TSTP Solution File: NUM649+4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM649+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 13:30:00 EDT 2022
% Result : Timeout 300.07s 300.31s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM649+4 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.32 % Computer : n008.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jul 5 05:06:23 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.93/1.21 ============================== Prover9 ===============================
% 0.93/1.21 Prover9 (32) version 2009-11A, November 2009.
% 0.93/1.21 Process 27485 was started by sandbox2 on n008.cluster.edu,
% 0.93/1.21 Tue Jul 5 05:06:24 2022
% 0.93/1.21 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_27331_n008.cluster.edu".
% 0.93/1.21 ============================== end of head ===========================
% 0.93/1.21
% 0.93/1.21 ============================== INPUT =================================
% 0.93/1.21
% 0.93/1.21 % Reading from file /tmp/Prover9_27331_n008.cluster.edu
% 0.93/1.21
% 0.93/1.21 set(prolog_style_variables).
% 0.93/1.21 set(auto2).
% 0.93/1.21 % set(auto2) -> set(auto).
% 0.93/1.21 % set(auto) -> set(auto_inference).
% 0.93/1.21 % set(auto) -> set(auto_setup).
% 0.93/1.21 % set(auto_setup) -> set(predicate_elim).
% 0.93/1.21 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.93/1.21 % set(auto) -> set(auto_limits).
% 0.93/1.21 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.93/1.21 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.93/1.21 % set(auto) -> set(auto_denials).
% 0.93/1.21 % set(auto) -> set(auto_process).
% 0.93/1.21 % set(auto2) -> assign(new_constants, 1).
% 0.93/1.21 % set(auto2) -> assign(fold_denial_max, 3).
% 0.93/1.21 % set(auto2) -> assign(max_weight, "200.000").
% 0.93/1.21 % set(auto2) -> assign(max_hours, 1).
% 0.93/1.21 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.93/1.21 % set(auto2) -> assign(max_seconds, 0).
% 0.93/1.21 % set(auto2) -> assign(max_minutes, 5).
% 0.93/1.21 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.93/1.21 % set(auto2) -> set(sort_initial_sos).
% 0.93/1.21 % set(auto2) -> assign(sos_limit, -1).
% 0.93/1.21 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.93/1.21 % set(auto2) -> assign(max_megs, 400).
% 0.93/1.21 % set(auto2) -> assign(stats, some).
% 0.93/1.21 % set(auto2) -> clear(echo_input).
% 0.93/1.21 % set(auto2) -> set(quiet).
% 0.93/1.21 % set(auto2) -> clear(print_initial_clauses).
% 0.93/1.21 % set(auto2) -> clear(print_given).
% 0.93/1.21 assign(lrs_ticks,-1).
% 0.93/1.21 assign(sos_limit,10000).
% 0.93/1.21 assign(order,kbo).
% 0.93/1.21 set(lex_order_vars).
% 0.93/1.21 clear(print_given).
% 0.93/1.21
% 0.93/1.21 % formulas(sos). % not echoed (359 formulas)
% 0.93/1.21
% 0.93/1.21 ============================== end of input ==========================
% 0.93/1.21
% 0.93/1.21 % From the command line: assign(max_seconds, 300).
% 0.93/1.21
% 0.93/1.21 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.93/1.21
% 0.93/1.21 % Formulas that are not ordinary clauses:
% 0.93/1.21 1 (all B_1 all B_2 gg_bool(scratc1340626988_amone(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__41979__15922_ONUM649__thf__4__p_Obnd__amone) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 2 (all B_1 all B_2 gg_bool(scratc522637729_d_and(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__41979__15922_ONUM649__thf__4__p_Obnd__d__and) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 3 (all B_1 gg_bool(scratc630102909_d_not(B_1))) # label(gsy_c_Scratch__tptp__translate__41979__15922_ONUM649__thf__4__p_Obnd__d__not) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 4 (all B_1 all B_2 all B_3 gg_bool(scratc388153991nd_ec3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__41979__15922_ONUM649__thf__4__p_Obnd__ec3) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 5 (all B_1 all B_2 gg_TPTP_ind(scratc388154056nd_ect(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__41979__15922_ONUM649__thf__4__p_Obnd__ect) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 6 (all B_1 gg_TPTP_ind(scratc389006842nd_eps(B_1))) # label(gsy_c_Scratch__tptp__translate__41979__15922_ONUM649__thf__4__p_Obnd__eps) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 7 (all B_1 all B_2 gg_TPTP_ind(scratc421921649nd_ind(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__41979__15922_ONUM649__thf__4__p_Obnd__ind) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 8 (all B_1 all B_2 gg_bool(scratc667355260d_l_ec(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__41979__15922_ONUM649__thf__4__p_Obnd__l__ec) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 9 (all B_1 all B_2 all B_3 gg_bool(scratc471753026nd_or3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__41979__15922_ONUM649__thf__4__p_Obnd__or3) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 10 (all B_1 all B_2 gg_bool(aa_bool_bool(B_1,B_2))) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 11 (all B_1 all B_2 gg_bool(aa_TPTP_ind_bool(B_1,B_2))) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 12 (all B_1 all B_2 gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2))) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 13 (all B_1 all B_2 gg_bool(aa_fun171081125l_bool(B_1,B_2))) # label(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__HOL__Obool) # label(hypothesis) # label(non_clause). [assumption].
% 0.93/1.21 14 (all B_1 all B_2 gg_TPTP_ind(aa_fun1431113780TP_ind(B_1,B_2))) # label(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 15 (all B_1 all B_2 gg_TPTP_ind(aa_fun277296641TP_ind(B_1,B_2))) # label(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__TPTP____Interpret__Oind_J_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 16 (all B_1 gg_bool(fEx_TPTP_ind(B_1))) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 17 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1906731377_prop1,X),Xa)) <-> pp(scratc471753026nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc799262602d_n_is,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc352876733_29_ii,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc421593659nd_iii,X),Xa))))) # label(fact_def__d__29__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 18 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc421593659nd_iii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc534619956n_some,aa_TPT43085870d_bool(scratc1459190838ffprop(Xa),X))))) # label(fact_def__iii) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 19 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc352876733_29_ii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc534619956n_some,aa_TPT43085870d_bool(scratc1459190838ffprop(X),Xa))))) # label(fact_def__d__29__ii) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 20 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1459190838ffprop(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc799262602d_n_is,X),aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(Xa),Xb))))) # label(fact_def__diffprop) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 21 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1318369202_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc462901194nd_nis,aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(X),Xb))))) # label(fact_def__d__28__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 22 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc730007027_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc462901194nd_nis,Xa),aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(X),Xa))))) # label(fact_def__d__27__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 23 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc141644852_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc799262602d_n_is,aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(Xa),X))))) # label(fact_def__d__26__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 24 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1700766325_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc799262602d_n_is,aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(X),Xa)),Xb)),aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(X),aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(Xa),Xb)))))) # label(fact_def__d__25__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 25 (all X scratc799721788d_n_pl(X) = aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,aa_TPTP_ind_TPTP_ind(scratc2022732712d_plus,X))) # label(fact_def__n__pl) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 26 (all X aa_TPTP_ind_TPTP_ind(scratc2022732712d_plus,X) = scratc421921649nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc139397967d_d_Pi,scratc462376403nd_nat),aTP_Lamm_ae),aa_TPT43085870d_bool(scratc1112404151_prop2,X))) # label(fact_def__plus) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 27 (all X aa_TPTP_ind_TPTP_ind(scratc554573551d_24_g,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc141432079_Sigma,scratc462376403nd_nat),aTP_Lamm_af(X))) # label(fact_def__d__24__g) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 28 (all X (pp(aa_TPTP_ind_bool(scratc862321987_prop4,X)) <-> pp(aa_fun171081125l_bool(scratc1938278962l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc139397967d_d_Pi,scratc462376403nd_nat),aTP_Lamm_ae)),aa_TPT43085870d_bool(scratc1112404151_prop2,X))))) # label(fact_def__prop4) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 29 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc862321986_prop3(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc799262602d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,X),Xb)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,Xa),Xb))))) # label(fact_def__prop3) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 30 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1112404151_prop2,X),Xa)) <-> pp(scratc522637729_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc799262602d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,Xa),scratc352715505nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,X)),aa_TPTP_ind_bool(scratc1112404150_prop1,Xa))))) # label(fact_def__d__24__prop2) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 31 (all X (pp(aa_TPTP_ind_bool(scratc1112404150_prop1,X)) <-> pp(aa_fun171081125l_bool(scratc2095095201_n_all,aa_TPT43085870d_bool(aTP_Lamm_ag,X))))) # label(fact_def__d__24__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 32 (all X (pp(aa_TPTP_ind_bool(scratc524041975_prop1,X)) <-> pp(aa_bool_bool(scratc668011265d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc799262602d_n_is,X),scratc352715505nd_n_1)),aa_fun171081125l_bool(scratc534619956n_some,aa_TPT43085870d_bool(aTP_Lamm_ah,X)))))) # label(fact_def__d__23__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 33 (all X (pp(aa_TPTP_ind_bool(scratc2083163448_prop1,X)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc462901194nd_nis,aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,X)),X)))) # label(fact_def__d__22__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 34 (all X (pp(aa_TPTP_ind_bool(scratc877045122_cond2,X)) <-> pp(aa_fun171081125l_bool(scratc2095095201_n_all,aa_TPT43085870d_bool(aTP_Lamm_ai,X))))) # label(fact_def__cond2) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 35 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc462901194nd_nis,X),Xa)) <-> pp(scratc630102909_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc799262602d_n_is,X),Xa))))) # label(fact_def__nis) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 36 (all X all Xa all Xb all Xc all Xd scratc1937480501indeq2(X,Xa,Xb,Xc,Xd) = aa_TPT1424761345TP_ind(scratc408843325_indeq(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1368214963d_11_i(X,Xa,Xb),Xc),Xd))) # label(fact_def__indeq2) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 37 (all X all Xa all Xb scratc1368214963d_11_i(X,Xa,Xb) = scratc408843325_indeq(X,Xa,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc139397967d_d_Pi,X),aTP_Lamm_ak(Xb)))) # label(fact_def__d__11__i) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 38 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc6487004fixfu2(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc680134506all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ap(X),Xa),Xb),Xc))))) # label(fact_def__fixfu2) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 39 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc408843325_indeq(X,Xa,Xb),Xc),Xd) = scratc421921649nd_ind(Xb,aa_TPT43085870d_bool(scratc862321985_prop2(X,Xa,Xb,Xc),Xd))) # label(fact_def__indeq) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 40 (all X all Xa all Xb all Xc all Xd all Xe (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc862321985_prop2(X,Xa,Xb,Xc),Xd),Xe)) <-> pp(aa_fun171081125l_bool(scratc1938278962l_some(X),aa_TPT43085870d_bool(scratc1659726777_prop1(X,Xa,Xb,Xc,Xd),Xe))))) # label(fact_def__prop2) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 41 (all X all Xa all Xb all Xc all Xd all Xe all Xf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1659726777_prop1(X,Xa,Xb,Xc,Xd),Xe),Xf)) <-> pp(scratc522637729_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2083973041d_esti(X),Xf),aa_TPTP_ind_TPTP_ind(scratc157159178_ecect(X,Xa),Xd)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1280602241d_e_is(Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,Xc),Xf)),Xe))))) # label(fact_def__d__10__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 42 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1842444758_fixfu(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc680134506all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ar(X),Xa),Xb),Xc))))) # label(fact_def__fixfu) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 43 (all X all Xa scratc157159178_ecect(X,Xa) = scratc1280602236d_e_in(aa_TPTP_ind_TPTP_ind(scratc733414551_power,X),scratc1066816377d_anec(X,Xa))) # label(fact_def__ecect) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 44 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc403311653ectelt(X,Xa),Xb) = aa_TPTP_ind_TPTP_ind(scratc518513530ectset(X,Xa),aa_TPTP_ind_TPTP_ind(scratc157749569_ecelt(X,Xa),Xb))) # label(fact_def__ectelt) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 45 (all X all Xa scratc518513530ectset(X,Xa) = scratc471949888nd_out(aa_TPTP_ind_TPTP_ind(scratc733414551_power,X),scratc1066816377d_anec(X,Xa))) # label(fact_def__ectset) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 46 (all X all Xa scratc388154056nd_ect(X,Xa) = aa_fun1431113780TP_ind(scratc406386280_d_Sep(aa_TPTP_ind_TPTP_ind(scratc733414551_power,X)),scratc1066816377d_anec(X,Xa))) # label(fact_def__ect) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 47 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc1066816377d_anec(X,Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1938278962l_some(X),aa_TPT43085870d_bool(scratc388154052nd_ecp(X,Xa),Xb))))) # label(fact_def__anec) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 48 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc388154052nd_ecp(X,Xa),Xb),Xc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1280602241d_e_is(aa_TPTP_ind_TPTP_ind(scratc733414551_power,X)),Xb),aa_TPTP_ind_TPTP_ind(scratc157749569_ecelt(X,Xa),Xc))))) # label(fact_def__ecp) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 49 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc157749569_ecelt(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc406386280_d_Sep(X),aa_TPT43085870d_bool(Xa,Xb))) # label(fact_def__ecelt) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 50 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc624630876unmore(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc406386280_d_Sep(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_at(X),Xa),Xb))) # label(fact_def__unmore) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 51 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1844254395etprop(X,Xa),Xb),Xc)) <-> pp(scratc522637729_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2083973041d_esti(X),Xc),Xa),scratc630102909_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2083973041d_esti(X),Xc),Xb)))))) # label(fact_def__nissetprop) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.21 52 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1869713579t_disj(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc355698419nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_au(X),Xa),Xb))))) # label(fact_def__st__disj) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 53 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc868931836d_incl(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc355698419nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_av(X),Xa),Xb))))) # label(fact_def__incl) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 54 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc462888878nempty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1938278962l_some(X),aa_TPT43085870d_bool(aTP_Lamm_aw(X),Xa))))) # label(fact_def__nonempty) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 55 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1612571967_empty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc680134506all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X)),scratc463294783nd_non(X,aa_TPT43085870d_bool(aTP_Lamm_aw(X),Xa)))))) # label(fact_def__empty) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 56 (all X scratc2083973041d_esti(X) = scratc1785162163bnd_in) # label(fact_def__esti) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 57 (all X all Xa (scratc1062290050d_r_ec(X,Xa) <-> (pp(X) -> pp(scratc630102909_d_not(Xa))))) # label(fact_def__r__ec) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 58 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc1322450728hangef(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc141432079_Sigma,X),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_ax(X),Xb),Xc),Xd))) # label(fact_def__changef) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 59 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc386540327wissel(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc141432079_Sigma,X),scratc1783624082sel_wb(X,Xa,Xb))) # label(fact_def__wissel) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 60 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1783624082sel_wb(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc422315244nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1280602241d_e_is(X),Xc),Xb),X,Xa),aa_TPTP_ind_TPTP_ind(scratc1783624081sel_wa(X,Xa,Xb),Xc))) # label(fact_def__wissel__wb) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 61 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1783624081sel_wa(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc422315244nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1280602241d_e_is(X),Xc),Xa),X,Xb),Xc)) # label(fact_def__wissel__wa) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 62 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc422315244nd_ite(X,Xa,Xb),Xc) = scratc421921649nd_ind(Xa,aa_TPT43085870d_bool(scratc862321984_prop1(X,Xa,Xb),Xc))) # label(fact_def__ite) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 63 (all X all Xa all Xb all Xc all Xd (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc862321984_prop1(X,Xa,Xb),Xc),Xd)) <-> pp(scratc522637729_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc421856062nd_imp,X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1280602241d_e_is(Xa),Xd),Xb)),aa_bool_bool(aa_boo1142376798l_bool(scratc421856062nd_imp,scratc630102909_d_not(X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1280602241d_e_is(Xa),Xd),Xc)))))) # label(fact_def__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 64 (all X all Xa scratc1145756258second(X,Xa) = scratc861928390_proj1) # label(fact_def__second) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 65 (all X all Xa scratc1793728514_first(X,Xa) = scratc861928389_proj0) # label(fact_def__first) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 66 (all X all Xa scratc800262640d_pair(X,Xa) = scratc1931068968d_pair) # label(fact_def__d__pair) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 67 (all X all Xa scratc471949888nd_out(X,Xa) = scratc93327544d_soft(aa_fun1431113780TP_ind(scratc406386280_d_Sep(X),Xa),X,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc141432079_Sigma,aa_fun1431113780TP_ind(scratc406386280_d_Sep(X),Xa)),scratc1280602236d_e_in(X,Xa)))) # label(fact_def__out) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 68 (all X all Xa all Xb (gg_TPTP_ind(Xb) -> aa_TPTP_ind_TPTP_ind(scratc1280602236d_e_in(X,Xa),Xb) = Xb)) # label(fact_def__e__in) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 69 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc127802993_inj_h(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc141432079_Sigma,X),aa_TPT1424761345TP_ind(aTP_Lamm_ay(Xc),Xd))) # label(fact_def__inj__h) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 70 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc870178211d_invf(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc141432079_Sigma,Xa),scratc93327544d_soft(X,Xa,Xb))) # label(fact_def__invf) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 71 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1728438615ective(X),Xa),Xb)) <-> pp(scratc522637729_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1544719385ective(X),Xa),Xb),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1379999690ective(X),Xa),Xb))))) # label(fact_def__bijective) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 72 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1379999690ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc355698419nd_all(Xa),aa_TPT43085870d_bool(scratc1751086445_image(X,Xa),Xb))))) # label(fact_def__surjective) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 73 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1308491778nverse(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc141432079_Sigma,Xa),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_az(X),Xa),Xb))) # label(fact_def__inverse) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 74 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc93327544d_soft(X,Xa,Xb),Xc) = scratc421921649nd_ind(X,aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ba(Xa),Xb),Xc))) # label(fact_def__soft) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 75 (all X all Xa scratc873914742d_tofs(X,Xa) = scratc1784637373bnd_ap) # label(fact_def__tofs) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 76 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1751086445_image(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1938278962l_some(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ba(Xa),Xb),Xc))))) # label(fact_def__image) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 77 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1544719385ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc355698419nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bc(X),Xa),Xb))))) # label(fact_def__injective) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 78 (all X all Xa scratc421921649nd_ind(X,Xa) = scratc389006842nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bd(X),Xa))) # label(fact_def__ind) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 79 (all X all Xa (pp(aa_fun171081125l_bool(scratc471490680nd_one(X),Xa)) <-> pp(scratc522637729_d_and(scratc1340626988_amone(X,Xa),aa_fun171081125l_bool(scratc1938278962l_some(X),Xa))))) # label(fact_def__one) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 80 (all X all Xa (pp(scratc1340626988_amone(X,Xa)) <-> pp(aa_fun171081125l_bool(scratc680134506all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X)),aa_fun1584354236d_bool(aTP_Lamm_bf(X),Xa))))) # label(fact_def__amone) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 81 (all X scratc1280602241d_e_is(X) = fequal_TPTP_ind) # label(fact_def__e__is) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 82 (all X all Xa all Xb (scratc1786773508_orec3(X,Xa,Xb) <-> pp(scratc522637729_d_and(scratc471753026nd_or3(X,Xa,Xb),scratc388153991nd_ec3(X,Xa,Xb))))) # label(fact_def__orec3) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 83 (all X all Xa all Xb (pp(scratc388153991nd_ec3(X,Xa,Xb)) <-> scratc1066750730d_and3(scratc667355260d_l_ec(X,Xa),scratc667355260d_l_ec(Xa,Xb),scratc667355260d_l_ec(Xb,X)))) # label(fact_def__ec3) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 84 (all X all Xa all Xb (scratc1066750730d_and3(X,Xa,Xb) <-> pp(scratc522637729_d_and(X,scratc522637729_d_and(Xa,Xb))))) # label(fact_def__and3) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 85 (all X all Xa all Xb (pp(scratc471753026nd_or3(X,Xa,Xb)) <-> pp(aa_bool_bool(scratc668011265d_l_or(X),aa_bool_bool(scratc668011265d_l_or(Xa),Xb))))) # label(fact_def__or3) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 86 (all X all Xa (pp(aa_fun171081125l_bool(scratc1938278962l_some(X),Xa)) <-> pp(scratc630102909_d_not(aa_fun171081125l_bool(scratc680134506all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X)),scratc463294783nd_non(X,Xa)))))) # label(fact_def__l__some) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 87 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc463294783nd_non(X,Xa),Xb)) <-> pp(scratc630102909_d_not(aa_TPTP_ind_bool(Xa,Xb))))) # label(fact_def__non) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 88 (all X