TSTP Solution File: NUM650+4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM650+4 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n008.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 13:30:01 EDT 2022
% Result : Timeout 300.05s 300.32s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM650+4 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jul 7 10:52:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.90/1.22 ============================== Prover9 ===============================
% 0.90/1.22 Prover9 (32) version 2009-11A, November 2009.
% 0.90/1.22 Process 9583 was started by sandbox2 on n008.cluster.edu,
% 0.90/1.22 Thu Jul 7 10:52:24 2022
% 0.90/1.22 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_9429_n008.cluster.edu".
% 0.90/1.22 ============================== end of head ===========================
% 0.90/1.22
% 0.90/1.22 ============================== INPUT =================================
% 0.90/1.22
% 0.90/1.22 % Reading from file /tmp/Prover9_9429_n008.cluster.edu
% 0.90/1.22
% 0.90/1.22 set(prolog_style_variables).
% 0.90/1.22 set(auto2).
% 0.90/1.22 % set(auto2) -> set(auto).
% 0.90/1.22 % set(auto) -> set(auto_inference).
% 0.90/1.22 % set(auto) -> set(auto_setup).
% 0.90/1.22 % set(auto_setup) -> set(predicate_elim).
% 0.90/1.22 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.90/1.22 % set(auto) -> set(auto_limits).
% 0.90/1.22 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.90/1.22 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.90/1.22 % set(auto) -> set(auto_denials).
% 0.90/1.22 % set(auto) -> set(auto_process).
% 0.90/1.22 % set(auto2) -> assign(new_constants, 1).
% 0.90/1.22 % set(auto2) -> assign(fold_denial_max, 3).
% 0.90/1.22 % set(auto2) -> assign(max_weight, "200.000").
% 0.90/1.22 % set(auto2) -> assign(max_hours, 1).
% 0.90/1.22 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.90/1.22 % set(auto2) -> assign(max_seconds, 0).
% 0.90/1.22 % set(auto2) -> assign(max_minutes, 5).
% 0.90/1.22 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.90/1.22 % set(auto2) -> set(sort_initial_sos).
% 0.90/1.22 % set(auto2) -> assign(sos_limit, -1).
% 0.90/1.22 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.90/1.22 % set(auto2) -> assign(max_megs, 400).
% 0.90/1.22 % set(auto2) -> assign(stats, some).
% 0.90/1.22 % set(auto2) -> clear(echo_input).
% 0.90/1.22 % set(auto2) -> set(quiet).
% 0.90/1.22 % set(auto2) -> clear(print_initial_clauses).
% 0.90/1.22 % set(auto2) -> clear(print_given).
% 0.90/1.22 assign(lrs_ticks,-1).
% 0.90/1.22 assign(sos_limit,10000).
% 0.90/1.22 assign(order,kbo).
% 0.90/1.22 set(lex_order_vars).
% 0.90/1.22 clear(print_given).
% 0.90/1.22
% 0.90/1.22 % formulas(sos). % not echoed (362 formulas)
% 0.90/1.22
% 0.90/1.22 ============================== end of input ==========================
% 0.90/1.22
% 0.90/1.22 % From the command line: assign(max_seconds, 300).
% 0.90/1.22
% 0.90/1.22 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.90/1.22
% 0.90/1.22 % Formulas that are not ordinary clauses:
% 0.90/1.22 1 (all B_1 all B_2 gg_bool(scratc968938915_amone(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__42180__13359_ONUM650__thf__4__p_Obnd__amone) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 2 (all B_1 all B_2 gg_bool(scratc686076394_d_and(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__42180__13359_ONUM650__thf__4__p_Obnd__d__and) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 3 (all B_1 gg_bool(scratc793541574_d_not(B_1))) # label(gsy_c_Scratch__tptp__translate__42180__13359_ONUM650__thf__4__p_Obnd__d__not) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 4 (all B_1 all B_2 all B_3 gg_bool(scratc480136062nd_ec3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__42180__13359_ONUM650__thf__4__p_Obnd__ec3) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 5 (all B_1 all B_2 gg_TPTP_ind(scratc480136127nd_ect(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__42180__13359_ONUM650__thf__4__p_Obnd__ect) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 6 (all B_1 gg_TPTP_ind(scratc480988913nd_eps(B_1))) # label(gsy_c_Scratch__tptp__translate__42180__13359_ONUM650__thf__4__p_Obnd__eps) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 7 (all B_1 all B_2 gg_TPTP_ind(scratc513903720nd_ind(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__42180__13359_ONUM650__thf__4__p_Obnd__ind) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 8 (all B_1 all B_2 gg_bool(scratc295667187d_l_ec(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__42180__13359_ONUM650__thf__4__p_Obnd__l__ec) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 9 (all B_1 all B_2 all B_3 gg_bool(scratc563735097nd_or3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__42180__13359_ONUM650__thf__4__p_Obnd__or3) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 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].
% 0.90/1.22 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].
% 0.90/1.22 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].
% 0.90/1.22 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].
% 0.90/1.22 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].
% 0.90/1.22 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].
% 0.90/1.22 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].
% 0.90/1.22 17 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc852642874_prop1,X),Xa)) <-> pp(scratc563735097nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc427574529d_n_is,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc606347060_29_ii,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513575730nd_iii,X),Xa))))) # label(fact_def__d__29__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 18 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc513575730nd_iii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1709234475n_some,aa_TPT43085870d_bool(scratc1136248831ffprop(Xa),X))))) # label(fact_def__iii) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 19 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc606347060_29_ii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1709234475n_some,aa_TPT43085870d_bool(scratc1136248831ffprop(X),Xa))))) # label(fact_def__d__29__ii) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 20 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1136248831ffprop(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc427574529d_n_is,X),aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(Xa),Xb))))) # label(fact_def__diffprop) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 21 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc264280699_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc554883265nd_nis,aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(X),Xb))))) # label(fact_def__d__28__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 22 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1823402172_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc554883265nd_nis,Xa),aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(X),Xa))))) # label(fact_def__d__27__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 23 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1235039997_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc427574529d_n_is,aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(Xa),X))))) # label(fact_def__d__26__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 24 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc646677822_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc427574529d_n_is,aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(X),Xa)),Xb)),aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(X),aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(Xa),Xb)))))) # label(fact_def__d__25__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 25 (all X scratc428033715d_n_pl(X) = aa_TPT1424761345TP_ind(scratc505360646bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1525557361d_plus,X))) # label(fact_def__n__pl) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 26 (all X aa_TPTP_ind_TPTP_ind(scratc1525557361d_plus,X) = scratc513903720nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1915193542d_d_Pi,scratc554358474nd_nat),aTP_Lamm_ac),aa_TPT43085870d_bool(scratc58315648_prop2,X))) # label(fact_def__plus) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 27 (all X aa_TPTP_ind_TPTP_ind(scratc231631544d_24_g,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1965973720_Sigma,scratc554358474nd_nat),aTP_Lamm_ad(X))) # label(fact_def__d__24__g) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 28 (all X (pp(aa_TPTP_ind_bool(scratc490633914_prop4,X)) <-> pp(aa_fun171081125l_bool(scratc965409833l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1915193542d_d_Pi,scratc554358474nd_nat),aTP_Lamm_ac)),aa_TPT43085870d_bool(scratc58315648_prop2,X))))) # label(fact_def__prop4) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 29 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc490633913_prop3(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc427574529d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc505360646bnd_ap,X),Xb)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc505360646bnd_ap,Xa),Xb))))) # label(fact_def__prop3) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 30 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc58315648_prop2,X),Xa)) <-> pp(scratc686076394_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc427574529d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc505360646bnd_ap,Xa),scratc2003023802nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,X)),aa_TPTP_ind_bool(scratc58315647_prop1,Xa))))) # label(fact_def__d__24__prop2) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 31 (all X (pp(aa_TPTP_ind_bool(scratc58315647_prop1,X)) <-> pp(aa_fun171081125l_bool(scratc111050218_n_all,aa_TPT43085870d_bool(aTP_Lamm_ae,X))))) # label(fact_def__d__24__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 32 (all X (pp(aa_TPTP_ind_bool(scratc1617437120_prop1,X)) <-> pp(aa_bool_bool(scratc296323192d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc427574529d_n_is,X),scratc2003023802nd_n_1)),aa_fun171081125l_bool(scratc1709234475n_some,aa_TPT43085870d_bool(aTP_Lamm_af,X)))))) # label(fact_def__d__23__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 33 (all X (pp(aa_TPTP_ind_bool(scratc1029074945_prop1,X)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc554883265nd_nis,aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,X)),X)))) # label(fact_def__d__22__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 34 (all X (pp(aa_TPTP_ind_bool(scratc505357049_cond2,X)) <-> pp(aa_fun171081125l_bool(scratc111050218_n_all,aa_TPT43085870d_bool(aTP_Lamm_ag,X))))) # label(fact_def__cond2) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 35 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc554883265nd_nis,X),Xa)) <-> pp(scratc793541574_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc427574529d_n_is,X),Xa))))) # label(fact_def__nis) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 36 (all X all Xa all Xb all Xc all Xd scratc2100919166indeq2(X,Xa,Xb,Xc,Xd) = aa_TPT1424761345TP_ind(scratc37155252_indeq(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1045272956d_11_i(X,Xa,Xb),Xc),Xd))) # label(fact_def__indeq2) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 37 (all X all Xa all Xb scratc1045272956d_11_i(X,Xa,Xb) = scratc37155252_indeq(X,Xa,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1915193542d_d_Pi,X),aTP_Lamm_ai(Xb)))) # label(fact_def__d__11__i) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 38 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc169925669fixfu2(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1854749025all_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].
