TSTP Solution File: NUM638+4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM638+4 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 13:29:50 EDT 2022
% Result : Timeout 300.01s 300.38s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM638+4 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jul 7 11:57:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.88/1.22 ============================== Prover9 ===============================
% 0.88/1.22 Prover9 (32) version 2009-11A, November 2009.
% 0.88/1.22 Process 32166 was started by sandbox on n025.cluster.edu,
% 0.88/1.22 Thu Jul 7 11:57:14 2022
% 0.88/1.22 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_32013_n025.cluster.edu".
% 0.88/1.22 ============================== end of head ===========================
% 0.88/1.22
% 0.88/1.22 ============================== INPUT =================================
% 0.88/1.22
% 0.88/1.22 % Reading from file /tmp/Prover9_32013_n025.cluster.edu
% 0.88/1.22
% 0.88/1.22 set(prolog_style_variables).
% 0.88/1.22 set(auto2).
% 0.88/1.22 % set(auto2) -> set(auto).
% 0.88/1.22 % set(auto) -> set(auto_inference).
% 0.88/1.22 % set(auto) -> set(auto_setup).
% 0.88/1.22 % set(auto_setup) -> set(predicate_elim).
% 0.88/1.22 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.88/1.22 % set(auto) -> set(auto_limits).
% 0.88/1.22 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.88/1.22 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.88/1.22 % set(auto) -> set(auto_denials).
% 0.88/1.22 % set(auto) -> set(auto_process).
% 0.88/1.22 % set(auto2) -> assign(new_constants, 1).
% 0.88/1.22 % set(auto2) -> assign(fold_denial_max, 3).
% 0.88/1.22 % set(auto2) -> assign(max_weight, "200.000").
% 0.88/1.22 % set(auto2) -> assign(max_hours, 1).
% 0.88/1.22 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.88/1.22 % set(auto2) -> assign(max_seconds, 0).
% 0.88/1.22 % set(auto2) -> assign(max_minutes, 5).
% 0.88/1.22 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.88/1.22 % set(auto2) -> set(sort_initial_sos).
% 0.88/1.22 % set(auto2) -> assign(sos_limit, -1).
% 0.88/1.22 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.88/1.22 % set(auto2) -> assign(max_megs, 400).
% 0.88/1.22 % set(auto2) -> assign(stats, some).
% 0.88/1.22 % set(auto2) -> clear(echo_input).
% 0.88/1.22 % set(auto2) -> set(quiet).
% 0.88/1.22 % set(auto2) -> clear(print_initial_clauses).
% 0.88/1.22 % set(auto2) -> clear(print_given).
% 0.88/1.22 assign(lrs_ticks,-1).
% 0.88/1.22 assign(sos_limit,10000).
% 0.88/1.22 assign(order,kbo).
% 0.88/1.22 set(lex_order_vars).
% 0.88/1.22 clear(print_given).
% 0.88/1.22
% 0.88/1.22 % formulas(sos). % not echoed (292 formulas)
% 0.88/1.22
% 0.88/1.22 ============================== end of input ==========================
% 0.88/1.22
% 0.88/1.22 % From the command line: assign(max_seconds, 300).
% 0.88/1.22
% 0.88/1.22 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.88/1.22
% 0.88/1.22 % Formulas that are not ordinary clauses:
% 0.88/1.22 1 (all B_1 all B_2 gg_bool(scratc89584109_amone(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__39750__6583_ONUM638__thf__4__p_Obnd__amone) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.22 2 (all B_1 all B_2 gg_bool(scratc1595910176_d_and(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__39750__6583_ONUM638__thf__4__p_Obnd__d__and) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.22 3 (all B_1 gg_bool(scratc1703375356_d_not(B_1))) # label(gsy_c_Scratch__tptp__translate__39750__6583_ONUM638__thf__4__p_Obnd__d__not) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.22 4 (all B_1 all B_2 all B_3 gg_bool(scratc918842568nd_ec3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__39750__6583_ONUM638__thf__4__p_Obnd__ec3) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.22 5 (all B_1 all B_2 gg_TPTP_ind(scratc918842633nd_ect(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__39750__6583_ONUM638__thf__4__p_Obnd__ect) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.22 6 (all B_1 gg_TPTP_ind(scratc919695419nd_eps(B_1))) # label(gsy_c_Scratch__tptp__translate__39750__6583_ONUM638__thf__4__p_Obnd__eps) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.22 7 (all B_1 all B_2 gg_TPTP_ind(scratc952610226nd_ind(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__39750__6583_ONUM638__thf__4__p_Obnd__ind) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.22 8 (all B_1 all B_2 gg_bool(scratc1563796029d_l_ec(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__39750__6583_ONUM638__thf__4__p_Obnd__l__ec) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.22 9 (all B_1 all B_2 all B_3 gg_bool(scratc1002441603nd_or3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__39750__6583_ONUM638__thf__4__p_Obnd__or3) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.22 10 (all B_1 all B_2 gg_bool(aa_bool_bool(B_1,B_2))) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.22 11 (all B_1 all B_2 gg_bool(aa_TPTP_ind_bool(B_1,B_2))) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 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].
% 0.88/1.23 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].
% 0.88/1.23 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].
% 0.88/1.23 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].
% 0.88/1.23 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].
% 0.88/1.23 17 (all X (pp(aa_TPTP_ind_bool(scratc232810230_prop1,X)) <-> pp(aa_bool_bool(scratc1564452034d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1695703371d_n_is,X),scratc135260400nd_n_1)),aa_fun171081125l_bool(scratc882471029n_some,aa_TPT43085870d_bool(aTP_Lamm_aa,X)))))) # label(fact_def__d__23__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 18 (all X (pp(aa_TPTP_ind_bool(scratc1791931703_prop1,X)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc993589771nd_nis,aa_TPTP_ind_TPTP_ind(scratc110611510rdsucc,X)),X)))) # label(fact_def__d__22__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 19 (all X (pp(aa_TPTP_ind_bool(scratc1773485891_cond2,X)) <-> pp(aa_fun171081125l_bool(scratc1020884000_n_all,aa_TPT43085870d_bool(aTP_Lamm_ac,X))))) # label(fact_def__cond2) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 20 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc993589771nd_nis,X),Xa)) <-> pp(scratc1703375356_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1695703371d_n_is,X),Xa))))) # label(fact_def__nis) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 21 (all X all Xa all Xb all Xc all Xd scratc863269300indeq2(X,Xa,Xb,Xc,Xd) = aa_TPT1424761345TP_ind(scratc1305284094_indeq(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc889509042d_11_i(X,Xa,Xb),Xc),Xd))) # label(fact_def__indeq2) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 22 (all X all Xa all Xb scratc889509042d_11_i(X,Xa,Xb) = scratc1305284094_indeq(X,Xa,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1035838736d_d_Pi,X),aTP_Lamm_ae(Xb)))) # label(fact_def__d__11__i) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 23 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1079759451fixfu2(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1027985579all_of(aa_TPT43085870d_bool(aTP_Lamm_af,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_aj(X),Xa),Xb),Xc))))) # label(fact_def__fixfu2) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 24 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1305284094_indeq(X,Xa,Xb),Xc),Xd) = scratc952610226nd_ind(Xb,aa_TPT43085870d_bool(scratc1758762754_prop2(X,Xa,Xb,Xc),Xd))) # label(fact_def__indeq) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 25 (all X all Xa all Xb all Xc all Xd all Xe (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1758762754_prop2(X,Xa,Xb,Xc),Xd),Xe)) <-> pp(aa_fun171081125l_bool(scratc138646387l_some(X),aa_TPT43085870d_bool(scratc1368495032_prop1(X,Xa,Xb,Xc,Xd),Xe))))) # label(fact_def__prop2) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 26 (all X all Xa all Xb all Xc all Xd all Xe all Xf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1368495032_prop1(X,Xa,Xb,Xc,Xd),Xe),Xf)) <-> pp(scratc1595910176_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1866517936d_esti(X),Xf),aa_TPTP_ind_TPTP_ind(scratc1053599947_ecect(X,Xa),Xd)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc29559362d_e_is(Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc585768252bnd_ap,Xc),Xf)),Xe))))) # label(fact_def__d__10__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 27 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc591401879_fixfu(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1027985579all_of(aa_TPT43085870d_bool(aTP_Lamm_af,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_al(X),Xa),Xb),Xc))))) # label(fact_def__fixfu) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 28 (all X all Xa scratc1053599947_ecect(X,Xa) = scratc29559357d_e_in(aa_TPTP_ind_TPTP_ind(scratc1629855320_power,X),scratc849361272d_anec(X,Xa))) # label(fact_def__ecect) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 29 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1476584100ectelt(X,Xa),Xb) = aa_TPTP_ind_TPTP_ind(scratc1591785977ectset(X,Xa),aa_TPTP_ind_TPTP_ind(scratc1054190338_ecelt(X,Xa),Xb))) # label(fact_def__ectelt) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 30 (all X all Xa scratc1591785977ectset(X,Xa) = scratc1002638465nd_out(aa_TPTP_ind_TPTP_ind(scratc1629855320_power,X),scratc849361272d_anec(X,Xa))) # label(fact_def__ectset) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 31 (all X all Xa scratc918842633nd_ect(X,Xa) = aa_fun1431113780TP_ind(scratc1479658727_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1629855320_power,X)),scratc849361272d_anec(X,Xa))) # label(fact_def__ect) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 32 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc849361272d_anec(X,Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc138646387l_some(X),aa_TPT43085870d_bool(scratc918842629nd_ecp(X,Xa),Xb))))) # label(fact_def__anec) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 33 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc918842629nd_ecp(X,Xa),Xb),Xc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc29559362d_e_is(aa_TPTP_ind_TPTP_ind(scratc1629855320_power,X)),Xb),aa_TPTP_ind_TPTP_ind(scratc1054190338_ecelt(X,Xa),Xc))))) # label(fact_def__ecp) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 34 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1054190338_ecelt(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc1479658727_d_Sep(X),aa_TPT43085870d_bool(Xa,Xb))) # label(fact_def__ecelt) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 35 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1697903323unmore(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc1479658727_d_Sep(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_an(X),Xa),Xb))) # label(fact_def__unmore) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 36 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2140343866etprop(X,Xa),Xb),Xc)) <-> pp(scratc1595910176_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1866517936d_esti(X),Xc),Xa),scratc1703375356_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1866517936d_esti(X),Xc),Xb)))))) # label(fact_def__nissetprop) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 37 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1391007658t_disj(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc886386996nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ao(X),Xa),Xb))))) # label(fact_def__st__disj) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 