scratc355698419nd_all(X) = scratc680134506all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X))) # label(fact_def__all) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 89 (all X all Xa (scratc1416779179_l_iff(X,Xa) <-> pp(scratc522637729_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc421856062nd_imp,X),Xa),aa_bool_bool(aa_boo1142376798l_bool(scratc421856062nd_imp,Xa),X))))) # label(fact_def__l__iff) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 90 (all X all Xa (scratc1290664943d_orec(X,Xa) <-> pp(scratc522637729_d_and(aa_bool_bool(scratc668011265d_l_or(X),Xa),scratc667355260d_l_ec(X,Xa))))) # label(fact_def__orec) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 91 (all X scratc668011265d_l_or(X) = aa_boo1142376798l_bool(scratc421856062nd_imp,scratc630102909_d_not(X))) # label(fact_def__l__or) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 92 (all X all Xa (pp(scratc522637729_d_and(X,Xa)) <-> pp(scratc630102909_d_not(scratc667355260d_l_ec(X,Xa))))) # label(fact_def__d__and) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 93 (all X all Xa (pp(scratc667355260d_l_ec(X,Xa)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc421856062nd_imp,X),scratc630102909_d_not(Xa))))) # label(fact_def__l__ec) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 94 scratc26090777bvious <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc421856062nd_imp,fFalse),fFalse)) # label(fact_def__obvious) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 95 (all X (scratc536992336nd_wel(X) <-> pp(scratc630102909_d_not(scratc630102909_d_not(X))))) # label(fact_def__wel) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 96 (all X (pp(scratc630102909_d_not(X)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc421856062nd_imp,X),fFalse)))) # label(fact_def__d__not) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 97 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc139397967d_d_Pi,X),Xa) = aa_fun1431113780TP_ind(scratc406386280_d_Sep(aa_TPTP_ind_TPTP_ind(scratc733414551_power,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc141432079_Sigma,X),aTP_Lamm_bg(Xa)))),aa_fun1913827119d_bool(aTP_Lamm_bh(X),Xa))) # label(fact_def__d__Pi) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 98 (all X (gg_TPTP_ind(X) -> (pp(aa_TPTP_ind_bool(scratc1766994056pair_p,X)) <-> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1931068968d_pair,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,X),scratc177293891ptyset)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,X),aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,scratc177293891ptyset))) = X))) # label(fact_def__pair__p) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 99 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc260231321eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bi,Xa)),scratc861928390_proj1)) # label(fact_def__ap) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 100 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1544167179etprod(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc141432079_Sigma,X),aTP_Lamm_ak(Xa))) # label(fact_def__setprod) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 101 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc141432079_Sigma,X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc542734443munion,X),aTP_Lamm_bj(Xa))) # label(fact_def__d__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 102 (all X aa_TPTP_ind_TPTP_ind(scratc861928390_proj1,X) = aa_fun277296641TP_ind(scratc260231321eplSep(X,aTP_Lamm_bk),scratc423499675_d_Unj)) # label(fact_def__proj1) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 103 (all X aa_TPTP_ind_TPTP_ind(scratc861928389_proj0,X) = aa_fun277296641TP_ind(scratc260231321eplSep(X,aTP_Lamm_bl),scratc423499675_d_Unj)) # label(fact_def__proj0) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 104 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1931068968d_pair,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1536591542nunion(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1378264925d_repl,X),scratc529598049d_Inj0)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1378264925d_repl,Xa),scratc529598050d_Inj1))) # label(fact_def__pair) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 105 (all X aa_TPTP_ind_TPTP_ind(scratc529598049d_Inj0,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1378264925d_repl,X),scratc529598050d_Inj1)) # label(fact_def__d__Inj0) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 106 (all X (pp(aa_TPTP_ind_bool(scratc1421826333_nat_p,X)) <-> (all X1 (pp(aa_TPTP_ind_bool(X1,scratc177293891ptyset)) -> ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(X1,X2)) -> pp(aa_TPTP_ind_bool(X1,aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,X2)))))) -> pp(aa_TPTP_ind_bool(X1,X))))))) # label(fact_def__nat__p) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 107 (all X aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1536591542nunion(X),aa_TPTP_ind_TPTP_ind(scratc1851974021d_Sing,X))) # label(fact_def__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 108 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc2135478549In_rec(X),Xa) = scratc389006842nd_eps(aa_TPT43085870d_bool(scratc123332402_rec_G(X),Xa))) # label(fact_def__d__In__rec) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 109 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc123332402_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(scratc1785162163bnd_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].
% 0.93/1.22 110 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1452877084tminus(X),Xa) = aa_fun1431113780TP_ind(scratc406386280_d_Sep(X),aa_TPT43085870d_bool(aTP_Lamm_bo,Xa))) # label(fact_def__setminus) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 111 (all X all Xa scratc260231321eplSep(X,Xa) = aa_TPT494704832TP_ind(scratc1378264925d_repl,aa_fun1431113780TP_ind(scratc406386280_d_Sep(X),Xa))) # label(fact_def__d__ReplSep) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 112 (all X all Xa aa_fun1431113780TP_ind(scratc406386280_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1785162155bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1785162163bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1378264925d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bp(X),Xa))),scratc177293891ptyset)) # label(fact_def__d__Sep) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 113 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc542734443munion,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1240676417_union,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1378264925d_repl,X),Xa))) # label(fact_def__famunion) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 114 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1536591542nunion(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1240676417_union,aa_TPTP_ind_TPTP_ind(scratc35918457_UPair(X),Xa))) # label(fact_def__binunion) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 115 (all X aa_TPTP_ind_TPTP_ind(scratc1851974021d_Sing,X) = aa_TPTP_ind_TPTP_ind(scratc35918457_UPair(X),X)) # label(fact_def__d__Sing) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 116 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc35918457_UPair(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1378264925d_repl,aa_TPTP_ind_TPTP_ind(scratc733414551_power,aa_TPTP_ind_TPTP_ind(scratc733414551_power,scratc177293891ptyset))),aa_TPT1424761345TP_ind(aTP_Lamm_bq(X),Xa))) # label(fact_def__d__UPair) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 117 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc460802021nd_nIn,X),Xa)) <-> -pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X),Xa)))) # label(fact_def__nIn) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 118 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1785162155bnd_if(X,Xa),Xb) = scratc389006842nd_eps(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_br(X),Xa),Xb))) # label(fact_def__if) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 119 (all X (pp(aa_TPTP_ind_bool(scratc421856302closed,X)) <-> pp(aa_TPTP_ind_bool(scratc136957669closed,X)) & pp(aa_TPTP_ind_bool(scratc301690683closed,X)) & pp(aa_TPTP_ind_bool(scratc1867236305closed,X)))) # label(fact_def__d__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 120 (all X (pp(aa_TPTP_ind_bool(scratc1867236305closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X1),X)) -> (all X2 ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X3),X1)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,aa_TPTP_ind_TPTP_ind(X2,X3)),X))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1378264925d_repl,X1),X2)),X))))))))) # label(fact_def__d__Repl__closed) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 121 (all X (pp(aa_TPTP_ind_bool(scratc301690683closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,aa_TPTP_ind_TPTP_ind(scratc733414551_power,X1)),X))))))) # label(fact_def__d__Power__closed) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 122 (all X (pp(aa_TPTP_ind_bool(scratc136957669closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,aa_TPTP_ind_TPTP_ind(scratc1240676417_union,X1)),X))))))) # label(fact_def__d__Union__closed) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 123 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1950324903d_Subq,X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X2),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X2),Xa))))))) # label(fact_def__d__Subq) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 124 (all X all Xa (pp(aa_fun171081125l_bool(scratc680134506all_of(X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (scratc1535182127_is_of(X2,X) -> pp(aa_TPTP_ind_bool(Xa,X2))))))) # label(fact_def__all__of) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 125 (all X all Xa (scratc1535182127_is_of(X,Xa) <-> pp(aa_TPTP_ind_bool(Xa,X)))) # label(fact_def__is__of) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 126 (all X0 pp(aa_fun171081125l_bool(scratc680134506all_of(aa_TPT43085870d_bool(aTP_Lamm_dh,X0)),aa_TPT43085870d_bool(aTP_Lamm_dj,X0)))) # label(fact_isseti) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 127 (all X0 all X12 pp(aa_fun171081125l_bool(scratc680134506all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X0)),aa_fun1584354236d_bool(aTP_Lamm_dk(X0),X12)))) # label(fact_estie) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 128 (all X0 all X12 pp(aa_fun171081125l_bool(scratc680134506all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X0)),aa_fun1584354236d_bool(aTP_Lamm_dl(X0),X12)))) # label(fact_estii) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 129 (all X0 all X12 scratc1535182127_is_of(aa_fun1431113780TP_ind(scratc406386280_d_Sep(X0),X12),aa_TPT43085870d_bool(aTP_Lamm_dh,X0))) # label(fact_setof__p) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 130 (all X0 all X12 pp(aa_fun171081125l_bool(scratc680134506all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X0)),aa_TPT43085870d_bool(aTP_Lamm_dn(X0),X12)))) # label(fact_secondis1) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 131 (all X0 all X12 pp(aa_fun171081125l_bool(scratc680134506all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X0)),aa_TPT43085870d_bool(aTP_Lamm_dp(X0),X12)))) # label(fact_firstis1) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 132 (all X0 all X12 pp(aa_fun171081125l_bool(scratc680134506all_of(aa_TPT43085870d_bool(aTP_Lamm_dq(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_dr(X0),X12)))) # label(fact_pairis1) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 133 (all X0 all X12 pp(aa_fun171081125l_bool(scratc680134506all_of(aa_TPT43085870d_bool(aTP_Lamm_dq(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_ds(X0),X12)))) # label(fact_second__p) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 134 (all X0 all X12 pp(aa_fun171081125l_bool(scratc680134506all_of(aa_TPT43085870d_bool(aTP_Lamm_dq(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_dt(X0),X12)))) # label(fact_first__p) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 135 (all X0 all X12 pp(aa_fun171081125l_bool(scratc680134506all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X0)),aa_TPT43085870d_bool(aTP_Lamm_dv(X0),X12)))) # label(fact_e__pair__p) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 136 (all X0 all X12 pp(aa_fun171081125l_bool(scratc680134506all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X0)),aa_fun1584354236d_bool(aTP_Lamm_dw(X0),X12)))) # label(fact_otax2) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 137 (all X0 all X12 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1544719385ective(aa_fun1431113780TP_ind(scratc406386280_d_Sep(X0),X12)),X0),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc141432079_Sigma,aa_fun1431113780TP_ind(scratc406386280_d_Sep(X0),X12)),scratc1280602236d_e_in(X0,X12))))) # label(fact_otax1) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 