% 0.90/1.22 39 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc37155252_indeq(X,Xa,Xb),Xc),Xd) = scratc513903720nd_ind(Xb,aa_TPT43085870d_bool(scratc490633912_prop2(X,Xa,Xb,Xc),Xd))) # label(fact_def__indeq) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 40 (all X all Xa all Xb all Xc all Xd all Xe (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc490633912_prop2(X,Xa,Xb,Xc),Xd),Xe)) <-> pp(aa_fun171081125l_bool(scratc965409833l_some(X),aa_TPT43085870d_bool(scratc605638274_prop1(X,Xa,Xb,Xc,Xd),Xe))))) # label(fact_def__prop2) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 41 (all X all Xa all Xb all Xc all Xd all Xe all Xf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc605638274_prop1(X,Xa,Xb,Xc,Xd),Xe),Xf)) <-> pp(scratc686076394_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1586797690d_esti(X),Xf),aa_TPTP_ind_TPTP_ind(scratc1932954753_ecect(X,Xa),Xd)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908914168d_e_is(Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc505360646bnd_ap,Xc),Xf)),Xe))))) # label(fact_def__d__10__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 42 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1470756685_fixfu(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1854749025all_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].
% 0.90/1.22 43 (all X all Xa scratc1932954753_ecect(X,Xa) = scratc908914163d_e_in(aa_TPTP_ind_TPTP_ind(scratc361726478_power,X),scratc569641026d_anec(X,Xa))) # label(fact_def__ecect) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 44 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc566750318ectelt(X,Xa),Xb) = aa_TPTP_ind_TPTP_ind(scratc681952195ectset(X,Xa),aa_TPTP_ind_TPTP_ind(scratc1933545144_ecelt(X,Xa),Xb))) # label(fact_def__ectelt) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 45 (all X all Xa scratc681952195ectset(X,Xa) = scratc563931959nd_out(aa_TPTP_ind_TPTP_ind(scratc361726478_power,X),scratc569641026d_anec(X,Xa))) # label(fact_def__ectset) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 46 (all X all Xa scratc480136127nd_ect(X,Xa) = aa_fun1431113780TP_ind(scratc569824945_d_Sep(aa_TPTP_ind_TPTP_ind(scratc361726478_power,X)),scratc569641026d_anec(X,Xa))) # label(fact_def__ect) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 47 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc569641026d_anec(X,Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc965409833l_some(X),aa_TPT43085870d_bool(scratc480136123nd_ecp(X,Xa),Xb))))) # label(fact_def__anec) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 48 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc480136123nd_ecp(X,Xa),Xb),Xc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908914168d_e_is(aa_TPTP_ind_TPTP_ind(scratc361726478_power,X)),Xb),aa_TPTP_ind_TPTP_ind(scratc1933545144_ecelt(X,Xa),Xc))))) # label(fact_def__ecp) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 49 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1933545144_ecelt(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc569824945_d_Sep(X),aa_TPT43085870d_bool(Xa,Xb))) # label(fact_def__ecelt) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 50 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc788069541unmore(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc569824945_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].
% 0.90/1.22 51 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1278348804etprop(X,Xa),Xb),Xc)) <-> pp(scratc686076394_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1586797690d_esti(X),Xc),Xa),scratc793541574_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1586797690d_esti(X),Xc),Xb)))))) # label(fact_def__nissetprop) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 52 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1546771572t_disj(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc447680490nd_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].
% 0.90/1.22 53 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc371756485d_incl(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc447680490nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_at(X),Xa),Xb))))) # label(fact_def__incl) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 54 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc139946871nempty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc965409833l_some(X),aa_TPT43085870d_bool(aTP_Lamm_au(X),Xa))))) # label(fact_def__nonempty) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 55 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1240883894_empty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1854749025all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),scratc555276854nd_non(X,aa_TPT43085870d_bool(aTP_Lamm_au(X),Xa)))))) # label(fact_def__empty) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 56 (all X scratc1586797690d_esti(X) = scratc505885436bnd_in) # label(fact_def__esti) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 57 (all X all Xa (scratc690601977d_r_ec(X,Xa) <-> (pp(X) -> pp(scratc793541574_d_not(Xa))))) # label(fact_def__r__ec) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 58 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc349581599hangef(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1965973720_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].
% 0.90/1.22 59 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc549978992wissel(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1965973720_Sigma,X),scratc1217718491sel_wb(X,Xa,Xb))) # label(fact_def__wissel) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 60 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1217718491sel_wb(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc514297315nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908914168d_e_is(X),Xc),Xb),X,Xa),aa_TPTP_ind_TPTP_ind(scratc1217718490sel_wa(X,Xa,Xb),Xc))) # label(fact_def__wissel__wb) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 61 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1217718490sel_wa(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc514297315nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908914168d_e_is(X),Xc),Xa),X,Xb),Xc)) # label(fact_def__wissel__wa) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 62 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc514297315nd_ite(X,Xa,Xb),Xc) = scratc513903720nd_ind(Xa,aa_TPT43085870d_bool(scratc490633911_prop1(X,Xa,Xb),Xc))) # label(fact_def__ite) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 63 (all X all Xa all Xb all Xc all Xd (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc490633911_prop1(X,Xa,Xb),Xc),Xd)) <-> pp(scratc686076394_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc513838133nd_imp,X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908914168d_e_is(Xa),Xd),Xb)),aa_bool_bool(aa_boo1142376798l_bool(scratc513838133nd_imp,scratc793541574_d_not(X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908914168d_e_is(Xa),Xd),Xc)))))) # label(fact_def__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 64 (all X all Xa scratc1309194923second(X,Xa) = scratc490240317_proj1) # label(fact_def__second) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 65 (all X all Xa scratc1422040441_first(X,Xa) = scratc490240316_proj0) # label(fact_def__first) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 66 (all X all Xa scratc1974877159d_pair(X,Xa) = scratc1433893617d_pair) # label(fact_def__d__pair) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 67 (all X all Xa scratc563931959nd_out(X,Xa) = scratc1743635841d_soft(aa_fun1431113780TP_ind(scratc569824945_d_Sep(X),Xa),X,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1965973720_Sigma,aa_fun1431113780TP_ind(scratc569824945_d_Sep(X),Xa)),scratc908914163d_e_in(X,Xa)))) # label(fact_def__out) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 68 (all X all Xa all Xb (gg_TPTP_ind(Xb) -> aa_TPTP_ind_TPTP_ind(scratc908914163d_e_in(X,Xa),Xb) = Xb)) # label(fact_def__e__in) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 69 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc291241658_inj_h(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1965973720_Sigma,X),aa_TPT1424761345TP_ind(aTP_Lamm_aw(Xc),Xd))) # label(fact_def__inj__h) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 70 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc373002860d_invf(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1965973720_Sigma,Xa),scratc1743635841d_soft(X,Xa,Xb))) # label(fact_def__invf) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 71 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1981908942ective(X),Xa),Xb)) <-> pp(scratc686076394_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1798189712ective(X),Xa),Xb),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc814094099ective(X),Xa),Xb))))) # label(fact_def__bijective) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 72 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc814094099ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc447680490nd_all(Xa),aa_TPT43085870d_bool(scratc1379398372_image(X,Xa),Xb))))) # label(fact_def__surjective) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 73 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc335622649nverse(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1965973720_Sigma,Xa),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ax(X),Xa),Xb))) # label(fact_def__inverse) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 74 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1743635841d_soft(X,Xa,Xb),Xc) = scratc513903720nd_ind(X,aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(Xa),Xb),Xc))) # label(fact_def__soft) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 75 (all X all Xa scratc376739391d_tofs(X,Xa) = scratc505360646bnd_ap) # label(fact_def__tofs) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 76 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1379398372_image(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc965409833l_some(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(Xa),Xb),Xc))))) # label(fact_def__image) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 77 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1798189712ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc447680490nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ba(X),Xa),Xb))))) # label(fact_def__injective) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 78 (all X all Xa scratc513903720nd_ind(X,Xa) = scratc480988913nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bb(X),Xa))) # label(fact_def__ind) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 79 (all X all Xa (pp(aa_fun171081125l_bool(scratc563472751nd_one(X),Xa)) <-> pp(scratc686076394_d_and(scratc968938915_amone(X,Xa),aa_fun171081125l_bool(scratc965409833l_some(X),Xa))))) # label(fact_def__one) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 80 (all X all Xa (pp(scratc968938915_amone(X,Xa)) <-> pp(aa_fun171081125l_bool(scratc1854749025all_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].
