TSTP Solution File: NUM646+4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM646+4 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 13:29:57 EDT 2022
% Result : Timeout 300.04s 300.32s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM646+4 : TPTP v8.1.0. Released v7.3.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Wed Jul 6 12:52:48 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.96/1.25 ============================== Prover9 ===============================
% 0.96/1.25 Prover9 (32) version 2009-11A, November 2009.
% 0.96/1.25 Process 11199 was started by sandbox on n021.cluster.edu,
% 0.96/1.25 Wed Jul 6 12:52:49 2022
% 0.96/1.25 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_11044_n021.cluster.edu".
% 0.96/1.25 ============================== end of head ===========================
% 0.96/1.25
% 0.96/1.25 ============================== INPUT =================================
% 0.96/1.25
% 0.96/1.25 % Reading from file /tmp/Prover9_11044_n021.cluster.edu
% 0.96/1.25
% 0.96/1.25 set(prolog_style_variables).
% 0.96/1.25 set(auto2).
% 0.96/1.25 % set(auto2) -> set(auto).
% 0.96/1.25 % set(auto) -> set(auto_inference).
% 0.96/1.25 % set(auto) -> set(auto_setup).
% 0.96/1.25 % set(auto_setup) -> set(predicate_elim).
% 0.96/1.25 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.96/1.25 % set(auto) -> set(auto_limits).
% 0.96/1.25 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.96/1.25 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.96/1.25 % set(auto) -> set(auto_denials).
% 0.96/1.25 % set(auto) -> set(auto_process).
% 0.96/1.25 % set(auto2) -> assign(new_constants, 1).
% 0.96/1.25 % set(auto2) -> assign(fold_denial_max, 3).
% 0.96/1.25 % set(auto2) -> assign(max_weight, "200.000").
% 0.96/1.25 % set(auto2) -> assign(max_hours, 1).
% 0.96/1.25 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.96/1.25 % set(auto2) -> assign(max_seconds, 0).
% 0.96/1.25 % set(auto2) -> assign(max_minutes, 5).
% 0.96/1.25 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.96/1.25 % set(auto2) -> set(sort_initial_sos).
% 0.96/1.25 % set(auto2) -> assign(sos_limit, -1).
% 0.96/1.25 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.96/1.25 % set(auto2) -> assign(max_megs, 400).
% 0.96/1.25 % set(auto2) -> assign(stats, some).
% 0.96/1.25 % set(auto2) -> clear(echo_input).
% 0.96/1.25 % set(auto2) -> set(quiet).
% 0.96/1.25 % set(auto2) -> clear(print_initial_clauses).
% 0.96/1.25 % set(auto2) -> clear(print_given).
% 0.96/1.25 assign(lrs_ticks,-1).
% 0.96/1.25 assign(sos_limit,10000).
% 0.96/1.25 assign(order,kbo).
% 0.96/1.25 set(lex_order_vars).
% 0.96/1.25 clear(print_given).
% 0.96/1.25
% 0.96/1.25 % formulas(sos). % not echoed (343 formulas)
% 0.96/1.25
% 0.96/1.25 ============================== end of input ==========================
% 0.96/1.25
% 0.96/1.25 % From the command line: assign(max_seconds, 300).
% 0.96/1.25
% 0.96/1.25 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.96/1.25
% 0.96/1.25 % Formulas that are not ordinary clauses:
% 0.96/1.25 1 (all B_1 all B_2 gg_bool(scratc97476125_amone(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__41368__4731_ONUM646__thf__4__p_Obnd__amone) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 2 (all B_1 all B_2 gg_bool(scratc1760708592_d_and(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__41368__4731_ONUM646__thf__4__p_Obnd__d__and) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 3 (all B_1 gg_bool(scratc1868173772_d_not(B_1))) # label(gsy_c_Scratch__tptp__translate__41368__4731_ONUM646__thf__4__p_Obnd__d__not) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 4 (all B_1 all B_2 all B_3 gg_bool(scratc1528557816nd_ec3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__41368__4731_ONUM646__thf__4__p_Obnd__ec3) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 5 (all B_1 all B_2 gg_TPTP_ind(scratc1528557881nd_ect(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__41368__4731_ONUM646__thf__4__p_Obnd__ect) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 6 (all B_1 gg_TPTP_ind(scratc1529410667nd_eps(B_1))) # label(gsy_c_Scratch__tptp__translate__41368__4731_ONUM646__thf__4__p_Obnd__eps) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 7 (all B_1 all B_2 gg_TPTP_ind(scratc1562325474nd_ind(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__41368__4731_ONUM646__thf__4__p_Obnd__ind) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 8 (all B_1 all B_2 gg_bool(scratc1571688045d_l_ec(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__41368__4731_ONUM646__thf__4__p_Obnd__l__ec) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 9 (all B_1 all B_2 all B_3 gg_bool(scratc1612156851nd_or3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__41368__4731_ONUM646__thf__4__p_Obnd__or3) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 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].