138 (all X0 all X12 pp(aa_fun171081125l_bool(scratc680134506all_of(aa_fun1584354236d_bool(aTP_Lamm_dx(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_dy(X0),X12)))) # label(fact_e__inp) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 139 (all X0 all X12 pp(aa_fun171081125l_bool(scratc680134506all_of(aa_fun1584354236d_bool(aTP_Lamm_dx(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_dz(X0),X12)))) # label(fact_e__in__p) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 140 (all X0 all X12 pp(aa_fun171081125l_bool(scratc680134506all_of(aa_TPT43085870d_bool(aTP_Lamm_ea(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_ed(X0),X12)))) # label(fact_e__fisi) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 141 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc471490680nd_one(X0),X12)) -> pp(aa_TPTP_ind_bool(X12,scratc421921649nd_ind(X0,X12))))) # label(fact_oneax) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 142 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc471490680nd_one(X0),X12)) -> scratc1535182127_is_of(scratc421921649nd_ind(X0,X12),aa_TPT43085870d_bool(aTP_Lamm_al,X0)))) # label(fact_ind__p) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 143 (all X0 all X12 pp(aa_fun171081125l_bool(scratc680134506all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X0)),aa_fun1584354236d_bool(aTP_Lamm_ef(X0),X12)))) # label(fact_e__isp) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 144 (all X0 pp(aa_fun171081125l_bool(scratc680134506all_of(aa_TPT43085870d_bool(aTP_Lamm_al,X0)),aa_TPT43085870d_bool(aTP_Lamm_eg,X0)))) # label(fact_refis) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 145 (all X0 (scratc536992336nd_wel(X0) -> pp(X0))) # label(fact_l__et) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 146 (all X0 all X12 all X22 all X32 (pp(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1785162155bnd_if(X0,X22),X32))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X12),X22))))) # label(fact_k__If__In__then__E) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 147 (all X0 all X12 all X22 ((pp(X0) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X12),X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,aa_TPTP_ind_TPTP_ind(scratc1785162155bnd_if(X0,X12),scratc177293891ptyset)),aa_TPTP_ind_TPTP_ind(scratc1785162155bnd_if(X0,X22),aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,scratc177293891ptyset)))))) # label(fact_k__If__In__01) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 148 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X33),X0)) -> aa_TPTP_ind_TPTP_ind(X12,X33) = aa_TPTP_ind_TPTP_ind(X22,X33)))) -> aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc141432079_Sigma,X0),X12) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc141432079_Sigma,X0),X22))) # label(fact_xi__ext) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 149 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc139397967d_d_Pi,X0),X12))) -> (all X32 (gg_TPTP_ind(X32) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X32),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc139397967d_d_Pi,X0),X12))) -> ((all X42 (gg_TPTP_ind(X42) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X42),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,X22),X42) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,X32),X42)))) -> X22 = X32))))))) # label(fact_k__Pi__ext) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 150 (all X0 all X12 all X22 all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc139397967d_d_Pi,X0),X12))) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X32),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,X22),X32)),aa_TPTP_ind_TPTP_ind(X12,X32)))))) # label(fact_ap__Pi) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 151 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X33),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,aa_TPTP_ind_TPTP_ind(X22,X33)),aa_TPTP_ind_TPTP_ind(X12,X33)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc141432079_Sigma,X0),X22)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc139397967d_d_Pi,X0),X12))))) # label(fact_lam__Pi) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 152 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X22),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc141432079_Sigma,X0),X12)),X22) = aa_TPTP_ind_TPTP_ind(X12,X22))) # label(fact_beta) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 153 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc141432079_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,aa_TPTP_ind_TPTP_ind(scratc861928390_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc861928389_proj0,X22)))))) # label(fact_proj1__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 154 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc141432079_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,aa_TPTP_ind_TPTP_ind(scratc861928389_proj0,X22)),X0)))) # label(fact_proj0__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 155 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc141432079_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1931068968d_pair,aa_TPTP_ind_TPTP_ind(scratc861928389_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc861928390_proj1,X22)) = X22))) # label(fact_proj__Sigma__eta) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 156 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc141432079_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1931068968d_pair,aa_TPTP_ind_TPTP_ind(scratc861928389_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc861928390_proj1,X22)) = X22 & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,aa_TPTP_ind_TPTP_ind(scratc861928389_proj0,X22)),X0)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,aa_TPTP_ind_TPTP_ind(scratc861928390_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc861928389_proj0,X22))))))) # label(fact_k__Sigma__eta__proj0__proj1) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 157 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X22),X0)) -> (all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X32),aa_TPTP_ind_TPTP_ind(X12,X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1931068968d_pair,X22),X32)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc141432079_Sigma,X0),X12))))))) # label(fact_pair__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 158 (all X0 all X12 (gg_TPTP_ind(X12) -> aa_TPTP_ind_TPTP_ind(scratc861928390_proj1,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1931068968d_pair,X0),X12)) = X12)) # label(fact_proj1__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 159 (all X0 all X12 (gg_TPTP_ind(X0) -> aa_TPTP_ind_TPTP_ind(scratc861928389_proj0,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1931068968d_pair,X0),X12)) = X0)) # label(fact_proj0__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 160 (all X0 (pp(aa_TPTP_ind_bool(scratc1421826333_nat_p,X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X0),scratc31583603_omega)))) # label(fact_nat__p__omega) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 161 (all X0 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X0),scratc31583603_omega)) -> pp(aa_TPTP_ind_bool(scratc1421826333_nat_p,X0)))) # label(fact_omega__nat__p) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 162 (all X0 (gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(scratc1421826333_nat_p,X0)) -> X0 = scratc177293891ptyset | (exists X13 (gg_TPTP_ind(X13) & pp(aa_TPTP_ind_bool(scratc1421826333_nat_p,X13)) & X0 = aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,X13)))))) # label(fact_nat__inv) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 163 (all X0 (pp(aa_TPTP_ind_bool(X0,scratc177293891ptyset)) -> ((all X13 (gg_TPTP_ind(X13) -> (pp(aa_TPTP_ind_bool(scratc1421826333_nat_p,X13)) -> (pp(aa_TPTP_ind_bool(X0,X13)) -> pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,X13))))))) -> (all X12 (pp(aa_TPTP_ind_bool(scratc1421826333_nat_p,X12)) -> pp(aa_TPTP_ind_bool(X0,X12))))))) # label(fact_nat__ind) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 164 (all X0 (pp(aa_TPTP_ind_bool(scratc1421826333_nat_p,X0)) -> pp(aa_TPTP_ind_bool(scratc1421826333_nat_p,aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,X0))))) # label(fact_nat__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 165 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,X0) = aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,X12) -> X0 = X12))) # label(fact_ordsucc__inj) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 166 (all X0 aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,X0) != scratc177293891ptyset) # label(fact_neq__ordsucc__0) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 167 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X22),aa_fun1431113780TP_ind(scratc406386280_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(X12,X22)))) # label(fact_k__SepE2) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 168 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X22),aa_fun1431113780TP_ind(scratc406386280_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X22),X0)))) # label(fact_k__SepE1) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 169 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X22),X0)) -> (pp(aa_TPTP_ind_bool(X12,X22)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X22),aa_fun1431113780TP_ind(scratc406386280_d_Sep(X0),X12)))))) # label(fact_k__SepI) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 170 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc733414551_power,X0)))) # label(fact_k__Self__In__Power) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 171 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1950324903d_Subq,X12),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc733414551_power,X0))))) # label(fact_k__PowerI) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 172 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc733414551_power,X0))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1950324903d_Subq,X12),X0)))) # label(fact_k__PowerE) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 173 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> aa_TPTP_ind_TPTP_ind(scratc1785162155bnd_if(X0,X12),X22) = X12 | aa_TPTP_ind_TPTP_ind(scratc1785162155bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__or) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 174 (all X0 all X12 all X22 (gg_TPTP_ind(X12) -> (pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc1785162155bnd_if(X0,X12),X22) = X12))) # label(fact_if__i__1) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 175 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (-pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc1785162155bnd_if(X0,X12),X22) = X22))) # label(fact_if__i__0) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 176 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> pp(X0) & aa_TPTP_ind_TPTP_ind(scratc1785162155bnd_if(X0,X12),X22) = X12 | -pp(X0) & aa_TPTP_ind_TPTP_ind(scratc1785162155bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__correct) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 177 (all X0 pp(aa_TPTP_ind_bool(scratc421856302closed,aa_TPTP_ind_TPTP_ind(scratc1854883115univof,X0)))) # label(fact_k__UnivOf__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 178 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc1854883115univof,X0)))) # label(fact_k__UnivOf__In) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 179 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1378264925d_repl,X0),X12))) <-> (exists X3 (gg_TPTP_ind(X3) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X3),X0)) & X22 = aa_TPTP_ind_TPTP_ind(X12,X3)))))) # label(fact_k__ReplEq) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 180 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc733414551_power,X0))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1950324903d_Subq,X12),X0)))) # label(fact_k__PowerEq) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 181 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1240676417_union,X0))) <-> (exists X2 (gg_TPTP_ind(X2) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X12),X2)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X2),X0)))))) # label(fact_k__UnionEq) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 182 -(exists X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X0),scratc177293891ptyset))) # label(fact_k__EmptyAx) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 183 (all X0 ((all X13 (gg_TPTP_ind(X13) -> ((all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_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].