% 0.90/1.22 81 (all X scratc908914168d_e_is(X) = fequal_TPTP_ind) # label(fact_def__e__is) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 82 (all X all Xa all Xb (scratc1415085435_orec3(X,Xa,Xb) <-> pp(scratc686076394_d_and(scratc563735097nd_or3(X,Xa,Xb),scratc480136062nd_ec3(X,Xa,Xb))))) # label(fact_def__orec3) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 83 (all X all Xa all Xb (pp(scratc480136062nd_ec3(X,Xa,Xb)) <-> scratc569575379d_and3(scratc295667187d_l_ec(X,Xa),scratc295667187d_l_ec(Xa,Xb),scratc295667187d_l_ec(Xb,X)))) # label(fact_def__ec3) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 84 (all X all Xa all Xb (scratc569575379d_and3(X,Xa,Xb) <-> pp(scratc686076394_d_and(X,scratc686076394_d_and(Xa,Xb))))) # label(fact_def__and3) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 85 (all X all Xa all Xb (pp(scratc563735097nd_or3(X,Xa,Xb)) <-> pp(aa_bool_bool(scratc296323192d_l_or(X),aa_bool_bool(scratc296323192d_l_or(Xa),Xb))))) # label(fact_def__or3) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 86 (all X all Xa (pp(aa_fun171081125l_bool(scratc965409833l_some(X),Xa)) <-> pp(scratc793541574_d_not(aa_fun171081125l_bool(scratc1854749025all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),scratc555276854nd_non(X,Xa)))))) # label(fact_def__l__some) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 87 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc555276854nd_non(X,Xa),Xb)) <-> pp(scratc793541574_d_not(aa_TPTP_ind_bool(Xa,Xb))))) # label(fact_def__non) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 88 (all X scratc447680490nd_all(X) = scratc1854749025all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X))) # label(fact_def__all) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 89 (all X all Xa (scratc1580217844_l_iff(X,Xa) <-> pp(scratc686076394_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc513838133nd_imp,X),Xa),aa_bool_bool(aa_boo1142376798l_bool(scratc513838133nd_imp,Xa),X))))) # label(fact_def__l__iff) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 90 (all X all Xa (scratc793489592d_orec(X,Xa) <-> pp(scratc686076394_d_and(aa_bool_bool(scratc296323192d_l_or(X),Xa),scratc295667187d_l_ec(X,Xa))))) # label(fact_def__orec) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 91 (all X scratc296323192d_l_or(X) = aa_boo1142376798l_bool(scratc513838133nd_imp,scratc793541574_d_not(X))) # label(fact_def__l__or) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 92 (all X all Xa (pp(scratc686076394_d_and(X,Xa)) <-> pp(scratc793541574_d_not(scratc295667187d_l_ec(X,Xa))))) # label(fact_def__d__and) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 93 (all X all Xa (pp(scratc295667187d_l_ec(X,Xa)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc513838133nd_imp,X),scratc793541574_d_not(Xa))))) # label(fact_def__l__ec) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 94 scratc1200705296bvious <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc513838133nd_imp,fFalse),fFalse)) # label(fact_def__obvious) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 95 (all X (scratc628974407nd_wel(X) <-> pp(scratc793541574_d_not(scratc793541574_d_not(X))))) # label(fact_def__wel) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 96 (all X (pp(scratc793541574_d_not(X)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc513838133nd_imp,X),fFalse)))) # label(fact_def__d__not) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 97 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1915193542d_d_Pi,X),Xa) = aa_fun1431113780TP_ind(scratc569824945_d_Sep(aa_TPTP_ind_TPTP_ind(scratc361726478_power,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1965973720_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].
% 0.90/1.22 98 (all X (gg_TPTP_ind(X) -> (pp(aa_TPTP_ind_bool(scratc794124927pair_p,X)) <-> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1433893617d_pair,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc505360646bnd_ap,X),scratc2001835532ptyset)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc505360646bnd_ap,X),aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,scratc2001835532ptyset))) = X))) # label(fact_def__pair__p) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 99 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc505360646bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc1841809378eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bg,Xa)),scratc490240317_proj1)) # label(fact_def__ap) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 100 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc571298050etprod(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1965973720_Sigma,X),aTP_Lamm_ai(Xa))) # label(fact_def__setprod) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 101 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1965973720_Sigma,X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc219792436munion,X),aTP_Lamm_bh(Xa))) # label(fact_def__d__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 102 (all X aa_TPTP_ind_TPTP_ind(scratc490240317_proj1,X) = aa_fun277296641TP_ind(scratc1841809378eplSep(X,aTP_Lamm_bi),scratc586938340_d_Unj)) # label(fact_def__proj1) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 103 (all X aa_TPTP_ind_TPTP_ind(scratc490240316_proj0,X) = aa_fun277296641TP_ind(scratc1841809378eplSep(X,aTP_Lamm_bj),scratc586938340_d_Unj)) # label(fact_def__proj0) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 104 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1433893617d_pair,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1213649535nunion(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc881089574d_repl,X),scratc1704212568d_Inj0)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc881089574d_repl,Xa),scratc1704212569d_Inj1))) # label(fact_def__pair) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 105 (all X aa_TPTP_ind_TPTP_ind(scratc1704212568d_Inj0,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc881089574d_repl,X),scratc1704212569d_Inj1)) # label(fact_def__d__Inj0) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 106 (all X (pp(aa_TPTP_ind_bool(scratc1585264998_nat_p,X)) <-> (all X1 (pp(aa_TPTP_ind_bool(X1,scratc2001835532ptyset)) -> ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(X1,X2)) -> pp(aa_TPTP_ind_bool(X1,aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,X2)))))) -> pp(aa_TPTP_ind_bool(X1,X))))))) # label(fact_def__nat__p) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 107 (all X aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1213649535nunion(X),aa_TPTP_ind_TPTP_ind(scratc879104892d_Sing,X))) # label(fact_def__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 108 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1569572958In_rec(X),Xa) = scratc480988913nd_eps(aa_TPT43085870d_bool(scratc1945089705_rec_G(X),Xa))) # label(fact_def__d__In__rec) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 109 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1945089705_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(scratc505885436bnd_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].
% 0.90/1.22 110 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1129935077tminus(X),Xa) = aa_fun1431113780TP_ind(scratc569824945_d_Sep(X),aa_TPT43085870d_bool(aTP_Lamm_bm,Xa))) # label(fact_def__setminus) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 111 (all X all Xa scratc1841809378eplSep(X,Xa) = aa_TPT494704832TP_ind(scratc881089574d_repl,aa_fun1431113780TP_ind(scratc569824945_d_Sep(X),Xa))) # label(fact_def__d__ReplSep) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 112 (all X all Xa aa_fun1431113780TP_ind(scratc569824945_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc505885428bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc505885436bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc881089574d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bn(X),Xa))),scratc2001835532ptyset)) # label(fact_def__d__Sep) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 113 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc219792436munion,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc868988344_union,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc881089574d_repl,X),Xa))) # label(fact_def__famunion) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 114 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1213649535nunion(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc868988344_union,aa_TPTP_ind_TPTP_ind(scratc1860460098_UPair(X),Xa))) # label(fact_def__binunion) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.22 115 (all X aa_TPTP_ind_TPTP_ind(scratc879104892d_Sing,X) = aa_TPTP_ind_TPTP_ind(scratc1860460098_UPair(X),X)) # label(fact_def__d__Sing) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 116 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1860460098_UPair(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc881089574d_repl,aa_TPTP_ind_TPTP_ind(scratc361726478_power,aa_TPTP_ind_TPTP_ind(scratc361726478_power,scratc2001835532ptyset))),aa_TPT1424761345TP_ind(aTP_Lamm_bo(X),Xa))) # label(fact_def__d__UPair) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 117 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc552784092nd_nIn,X),Xa)) <-> -pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X),Xa)))) # label(fact_def__nIn) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 118 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc505885428bnd_if(X,Xa),Xb) = scratc480988913nd_eps(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bp(X),Xa),Xb))) # label(fact_def__if) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 119 (all X (pp(aa_TPTP_ind_bool(scratc96129957closed,X)) <-> pp(aa_TPTP_ind_bool(scratc1053444270closed,X)) & pp(aa_TPTP_ind_bool(scratc1218177284closed,X)) & pp(aa_TPTP_ind_bool(scratc176375752closed,X)))) # label(fact_def__d__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 120 (all X (pp(aa_TPTP_ind_bool(scratc176375752closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X1),X)) -> (all X2 ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X3),X1)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,aa_TPTP_ind_TPTP_ind(X2,X3)),X))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc881089574d_repl,X1),X2)),X))))))))) # label(fact_def__d__Repl__closed) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 121 (all X (pp(aa_TPTP_ind_bool(scratc1218177284closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,aa_TPTP_ind_TPTP_ind(scratc361726478_power,X1)),X))))))) # label(fact_def__d__Power__closed) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 122 (all X (pp(aa_TPTP_ind_bool(scratc1053444270closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,aa_TPTP_ind_TPTP_ind(scratc868988344_union,X1)),X))))))) # label(fact_def__d__Union__closed) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 123 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc977455774d_Subq,X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X2),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X2),Xa))))))) # label(fact_def__d__Subq) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 124 (all X all Xa (pp(aa_fun171081125l_bool(scratc1854749025all_of(X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (scratc1698620792_is_of(X2,X) -> pp(aa_TPTP_ind_bool(Xa,X2))))))) # label(fact_def__all__of) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 125 (all X all Xa (scratc1698620792_is_of(X,Xa) <-> pp(aa_TPTP_ind_bool(Xa,X)))) # label(fact_def__is__of) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 126 (all X0 pp(aa_fun171081125l_bool(scratc1854749025all_of(aa_TPT43085870d_bool(aTP_Lamm_dj,X0)),aa_TPT43085870d_bool(aTP_Lamm_dl,X0)))) # label(fact_isseti) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 127 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1854749025all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_dm(X0),X12)))) # label(fact_estie) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 128 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1854749025all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_dn(X0),X12)))) # label(fact_estii) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 129 (all X0 all X12 scratc1698620792_is_of(aa_fun1431113780TP_ind(scratc569824945_d_Sep(X0),X12),aa_TPT43085870d_bool(aTP_Lamm_dj,X0))) # label(fact_setof__p) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 130 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1854749025all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_dp(X0),X12)))) # label(fact_secondis1) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 131 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1854749025all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_dr(X0),X12)))) # label(fact_firstis1) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 132 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1854749025all_of(aa_TPT43085870d_bool(aTP_Lamm_ds(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_dt(X0),X12)))) # label(fact_pairis1) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 133 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1854749025all_of(aa_TPT43085870d_bool(aTP_Lamm_ds(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_du(X0),X12)))) # label(fact_second__p) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 134 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1854749025all_of(aa_TPT43085870d_bool(aTP_Lamm_ds(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_dv(X0),X12)))) # label(fact_first__p) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 