% 0.96/1.25 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].
% 0.96/1.25 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].
% 0.96/1.25 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].
% 0.96/1.25 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].
% 0.96/1.25 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].
% 0.96/1.25 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].
% 0.96/1.25 17 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc420398977_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1603305019nd_nis,aa_TPTP_ind_TPTP_ind(scratc1704054573d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1704054573d_n_pl(X),Xb))))) # label(fact_def__d__28__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 18 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1979520450_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1603305019nd_nis,Xa),aa_TPTP_ind_TPTP_ind(scratc1704054573d_n_pl(X),Xa))))) # label(fact_def__d__27__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 19 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1391158275_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1703595387d_n_is,aa_TPTP_ind_TPTP_ind(scratc1704054573d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1704054573d_n_pl(Xa),X))))) # label(fact_def__d__26__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 20 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc802796100_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1703595387d_n_is,aa_TPTP_ind_TPTP_ind(scratc1704054573d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1704054573d_n_pl(X),Xa)),Xb)),aa_TPTP_ind_TPTP_ind(scratc1704054573d_n_pl(X),aa_TPTP_ind_TPTP_ind(scratc1704054573d_n_pl(Xa),Xb)))))) # label(fact_def__d__25__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 21 (all X scratc1704054573d_n_pl(X) = aa_TPT1424761345TP_ind(scratc327060748bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1632887159d_plus,X))) # label(fact_def__n__pl) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 22 (all X aa_TPTP_ind_TPTP_ind(scratc1632887159d_plus,X) = scratc1562325474nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1043730752d_d_Pi,scratc1602780228nd_nat),aTP_Lamm_ad),aa_TPT43085870d_bool(scratc214433926_prop2,X))) # label(fact_def__plus) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 23 (all X aa_TPTP_ind_TPTP_ind(scratc2003131838d_24_g,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1589990366_Sigma,scratc1602780228nd_nat),aTP_Lamm_ae(X))) # label(fact_def__d__24__g) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 24 (all X (pp(aa_TPTP_ind_bool(scratc1766654772_prop4,X)) <-> pp(aa_fun171081125l_bool(scratc317253539l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1043730752d_d_Pi,scratc1602780228nd_nat),aTP_Lamm_ad)),aa_TPT43085870d_bool(scratc214433926_prop2,X))))) # label(fact_def__prop4) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 25 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1766654771_prop3(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1703595387d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,X),Xb)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,Xa),Xb))))) # label(fact_def__prop3) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 26 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc214433926_prop2,X),Xa)) <-> pp(scratc1760708592_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1703595387d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,Xa),scratc2110353600nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,X)),aa_TPTP_ind_bool(scratc214433925_prop1,Xa))))) # label(fact_def__d__24__prop2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 27 (all X (pp(aa_TPTP_ind_bool(scratc214433925_prop1,X)) <-> pp(aa_fun171081125l_bool(scratc1185682416_n_all,aa_TPT43085870d_bool(aTP_Lamm_af,X))))) # label(fact_def__d__24__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 28 (all X (pp(aa_TPTP_ind_bool(scratc1773555398_prop1,X)) <-> pp(aa_bool_bool(scratc1572344050d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1703595387d_n_is,X),scratc2110353600nd_n_1)),aa_fun171081125l_bool(scratc1061078181n_some,aa_TPT43085870d_bool(aTP_Lamm_ag,X)))))) # label(fact_def__d__23__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 29 (all X (pp(aa_TPTP_ind_bool(scratc1185193223_prop1,X)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1603305019nd_nis,aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,X)),X)))) # label(fact_def__d__22__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 30 (all X (pp(aa_TPTP_ind_bool(scratc1781377907_cond2,X)) <-> pp(aa_fun171081125l_bool(scratc1185682416_n_all,aa_TPT43085870d_bool(aTP_Lamm_ah,X))))) # label(fact_def__cond2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 31 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1603305019nd_nis,X),Xa)) <-> pp(scratc1868173772_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1703595387d_n_is,X),Xa))))) # label(fact_def__nis) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 