% 0.93/1.22 184 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1950324903d_Subq,X0),X12)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1950324903d_Subq,X12),X0)) -> X0 = X12)))) # label(fact_set__ext) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 185 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cw,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc462901194nd_nis,Uu),scratc352715505nd_n_1)) -> pp(aa_fun171081125l_bool(scratc534619956n_some,aa_TPT43085870d_bool(aTP_Lamm_ah,Uu)))))) # label(fact_ATP_Olambda__1) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 186 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cv,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc462901194nd_nis,Uu),scratc352715505nd_n_1)) -> pp(aa_fun171081125l_bool(scratc63403814_n_one,aa_TPT43085870d_bool(aTP_Lamm_ah,Uu)))))) # label(fact_ATP_Olambda__2) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 187 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cs,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc799262602d_n_is,aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(Uu),scratc352715505nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,Uu))))) # label(fact_ATP_Olambda__3) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 188 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cp,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc799262602d_n_is,aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(scratc352715505nd_n_1),Uu)),aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,Uu))))) # label(fact_ATP_Olambda__4) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 189 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cu,Uu)) <-> pp(aa_fun171081125l_bool(scratc471490680nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc139397967d_d_Pi,scratc462376403nd_nat),aTP_Lamm_ae)),aa_TPT43085870d_bool(aTP_Lamm_ct,Uu))))) # label(fact_ATP_Olambda__5) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 190 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dc,Uu)) <-> (pp(aa_TPTP_ind_bool(scratc877045121_cond1,Uu)) -> (pp(aa_TPTP_ind_bool(scratc877045122_cond2,Uu)) -> pp(aa_fun171081125l_bool(scratc680134506all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_db,Uu))))))) # label(fact_ATP_Olambda__6) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 191 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cm,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc799262602d_n_is,aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(Uu),scratc352715505nd_n_1))))) # label(fact_ATP_Olambda__7) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 192 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cj,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc799262602d_n_is,aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(scratc352715505nd_n_1),Uu))))) # label(fact_ATP_Olambda__8) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 193 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cx,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc462901194nd_nis,aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__9) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 194 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dg,Uu)) <-> scratc1535182127_is_of(aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,Uu),aTP_Lamm_a))) # label(fact_ATP_Olambda__10) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.22 195 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_df,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc462901194nd_nis,aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,Uu)),scratc352715505nd_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_da,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,Uu),aa_TPTP_ind_TPTP_ind(scratc733414551_power,scratc462376403nd_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(scratc1785162163bnd_in,Uu),scratc462376403nd_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_de,Uu)) <-> pp(aa_fun171081125l_bool(scratc680134506all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dd,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_cz,Uu)) <-> pp(aa_fun171081125l_bool(scratc680134506all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cy,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_cr,Uu)) <-> pp(aa_fun171081125l_bool(scratc680134506all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cq,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_co,Uu)) <-> pp(aa_fun171081125l_bool(scratc680134506all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cn,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_cl,Uu)) <-> pp(aa_fun171081125l_bool(scratc680134506all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ck,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_ci,Uu)) <-> pp(aa_fun171081125l_bool(scratc680134506all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ch,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_cg,Uu)) <-> pp(aa_fun171081125l_bool(scratc680134506all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cf,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_cd,Uu)) <-> pp(aa_fun171081125l_bool(scratc680134506all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cc,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_cb,Uu)) <-> pp(aa_fun171081125l_bool(scratc680134506all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ca,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_bz,Uu)) <-> pp(aa_fun171081125l_bool(scratc680134506all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_by,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_bw,Uu)) <-> pp(aa_fun171081125l_bool(scratc680134506all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bv,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_bt,Uu)) <-> pp(aa_fun171081125l_bool(scratc680134506all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bs,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_ad,Uu)) <-> pp(aa_fun171081125l_bool(scratc680134506all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ac,Uu))))) # label(fact_ATP_Olambda__26) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 211 (all Uu aa_TPT494704832TP_ind(aTP_Lamm_bm,Uu) = aa_TPT494704832TP_ind(scratc1378264925d_repl,aa_TPTP_ind_TPTP_ind(scratc1452877084tminus(Uu),aa_TPTP_ind_TPTP_ind(scratc1851974021d_Sing,scratc177293891ptyset)))) # label(fact_ATP_Olambda__27) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 212 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_aj,Uu)) <-> Uu != scratc177293891ptyset))) # 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_bk,Uu)) <-> (exists X2 (gg_TPTP_ind(X2) & aa_TPTP_ind_TPTP_ind(scratc529598050d_Inj1,X2) = Uu))))) # 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_bl,Uu)) <-> (exists X2 (gg_TPTP_ind(X2) & aa_TPTP_ind_TPTP_ind(scratc529598049d_Inj0,X2) = Uu))))) # label(fact_ATP_Olambda__30) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 215 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ac,Uu),Uua)) <-> scratc1786773508_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc799262602d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc534619956n_some,aa_TPT43085870d_bool(aTP_Lamm_aa(Uu),Uua)),aa_fun171081125l_bool(scratc534619956n_some,aa_TPT43085870d_bool(aTP_Lamm_ab(Uu),Uua))))) # 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_eg,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1280602241d_e_is(Uu),Uua),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_ct,Uu),Uua)) <-> pp(scratc522637729_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc799262602d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,Uua),scratc352715505nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,Uu)),aa_fun171081125l_bool(scratc2095095201_n_all,aa_TPT43085870d_bool(aTP_Lamm_ag,Uua)))))) # 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_dd,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc799262602d_n_is,aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc799262602d_n_is,Uu),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_cn,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc799262602d_n_is,aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(Uu),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_cq,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc799262602d_n_is,aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(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_ag,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc799262602d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,Uu),aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,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_cy,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc462901194nd_nis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc462901194nd_nis,aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,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_ai,Uu),Uua)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc421856062nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc799262597d_n_in,Uua),Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc799262597d_n_in,aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,Uua)),Uu))))) # 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_cc,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc799262602d_n_is,aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(Uua),Uu))))) # label(fact_ATP_Olambda__40) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 225 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bj(Uu),Uua) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1378264925d_repl,aa_TPTP_ind_TPTP_ind(Uu,Uua)),aa_TPT1424761345TP_ind(scratc1931068968d_pair,Uua))) # 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_dj,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc680134506all_of(aa_TPT43085870d_bool(aTP_Lamm_dh,Uu)),aa_TPT43085870d_bool(aTP_Lamm_di(Uu),Uua))))) # label(fact_ATP_Olambda__42) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 227 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ch,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc799262602d_n_is,aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,Uu)),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_ck,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc799262602d_n_is,aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,Uua)))))) # label(fact_ATP_Olambda__44) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 229 (all Uu all Uua aa_fun277296641TP_ind(aa_TPT494704832TP_ind(aTP_Lamm_bn,Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1536591542nunion(aa_TPTP_ind_TPTP_ind(scratc1851974021d_Sing,scratc177293891ptyset)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1378264925d_repl,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_ca,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc462901194nd_nis,Uua),aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__46) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 231 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ah,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc799262602d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,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_dh,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,Uua),aa_TPTP_ind_TPTP_ind(scratc733414551_power,Uu))))) # 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_db,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc799262597d_n_in,Uua),Uu)))) # 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_bo,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc460802021nd_nIn,Uua),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_al,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_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_cf,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc680134506all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ce(Uu),Uua))))) # 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_by,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc680134506all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bx(Uu),Uua))))) # 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_bv,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc680134506all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bu(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_bs,Uu),Uua)) <-> pp(scratc1340626988_amone(scratc462376403nd_nat,aa_TPT43085870d_bool(aTP_Lamm_aa(Uu),Uua))))) # label(fact_ATP_Olambda__55) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 240 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_af(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1910244085rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,Uu),Uua))) # label(fact_ATP_Olambda__56) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 241 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bg(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1240676417_union,aa_TPTP_ind_TPTP_ind(Uu,Uua))) # label(fact_ATP_Olambda__57) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 242 (all Uu all Uua (gg_TPTP_ind(Uua) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bi,Uu),Uua)) <-> (exists X3 (gg_TPTP_ind(X3) & Uua = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1931068968d_pair,Uu),X3)))))) # label(fact_ATP_Olambda__58) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 243 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dr(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1280602241d_e_is(aa_TPTP_ind_TPTP_ind(scratc1544167179etprod(Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc800262640d_pair(Uu,Uua),aa_TPTP_ind_TPTP_ind(scratc1793728514_first(Uu,Uua),Uub)),aa_TPTP_ind_TPTP_ind(scratc1145756258second(Uu,Uua),Uub))),Uub)))) # label(fact_ATP_Olambda__59) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 244 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_bq(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc1785162155bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,scratc177293891ptyset),Uub),Uu),Uua)) # label(fact_ATP_Olambda__60) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 245 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_fun1235454963TP_ind(aTP_Lamm_bp(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc1785162155bnd_if(aa_TPTP_ind_bool(Uua,Uub),Uub),scratc389006842nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bd(Uu),Uua)))) # label(fact_ATP_Olambda__61) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 246 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aw(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2083973041d_esti(Uu),Uub),Uua)))) # label(fact_ATP_Olambda__62) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 247 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_dk(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2083973041d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc406386280_d_Sep(Uu),Uua))) -> pp(aa_TPTP_ind_bool(Uua,Uub))))) # label(fact_ATP_Olambda__63) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 248 