TSTP Solution File: NUM656+4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM656+4 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 13:30:08 EDT 2022
% Result : Timeout 300.03s 300.33s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM656+4 : TPTP v8.1.0. Released v7.3.0.
% 0.00/0.11 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Wed Jul 6 10:38:21 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.89/1.21 ============================== Prover9 ===============================
% 0.89/1.21 Prover9 (32) version 2009-11A, November 2009.
% 0.89/1.21 Process 7070 was started by sandbox on n006.cluster.edu,
% 0.89/1.21 Wed Jul 6 10:38:22 2022
% 0.89/1.21 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_6916_n006.cluster.edu".
% 0.89/1.21 ============================== end of head ===========================
% 0.89/1.21
% 0.89/1.21 ============================== INPUT =================================
% 0.89/1.21
% 0.89/1.21 % Reading from file /tmp/Prover9_6916_n006.cluster.edu
% 0.89/1.21
% 0.89/1.21 set(prolog_style_variables).
% 0.89/1.21 set(auto2).
% 0.89/1.21 % set(auto2) -> set(auto).
% 0.89/1.21 % set(auto) -> set(auto_inference).
% 0.89/1.21 % set(auto) -> set(auto_setup).
% 0.89/1.21 % set(auto_setup) -> set(predicate_elim).
% 0.89/1.21 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.89/1.21 % set(auto) -> set(auto_limits).
% 0.89/1.21 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.89/1.21 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.89/1.21 % set(auto) -> set(auto_denials).
% 0.89/1.21 % set(auto) -> set(auto_process).
% 0.89/1.21 % set(auto2) -> assign(new_constants, 1).
% 0.89/1.21 % set(auto2) -> assign(fold_denial_max, 3).
% 0.89/1.21 % set(auto2) -> assign(max_weight, "200.000").
% 0.89/1.21 % set(auto2) -> assign(max_hours, 1).
% 0.89/1.21 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.89/1.21 % set(auto2) -> assign(max_seconds, 0).
% 0.89/1.21 % set(auto2) -> assign(max_minutes, 5).
% 0.89/1.21 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.89/1.21 % set(auto2) -> set(sort_initial_sos).
% 0.89/1.21 % set(auto2) -> assign(sos_limit, -1).
% 0.89/1.21 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.89/1.21 % set(auto2) -> assign(max_megs, 400).
% 0.89/1.21 % set(auto2) -> assign(stats, some).
% 0.89/1.21 % set(auto2) -> clear(echo_input).
% 0.89/1.21 % set(auto2) -> set(quiet).
% 0.89/1.21 % set(auto2) -> clear(print_initial_clauses).
% 0.89/1.21 % set(auto2) -> clear(print_given).
% 0.89/1.21 assign(lrs_ticks,-1).
% 0.89/1.21 assign(sos_limit,10000).
% 0.89/1.21 assign(order,kbo).
% 0.89/1.21 set(lex_order_vars).
% 0.89/1.21 clear(print_given).
% 0.89/1.21
% 0.89/1.21 % formulas(sos). % not echoed (403 formulas)
% 0.89/1.21
% 0.89/1.21 ============================== end of input ==========================
% 0.89/1.21
% 0.89/1.21 % From the command line: assign(max_seconds, 300).
% 0.89/1.21
% 0.89/1.21 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.89/1.21
% 0.89/1.21 % Formulas that are not ordinary clauses:
% 0.89/1.21 1 (all B_1 all B_2 gg_bool(scratc1938294688_amone(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__43415__7632_ONUM656__thf__4__p_Obnd__amone) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 2 (all B_1 all B_2 gg_bool(scratc317128493_d_and(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__43415__7632_ONUM656__thf__4__p_Obnd__d__and) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 3 (all B_1 gg_bool(scratc424593673_d_not(B_1))) # label(gsy_c_Scratch__tptp__translate__43415__7632_ONUM656__thf__4__p_Obnd__d__not) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 4 (all B_1 all B_2 all B_3 gg_bool(scratc1135078395nd_ec3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__43415__7632_ONUM656__thf__4__p_Obnd__ec3) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 5 (all B_1 all B_2 gg_TPTP_ind(scratc1135078460nd_ect(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__43415__7632_ONUM656__thf__4__p_Obnd__ect) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 6 (all B_1 gg_TPTP_ind(scratc1135931246nd_eps(B_1))) # label(gsy_c_Scratch__tptp__translate__43415__7632_ONUM656__thf__4__p_Obnd__eps) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 7 (all B_1 all B_2 gg_TPTP_ind(scratc1168846053nd_ind(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__43415__7632_ONUM656__thf__4__p_Obnd__ind) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 8 (all B_1 all B_2 gg_bool(scratc1265022960d_l_ec(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__43415__7632_ONUM656__thf__4__p_Obnd__l__ec) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 9 (all B_1 all B_2 all B_3 gg_bool(scratc1218677430nd_or3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__43415__7632_ONUM656__thf__4__p_Obnd__or3) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 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].
% 0.89/1.21 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].
% 0.89/1.21 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].
% 0.89/1.21 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].
% 0.89/1.21 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].
% 0.89/1.21 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].
% 0.89/1.21 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].
% 0.89/1.21 17 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc120891389lessis,X),Xa)) <-> pp(aa_bool_bool(scratc1265678965d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1168518063nd_iii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,X),Xa))))) # label(fact_def__lessis) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 18 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc254875001moreis,X),Xa)) <-> pp(aa_bool_bool(scratc1265678965d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,X),Xa))))) # label(fact_def__moreis) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 19 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1892517117_prop1,X),Xa)) <-> pp(scratc1218677430nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1168518063nd_iii,X),Xa))))) # label(fact_def__d__29__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 20 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1168518063nd_iii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1236589736n_some,aa_TPT43085870d_bool(scratc1482924994ffprop(Xa),X))))) # label(fact_def__iii) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 21 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1236589736n_some,aa_TPT43085870d_bool(scratc1482924994ffprop(X),Xa))))) # label(fact_def__d__29__ii) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 22 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1482924994ffprop(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,X),aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(Xa),Xb))))) # label(fact_def__diffprop) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 23 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1304154942_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1209825598nd_nis,aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(X),Xb))))) # label(fact_def__d__28__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 24 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc715792767_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1209825598nd_nis,Xa),aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(X),Xa))))) # label(fact_def__d__27__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 25 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc127430592_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(Xa),X))))) # label(fact_def__d__26__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 26 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1686552065_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(X),Xa)),Xb)),aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(X),aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(Xa),Xb)))))) # label(fact_def__d__25__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 27 (all X scratc1397389488d_n_pl(X) = aa_TPT1424761345TP_ind(scratc213164361bnd_ap,aa_TPTP_ind_TPTP_ind(scratc382314292d_plus,X))) # label(fact_def__n__pl) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 28 (all X aa_TPTP_ind_TPTP_ind(scratc382314292d_plus,X) = scratc1168846053nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc737065667d_d_Pi,scratc1209300807nd_nat),aTP_Lamm_ac),aa_TPT43085870d_bool(scratc1098189891_prop2,X))) # label(fact_def__plus) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 29 (all X aa_TPTP_ind_TPTP_ind(scratc578307707d_24_g,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc165166235_Sigma,scratc1209300807nd_nat),aTP_Lamm_ad(X))) # label(fact_def__d__24__g) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 30 (all X (pp(aa_TPTP_ind_bool(scratc1459989687_prop4,X)) <-> pp(aa_fun171081125l_bool(scratc492765094l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc737065667d_d_Pi,scratc1209300807nd_nat),aTP_Lamm_ac)),aa_TPT43085870d_bool(scratc1098189891_prop2,X))))) # label(fact_def__prop4) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 31 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1459989686_prop3(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,X),Xb)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,Xa),Xb))))) # label(fact_def__prop3) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 32 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1098189891_prop2,X),Xa)) <-> pp(scratc317128493_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,Xa),scratc859780733nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,X)),aa_TPTP_ind_bool(scratc1098189890_prop1,Xa))))) # label(fact_def__d__24__prop2) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 33 (all X (pp(aa_TPTP_ind_bool(scratc1098189890_prop1,X)) <-> pp(aa_fun171081125l_bool(scratc1889585965_n_all,aa_TPT43085870d_bool(aTP_Lamm_ae,X))))) # label(fact_def__d__24__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 34 (all X (pp(aa_TPTP_ind_bool(scratc509827715_prop1,X)) <-> pp(aa_bool_bool(scratc1265678965d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,X),scratc859780733nd_n_1)),aa_fun171081125l_bool(scratc1236589736n_some,aa_TPT43085870d_bool(aTP_Lamm_af,X)))))) # label(fact_def__d__23__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 35 (all X (pp(aa_TPTP_ind_bool(scratc2068949188_prop1,X)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1209825598nd_nis,aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,X)),X)))) # label(fact_def__d__22__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 36 (all X (pp(aa_TPTP_ind_bool(scratc1474712822_cond2,X)) <-> pp(aa_fun171081125l_bool(scratc1889585965_n_all,aa_TPT43085870d_bool(aTP_Lamm_ag,X))))) # label(fact_def__cond2) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 37 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1209825598nd_nis,X),Xa)) <-> pp(scratc424593673_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,X),Xa))))) # label(fact_def__nis) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 38 (all X all Xa all Xb all Xc all Xd scratc1731971265indeq2(X,Xa,Xb,Xc,Xd) = aa_TPT1424761345TP_ind(scratc1006511025_indeq(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1391949119d_11_i(X,Xa,Xb),Xc),Xd))) # label(fact_def__indeq2) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 39 (all X all Xa all Xb scratc1391949119d_11_i(X,Xa,Xb) = scratc1006511025_indeq(X,Xa,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc737065667d_d_Pi,X),aTP_Lamm_ai(Xb)))) # label(fact_def__d__11__i) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 40 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1948461416fixfu2(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_an(X),Xa),Xb),Xc))))) # label(fact_def__fixfu2) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 41 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1006511025_indeq(X,Xa,Xb),Xc),Xd) = scratc1168846053nd_ind(Xb,aa_TPT43085870d_bool(scratc1459989685_prop2(X,Xa,Xb,Xc),Xd))) # label(fact_def__indeq) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 42 (all X all Xa all Xb all Xc all Xd all Xe (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1459989685_prop2(X,Xa,Xb,Xc),Xd),Xe)) <-> pp(aa_fun171081125l_bool(scratc492765094l_some(X),aa_TPT43085870d_bool(scratc1645512517_prop1(X,Xa,Xb,Xc,Xd),Xe))))) # label(fact_def__prop2) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 43 (all X all Xa all Xb all Xc all Xd all Xe all