32 (all X all Xa all Xb all Xc all Xd scratc1028067716indeq2(X,Xa,Xb,Xc,Xd) = aa_TPT1424761345TP_ind(scratc1313176110_indeq(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc669289602d_11_i(X,Xa,Xb),Xc),Xd))) # label(fact_def__indeq2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 33 (all X all Xa all Xb scratc669289602d_11_i(X,Xa,Xb) = scratc1313176110_indeq(X,Xa,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1043730752d_d_Pi,X),aTP_Lamm_aj(Xb)))) # label(fact_def__d__11__i) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 34 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1244557867fixfu2(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1206592731all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ao(X),Xa),Xb),Xc))))) # label(fact_def__fixfu2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 35 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1313176110_indeq(X,Xa,Xb),Xc),Xd) = scratc1562325474nd_ind(Xb,aa_TPT43085870d_bool(scratc1766654770_prop2(X,Xa,Xb,Xc),Xd))) # label(fact_def__indeq) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 36 (all X all Xa all Xb all Xc all Xd all Xe (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1766654770_prop2(X,Xa,Xb,Xc),Xd),Xe)) <-> pp(aa_fun171081125l_bool(scratc317253539l_some(X),aa_TPT43085870d_bool(scratc761756552_prop1(X,Xa,Xb,Xc,Xd),Xe))))) # label(fact_def__prop2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 37 (all X all Xa all Xb all Xc all Xd all Xe all Xf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc761756552_prop1(X,Xa,Xb,Xc,Xd),Xe),Xf)) <-> pp(scratc1760708592_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1694127488d_esti(X),Xf),aa_TPTP_ind_TPTP_ind(scratc1061491963_ecect(X,Xa),Xd)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc37451378d_e_is(Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,Xc),Xf)),Xe))))) # label(fact_def__d__10__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.25 38 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc599293895_fixfu(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1206592731all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_aq(X),Xa),Xb),Xc))))) # label(fact_def__fixfu) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 39 (all X all Xa scratc1061491963_ecect(X,Xa) = scratc37451373d_e_in(aa_TPTP_ind_TPTP_ind(scratc1637747336_power,X),scratc676970824d_anec(X,Xa))) # label(fact_def__ecect) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 40 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1641382516ectelt(X,Xa),Xb) = aa_TPTP_ind_TPTP_ind(scratc1756584393ectset(X,Xa),aa_TPTP_ind_TPTP_ind(scratc1062082354_ecelt(X,Xa),Xb))) # label(fact_def__ectelt) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 41 (all X all Xa scratc1756584393ectset(X,Xa) = scratc1612353713nd_out(aa_TPTP_ind_TPTP_ind(scratc1637747336_power,X),scratc676970824d_anec(X,Xa))) # label(fact_def__ectset) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 42 (all X all Xa scratc1528557881nd_ect(X,Xa) = aa_fun1431113780TP_ind(scratc1644457143_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1637747336_power,X)),scratc676970824d_anec(X,Xa))) # label(fact_def__ect) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 43 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc676970824d_anec(X,Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc317253539l_some(X),aa_TPT43085870d_bool(scratc1528557877nd_ecp(X,Xa),Xb))))) # label(fact_def__anec) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 44 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1528557877nd_ecp(X,Xa),Xb),Xc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc37451378d_e_is(aa_TPTP_ind_TPTP_ind(scratc1637747336_power,X)),Xb),aa_TPTP_ind_TPTP_ind(scratc1062082354_ecelt(X,Xa),Xc))))) # label(fact_def__ecp) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 45 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1062082354_ecelt(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc1644457143_d_Sep(X),aa_TPT43085870d_bool(Xa,Xb))) # label(fact_def__ecelt) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 46 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1862701739unmore(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc1644457143_d_Sep(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_as(X),Xa),Xb))) # label(fact_def__unmore) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 47 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1987304970etprop(X,Xa),Xb),Xc)) <-> pp(scratc1760708592_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1694127488d_esti(X),Xc),Xa),scratc1868173772_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1694127488d_esti(X),Xc),Xb)))))) # label(fact_def__nissetprop) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 48 