38 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc651476731d_incl(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc886386996nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ap(X),Xa),Xb))))) # label(fact_def__incl) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 39 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2131666605nempty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc138646387l_some(X),aa_TPT43085870d_bool(aTP_Lamm_aq(X),Xa))))) # label(fact_def__nonempty) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 40 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc361529088_empty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1027985579all_of(aa_TPT43085870d_bool(aTP_Lamm_af,X)),scratc993983360nd_non(X,aa_TPT43085870d_bool(aTP_Lamm_aq(X),Xa)))))) # label(fact_def__empty) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 41 (all X scratc1866517936d_esti(X) = scratc586293042bnd_in) # label(fact_def__esti) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 42 (all X all Xa (scratc1958730819d_r_ec(X,Xa) <-> (pp(X) -> pp(scratc1703375356_d_not(Xa))))) # label(fact_def__r__ec) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 43 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc1670301801hangef(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1810209806_Sigma,X),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_ar(X),Xb),Xc),Xd))) # label(fact_def__changef) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 44 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1459812774wissel(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1810209806_Sigma,X),scratc2079713553sel_wb(X,Xa,Xb))) # label(fact_def__wissel) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 45 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc2079713553sel_wb(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc953003821nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc29559362d_e_is(X),Xc),Xb),X,Xa),aa_TPTP_ind_TPTP_ind(scratc2079713552sel_wa(X,Xa,Xb),Xc))) # label(fact_def__wissel__wb) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 46 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc2079713552sel_wa(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc953003821nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc29559362d_e_is(X),Xc),Xa),X,Xb),Xc)) # label(fact_def__wissel__wa) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 47 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc953003821nd_ite(X,Xa,Xb),Xc) = scratc952610226nd_ind(Xa,aa_TPT43085870d_bool(scratc1758762753_prop1(X,Xa,Xb),Xc))) # label(fact_def__ite) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 48 (all X all Xa all Xb all Xc all Xd (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1758762753_prop1(X,Xa,Xb),Xc),Xd)) <-> pp(scratc1595910176_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc952544639nd_imp,X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc29559362d_e_is(Xa),Xd),Xb)),aa_bool_bool(aa_boo1142376798l_bool(scratc952544639nd_imp,scratc1703375356_d_not(X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc29559362d_e_is(Xa),Xd),Xc)))))) # label(fact_def__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 49 (all X all Xa scratc71545057second(X,Xa) = scratc1758369159_proj1) # label(fact_def__second) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 50 (all X all Xa scratc542685635_first(X,Xa) = scratc1758369158_proj0) # label(fact_def__first) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 51 (all X all Xa scratc1148113713d_pair(X,Xa) = scratc1713613863d_pair) # label(fact_def__d__pair) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 52 (all X all Xa scratc1002638465nd_out(X,Xa) = scratc2023356087d_soft(aa_fun1431113780TP_ind(scratc1479658727_d_Sep(X),Xa),X,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1810209806_Sigma,aa_fun1431113780TP_ind(scratc1479658727_d_Sep(X),Xa)),scratc29559357d_e_in(X,Xa)))) # label(fact_def__out) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 53 (all X all Xa all Xb (gg_TPTP_ind(Xb) -> aa_TPTP_ind_TPTP_ind(scratc29559357d_e_in(X,Xa),Xb) = Xb)) # label(fact_def__e__in) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 54 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc1201075440_inj_h(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1810209806_Sigma,X),aa_TPT1424761345TP_ind(aTP_Lamm_as(Xc),Xd))) # label(fact_def__inj__h) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 55 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc652723106d_invf(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1810209806_Sigma,Xa),scratc2023356087d_soft(X,Xa,Xb))) # label(fact_def__invf) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.23 56 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1752111640ective(X),Xa),Xb)) <-> pp(scratc1595910176_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1568392410ective(X),Xa),Xb),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1676089161ective(X),Xa),Xb))))) # label(fact_def__bijective) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 57 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1676089161ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc886386996nd_all(Xa),aa_TPT43085870d_bool(scratc500043566_image(X,Xa),Xb))))) # label(fact_def__surjective) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 58 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1656342851nverse(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1810209806_Sigma,Xa),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_at(X),Xa),Xb))) # label(fact_def__inverse) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 59 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc2023356087d_soft(X,Xa,Xb),Xc) = scratc952610226nd_ind(X,aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_au(Xa),Xb),Xc))) # label(fact_def__soft) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 60 (all X all Xa scratc656459637d_tofs(X,Xa) = scratc585768252bnd_ap) # label(fact_def__tofs) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 61 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc500043566_image(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc138646387l_some(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_au(Xa),Xb),Xc))))) # label(fact_def__image) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 62 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1568392410ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc886386996nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aw(X),Xa),Xb))))) # label(fact_def__injective) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 63 (all X all Xa scratc952610226nd_ind(X,Xa) = scratc919695419nd_eps(aa_fun1584354236d_bool(aTP_Lamm_ax(X),Xa))) # label(fact_def__ind) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 64 (all X all Xa (pp(aa_fun171081125l_bool(scratc1002179257nd_one(X),Xa)) <-> pp(scratc1595910176_d_and(scratc89584109_amone(X,Xa),aa_fun171081125l_bool(scratc138646387l_some(X),Xa))))) # label(fact_def__one) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 65 (all X all Xa (pp(scratc89584109_amone(X,Xa)) <-> pp(aa_fun171081125l_bool(scratc1027985579all_of(aa_TPT43085870d_bool(aTP_Lamm_af,X)),aa_fun1584354236d_bool(aTP_Lamm_az(X),Xa))))) # label(fact_def__amone) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 66 (all X scratc29559362d_e_is(X) = fequal_TPTP_ind) # label(fact_def__e__is) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 67 (all X all Xa all Xb (scratc535730629_orec3(X,Xa,Xb) <-> pp(scratc1595910176_d_and(scratc1002441603nd_or3(X,Xa,Xb),scratc918842568nd_ec3(X,Xa,Xb))))) # label(fact_def__orec3) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 68 (all X all Xa all Xb (pp(scratc918842568nd_ec3(X,Xa,Xb)) <-> scratc849295625d_and3(scratc1563796029d_l_ec(X,Xa),scratc1563796029d_l_ec(Xa,Xb),scratc1563796029d_l_ec(Xb,X)))) # label(fact_def__ec3) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 69 (all X all Xa all Xb (scratc849295625d_and3(X,Xa,Xb) <-> pp(scratc1595910176_d_and(X,scratc1595910176_d_and(Xa,Xb))))) # label(fact_def__and3) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 70 (all X all Xa all Xb (pp(scratc1002441603nd_or3(X,Xa,Xb)) <-> pp(aa_bool_bool(scratc1564452034d_l_or(X),aa_bool_bool(scratc1564452034d_l_or(Xa),Xb))))) # label(fact_def__or3) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 71 (all X all Xa (pp(aa_fun171081125l_bool(scratc138646387l_some(X),Xa)) <-> pp(scratc1703375356_d_not(aa_fun171081125l_bool(scratc1027985579all_of(aa_TPT43085870d_bool(aTP_Lamm_af,X)),scratc993983360nd_non(X,Xa)))))) # label(fact_def__l__some) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 72 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc993983360nd_non(X,Xa),Xb)) <-> pp(scratc1703375356_d_not(aa_TPTP_ind_bool(Xa,Xb))))) # label(fact_def__non) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 73 (all X scratc886386996nd_all(X) = scratc1027985579all_of(aa_TPT43085870d_bool(aTP_Lamm_af,X))) # label(fact_def__all) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 74 (all X all Xa (scratc342567978_l_iff(X,Xa) <-> pp(scratc1595910176_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc952544639nd_imp,X),Xa),aa_bool_bool(aa_boo1142376798l_bool(scratc952544639nd_imp,Xa),X))))) # label(fact_def__l__iff) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 75 (all X all Xa (scratc1073209838d_orec(X,Xa) <-> pp(scratc1595910176_d_and(aa_bool_bool(scratc1564452034d_l_or(X),Xa),scratc1563796029d_l_ec(X,Xa))))) # label(fact_def__orec) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 76 (all X scratc1564452034d_l_or(X) = aa_boo1142376798l_bool(scratc952544639nd_imp,scratc1703375356_d_not(X))) # label(fact_def__l__or) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 77 (all X all Xa (pp(scratc1595910176_d_and(X,Xa)) <-> pp(scratc1703375356_d_not(scratc1563796029d_l_ec(X,Xa))))) # label(fact_def__d__and) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 78 (all X all Xa (pp(scratc1563796029d_l_ec(X,Xa)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc952544639nd_imp,X),scratc1703375356_d_not(Xa))))) # label(fact_def__l__ec) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 79 scratc373941850bvious <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc952544639nd_imp,fFalse),fFalse)) # label(fact_def__obvious) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 80 (all X (scratc1067680913nd_wel(X) <-> pp(scratc1703375356_d_not(scratc1703375356_d_not(X))))) # label(fact_def__wel) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 81 (all X (pp(scratc1703375356_d_not(X)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc952544639nd_imp,X),fFalse)))) # label(fact_def__d__not) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 82 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1035838736d_d_Pi,X),Xa) = aa_fun1431113780TP_ind(scratc1479658727_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1629855320_power,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1810209806_Sigma,X),aTP_Lamm_ba(Xa)))),aa_fun1913827119d_bool(aTP_Lamm_bb(X),Xa))) # label(fact_def__d__Pi) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 83 (all X (gg_TPTP_ind(X) -> (pp(aa_TPTP_ind_bool(scratc2114845129pair_p,X)) <-> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1713613863d_pair,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc585768252bnd_ap,X),scratc1846071618ptyset)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc585768252bnd_ap,X),aa_TPTP_ind_TPTP_ind(scratc110611510rdsucc,scratc1846071618ptyset))) = X))) # label(fact_def__pair__p) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 