambda__51) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 252 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hx,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hw,Uu))))) # label(fact_ATP_Olambda__52) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 253 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hv,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hu,Uu))))) # label(fact_ATP_Olambda__53) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 254 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hs,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hr,Uu))))) # label(fact_ATP_Olambda__54) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 255 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hp,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ho,Uu))))) # label(fact_ATP_Olambda__55) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 256 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hm,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hl,Uu))))) # label(fact_ATP_Olambda__56) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 257 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hj,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hi,Uu))))) # label(fact_ATP_Olambda__57) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 258 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hg,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hf,Uu))))) # label(fact_ATP_Olambda__58) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 259 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hd,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hc,Uu))))) # label(fact_ATP_Olambda__59) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 260 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_hb,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ha,Uu))))) # label(fact_ATP_Olambda__60) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 261 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gx,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gw,Uu))))) # label(fact_ATP_Olambda__61) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 262 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gu,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gt,Uu))))) # label(fact_ATP_Olambda__62) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 263 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gr,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gq,Uu))))) # label(fact_ATP_Olambda__63) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 264 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_go,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gn,Uu))))) # label(fact_ATP_Olambda__64) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 265 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gl,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gk,Uu))))) # label(fact_ATP_Olambda__65) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 266 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gi,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gh,Uu))))) # label(fact_ATP_Olambda__66) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 267 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gf,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ge,Uu))))) # label(fact_ATP_Olambda__67) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 268 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_gb,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ga,Uu))))) # label(fact_ATP_Olambda__68) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 269 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fx,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fw,Uu))))) # label(fact_ATP_Olambda__69) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 270 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ft,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fs,Uu))))) # label(fact_ATP_Olambda__70) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 271 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fp,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fo,Uu))))) # label(fact_ATP_Olambda__71) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 272 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fm,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fl,Uu))))) # label(fact_ATP_Olambda__72) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 273 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fj,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fi,Uu))))) # label(fact_ATP_Olambda__73) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 274 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fg,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ff,Uu))))) # label(fact_ATP_Olambda__74) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 275 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fd,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fc,Uu))))) # label(fact_ATP_Olambda__75) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 276 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_fa,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ez,Uu))))) # label(fact_ATP_Olambda__76) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 277 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ex,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ew,Uu))))) # label(fact_ATP_Olambda__77) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 278 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_eu,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_et,Uu))))) # label(fact_ATP_Olambda__78) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 279 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_er,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eq,Uu))))) # label(fact_ATP_Olambda__79) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 280 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_eo,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_en,Uu))))) # label(fact_ATP_Olambda__80) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 281 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_el,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ek,Uu))))) # label(fact_ATP_Olambda__81) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 282 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_eh,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eg,Uu))))) # label(fact_ATP_Olambda__82) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 283 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ed,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ec,Uu))))) # label(fact_ATP_Olambda__83) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 284 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dz,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dy,Uu))))) # label(fact_ATP_Olambda__84) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 285 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dv,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_du,Uu))))) # label(fact_ATP_Olambda__85) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 286 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dr,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dq,Uu))))) # label(fact_ATP_Olambda__86) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 287 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dn,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dm,Uu))))) # label(fact_ATP_Olambda__87) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 288 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dj,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_di,Uu))))) # label(fact_ATP_Olambda__88) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 289 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dc,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_db,Uu))))) # label(fact_ATP_Olambda__89) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 290 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_da,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cz,Uu))))) # label(fact_ATP_Olambda__90) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 291 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cy,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cx,Uu))))) # label(fact_ATP_Olambda__91) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 292 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cw,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cv,Uu))))) # label(fact_ATP_Olambda__92) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 293 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cu,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ct,Uu))))) # label(fact_ATP_Olambda__93) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 294 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cs,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cr,Uu))))) # label(fact_ATP_Olambda__94) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 295 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cq,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cp,Uu))))) # label(fact_ATP_Olambda__95) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 296 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_co,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cn,Uu))))) # label(fact_ATP_Olambda__96) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 297 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cj,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ci,Uu))))) # label(fact_ATP_Olambda__97) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 298 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cg,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cf,Uu))))) # label(fact_ATP_Olambda__98) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 299 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cd,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cc,Uu))))) # label(fact_ATP_Olambda__99) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 300 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ca,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bz,Uu))))) # label(fact_ATP_Olambda__100) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 301 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_by,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bx,Uu))))) # label(fact_ATP_Olambda__101) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 302 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bw,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bv,Uu))))) # label(fact_ATP_Olambda__102) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 303 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ac,Uu)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ab,Uu))))) # label(fact_ATP_Olambda__103) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 304 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dd,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,scratc1230440946nd_n_1),aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uu))))) # label(fact_ATP_Olambda__104) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 305 (all Uu aa_TPT494704832TP_ind(aTP_Lamm_bo,Uu) = aa_TPT494704832TP_ind(scratc108506718d_repl,aa_TPTP_ind_TPTP_ind(scratc1416596253tminus(Uu),aa_TPTP_ind_TPTP_ind(scratc621669188d_Sing,scratc141013060ptyset)))) # label(fact_ATP_Olambda__105) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 306 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_al,Uu)) <-> Uu != scratc141013060ptyset))) # label(fact_ATP_Olambda__106) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 307 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_bm,Uu)) <-> (exists X2 (gg_TPTP_ind(X2) & aa_TPTP_ind_TPTP_ind(scratc1446776865d_Inj1,X2) = Uu))))) # label(fact_ATP_Olambda__107) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 308 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_bn,Uu)) <-> (exists X2 (gg_TPTP_ind(X2) & aa_TPTP_ind_TPTP_ind(scratc1446776864d_Inj0,X2) = Uu))))) # label(fact_ATP_Olambda__108) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 309 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iy,Uu),Uua)) <-> scratc1366407491_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,Uu),Uua)))) # label(fact_ATP_Olambda__109) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 310 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iw,Uu),Uua)) <-> pp(scratc781617665nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__110) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 311 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_iu,Uu),Uua)) <-> pp(scratc698018630nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__111) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 312 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jg,Uu),Uua)) <-> scratc1366407491_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1451798771n_some,aa_TPT43085870d_bool(aTP_Lamm_je(Uu),Uua)),aa_fun171081125l_bool(scratc1451798771n_some,aa_TPT43085870d_bool(aTP_Lamm_jf(Uu),Uua))))) # label(fact_ATP_Olambda__112) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 313 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jc,Uu),Uua)) <-> pp(scratc781617665nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1451798771n_some,aa_TPT43085870d_bool(scratc1422910007ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc1451798771n_some,aa_TPT43085870d_bool(scratc1422910007ffprop(Uua),Uu)))))) # label(fact_ATP_Olambda__113) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 314 