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_di(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc868931836d_incl(Uu),Uua),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc868931836d_incl(Uu),Uub),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1280602241d_e_is(aa_TPTP_ind_TPTP_ind(scratc733414551_power,Uu)),Uua),Uub)))))) # label(fact_ATP_Olambda__64) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 249 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ds(Uu),Uua),Uub)) <-> scratc1535182127_is_of(aa_TPTP_ind_TPTP_ind(scratc1145756258second(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_al,Uua)))) # label(fact_ATP_Olambda__65) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 250 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dt(Uu),Uua),Uub)) <-> scratc1535182127_is_of(aa_TPTP_ind_TPTP_ind(scratc1793728514_first(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_al,Uu)))) # label(fact_ATP_Olambda__66) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 251 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_dz(Uu),Uua),Uub)) <-> scratc1535182127_is_of(aa_TPTP_ind_TPTP_ind(scratc1280602236d_e_in(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_al,Uu)))) # label(fact_ATP_Olambda__67) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 252 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ed(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc680134506all_of(aa_TPT43085870d_bool(aTP_Lamm_ea(Uu),Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ec(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__68) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 253 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bu(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc799262602d_n_is,aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(Uu),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc799262602d_n_is,Uua),Uub))))) # label(fact_ATP_Olambda__69) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 254 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ce(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc799262602d_n_is,aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__70) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 255 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bx(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc462901194nd_nis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc462901194nd_nis,aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(Uu),Uub)))))) # label(fact_ATP_Olambda__71) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 256 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bd(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,Uub),Uu)) & pp(aa_TPTP_ind_bool(Uua,Uub)))) # label(fact_ATP_Olambda__72) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 257 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_dw(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1751086445_image(aa_fun1431113780TP_ind(scratc406386280_d_Sep(Uu),Uua),Uu),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc141432079_Sigma,aa_fun1431113780TP_ind(scratc406386280_d_Sep(Uu),Uua)),scratc1280602236d_e_in(Uu,Uua))),Uub))))) # label(fact_ATP_Olambda__73) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 258 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_dl(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2083973041d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc406386280_d_Sep(Uu),Uua)))))) # label(fact_ATP_Olambda__74) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 259 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ef(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc680134506all_of(aa_TPT43085870d_bool(aTP_Lamm_al,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_ee(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__75) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 260 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bf(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc680134506all_of(aa_TPT43085870d_bool(aTP_Lamm_al,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_be(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__76) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 261 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dv(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc680134506all_of(aa_TPT43085870d_bool(aTP_Lamm_al,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_du(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__77) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 262 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dp(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc680134506all_of(aa_TPT43085870d_bool(aTP_Lamm_al,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_do(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__78) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 263 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dn(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc680134506all_of(aa_TPT43085870d_bool(aTP_Lamm_al,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dm(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__79) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 264 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ea(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,Uub),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc139397967d_d_Pi,Uu),aTP_Lamm_ak(Uua)))))) # label(fact_ATP_Olambda__80) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 265 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc799262602d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(Uua),Uub))))) # label(fact_ATP_Olambda__81) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 266 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ab(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc799262602d_n_is,Uua),aa_TPTP_ind_TPTP_ind(scratc799721788d_n_pl(Uu),Uub))))) # label(fact_ATP_Olambda__82) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 267 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dq(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,Uub),aa_TPTP_ind_TPTP_ind(scratc1544167179etprod(Uu),Uua))))) # label(fact_ATP_Olambda__83) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 268 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_dx(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,Uub),aa_fun1431113780TP_ind(scratc406386280_d_Sep(Uu),Uua))))) # label(fact_ATP_Olambda__84) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 269 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_ay(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,Uu),Uub))) # label(fact_ATP_Olambda__85) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 270 (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,aa_TPTP_ind_TPTP_ind(scratc1280602236d_e_in(Uu,Uua),Uub))))) # label(fact_ATP_Olambda__86) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 271 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1913827119d_bool(aTP_Lamm_bh(Uu),Uua),Uub)) <-> (all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,X3),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1785162163bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,Uub),X3)),aa_TPTP_ind_TPTP_ind(Uua,X3)))))))) # label(fact_ATP_Olambda__87) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 272 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_az(Uu),Uua),Uub),Uuc) = aa_TPTP_ind_TPTP_ind(scratc1785162155bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1751086445_image(Uu,Uua),Uub),Uuc),aa_TPTP_ind_TPTP_ind(scratc93327544d_soft(Uu,Uua,Uub),Uuc)),scratc177293891ptyset)) # label(fact_ATP_Olambda__88) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 273 (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(scratc1280602241d_e_is(Uu),aa_TPTP_ind_TPTP_ind(scratc1793728514_first(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc800262640d_pair(Uu,Uua),Uub),Uuc))),Uub)))) # label(fact_ATP_Olambda__89) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 274 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dm(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1280602241d_e_is(Uua),aa_TPTP_ind_TPTP_ind(scratc1145756258second(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc800262640d_pair(Uu,Uua),Uub),Uuc))),Uuc)))) # label(fact_ATP_Olambda__90) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 275 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_eb(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1280602241d_e_is(Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,Uua),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,Uub),Uuc))))) # label(fact_ATP_Olambda__91) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 276 (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(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2083973041d_esti(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__92) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 277 (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_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1280602241d_e_is(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__93) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 278 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_du(Uu),Uua),Uub),Uuc)) <-> scratc1535182127_is_of(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc800262640d_pair(Uu,Uua),Uub),Uuc),aa_TPT43085870d_bool(aTP_Lamm_dq(Uu),Uua)))) # label(fact_ATP_Olambda__94) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 279 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_au(Uu),Uua),Uub),Uuc)) <-> pp(scratc667355260d_l_ec(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2083973041d_esti(Uu),Uuc),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2083973041d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__95) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 280 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_av(Uu),Uua),Uub),Uuc)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc421856062nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2083973041d_esti(Uu),Uuc),Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2083973041d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__96) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 281 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ec(Uu),Uua),Uub),Uuc)) <-> (pp(aa_fun171081125l_bool(scratc680134506all_of(aa_TPT43085870d_bool(aTP_Lamm_al,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_eb(Uua),Uub),Uuc))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1280602241d_e_is(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc139397967d_d_Pi,Uu),aTP_Lamm_ak(Uua))),Uub),Uuc))))) # label(fact_ATP_Olambda__97) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 282 (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_br(Uu),Uua),Uub),Uuc)) <-> pp(Uu) & Uuc = Uua | -pp(Uu) & Uuc = Uub))) # label(fact_ATP_Olambda__98) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 283 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_ee(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1280602241d_e_is(Uu),Uub),Uuc)) -> pp(aa_TPTP_ind_bool(Uua,Uuc)))))) # label(fact_ATP_Olambda__99) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 284 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_be(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(scratc1280602241d_e_is(Uu),Uub),Uuc)))))) # label(fact_ATP_Olambda__100) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 285 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bc(Uu),Uua),Uub),Uuc)) <-> pp(aa_fun171081125l_bool(scratc355698419nd_all(Uu),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_bb(Uu),Uua),Uub),Uuc))))) # label(fact_ATP_Olambda__101) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 286 (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_fun171081125l_bool(scratc1938278962l_some(Uua),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_as(Uu),Uub),Uuc))))) # label(fact_ATP_Olambda__102) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 287 (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_bb(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc421856062nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1280602241d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,Uub),Uud))),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1280602241d_e_is(Uu),Uuc),Uud))))) # label(fact_ATP_Olambda__103) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 288 (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_aq(Uu),Uua),Uub),Uuc),Uud)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1280602241d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,Uub),Uud)))))) # label(fact_ATP_Olambda__104) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 289 (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(scratc680134506all_of(aa_TPT43085870d_bool(aTP_Lamm_al,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_ao(Uu),Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__105) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 290 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ar(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_fun171081125l_bool(scratc680134506all_of(aa_TPT43085870d_bool(aTP_Lamm_al,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_aq(Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__106) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 291 (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_ax(Uu),Uua),Uub),Uuc),Uud) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,aa_TPTP_ind_TPTP_ind(scratc386540327wissel(Uu,Uub),Uuc)),Uud))) # label(fact_ATP_Olambda__107) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 292 (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_ao(Uu),Uua),Uub),Uuc),Uud),Uue)) <-> pp(aa_fun171081125l_bool(scratc680134506all_of(aa_TPT43085870d_bool(aTP_Lamm_al,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_an(Uu),Uua),Uub),Uuc),Uud),Uue))))) # label(fact_ATP_Olambda__108) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 293 (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_am(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(scratc1280602241d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,Uub),Uuc)),Uue)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1784637373bnd_ap,Uub),Uud)),Uuf))))))) # label(fact_ATP_Olambda__109) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 294 (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_an(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)) <-> pp(aa_fun171081125l_bool(scratc680134506all_of(aa_TPT43085870d_bool(aTP_Lamm_al,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_am(Uua),Uub),Uuc),Uud),Uue),Uuf))))) # label(fact_ATP_Olambda__110) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 295 (all Uu all Uua (gg_TPTP_ind(Uu) -> aa_TPTP_ind_TPTP_ind(aTP_Lamm_ak(Uu),Uua) = Uu)) # label(fact_ATP_Olambda__111) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 296 (all Uu aa_TPTP_ind_TPTP_ind(aTP_Lamm_ae,Uu) = scratc462376403nd_nat) # label(fact_ATP_Olambda__112) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 297 (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].