84 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc585768252bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc556320792eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bc,Xa)),scratc1758369159_proj1)) # label(fact_def__ap) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 85 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1892018252etprod(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1810209806_Sigma,X),aTP_Lamm_ae(Xa))) # label(fact_def__setprod) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 86 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1810209806_Sigma,X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc64028522munion,X),aTP_Lamm_bd(Xa))) # label(fact_def__d__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 87 (all X aa_TPTP_ind_TPTP_ind(scratc1758369159_proj1,X) = aa_fun277296641TP_ind(scratc556320792eplSep(X,aTP_Lamm_be),scratc1496772122_d_Unj)) # label(fact_def__proj1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 88 (all X aa_TPTP_ind_TPTP_ind(scratc1758369158_proj0,X) = aa_fun277296641TP_ind(scratc556320792eplSep(X,aTP_Lamm_bf),scratc1496772122_d_Unj)) # label(fact_def__proj0) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 89 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1713613863d_pair,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1057885621nunion(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1160809820d_repl,X),scratc877449122d_Inj0)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1160809820d_repl,Xa),scratc877449123d_Inj1))) # label(fact_def__pair) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 90 (all X aa_TPTP_ind_TPTP_ind(scratc877449122d_Inj0,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1160809820d_repl,X),scratc877449123d_Inj1)) # label(fact_def__d__Inj0) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 91 (all X (pp(aa_TPTP_ind_bool(scratc347615132_nat_p,X)) <-> (all X1 (pp(aa_TPTP_ind_bool(X1,scratc1846071618ptyset)) -> ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(X1,X2)) -> pp(aa_TPTP_ind_bool(X1,aa_TPTP_ind_TPTP_ind(scratc110611510rdsucc,X2)))))) -> pp(aa_TPTP_ind_bool(X1,X))))))) # label(fact_def__nat__p) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 92 (all X aa_TPTP_ind_TPTP_ind(scratc110611510rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1057885621nunion(X),aa_TPTP_ind_TPTP_ind(scratc52341446d_Sing,X))) # label(fact_def__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 93 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc284084372In_rec(X),Xa) = scratc919695419nd_eps(aa_TPT43085870d_bool(scratc1774108403_rec_G(X),Xa))) # label(fact_def__d__In__rec) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 94 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1774108403_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(scratc586293042bnd_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].
% 0.92/1.23 95 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc974171163tminus(X),Xa) = aa_fun1431113780TP_ind(scratc1479658727_d_Sep(X),aa_TPT43085870d_bool(aTP_Lamm_bi,Xa))) # label(fact_def__setminus) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 96 (all X all Xa scratc556320792eplSep(X,Xa) = aa_TPT494704832TP_ind(scratc1160809820d_repl,aa_fun1431113780TP_ind(scratc1479658727_d_Sep(X),Xa))) # label(fact_def__d__ReplSep) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 97 (all X all Xa aa_fun1431113780TP_ind(scratc1479658727_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc586293034bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc586293042bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1160809820d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bj(X),Xa))),scratc1846071618ptyset)) # label(fact_def__d__Sep) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 98 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc64028522munion,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc2137117186_union,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1160809820d_repl,X),Xa))) # label(fact_def__famunion) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 99 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1057885621nunion(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc2137117186_union,aa_TPTP_ind_TPTP_ind(scratc1704696184_UPair(X),Xa))) # label(fact_def__binunion) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 100 (all X aa_TPTP_ind_TPTP_ind(scratc52341446d_Sing,X) = aa_TPTP_ind_TPTP_ind(scratc1704696184_UPair(X),X)) # label(fact_def__d__Sing) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 101 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1704696184_UPair(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1160809820d_repl,aa_TPTP_ind_TPTP_ind(scratc1629855320_power,aa_TPTP_ind_TPTP_ind(scratc1629855320_power,scratc1846071618ptyset))),aa_TPT1424761345TP_ind(aTP_Lamm_bk(X),Xa))) # label(fact_def__d__UPair) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 102 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc991490598nd_nIn,X),Xa)) <-> -pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X),Xa)))) # label(fact_def__nIn) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 103 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc586293034bnd_if(X,Xa),Xb) = scratc919695419nd_eps(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bl(X),Xa),Xb))) # label(fact_def__if) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 104 (all X (pp(aa_TPTP_ind_bool(scratc2072632303closed,X)) <-> pp(aa_TPTP_ind_bool(scratc2109315044closed,X)) & pp(aa_TPTP_ind_bool(scratc126564410closed,X)) & pp(aa_TPTP_ind_bool(scratc499043090closed,X)))) # label(fact_def__d__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 105 (all X (pp(aa_TPTP_ind_bool(scratc499043090closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X1),X)) -> (all X2 ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X3),X1)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,aa_TPTP_ind_TPTP_ind(X2,X3)),X))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1160809820d_repl,X1),X2)),X))))))))) # label(fact_def__d__Repl__closed) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 106 (all X (pp(aa_TPTP_ind_bool(scratc126564410closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,aa_TPTP_ind_TPTP_ind(scratc1629855320_power,X1)),X))))))) # label(fact_def__d__Power__closed) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 107 (all X (pp(aa_TPTP_ind_bool(scratc2109315044closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,aa_TPTP_ind_TPTP_ind(scratc2137117186_union,X1)),X))))))) # label(fact_def__d__Union__closed) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 108 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc150692328d_Subq,X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X2),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X2),Xa))))))) # label(fact_def__d__Subq) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 109 (all X all Xa (pp(aa_fun171081125l_bool(scratc1027985579all_of(X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (scratc460970926_is_of(X2,X) -> pp(aa_TPTP_ind_bool(Xa,X2))))))) # label(fact_def__all__of) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 110 (all X all Xa (scratc460970926_is_of(X,Xa) <-> pp(aa_TPTP_ind_bool(Xa,X)))) # label(fact_def__is__of) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 111 (all X0 pp(aa_fun171081125l_bool(scratc1027985579all_of(aa_TPT43085870d_bool(aTP_Lamm_bx,X0)),aa_TPT43085870d_bool(aTP_Lamm_bz,X0)))) # label(fact_isseti) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 112 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1027985579all_of(aa_TPT43085870d_bool(aTP_Lamm_af,X0)),aa_fun1584354236d_bool(aTP_Lamm_ca(X0),X12)))) # label(fact_estie) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 113 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1027985579all_of(aa_TPT43085870d_bool(aTP_Lamm_af,X0)),aa_fun1584354236d_bool(aTP_Lamm_cb(X0),X12)))) # label(fact_estii) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 114 (all X0 all X12 scratc460970926_is_of(aa_fun1431113780TP_ind(scratc1479658727_d_Sep(X0),X12),aa_TPT43085870d_bool(aTP_Lamm_bx,X0))) # label(fact_setof__p) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 115 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1027985579all_of(aa_TPT43085870d_bool(aTP_Lamm_af,X0)),aa_TPT43085870d_bool(aTP_Lamm_cd(X0),X12)))) # label(fact_secondis1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 116 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1027985579all_of(aa_TPT43085870d_bool(aTP_Lamm_af,X0)),aa_TPT43085870d_bool(aTP_Lamm_cf(X0),X12)))) # label(fact_firstis1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 117 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1027985579all_of(aa_TPT43085870d_bool(aTP_Lamm_cg(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_ch(X0),X12)))) # label(fact_pairis1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 118 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1027985579all_of(aa_TPT43085870d_bool(aTP_Lamm_cg(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_ci(X0),X12)))) # label(fact_second__p) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 119 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1027985579all_of(aa_TPT43085870d_bool(aTP_Lamm_cg(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_cj(X0),X12)))) # label(fact_first__p) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 120 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1027985579all_of(aa_TPT43085870d_bool(aTP_Lamm_af,X0)),aa_TPT43085870d_bool(aTP_Lamm_cl(X0),X12)))) # label(fact_e__pair__p) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 121 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1027985579all_of(aa_TPT43085870d_bool(aTP_Lamm_af,X0)),aa_fun1584354236d_bool(aTP_Lamm_cm(X0),X12)))) # label(fact_otax2) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 122 (all X0 all X12 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1568392410ective(aa_fun1431113780TP_ind(scratc1479658727_d_Sep(X0),X12)),X0),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1810209806_Sigma,aa_fun1431113780TP_ind(scratc1479658727_d_Sep(X0),X12)),scratc29559357d_e_in(X0,X12))))) # label(fact_otax1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 123 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1027985579all_of(aa_fun1584354236d_bool(aTP_Lamm_cn(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_co(X0),X12)))) # label(fact_e__inp) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 124 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1027985579all_of(aa_fun1584354236d_bool(aTP_Lamm_cn(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_cp(X0),X12)))) # label(fact_e__in__p) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 125 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1027985579all_of(aa_TPT43085870d_bool(aTP_Lamm_cq(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_ct(X0),X12)))) # label(fact_e__fisi) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 126 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc1002179257nd_one(X0),X12)) -> pp(aa_TPTP_ind_bool(X12,scratc952610226nd_ind(X0,X12))))) # label(fact_oneax) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 127 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc1002179257nd_one(X0),X12)) -> scratc460970926_is_of(scratc952610226nd_ind(X0,X12),aa_TPT43085870d_bool(aTP_Lamm_af,X0)))) # label(fact_ind__p) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 