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ja,Uu),Uua)) <-> pp(scratc698018630nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1451798771n_some,aa_TPT43085870d_bool(scratc1422910007ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc1451798771n_some,aa_TPT43085870d_bool(scratc1422910007ffprop(Uua),Uu)))))) # label(fact_ATP_Olambda__114) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 315 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lw,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc860236224d_e_is(Uu),Uua),Uua)))) # label(fact_ATP_Olambda__115) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 316 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bz,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(aa_TPTP_ind_TPTP_ind(scratc379618174d_n_ts(Uu),Uua)),Uua)),aa_TPTP_ind_TPTP_ind(scratc379618174d_n_ts(aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uu)),Uua))))) # label(fact_ATP_Olambda__116) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 317 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cc,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(aa_TPTP_ind_TPTP_ind(scratc379618174d_n_ts(Uu),Uua)),Uu)),aa_TPTP_ind_TPTP_ind(scratc379618174d_n_ts(Uu),aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uua)))))) # label(fact_ATP_Olambda__117) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 318 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kj,Uu),Uua)) <-> pp(scratc769812514_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,Uua),scratc1230440946nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uu)),aa_fun171081125l_bool(scratc194786338_n_all,aa_TPT43085870d_bool(aTP_Lamm_ai,Uua)))))) # label(fact_ATP_Olambda__118) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 319 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cp,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uua),scratc1230440946nd_n_1)),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc707559022moreis,Uua),Uu))))) # label(fact_ATP_Olambda__119) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 320 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cl,Uu),Uua)) <-> pp(scratc769812514_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,Uua),scratc1230440946nd_n_1)),Uu),aa_fun171081125l_bool(scratc194786338_n_all,aa_TPT43085870d_bool(aTP_Lamm_ag(Uu),Uua)))))) # label(fact_ATP_Olambda__120) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 321 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kt,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__121) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 322 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cf,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(scratc379618174d_n_ts(aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(aa_TPTP_ind_TPTP_ind(scratc379618174d_n_ts(Uu),Uua)),Uua))))) # label(fact_ATP_Olambda__122) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 323 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cn,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uua)),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc707559022moreis,Uua),Uu))))) # label(fact_ATP_Olambda__123) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 324 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kd,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__124) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 325 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ct,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,Uua),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),scratc1230440946nd_n_1))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc573575410lessis,Uua),Uu))))) # label(fact_ATP_Olambda__125) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 326 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ci,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(scratc379618174d_n_ts(Uu),aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(aa_TPTP_ind_TPTP_ind(scratc379618174d_n_ts(Uu),Uua)),Uu))))) # label(fact_ATP_Olambda__126) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 327 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cr,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,Uua),aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uu))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc573575410lessis,Uua),Uu))))) # label(fact_ATP_Olambda__127) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 328 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kg,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__128) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 329 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ai,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,Uu),aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,Uu),Uua)))))) # label(fact_ATP_Olambda__129) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 330 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cx,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc573575410lessis,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uua),scratc1230440946nd_n_1)),Uu))))) # label(fact_ATP_Olambda__130) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 331 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ko,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc772765833nd_nis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc772765833nd_nis,aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uua)))))) # label(fact_ATP_Olambda__131) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 332 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ak,Uu),Uua)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc731720701nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896580d_n_in,Uua),Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896580d_n_in,aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uua)),Uu))))) # label(fact_ATP_Olambda__132) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 333 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cv,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc573575410lessis,aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uua)),Uu))))) # label(fact_ATP_Olambda__133) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 334 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_db,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc707559022moreis,Uua),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),scratc1230440946nd_n_1)))))) # label(fact_ATP_Olambda__134) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 335 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cz,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,Uua),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc707559022moreis,Uua),aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uu)))))) # label(fact_ATP_Olambda__135) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 336 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bx,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(scratc379618174d_n_ts(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc379618174d_n_ts(Uua),Uu))))) # label(fact_ATP_Olambda__136) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 337 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_js,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uua),Uu))))) # label(fact_ATP_Olambda__137) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 338 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_is,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,Uua),Uu))))) # label(fact_ATP_Olambda__138) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 339 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_io,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc707559022moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc573575410lessis,Uua),Uu))))) # label(fact_ATP_Olambda__139) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 340 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_im,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc573575410lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc707559022moreis,Uua),Uu))))) # label(fact_ATP_Olambda__140) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 341 (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(scratc731458298nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,Uua),Uu))))) # label(fact_ATP_Olambda__141) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 342 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ic,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,Uu),Uua)) -> pp(scratc877277694_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc573575410lessis,Uu),Uua)))))) # label(fact_ATP_Olambda__142) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 343 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ik,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc707559022moreis,Uu),Uua)) -> pp(scratc877277694_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,Uu),Uua)))))) # label(fact_ATP_Olambda__143) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 344 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ii,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc573575410lessis,Uu),Uua)) -> pp(scratc877277694_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,Uu),Uua)))))) # label(fact_ATP_Olambda__144) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 345 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ia,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,Uu),Uua)) -> pp(scratc877277694_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc707559022moreis,Uu),Uua)))))) # label(fact_ATP_Olambda__145) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 346 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hc,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uua)),Uu)))) # label(fact_ATP_Olambda__146) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 347 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_ae(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,Uu),Uua)),Uua)) # label(fact_ATP_Olambda__147) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 348 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bl(Uu),Uua) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc108506718d_repl,aa_TPTP_ind_TPTP_ind(Uu,Uua)),aa_TPT1424761345TP_ind(scratc661310761d_pair,Uua))) # label(fact_ATP_Olambda__148) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 349 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kz,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aa_TPT43085870d_bool(aTP_Lamm_kx,Uu)),aa_TPT43085870d_bool(aTP_Lamm_ky(Uu),Uua))))) # label(fact_ATP_Olambda__149) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 350 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jx,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uu)),Uua))))) # label(fact_ATP_Olambda__150) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 351 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ka,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uua)))))) # label(fact_ATP_Olambda__151) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 352 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ig,Uu),Uua)) <-> (pp(scratc877277694_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc573575410lessis,Uu),Uua))))) # label(fact_ATP_Olambda__152) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 353 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hy,Uu),Uua)) <-> (pp(scratc877277694_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc707559022moreis,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__153) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 354 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hw,Uu),Uua)) <-> (pp(scratc877277694_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc573575410lessis,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__154) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 355 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ie,Uu),Uua)) <-> (pp(scratc877277694_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc707559022moreis,Uu),Uua))))) # label(fact_ATP_Olambda__155) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 356 (all Uu all Uua aa_fun277296641TP_ind(aa_TPT494704832TP_ind(aTP_Lamm_bp,Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1500310711nunion(aa_TPTP_ind_TPTP_ind(scratc621669188d_Sing,scratc141013060ptyset)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc108506718d_repl,Uu),Uua))) # label(fact_ATP_Olambda__156) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 357 (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(scratc772765833nd_nis,Uua),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__157) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 358 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ha,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,Uu),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__158) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 359 (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(scratc378896585d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uua))))) # label(fact_ATP_Olambda__159) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 360 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kx,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,Uua),aa_TPTP_ind_TPTP_ind(scratc313048534_power,Uu))))) # label(fact_ATP_Olambda__160) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 361 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_kr,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896580d_n_in,Uua),Uu)))) # label(fact_ATP_Olambda__161) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 362 (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(scratc770666660nd_nIn,Uua),Uu)))) # label(fact_ATP_Olambda__162) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 