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1170788218t_disj(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1496102244nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_at(X),Xa),Xb))))) # label(fact_def__st__disj) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 49 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc479086283d_incl(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1496102244nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_au(X),Xa),Xb))))) # label(fact_def__incl) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 50 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1911447165nempty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc317253539l_some(X),aa_TPT43085870d_bool(aTP_Lamm_av(X),Xa))))) # label(fact_def__nonempty) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 51 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc369421104_empty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1206592731all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X)),scratc1603698608nd_non(X,aa_TPT43085870d_bool(aTP_Lamm_av(X),Xa)))))) # label(fact_def__empty) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 52 (all X scratc1694127488d_esti(X) = scratc327585538bnd_in) # label(fact_def__esti) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 53 (all X all Xa (scratc1966622835d_r_ec(X,Xa) <-> (pp(X) -> pp(scratc1868173772_d_not(Xa))))) # label(fact_def__r__ec) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 54 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc1848908953hangef(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1589990366_Sigma,X),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_aw(X),Xb),Xc),Xd))) # label(fact_def__changef) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 55 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1624611190wissel(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1589990366_Sigma,X),scratc1926674657sel_wb(X,Xa,Xb))) # label(fact_def__wissel) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 56 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1926674657sel_wb(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc1562719069nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc37451378d_e_is(X),Xc),Xb),X,Xa),aa_TPTP_ind_TPTP_ind(scratc1926674656sel_wa(X,Xa,Xb),Xc))) # label(fact_def__wissel__wb) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 57 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1926674656sel_wa(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc1562719069nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc37451378d_e_is(X),Xc),Xa),X,Xb),Xc)) # label(fact_def__wissel__wa) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 58 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1562719069nd_ite(X,Xa,Xb),Xc) = scratc1562325474nd_ind(Xa,aa_TPT43085870d_bool(scratc1766654769_prop1(X,Xa,Xb),Xc))) # label(fact_def__ite) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 59 (all X all Xa all Xb all Xc all Xd (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1766654769_prop1(X,Xa,Xb),Xc),Xd)) <-> pp(scratc1760708592_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1562259887nd_imp,X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc37451378d_e_is(Xa),Xd),Xb)),aa_bool_bool(aa_boo1142376798l_bool(scratc1562259887nd_imp,scratc1868173772_d_not(X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc37451378d_e_is(Xa),Xd),Xc)))))) # label(fact_def__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 60 (all X all Xa scratc236343473second(X,Xa) = scratc1766261175_proj1) # label(fact_def__second) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 61 (all X all Xa scratc550577651_first(X,Xa) = scratc1766261174_proj0) # label(fact_def__first) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 62 (all X all Xa scratc1326720865d_pair(X,Xa) = scratc1541223415d_pair) # label(fact_def__d__pair) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 63 (all X all Xa scratc1612353713nd_out(X,Xa) = scratc1850965639d_soft(aa_fun1431113780TP_ind(scratc1644457143_d_Sep(X),Xa),X,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1589990366_Sigma,aa_fun1431113780TP_ind(scratc1644457143_d_Sep(X),Xa)),scratc37451373d_e_in(X,Xa)))) # label(fact_def__out) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 64 (all X all Xa all Xb (gg_TPTP_ind(Xb) -> aa_TPTP_ind_TPTP_ind(scratc37451373d_e_in(X,Xa),Xb) = Xb)) # label(fact_def__e__in) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 65 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc1365873856_inj_h(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1589990366_Sigma,X),aa_TPT1424761345TP_ind(aTP_Lamm_ax(Xc),Xd))) # label(fact_def__inj__h) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 66 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc480332658d_invf(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1589990366_Sigma,Xa),scratc1850965639d_soft(X,Xa,Xb))) # label(fact_def__invf) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 