Xf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1645512517_prop1(X,Xa,Xb,Xc,Xd),Xe),Xf)) <-> pp(scratc317128493_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc443554621d_esti(X),Xf),aa_TPTP_ind_TPTP_ind(scratc754826878_ecect(X,Xa),Xd)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1878269941d_e_is(Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,Xc),Xf)),Xe))))) # label(fact_def__d__10__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 44 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc292628810_fixfu(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ap(X),Xa),Xb),Xc))))) # label(fact_def__fixfu) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 45 (all X all Xa scratc754826878_ecect(X,Xa) = scratc1878269936d_e_in(aa_TPTP_ind_TPTP_ind(scratc1331082251_power,X),scratc1573881605d_anec(X,Xa))) # label(fact_def__ecect) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 46 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc197802417ectelt(X,Xa),Xb) = aa_TPTP_ind_TPTP_ind(scratc313004294ectset(X,Xa),aa_TPTP_ind_TPTP_ind(scratc755417269_ecelt(X,Xa),Xb))) # label(fact_def__ectelt) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 47 (all X all Xa scratc313004294ectset(X,Xa) = scratc1218874292nd_out(aa_TPTP_ind_TPTP_ind(scratc1331082251_power,X),scratc1573881605d_anec(X,Xa))) # label(fact_def__ectset) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 48 (all X all Xa scratc1135078460nd_ect(X,Xa) = aa_fun1431113780TP_ind(scratc200877044_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1331082251_power,X)),scratc1573881605d_anec(X,Xa))) # label(fact_def__ect) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 49 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc1573881605d_anec(X,Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc492765094l_some(X),aa_TPT43085870d_bool(scratc1135078456nd_ecp(X,Xa),Xb))))) # label(fact_def__anec) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 50 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1135078456nd_ecp(X,Xa),Xb),Xc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1878269941d_e_is(aa_TPTP_ind_TPTP_ind(scratc1331082251_power,X)),Xb),aa_TPTP_ind_TPTP_ind(scratc755417269_ecelt(X,Xa),Xc))))) # label(fact_def__ecp) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 51 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc755417269_ecelt(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc200877044_d_Sep(X),aa_TPT43085870d_bool(Xa,Xb))) # label(fact_def__ecelt) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 52 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc419121640unmore(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc200877044_d_Sep(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ar(X),Xa),Xb))) # label(fact_def__unmore) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 53 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1403271239etprop(X,Xa),Xb),Xc)) <-> pp(scratc317128493_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc443554621d_esti(X),Xc),Xa),scratc424593673_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc443554621d_esti(X),Xc),Xb)))))) # label(fact_def__nissetprop) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 54 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1893447735t_disj(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1102622823nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_as(X),Xa),Xb))))) # label(fact_def__st__disj) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 55 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1375997064d_incl(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1102622823nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_at(X),Xa),Xb))))) # label(fact_def__incl) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 56 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc486623034nempty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc492765094l_some(X),aa_TPT43085870d_bool(aTP_Lamm_au(X),Xa))))) # label(fact_def__nonempty) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 57 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc62756019_empty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),scratc1210219187nd_non(X,aa_TPT43085870d_bool(aTP_Lamm_au(X),Xa)))))) # label(fact_def__empty) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 58 (all X scratc443554621d_esti(X) = scratc213689151bnd_in) # label(fact_def__esti) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 59 (all X all Xa (scratc1659957750d_r_ec(X,Xa) <-> (pp(X) -> pp(scratc424593673_d_not(Xa))))) # label(fact_def__r__ec) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 60 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc2024420508hangef(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc165166235_Sigma,X),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_av(X),Xb),Xc),Xd))) # label(fact_def__changef) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 61 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc181031091wissel(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc165166235_Sigma,X),scratc1342640926sel_wb(X,Xa,Xb))) # label(fact_def__wissel) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 62 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1342640926sel_wb(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc1169239648nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1878269941d_e_is(X),Xc),Xb),X,Xa),aa_TPTP_ind_TPTP_ind(scratc1342640925sel_wa(X,Xa,Xb),Xc))) # label(fact_def__wissel__wb) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 63 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1342640925sel_wa(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc1169239648nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1878269941d_e_is(X),Xc),Xa),X,Xb),Xc)) # label(fact_def__wissel__wa) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 64 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1169239648nd_ite(X,Xa,Xb),Xc) = scratc1168846053nd_ind(Xa,aa_TPT43085870d_bool(scratc1459989684_prop1(X,Xa,Xb),Xc))) # label(fact_def__ite) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 65 (all X all Xa all Xb all Xc all Xd (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1459989684_prop1(X,Xa,Xb),Xc),Xd)) <-> pp(scratc317128493_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1168780466nd_imp,X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1878269941d_e_is(Xa),Xd),Xb)),aa_bool_bool(aa_boo1142376798l_bool(scratc1168780466nd_imp,scratc424593673_d_not(X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1878269941d_e_is(Xa),Xd),Xc)))))) # label(fact_def__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 66 (all X all Xa scratc940247022second(X,Xa) = scratc1459596090_proj1) # label(fact_def__second) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 67 (all X all Xa scratc243912566_first(X,Xa) = scratc1459596089_proj0) # label(fact_def__first) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 68 (all X all Xa scratc1502232420d_pair(X,Xa) = scratc290650548d_pair) # label(fact_def__d__pair) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 69 (all X all Xa scratc1218874292nd_out(X,Xa) = scratc600392772d_soft(aa_fun1431113780TP_ind(scratc200877044_d_Sep(X),Xa),X,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc165166235_Sigma,aa_fun1431113780TP_ind(scratc200877044_d_Sep(X),Xa)),scratc1878269936d_e_in(X,Xa)))) # label(fact_def__out) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 70 (all X all Xa all Xb (gg_TPTP_ind(Xb) -> aa_TPTP_ind_TPTP_ind(scratc1878269936d_e_in(X,Xa),Xb) = Xb)) # label(fact_def__e__in) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 71 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc2069777405_inj_h(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc165166235_Sigma,X),aa_TPT1424761345TP_ind(aTP_Lamm_aw(Xc),Xd))) # label(fact_def__inj__h) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 72 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1377243439d_invf(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc165166235_Sigma,Xa),scratc600392772d_soft(X,Xa,Xb))) # label(fact_def__invf) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 73 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1739693259ective(X),Xa),Xb)) <-> pp(scratc317128493_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1555974029ective(X),Xa),Xb),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc939016534ective(X),Xa),Xb))))) # label(fact_def__bijective) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 74 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc939016534ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1102622823nd_all(Xa),aa_TPT43085870d_bool(scratc201270497_image(X,Xa),Xb))))) # label(fact_def__surjective) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 75 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc2010461558nverse(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc165166235_Sigma,Xa),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ax(X),Xa),Xb))) # label(fact_def__inverse) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 76 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc600392772d_soft(X,Xa,Xb),Xc) = scratc1168846053nd_ind(X,aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(Xa),Xb),Xc))) # label(fact_def__soft) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 77 (all X all Xa scratc1380979970d_tofs(X,Xa) = scratc213164361bnd_ap) # label(fact_def__tofs) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 78 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc201270497_image(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc492765094l_some(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(Xa),Xb),Xc))))) # label(fact_def__image) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 79 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1555974029ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1102622823nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ba(X),Xa),Xb))))) # label(fact_def__injective) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 80 (all X all Xa scratc1168846053nd_ind(X,Xa) = scratc1135931246nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bb(X),Xa))) # label(fact_def__ind) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 81 (all X all Xa (pp(aa_fun171081125l_bool(scratc1218415084nd_one(X),Xa)) <-> pp(scratc317128493_d_and(scratc1938294688_amone(X,Xa),aa_fun171081125l_bool(scratc492765094l_some(X),Xa))))) # label(fact_def__one) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 82 (all X all Xa (pp(scratc1938294688_amone(X,Xa)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),aa_fun1584354236d_bool(aTP_Lamm_bd(X),Xa))))) # label(fact_def__amone) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 83 (all X scratc1878269941d_e_is(X) = fequal_TPTP_ind) # label(fact_def__e__is) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 84 (all X all Xa all Xb (scratc236957560_orec3(X,Xa,Xb) <-> pp(scratc317128493_d_and(scratc1218677430nd_or3(X,Xa,Xb),scratc1135078395nd_ec3(X,Xa,Xb))))) # label(fact_def__orec3) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 85 (all X all Xa all Xb (pp(scratc1135078395nd_ec3(X,Xa,Xb)) <-> scratc1573815958d_and3(scratc1265022960d_l_ec(X,Xa),scratc1265022960d_l_ec(Xa,Xb),scratc1265022960d_l_ec(Xb,X)))) # label(fact_def__ec3) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 86 (all X all Xa all Xb (scratc1573815958d_and3(X,Xa,Xb) <-> pp(scratc317128493_d_and(X,scratc317128493_d_and(Xa,Xb))))) # label(fact_def__and3) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 87 (all X all Xa all Xb (pp(scratc1218677430nd_or3(X,Xa,Xb)) <-> pp(aa_bool_bool(scratc1265678965d_l_or(X),aa_bool_bool(scratc1265678965d_l_or(Xa),Xb))))) # label(fact_def__or3) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 88 (all X all Xa (pp(aa_fun171081125l_bool(scratc492765094l_some(X),Xa)) <-> pp(scratc424593673_d_not(aa_fun171081125l_bool(scratc1382104286all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),scratc1210219187nd_non(X,Xa)))))) # label(fact_def__l__some) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 89 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc1210219187nd_non(X,Xa),Xb)) <-> pp(scratc424593673_d_not(aa_TPTP_ind_bool(Xa,Xb))))) # label(fact_def__non) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 90 (all X scratc1102622823nd_all(X) = scratc1382104286all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X))) # label(fact_def__all) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 91 (all X all Xa (scratc1211269943_l_iff(X,Xa) <-> pp(scratc317128493_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1168780466nd_imp,X),Xa),aa_bool_bool(aa_boo1142376798l_bool(scratc1168780466nd_imp,Xa),X))))) # label(fact_def__l__iff) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 92 (all X all Xa (scratc1797730171d_orec(X,Xa) <-> pp(scratc317128493_d_and(aa_bool_bool(scratc1265678965d_l_or(X),Xa),scratc1265022960d_l_ec(X,Xa))))) # label(fact_def__orec) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 93 (all X scratc1265678965d_l_or(X) = aa_boo1142376798l_bool(scratc1168780466nd_imp,scratc424593673_d_not(X))) # label(fact_def__l__or) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 94 (all X all Xa (pp(scratc317128493_d_and(X,Xa)) <-> pp(scratc424593673_d_not(scratc1265022960d_l_ec(X,Xa))))) # label(fact_def__d__and) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 95 (all X all Xa (pp(scratc1265022960d_l_ec(X,Xa)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1168780466nd_imp,X),scratc424593673_d_not(Xa))))) # label(fact_def__l__ec) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 96 scratc728060557bvious <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1168780466nd_imp,fFalse),fFalse)) # label(fact_def__obvious) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 97 (all X (scratc1283916740nd_wel(X) <-> pp(scratc424593673_d_not(scratc424593673_d_not(X))))) # label(fact_def__wel) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 98 (all X (pp(scratc424593673_d_not(X)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1168780466nd_imp,X),fFalse)))) # label(fact_def__d__not) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 99 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc737065667d_d_Pi,X),Xa) = aa_fun1431113780TP_ind(scratc200877044_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1331082251_power,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc165166235_Sigma,X),aTP_Lamm_be(Xa)))),aa_fun1913827119d_bool(aTP_Lamm_bf(X),Xa))) # label(fact_def__d__Pi) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 100 (all X (gg_TPTP_ind(X) -> (pp(aa_TPTP_ind_bool(scratc321480188pair_p,X)) <-> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc290650548d_pair,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,X),scratc201028047ptyset)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,X),aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,scratc201028047ptyset))) = X))) # label(fact_def__pair__p) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 101 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc1966731813eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bg,Xa)),scratc1459596090_proj1)) # label(fact_def__ap) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 102 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc98653311etprod(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc165166235_Sigma,X),aTP_Lamm_ai(Xa))) # label(fact_def__setprod) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 103 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc165166235_Sigma,X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc566468599munion,X),aTP_Lamm_bh(Xa))) # label(fact_def__d__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 104 (all X aa_TPTP_ind_TPTP_ind(scratc1459596090_proj1,X) = aa_fun277296641TP_ind(scratc1966731813eplSep(X,aTP_Lamm_bi),scratc217990439_d_Unj)) # label(fact_def__proj1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 105 (all X aa_TPTP_ind_TPTP_ind(scratc1459596089_proj0,X) = aa_fun277296641TP_ind(scratc1966731813eplSep(X,aTP_Lamm_bj),scratc217990439_d_Unj)) # label(fact_def__proj0) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 106 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc290650548d_pair,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1560325698nunion(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1885330153d_repl,X),scratc1231567829d_Inj0)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1885330153d_repl,Xa),scratc1231567830d_Inj1))) # label(fact_def__pair) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 107 (all X aa_TPTP_ind_TPTP_ind(scratc1231567829d_Inj0,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1885330153d_repl,X),scratc1231567830d_Inj1)) # label(fact_def__d__Inj0) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 108 (all X (pp(aa_TPTP_ind_bool(scratc1216317097_nat_p,X)) <-> (all X1 (pp(aa_TPTP_ind_bool(X1,scratc201028047ptyset)) -> ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(X1,X2)) -> pp(aa_TPTP_ind_bool(X1,aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,X2)))))) -> pp(aa_TPTP_ind_bool(X1,X))))))) # label(fact_def__nat__p) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 109 (all X aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1560325698nunion(X),aa_TPTP_ind_TPTP_ind(scratc406460153d_Sing,X))) # label(fact_def__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 110 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1694495393In_rec(X),Xa) = scratc1135931246nd_eps(aa_TPT43085870d_bool(scratc1837477542_rec_G(X),Xa))) # label(fact_def__d__In__rec) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 111 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1837477542_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(scratc213689151bnd_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].
% 0.89/1.21 112 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1476611240tminus(X),Xa) = aa_fun1431113780TP_ind(scratc200877044_d_Sep(X),aa_TPT43085870d_bool(aTP_Lamm_bm,Xa))) # label(fact_def__setminus) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 113 (all X all Xa scratc1966731813eplSep(X,Xa) = aa_TPT494704832TP_ind(scratc1885330153d_repl,aa_fun1431113780TP_ind(scratc200877044_d_Sep(X),Xa))) # label(fact_def__d__ReplSep) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.21 114 (all X all Xa aa_fun1431113780TP_ind(scratc200877044_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc213689143bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc213689151bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1885330153d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bn(X),Xa))),scratc201028047ptyset)) # label(fact_def__d__Sep) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 115 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc566468599munion,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1838344117_union,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1885330153d_repl,X),Xa))) # label(fact_def__famunion) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 116 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1560325698nunion(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1838344117_union,aa_TPTP_ind_TPTP_ind(scratc59652613_UPair(X),Xa))) # label(fact_def__binunion) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 117 (all X aa_TPTP_ind_TPTP_ind(scratc406460153d_Sing,X) = aa_TPTP_ind_TPTP_ind(scratc59652613_UPair(X),X)) # label(fact_def__d__Sing) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 118 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc59652613_UPair(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1885330153d_repl,aa_TPTP_ind_TPTP_ind(scratc1331082251_power,aa_TPTP_ind_TPTP_ind(scratc1331082251_power,scratc201028047ptyset))),aa_TPT1424761345TP_ind(aTP_Lamm_bo(X),Xa))) # label(fact_def__d__UPair) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 119 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1207726425nd_nIn,X),Xa)) <-> -pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X),Xa)))) # label(fact_def__nIn) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 120 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc213689143bnd_if(X,Xa),Xb) = scratc1135931246nd_eps(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bp(X),Xa),Xb))) # label(fact_def__if) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 121 (all X (pp(aa_TPTP_ind_bool(scratc2136001442closed,X)) <-> pp(aa_TPTP_ind_bool(scratc328851057closed,X)) & pp(aa_TPTP_ind_bool(scratc493584071closed,X)) & pp(aa_TPTP_ind_bool(scratc656609605closed,X)))) # label(fact_def__d__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 122 (all X (pp(aa_TPTP_ind_bool(scratc656609605closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X1),X)) -> (all X2 ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X3),X1)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,aa_TPTP_ind_TPTP_ind(X2,X3)),X))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1885330153d_repl,X1),X2)),X))))))))) # label(fact_def__d__Repl__closed) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 123 (all X (pp(aa_TPTP_ind_bool(scratc493584071closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,aa_TPTP_ind_TPTP_ind(scratc1331082251_power,X1)),X))))))) # label(fact_def__d__Power__closed) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 124 (all X (pp(aa_TPTP_ind_bool(scratc328851057closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,aa_TPTP_ind_TPTP_ind(scratc1838344117_union,X1)),X))))))) # label(fact_def__d__Union__closed) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 125 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc504811035d_Subq,X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X2),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X2),Xa))))))) # label(fact_def__d__Subq) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 126 (all X all Xa (pp(aa_fun171081125l_bool(scratc1382104286all_of(X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (scratc1329672891_is_of(X2,X) -> pp(aa_TPTP_ind_bool(Xa,X2))))))) # label(fact_def__all__of) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 127 (all X all Xa (scratc1329672891_is_of(X,Xa) <-> pp(aa_TPTP_ind_bool(Xa,X)))) # label(fact_def__is__of) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 128 (all X0 pp(aa_fun171081125l_bool(scratc1382104286all_of(aa_TPT43085870d_bool(aTP_Lamm_ej,X0)),aa_TPT43085870d_bool(aTP_Lamm_el,X0)))) # label(fact_isseti) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 129 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1382104286all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_em(X0),X12)))) # label(fact_estie) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 130 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1382104286all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_en(X0),X12)))) # label(fact_estii) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 131 (all X0 all X12 scratc1329672891_is_of(aa_fun1431113780TP_ind(scratc200877044_d_Sep(X0),X12),aa_TPT43085870d_bool(aTP_Lamm_ej,X0))) # label(fact_setof__p) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 132 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1382104286all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_ep(X0),X12)))) # label(fact_secondis1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 133 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1382104286all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_er(X0),X12)))) # label(fact_firstis1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 134 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1382104286all_of(aa_TPT43085870d_bool(aTP_Lamm_es(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_et(X0),X12)))) # label(fact_pairis1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 135 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1382104286all_of(aa_TPT43085870d_bool(aTP_Lamm_es(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_eu(X0),X12)))) # label(fact_second__p) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 136 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1382104286all_of(aa_TPT43085870d_bool(aTP_Lamm_es(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_ev(X0),X12)))) # label(fact_first__p) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 137 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1382104286all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_ex(X0),X12)))) # label(fact_e__pair__p) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 138 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1382104286all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_ey(X0),X12)))) # label(fact_otax2) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 139 (all X0 all X12 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1555974029ective(aa_fun1431113780TP_ind(scratc200877044_d_Sep(X0),X12)),X0),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc165166235_Sigma,aa_fun1431113780TP_ind(scratc200877044_d_Sep(X0),X12)),scratc1878269936d_e_in(X0,X12))))) # label(fact_otax1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 140 