363 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_an,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,Uua),Uu)))) # label(fact_ATP_Olambda__163) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 364 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jv,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ju(Uu),Uua))))) # label(fact_ATP_Olambda__164) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.40 365 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jo,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jn(Uu),Uua))))) # label(fact_ATP_Olambda__165) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 366 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jl,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_jk(Uu),Uua))))) # label(fact_ATP_Olambda__166) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 367 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hu,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ht(Uu),Uua))))) # label(fact_ATP_Olambda__167) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 368 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hr,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hq(Uu),Uua))))) # label(fact_ATP_Olambda__168) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 369 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ho,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hn(Uu),Uua))))) # label(fact_ATP_Olambda__169) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 370 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hl,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hk(Uu),Uua))))) # label(fact_ATP_Olambda__170) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 371 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hi,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_hh(Uu),Uua))))) # label(fact_ATP_Olambda__171) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 372 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hf,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_he(Uu),Uua))))) # label(fact_ATP_Olambda__172) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 373 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gw,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gv(Uu),Uua))))) # label(fact_ATP_Olambda__173) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 374 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gt,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gs(Uu),Uua))))) # label(fact_ATP_Olambda__174) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 375 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gq,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gp(Uu),Uua))))) # label(fact_ATP_Olambda__175) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 376 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gn,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gm(Uu),Uua))))) # label(fact_ATP_Olambda__176) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 377 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gk,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gj(Uu),Uua))))) # label(fact_ATP_Olambda__177) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 378 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gh,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gg(Uu),Uua))))) # label(fact_ATP_Olambda__178) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 379 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ge,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gd(Uu),Uua))))) # label(fact_ATP_Olambda__179) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 380 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ga,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fz(Uu),Uua))))) # label(fact_ATP_Olambda__180) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 381 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fw,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fv(Uu),Uua))))) # label(fact_ATP_Olambda__181) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 382 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fs,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fr(Uu),Uua))))) # label(fact_ATP_Olambda__182) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 383 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fo,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fn(Uu),Uua))))) # label(fact_ATP_Olambda__183) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 384 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fl,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fk(Uu),Uua))))) # label(fact_ATP_Olambda__184) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 385 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fi,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fh(Uu),Uua))))) # label(fact_ATP_Olambda__185) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 386 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ff,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fe(Uu),Uua))))) # label(fact_ATP_Olambda__186) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 387 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fc,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_fb(Uu),Uua))))) # label(fact_ATP_Olambda__187) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 388 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ez,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ey(Uu),Uua))))) # label(fact_ATP_Olambda__188) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 389 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ew,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ev(Uu),Uua))))) # label(fact_ATP_Olambda__189) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 390 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_et,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_es(Uu),Uua))))) # label(fact_ATP_Olambda__190) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 391 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eq,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ep(Uu),Uua))))) # label(fact_ATP_Olambda__191) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 392 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_en,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_em(Uu),Uua))))) # label(fact_ATP_Olambda__192) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 393 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ek,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ej(Uu),Uua))))) # label(fact_ATP_Olambda__193) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 394 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eg,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ef(Uu),Uua))))) # label(fact_ATP_Olambda__194) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 395 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ec,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eb(Uu),Uua))))) # label(fact_ATP_Olambda__195) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 396 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dy,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dx(Uu),Uua))))) # label(fact_ATP_Olambda__196) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 397 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_du,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dt(Uu),Uua))))) # label(fact_ATP_Olambda__197) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 398 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dq,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dp(Uu),Uua))))) # label(fact_ATP_Olambda__198) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 399 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dm,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dl(Uu),Uua))))) # label(fact_ATP_Olambda__199) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 400 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_di,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dh(Uu),Uua))))) # label(fact_ATP_Olambda__200) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 401 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bv,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bu(Uu),Uua))))) # label(fact_ATP_Olambda__201) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 402 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ab,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa(Uu),Uua))))) # label(fact_ATP_Olambda__202) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 403 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ji,Uu),Uua)) <-> pp(scratc920260971_amone(scratc772241042nd_nat,aa_TPT43085870d_bool(aTP_Lamm_je(Uu),Uua))))) # label(fact_ATP_Olambda__203) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 404 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_ah(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,Uu),Uua))) # label(fact_ATP_Olambda__204) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 405 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bi(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc820310400_union,aa_TPTP_ind_TPTP_ind(Uu,Uua))) # label(fact_ATP_Olambda__205) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 406 (all Uu all Uua (gg_TPTP_ind(Uua) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bk,Uu),Uua)) <-> (exists X3 (gg_TPTP_ind(X3) & Uua = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc661310761d_pair,Uu),X3)))))) # label(fact_ATP_Olambda__206) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 407 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lh(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc860236224d_e_is(aa_TPTP_ind_TPTP_ind(scratc313862346etprod(Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1717441455d_pair(Uu,Uua),aa_TPTP_ind_TPTP_ind(scratc1373362497_first(Uu,Uua),Uub)),aa_TPTP_ind_TPTP_ind(scratc1392931043second(Uu,Uua),Uub))),Uub)))) # label(fact_ATP_Olambda__207) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 408 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_bs(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc1025384748bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,scratc141013060ptyset),Uub),Uu),Uua)) # label(fact_ATP_Olambda__208) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 409 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_fun1235454963TP_ind(aTP_Lamm_br(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc1025384748bnd_if(aa_TPTP_ind_bool(Uua,Uub),Uub),scratc698871481nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bf(Uu),Uua)))) # label(fact_ATP_Olambda__209) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 410 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ay(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc814214834d_esti(Uu),Uub),Uua)))) # label(fact_ATP_Olambda__210) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 411 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_la(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc814214834d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc653561065_d_Sep(Uu),Uua))) -> pp(aa_TPTP_ind_bool(Uua,Uub))))) # label(fact_ATP_Olambda__211) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 412 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ky(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1746657277d_incl(Uu),Uua),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1746657277d_incl(Uu),Uub),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc860236224d_e_is(aa_TPTP_ind_TPTP_ind(scratc313048534_power,Uu)),Uua),Uub)))))) # label(fact_ATP_Olambda__212) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 413 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_li(Uu),Uua),Uub)) <-> scratc1782356912_is_of(aa_TPTP_ind_TPTP_ind(scratc1392931043second(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_an,Uua)))) # label(fact_ATP_Olambda__213) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 414 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lj(Uu),Uua),Uub)) <-> scratc1782356912_is_of(aa_TPTP_ind_TPTP_ind(scratc1373362497_first(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_an,Uu)))) # label(fact_ATP_Olambda__214) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 415 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_lp(Uu),Uua),Uub)) <-> scratc1782356912_is_of(aa_TPTP_ind_TPTP_ind(scratc860236219d_e_in(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_an,Uu)))) # label(fact_ATP_Olambda__215) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 416 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lt(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aa_TPT43085870d_bool(aTP_Lamm_lq(Uu),Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ls(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__216) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 417 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fb(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__217) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 418 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_es(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,Uu),Uua))))) # label(fact_ATP_Olambda__218) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 419 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jk(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,Uua),Uub))))) # label(fact_ATP_Olambda__219) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 420 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ey(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__220) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 421 