67 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1699567176ective(X),Xa),Xb)) <-> pp(scratc1760708592_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1515847946ective(X),Xa),Xb),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1523050265ective(X),Xa),Xb))))) # label(fact_def__bijective) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 68 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1523050265ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1496102244nd_all(Xa),aa_TPT43085870d_bool(scratc507935582_image(X,Xa),Xb))))) # label(fact_def__surjective) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 69 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1834950003nverse(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1589990366_Sigma,Xa),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ay(X),Xa),Xb))) # label(fact_def__inverse) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 70 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1850965639d_soft(X,Xa,Xb),Xc) = scratc1562325474nd_ind(X,aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_az(Xa),Xb),Xc))) # label(fact_def__soft) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 71 (all X all Xa scratc484069189d_tofs(X,Xa) = scratc327060748bnd_ap) # label(fact_def__tofs) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 72 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc507935582_image(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc317253539l_some(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_az(Xa),Xb),Xc))))) # label(fact_def__image) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 73 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1515847946ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1496102244nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bb(X),Xa),Xb))))) # label(fact_def__injective) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 74 (all X all Xa scratc1562325474nd_ind(X,Xa) = scratc1529410667nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bc(X),Xa))) # label(fact_def__ind) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 75 (all X all Xa (pp(aa_fun171081125l_bool(scratc1611894505nd_one(X),Xa)) <-> pp(scratc1760708592_d_and(scratc97476125_amone(X,Xa),aa_fun171081125l_bool(scratc317253539l_some(X),Xa))))) # label(fact_def__one) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 76 (all X all Xa (pp(scratc97476125_amone(X,Xa)) <-> pp(aa_fun171081125l_bool(scratc1206592731all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X)),aa_fun1584354236d_bool(aTP_Lamm_be(X),Xa))))) # label(fact_def__amone) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 77 (all X scratc37451378d_e_is(X) = fequal_TPTP_ind) # label(fact_def__e__is) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 78 (all X all Xa all Xb (scratc543622645_orec3(X,Xa,Xb) <-> pp(scratc1760708592_d_and(scratc1612156851nd_or3(X,Xa,Xb),scratc1528557816nd_ec3(X,Xa,Xb))))) # label(fact_def__orec3) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 79 (all X all Xa all Xb (pp(scratc1528557816nd_ec3(X,Xa,Xb)) <-> scratc676905177d_and3(scratc1571688045d_l_ec(X,Xa),scratc1571688045d_l_ec(Xa,Xb),scratc1571688045d_l_ec(Xb,X)))) # label(fact_def__ec3) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 80 (all X all Xa all Xb (scratc676905177d_and3(X,Xa,Xb) <-> pp(scratc1760708592_d_and(X,scratc1760708592_d_and(Xa,Xb))))) # label(fact_def__and3) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 81 (all X all Xa all Xb (pp(scratc1612156851nd_or3(X,Xa,Xb)) <-> pp(aa_bool_bool(scratc1572344050d_l_or(X),aa_bool_bool(scratc1572344050d_l_or(Xa),Xb))))) # label(fact_def__or3) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 82 (all X all Xa (pp(aa_fun171081125l_bool(scratc317253539l_some(X),Xa)) <-> pp(scratc1868173772_d_not(aa_fun171081125l_bool(scratc1206592731all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X)),scratc1603698608nd_non(X,Xa)))))) # label(fact_def__l__some) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 83 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc1603698608nd_non(X,Xa),Xb)) <-> pp(scratc1868173772_d_not(aa_TPTP_ind_bool(Xa,Xb))))) # label(fact_def__non) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 84 (all X scratc1496102244nd_all(X) = scratc1206592731all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X))) # label(fact_def__all) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 85 (all X all Xa (scratc507366394_l_iff(X,Xa) <-> pp(scratc1760708592_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1562259887nd_imp,X),Xa),aa_bool_bool(aa_boo1142376798l_bool(scratc1562259887nd_imp,Xa),X))))) # label(fact_def__l__iff) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 86 (all X all Xa (scratc900819390d_orec(X,Xa) <-> pp(scratc1760708592_d_and(aa_bool_bool(scratc1572344050d_l_or(X),Xa),scratc1571688045d_l_ec(X,Xa))))) # label(fact_def__orec) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 