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1382104286all_of(aa_fun1584354236d_bool(aTP_Lamm_ez(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_fa(X0),X12)))) # label(fact_e__inp) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 141 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1382104286all_of(aa_fun1584354236d_bool(aTP_Lamm_ez(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_fb(X0),X12)))) # label(fact_e__in__p) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 142 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1382104286all_of(aa_TPT43085870d_bool(aTP_Lamm_fc(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_ff(X0),X12)))) # label(fact_e__fisi) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 143 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc1218415084nd_one(X0),X12)) -> pp(aa_TPTP_ind_bool(X12,scratc1168846053nd_ind(X0,X12))))) # label(fact_oneax) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 144 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc1218415084nd_one(X0),X12)) -> scratc1329672891_is_of(scratc1168846053nd_ind(X0,X12),aa_TPT43085870d_bool(aTP_Lamm_aj,X0)))) # label(fact_ind__p) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 145 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1382104286all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_fh(X0),X12)))) # label(fact_e__isp) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 146 (all X0 pp(aa_fun171081125l_bool(scratc1382104286all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_fi,X0)))) # label(fact_refis) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 147 (all X0 (scratc1283916740nd_wel(X0) -> pp(X0))) # label(fact_l__et) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 148 (all X0 all X12 all X22 all X32 (pp(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc213689143bnd_if(X0,X22),X32))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X12),X22))))) # label(fact_k__If__In__then__E) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 149 (all X0 all X12 all X22 ((pp(X0) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X12),X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,aa_TPTP_ind_TPTP_ind(scratc213689143bnd_if(X0,X12),scratc201028047ptyset)),aa_TPTP_ind_TPTP_ind(scratc213689143bnd_if(X0,X22),aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,scratc201028047ptyset)))))) # label(fact_k__If__In__01) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 150 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X33),X0)) -> aa_TPTP_ind_TPTP_ind(X12,X33) = aa_TPTP_ind_TPTP_ind(X22,X33)))) -> aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc165166235_Sigma,X0),X12) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc165166235_Sigma,X0),X22))) # label(fact_xi__ext) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 151 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc737065667d_d_Pi,X0),X12))) -> (all X32 (gg_TPTP_ind(X32) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X32),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc737065667d_d_Pi,X0),X12))) -> ((all X42 (gg_TPTP_ind(X42) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X42),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,X22),X42) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,X32),X42)))) -> X22 = X32))))))) # label(fact_k__Pi__ext) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 152 (all X0 all X12 all X22 all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc737065667d_d_Pi,X0),X12))) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X32),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,X22),X32)),aa_TPTP_ind_TPTP_ind(X12,X32)))))) # label(fact_ap__Pi) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 153 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X33),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,aa_TPTP_ind_TPTP_ind(X22,X33)),aa_TPTP_ind_TPTP_ind(X12,X33)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc165166235_Sigma,X0),X22)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc737065667d_d_Pi,X0),X12))))) # label(fact_lam__Pi) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 154 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X22),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc165166235_Sigma,X0),X12)),X22) = aa_TPTP_ind_TPTP_ind(X12,X22))) # label(fact_beta) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 155 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc165166235_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,aa_TPTP_ind_TPTP_ind(scratc1459596090_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1459596089_proj0,X22)))))) # label(fact_proj1__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 156 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc165166235_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,aa_TPTP_ind_TPTP_ind(scratc1459596089_proj0,X22)),X0)))) # label(fact_proj0__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 157 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc165166235_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc290650548d_pair,aa_TPTP_ind_TPTP_ind(scratc1459596089_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1459596090_proj1,X22)) = X22))) # label(fact_proj__Sigma__eta) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 158 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc165166235_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc290650548d_pair,aa_TPTP_ind_TPTP_ind(scratc1459596089_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1459596090_proj1,X22)) = X22 & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,aa_TPTP_ind_TPTP_ind(scratc1459596089_proj0,X22)),X0)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,aa_TPTP_ind_TPTP_ind(scratc1459596090_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1459596089_proj0,X22))))))) # label(fact_k__Sigma__eta__proj0__proj1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 159 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X22),X0)) -> (all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X32),aa_TPTP_ind_TPTP_ind(X12,X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc290650548d_pair,X22),X32)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc165166235_Sigma,X0),X12))))))) # label(fact_pair__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 160 (all X0 all X12 (gg_TPTP_ind(X12) -> aa_TPTP_ind_TPTP_ind(scratc1459596090_proj1,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc290650548d_pair,X0),X12)) = X12)) # label(fact_proj1__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 161 (all X0 all X12 (gg_TPTP_ind(X0) -> aa_TPTP_ind_TPTP_ind(scratc1459596089_proj0,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc290650548d_pair,X0),X12)) = X0)) # label(fact_proj0__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 162 (all X0 (pp(aa_TPTP_ind_bool(scratc1216317097_nat_p,X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X0),scratc629251303_omega)))) # label(fact_nat__p__omega) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 163 (all X0 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X0),scratc629251303_omega)) -> pp(aa_TPTP_ind_bool(scratc1216317097_nat_p,X0)))) # label(fact_omega__nat__p) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 164 (all X0 (gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(scratc1216317097_nat_p,X0)) -> X0 = scratc201028047ptyset | (exists X13 (gg_TPTP_ind(X13) & pp(aa_TPTP_ind_bool(scratc1216317097_nat_p,X13)) & X0 = aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,X13)))))) # label(fact_nat__inv) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 165 (all X0 (pp(aa_TPTP_ind_bool(X0,scratc201028047ptyset)) -> ((all X13 (gg_TPTP_ind(X13) -> (pp(aa_TPTP_ind_bool(scratc1216317097_nat_p,X13)) -> (pp(aa_TPTP_ind_bool(X0,X13)) -> pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,X13))))))) -> (all X12 (pp(aa_TPTP_ind_bool(scratc1216317097_nat_p,X12)) -> pp(aa_TPTP_ind_bool(X0,X12))))))) # label(fact_nat__ind) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 166 (all X0 (pp(aa_TPTP_ind_bool(scratc1216317097_nat_p,X0)) -> pp(aa_TPTP_ind_bool(scratc1216317097_nat_p,aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,X0))))) # label(fact_nat__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 167 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,X0) = aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,X12) -> X0 = X12))) # label(fact_ordsucc__inj) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 168 (all X0 aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,X0) != scratc201028047ptyset) # label(fact_neq__ordsucc__0) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 169 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X22),aa_fun1431113780TP_ind(scratc200877044_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(X12,X22)))) # label(fact_k__SepE2) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 170 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X22),aa_fun1431113780TP_ind(scratc200877044_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X22),X0)))) # label(fact_k__SepE1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 171 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X22),X0)) -> (pp(aa_TPTP_ind_bool(X12,X22)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X22),aa_fun1431113780TP_ind(scratc200877044_d_Sep(X0),X12)))))) # label(fact_k__SepI) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 172 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc1331082251_power,X0)))) # label(fact_k__Self__In__Power) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 173 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc504811035d_Subq,X12),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1331082251_power,X0))))) # label(fact_k__PowerI) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 174 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1331082251_power,X0))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc504811035d_Subq,X12),X0)))) # label(fact_k__PowerE) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 175 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> aa_TPTP_ind_TPTP_ind(scratc213689143bnd_if(X0,X12),X22) = X12 | aa_TPTP_ind_TPTP_ind(scratc213689143bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__or) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 176 (all X0 all X12 all X22 (gg_TPTP_ind(X12) -> (pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc213689143bnd_if(X0,X12),X22) = X12))) # label(fact_if__i__1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 177 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (-pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc213689143bnd_if(X0,X12),X22) = X22))) # label(fact_if__i__0) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 178 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> pp(X0) & aa_TPTP_ind_TPTP_ind(scratc213689143bnd_if(X0,X12),X22) = X12 | -pp(X0) & aa_TPTP_ind_TPTP_ind(scratc213689143bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__correct) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 179 (all X0 pp(aa_TPTP_ind_bool(scratc2136001442closed,aa_TPTP_ind_TPTP_ind(scratc1649373879univof,X0)))) # label(fact_k__UnivOf__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 180 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc1649373879univof,X0)))) # label(fact_k__UnivOf__In) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 181 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1885330153d_repl,X0),X12))) <-> (exists X3 (gg_TPTP_ind(X3) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X3),X0)) & X22 = aa_TPTP_ind_TPTP_ind(X12,X3)))))) # label(fact_k__ReplEq) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 182 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1331082251_power,X0))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc504811035d_Subq,X12),X0)))) # label(fact_k__PowerEq) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 183 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1838344117_union,X0))) <-> (exists X2 (gg_TPTP_ind(X2) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X12),X2)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X2),X0)))))) # label(fact_k__UnionEq) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 184 -(exists X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X0),scratc201028047ptyset))) # label(fact_k__EmptyAx) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 185 (all X0 ((all X13 (gg_TPTP_ind(X13) -> ((all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_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].