% 0.93/1.23 298 (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].
% 0.93/1.23 299 (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].
% 0.93/1.23 300 (all P (gg_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.23 301 (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].
% 0.93/1.23 302 (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].
% 0.93/1.23 303 (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].
% 0.93/1.23 304 (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].
% 0.93/1.23 305 (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].
% 0.93/1.23 306 (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].
% 0.93/1.23 307 (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].
% 0.93/1.25 308 (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].
% 0.93/1.25 309 (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].
% 0.93/1.25
% 0.93/1.25 ============================== end of process non-clausal formulas ===
% 0.93/1.25
% 0.93/1.25 ============================== PROCESS INITIAL CLAUSES ===============
% 0.93/1.25
% 0.93/1.25 ============================== PREDICATE ELIMINATION =================
% 0.93/1.25 310 -gg_bool(A) | A = fTrue | A = fFalse # label(help_fFalse_1_1_T) # label(axiom). [clausify(300)].
% 0.93/1.25 311 gg_bool(undefined_bool(bool)) # label(gsy_c_HOL_Oundefined_001t__HOL__Obool) # label(axiom). [assumption].
% 0.93/1.25 312 gg_bool(scratc1340626988_amone(A,B)) # label(gsy_c_Scratch__tptp__translate__41979__15922_ONUM649__thf__4__p_Obnd__amone) # label(axiom). [clausify(1)].
% 0.93/1.25 313 gg_bool(scratc522637729_d_and(A,B)) # label(gsy_c_Scratch__tptp__translate__41979__15922_ONUM649__thf__4__p_Obnd__d__and) # label(axiom). [clausify(2)].
% 0.93/1.25 314 gg_bool(scratc630102909_d_not(A)) # label(gsy_c_Scratch__tptp__translate__41979__15922_ONUM649__thf__4__p_Obnd__d__not) # label(axiom). [clausify(3)].
% 0.93/1.25 315 gg_bool(scratc388153991nd_ec3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__41979__15922_ONUM649__thf__4__p_Obnd__ec3) # label(axiom). [clausify(4)].
% 0.93/1.25 316 gg_bool(scratc667355260d_l_ec(A,B)) # label(gsy_c_Scratch__tptp__translate__41979__15922_ONUM649__thf__4__p_Obnd__l__ec) # label(axiom). [clausify(8)].
% 0.93/1.25 317 gg_bool(scratc471753026nd_or3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__41979__15922_ONUM649__thf__4__p_Obnd__or3) # label(axiom). [clausify(9)].
% 0.93/1.25 318 gg_bool(aa_bool_bool(A,B)) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom). [clausify(10)].
% 0.93/1.25 319 gg_bool(aa_TPTP_ind_bool(A,B)) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom). [clausify(11)].
% 0.93/1.25 320 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)].
% 0.93/1.25 321 gg_bool(fEx_TPTP_ind(A)) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom). [clausify(16)].
% 0.93/1.25 322 gg_bool(fFalse) # label(gsy_c_fFalse) # label(axiom). [assumption].
% 0.93/1.25 323 gg_bool(fTrue) # label(gsy_c_fTrue) # label(axiom). [assumption].
% 0.93/1.25 Derived: undefined_bool(bool) = fTrue | undefined_bool(bool) = fFalse. [resolve(310,a,311,a)].
% 0.93/1.25 Derived: scratc1340626988_amone(A,B) = fTrue | scratc1340626988_amone(A,B) = fFalse. [resolve(310,a,312,a)].
% 0.93/1.25 Derived: scratc522637729_d_and(A,B) = fTrue | scratc522637729_d_and(A,B) = fFalse. [resolve(310,a,313,a)].
% 0.93/1.25 Derived: scratc630102909_d_not(A) = fTrue | scratc630102909_d_not(A) = fFalse. [resolve(310,a,314,a)].
% 0.93/1.25 Derived: scratc388153991nd_ec3(A,B,C) = fTrue | scratc388153991nd_ec3(A,B,C) = fFalse. [resolve(310,a,315,a)].
% 0.93/1.25 Derived: scratc667355260d_l_ec(A,B) = fTrue | scratc667355260d_l_ec(A,B) = fFalse. [resolve(310,a,316,a)].
% 0.93/1.25 Derived: scratc471753026nd_or3(A,B,C) = fTrue | scratc471753026nd_or3(A,B,C) = fFalse. [resolve(310,a,317,a)].
% 0.93/1.25 Derived: aa_bool_bool(A,B) = fTrue | aa_bool_bool(A,B) = fFalse. [resolve(310,a,318,a)].
% 0.93/1.25 Derived: aa_TPTP_ind_bool(A,B) = fTrue | aa_TPTP_ind_bool(A,B) = fFalse. [resolve(310,a,319,a)].
% 0.93/1.25 Derived: aa_fun171081125l_bool(A,B) = fTrue | aa_fun171081125l_bool(A,B) = fFalse. [resolve(310,a,320,a)].
% 0.93/1.25 Derived: fEx_TPTP_ind(A) = fTrue | fEx_TPTP_ind(A) = fFalse. [resolve(310,a,321,a)].
% 0.93/1.25 Derived: fFalse = fTrue | fFalse = fFalse. [resolve(310,a,322,a)].
% 0.93/1.25 Derived: fTrue = fTrue | fTrue = fFalse. [resolve(310,a,323,a)].
% 0.93/1.51 324 scratc1062290050d_r_ec(A,B) | pp(A) # label(fact_def__r__ec) # label(axiom). [clausify(57)].
% 0.93/1.51 325 -scratc1062290050d_r_ec(A,B) | -pp(A) | pp(scratc630102909_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(57)].
% 0.93/1.51 326 scratc1062290050d_r_ec(A,B) | -pp(scratc630102909_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(57)].
% 0.93/1.51 327 scratc1416779179_l_iff(A,B) | -pp(scratc522637729_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc421856062nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc421856062nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(89)].
% 0.93/1.51 328 -scratc1416779179_l_iff(A,B) | pp(scratc522637729_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc421856062nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc421856062nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(89)].
% 0.93/1.51 329 scratc1290664943d_orec(A,B) | -pp(scratc522637729_d_and(aa_bool_bool(scratc668011265d_l_or(A),B),scratc667355260d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(90)].
% 0.93/1.51 330 -scratc1290664943d_orec(A,B) | pp(scratc522637729_d_and(aa_bool_bool(scratc668011265d_l_or(A),B),scratc667355260d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(90)].
% 0.93/1.51 331 scratc536992336nd_wel(A) | -pp(scratc630102909_d_not(scratc630102909_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(95)].
% 0.93/1.51 332 -scratc536992336nd_wel(A) | pp(scratc630102909_d_not(scratc630102909_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(95)].
% 0.93/1.51 333 -scratc536992336nd_wel(A) | pp(A) # label(fact_l__et) # label(axiom). [clausify(145)].
% 0.93/1.51 Derived: pp(A) | -pp(scratc630102909_d_not(scratc630102909_d_not(A))). [resolve(333,a,331,a)].
% 0.93/1.51
% 0.93/1.51 ============================== end predicate elimination =============
% 0.93/1.51
% 0.93/1.51 Auto_denials: (non-Horn, no changes).