135 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1854749025all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_dx(X0),X12)))) # label(fact_e__pair__p) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 136 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1854749025all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_dy(X0),X12)))) # label(fact_otax2) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 137 (all X0 all X12 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1798189712ective(aa_fun1431113780TP_ind(scratc569824945_d_Sep(X0),X12)),X0),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1965973720_Sigma,aa_fun1431113780TP_ind(scratc569824945_d_Sep(X0),X12)),scratc908914163d_e_in(X0,X12))))) # label(fact_otax1) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 138 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1854749025all_of(aa_fun1584354236d_bool(aTP_Lamm_dz(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_ea(X0),X12)))) # label(fact_e__inp) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 139 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1854749025all_of(aa_fun1584354236d_bool(aTP_Lamm_dz(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_eb(X0),X12)))) # label(fact_e__in__p) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 140 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1854749025all_of(aa_TPT43085870d_bool(aTP_Lamm_ec(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_ef(X0),X12)))) # label(fact_e__fisi) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 141 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc563472751nd_one(X0),X12)) -> pp(aa_TPTP_ind_bool(X12,scratc513903720nd_ind(X0,X12))))) # label(fact_oneax) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 142 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc563472751nd_one(X0),X12)) -> scratc1698620792_is_of(scratc513903720nd_ind(X0,X12),aa_TPT43085870d_bool(aTP_Lamm_aj,X0)))) # label(fact_ind__p) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 143 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1854749025all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_eh(X0),X12)))) # label(fact_e__isp) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 144 (all X0 pp(aa_fun171081125l_bool(scratc1854749025all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_ei,X0)))) # label(fact_refis) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 145 (all X0 (scratc628974407nd_wel(X0) -> pp(X0))) # label(fact_l__et) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 146 (all X0 all X12 all X22 all X32 (pp(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc505885428bnd_if(X0,X22),X32))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X12),X22))))) # label(fact_k__If__In__then__E) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 147 (all X0 all X12 all X22 ((pp(X0) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X12),X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,aa_TPTP_ind_TPTP_ind(scratc505885428bnd_if(X0,X12),scratc2001835532ptyset)),aa_TPTP_ind_TPTP_ind(scratc505885428bnd_if(X0,X22),aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,scratc2001835532ptyset)))))) # label(fact_k__If__In__01) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 148 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X33),X0)) -> aa_TPTP_ind_TPTP_ind(X12,X33) = aa_TPTP_ind_TPTP_ind(X22,X33)))) -> aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1965973720_Sigma,X0),X12) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1965973720_Sigma,X0),X22))) # label(fact_xi__ext) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 149 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1915193542d_d_Pi,X0),X12))) -> (all X32 (gg_TPTP_ind(X32) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X32),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1915193542d_d_Pi,X0),X12))) -> ((all X42 (gg_TPTP_ind(X42) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X42),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc505360646bnd_ap,X22),X42) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc505360646bnd_ap,X32),X42)))) -> X22 = X32))))))) # label(fact_k__Pi__ext) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 150 (all X0 all X12 all X22 all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1915193542d_d_Pi,X0),X12))) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X32),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc505360646bnd_ap,X22),X32)),aa_TPTP_ind_TPTP_ind(X12,X32)))))) # label(fact_ap__Pi) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 151 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X33),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,aa_TPTP_ind_TPTP_ind(X22,X33)),aa_TPTP_ind_TPTP_ind(X12,X33)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1965973720_Sigma,X0),X22)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1915193542d_d_Pi,X0),X12))))) # label(fact_lam__Pi) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 152 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X22),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc505360646bnd_ap,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1965973720_Sigma,X0),X12)),X22) = aa_TPTP_ind_TPTP_ind(X12,X22))) # label(fact_beta) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 153 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1965973720_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,aa_TPTP_ind_TPTP_ind(scratc490240317_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc490240316_proj0,X22)))))) # label(fact_proj1__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 154 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1965973720_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,aa_TPTP_ind_TPTP_ind(scratc490240316_proj0,X22)),X0)))) # label(fact_proj0__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 155 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1965973720_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1433893617d_pair,aa_TPTP_ind_TPTP_ind(scratc490240316_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc490240317_proj1,X22)) = X22))) # label(fact_proj__Sigma__eta) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 156 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1965973720_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1433893617d_pair,aa_TPTP_ind_TPTP_ind(scratc490240316_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc490240317_proj1,X22)) = X22 & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,aa_TPTP_ind_TPTP_ind(scratc490240316_proj0,X22)),X0)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,aa_TPTP_ind_TPTP_ind(scratc490240317_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc490240316_proj0,X22))))))) # label(fact_k__Sigma__eta__proj0__proj1) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 157 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X22),X0)) -> (all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X32),aa_TPTP_ind_TPTP_ind(X12,X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1433893617d_pair,X22),X32)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1965973720_Sigma,X0),X12))))))) # label(fact_pair__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 158 (all X0 all X12 (gg_TPTP_ind(X12) -> aa_TPTP_ind_TPTP_ind(scratc490240317_proj1,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1433893617d_pair,X0),X12)) = X12)) # label(fact_proj1__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 159 (all X0 all X12 (gg_TPTP_ind(X0) -> aa_TPTP_ind_TPTP_ind(scratc490240316_proj0,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1433893617d_pair,X0),X12)) = X0)) # label(fact_proj0__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 160 (all X0 (pp(aa_TPTP_ind_bool(scratc1585264998_nat_p,X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X0),scratc1807379178_omega)))) # label(fact_nat__p__omega) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 161 (all X0 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X0),scratc1807379178_omega)) -> pp(aa_TPTP_ind_bool(scratc1585264998_nat_p,X0)))) # label(fact_omega__nat__p) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 162 (all X0 (gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(scratc1585264998_nat_p,X0)) -> X0 = scratc2001835532ptyset | (exists X13 (gg_TPTP_ind(X13) & pp(aa_TPTP_ind_bool(scratc1585264998_nat_p,X13)) & X0 = aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,X13)))))) # label(fact_nat__inv) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 163 (all X0 (pp(aa_TPTP_ind_bool(X0,scratc2001835532ptyset)) -> ((all X13 (gg_TPTP_ind(X13) -> (pp(aa_TPTP_ind_bool(scratc1585264998_nat_p,X13)) -> (pp(aa_TPTP_ind_bool(X0,X13)) -> pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,X13))))))) -> (all X12 (pp(aa_TPTP_ind_bool(scratc1585264998_nat_p,X12)) -> pp(aa_TPTP_ind_bool(X0,X12))))))) # label(fact_nat__ind) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 164 (all X0 (pp(aa_TPTP_ind_bool(scratc1585264998_nat_p,X0)) -> pp(aa_TPTP_ind_bool(scratc1585264998_nat_p,aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,X0))))) # label(fact_nat__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 165 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,X0) = aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,X12) -> X0 = X12))) # label(fact_ordsucc__inj) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 166 (all X0 aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,X0) != scratc2001835532ptyset) # label(fact_neq__ordsucc__0) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 167 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X22),aa_fun1431113780TP_ind(scratc569824945_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(X12,X22)))) # label(fact_k__SepE2) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 168 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X22),aa_fun1431113780TP_ind(scratc569824945_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X22),X0)))) # label(fact_k__SepE1) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 169 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X22),X0)) -> (pp(aa_TPTP_ind_bool(X12,X22)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X22),aa_fun1431113780TP_ind(scratc569824945_d_Sep(X0),X12)))))) # label(fact_k__SepI) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 170 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc361726478_power,X0)))) # label(fact_k__Self__In__Power) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 171 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc977455774d_Subq,X12),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc361726478_power,X0))))) # label(fact_k__PowerI) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 172 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc361726478_power,X0))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc977455774d_Subq,X12),X0)))) # label(fact_k__PowerE) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 173 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> aa_TPTP_ind_TPTP_ind(scratc505885428bnd_if(X0,X12),X22) = X12 | aa_TPTP_ind_TPTP_ind(scratc505885428bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__or) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 174 (all X0 all X12 all X22 (gg_TPTP_ind(X12) -> (pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc505885428bnd_if(X0,X12),X22) = X12))) # label(fact_if__i__1) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 175 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (-pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc505885428bnd_if(X0,X12),X22) = X22))) # label(fact_if__i__0) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 176 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> pp(X0) & aa_TPTP_ind_TPTP_ind(scratc505885428bnd_if(X0,X12),X22) = X12 | -pp(X0) & aa_TPTP_ind_TPTP_ind(scratc505885428bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__correct) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 177 (all X0 pp(aa_TPTP_ind_bool(scratc96129957closed,aa_TPTP_ind_TPTP_ind(scratc2018321780univof,X0)))) # label(fact_k__UnivOf__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 178 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc2018321780univof,X0)))) # label(fact_k__UnivOf__In) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 179 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc881089574d_repl,X0),X12))) <-> (exists X3 (gg_TPTP_ind(X3) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X3),X0)) & X22 = aa_TPTP_ind_TPTP_ind(X12,X3)))))) # label(fact_k__ReplEq) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 180 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc361726478_power,X0))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc977455774d_Subq,X12),X0)))) # label(fact_k__PowerEq) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 181 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc868988344_union,X0))) <-> (exists X2 (gg_TPTP_ind(X2) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X12),X2)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X2),X0)))))) # label(fact_k__UnionEq) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 182 -(exists X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,X0),scratc2001835532ptyset))) # label(fact_k__EmptyAx) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 183 (all X0 ((all X13 (gg_TPTP_ind(X13) -> ((all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_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].