% 0.89/1.22 186 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc504811035d_Subq,X0),X12)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc504811035d_Subq,X12),X0)) -> X0 = X12)))) # label(fact_set__ext) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 187 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dy,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1209825598nd_nis,Uu),scratc859780733nd_n_1)) -> pp(aa_fun171081125l_bool(scratc1236589736n_some,aa_TPT43085870d_bool(aTP_Lamm_af,Uu)))))) # label(fact_ATP_Olambda__1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 188 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dx,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1209825598nd_nis,Uu),scratc859780733nd_n_1)) -> pp(aa_fun171081125l_bool(scratc2005378226_n_one,aa_TPT43085870d_bool(aTP_Lamm_af,Uu)))))) # label(fact_ATP_Olambda__2) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 189 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_du,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(Uu),scratc859780733nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,Uu))))) # label(fact_ATP_Olambda__3) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 190 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dr,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(scratc859780733nd_n_1),Uu)),aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,Uu))))) # label(fact_ATP_Olambda__4) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 191 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dw,Uu)) <-> pp(aa_fun171081125l_bool(scratc1218415084nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc737065667d_d_Pi,scratc1209300807nd_nat),aTP_Lamm_ac)),aa_TPT43085870d_bool(aTP_Lamm_dv,Uu))))) # label(fact_ATP_Olambda__5) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 192 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ee,Uu)) <-> (pp(aa_TPTP_ind_bool(scratc1474712821_cond1,Uu)) -> (pp(aa_TPTP_ind_bool(scratc1474712822_cond2,Uu)) -> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ed,Uu))))))) # label(fact_ATP_Olambda__6) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 193 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_do,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(Uu),scratc859780733nd_n_1))))) # label(fact_ATP_Olambda__7) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 194 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dl,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(scratc859780733nd_n_1),Uu))))) # label(fact_ATP_Olambda__8) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 195 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dz,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1209825598nd_nis,aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__9) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 196 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ei,Uu)) <-> scratc1329672891_is_of(aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,Uu),aTP_Lamm_a))) # label(fact_ATP_Olambda__10) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 197 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_eh,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1209825598nd_nis,aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,Uu)),scratc859780733nd_n_1)))) # label(fact_ATP_Olambda__11) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 198 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ec,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,Uu),aa_TPTP_ind_TPTP_ind(scratc1331082251_power,scratc1209300807nd_nat))))) # label(fact_ATP_Olambda__12) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 199 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_a,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,Uu),scratc1209300807nd_nat)))) # label(fact_ATP_Olambda__13) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 200 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_eg,Uu)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ef,Uu))))) # label(fact_ATP_Olambda__14) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 201 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_eb,Uu)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ea,Uu))))) # label(fact_ATP_Olambda__15) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 202 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dt,Uu)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ds,Uu))))) # label(fact_ATP_Olambda__16) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 203 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dq,Uu)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dp,Uu))))) # label(fact_ATP_Olambda__17) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 204 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dn,Uu)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dm,Uu))))) # label(fact_ATP_Olambda__18) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 205 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dk,Uu)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dj,Uu))))) # label(fact_ATP_Olambda__19) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 206 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_di,Uu)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dh,Uu))))) # label(fact_ATP_Olambda__20) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 207 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_df,Uu)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_de,Uu))))) # label(fact_ATP_Olambda__21) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 208 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dd,Uu)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dc,Uu))))) # label(fact_ATP_Olambda__22) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 209 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_db,Uu)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_da,Uu))))) # label(fact_ATP_Olambda__23) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 210 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cy,Uu)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cx,Uu))))) # label(fact_ATP_Olambda__24) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 211 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cv,Uu)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cu,Uu))))) # label(fact_ATP_Olambda__25) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 212 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ct,Uu)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cs,Uu))))) # label(fact_ATP_Olambda__26) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 213 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cp,Uu)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_co,Uu))))) # label(fact_ATP_Olambda__27) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 214 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cn,Uu)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cm,Uu))))) # label(fact_ATP_Olambda__28) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 215 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cl,Uu)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ck,Uu))))) # label(fact_ATP_Olambda__29) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 216 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cj,Uu)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ci,Uu))))) # label(fact_ATP_Olambda__30) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 217 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ch,Uu)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cg,Uu))))) # label(fact_ATP_Olambda__31) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 218 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cf,Uu)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ce,Uu))))) # label(fact_ATP_Olambda__32) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 219 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cd,Uu)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cc,Uu))))) # label(fact_ATP_Olambda__33) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 220 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cb,Uu)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ca,Uu))))) # label(fact_ATP_Olambda__34) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 221 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bz,Uu)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_by,Uu))))) # label(fact_ATP_Olambda__35) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 222 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bw,Uu))))) # label(fact_ATP_Olambda__36) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 223 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bv,Uu)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bu,Uu))))) # label(fact_ATP_Olambda__37) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 224 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bt,Uu)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bs,Uu))))) # label(fact_ATP_Olambda__38) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 225 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_br,Uu)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bq,Uu))))) # label(fact_ATP_Olambda__39) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 226 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ab,Uu)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,Uu))))) # label(fact_ATP_Olambda__40) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 227 (all Uu aa_TPT494704832TP_ind(aTP_Lamm_bk,Uu) = aa_TPT494704832TP_ind(scratc1885330153d_repl,aa_TPTP_ind_TPTP_ind(scratc1476611240tminus(Uu),aa_TPTP_ind_TPTP_ind(scratc406460153d_Sing,scratc201028047ptyset)))) # label(fact_ATP_Olambda__41) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 228 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_ah,Uu)) <-> Uu != scratc201028047ptyset))) # label(fact_ATP_Olambda__42) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 229 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_bi,Uu)) <-> (exists X2 (gg_TPTP_ind(X2) & aa_TPTP_ind_TPTP_ind(scratc1231567830d_Inj1,X2) = Uu))))) # label(fact_ATP_Olambda__43) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 230 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_bj,Uu)) <-> (exists X2 (gg_TPTP_ind(X2) & aa_TPTP_ind_TPTP_ind(scratc1231567829d_Inj0,X2) = Uu))))) # label(fact_ATP_Olambda__44) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 231 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ck,Uu),Uua)) <-> scratc236957560_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1168518063nd_iii,Uu),Uua)))) # label(fact_ATP_Olambda__45) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 232 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ci,Uu),Uua)) <-> pp(scratc1218677430nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1168518063nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__46) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 233 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cg,Uu),Uua)) <-> pp(scratc1135078395nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1168518063nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__47) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 234 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cs,Uu),Uua)) <-> scratc236957560_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1236589736n_some,aa_TPT43085870d_bool(aTP_Lamm_cq(Uu),Uua)),aa_fun171081125l_bool(scratc1236589736n_some,aa_TPT43085870d_bool(aTP_Lamm_cr(Uu),Uua))))) # label(fact_ATP_Olambda__48) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 235 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_co,Uu),Uua)) <-> pp(scratc1218677430nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1236589736n_some,aa_TPT43085870d_bool(scratc1482924994ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc1236589736n_some,aa_TPT43085870d_bool(scratc1482924994ffprop(Uua),Uu)))))) # label(fact_ATP_Olambda__49) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 236 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cm,Uu),Uua)) <-> pp(scratc1135078395nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1236589736n_some,aa_TPT43085870d_bool(scratc1482924994ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc1236589736n_some,aa_TPT43085870d_bool(scratc1482924994ffprop(Uua),Uu)))))) # label(fact_ATP_Olambda__50) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 237 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fi,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1878269941d_e_is(Uu),Uua),Uua)))) # label(fact_ATP_Olambda__51) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 238 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dv,Uu),Uua)) <-> pp(scratc317128493_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,Uua),scratc859780733nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,Uu)),aa_fun171081125l_bool(scratc1889585965_n_all,aa_TPT43085870d_bool(aTP_Lamm_ae,Uua)))))) # label(fact_ATP_Olambda__52) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.22 239 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ef,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__53) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 240 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dp,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__54) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 241 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ds,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__55) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 242 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ae,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,Uu),aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,Uu),Uua)))))) # label(fact_ATP_Olambda__56) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 243 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ea,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1209825598nd_nis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1209825598nd_nis,aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,Uua)))))) # label(fact_ATP_Olambda__57) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 244 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ag,Uu),Uua)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1168780466nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930297d_n_in,Uua),Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930297d_n_in,aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,Uua)),Uu))))) # label(fact_ATP_Olambda__58) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 245 