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ep(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__221) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 422 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ev(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uua),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__222) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 423 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_em(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uub),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__223) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 424 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(scratc379618174d_n_ts(aa_TPTP_ind_TPTP_ind(scratc379618174d_n_ts(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc379618174d_n_ts(Uu),aa_TPTP_ind_TPTP_ind(scratc379618174d_n_ts(Uua),Uub)))))) # label(fact_ATP_Olambda__224) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 425 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ju(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__225) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 426 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bu(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(scratc379618174d_n_ts(Uu),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uua),Uub))),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(aa_TPTP_ind_TPTP_ind(scratc379618174d_n_ts(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc379618174d_n_ts(Uu),Uub)))))) # label(fact_ATP_Olambda__226) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 427 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ag(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(scratc679939252rdsucc,Uub))),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,Uua),Uub)),Uu))))) # label(fact_ATP_Olambda__227) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 428 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gv(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__228) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 429 (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(scratc1926009596_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__229) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 430 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hh(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc707559022moreis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,Uu),Uub)))))) # label(fact_ATP_Olambda__230) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 431 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fn(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc707559022moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc707559022moreis,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__231) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 432 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fk(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc707559022moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc707559022moreis,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__232) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 433 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hk(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc707559022moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,Uu),Uub)))))) # label(fact_ATP_Olambda__233) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 434 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fh(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc573575410lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc573575410lessis,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__234) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 435 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fe(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc573575410lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc573575410lessis,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__235) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 436 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_he(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc573575410lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc573575410lessis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc573575410lessis,Uu),Uub)))))) # label(fact_ATP_Olambda__236) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 437 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hq(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc573575410lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__237) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 438 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gs(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__238) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 439 (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(scratc378896585d_n_is,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__239) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 440 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jn(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc772765833nd_nis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc772765833nd_nis,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uub)))))) # label(fact_ATP_Olambda__240) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 441 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gp(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__241) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 442 (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(scratc731458298nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uub),Uua)))))) # label(fact_ATP_Olambda__242) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 443 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_hn(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc573575410lessis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__243) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 444 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ht(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,Uu),Uub)))))) # label(fact_ATP_Olambda__244) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 445 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bf(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,Uub),Uu)) & pp(aa_TPTP_ind_bool(Uua,Uub)))) # label(fact_ATP_Olambda__245) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 446 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_lm(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1330720428_image(aa_fun1431113780TP_ind(scratc653561065_d_Sep(Uu),Uua),Uu),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc105151248_Sigma,aa_fun1431113780TP_ind(scratc653561065_d_Sep(Uu),Uua)),scratc860236219d_e_in(Uu,Uua))),Uub))))) # label(fact_ATP_Olambda__246) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 447 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_lb(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc814214834d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc653561065_d_Sep(Uu),Uua)))))) # label(fact_ATP_Olambda__247) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 448 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_lv(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aa_TPT43085870d_bool(aTP_Lamm_an,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_lu(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__248) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 449 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bh(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aa_TPT43085870d_bool(aTP_Lamm_an,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bg(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__249) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 450 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ll(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aa_TPT43085870d_bool(aTP_Lamm_an,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_lk(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__250) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 451 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lf(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aa_TPT43085870d_bool(aTP_Lamm_an,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_le(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__251) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 452 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ld(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aa_TPT43085870d_bool(aTP_Lamm_an,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_lc(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__252) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 453 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lq(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,Uub),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1866515598d_d_Pi,Uu),aTP_Lamm_am(Uua)))))) # label(fact_ATP_Olambda__253) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 454 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_je(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uua),Uub))))) # label(fact_ATP_Olambda__254) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 455 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_jf(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,Uua),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uub))))) # label(fact_ATP_Olambda__255) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 456 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_lg(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,Uub),aa_TPTP_ind_TPTP_ind(scratc313862346etprod(Uu),Uua))))) # label(fact_ATP_Olambda__256) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 457 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ln(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,Uub),aa_fun1431113780TP_ind(scratc653561065_d_Sep(Uu),Uua))))) # label(fact_ATP_Olambda__257) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 458 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_ba(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,Uu),Uub))) # label(fact_ATP_Olambda__258) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 459 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gd(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gc(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__259) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 460 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fz(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fy(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__260) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 461 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fv(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fu(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__261) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 462 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fr(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fq(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__262) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 463 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ej(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ei(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__263) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 464 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ef(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ee(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__264) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 465 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eb(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ea(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__265) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 466 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dx(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dw(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__266) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 467 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dt(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ds(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__267) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 468 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dp(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_do(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__268) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 469 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dl(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dk(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__269) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 470 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dh(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dg(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__270) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 471 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_lo(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(Uua,aa_TPTP_ind_TPTP_ind(scratc860236219d_e_in(Uu,Uua),Uub))))) # label(fact_ATP_Olambda__271) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 472 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1913827119d_bool(aTP_Lamm_bj(Uu),Uua),Uub)) <-> (all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,X3),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1025384756bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,Uub),X3)),aa_TPTP_ind_TPTP_ind(Uua,X3)))))))) # label(fact_ATP_Olambda__272) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 473 