% 0.93/1.23 184 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc977455774d_Subq,X0),X12)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc977455774d_Subq,X12),X0)) -> X0 = X12)))) # label(fact_set__ext) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 185 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cy,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc554883265nd_nis,Uu),scratc2003023802nd_n_1)) -> pp(aa_fun171081125l_bool(scratc1709234475n_some,aa_TPT43085870d_bool(aTP_Lamm_af,Uu)))))) # label(fact_ATP_Olambda__1) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 186 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cx,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc554883265nd_nis,Uu),scratc2003023802nd_n_1)) -> pp(aa_fun171081125l_bool(scratc226842479_n_one,aa_TPT43085870d_bool(aTP_Lamm_af,Uu)))))) # label(fact_ATP_Olambda__2) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 187 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cu,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc427574529d_n_is,aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(Uu),scratc2003023802nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,Uu))))) # label(fact_ATP_Olambda__3) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 188 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cr,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc427574529d_n_is,aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(scratc2003023802nd_n_1),Uu)),aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,Uu))))) # label(fact_ATP_Olambda__4) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 189 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cw,Uu)) <-> pp(aa_fun171081125l_bool(scratc563472751nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1915193542d_d_Pi,scratc554358474nd_nat),aTP_Lamm_ac)),aa_TPT43085870d_bool(aTP_Lamm_cv,Uu))))) # label(fact_ATP_Olambda__5) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 190 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_de,Uu)) <-> (pp(aa_TPTP_ind_bool(scratc505357048_cond1,Uu)) -> (pp(aa_TPTP_ind_bool(scratc505357049_cond2,Uu)) -> pp(aa_fun171081125l_bool(scratc1854749025all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dd,Uu))))))) # label(fact_ATP_Olambda__6) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 191 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_co,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc427574529d_n_is,aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(Uu),scratc2003023802nd_n_1))))) # label(fact_ATP_Olambda__7) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 192 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cl,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc427574529d_n_is,aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(scratc2003023802nd_n_1),Uu))))) # label(fact_ATP_Olambda__8) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 193 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cz,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc554883265nd_nis,aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__9) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 194 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_di,Uu)) <-> scratc1698620792_is_of(aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,Uu),aTP_Lamm_a))) # label(fact_ATP_Olambda__10) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 195 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dh,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc554883265nd_nis,aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,Uu)),scratc2003023802nd_n_1)))) # label(fact_ATP_Olambda__11) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 196 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dc,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,Uu),aa_TPTP_ind_TPTP_ind(scratc361726478_power,scratc554358474nd_nat))))) # label(fact_ATP_Olambda__12) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 197 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_a,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,Uu),scratc554358474nd_nat)))) # label(fact_ATP_Olambda__13) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 198 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dg,Uu)) <-> pp(aa_fun171081125l_bool(scratc1854749025all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_df,Uu))))) # label(fact_ATP_Olambda__14) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 199 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_db,Uu)) <-> pp(aa_fun171081125l_bool(scratc1854749025all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_da,Uu))))) # label(fact_ATP_Olambda__15) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 200 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ct,Uu)) <-> pp(aa_fun171081125l_bool(scratc1854749025all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cs,Uu))))) # label(fact_ATP_Olambda__16) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 201 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cq,Uu)) <-> pp(aa_fun171081125l_bool(scratc1854749025all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cp,Uu))))) # label(fact_ATP_Olambda__17) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 202 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cn,Uu)) <-> pp(aa_fun171081125l_bool(scratc1854749025all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cm,Uu))))) # label(fact_ATP_Olambda__18) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 203 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ck,Uu)) <-> pp(aa_fun171081125l_bool(scratc1854749025all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cj,Uu))))) # label(fact_ATP_Olambda__19) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 204 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ci,Uu)) <-> pp(aa_fun171081125l_bool(scratc1854749025all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ch,Uu))))) # label(fact_ATP_Olambda__20) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 205 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cf,Uu)) <-> pp(aa_fun171081125l_bool(scratc1854749025all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ce,Uu))))) # label(fact_ATP_Olambda__21) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 206 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cd,Uu)) <-> pp(aa_fun171081125l_bool(scratc1854749025all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cc,Uu))))) # label(fact_ATP_Olambda__22) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 207 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cb,Uu)) <-> pp(aa_fun171081125l_bool(scratc1854749025all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ca,Uu))))) # label(fact_ATP_Olambda__23) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 208 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_by,Uu)) <-> pp(aa_fun171081125l_bool(scratc1854749025all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bx,Uu))))) # label(fact_ATP_Olambda__24) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 209 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bv,Uu)) <-> pp(aa_fun171081125l_bool(scratc1854749025all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bu,Uu))))) # label(fact_ATP_Olambda__25) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 210 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bt,Uu)) <-> pp(aa_fun171081125l_bool(scratc1854749025all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bs,Uu))))) # label(fact_ATP_Olambda__26) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 211 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ab,Uu)) <-> pp(aa_fun171081125l_bool(scratc1854749025all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,Uu))))) # label(fact_ATP_Olambda__27) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 212 (all Uu aa_TPT494704832TP_ind(aTP_Lamm_bk,Uu) = aa_TPT494704832TP_ind(scratc881089574d_repl,aa_TPTP_ind_TPTP_ind(scratc1129935077tminus(Uu),aa_TPTP_ind_TPTP_ind(scratc879104892d_Sing,scratc2001835532ptyset)))) # label(fact_ATP_Olambda__28) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 213 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_ah,Uu)) <-> Uu != scratc2001835532ptyset))) # label(fact_ATP_Olambda__29) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 214 (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(scratc1704212569d_Inj1,X2) = Uu))))) # label(fact_ATP_Olambda__30) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 215 (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(scratc1704212568d_Inj0,X2) = Uu))))) # label(fact_ATP_Olambda__31) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 216 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bs,Uu),Uua)) <-> scratc1415085435_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc427574529d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1709234475n_some,aa_TPT43085870d_bool(aTP_Lamm_bq(Uu),Uua)),aa_fun171081125l_bool(scratc1709234475n_some,aa_TPT43085870d_bool(aTP_Lamm_br(Uu),Uua))))) # label(fact_ATP_Olambda__32) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 217 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,Uu),Uua)) <-> pp(scratc563735097nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc427574529d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1709234475n_some,aa_TPT43085870d_bool(scratc1136248831ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc1709234475n_some,aa_TPT43085870d_bool(scratc1136248831ffprop(Uua),Uu)))))) # label(fact_ATP_Olambda__33) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 218 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ei,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908914168d_e_is(Uu),Uua),Uua)))) # label(fact_ATP_Olambda__34) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 219 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cv,Uu),Uua)) <-> pp(scratc686076394_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc427574529d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc505360646bnd_ap,Uua),scratc2003023802nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,Uu)),aa_fun171081125l_bool(scratc111050218_n_all,aa_TPT43085870d_bool(aTP_Lamm_ae,Uua)))))) # label(fact_ATP_Olambda__35) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 220 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_df,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc427574529d_n_is,aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc427574529d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__36) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 221 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cp,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc427574529d_n_is,aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__37) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 222 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cs,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc427574529d_n_is,aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__38) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 223 (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(scratc427574529d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc505360646bnd_ap,Uu),aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc505360646bnd_ap,Uu),Uua)))))) # label(fact_ATP_Olambda__39) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 224 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_da,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc554883265nd_nis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc554883265nd_nis,aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,Uua)))))) # label(fact_ATP_Olambda__40) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 225 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ag,Uu),Uua)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc513838133nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc427574524d_n_in,Uua),Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc427574524d_n_in,aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,Uua)),Uu))))) # label(fact_ATP_Olambda__41) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 226 (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(scratc427574529d_n_is,aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(Uua),Uu))))) # label(fact_ATP_Olambda__42) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 227 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bh(Uu),Uua) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc881089574d_repl,aa_TPTP_ind_TPTP_ind(Uu,Uua)),aa_TPT1424761345TP_ind(scratc1433893617d_pair,Uua))) # label(fact_ATP_Olambda__43) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 228 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dl,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1854749025all_of(aa_TPT43085870d_bool(aTP_Lamm_dj,Uu)),aa_TPT43085870d_bool(aTP_Lamm_dk(Uu),Uua))))) # label(fact_ATP_Olambda__44) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 229 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cj,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc427574529d_n_is,aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,Uu)),Uua))))) # label(fact_ATP_Olambda__45) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 230 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cm,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc427574529d_n_is,aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,Uua)))))) # label(fact_ATP_Olambda__46) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 231 (all Uu all Uua aa_fun277296641TP_ind(aa_TPT494704832TP_ind(aTP_Lamm_bl,Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1213649535nunion(aa_TPTP_ind_TPTP_ind(scratc879104892d_Sing,scratc2001835532ptyset)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc881089574d_repl,Uu),Uua))) # label(fact_ATP_Olambda__47) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 232 (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(scratc554883265nd_nis,Uua),aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__48) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 233 (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(scratc427574529d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,Uua))))) # label(fact_ATP_Olambda__49) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 234 (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(scratc505885436bnd_in,Uua),aa_TPTP_ind_TPTP_ind(scratc361726478_power,Uu))))) # label(fact_ATP_Olambda__50) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 235 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dd,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc427574524d_n_in,Uua),Uu)))) # label(fact_ATP_Olambda__51) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 236 (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(scratc552784092nd_nIn,Uua),Uu)))) # label(fact_ATP_Olambda__52) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 237 (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(scratc505885436bnd_in,Uua),Uu)))) # label(fact_ATP_Olambda__53) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 238 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ch,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1854749025all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cg(Uu),Uua))))) # label(fact_ATP_Olambda__54) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 239 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ca,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1854749025all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bz(Uu),Uua))))) # label(fact_ATP_Olambda__55) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 240 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bx,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1854749025all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bw(Uu),Uua))))) # label(fact_ATP_Olambda__56) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 241 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bu,Uu),Uua)) <-> pp(scratc968938915_amone(scratc554358474nd_nat,aa_TPT43085870d_bool(aTP_Lamm_bq(Uu),Uua))))) # label(fact_ATP_Olambda__57) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 242 