87 (all X scratc1572344050d_l_or(X) = aa_boo1142376798l_bool(scratc1562259887nd_imp,scratc1868173772_d_not(X))) # label(fact_def__l__or) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 88 (all X all Xa (pp(scratc1760708592_d_and(X,Xa)) <-> pp(scratc1868173772_d_not(scratc1571688045d_l_ec(X,Xa))))) # label(fact_def__d__and) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 89 (all X all Xa (pp(scratc1571688045d_l_ec(X,Xa)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1562259887nd_imp,X),scratc1868173772_d_not(Xa))))) # label(fact_def__l__ec) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 90 scratc552549002bvious <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1562259887nd_imp,fFalse),fFalse)) # label(fact_def__obvious) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 91 (all X (scratc1677396161nd_wel(X) <-> pp(scratc1868173772_d_not(scratc1868173772_d_not(X))))) # label(fact_def__wel) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 92 (all X (pp(scratc1868173772_d_not(X)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1562259887nd_imp,X),fFalse)))) # label(fact_def__d__not) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 93 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1043730752d_d_Pi,X),Xa) = aa_fun1431113780TP_ind(scratc1644457143_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1637747336_power,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1589990366_Sigma,X),aTP_Lamm_bf(Xa)))),aa_fun1913827119d_bool(aTP_Lamm_bg(X),Xa))) # label(fact_def__d__Pi) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 94 (all X (gg_TPTP_ind(X) -> (pp(aa_TPTP_ind_bool(scratc145968633pair_p,X)) <-> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1541223415d_pair,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,X),scratc1625852178ptyset)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,X),aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,scratc1625852178ptyset))) = X))) # label(fact_def__pair__p) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 95 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc403281896eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bh,Xa)),scratc1766261175_proj1)) # label(fact_def__ap) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 96 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc2070625404etprod(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1589990366_Sigma,X),aTP_Lamm_aj(Xa))) # label(fact_def__setprod) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 97 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1589990366_Sigma,X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1991292730munion,X),aTP_Lamm_bi(Xa))) # label(fact_def__d__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 98 (all X aa_TPTP_ind_TPTP_ind(scratc1766261175_proj1,X) = aa_fun277296641TP_ind(scratc403281896eplSep(X,aTP_Lamm_bj),scratc1661570538_d_Unj)) # label(fact_def__proj1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 99 (all X aa_TPTP_ind_TPTP_ind(scratc1766261174_proj0,X) = aa_fun277296641TP_ind(scratc403281896eplSep(X,aTP_Lamm_bk),scratc1661570538_d_Unj)) # label(fact_def__proj0) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 100 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1541223415d_pair,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc837666181nunion(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc988419372d_repl,X),scratc1056056274d_Inj0)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc988419372d_repl,Xa),scratc1056056275d_Inj1))) # label(fact_def__pair) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 101 (all X aa_TPTP_ind_TPTP_ind(scratc1056056274d_Inj0,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc988419372d_repl,X),scratc1056056275d_Inj1)) # label(fact_def__d__Inj0) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 102 (all X (pp(aa_TPTP_ind_bool(scratc512413548_nat_p,X)) <-> (all X1 (pp(aa_TPTP_ind_bool(X1,scratc1625852178ptyset)) -> ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(X1,X2)) -> pp(aa_TPTP_ind_bool(X1,aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,X2)))))) -> pp(aa_TPTP_ind_bool(X1,X))))))) # label(fact_def__nat__p) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 103 (all X aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc837666181nunion(X),aa_TPTP_ind_TPTP_ind(scratc230948598d_Sing,X))) # label(fact_def__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 104 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc131045476In_rec(X),Xa) = scratc1529410667nd_eps(aa_TPT43085870d_bool(scratc1798490915_rec_G(X),Xa))) # label(fact_def__d__In__rec) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 105 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1798490915_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(scratc327585538bnd_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].