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_de,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(Uua),Uu))))) # label(fact_ATP_Olambda__59) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 246 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ce,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1168518063nd_iii,Uua),Uu))))) # label(fact_ATP_Olambda__60) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 247 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ca,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc254875001moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc120891389lessis,Uua),Uu))))) # label(fact_ATP_Olambda__61) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 248 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_by,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc120891389lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc254875001moreis,Uua),Uu))))) # label(fact_ATP_Olambda__62) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 249 (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(scratc1168518063nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,Uua),Uu))))) # label(fact_ATP_Olambda__63) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 250 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,Uu),Uua)) -> pp(scratc424593673_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc120891389lessis,Uu),Uua)))))) # label(fact_ATP_Olambda__64) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 251 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bw,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc254875001moreis,Uu),Uua)) -> pp(scratc424593673_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1168518063nd_iii,Uu),Uua)))))) # label(fact_ATP_Olambda__65) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 252 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bu,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc120891389lessis,Uu),Uua)) -> pp(scratc424593673_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,Uu),Uua)))))) # label(fact_ATP_Olambda__66) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 253 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bh(Uu),Uua) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1885330153d_repl,aa_TPTP_ind_TPTP_ind(Uu,Uua)),aa_TPT1424761345TP_ind(scratc290650548d_pair,Uua))) # label(fact_ATP_Olambda__67) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 254 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_el,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aa_TPT43085870d_bool(aTP_Lamm_ej,Uu)),aa_TPT43085870d_bool(aTP_Lamm_ek(Uu),Uua))))) # label(fact_ATP_Olambda__68) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 255 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dj,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,Uu)),Uua))))) # label(fact_ATP_Olambda__69) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 256 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dm,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,Uua)))))) # label(fact_ATP_Olambda__70) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 257 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bs,Uu),Uua)) <-> (pp(scratc424593673_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc364131377_29_ii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc120891389lessis,Uu),Uua))))) # label(fact_ATP_Olambda__71) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 258 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bq,Uu),Uua)) <-> (pp(scratc424593673_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1168518063nd_iii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc254875001moreis,Uu),Uua))))) # label(fact_ATP_Olambda__72) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 259 (all Uu all Uua aa_fun277296641TP_ind(aa_TPT494704832TP_ind(aTP_Lamm_bl,Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1560325698nunion(aa_TPTP_ind_TPTP_ind(scratc406460153d_Sing,scratc201028047ptyset)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1885330153d_repl,Uu),Uua))) # label(fact_ATP_Olambda__73) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 260 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dc,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1209825598nd_nis,Uua),aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__74) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 261 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_af,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,Uua))))) # label(fact_ATP_Olambda__75) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 262 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ej,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,Uua),aa_TPTP_ind_TPTP_ind(scratc1331082251_power,Uu))))) # label(fact_ATP_Olambda__76) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 263 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ed,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930297d_n_in,Uua),Uu)))) # label(fact_ATP_Olambda__77) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 264 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bm,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1207726425nd_nIn,Uua),Uu)))) # label(fact_ATP_Olambda__78) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 265 (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(scratc213689151bnd_in,Uua),Uu)))) # label(fact_ATP_Olambda__79) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 266 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dh,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dg(Uu),Uua))))) # label(fact_ATP_Olambda__80) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 267 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_da,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cz(Uu),Uua))))) # label(fact_ATP_Olambda__81) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 268 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cx,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cw(Uu),Uua))))) # label(fact_ATP_Olambda__82) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 269 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cu,Uu),Uua)) <-> pp(scratc1938294688_amone(scratc1209300807nd_nat,aa_TPT43085870d_bool(aTP_Lamm_cq(Uu),Uua))))) # label(fact_ATP_Olambda__83) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 270 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_ad(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc464730217rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,Uu),Uua))) # label(fact_ATP_Olambda__84) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 271 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_be(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1838344117_union,aa_TPTP_ind_TPTP_ind(Uu,Uua))) # label(fact_ATP_Olambda__85) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 272 (all Uu all Uua (gg_TPTP_ind(Uua) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bg,Uu),Uua)) <-> (exists X3 (gg_TPTP_ind(X3) & Uua = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc290650548d_pair,Uu),X3)))))) # label(fact_ATP_Olambda__86) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 273 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_et(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1878269941d_e_is(aa_TPTP_ind_TPTP_ind(scratc98653311etprod(Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1502232420d_pair(Uu,Uua),aa_TPTP_ind_TPTP_ind(scratc243912566_first(Uu,Uua),Uub)),aa_TPTP_ind_TPTP_ind(scratc940247022second(Uu,Uua),Uub))),Uub)))) # label(fact_ATP_Olambda__87) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 274 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_bo(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc213689143bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,scratc201028047ptyset),Uub),Uu),Uua)) # label(fact_ATP_Olambda__88) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 275 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_fun1235454963TP_ind(aTP_Lamm_bn(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc213689143bnd_if(aa_TPTP_ind_bool(Uua,Uub),Uub),scratc1135931246nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bb(Uu),Uua)))) # label(fact_ATP_Olambda__89) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 276 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_au(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc443554621d_esti(Uu),Uub),Uua)))) # label(fact_ATP_Olambda__90) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 277 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_em(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc443554621d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc200877044_d_Sep(Uu),Uua))) -> pp(aa_TPTP_ind_bool(Uua,Uub))))) # label(fact_ATP_Olambda__91) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 278 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ek(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1375997064d_incl(Uu),Uua),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1375997064d_incl(Uu),Uub),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1878269941d_e_is(aa_TPTP_ind_TPTP_ind(scratc1331082251_power,Uu)),Uua),Uub)))))) # label(fact_ATP_Olambda__92) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 279 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eu(Uu),Uua),Uub)) <-> scratc1329672891_is_of(aa_TPTP_ind_TPTP_ind(scratc940247022second(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)))) # label(fact_ATP_Olambda__93) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 280 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ev(Uu),Uua),Uub)) <-> scratc1329672891_is_of(aa_TPTP_ind_TPTP_ind(scratc243912566_first(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)))) # label(fact_ATP_Olambda__94) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 281 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_fb(Uu),Uua),Uub)) <-> scratc1329672891_is_of(aa_TPTP_ind_TPTP_ind(scratc1878269936d_e_in(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)))) # label(fact_ATP_Olambda__95) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 282 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ff(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aa_TPT43085870d_bool(aTP_Lamm_fc(Uu),Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fe(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__96) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 283 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cw(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(Uu),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,Uua),Uub))))) # label(fact_ATP_Olambda__97) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 284 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dg(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__98) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 285 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cz(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1209825598nd_nis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1209825598nd_nis,aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(Uu),Uub)))))) # label(fact_ATP_Olambda__99) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 286 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bb(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,Uub),Uu)) & pp(aa_TPTP_ind_bool(Uua,Uub)))) # label(fact_ATP_Olambda__100) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 287 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ey(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc201270497_image(aa_fun1431113780TP_ind(scratc200877044_d_Sep(Uu),Uua),Uu),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc165166235_Sigma,aa_fun1431113780TP_ind(scratc200877044_d_Sep(Uu),Uua)),scratc1878269936d_e_in(Uu,Uua))),Uub))))) # label(fact_ATP_Olambda__101) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 288 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_en(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc443554621d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc200877044_d_Sep(Uu),Uua)))))) # label(fact_ATP_Olambda__102) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 289 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_fh(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_fg(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__103) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 290 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bd(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bc(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__104) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 291 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ex(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ew(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__105) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 292 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_er(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_eq(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__106) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 293 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ep(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_eo(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__107) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 294 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fc(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,Uub),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc737065667d_d_Pi,Uu),aTP_Lamm_ai(Uua)))))) # label(fact_ATP_Olambda__108) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 295 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cq(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(Uua),Uub))))) # label(fact_ATP_Olambda__109) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 296 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cr(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1396930302d_n_is,Uua),aa_TPTP_ind_TPTP_ind(scratc1397389488d_n_pl(Uu),Uub))))) # label(fact_ATP_Olambda__110) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 297 (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(scratc213689151bnd_in,Uub),aa_TPTP_ind_TPTP_ind(scratc98653311etprod(Uu),Uua))))) # label(fact_ATP_Olambda__111) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 298 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ez(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,Uub),aa_fun1431113780TP_ind(scratc200877044_d_Sep(Uu),Uua))))) # label(fact_ATP_Olambda__112) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 299 