% 0.93/1.51
% 0.93/1.51 Term ordering decisions:
% 0.93/1.51 Function symbol KB weights: scratc1785162163bnd_in=1. scratc1910244085rdsucc=1. aTP_Lamm_a=1. scratc799262602d_n_is=1. scratc1784637373bnd_ap=1. aTP_Lamm_al=1. scratc177293891ptyset=1. scratc141432079_Sigma=1. scratc462901194nd_nis=1. scratc352715505nd_n_1=1. fFalse=1. scratc139397967d_d_Pi=1. scratc1421826333_nat_p=1. scratc462376403nd_nat=1. scratc733414551_power=1. scratc1378264925d_repl=1. scratc421856062nd_imp=1. fTrue=1. scratc534619956n_some=1. scratc1931068968d_pair=1. scratc1950324903d_Subq=1. scratc1240676417_union=1. scratc1867236305closed=1. scratc861928389_proj0=1. aTP_Lamm_ah=1. scratc799262597d_n_in=1. scratc861928390_proj1=1. scratc2095095201_n_all=1. aTP_Lamm_ae=1. aTP_Lamm_ag=1. aTP_Lamm_dh=1. scratc136957669closed=1. scratc301690683closed=1. aTP_Lamm_cy=1. aTP_Lamm_dc=1. aTP_Lamm_dd=1. scratc1112404151_prop2=1. scratc31583603_omega=1. scratc421856302closed=1. scratc529598050d_Inj1=1. aTP_Lamm_ac=1. aTP_Lamm_ai=1. aTP_Lamm_bi=1. aTP_Lamm_bk=1. aTP_Lamm_bl=1. aTP_Lamm_bs=1. aTP_Lamm_bv=1. aTP_Lamm_by=1. aTP_Lamm_ca=1. aTP_Lamm_cc=1. aTP_Lamm_cf=1. aTP_Lamm_ch=1. aTP_Lamm_ck=1. aTP_Lamm_cn=1. aTP_Lamm_cq=1. aTP_Lamm_ct=1. aTP_Lamm_cv=1. aTP_Lamm_cw=1. aTP_Lamm_db=1. fconj=1. fimplies=1. scratc1112404150_prop1=1. scratc1851974021d_Sing=1. scratc352876733_29_ii=1. scratc421593659nd_iii=1. scratc529598049d_Inj0=1. scratc877045122_cond2=1. aTP_Lamm_bo=1. aTP_Lamm_bt=1. aTP_Lamm_bw=1. aTP_Lamm_bz=1. aTP_Lamm_cb=1. aTP_Lamm_cd=1. aTP_Lamm_cg=1. aTP_Lamm_ci=1. aTP_Lamm_cj=1. aTP_Lamm_cl=1. aTP_Lamm_cm=1. aTP_Lamm_co=1. aTP_Lamm_cp=1. aTP_Lamm_cr=1. aTP_Lamm_cs=1. aTP_Lamm_cu=1. aTP_Lamm_cx=1. aTP_Lamm_cz=1. aTP_Lamm_da=1. aTP_Lamm_de=1. aTP_Lamm_df=1. aTP_Lamm_dg=1. aTP_Lamm_dj=1. aTP_Lamm_eg=1. fequal_TPTP_ind=1. scratc1854883115univof=1. scratc423499675_d_Unj=1. scratc460802021nd_nIn=1. scratc63403814_n_one=1. scratc877045121_cond1=1. aTP_Lamm_ad=1. aTP_Lamm_aj=1. aTP_Lamm_bm=1. aTP_Lamm_bn=1. bool=1. scratc141644852_prop1=1. scratc1612571967_empty=1. scratc1766994056pair_p=1. scratc1906731377_prop1=1. scratc2022732712d_plus=1. scratc2083163448_prop1=1. scratc462888878nempty=1. scratc524041975_prop1=1. scratc542734443munion=1. scratc730007027_prop1=1. scratc862321987_prop4=1. scratc2143446973d_i1_s=1. scratc554573551d_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. scratc522637729_d_and=1. aa_TPT1123896796d_bool=1. scratc1785162155bnd_if=1. scratc667355260d_l_ec=1. aa_fun1212484691d_bool=1. aa_TPT985247859d_bool=1. scratc1280602236d_e_in=1. scratc800262640d_pair=1. aa_fun987228051d_bool=1. scratc1340626988_amone=1. scratc421921649nd_ind=1. scratc1145756258second=1. scratc1751086445_image=1. scratc1793728514_first=1. aa_TPT125613450d_bool=1. scratc463294783nd_non=1. aa_fun1913827119d_bool=1. scratc1066816377d_anec=1. aa_TPT1791839040TP_ind=1. aa_fun1107270209d_bool=1. aa_fun845057962d_bool=1. scratc157749569_ecelt=1. scratc260231321eplSep=1. scratc388154052nd_ecp=1. scratc157159178_ecect=1. aa_TPT1781712639TP_ind=1. aa_TPT2142672771l_bool=1. aa_fun1235454963TP_ind=1. cOMBB_658106424TP_ind=1. cOMBS_2003118649l_bool=1. scratc1842444758_fixfu=1. scratc1844254395etprop=1. scratc386540327wissel=1. scratc388154056nd_ect=1. scratc471949888nd_out=1. scratc518513530ectset=1. scratc6487004fixfu2=1. scratc1308491778nverse=1. scratc403311653ectelt=1. scratc624630876unmore=1. scratc870178211d_invf=1. scratc873914742d_tofs=1. f1=1. f12=1. f13=1. f20=1. f24=1. scratc680134506all_of=1. scratc799721788d_n_pl=1. scratc1280602241d_e_is=1. scratc406386280_d_Sep=1. scratc2083973041d_esti=1. scratc630102909_d_not=1. scratc1938278962l_some=1. scratc355698419nd_all=1. scratc123332402_rec_G=1. aTP_Lamm_ak=1. aTP_Lamm_dq=1. scratc471490680nd_one=1. scratc668011265d_l_or=1. aTP_Lamm_aa=1. aTP_Lamm_am=1. aTP_Lamm_aw=1. aTP_Lamm_be=1. aTP_Lamm_br=1. aTP_Lamm_di=1. aTP_Lamm_ee=1. scratc1459190838ffprop=1. scratc868931836d_incl=1. aTP_Lamm_aq=1. aTP_Lamm_ba=1. aTP_Lamm_bd=1. aTP_Lamm_bh=1. aTP_Lamm_bu=1. aTP_Lamm_bx=1. aTP_Lamm_ea=1. aTP_Lamm_ec=1. scratc1544167179etprod=1. scratc1544719385ective=1. scratc389006842nd_eps=1. aTP_Lamm_ab=1. aTP_Lamm_an=1. aTP_Lamm_ao=1. aTP_Lamm_ap=1. aTP_Lamm_ar=1. aTP_Lamm_as=1. aTP_Lamm_au=1. aTP_Lamm_av=1. aTP_Lamm_bb=1. aTP_Lamm_bc=1. aTP_Lamm_bf=1. aTP_Lamm_ce=1. aTP_Lamm_dk=1. aTP_Lamm_dl=1. aTP_Lamm_dm=1. aTP_Lamm_do=1. aTP_Lamm_du=1. aTP_Lamm_dw=1. aTP_Lamm_dx=1. aTP_Lamm_eb=1. fEx_TPTP_ind=1. scratc1379999690ective=1. scratc1536591542nunion=1. aTP_Lamm_at=1. aTP_Lamm_dn=1. aTP_Lamm_dp=1. aTP_Lamm_dr=1. aTP_Lamm_ds=1. aTP_Lamm_dt=1. aTP_Lamm_dv=1. aTP_Lamm_dy=1. aTP_Lamm_dz=1. aTP_Lamm_ed=1. aTP_Lamm_ef=1. scratc2135478549In_rec=1. scratc35918457_UPair=1. aTP_Lamm_af=1. aTP_Lamm_ax=1. aTP_Lamm_ay=1. aTP_Lamm_az=1. aTP_Lamm_bg=1. aTP_Lamm_bj=1. aTP_Lamm_bp=1. aTP_Lamm_bq=1. cOMBC_1555011498d_bool=1. scratc1318369202_prop1=1. scratc1452877084tminus=1. scratc1700766325_prop1=1. scratc1728438615ective=1. scratc1869713579t_disj=1. scratc862321986_prop3=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. scratc471753026nd_or3=1. scratc388153991nd_ec3=1. scratc93327544d_soft=1. scratc408843325_indeq=1. scratc422315244nd_ite=1. scratc862321984_prop1=1. scratc1368214963d_11_i=1. scratc1783624081sel_wa=1. scratc1783624082sel_wb=1. f5=1. f7=1. f14=1. f16=1. f19=1. f25=1. scratc862321985_prop2=1. scratc127802993_inj_h=1. scratc1322450728hangef=1. f3=1. f4=1. f15=1. scratc1659726777_prop1=1. scratc1937480501indeq2=1. f6=1.
% 2.18/2.48
% 2.18/2.48 ============================== end of process initial clauses ========
% 2.18/2.48
% 2.18/2.48 ============================== CLAUSES FOR SEARCH ====================
% 2.18/2.48
% 2.18/2.48 ============================== end of clauses for search =============
% 2.18/2.48
% 2.18/2.48 ============================== SEARCH ================================
% 2.18/2.48
% 2.18/2.48 % Starting search at 0.36 seconds.
% 2.18/2.48
% 2.18/2.48 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 46 (0.00 of 1.21 sec).
% 2.18/2.48
% 2.18/2.48 Low Water (keep): wt=36.000, iters=3345
% 2.18/2.48
% 2.18/2.48 Low Water (keep): wt=35.000, iters=3401
% 2.18/2.48
% 2.18/2.48 Low Water (keep): wt=33.000, iters=3334
% 2.18/2.48
% 2.18/2.48 Low Water (keep): wt=31.00Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------