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_bb(Uu),Uua),Uub),Uuc) = aa_TPTP_ind_TPTP_ind(scratc1025384748bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1330720428_image(Uu,Uua),Uub),Uuc),aa_TPTP_ind_TPTP_ind(scratc971052985d_soft(Uu,Uua,Uub),Uuc)),scratc141013060ptyset)) # label(fact_ATP_Olambda__273) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 474 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_le(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc860236224d_e_is(Uu),aa_TPTP_ind_TPTP_ind(scratc1373362497_first(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1717441455d_pair(Uu,Uua),Uub),Uuc))),Uub)))) # label(fact_ATP_Olambda__274) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 475 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_lc(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc860236224d_e_is(Uua),aa_TPTP_ind_TPTP_ind(scratc1392931043second(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1717441455d_pair(Uu,Uua),Uub),Uuc))),Uuc)))) # label(fact_ATP_Olambda__275) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 476 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_lr(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc860236224d_e_is(Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,Uua),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,Uub),Uuc))))) # label(fact_ATP_Olambda__276) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 477 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_au(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc814214834d_esti(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__277) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 478 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bc(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc860236224d_e_is(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__278) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 479 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_lk(Uu),Uua),Uub),Uuc)) <-> scratc1782356912_is_of(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1717441455d_pair(Uu,Uua),Uub),Uuc),aa_TPT43085870d_bool(aTP_Lamm_lg(Uu),Uua)))) # label(fact_ATP_Olambda__279) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 480 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aw(Uu),Uua),Uub),Uuc)) <-> pp(scratc246989243d_l_ec(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc814214834d_esti(Uu),Uuc),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc814214834d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__280) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 481 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ax(Uu),Uua),Uub),Uuc)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc731720701nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc814214834d_esti(Uu),Uuc),Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc814214834d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__281) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 482 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ls(Uu),Uua),Uub),Uuc)) <-> (pp(aa_fun171081125l_bool(scratc1597313321all_of(aa_TPT43085870d_bool(aTP_Lamm_an,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_lr(Uua),Uub),Uuc))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc860236224d_e_is(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1866515598d_d_Pi,Uu),aTP_Lamm_am(Uua))),Uub),Uuc))))) # label(fact_ATP_Olambda__282) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 483 (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_bt(Uu),Uua),Uub),Uuc)) <-> pp(Uu) & Uuc = Uua | -pp(Uu) & Uuc = Uub))) # label(fact_ATP_Olambda__283) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 484 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ei(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__284) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 485 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dw(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc707559022moreis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__285) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 486 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ea(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc707559022moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__286) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 487 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dk(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc707559022moreis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc707559022moreis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc707559022moreis,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__287) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 488 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dg(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc573575410lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc573575410lessis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc573575410lessis,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__288) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 489 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ds(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc573575410lessis,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__289) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 490 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_gc(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__290) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 491 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fy(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1926009596_29_ii,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uuc),Uua))))))) # label(fact_ATP_Olambda__291) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 492 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fu(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__292) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 493 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fq(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc378896585d_n_is,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uub),Uu)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uuc),Uua))))))) # label(fact_ATP_Olambda__293) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 494 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_do(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc573575410lessis,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__294) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 495 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ee(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,Uu),Uua)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,Uub),Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc731458298nd_iii,aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uu),Uub)),aa_TPTP_ind_TPTP_ind(scratc379355771d_n_pl(Uua),Uuc))))))) # label(fact_ATP_Olambda__295) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 496 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_lu(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc860236224d_e_is(Uu),Uub),Uuc)) -> pp(aa_TPTP_ind_bool(Uua,Uuc)))))) # label(fact_ATP_Olambda__296) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 497 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bg(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(scratc860236224d_e_is(Uu),Uub),Uuc)))))) # label(fact_ATP_Olambda__297) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 498 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_be(Uu),Uua),Uub),Uuc)) <-> pp(aa_fun171081125l_bool(scratc665563058nd_all(Uu),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_bd(Uu),Uua),Uub),Uuc))))) # label(fact_ATP_Olambda__298) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 499 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_av(Uu),Uua),Uub),Uuc)) <-> pp(aa_fun171081125l_bool(scratc707974129l_some(Uua),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_au(Uu),Uub),Uuc))))) # label(fact_ATP_Olambda__299) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 500 (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_bd(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc731720701nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc860236224d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,Uub),Uud))),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc860236224d_e_is(Uu),Uuc),Uud))))) # label(fact_ATP_Olambda__300) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 501 (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_as(Uu),Uua),Uub),Uuc),Uud)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc860236224d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,Uub),Uud)))))) # label(fact_ATP_Olambda__301) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 502 (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_ar(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aa_TPT43085870d_bool(aTP_Lamm_an,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_aq(Uu),Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__302) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 503 (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_at(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aa_TPT43085870d_bool(aTP_Lamm_an,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_as(Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__303) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 504 (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_az(Uu),Uua),Uub),Uuc),Uud) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,aa_TPTP_ind_TPTP_ind(scratc633715112wissel(Uu,Uub),Uuc)),Uud))) # label(fact_ATP_Olambda__304) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 505 (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_aq(Uu),Uua),Uub),Uuc),Uud),Uue)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aa_TPT43085870d_bool(aTP_Lamm_an,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_ap(Uu),Uua),Uub),Uuc),Uud),Uue))))) # label(fact_ATP_Olambda__305) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 506 (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_ao(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(scratc860236224d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,Uub),Uuc)),Uue)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1024859966bnd_ap,Uub),Uud)),Uuf))))))) # label(fact_ATP_Olambda__306) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.41 507 (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_ap(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)) <-> pp(aa_fun171081125l_bool(scratc1597313321all_of(aa_TPT43085870d_bool(aTP_Lamm_an,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_ao(Uua),Uub),Uuc),Uud),Uue),Uuf))))) # label(fact_ATP_Olambda__307) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.45 508 (all Uu all Uua (gg_TPTP_ind(Uu) -> aa_TPTP_ind_TPTP_ind(aTP_Lamm_am(Uu),Uua) = Uu)) # label(fact_ATP_Olambda__308) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.45 509 (all Uu (gg_TPTP_ind(Uu) -> aa_TPTP_ind_TPTP_ind(aTP_Lamm_af,Uu) = Uu)) # label(fact_ATP_Olambda__309) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.45 510 (all Uu aa_TPTP_ind_TPTP_ind(aTP_Lamm_ad,Uu) = scratc772241042nd_nat) # label(fact_ATP_Olambda__310) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.45 511 (all P all Q (-pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)) | pp(Q))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.45 512 (all P all Q (-pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)) | pp(P))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.45 513 (all P all Q (-pp(P) | -pp(Q) | pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.45 514 (all P (gg_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.45 515 (all P all Q (-pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) | -pp(P) | pp(Q))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.45 516 (all Q all P (-pp(Q) | pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)))) # label(help_fimplies_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.45 517 (all P all Q (pp(P) | pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)))) # label(help_fimplies_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.45 518 (all P all X7 (-pp(aa_TPTP_ind_bool(P,X7)) | pp(fEx_TPTP_ind(P)))) # label(help_fEx_1_1_fEx_001t__TPTP____Interpret__Oind_U) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.45 519 (all X7 all Y (X7 != Y | pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)))) # label(help_fequal_2_1_fequal_001t__TPTP____Interpret__Oind_T) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.45 520 (all X7 all Y (gg_TPTP_ind(X7) & gg_TPTP_ind(Y) -> -pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) | X7 = Y)) # label(help_fequal_1_1_fequal_001t__TPTP____Interpret__Oind_T) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.45 521 (all P all Q all R aa_TPTP_ind_bool(cOMBS_2003118649l_bool(P,Q),R) = aa_bool_bool(aa_TPT2142672771l_bool(P,R),aa_TPTP_ind_bool(Q,R))) # label(help_COMBS_1_1_COMBS_001t__TPTP____Interpret__Oind_001t__HOL__Obool_001t__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.45 522 (all P all Q all R aa_TPTP_ind_bool(aa_TPT43085870d_bool(cOMBC_1555011498d_bool(P),Q),R) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind_001t__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.45 523 (all P all Q all R aa_TPT2142672771l_bool(cOMBB_658106424TP_ind(P,Q),R) = aa_boo1142376798l_bool(P,aa_TPTP_ind_bool(Q,R))) # label(help_COMBB_1_1_COMBB_001t__HOL__Obool_001t__fun_It__HOL__Obool_Mt__HOL__Obool_J_001t__TPTP____Interpret__Oind_U) # label(axiom) # label(non_clause). [assumption].