128 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1027985579all_of(aa_TPT43085870d_bool(aTP_Lamm_af,X0)),aa_fun1584354236d_bool(aTP_Lamm_cv(X0),X12)))) # label(fact_e__isp) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 129 (all X0 pp(aa_fun171081125l_bool(scratc1027985579all_of(aa_TPT43085870d_bool(aTP_Lamm_af,X0)),aa_TPT43085870d_bool(aTP_Lamm_cw,X0)))) # label(fact_refis) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 130 (all X0 (scratc1067680913nd_wel(X0) -> pp(X0))) # label(fact_l__et) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 131 (all X0 all X12 all X22 all X32 (pp(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc586293034bnd_if(X0,X22),X32))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X12),X22))))) # label(fact_k__If__In__then__E) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 132 (all X0 all X12 all X22 ((pp(X0) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X12),X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,aa_TPTP_ind_TPTP_ind(scratc586293034bnd_if(X0,X12),scratc1846071618ptyset)),aa_TPTP_ind_TPTP_ind(scratc586293034bnd_if(X0,X22),aa_TPTP_ind_TPTP_ind(scratc110611510rdsucc,scratc1846071618ptyset)))))) # label(fact_k__If__In__01) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 133 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X33),X0)) -> aa_TPTP_ind_TPTP_ind(X12,X33) = aa_TPTP_ind_TPTP_ind(X22,X33)))) -> aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1810209806_Sigma,X0),X12) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1810209806_Sigma,X0),X22))) # label(fact_xi__ext) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 134 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1035838736d_d_Pi,X0),X12))) -> (all X32 (gg_TPTP_ind(X32) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X32),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1035838736d_d_Pi,X0),X12))) -> ((all X42 (gg_TPTP_ind(X42) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X42),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc585768252bnd_ap,X22),X42) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc585768252bnd_ap,X32),X42)))) -> X22 = X32))))))) # label(fact_k__Pi__ext) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 135 (all X0 all X12 all X22 all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1035838736d_d_Pi,X0),X12))) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X32),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc585768252bnd_ap,X22),X32)),aa_TPTP_ind_TPTP_ind(X12,X32)))))) # label(fact_ap__Pi) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 136 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X33),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,aa_TPTP_ind_TPTP_ind(X22,X33)),aa_TPTP_ind_TPTP_ind(X12,X33)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1810209806_Sigma,X0),X22)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1035838736d_d_Pi,X0),X12))))) # label(fact_lam__Pi) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 137 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X22),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc585768252bnd_ap,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1810209806_Sigma,X0),X12)),X22) = aa_TPTP_ind_TPTP_ind(X12,X22))) # label(fact_beta) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 138 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1810209806_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,aa_TPTP_ind_TPTP_ind(scratc1758369159_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1758369158_proj0,X22)))))) # label(fact_proj1__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 139 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1810209806_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,aa_TPTP_ind_TPTP_ind(scratc1758369158_proj0,X22)),X0)))) # label(fact_proj0__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 140 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1810209806_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1713613863d_pair,aa_TPTP_ind_TPTP_ind(scratc1758369158_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1758369159_proj1,X22)) = X22))) # label(fact_proj__Sigma__eta) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 141 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1810209806_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1713613863d_pair,aa_TPTP_ind_TPTP_ind(scratc1758369158_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1758369159_proj1,X22)) = X22 & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,aa_TPTP_ind_TPTP_ind(scratc1758369158_proj0,X22)),X0)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,aa_TPTP_ind_TPTP_ind(scratc1758369159_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1758369158_proj0,X22))))))) # label(fact_k__Sigma__eta__proj0__proj1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 142 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X22),X0)) -> (all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X32),aa_TPTP_ind_TPTP_ind(X12,X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1713613863d_pair,X22),X32)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1810209806_Sigma,X0),X12))))))) # label(fact_pair__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 143 (all X0 all X12 (gg_TPTP_ind(X12) -> aa_TPTP_ind_TPTP_ind(scratc1758369159_proj1,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1713613863d_pair,X0),X12)) = X12)) # label(fact_proj1__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 144 (all X0 all X12 (gg_TPTP_ind(X0) -> aa_TPTP_ind_TPTP_ind(scratc1758369158_proj0,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1713613863d_pair,X0),X12)) = X0)) # label(fact_proj0__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 145 (all X0 (pp(aa_TPTP_ind_bool(scratc347615132_nat_p,X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X0),scratc928024372_omega)))) # label(fact_nat__p__omega) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 146 (all X0 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X0),scratc928024372_omega)) -> pp(aa_TPTP_ind_bool(scratc347615132_nat_p,X0)))) # label(fact_omega__nat__p) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 147 (all X0 (gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(scratc347615132_nat_p,X0)) -> X0 = scratc1846071618ptyset | (exists X13 (gg_TPTP_ind(X13) & pp(aa_TPTP_ind_bool(scratc347615132_nat_p,X13)) & X0 = aa_TPTP_ind_TPTP_ind(scratc110611510rdsucc,X13)))))) # label(fact_nat__inv) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 148 (all X0 (pp(aa_TPTP_ind_bool(X0,scratc1846071618ptyset)) -> ((all X13 (gg_TPTP_ind(X13) -> (pp(aa_TPTP_ind_bool(scratc347615132_nat_p,X13)) -> (pp(aa_TPTP_ind_bool(X0,X13)) -> pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc110611510rdsucc,X13))))))) -> (all X12 (pp(aa_TPTP_ind_bool(scratc347615132_nat_p,X12)) -> pp(aa_TPTP_ind_bool(X0,X12))))))) # label(fact_nat__ind) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 149 (all X0 (pp(aa_TPTP_ind_bool(scratc347615132_nat_p,X0)) -> pp(aa_TPTP_ind_bool(scratc347615132_nat_p,aa_TPTP_ind_TPTP_ind(scratc110611510rdsucc,X0))))) # label(fact_nat__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 150 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (aa_TPTP_ind_TPTP_ind(scratc110611510rdsucc,X0) = aa_TPTP_ind_TPTP_ind(scratc110611510rdsucc,X12) -> X0 = X12))) # label(fact_ordsucc__inj) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 151 (all X0 aa_TPTP_ind_TPTP_ind(scratc110611510rdsucc,X0) != scratc1846071618ptyset) # label(fact_neq__ordsucc__0) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 152 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X22),aa_fun1431113780TP_ind(scratc1479658727_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(X12,X22)))) # label(fact_k__SepE2) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 153 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X22),aa_fun1431113780TP_ind(scratc1479658727_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X22),X0)))) # label(fact_k__SepE1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 154 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X22),X0)) -> (pp(aa_TPTP_ind_bool(X12,X22)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X22),aa_fun1431113780TP_ind(scratc1479658727_d_Sep(X0),X12)))))) # label(fact_k__SepI) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 155 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc1629855320_power,X0)))) # label(fact_k__Self__In__Power) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 156 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc150692328d_Subq,X12),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1629855320_power,X0))))) # label(fact_k__PowerI) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 157 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1629855320_power,X0))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc150692328d_Subq,X12),X0)))) # label(fact_k__PowerE) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 158 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> aa_TPTP_ind_TPTP_ind(scratc586293034bnd_if(X0,X12),X22) = X12 | aa_TPTP_ind_TPTP_ind(scratc586293034bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__or) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 159 (all X0 all X12 all X22 (gg_TPTP_ind(X12) -> (pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc586293034bnd_if(X0,X12),X22) = X12))) # label(fact_if__i__1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 160 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (-pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc586293034bnd_if(X0,X12),X22) = X22))) # label(fact_if__i__0) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 161 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> pp(X0) & aa_TPTP_ind_TPTP_ind(scratc586293034bnd_if(X0,X12),X22) = X12 | -pp(X0) & aa_TPTP_ind_TPTP_ind(scratc586293034bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__correct) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 162 (all X0 pp(aa_TPTP_ind_bool(scratc2072632303closed,aa_TPTP_ind_TPTP_ind(scratc780671914univof,X0)))) # label(fact_k__UnivOf__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 163 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc780671914univof,X0)))) # label(fact_k__UnivOf__In) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 164 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1160809820d_repl,X0),X12))) <-> (exists X3 (gg_TPTP_ind(X3) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X3),X0)) & X22 = aa_TPTP_ind_TPTP_ind(X12,X3)))))) # label(fact_k__ReplEq) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 165 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1629855320_power,X0))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc150692328d_Subq,X12),X0)))) # label(fact_k__PowerEq) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 166 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc2137117186_union,X0))) <-> (exists X2 (gg_TPTP_ind(X2) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X12),X2)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X2),X0)))))) # label(fact_k__UnionEq) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 167 -(exists X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X0),scratc1846071618ptyset))) # label(fact_k__EmptyAx) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 168 (all X0 ((all X13 (gg_TPTP_ind(X13) -> ((all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_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].