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_ad(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc937374956rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc505360646bnd_ap,Uu),Uua))) # label(fact_ATP_Olambda__58) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 243 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_be(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc868988344_union,aa_TPTP_ind_TPTP_ind(Uu,Uua))) # label(fact_ATP_Olambda__59) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 244 (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(scratc1433893617d_pair,Uu),X3)))))) # label(fact_ATP_Olambda__60) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 245 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dt(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908914168d_e_is(aa_TPTP_ind_TPTP_ind(scratc571298050etprod(Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1974877159d_pair(Uu,Uua),aa_TPTP_ind_TPTP_ind(scratc1422040441_first(Uu,Uua),Uub)),aa_TPTP_ind_TPTP_ind(scratc1309194923second(Uu,Uua),Uub))),Uub)))) # label(fact_ATP_Olambda__61) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 246 (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(scratc505885428bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,scratc2001835532ptyset),Uub),Uu),Uua)) # label(fact_ATP_Olambda__62) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 247 (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(scratc505885428bnd_if(aa_TPTP_ind_bool(Uua,Uub),Uub),scratc480988913nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bb(Uu),Uua)))) # label(fact_ATP_Olambda__63) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 248 (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(scratc1586797690d_esti(Uu),Uub),Uua)))) # label(fact_ATP_Olambda__64) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 249 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_dm(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1586797690d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc569824945_d_Sep(Uu),Uua))) -> pp(aa_TPTP_ind_bool(Uua,Uub))))) # label(fact_ATP_Olambda__65) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 250 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dk(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc371756485d_incl(Uu),Uua),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc371756485d_incl(Uu),Uub),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908914168d_e_is(aa_TPTP_ind_TPTP_ind(scratc361726478_power,Uu)),Uua),Uub)))))) # label(fact_ATP_Olambda__66) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 251 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_du(Uu),Uua),Uub)) <-> scratc1698620792_is_of(aa_TPTP_ind_TPTP_ind(scratc1309194923second(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)))) # label(fact_ATP_Olambda__67) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 252 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dv(Uu),Uua),Uub)) <-> scratc1698620792_is_of(aa_TPTP_ind_TPTP_ind(scratc1422040441_first(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)))) # label(fact_ATP_Olambda__68) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 253 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_eb(Uu),Uua),Uub)) <-> scratc1698620792_is_of(aa_TPTP_ind_TPTP_ind(scratc908914163d_e_in(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)))) # label(fact_ATP_Olambda__69) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 254 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ef(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1854749025all_of(aa_TPT43085870d_bool(aTP_Lamm_ec(Uu),Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ee(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__70) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 255 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bw(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc427574529d_n_is,aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(Uu),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc427574529d_n_is,Uua),Uub))))) # label(fact_ATP_Olambda__71) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 256 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cg(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc427574529d_n_is,aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__72) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 257 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bz(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc554883265nd_nis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc554883265nd_nis,aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(Uu),Uub)))))) # label(fact_ATP_Olambda__73) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 258 (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(scratc505885436bnd_in,Uub),Uu)) & pp(aa_TPTP_ind_bool(Uua,Uub)))) # label(fact_ATP_Olambda__74) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 259 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_dy(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1379398372_image(aa_fun1431113780TP_ind(scratc569824945_d_Sep(Uu),Uua),Uu),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1965973720_Sigma,aa_fun1431113780TP_ind(scratc569824945_d_Sep(Uu),Uua)),scratc908914163d_e_in(Uu,Uua))),Uub))))) # label(fact_ATP_Olambda__75) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 260 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_dn(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1586797690d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc569824945_d_Sep(Uu),Uua)))))) # label(fact_ATP_Olambda__76) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 261 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_eh(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1854749025all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_eg(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__77) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 262 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bd(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1854749025all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bc(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__78) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 263 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dx(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1854749025all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dw(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__79) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 264 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dr(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1854749025all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dq(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__80) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 265 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dp(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1854749025all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_do(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__81) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 266 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ec(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,Uub),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1915193542d_d_Pi,Uu),aTP_Lamm_ai(Uua)))))) # label(fact_ATP_Olambda__82) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 267 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bq(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc427574529d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(Uua),Uub))))) # label(fact_ATP_Olambda__83) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 268 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_br(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc427574529d_n_is,Uua),aa_TPTP_ind_TPTP_ind(scratc428033715d_n_pl(Uu),Uub))))) # label(fact_ATP_Olambda__84) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 269 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ds(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,Uub),aa_TPTP_ind_TPTP_ind(scratc571298050etprod(Uu),Uua))))) # label(fact_ATP_Olambda__85) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 270 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_dz(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,Uub),aa_fun1431113780TP_ind(scratc569824945_d_Sep(Uu),Uua))))) # label(fact_ATP_Olambda__86) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 271 (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(scratc505360646bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc505360646bnd_ap,Uu),Uub))) # label(fact_ATP_Olambda__87) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 272 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ea(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(Uua,aa_TPTP_ind_TPTP_ind(scratc908914163d_e_in(Uu,Uua),Uub))))) # label(fact_ATP_Olambda__88) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 273 (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(scratc505885436bnd_in,X3),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505885436bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc505360646bnd_ap,Uub),X3)),aa_TPTP_ind_TPTP_ind(Uua,X3)))))))) # label(fact_ATP_Olambda__89) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 274 (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(scratc505885428bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1379398372_image(Uu,Uua),Uub),Uuc),aa_TPTP_ind_TPTP_ind(scratc1743635841d_soft(Uu,Uua,Uub),Uuc)),scratc2001835532ptyset)) # label(fact_ATP_Olambda__90) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 275 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dq(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908914168d_e_is(Uu),aa_TPTP_ind_TPTP_ind(scratc1422040441_first(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1974877159d_pair(Uu,Uua),Uub),Uuc))),Uub)))) # label(fact_ATP_Olambda__91) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 276 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_do(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908914168d_e_is(Uua),aa_TPTP_ind_TPTP_ind(scratc1309194923second(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1974877159d_pair(Uu,Uua),Uub),Uuc))),Uuc)))) # label(fact_ATP_Olambda__92) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 277 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ed(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908914168d_e_is(Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc505360646bnd_ap,Uua),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc505360646bnd_ap,Uub),Uuc))))) # label(fact_ATP_Olambda__93) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 278 (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(scratc1586797690d_esti(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc505360646bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__94) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 279 (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(scratc908914168d_e_is(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc505360646bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__95) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 280 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dw(Uu),Uua),Uub),Uuc)) <-> scratc1698620792_is_of(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1974877159d_pair(Uu,Uua),Uub),Uuc),aa_TPT43085870d_bool(aTP_Lamm_ds(Uu),Uua)))) # label(fact_ATP_Olambda__96) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 281 (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(scratc295667187d_l_ec(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1586797690d_esti(Uu),Uuc),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1586797690d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__97) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 282 (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(scratc513838133nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1586797690d_esti(Uu),Uuc),Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1586797690d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__98) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 283 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ee(Uu),Uua),Uub),Uuc)) <-> (pp(aa_fun171081125l_bool(scratc1854749025all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ed(Uua),Uub),Uuc))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908914168d_e_is(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1915193542d_d_Pi,Uu),aTP_Lamm_ai(Uua))),Uub),Uuc))))) # label(fact_ATP_Olambda__99) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 284 (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__100) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 285 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_eg(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908914168d_e_is(Uu),Uub),Uuc)) -> pp(aa_TPTP_ind_bool(Uua,Uuc)))))) # label(fact_ATP_Olambda__101) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 286 (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(scratc908914168d_e_is(Uu),Uub),Uuc)))))) # label(fact_ATP_Olambda__102) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 287 (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(scratc447680490nd_all(Uu),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_az(Uu),Uua),Uub),Uuc))))) # label(fact_ATP_Olambda__103) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 288 (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(scratc965409833l_some(Uua),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aq(Uu),Uub),Uuc))))) # label(fact_ATP_Olambda__104) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 289 (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(scratc513838133nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908914168d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc505360646bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc505360646bnd_ap,Uub),Uud))),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908914168d_e_is(Uu),Uuc),Uud))))) # label(fact_ATP_Olambda__105) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 290 (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(scratc908914168d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc505360646bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc505360646bnd_ap,Uub),Uud)))))) # label(fact_ATP_Olambda__106) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 291 (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(scratc1854749025all_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__107) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 292 (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(scratc1854749025all_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__108) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 293 (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(scratc505360646bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc505360646bnd_ap,aa_TPTP_ind_TPTP_ind(scratc549978992wissel(Uu,Uub),Uuc)),Uud))) # label(fact_ATP_Olambda__109) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 294 (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(scratc1854749025all_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__110) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 295 (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(scratc908914168d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc505360646bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc505360646bnd_ap,Uub),Uuc)),Uue)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc505360646bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc505360646bnd_ap,Uub),Uud)),Uuf))))))) # label(fact_ATP_Olambda__111) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 296 (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(scratc1854749025all_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__112) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 297 (all Uu all Uua (gg_TPTP_ind(Uu) -> aa_TPTP_ind_TPTP_ind(aTP_Lamm_ai(Uu),Uua) = Uu)) # label(fact_ATP_Olambda__113) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 298 (all Uu aa_TPTP_ind_TPTP_ind(aTP_Lamm_ac,Uu) = scratc554358474nd_nat) # label(fact_ATP_Olambda__114) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 299 (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].