% 1.07/1.45
% 1.07/1.45 ============================== end of process non-clausal formulas ===
% 1.07/1.45
% 1.07/1.45 ============================== PROCESS INITIAL CLAUSES ===============
% 1.07/1.45
% 1.07/1.45 ============================== PREDICATE ELIMINATION =================
% 1.07/1.45 524 -gg_bool(A) | A = fTrue | A = fFalse # label(help_fFalse_1_1_T) # label(axiom). [clausify(514)].
% 1.07/1.45 525 gg_bool(undefined_bool(bool)) # label(gsy_c_HOL_Oundefined_001t__HOL__Obool) # label(axiom). [assumption].
% 1.07/1.45 526 gg_bool(scratc920260971_amone(A,B)) # label(gsy_c_Scratch__tptp__translate__53843__10784_ONUM712__thf__4__p_Obnd__amone) # label(axiom). [clausify(1)].
% 1.07/1.45 527 gg_bool(scratc769812514_d_and(A,B)) # label(gsy_c_Scratch__tptp__translate__53843__10784_ONUM712__thf__4__p_Obnd__d__and) # label(axiom). [clausify(2)].
% 1.07/1.45 528 gg_bool(scratc877277694_d_not(A)) # label(gsy_c_Scratch__tptp__translate__53843__10784_ONUM712__thf__4__p_Obnd__d__not) # label(axiom). [clausify(3)].
% 1.07/1.45 529 gg_bool(scratc698018630nd_ec3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__53843__10784_ONUM712__thf__4__p_Obnd__ec3) # label(axiom). [clausify(4)].
% 1.07/1.62 530 gg_bool(scratc246989243d_l_ec(A,B)) # label(gsy_c_Scratch__tptp__translate__53843__10784_ONUM712__thf__4__p_Obnd__l__ec) # label(axiom). [clausify(8)].
% 1.07/1.62 531 gg_bool(scratc781617665nd_or3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__53843__10784_ONUM712__thf__4__p_Obnd__or3) # label(axiom). [clausify(9)].
% 1.07/1.62 532 gg_bool(aa_bool_bool(A,B)) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom). [clausify(10)].
% 1.07/1.62 533 gg_bool(aa_TPTP_ind_bool(A,B)) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom). [clausify(11)].
% 1.07/1.62 534 gg_bool(aa_fun171081125l_bool(A,B)) # label(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__HOL__Obool) # label(hypothesis). [clausify(13)].
% 1.07/1.62 535 gg_bool(fEx_TPTP_ind(A)) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom). [clausify(16)].
% 1.07/1.62 536 gg_bool(fFalse) # label(gsy_c_fFalse) # label(axiom). [assumption].
% 1.07/1.62 537 gg_bool(fTrue) # label(gsy_c_fTrue) # label(axiom). [assumption].
% 1.07/1.62 Derived: undefined_bool(bool) = fTrue | undefined_bool(bool) = fFalse. [resolve(524,a,525,a)].
% 1.07/1.62 Derived: scratc920260971_amone(A,B) = fTrue | scratc920260971_amone(A,B) = fFalse. [resolve(524,a,526,a)].
% 1.07/1.62 Derived: scratc769812514_d_and(A,B) = fTrue | scratc769812514_d_and(A,B) = fFalse. [resolve(524,a,527,a)].
% 1.07/1.62 Derived: scratc877277694_d_not(A) = fTrue | scratc877277694_d_not(A) = fFalse. [resolve(524,a,528,a)].
% 1.07/1.62 Derived: scratc698018630nd_ec3(A,B,C) = fTrue | scratc698018630nd_ec3(A,B,C) = fFalse. [resolve(524,a,529,a)].
% 1.07/1.62 Derived: scratc246989243d_l_ec(A,B) = fTrue | scratc246989243d_l_ec(A,B) = fFalse. [resolve(524,a,530,a)].
% 1.07/1.62 Derived: scratc781617665nd_or3(A,B,C) = fTrue | scratc781617665nd_or3(A,B,C) = fFalse. [resolve(524,a,531,a)].
% 1.07/1.62 Derived: aa_bool_bool(A,B) = fTrue | aa_bool_bool(A,B) = fFalse. [resolve(524,a,532,a)].
% 1.07/1.62 Derived: aa_TPTP_ind_bool(A,B) = fTrue | aa_TPTP_ind_bool(A,B) = fFalse. [resolve(524,a,533,a)].
% 1.07/1.62 Derived: aa_fun171081125l_bool(A,B) = fTrue | aa_fun171081125l_bool(A,B) = fFalse. [resolve(524,a,534,a)].
% 1.07/1.62 Derived: fEx_TPTP_ind(A) = fTrue | fEx_TPTP_ind(A) = fFalse. [resolve(524,a,535,a)].
% 1.07/1.62 Derived: fFalse = fTrue | fFalse = fFalse. [resolve(524,a,536,a)].
% 1.07/1.62 Derived: fTrue = fTrue | fTrue = fFalse. [resolve(524,a,537,a)].
% 1.07/1.62 538 scratc641924033d_r_ec(A,B) | pp(A) # label(fact_def__r__ec) # label(axiom). [clausify(71)].
% 1.07/1.62 539 -scratc641924033d_r_ec(A,B) | -pp(A) | pp(scratc877277694_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(71)].
% 1.07/1.62 540 scratc641924033d_r_ec(A,B) | -pp(scratc877277694_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(71)].
% 1.07/1.62 541 scratc1663953964_l_iff(A,B) | -pp(scratc769812514_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc731720701nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc731720701nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(103)].
% 1.07/1.62 542 -scratc1663953964_l_iff(A,B) | pp(scratc769812514_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc731720701nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc731720701nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(103)].
% 1.07/1.62 543 scratc20906736d_orec(A,B) | -pp(scratc769812514_d_and(aa_bool_bool(scratc247645248d_l_or(A),B),scratc246989243d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(104)].
% 1.07/1.62 544 -scratc20906736d_orec(A,B) | pp(scratc769812514_d_and(aa_bool_bool(scratc247645248d_l_or(A),B),scratc246989243d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(104)].
% 1.07/1.62 545 scratc846856975nd_wel(A) | -pp(scratc877277694_d_not(scratc877277694_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(109)].
% 1.07/1.62 546 -scratc846856975nd_wel(A) | pp(scratc877277694_d_not(scratc877277694_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(109)].
% 1.07/1.62 547 -scratc846856975nd_wel(A) | pp(A) # label(fact_l__et) # label(axiom). [clausify(161)].
% 1.07/1.62 Derived: pp(A) | -pp(scratc877277694_d_not(scratc877277694_d_not(A))). [resolve(547,a,545,a)].
% 1.07/1.62
% 1.07/1.62 ============================== end predicate elimination =============
% 2.07/2.32
% 2.07/2.32 Auto_denials: (non-Horn, no changes).