% 0.92/1.24 169 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc150692328d_Subq,X0),X12)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc150692328d_Subq,X12),X0)) -> X0 = X12)))) # label(fact_set__ext) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 170 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bm,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc993589771nd_nis,Uu),scratc135260400nd_n_1)) -> pp(aa_fun171081125l_bool(scratc882471029n_some,aa_TPT43085870d_bool(aTP_Lamm_aa,Uu)))))) # label(fact_ATP_Olambda__1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 171 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ab,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc993589771nd_nis,Uu),scratc135260400nd_n_1)) -> pp(aa_fun171081125l_bool(scratc1136676261_n_one,aa_TPT43085870d_bool(aTP_Lamm_aa,Uu)))))) # label(fact_ATP_Olambda__2) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 172 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bs,Uu)) <-> (pp(aa_TPTP_ind_bool(scratc1773485890_cond1,Uu)) -> (pp(aa_TPTP_ind_bool(scratc1773485891_cond2,Uu)) -> pp(aa_fun171081125l_bool(scratc1027985579all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_br,Uu))))))) # label(fact_ATP_Olambda__3) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 173 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bn,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc993589771nd_nis,aa_TPTP_ind_TPTP_ind(scratc110611510rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__4) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 174 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bw,Uu)) <-> scratc460970926_is_of(aa_TPTP_ind_TPTP_ind(scratc110611510rdsucc,Uu),aTP_Lamm_a))) # label(fact_ATP_Olambda__5) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 175 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bv,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc993589771nd_nis,aa_TPTP_ind_TPTP_ind(scratc110611510rdsucc,Uu)),scratc135260400nd_n_1)))) # label(fact_ATP_Olambda__6) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 176 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,Uu),aa_TPTP_ind_TPTP_ind(scratc1629855320_power,scratc993064980nd_nat))))) # label(fact_ATP_Olambda__7) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 177 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_a,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,Uu),scratc993064980nd_nat)))) # label(fact_ATP_Olambda__8) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 178 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu)) <-> pp(aa_fun171081125l_bool(scratc1027985579all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bt,Uu))))) # label(fact_ATP_Olambda__9) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 179 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bp,Uu)) <-> pp(aa_fun171081125l_bool(scratc1027985579all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bo,Uu))))) # label(fact_ATP_Olambda__10) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 180 (all Uu aa_TPT494704832TP_ind(aTP_Lamm_bg,Uu) = aa_TPT494704832TP_ind(scratc1160809820d_repl,aa_TPTP_ind_TPTP_ind(scratc974171163tminus(Uu),aa_TPTP_ind_TPTP_ind(scratc52341446d_Sing,scratc1846071618ptyset)))) # label(fact_ATP_Olambda__11) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 181 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_ad,Uu)) <-> Uu != scratc1846071618ptyset))) # label(fact_ATP_Olambda__12) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 182 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_be,Uu)) <-> (exists X2 (gg_TPTP_ind(X2) & aa_TPTP_ind_TPTP_ind(scratc877449123d_Inj1,X2) = Uu))))) # label(fact_ATP_Olambda__13) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 183 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_bf,Uu)) <-> (exists X2 (gg_TPTP_ind(X2) & aa_TPTP_ind_TPTP_ind(scratc877449122d_Inj0,X2) = Uu))))) # label(fact_ATP_Olambda__14) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 184 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cw,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc29559362d_e_is(Uu),Uua),Uua)))) # label(fact_ATP_Olambda__15) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 185 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bt,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1695703371d_n_is,aa_TPTP_ind_TPTP_ind(scratc110611510rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc110611510rdsucc,Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1695703371d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__16) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 186 (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(scratc993589771nd_nis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc993589771nd_nis,aa_TPTP_ind_TPTP_ind(scratc110611510rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc110611510rdsucc,Uua)))))) # label(fact_ATP_Olambda__17) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 187 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ac,Uu),Uua)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc952544639nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1695703366d_n_in,Uua),Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1695703366d_n_in,aa_TPTP_ind_TPTP_ind(scratc110611510rdsucc,Uua)),Uu))))) # label(fact_ATP_Olambda__18) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 188 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bd(Uu),Uua) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1160809820d_repl,aa_TPTP_ind_TPTP_ind(Uu,Uua)),aa_TPT1424761345TP_ind(scratc1713613863d_pair,Uua))) # label(fact_ATP_Olambda__19) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 189 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bz,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1027985579all_of(aa_TPT43085870d_bool(aTP_Lamm_bx,Uu)),aa_TPT43085870d_bool(aTP_Lamm_by(Uu),Uua))))) # label(fact_ATP_Olambda__20) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 190 (all Uu all Uua aa_fun277296641TP_ind(aa_TPT494704832TP_ind(aTP_Lamm_bh,Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1057885621nunion(aa_TPTP_ind_TPTP_ind(scratc52341446d_Sing,scratc1846071618ptyset)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1160809820d_repl,Uu),Uua))) # label(fact_ATP_Olambda__21) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 191 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1695703371d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc110611510rdsucc,Uua))))) # label(fact_ATP_Olambda__22) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 192 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bx,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,Uua),aa_TPTP_ind_TPTP_ind(scratc1629855320_power,Uu))))) # label(fact_ATP_Olambda__23) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 193 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_br,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1695703366d_n_in,Uua),Uu)))) # label(fact_ATP_Olambda__24) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 194 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bi,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc991490598nd_nIn,Uua),Uu)))) # label(fact_ATP_Olambda__25) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 195 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_af,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,Uua),Uu)))) # label(fact_ATP_Olambda__26) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 196 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_ba(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc2137117186_union,aa_TPTP_ind_TPTP_ind(Uu,Uua))) # label(fact_ATP_Olambda__27) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 197 (all Uu all Uua (gg_TPTP_ind(Uua) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bc,Uu),Uua)) <-> (exists X3 (gg_TPTP_ind(X3) & Uua = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1713613863d_pair,Uu),X3)))))) # label(fact_ATP_Olambda__28) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 198 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ch(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc29559362d_e_is(aa_TPTP_ind_TPTP_ind(scratc1892018252etprod(Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1148113713d_pair(Uu,Uua),aa_TPTP_ind_TPTP_ind(scratc542685635_first(Uu,Uua),Uub)),aa_TPTP_ind_TPTP_ind(scratc71545057second(Uu,Uua),Uub))),Uub)))) # label(fact_ATP_Olambda__29) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 199 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_bk(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc586293034bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,scratc1846071618ptyset),Uub),Uu),Uua)) # label(fact_ATP_Olambda__30) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 200 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_fun1235454963TP_ind(aTP_Lamm_bj(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc586293034bnd_if(aa_TPTP_ind_bool(Uua,Uub),Uub),scratc919695419nd_eps(aa_fun1584354236d_bool(aTP_Lamm_ax(Uu),Uua)))) # label(fact_ATP_Olambda__31) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 201 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aq(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1866517936d_esti(Uu),Uub),Uua)))) # label(fact_ATP_Olambda__32) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 202 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ca(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1866517936d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc1479658727_d_Sep(Uu),Uua))) -> pp(aa_TPTP_ind_bool(Uua,Uub))))) # label(fact_ATP_Olambda__33) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 203 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_by(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc651476731d_incl(Uu),Uua),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc651476731d_incl(Uu),Uub),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc29559362d_e_is(aa_TPTP_ind_TPTP_ind(scratc1629855320_power,Uu)),Uua),Uub)))))) # label(fact_ATP_Olambda__34) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 204 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ci(Uu),Uua),Uub)) <-> scratc460970926_is_of(aa_TPTP_ind_TPTP_ind(scratc71545057second(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_af,Uua)))) # label(fact_ATP_Olambda__35) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 205 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cj(Uu),Uua),Uub)) <-> scratc460970926_is_of(aa_TPTP_ind_TPTP_ind(scratc542685635_first(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_af,Uu)))) # label(fact_ATP_Olambda__36) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 206 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_cp(Uu),Uua),Uub)) <-> scratc460970926_is_of(aa_TPTP_ind_TPTP_ind(scratc29559357d_e_in(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_af,Uu)))) # label(fact_ATP_Olambda__37) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 207 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ct(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1027985579all_of(aa_TPT43085870d_bool(aTP_Lamm_cq(Uu),Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cs(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__38) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 208 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ax(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,Uub),Uu)) & pp(aa_TPTP_ind_bool(Uua,Uub)))) # label(fact_ATP_Olambda__39) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 209 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_cm(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc500043566_image(aa_fun1431113780TP_ind(scratc1479658727_d_Sep(Uu),Uua),Uu),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1810209806_Sigma,aa_fun1431113780TP_ind(scratc1479658727_d_Sep(Uu),Uua)),scratc29559357d_e_in(Uu,Uua))),Uub))))) # label(fact_ATP_Olambda__40) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 210 