% 0.93/1.24 300 (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].
% 0.93/1.24 301 (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].
% 0.93/1.24 302 (all P (gg_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.24 303 (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].
% 0.93/1.24 304 (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].
% 0.93/1.24 305 (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].
% 0.93/1.24 306 (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].
% 0.93/1.26 307 (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].
% 0.93/1.26 308 (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].
% 0.93/1.26 309 (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].
% 0.93/1.26 310 (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].
% 0.93/1.26 311 (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].
% 0.93/1.26
% 0.93/1.26 ============================== end of process non-clausal formulas ===
% 0.93/1.26
% 0.93/1.26 ============================== PROCESS INITIAL CLAUSES ===============
% 0.93/1.26
% 0.93/1.26 ============================== PREDICATE ELIMINATION =================
% 0.93/1.26 312 -gg_bool(A) | A = fTrue | A = fFalse # label(help_fFalse_1_1_T) # label(axiom). [clausify(302)].
% 0.93/1.26 313 gg_bool(undefined_bool(bool)) # label(gsy_c_HOL_Oundefined_001t__HOL__Obool) # label(axiom). [assumption].
% 0.93/1.26 314 gg_bool(scratc968938915_amone(A,B)) # label(gsy_c_Scratch__tptp__translate__42180__13359_ONUM650__thf__4__p_Obnd__amone) # label(axiom). [clausify(1)].
% 0.93/1.26 315 gg_bool(scratc686076394_d_and(A,B)) # label(gsy_c_Scratch__tptp__translate__42180__13359_ONUM650__thf__4__p_Obnd__d__and) # label(axiom). [clausify(2)].
% 0.93/1.26 316 gg_bool(scratc793541574_d_not(A)) # label(gsy_c_Scratch__tptp__translate__42180__13359_ONUM650__thf__4__p_Obnd__d__not) # label(axiom). [clausify(3)].
% 0.93/1.26 317 gg_bool(scratc480136062nd_ec3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__42180__13359_ONUM650__thf__4__p_Obnd__ec3) # label(axiom). [clausify(4)].
% 0.93/1.26 318 gg_bool(scratc295667187d_l_ec(A,B)) # label(gsy_c_Scratch__tptp__translate__42180__13359_ONUM650__thf__4__p_Obnd__l__ec) # label(axiom). [clausify(8)].
% 0.93/1.26 319 gg_bool(scratc563735097nd_or3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__42180__13359_ONUM650__thf__4__p_Obnd__or3) # label(axiom). [clausify(9)].
% 0.93/1.26 320 gg_bool(aa_bool_bool(A,B)) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom). [clausify(10)].
% 0.93/1.26 321 gg_bool(aa_TPTP_ind_bool(A,B)) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom). [clausify(11)].
% 0.93/1.26 322 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)].
% 0.93/1.26 323 gg_bool(fEx_TPTP_ind(A)) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom). [clausify(16)].
% 0.93/1.26 324 gg_bool(fFalse) # label(gsy_c_fFalse) # label(axiom). [assumption].
% 0.93/1.26 325 gg_bool(fTrue) # label(gsy_c_fTrue) # label(axiom). [assumption].
% 0.93/1.26 Derived: undefined_bool(bool) = fTrue | undefined_bool(bool) = fFalse. [resolve(312,a,313,a)].
% 0.93/1.26 Derived: scratc968938915_amone(A,B) = fTrue | scratc968938915_amone(A,B) = fFalse. [resolve(312,a,314,a)].
% 0.93/1.26 Derived: scratc686076394_d_and(A,B) = fTrue | scratc686076394_d_and(A,B) = fFalse. [resolve(312,a,315,a)].
% 0.93/1.26 Derived: scratc793541574_d_not(A) = fTrue | scratc793541574_d_not(A) = fFalse. [resolve(312,a,316,a)].
% 0.93/1.26 Derived: scratc480136062nd_ec3(A,B,C) = fTrue | scratc480136062nd_ec3(A,B,C) = fFalse. [resolve(312,a,317,a)].
% 0.93/1.26 Derived: scratc295667187d_l_ec(A,B) = fTrue | scratc295667187d_l_ec(A,B) = fFalse. [resolve(312,a,318,a)].
% 0.93/1.53 Derived: scratc563735097nd_or3(A,B,C) = fTrue | scratc563735097nd_or3(A,B,C) = fFalse. [resolve(312,a,319,a)].
% 0.93/1.53 Derived: aa_bool_bool(A,B) = fTrue | aa_bool_bool(A,B) = fFalse. [resolve(312,a,320,a)].
% 0.93/1.53 Derived: aa_TPTP_ind_bool(A,B) = fTrue | aa_TPTP_ind_bool(A,B) = fFalse. [resolve(312,a,321,a)].
% 0.93/1.53 Derived: aa_fun171081125l_bool(A,B) = fTrue | aa_fun171081125l_bool(A,B) = fFalse. [resolve(312,a,322,a)].
% 0.93/1.53 Derived: fEx_TPTP_ind(A) = fTrue | fEx_TPTP_ind(A) = fFalse. [resolve(312,a,323,a)].
% 0.93/1.53 Derived: fFalse = fTrue | fFalse = fFalse. [resolve(312,a,324,a)].
% 0.93/1.53 Derived: fTrue = fTrue | fTrue = fFalse. [resolve(312,a,325,a)].
% 0.93/1.53 326 scratc690601977d_r_ec(A,B) | pp(A) # label(fact_def__r__ec) # label(axiom). [clausify(57)].
% 0.93/1.53 327 -scratc690601977d_r_ec(A,B) | -pp(A) | pp(scratc793541574_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(57)].
% 0.93/1.53 328 scratc690601977d_r_ec(A,B) | -pp(scratc793541574_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(57)].
% 0.93/1.53 329 scratc1580217844_l_iff(A,B) | -pp(scratc686076394_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc513838133nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc513838133nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(89)].
% 0.93/1.53 330 -scratc1580217844_l_iff(A,B) | pp(scratc686076394_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc513838133nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc513838133nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(89)].
% 0.93/1.53 331 scratc793489592d_orec(A,B) | -pp(scratc686076394_d_and(aa_bool_bool(scratc296323192d_l_or(A),B),scratc295667187d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(90)].
% 0.93/1.53 332 -scratc793489592d_orec(A,B) | pp(scratc686076394_d_and(aa_bool_bool(scratc296323192d_l_or(A),B),scratc295667187d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(90)].
% 0.93/1.53 333 scratc628974407nd_wel(A) | -pp(scratc793541574_d_not(scratc793541574_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(95)].
% 0.93/1.53 334 -scratc628974407nd_wel(A) | pp(scratc793541574_d_not(scratc793541574_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(95)].
% 0.93/1.53 335 -scratc628974407nd_wel(A) | pp(A) # label(fact_l__et) # label(axiom). [clausify(145)].