% 2.07/2.32
% 2.07/2.32 Term ordering decisions:
% 2.07/2.32 Function symbol KB weights: aTP_Lamm_a=1. scratc378896585d_n_is=1. scratc1025384756bnd_in=1. scratc679939252rdsucc=1. scratc731458298nd_iii=1. scratc1926009596_29_ii=1. scratc1024859966bnd_ap=1. scratc573575410lessis=1. scratc1230440946nd_n_1=1. aTP_Lamm_an=1. scratc707559022moreis=1. scratc105151248_Sigma=1. scratc141013060ptyset=1. scratc772241042nd_nat=1. scratc1866515598d_d_Pi=1. scratc772765833nd_nis=1. scratc1451798771n_some=1. fFalse=1. scratc1669001118_nat_p=1. scratc313048534_power=1. scratc731720701nd_imp=1. scratc108506718d_repl=1. fTrue=1. scratc194786338_n_all=1. scratc661310761d_pair=1. aTP_Lamm_ad=1. scratc720020070d_Subq=1. scratc2010746768closed=1. scratc441562372_proj0=1. scratc820310400_union=1. aTP_Lamm_aj=1. scratc378896580d_n_in=1. scratc441562373_proj1=1. aTP_Lamm_ai=1. aTP_Lamm_kx=1. scratc1858990822closed=1. scratc2023723836closed=1. aTP_Lamm_cn=1. aTP_Lamm_cp=1. aTP_Lamm_cr=1. aTP_Lamm_ct=1. aTP_Lamm_cv=1. aTP_Lamm_cx=1. aTP_Lamm_cz=1. aTP_Lamm_db=1. aTP_Lamm_hw=1. aTP_Lamm_hy=1. aTP_Lamm_ia=1. aTP_Lamm_ic=1. aTP_Lamm_ie=1. aTP_Lamm_ig=1. aTP_Lamm_ii=1. aTP_Lamm_ik=1. aTP_Lamm_im=1. aTP_Lamm_io=1. aTP_Lamm_iq=1. aTP_Lamm_is=1. aTP_Lamm_ko=1. aTP_Lamm_ks=1. aTP_Lamm_kt=1. scratc1446776865d_Inj1=1. scratc1758701234_omega=1. scratc1807384429closed=1. scratc468366776_prop2=1. scratc63695786_prop2=1. aTP_Lamm_ab=1. aTP_Lamm_ak=1. aTP_Lamm_bk=1. aTP_Lamm_bm=1. aTP_Lamm_bn=1. aTP_Lamm_bv=1. aTP_Lamm_bx=1. aTP_Lamm_bz=1. aTP_Lamm_cc=1. aTP_Lamm_cf=1. aTP_Lamm_ci=1. aTP_Lamm_cl=1. aTP_Lamm_di=1. aTP_Lamm_dm=1. aTP_Lamm_dq=1. aTP_Lamm_du=1. aTP_Lamm_dy=1. aTP_Lamm_ec=1. aTP_Lamm_eg=1. aTP_Lamm_ek=1. aTP_Lamm_en=1. aTP_Lamm_eq=1. aTP_Lamm_et=1. aTP_Lamm_ew=1. aTP_Lamm_ez=1. aTP_Lamm_fc=1. aTP_Lamm_ff=1. aTP_Lamm_fi=1. aTP_Lamm_fl=1. aTP_Lamm_fo=1. aTP_Lamm_fs=1. aTP_Lamm_fw=1. aTP_Lamm_ga=1. aTP_Lamm_ge=1. aTP_Lamm_gh=1. aTP_Lamm_gk=1. aTP_Lamm_gn=1. aTP_Lamm_gq=1. aTP_Lamm_gt=1. aTP_Lamm_gw=1. aTP_Lamm_ha=1. aTP_Lamm_hc=1. aTP_Lamm_hf=1. aTP_Lamm_hi=1. aTP_Lamm_hl=1. aTP_Lamm_ho=1. aTP_Lamm_hr=1. aTP_Lamm_hu=1. aTP_Lamm_iu=1. aTP_Lamm_iw=1. aTP_Lamm_iy=1. aTP_Lamm_ja=1. aTP_Lamm_jc=1. aTP_Lamm_jg=1. aTP_Lamm_ji=1. aTP_Lamm_jl=1. aTP_Lamm_jo=1. aTP_Lamm_jq=1. aTP_Lamm_js=1. aTP_Lamm_jv=1. aTP_Lamm_jx=1. aTP_Lamm_ka=1. aTP_Lamm_kd=1. aTP_Lamm_kg=1. aTP_Lamm_kj=1. aTP_Lamm_kl=1. aTP_Lamm_km=1. aTP_Lamm_kr=1. fconj=1. fimplies=1. scratc1446776864d_Inj0=1. scratc310578599_n_one=1. scratc456679105_cond2=1. scratc468366775_prop1=1. scratc621669188d_Sing=1. scratc63695785_prop1=1. aTP_Lamm_bq=1. aTP_Lamm_bw=1. aTP_Lamm_by=1. aTP_Lamm_ca=1. aTP_Lamm_cb=1. aTP_Lamm_cd=1. aTP_Lamm_ce=1. aTP_Lamm_cg=1. aTP_Lamm_ch=1. aTP_Lamm_cj=1. aTP_Lamm_ck=1. aTP_Lamm_cm=1. aTP_Lamm_co=1. aTP_Lamm_cq=1. aTP_Lamm_cs=1. aTP_Lamm_cu=1. aTP_Lamm_cw=1. aTP_Lamm_cy=1. aTP_Lamm_da=1. aTP_Lamm_dc=1. aTP_Lamm_dd=1. aTP_Lamm_de=1. aTP_Lamm_df=1. aTP_Lamm_dj=1. aTP_Lamm_dn=1. aTP_Lamm_dr=1. aTP_Lamm_dv=1. aTP_Lamm_dz=1. aTP_Lamm_ed=1. aTP_Lamm_eh=1. aTP_Lamm_el=1. aTP_Lamm_eo=1. aTP_Lamm_er=1. aTP_Lamm_eu=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_fx=1. aTP_Lamm_gb=1. aTP_Lamm_gf=1. aTP_Lamm_gi=1. aTP_Lamm_gl=1. aTP_Lamm_go=1. aTP_Lamm_gr=1. aTP_Lamm_gu=1. aTP_Lamm_gx=1. aTP_Lamm_gy=1. aTP_Lamm_gz=1. aTP_Lamm_hb=1. aTP_Lamm_hd=1. aTP_Lamm_hg=1. aTP_Lamm_hj=1. aTP_Lamm_hm=1. aTP_Lamm_hp=1. aTP_Lamm_hs=1. aTP_Lamm_hv=1. aTP_Lamm_hx=1. aTP_Lamm_hz=1. aTP_Lamm_ib=1. aTP_Lamm_id=1. aTP_Lamm_if=1. aTP_Lamm_ih=1. aTP_Lamm_ij=1. aTP_Lamm_il=1. aTP_Lamm_in=1. aTP_Lamm_ip=1. aTP_Lamm_ir=1. aTP_Lamm_it=1. aTP_Lamm_iv=1. aTP_Lamm_ix=1. aTP_Lamm_iz=1. aTP_Lamm_jb=1. aTP_Lamm_jd=1. aTP_Lamm_jh=1. aTP_Lamm_jj=1. aTP_Lamm_jm=1. aTP_Lamm_jp=1. aTP_Lamm_jr=1. aTP_Lamm_jt=1. aTP_Lamm_jw=1. aTP_Lamm_jy=1. aTP_Lamm_jz=1. aTP_Lamm_kb=1. aTP_Lamm_kc=1. aTP_Lamm_ke=1. aTP_Lamm_kf=1. aTP_Lamm_kh=1. aTP_Lamm_ki=1. aTP_Lamm_kk=1. aTP_Lamm_kn=1. aTP_Lamm_