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_cb(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1866517936d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc1479658727_d_Sep(Uu),Uua)))))) # label(fact_ATP_Olambda__41) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 211 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_cv(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1027985579all_of(aa_TPT43085870d_bool(aTP_Lamm_af,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_cu(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__42) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 212 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_az(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1027985579all_of(aa_TPT43085870d_bool(aTP_Lamm_af,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_ay(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__43) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 213 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cl(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1027985579all_of(aa_TPT43085870d_bool(aTP_Lamm_af,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ck(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__44) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 214 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cf(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1027985579all_of(aa_TPT43085870d_bool(aTP_Lamm_af,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ce(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__45) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 215 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cd(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1027985579all_of(aa_TPT43085870d_bool(aTP_Lamm_af,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cc(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__46) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 216 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cq(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,Uub),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1035838736d_d_Pi,Uu),aTP_Lamm_ae(Uua)))))) # label(fact_ATP_Olambda__47) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 217 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cg(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,Uub),aa_TPTP_ind_TPTP_ind(scratc1892018252etprod(Uu),Uua))))) # label(fact_ATP_Olambda__48) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 218 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_cn(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,Uub),aa_fun1431113780TP_ind(scratc1479658727_d_Sep(Uu),Uua))))) # label(fact_ATP_Olambda__49) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 219 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_as(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc585768252bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc585768252bnd_ap,Uu),Uub))) # label(fact_ATP_Olambda__50) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 220 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_co(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(Uua,aa_TPTP_ind_TPTP_ind(scratc29559357d_e_in(Uu,Uua),Uub))))) # label(fact_ATP_Olambda__51) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 221 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1913827119d_bool(aTP_Lamm_bb(Uu),Uua),Uub)) <-> (all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,X3),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc586293042bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc585768252bnd_ap,Uub),X3)),aa_TPTP_ind_TPTP_ind(Uua,X3)))))))) # label(fact_ATP_Olambda__52) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 222 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_at(Uu),Uua),Uub),Uuc) = aa_TPTP_ind_TPTP_ind(scratc586293034bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc500043566_image(Uu,Uua),Uub),Uuc),aa_TPTP_ind_TPTP_ind(scratc2023356087d_soft(Uu,Uua,Uub),Uuc)),scratc1846071618ptyset)) # label(fact_ATP_Olambda__53) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 223 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ce(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc29559362d_e_is(Uu),aa_TPTP_ind_TPTP_ind(scratc542685635_first(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1148113713d_pair(Uu,Uua),Uub),Uuc))),Uub)))) # label(fact_ATP_Olambda__54) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 224 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cc(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc29559362d_e_is(Uua),aa_TPTP_ind_TPTP_ind(scratc71545057second(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1148113713d_pair(Uu,Uua),Uub),Uuc))),Uuc)))) # label(fact_ATP_Olambda__55) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 225 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cr(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc29559362d_e_is(Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc585768252bnd_ap,Uua),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc585768252bnd_ap,Uub),Uuc))))) # label(fact_ATP_Olambda__56) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 226 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_am(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1866517936d_esti(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc585768252bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__57) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 227 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_au(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc29559362d_e_is(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc585768252bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__58) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 228 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ck(Uu),Uua),Uub),Uuc)) <-> scratc460970926_is_of(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1148113713d_pair(Uu,Uua),Uub),Uuc),aa_TPT43085870d_bool(aTP_Lamm_cg(Uu),Uua)))) # label(fact_ATP_Olambda__59) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 229 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ao(Uu),Uua),Uub),Uuc)) <-> pp(scratc1563796029d_l_ec(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1866517936d_esti(Uu),Uuc),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1866517936d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__60) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 230 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ap(Uu),Uua),Uub),Uuc)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc952544639nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1866517936d_esti(Uu),Uuc),Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1866517936d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__61) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 231 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cs(Uu),Uua),Uub),Uuc)) <-> (pp(aa_fun171081125l_bool(scratc1027985579all_of(aa_TPT43085870d_bool(aTP_Lamm_af,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cr(Uua),Uub),Uuc))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc29559362d_e_is(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1035838736d_d_Pi,Uu),aTP_Lamm_ae(Uua))),Uub),Uuc))))) # label(fact_ATP_Olambda__62) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 232 (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_bl(Uu),Uua),Uub),Uuc)) <-> pp(Uu) & Uuc = Uua | -pp(Uu) & Uuc = Uub))) # label(fact_ATP_Olambda__63) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 233 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_cu(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc29559362d_e_is(Uu),Uub),Uuc)) -> pp(aa_TPTP_ind_bool(Uua,Uuc)))))) # label(fact_ATP_Olambda__64) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 234 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_ay(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(scratc29559362d_e_is(Uu),Uub),Uuc)))))) # label(fact_ATP_Olambda__65) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 235 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aw(Uu),Uua),Uub),Uuc)) <-> pp(aa_fun171081125l_bool(scratc886386996nd_all(Uu),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_av(Uu),Uua),Uub),Uuc))))) # label(fact_ATP_Olambda__66) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 236 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_an(Uu),Uua),Uub),Uuc)) <-> pp(aa_fun171081125l_bool(scratc138646387l_some(Uua),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_am(Uu),Uub),Uuc))))) # label(fact_ATP_Olambda__67) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 237 (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_av(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc952544639nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc29559362d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc585768252bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc585768252bnd_ap,Uub),Uud))),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc29559362d_e_is(Uu),Uuc),Uud))))) # label(fact_ATP_Olambda__68) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 238 (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_ak(Uu),Uua),Uub),Uuc),Uud)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc29559362d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc585768252bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc585768252bnd_ap,Uub),Uud)))))) # label(fact_ATP_Olambda__69) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 239 (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_aj(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_fun171081125l_bool(scratc1027985579all_of(aa_TPT43085870d_bool(aTP_Lamm_af,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_ai(Uu),Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__70) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 240 (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_al(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_fun171081125l_bool(scratc1027985579all_of(aa_TPT43085870d_bool(aTP_Lamm_af,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_ak(Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__71) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 241 (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_ar(Uu),Uua),Uub),Uuc),Uud) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc585768252bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc585768252bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1459812774wissel(Uu,Uub),Uuc)),Uud))) # label(fact_ATP_Olambda__72) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 242 (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_ai(Uu),Uua),Uub),Uuc),Uud),Uue)) <-> pp(aa_fun171081125l_bool(scratc1027985579all_of(aa_TPT43085870d_bool(aTP_Lamm_af,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_ah(Uu),Uua),Uub),Uuc),Uud),Uue))))) # label(fact_ATP_Olambda__73) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 243 (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_ag(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(scratc29559362d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc585768252bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc585768252bnd_ap,Uub),Uuc)),Uue)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc585768252bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc585768252bnd_ap,Uub),Uud)),Uuf))))))) # label(fact_ATP_Olambda__74) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 244 (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_ah(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)) <-> pp(aa_fun171081125l_bool(scratc1027985579all_of(aa_TPT43085870d_bool(aTP_Lamm_af,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_ag(Uua),Uub),Uuc),Uud),Uue),Uuf))))) # label(fact_ATP_Olambda__75) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 245 (all Uu all Uua (gg_TPTP_ind(Uu) -> aa_TPTP_ind_TPTP_ind(aTP_Lamm_ae(Uu),Uua) = Uu)) # label(fact_ATP_Olambda__76) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 246 (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].