% 0.93/1.53 Derived: pp(A) | -pp(scratc793541574_d_not(scratc793541574_d_not(A))). [resolve(335,a,333,a)].
% 0.93/1.53
% 0.93/1.53 ============================== end predicate elimination =============
% 0.93/1.53
% 0.93/1.53 Auto_denials: (non-Horn, no changes).
% 0.93/1.53
% 0.93/1.53 Term ordering decisions:
% 0.93/1.53 Function symbol KB weights: scratc505885436bnd_in=1. scratc937374956rdsucc=1. aTP_Lamm_a=1. scratc427574529d_n_is=1. scratc505360646bnd_ap=1. aTP_Lamm_aj=1. scratc2001835532ptyset=1. scratc1965973720_Sigma=1. scratc554883265nd_nis=1. scratc2003023802nd_n_1=1. fFalse=1. scratc1585264998_nat_p=1. scratc1915193542d_d_Pi=1. scratc361726478_power=1. scratc554358474nd_nat=1. scratc513838133nd_imp=1. scratc881089574d_repl=1. scratc1709234475n_some=1. fTrue=1. scratc1433893617d_pair=1. scratc977455774d_Subq=1. scratc176375752closed=1. scratc490240316_proj0=1. scratc868988344_union=1. aTP_Lamm_af=1. scratc427574524d_n_in=1. scratc490240317_proj1=1. scratc111050218_n_all=1. aTP_Lamm_ac=1. aTP_Lamm_ae=1. aTP_Lamm_dj=1. scratc1053444270closed=1. scratc1218177284closed=1. aTP_Lamm_da=1. aTP_Lamm_de=1. aTP_Lamm_df=1. scratc1704212569d_Inj1=1. scratc1807379178_omega=1. scratc58315648_prop2=1. scratc96129957closed=1. aTP_Lamm_aa=1. aTP_Lamm_ag=1. aTP_Lamm_bg=1. aTP_Lamm_bi=1. aTP_Lamm_bj=1. aTP_Lamm_bs=1. aTP_Lamm_bu=1. aTP_Lamm_bx=1. aTP_Lamm_ca=1. aTP_Lamm_cc=1. aTP_Lamm_ce=1. aTP_Lamm_ch=1. aTP_Lamm_cj=1. aTP_Lamm_cm=1. aTP_Lamm_cp=1. aTP_Lamm_cs=1. aTP_Lamm_cv=1. aTP_Lamm_cx=1. aTP_Lamm_cy=1. aTP_Lamm_dd=1. fconj=1. fimplies=1. scratc1704212568d_Inj0=1. scratc505357049_cond2=1. scratc513575730nd_iii=1. scratc58315647_prop1=1. scratc606347060_29_ii=1. scratc879104892d_Sing=1. aTP_Lamm_bm=1. aTP_Lamm_bt=1. aTP_Lamm_bv=1. aTP_Lamm_by=1. aTP_Lamm_cb=1. aTP_Lamm_cd=1. aTP_Lamm_cf=1. aTP_Lamm_ci=1. aTP_Lamm_ck=1. aTP_Lamm_cl=1. aTP_Lamm_cn=1. aTP_Lamm_co=1. aTP_Lamm_cq=1. aTP_Lamm_cr=1. aTP_Lamm_ct=1. aTP_Lamm_cu=1. aTP_Lamm_cw=1. aTP_Lamm_cz=1. aTP_Lamm_db=1. aTP_Lamm_dc=1. aTP_Lamm_dg=1. aTP_Lamm_dh=1. aTP_Lamm_di=1. aTP_Lamm_dl=1. aTP_Lamm_ei=1. fequal_TPTP_ind=1. scratc2018321780univof=1. scratc226842479_n_one=1. scratc505357048_cond1=1. scratc552784092nd_nIn=1. scratc586938340_d_Unj=1. aTP_Lamm_ab=1. aTP_Lamm_ah=1. aTP_Lamm_bk=1. aTP_Lamm_bl=1. bool=1. scratc1029074945_prop1=1. scratc1235039997_prop1=1. scratc1240883894_empty=1. scratc139946871nempty=1. scratc1525557361d_plus=1. scratc1617437120_prop1=1. scratc1823402172_prop1=1. scratc219792436munion=1. scratc490633914_prop4=1. scratc794124927pair_p=1. scratc852642874_prop1=1. scratc1771758900d_i1_s=1. scratc231631544d_24_g=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_fun1584354236d_bool=1. aa_bool_bool=1. aa_fun1431113780TP_ind=1. aa_boo1142376798l_bool=1. scratc686076394_d_and=1. aa_TPT1123896796d_bool=1. scratc505885428bnd_if=1. scratc295667187d_l_ec=1. aa_fun1212484691d_bool=1. aa_TPT985247859d_bool=1. scratc908914163d_e_in=1. scratc1974877159d_pair=1. aa_fun987228051d_bool=1. scratc513903720nd_ind=1. scratc968938915_amone=1. scratc1309194923second=1. scratc1379398372_image=1. scratc1422040441_first=1. aa_TPT125613450d_bool=1. scratc555276854nd_non=1. aa_fun1913827119d_bool=1. scratc569641026d_anec=1. aa_TPT1791839040TP_ind=1. aa_fun1107270209d_bool=1. aa_fun845057962d_bool=1. scratc1841809378eplSep=1. scratc1933545144_ecelt=1. scratc480136123nd_ecp=1. scratc1932954753_ecect=1. aa_TPT1781712639TP_ind=1. aa_TPT2142672771l_bool=1. aa_fun1235454963TP_ind=1. cOMBB_658106424TP_ind=1. cOMBS_2003118649l_bool=1. scratc1278348804etprop=1. scratc1470756685_fixfu=1. scratc169925669fixfu2=1. scratc480136127nd_ect=1. scratc549978992wissel=1. scratc563931959nd_out=1. scratc681952195ectset=1. scratc335622649nverse=1. scratc373002860d_invf=1. scratc376739391d_tofs=1. scratc566750318ectelt=1. scratc788069541unmore=1. f1=1. f12=1. f13=1. f20=1. f24=1. scratc1854749025all_of=1. scratc428033715d_n_pl=1. scratc908914168d_e_is=1. scratc569824945_d_Sep=1. scratc1586797690d_esti=1. scratc793541574_d_not=1. scratc965409833l_some=1. scratc447680490nd_all=1. scratc1136248831ffprop=1. scratc1945089705_rec_G=1. aTP_Lamm_ai=1. aTP_Lamm_ds=1. scratc296323192d_l_or=1. scratc563472751nd_one=1. aTP_Lamm_ak=1. aTP_Lamm_au=1. aTP_Lamm_bc=1. aTP_Lamm_bp=1. aTP_Lamm_bq=1. aTP_Lamm_dk=1. aTP_Lamm_eg=1. scratc371756485d_incl=1. aTP_Lamm_ao=1. aTP_Lamm_ay=1. aTP_Lamm_bb=1. aTP_Lamm_bf=1. aTP_Lamm_bw=1. aTP_Lamm_bz=1. aTP_Lamm_ec=1. aTP_Lamm_ee=1. scratc1798189712ective=1. scratc480988913nd_eps=1. scratc571298050etprod=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_br=1. aTP_Lamm_cg=1. aTP_Lamm_dm=1. aTP_Lamm_dn=1. aTP_Lamm_do=1. aTP_Lamm_dq=1. aTP_Lamm_dw=1. aTP_Lamm_dy=1. aTP_Lamm_dz=1. aTP_Lamm_ed=1. fEx_TPTP_ind=1. scratc1213649535nunion=1. scratc814094099ective=1. aTP_Lamm_ar=1. aTP_Lamm_dp=1. aTP_Lamm_dr=1. aTP_Lamm_dt=1. aTP_Lamm_du=1. aTP_Lamm_dv=1. aTP_Lamm_dx=1. aTP_Lamm_ea=1. aTP_Lamm_eb=1. aTP_Lamm_ef=1. aTP_Lamm_eh=1. scratc1569572958In_rec=1. scratc1860460098_UPair=1. aTP_Lamm_ad=1. aTP_Lamm_av=1. aTP_Lamm_aw=1. aTP_Lamm_ax=1. aTP_Lamm_be=1. aTP_Lamm_bh=1. aTP_Lamm_bn=1. aTP_Lamm_bo=1. cOMBC_1555011498d_bool=1. scratc1129935077tminus=1. scratc1546771572t_disj=1. scratc1981908942ective=1. scratc264280699_prop1=1. scratc490633913_prop3=1. scratc646677822_prop1=1. undefined_bool=1. undefined_TPTP_ind=1. f2=1. f8=1. f9=1. f10=1. f11=1. f17=1. f18=1. f21=1. f22=1. f23=1. scratc563735097nd_or3=1. scratc480136062nd_ec3=1. scratc1743635841d_soft=1. scratc37155252_indeq=1. scratc490633911_prop1=1. scratc514297315nd_ite=1. scratc1045272956d_11_i=1. scratc1217718490sel_wa=1. scratc1217718491sel_wb=1. f5=1. f7=1. f14=1. f16=1. f19=1. f25=1. scratc490633912_prop2=1. scratc291241658_inj_h=1. scratc349581599hangef=1. f3=1. f4=1. f15=1.Cputime limit exceeded (core dumped)
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