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_aw(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,Uu),Uub))) # label(fact_ATP_Olambda__113) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 300 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_fa(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(Uua,aa_TPTP_ind_TPTP_ind(scratc1878269936d_e_in(Uu,Uua),Uub))))) # label(fact_ATP_Olambda__114) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 301 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1913827119d_bool(aTP_Lamm_bf(Uu),Uua),Uub)) <-> (all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,X3),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc213689151bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,Uub),X3)),aa_TPTP_ind_TPTP_ind(Uua,X3)))))))) # label(fact_ATP_Olambda__115) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 302 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ax(Uu),Uua),Uub),Uuc) = aa_TPTP_ind_TPTP_ind(scratc213689143bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc201270497_image(Uu,Uua),Uub),Uuc),aa_TPTP_ind_TPTP_ind(scratc600392772d_soft(Uu,Uua,Uub),Uuc)),scratc201028047ptyset)) # label(fact_ATP_Olambda__116) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 303 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_eq(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1878269941d_e_is(Uu),aa_TPTP_ind_TPTP_ind(scratc243912566_first(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1502232420d_pair(Uu,Uua),Uub),Uuc))),Uub)))) # label(fact_ATP_Olambda__117) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 304 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_eo(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1878269941d_e_is(Uua),aa_TPTP_ind_TPTP_ind(scratc940247022second(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1502232420d_pair(Uu,Uua),Uub),Uuc))),Uuc)))) # label(fact_ATP_Olambda__118) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 305 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fd(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1878269941d_e_is(Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,Uua),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,Uub),Uuc))))) # label(fact_ATP_Olambda__119) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 306 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aq(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc443554621d_esti(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__120) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 307 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1878269941d_e_is(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__121) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 308 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ew(Uu),Uua),Uub),Uuc)) <-> scratc1329672891_is_of(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1502232420d_pair(Uu,Uua),Uub),Uuc),aa_TPT43085870d_bool(aTP_Lamm_es(Uu),Uua)))) # label(fact_ATP_Olambda__122) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 309 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_as(Uu),Uua),Uub),Uuc)) <-> pp(scratc1265022960d_l_ec(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc443554621d_esti(Uu),Uuc),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc443554621d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__123) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 310 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_at(Uu),Uua),Uub),Uuc)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1168780466nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc443554621d_esti(Uu),Uuc),Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc443554621d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__124) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 311 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fe(Uu),Uua),Uub),Uuc)) <-> (pp(aa_fun171081125l_bool(scratc1382104286all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fd(Uua),Uub),Uuc))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1878269941d_e_is(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc737065667d_d_Pi,Uu),aTP_Lamm_ai(Uua))),Uub),Uuc))))) # label(fact_ATP_Olambda__125) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 312 (all Uu all Uua all Uub all Uuc (gg_TPTP_ind(Uua) & gg_TPTP_ind(Uub) & gg_TPTP_ind(Uuc) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bp(Uu),Uua),Uub),Uuc)) <-> pp(Uu) & Uuc = Uua | -pp(Uu) & Uuc = Uub))) # label(fact_ATP_Olambda__126) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 313 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_fg(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1878269941d_e_is(Uu),Uub),Uuc)) -> pp(aa_TPTP_ind_bool(Uua,Uuc)))))) # label(fact_ATP_Olambda__127) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 314 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bc(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(Uua,Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1878269941d_e_is(Uu),Uub),Uuc)))))) # label(fact_ATP_Olambda__128) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 315 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ba(Uu),Uua),Uub),Uuc)) <-> pp(aa_fun171081125l_bool(scratc1102622823nd_all(Uu),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_az(Uu),Uua),Uub),Uuc))))) # label(fact_ATP_Olambda__129) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 316 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ar(Uu),Uua),Uub),Uuc)) <-> pp(aa_fun171081125l_bool(scratc492765094l_some(Uua),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aq(Uu),Uub),Uuc))))) # label(fact_ATP_Olambda__130) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 317 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_az(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1168780466nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1878269941d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,Uub),Uud))),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1878269941d_e_is(Uu),Uuc),Uud))))) # label(fact_ATP_Olambda__131) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 318 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_ao(Uu),Uua),Uub),Uuc),Uud)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1878269941d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,Uub),Uud)))))) # label(fact_ATP_Olambda__132) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 319 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_an(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_am(Uu),Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__133) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 320 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ap(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_ao(Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__134) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 321 (all Uu all Uua all Uub all Uuc all Uud aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_av(Uu),Uua),Uub),Uuc),Uud) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,aa_TPTP_ind_TPTP_ind(scratc181031091wissel(Uu,Uub),Uuc)),Uud))) # label(fact_ATP_Olambda__135) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 322 (all Uu all Uua all Uub all Uuc all Uud all Uue (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_am(Uu),Uua),Uub),Uuc),Uud),Uue)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_al(Uu),Uua),Uub),Uuc),Uud),Uue))))) # label(fact_ATP_Olambda__136) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 323 (all Uu all Uua all Uub all Uuc all Uud all Uue all Uuf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_ak(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uue),Uuf)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1878269941d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,Uub),Uuc)),Uue)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc213164361bnd_ap,Uub),Uud)),Uuf))))))) # label(fact_ATP_Olambda__137) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 324 (all Uu all Uua all Uub all Uuc all Uud all Uue all Uuf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_al(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)) <-> pp(aa_fun171081125l_bool(scratc1382104286all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_ak(Uua),Uub),Uuc),Uud),Uue),Uuf))))) # label(fact_ATP_Olambda__138) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 325 (all Uu all Uua (gg_TPTP_ind(Uu) -> aa_TPTP_ind_TPTP_ind(aTP_Lamm_ai(Uu),Uua) = Uu)) # label(fact_ATP_Olambda__139) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 326 (all Uu aa_TPTP_ind_TPTP_ind(aTP_Lamm_ac,Uu) = scratc1209300807nd_nat) # label(fact_ATP_Olambda__140) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 327 (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].
% 0.89/1.23 328 (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].
% 0.89/1.23 329 (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].
% 0.89/1.23 330 (all P (gg_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.23 331 (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].
% 0.89/1.25 332 (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].
% 0.89/1.25 333 (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].
% 0.89/1.25 334 (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].
% 0.89/1.25 335 (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].
% 0.89/1.25 336 (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].
% 0.89/1.25 337 (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].
% 0.89/1.25 338 (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].
% 0.89/1.25 339 (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].
% 0.89/1.25
% 0.89/1.25 ============================== end of process non-clausal formulas ===
% 0.89/1.25
% 0.89/1.25 ============================== PROCESS INITIAL CLAUSES ===============
% 0.89/1.25
% 0.89/1.25 ============================== PREDICATE ELIMINATION =================
% 0.89/1.25 340 -gg_bool(A) | A = fTrue | A = fFalse # label(help_fFalse_1_1_T) # label(axiom). [clausify(330)].
% 0.89/1.25 341 gg_bool(undefined_bool(bool)) # label(gsy_c_HOL_Oundefined_001t__HOL__Obool) # label(axiom). [assumption].
% 0.89/1.25 342 gg_bool(scratc1938294688_amone(A,B)) # label(gsy_c_Scratch__tptp__translate__43415__7632_ONUM656__thf__4__p_Obnd__amone) # label(axiom). [clausify(1)].
% 0.89/1.25 343 gg_bool(scratc317128493_d_and(A,B)) # label(gsy_c_Scratch__tptp__translate__43415__7632_ONUM656__thf__4__p_Obnd__d__and) # label(axiom). [clausify(2)].
% 0.89/1.25 344 gg_bool(scratc424593673_d_not(A)) # label(gsy_c_Scratch__tptp__translate__43415__7632_ONUM656__thf__4__p_Obnd__d__not) # label(axiom). [clausify(3)].
% 0.89/1.25 345 gg_bool(scratc1135078395nd_ec3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__43415__7632_ONUM656__thf__4__p_Obnd__ec3) # label(axiom). [clausify(4)].
% 0.89/1.25 346 gg_bool(scratc1265022960d_l_ec(A,B)) # label(gsy_c_Scratch__tptp__translate__43415__7632_ONUM656__thf__4__p_Obnd__l__ec) # label(axiom). [clausify(8)].
% 0.89/1.25 347 gg_bool(scratc1218677430nd_or3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__43415__7632_ONUM656__thf__4__p_Obnd__or3) # label(axiom). [clausify(9)].
% 0.89/1.25 348 gg_bool(aa_bool_bool(A,B)) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom). [clausify(10)].
% 0.89/1.25 349 gg_bool(aa_TPTP_ind_bool(A,B)) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom). [clausify(11)].
% 0.89/1.25 350 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)].
% 0.89/1.25 351 gg_bool(fEx_TPTP_ind(A)) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom). [clausify(16)].
% 0.89/1.25 352 gg_bool(fFalse) # label(gsy_c_fFalse) # label(axiom). [assumption].
% 0.89/1.25 353 gg_bool(fTrue) # label(gsy_c_fTrue) # label(axiom). [assumption].
% 0.89/1.25 Derived: undefined_bool(bool) = fTrue | undefined_bool(bool) = fFalse. [resolve(340,a,341,a)].
% 0.89/1.25 Derived: scratc1938294688_amone(A,B) = fTrue | scratc1938294688_amone(A,B) = fFalse. [resolve(340,a,342,a)].
% 0.89/1.58 Derived: scratc317128493_d_and(A,B) = fTrue | scratc317128493_d_and(A,B) = fFalse. [resolve(340,a,343,a)].
% 0.89/1.58 Derived: scratc424593673_d_not(A) = fTrue | scratc424593673_d_not(A) = fFalse. [resolve(340,a,344,a)].
% 0.89/1.58 Derived: scratc1135078395nd_ec3(A,B,C) = fTrue | scratc1135078395nd_ec3(A,B,C) = fFalse. [resolve(340,a,345,a)].
% 0.89/1.58 Derived: scratc1265022960d_l_ec(A,B) = fTrue | scratc1265022960d_l_ec(A,B) = fFalse. [resolve(340,a,346,a)].
% 0.89/1.58 Derived: scratc1218677430nd_or3(A,B,C) = fTrue | scratc1218677430nd_or3(A,B,C) = fFalse. [resolve(340,a,347,a)].
% 0.89/1.58 Derived: aa_bool_bool(A,B) = fTrue | aa_bool_bool(A,B) = fFalse. [resolve(340,a,348,a)].
% 0.89/1.58 Derived: aa_TPTP_ind_bool(A,B) = fTrue | aa_TPTP_ind_bool(A,B) = fFalse. [resolve(340,a,349,a)].
% 0.89/1.58 Derived: aa_fun171081125l_bool(A,B) = fTrue | aa_fun171081125l_bool(A,B) = fFalse. [resolve(340,a,350,a)].
% 0.89/1.58 Derived: fEx_TPTP_ind(A) = fTrue | fEx_TPTP_ind(A) = fFalse. [resolve(340,a,351,a)].
% 0.89/1.58 Derived: fFalse = fTrue | fFalse = fFalse. [resolve(340,a,352,a)].
% 0.89/1.58 Derived: fTrue = fTrue | fTrue = fFalse. [resolve(340,a,353,a)].
% 0.89/1.58 354 scratc1659957750d_r_ec(A,B) | pp(A) # label(fact_def__r__ec) # label(axiom). [clausify(59)].
% 0.89/1.58 355 -scratc1659957750d_r_ec(A,B) | -pp(A) | pp(scratc424593673_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(59)].
% 0.89/1.58 356 scratc1659957750d_r_ec(A,B) | -pp(scratc424593673_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(59)].
% 0.89/1.58 357 scratc1211269943_l_iff(A,B) | -pp(scratc317128493_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1168780466nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc1168780466nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(91)].
% 0.89/1.58 358 -scratc1211269943_l_iff(A,B) | pp(scratc317128493_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1168780466nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc1168780466nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(91)].
% 0.89/1.58 359 scratc1797730171d_orec(A,B) | -pp(scratc317128493_d_and(aa_bool_bool(scratc1265678965d_l_or(A),B),scratc1265022960d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(92)].
% 0.89/1.58 360 -scratc1797730171d_orec(A,B) | pp(scratc317128493_d_and(aa_bool_bool(scratc1265678965d_l_or(A),B),scratc1265022960d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(92)].
% 0.89/1.58 361 scratc1283916740nd_wel(A) | -pp(scratc424593673_d_not(scratc424593673_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(97)].