% 0.92/1.24 247 (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].
% 0.92/1.24 248 (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].
% 0.92/1.24 249 (all P (gg_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 250 (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].
% 0.92/1.24 251 (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].
% 0.92/1.24 252 (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].
% 0.92/1.24 253 (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].
% 0.92/1.24 254 (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].
% 0.92/1.24 255 (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].
% 0.92/1.24 256 (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].
% 0.92/1.26 257 (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].
% 0.92/1.26 258 (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].
% 0.92/1.26
% 0.92/1.26 ============================== end of process non-clausal formulas ===
% 0.92/1.26
% 0.92/1.26 ============================== PROCESS INITIAL CLAUSES ===============
% 0.92/1.26
% 0.92/1.26 ============================== PREDICATE ELIMINATION =================
% 0.92/1.26 259 -gg_bool(A) | A = fTrue | A = fFalse # label(help_fFalse_1_1_T) # label(axiom). [clausify(249)].
% 0.92/1.26 260 gg_bool(undefined_bool(bool)) # label(gsy_c_HOL_Oundefined_001t__HOL__Obool) # label(axiom). [assumption].
% 0.92/1.26 261 gg_bool(scratc89584109_amone(A,B)) # label(gsy_c_Scratch__tptp__translate__39750__6583_ONUM638__thf__4__p_Obnd__amone) # label(axiom). [clausify(1)].
% 0.92/1.26 262 gg_bool(scratc1595910176_d_and(A,B)) # label(gsy_c_Scratch__tptp__translate__39750__6583_ONUM638__thf__4__p_Obnd__d__and) # label(axiom). [clausify(2)].
% 0.92/1.26 263 gg_bool(scratc1703375356_d_not(A)) # label(gsy_c_Scratch__tptp__translate__39750__6583_ONUM638__thf__4__p_Obnd__d__not) # label(axiom). [clausify(3)].
% 0.92/1.26 264 gg_bool(scratc918842568nd_ec3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__39750__6583_ONUM638__thf__4__p_Obnd__ec3) # label(axiom). [clausify(4)].
% 0.92/1.26 265 gg_bool(scratc1563796029d_l_ec(A,B)) # label(gsy_c_Scratch__tptp__translate__39750__6583_ONUM638__thf__4__p_Obnd__l__ec) # label(axiom). [clausify(8)].
% 0.92/1.26 266 gg_bool(scratc1002441603nd_or3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__39750__6583_ONUM638__thf__4__p_Obnd__or3) # label(axiom). [clausify(9)].
% 0.92/1.26 267 gg_bool(aa_bool_bool(A,B)) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom). [clausify(10)].
% 0.92/1.26 268 gg_bool(aa_TPTP_ind_bool(A,B)) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom). [clausify(11)].
% 0.92/1.26 269 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)].
% 0.92/1.26 270 gg_bool(fEx_TPTP_ind(A)) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom). [clausify(16)].
% 0.92/1.26 271 gg_bool(fFalse) # label(gsy_c_fFalse) # label(axiom). [assumption].
% 0.92/1.26 272 gg_bool(fTrue) # label(gsy_c_fTrue) # label(axiom). [assumption].
% 0.92/1.26 Derived: undefined_bool(bool) = fTrue | undefined_bool(bool) = fFalse. [resolve(259,a,260,a)].
% 0.92/1.26 Derived: scratc89584109_amone(A,B) = fTrue | scratc89584109_amone(A,B) = fFalse. [resolve(259,a,261,a)].
% 0.92/1.26 Derived: scratc1595910176_d_and(A,B) = fTrue | scratc1595910176_d_and(A,B) = fFalse. [resolve(259,a,262,a)].
% 0.92/1.26 Derived: scratc1703375356_d_not(A) = fTrue | scratc1703375356_d_not(A) = fFalse. [resolve(259,a,263,a)].
% 0.92/1.26 Derived: scratc918842568nd_ec3(A,B,C) = fTrue | scratc918842568nd_ec3(A,B,C) = fFalse. [resolve(259,a,264,a)].
% 0.92/1.26 Derived: scratc1563796029d_l_ec(A,B) = fTrue | scratc1563796029d_l_ec(A,B) = fFalse. [resolve(259,a,265,a)].
% 0.92/1.26 Derived: scratc1002441603nd_or3(A,B,C) = fTrue | scratc1002441603nd_or3(A,B,C) = fFalse. [resolve(259,a,266,a)].
% 0.92/1.26 Derived: aa_bool_bool(A,B) = fTrue | aa_bool_bool(A,B) = fFalse. [resolve(259,a,267,a)].
% 0.92/1.26 Derived: aa_TPTP_ind_bool(A,B) = fTrue | aa_TPTP_ind_bool(A,B) = fFalse. [resolve(259,a,268,a)].
% 0.92/1.26 Derived: aa_fun171081125l_bool(A,B) = fTrue | aa_fun171081125l_bool(A,B) = fFalse. [resolve(259,a,269,a)].
% 0.92/1.26 Derived: fEx_TPTP_ind(A) = fTrue | fEx_TPTP_ind(A) = fFalse. [resolve(259,a,270,a)].
% 0.92/1.26 Derived: fFalse = fTrue | fFalse = fFalse. [resolve(259,a,271,a)].
% 0.92/1.46 Derived: fTrue = fTrue | fTrue = fFalse. [resolve(259,a,272,a)].
% 0.92/1.46 273 scratc1958730819d_r_ec(A,B) | pp(A) # label(fact_def__r__ec) # label(axiom). [clausify(42)].
% 0.92/1.46 274 -scratc1958730819d_r_ec(A,B) | -pp(A) | pp(scratc1703375356_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(42)].
% 0.92/1.46 275 scratc1958730819d_r_ec(A,B) | -pp(scratc1703375356_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(42)].
% 0.92/1.46 276 scratc535730629_orec3(A,B,C) | -pp(scratc1595910176_d_and(scratc1002441603nd_or3(A,B,C),scratc918842568nd_ec3(A,B,C))) # label(fact_def__orec3) # label(axiom). [clausify(67)].
% 0.92/1.46 277 -scratc535730629_orec3(A,B,C) | pp(scratc1595910176_d_and(scratc1002441603nd_or3(A,B,C),scratc918842568nd_ec3(A,B,C))) # label(fact_def__orec3) # label(axiom). [clausify(67)].
% 0.92/1.46 278 scratc342567978_l_iff(A,B) | -pp(scratc1595910176_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc952544639nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc952544639nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(74)].
% 0.92/1.46 279 -scratc342567978_l_iff(A,B) | pp(scratc1595910176_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc952544639nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc952544639nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(74)].
% 0.92/1.46 280 scratc1073209838d_orec(A,B) | -pp(scratc1595910176_d_and(aa_bool_bool(scratc1564452034d_l_or(A),B),scratc1563796029d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(75)].
% 0.92/1.46 281 -scratc1073209838d_orec(A,B) | pp(scratc1595910176_d_and(aa_bool_bool(scratc1564452034d_l_or(A),B),scratc1563796029d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(75)].
% 0.92/1.46 282 scratc1067680913nd_wel(A) | -pp(scratc1703375356_d_not(scratc1703375356_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(80)].
% 0.92/1.46 283 -scratc1067680913nd_wel(A) | pp(scratc1703375356_d_not(scratc1703375356_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(80)].
% 0.92/1.46 284 -scratc1067680913nd_wel(A) | pp(A) # label(fact_l__et) # label(axiom). [clausify(130)].
% 0.92/1.46 Derived: pp(A) | -pp(scratc1703375356_d_not(scratc1703375356_d_not(A))). [resolve(284,a,282,a)].
% 0.92/1.46
% 0.92/1.46 ============================== end predicate elimination =============
% 0.92/1.46
% 0.92/1.46 Auto_denials: (non-Horn, no changes).