kp=1. aTP_Lamm_kq=1. aTP_Lamm_ku=1. aTP_Lamm_kv=1. aTP_Lamm_kw=1. aTP_Lamm_kz=1. aTP_Lamm_lw=1. fequal_TPTP_ind=1. scratc2102057900univof=1. scratc456679104_cond1=1. scratc670674460_d_Unj=1. scratc770666660nd_nIn=1. aTP_Lamm_ac=1. aTP_Lamm_af=1. aTP_Lamm_al=1. aTP_Lamm_bo=1. aTP_Lamm_bp=1. bool=1. scratc105167447_times=1. scratc109333632428_id=1. scratc1192205950_empty=1. scratc1262694002_prop1=1. scratc1439126073_prop1=1. scratc1645091125_prop1=1. scratc2027488248_prop1=1. scratc426608047nempty=1. scratc441955970_prop4=1. scratc506453612munion=1. scratc536689223pair_p=1. scratc63695788_prop4=1. scratc652057960_prop1=1. scratc752974505d_plus=1. scratc85969652_prop1=1. scratc1723080956d_i1_s=1. scratc518292720d_24_g=1. scratc756739298_428_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. scratc769812514_d_and=1. aa_fun1431113780TP_ind=1. aa_boo1142376798l_bool=1. aa_TPT1123896796d_bool=1. scratc1025384748bnd_if=1. scratc246989243d_l_ec=1. aa_fun1212484691d_bool=1. aa_TPT985247859d_bool=1. scratc860236219d_e_in=1. scratc1717441455d_pair=1. scratc731786288nd_ind=1. aa_fun987228051d_bool=1. scratc920260971_amone=1. scratc1330720428_image=1. scratc1373362497_first=1. scratc1392931043second=1. aa_TPT125613450d_bool=1. scratc773159422nd_non=1. aa_fun1913827119d_bool=1. scratc1944541818d_anec=1. aa_TPT1791839040TP_ind=1. aa_fun1107270209d_bool=1. aa_fun845057962d_bool=1. scratc1023690266eplSep=1. scratc1884867200_ecelt=1. scratc698018691nd_ecp=1. scratc1884276809_ecect=1. aa_TPT1781712639TP_ind=1. aa_TPT2142672771l_bool=1. aa_fun1235454963TP_ind=1. cOMBB_658106424TP_ind=1. cOMBS_2003118649l_bool=1. scratc1422078741_fixfu=1. scratc253661789fixfu2=1. scratc460229692etprop=1. scratc633715112wissel=1. scratc698018695nd_ect=1. scratc765688315ectset=1. scratc781814527nd_out=1. scratc1747903652d_invf=1. scratc1751640183d_tofs=1. scratc650486438ectelt=1. scratc78186945nverse=1. scratc871805661unmore=1. f1=1. f12=1. f13=1. f20=1. f24=1. scratc1597313321all_of=1. scratc379355771d_n_pl=1. scratc379618174d_n_ts=1. scratc860236224d_e_is=1. scratc877277694_d_not=1. scratc653561065_d_Sep=1. scratc814214834d_esti=1. scratc707974129l_some=1. scratc1422910007ffprop=1. scratc665563058nd_all=1. scratc247645248d_l_or=1. scratc781355319nd_one=1. scratc1508860529_rec_G=1. aTP_Lamm_am=1. aTP_Lamm_lg=1. aTP_Lamm_ag=1. aTP_Lamm_ao=1. aTP_Lamm_ay=1. aTP_Lamm_bg=1. aTP_Lamm_bt=1. aTP_Lamm_dg=1. aTP_Lamm_dk=1. aTP_Lamm_do=1. aTP_Lamm_ds=1. aTP_Lamm_dw=1. aTP_Lamm_ea=1. aTP_Lamm_ee=1. aTP_Lamm_ei=1. aTP_Lamm_fq=1. aTP_Lamm_fu=1. aTP_Lamm_fy=1. aTP_Lamm_gc=1. aTP_Lamm_he=1. aTP_Lamm_hh=1. aTP_Lamm_hk=1. aTP_Lamm_hn=1. aTP_Lamm_hq=1. aTP_Lamm_ht=1. aTP_Lamm_je=1. aTP_Lamm_ky=1. aTP_Lamm_lu=1. scratc1746657277d_incl=1. aTP_Lamm_as=1. aTP_Lamm_bc=1. aTP_Lamm_bf=1. aTP_Lamm_bj=1. aTP_Lamm_em=1. aTP_Lamm_ep=1. aTP_Lamm_es=1. aTP_Lamm_ev=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_gg=1. aTP_Lamm_gj=1. aTP_Lamm_gm=1. aTP_Lamm_gp=1. aTP_Lamm_gs=1. aTP_Lamm_gv=1. aTP_Lamm_jk=1. aTP_Lamm_jn=1. aTP_Lamm_lq=1. aTP_Lamm_ls=1. scratc313862346etprod=1. scratc698871481nd_eps=1. scratc970368600ective=1. aTP_Lamm_aa=1. aTP_Lamm_ap=1. aTP_Lamm_aq=1. aTP_Lamm_ar=1. aTP_Lamm_at=1. aTP_Lamm_au=1. aTP_Lamm_aw=1. aTP_Lamm_ax=1. aTP_Lamm_bd=1. aTP_Lamm_be=1. aTP_Lamm_bh=1. aTP_Lamm_bu=1. aTP_Lamm_dh=1. aTP_Lamm_dl=1. aTP_Lamm_dp=1. aTP_Lamm_dt=1. aTP_Lamm_dx=1. aTP_Lamm_eb=1. aTP_Lamm_ef=1. aTP_Lamm_ej=1. aTP_Lamm_fr=1. aTP_Lamm_fv=1. aTP_Lamm_fz=1. aTP_Lamm_gd=1. aTP_Lamm_jf=1. aTP_Lamm_ju=1. aTP_Lamm_la=1. aTP_Lamm_lb=1. aTP_Lamm_lc=1. aTP_Lamm_le=1. aTP_Lamm_lk=1. aTP_Lamm_lm=1. aTP_Lamm_ln=1. aTP_Lamm_lr=1. fEx_TPTP_ind=1. scratc1247703976lbprop=1. scratc1500310711nunion=1. scratc2143458635ective=1. scratc379093365d_n_lb=1. scratc764504323nd_min=1. aTP_Lamm_av=1. aTP_Lamm_ld=1. aTP_Lamm_lf=1. aTP_Lamm_lh=1. aTP_Lamm_li=1. aTP_Lamm_lj=Cputime limit exceeded (core dumped)
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