% 0.89/1.58 362 -scratc1283916740nd_wel(A) | pp(scratc424593673_d_not(scratc424593673_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(97)].
% 0.89/1.58 363 -scratc1283916740nd_wel(A) | pp(A) # label(fact_l__et) # label(axiom). [clausify(147)].
% 0.89/1.58 Derived: pp(A) | -pp(scratc424593673_d_not(scratc424593673_d_not(A))). [resolve(363,a,361,a)].
% 0.89/1.58
% 0.89/1.58 ============================== end predicate elimination =============
% 0.89/1.58
% 0.89/1.58 Auto_denials: (non-Horn, no changes).
% 0.89/1.58
% 0.89/1.58 Term ordering decisions:
% 0.89/1.58 Function symbol KB weights: scratc213689151bnd_in=1. aTP_Lamm_a=1. scratc1396930302d_n_is=1. scratc464730217rdsucc=1. scratc213164361bnd_ap=1. aTP_Lamm_aj=1. scratc201028047ptyset=1. scratc165166235_Sigma=1. scratc1209825598nd_nis=1. scratc859780733nd_n_1=1. scratc364131377_29_ii=1. fFalse=1. scratc1209300807nd_nat=1. scratc1216317097_nat_p=1. scratc1236589736n_some=1. scratc1331082251_power=1. scratc737065667d_d_Pi=1. scratc1168518063nd_iii=1. scratc1168780466nd_imp=1. scratc1885330153d_repl=1. fTrue=1. scratc120891389lessis=1. scratc290650548d_pair=1. scratc254875001moreis=1. scratc504811035d_Subq=1. scratc1459596089_proj0=1. scratc1838344117_union=1. scratc656609605closed=1. aTP_Lamm_af=1. scratc1396930297d_n_in=1. scratc1459596090_proj1=1. scratc1889585965_n_all=1. aTP_Lamm_ac=1. aTP_Lamm_ae=1. aTP_Lamm_ej=1. scratc328851057closed=1. scratc493584071closed=1. aTP_Lamm_aa=1. aTP_Lamm_bq=1. aTP_Lamm_bs=1. aTP_Lamm_bu=1. aTP_Lamm_bw=1. aTP_Lamm_by=1. aTP_Lamm_ca=1. aTP_Lamm_cc=1. aTP_Lamm_ce=1. aTP_Lamm_ea=1. aTP_Lamm_ee=1. aTP_Lamm_ef=1. scratc1098189891_prop2=1. scratc1231567830d_Inj1=1. scratc2136001442closed=1. scratc629251303_omega=1. aTP_Lamm_ag=1. aTP_Lamm_bg=1. aTP_Lamm_bi=1. aTP_Lamm_bj=1. aTP_Lamm_cg=1. aTP_Lamm_ci=1. aTP_Lamm_ck=1. aTP_Lamm_cm=1. aTP_Lamm_co=1. aTP_Lamm_cs=1. aTP_Lamm_cu=1. aTP_Lamm_cx=1. aTP_Lamm_da=1. aTP_Lamm_dc=1. aTP_Lamm_de=1. aTP_Lamm_dh=1. aTP_Lamm_dj=1. aTP_Lamm_dm=1. aTP_Lamm_dp=1. aTP_Lamm_ds=1. aTP_Lamm_dv=1. aTP_Lamm_dx=1. aTP_Lamm_dy=1. aTP_Lamm_ed=1. fconj=1. fimplies=1. scratc1098189890_prop1=1. scratc1231567829d_Inj0=1. scratc1474712822_cond2=1. scratc406460153d_Sing=1. aTP_Lamm_bm=1. aTP_Lamm_br=1. aTP_Lamm_bt=1. aTP_Lamm_bv=1. aTP_Lamm_bx=1. aTP_Lamm_bz=1. aTP_Lamm_cb=1. aTP_Lamm_cd=1. aTP_Lamm_cf=1. aTP_Lamm_ch=1. aTP_Lamm_cj=1. aTP_Lamm_cl=1. aTP_Lamm_cn=1. aTP_Lamm_cp=1. aTP_Lamm_ct=1. aTP_Lamm_cv=1. aTP_Lamm_cy=1. aTP_Lamm_db=1. aTP_Lamm_dd=1. aTP_Lamm_df=1. aTP_Lamm_di=1. aTP_Lamm_dk=1. aTP_Lamm_dl=1. aTP_Lamm_dn=1. aTP_Lamm_do=1. aTP_Lamm_dq=1. aTP_Lamm_dr=1. aTP_Lamm_dt=1. aTP_Lamm_du=1. aTP_Lamm_dw=1. aTP_Lamm_dz=1. aTP_Lamm_eb=1. aTP_Lamm_ec=1. aTP_Lamm_eg=1. aTP_Lamm_eh=1. aTP_Lamm_ei=1. aTP_Lamm_el=1. aTP_Lamm_fi=1. fequal_TPTP_ind=1. scratc1207726425nd_nIn=1. scratc1474712821_cond1=1. scratc1649373879univof=1. scratc2005378226_n_one=1. scratc217990439_d_Unj=1. aTP_Lamm_ab=1. aTP_Lamm_ah=1. aTP_Lamm_bk=1. aTP_Lamm_bl=1. bool=1. scratc127430592_prop1=1. scratc1459989687_prop4=1. scratc1892517117_prop1=1. scratc2068949188_prop1=1. scratc321480188pair_p=1. scratc382314292d_plus=1. scratc486623034nempty=1. scratc509827715_prop1=1. scratc566468599munion=1. scratc62756019_empty=1. scratc715792767_prop1=1. scratc578307707d_24_g=1. scratc593631025d_i1_s=1. tPTP_ind=1. aa_TPTP_ind_bool=1. aa_TPT43085870d_bool=1. aa_TPTP_ind_TPTP_ind=1. aa_fun171081125l_bool=1. aa_TPT1424761345TP_ind=1. aa_TPT60673477d_bool=1. aa_fun277296641TP_ind=1. aa_TPT494704832TP_ind=1. aa_bool_bool=1. aa_fun1584354236d_bool=1. aa_fun1431113780TP_ind=1. aa_boo1142376798l_bool=1. scratc317128493_d_and=1. aa_TPT1123896796d_bool=1. scratc213689143bnd_if=1. scratc1265022960d_l_ec=1. aa_fun1212484691d_bool=1. aa_TPT985247859d_bool=1. scratc1878269936d_e_in=1. scratc1502232420d_pair=1. aa_fun987228051d_bool=1. scratc1168846053nd_ind=1. scratc1938294688_amone=1. scratc201270497_image=1. scratc243912566_first=1. scratc940247022second=1. aa_TPT125613450d_bool=1. scratc1210219187nd_non=1. aa_fun1913827119d_bool=1. scratc1573881605d_anec=1. aa_TPT1791839040TP_ind=1. aa_fun1107270209d_bool=1. aa_fun845057962d_bool=1. scratc1135078456nd_ecp=1. scratc1966731813eplSep=1. scratc755417269_ecelt=1. scratc754826878_ecect=1. aa_TPT1781712639TP_ind=1. aa_TPT2142672771l_bool=1. aa_fun1235454963TP_ind=1. cOMBB_658106424TP_ind=1. cOMBS_2003118649l_bool=1. scratc1135078460nd_ect=1. scratc1218874292nd_out=1. scratc1403271239etprop=1. scratc181031091wissel=1. scratc1948461416fixfu2=1. scratc292628810_fixfu=1. scratc313004294ectset=1. scratc1377243439d_invf=1. scratc1380979970d_tofs=1. scratc197802417ectelt=1. scratc2010461558nverse=1. scratc419121640unmore=1. f1=1. f12=1. f13=1. f20=1. f24=1. scratc1382104286all_of=1. scratc1397389488d_n_pl=1. scratc1878269941d_e_is=1. scratc424593673_d_not=1. scratc200877044_d_Sep=1. scratc443554621d_esti=1. scratc492765094l_some=1. scratc1482924994ffprop=1. scratc1102622823nd_all=1. scratc1265678965d_l_or=1. scratc1837477542_rec_G=1. aTP_Lamm_ai=1. aTP_Lamm_es=1. scratc1218415084nd_one=1. aTP_Lamm_ak=1. aTP_Lamm_au=1. aTP_Lamm_bc=1. aTP_Lamm_bp=1. aTP_Lamm_cq=1. aTP_Lamm_ek=1. aTP_Lamm_fg=1. scratc1375997064d_incl=1. aTP_Lamm_ao=1. aTP_Lamm_ay=1. aTP_Lamm_bb=1. aTP_Lamm_bf=1. aTP_Lamm_cw=1. aTP_Lamm_cz=1. aTP_Lamm_fc=1. aTP_Lamm_fe=1. scratc1135931246nd_eps=1. scratc1555974029ective=1. scratc98653311etprod=1. aTP_Lamm_al=1. aTP_Lamm_am=1. aTP_Lamm_an=1. aTP_Lamm_ap=1. aTP_Lamm_aq=1. aTP_Lamm_as=1. aTP_Lamm_at=1. aTP_Lamm_az=1. aTP_Lamm_ba=1. aTP_Lamm_bd=1. aTP_Lamm_cr=1. aTP_Lamm_dg=1. aTP_Lamm_em=1. aTP_Lamm_en=1. aTP_Lamm_eo=1. aTP_Lamm_eq=1. aTP_Lamm_ew=1. aTP_Lamm_ey=1. aTP_Lamm_ez=1. aTP_Lamm_fd=1. fEx_TPTP_ind=1. scratc1560325698nunion=1. scratc939016534ective=1. aTP_Lamm_ar=1. aTP_Lamm_ep=1. aTP_LCputime limit exceeded (core dumped)
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