% 0.92/1.46
% 0.92/1.46 Term ordering decisions:
% 0.92/1.46 Function symbol KB weights: scratc586293042bnd_in=1. aTP_Lamm_af=1. scratc585768252bnd_ap=1. scratc110611510rdsucc=1. scratc1846071618ptyset=1. scratc1810209806_Sigma=1. fFalse=1. scratc1629855320_power=1. scratc347615132_nat_p=1. scratc1160809820d_repl=1. scratc952544639nd_imp=1. aTP_Lamm_a=1. fTrue=1. scratc1035838736d_d_Pi=1. scratc993589771nd_nis=1. scratc135260400nd_n_1=1. scratc1713613863d_pair=1. scratc993064980nd_nat=1. scratc1695703371d_n_is=1. scratc150692328d_Subq=1. scratc1758369158_proj0=1. scratc2137117186_union=1. scratc499043090closed=1. aTP_Lamm_aa=1. scratc1695703366d_n_in=1. scratc1758369159_proj1=1. aTP_Lamm_bx=1. scratc126564410closed=1. scratc2109315044closed=1. aTP_Lamm_bo=1. aTP_Lamm_bs=1. aTP_Lamm_bt=1. scratc2072632303closed=1. scratc877449123d_Inj1=1. scratc882471029n_some=1. scratc928024372_omega=1. aTP_Lamm_ac=1. aTP_Lamm_bc=1. aTP_Lamm_be=1. aTP_Lamm_bf=1. aTP_Lamm_bm=1. aTP_Lamm_br=1. fconj=1. fimplies=1. scratc1773485891_cond2=1. scratc52341446d_Sing=1. scratc877449122d_Inj0=1. aTP_Lamm_ab=1. aTP_Lamm_bi=1. aTP_Lamm_bn=1. aTP_Lamm_bp=1. aTP_Lamm_bq=1. aTP_Lamm_bu=1. aTP_Lamm_bv=1. aTP_Lamm_bw=1. aTP_Lamm_bz=1. aTP_Lamm_cw=1. fequal_TPTP_ind=1. scratc1020884000_n_all=1. scratc1136676261_n_one=1. scratc1496772122_d_Unj=1. scratc1773485890_cond1=1. scratc780671914univof=1. scratc991490598nd_nIn=1. aTP_Lamm_ad=1. aTP_Lamm_bg=1. aTP_Lamm_bh=1. bool=1. scratc1791931703_prop1=1. scratc2114845129pair_p=1. scratc2131666605nempty=1. scratc232810230_prop1=1. scratc361529088_empty=1. scratc64028522munion=1. scratc892404094d_i1_s=1. tPTP_ind=1. aa_TPTP_ind_bool=1. aa_TPT43085870d_bool=1. aa_TPTP_ind_TPTP_ind=1. aa_fun171081125l_bool=1. aa_TPT60673477d_bool=1. aa_fun277296641TP_ind=1. aa_TPT1424761345TP_ind=1. aa_TPT494704832TP_ind=1. aa_fun1584354236d_bool=1. aa_bool_bool=1. aa_fun1431113780TP_ind=1. aa_boo1142376798l_bool=1. aa_TPT1123896796d_bool=1. scratc1595910176_d_and=1. scratc586293034bnd_if=1. scratc1563796029d_l_ec=1. aa_fun1212484691d_bool=1. aa_TPT985247859d_bool=1. scratc29559357d_e_in=1. scratc1148113713d_pair=1. aa_fun987228051d_bool=1. scratc500043566_image=1. scratc542685635_first=1. scratc71545057second=1. scratc952610226nd_ind=1. aa_TPT125613450d_bool=1. scratc89584109_amone=1. scratc993983360nd_non=1. aa_fun1913827119d_bool=1. scratc849361272d_anec=1. aa_TPT1791839040TP_ind=1. aa_fun1107270209d_bool=1. aa_fun845057962d_bool=1. scratc1054190338_ecelt=1. scratc556320792eplSep=1. scratc918842629nd_ecp=1. scratc1053599947_ecect=1. aa_TPT1781712639TP_ind=1. aa_TPT2142672771l_bool=1. aa_fun1235454963TP_ind=1. cOMBB_658106424TP_ind=1. cOMBS_2003118649l_bool=1. scratc1002638465nd_out=1. scratc1079759451fixfu2=1. scratc1459812774wissel=1. scratc1591785977ectset=1. scratc2140343866etprop=1. scratc591401879_fixfu=1. scratc918842633nd_ect=1. scratc1476584100ectelt=1. scratc1656342851nverse=1. scratc1697903323unmore=1. scratc652723106d_invf=1. scratc656459637d_tofs=1. f1=1. f12=1. f13=1. f20=1. f24=1. scratc1027985579all_of=1. scratc29559362d_e_is=1. scratc1479658727_d_Sep=1. scratc1866517936d_esti=1. scratc1703375356_d_not=1. scratc138646387l_some=1. scratc886386996nd_all=1. scratc1774108403_rec_G=1. aTP_Lamm_ae=1. aTP_Lamm_cg=1. scratc1564452034d_l_or=1. aTP_Lamm_ag=1. aTP_Lamm_aq=1. aTP_Lamm_ay=1. aTP_Lamm_bl=1. aTP_Lamm_by=1. aTP_Lamm_cu=1. scratc651476731d_incl=1. aTP_Lamm_ak=1. aTP_Lamm_au=1. aTP_Lamm_ax=1. aTP_Lamm_bb=1. aTP_Lamm_cq=1. aTP_Lamm_cs=1. scratc1002179257nd_one=1. scratc1568392410ective=1. scratc1892018252etprod=1. scratc919695419nd_eps=1. aTP_Lamm_ah=1. aTP_Lamm_ai=1. aTP_Lamm_aj=1. aTP_Lamm_al=1. aTP_Lamm_am=1. aTP_Lamm_ao=1. aTP_Lamm_ap=1. aTP_Lamm_av=1. aTP_Lamm_aw=1. aTP_Lamm_az=1. aTP_Lamm_ca=1. aTP_Lamm_cb=1. aTP_Lamm_cc=1. aTP_Lamm_ce=1. aTP_Lamm_ck=1. aTP_Lamm_cm=1. aTP_Lamm_cn=1. aTP_Lamm_cr=1. fEx_TPTP_ind=1. scratc1057885621nunion=1. scratc1676089161ective=1. aTP_Lamm_an=1. aTP_Lamm_cd=1. aTP_Lamm_cf=1. aTP_Lamm_ch=1. aTP_Lamm_ci=1. aTP_Lamm_cj=1. aTP_Lamm_cl=1. aTP_Lamm_co=1. aTP_Lamm_cp=1. aTP_Lamm_ct=1. aTP_Lamm_cv=1. scratc1704696184_UPair=1. scratc284084372In_rec=1. aTP_Lamm_ar=1. aTP_Lamm_as=1. aTP_Lamm_at=1. aTP_Lamm_ba=1. aTP_Lamm_bd=1. aTP_Lamm_bj=1. aTP_Lamm_bk=1. cOMBC_1555011498d_bool=1. scratc1391007658t_disj=1. scratc1752111640ective=1. scratc974171163tminus=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. scratc1002441603nd_or3=1. scratc2023356087d_soft=1. scratc918842568nd_ec3=1. scratc1305284094_indeq=1. scratc1758762753_prop1=1. scratc953003821nd_ite=1. scratc2079713552sel_wa=1. scratc2079713553sel_wb=1. scratc889509042d_11_i=1. f5=1. f7=1. f14=1. f16=1. f19=1. f25=1. scratc1758762754_prop2=1. scratc1201075440_inj_h=1. scratc1670301801hangef=1. f3=1. f4=1. f15=1. scratc1368495032_prop1=1. scratc863269300indeq2=1. f6=1.
% 3.12/3.43
% 3.12/3.43 ============================== end of process initial clauses ========
% 3.12/3.43
% 3.12/3.43 ============================== CLAUSES FOR SEARCH ====================
% 3.12/3.43
% 3.12/3.43 ============================== end of clauses for search =============
% 3.12/3.43
% 3.12/3.43 ============================== SEARCH ================================
% 3.12/3.43
% 3.12/3.43 % Starting search at 0.27 seconds.
% 3.12/3.43
% 3.12/3.43 Low Water (keep): wt=48.000, iters=3639
% 3.12/3.43
% 3.12/3.43 Low Water (keep): wt=38.000, iters=3438
% 3.12/3.43
% 3.12/3.43 Low Water (keep): wt=37.000, iters=3390
% 3.12/3.43
% 3.12/3.43 Low Water (keep): wt=36.000, iters=3362
% 3.12/3.43
% 3.12/3.43 Low Water (keep): wt=34.000, iters=3340
% 3.12/3.43
% 3.12/3.43 Low Water (keep): wt=33.000, iters=3381
% 3.12/3.43
% 3.12/3.43 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 28 (0.00 of 1.15 sec).
% 3.12/3.43
% 3.12/3.43 Low Water (keep): wt=24.000, iters=3411
% 3.12/3.43
% 3.12/3.43 Low Water (keep): wt=23.000, iters=3358
% 3.12/3.43
% 3.12/3.43 Low Water (keep): wt=22.000, iters=3364
% 3.12/3.43
% 3.12/3.43 Low Water (keep): wt=21.000, iters=3345
% 3.12/3.43
% 3.12/3.43 Low Water (keep): wt=20.000, iters=3406
% 3.12/3.43
% 3.12/3.43 Low Water (keep): wt=19.000, iters=3480
% 3.12/3.43
% 3.12/3.43 Low Water (keep): wt=18.000, iters=3333
% 3.12/3.43
% 3.12/3.43 Low Water (keep): wt=17.000, iters=3366
% 3.12/3.43
% 3.12/3.43 Low Water (displace): id=6689, wt=107.000
% 3.12/3.43
% 3.12/3.43 Low Water (displCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------