% 0.96/1.26 106 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc753951723tminus(X),Xa) = aa_fun1431113780TP_ind(scratc1644457143_d_Sep(X),aa_TPT43085870d_bool(aTP_Lamm_bn,Xa))) # label(fact_def__setminus) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 107 (all X all Xa scratc403281896eplSep(X,Xa) = aa_TPT494704832TP_ind(scratc988419372d_repl,aa_fun1431113780TP_ind(scratc1644457143_d_Sep(X),Xa))) # label(fact_def__d__ReplSep) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 108 (all X all Xa aa_fun1431113780TP_ind(scratc1644457143_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc327585530bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc327585538bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc988419372d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bo(X),Xa))),scratc1625852178ptyset)) # label(fact_def__d__Sep) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 109 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1991292730munion,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc2145009202_union,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc988419372d_repl,X),Xa))) # label(fact_def__famunion) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 110 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc837666181nunion(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc2145009202_union,aa_TPTP_ind_TPTP_ind(scratc1484476744_UPair(X),Xa))) # label(fact_def__binunion) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 111 (all X aa_TPTP_ind_TPTP_ind(scratc230948598d_Sing,X) = aa_TPTP_ind_TPTP_ind(scratc1484476744_UPair(X),X)) # label(fact_def__d__Sing) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 112 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1484476744_UPair(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc988419372d_repl,aa_TPTP_ind_TPTP_ind(scratc1637747336_power,aa_TPTP_ind_TPTP_ind(scratc1637747336_power,scratc1625852178ptyset))),aa_TPT1424761345TP_ind(aTP_Lamm_bp(X),Xa))) # label(fact_def__d__UPair) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 113 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1601205846nd_nIn,X),Xa)) <-> -pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X),Xa)))) # label(fact_def__nIn) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 114 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc327585530bnd_if(X,Xa),Xb) = scratc1529410667nd_eps(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bq(X),Xa),Xb))) # label(fact_def__if) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 115 (all X (pp(aa_TPTP_ind_bool(scratc2097014815closed,X)) <-> pp(aa_TPTP_ind_bool(scratc1582673844closed,X)) & pp(aa_TPTP_ind_bool(scratc1747406858closed,X)) & pp(aa_TPTP_ind_bool(scratc630177602closed,X)))) # label(fact_def__d__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 116 (all X (pp(aa_TPTP_ind_bool(scratc630177602closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X1),X)) -> (all X2 ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X3),X1)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,aa_TPTP_ind_TPTP_ind(X2,X3)),X))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc988419372d_repl,X1),X2)),X))))))))) # label(fact_def__d__Repl__closed) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 117 (all X (pp(aa_TPTP_ind_bool(scratc1747406858closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,aa_TPTP_ind_TPTP_ind(scratc1637747336_power,X1)),X))))))) # label(fact_def__d__Power__closed) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 118 (all X (pp(aa_TPTP_ind_bool(scratc1582673844closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,aa_TPTP_ind_TPTP_ind(scratc2145009202_union,X1)),X))))))) # label(fact_def__d__Union__closed) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 119 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc329299480d_Subq,X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X2),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X2),Xa))))))) # label(fact_def__d__Subq) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 120 (all X all Xa (pp(aa_fun171081125l_bool(scratc1206592731all_of(X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (scratc625769342_is_of(X2,X) -> pp(aa_TPTP_ind_bool(Xa,X2))))))) # label(fact_def__all__of) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 121 (all X all Xa (scratc625769342_is_of(X,Xa) <-> pp(aa_TPTP_ind_bool(Xa,X)))) # label(fact_def__is__of) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 122 (all X0 pp(aa_fun171081125l_bool(scratc1206592731all_of(aa_TPT43085870d_bool(aTP_Lamm_cy,X0)),aa_TPT43085870d_bool(aTP_Lamm_da,X0)))) # label(fact_isseti) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 123 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1206592731all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X0)),aa_fun1584354236d_bool(aTP_Lamm_db(X0),X12)))) # label(fact_estie) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 124 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1206592731all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X0)),aa_fun1584354236d_bool(aTP_Lamm_dc(X0),X12)))) # label(fact_estii) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 125 (all X0 all X12 scratc625769342_is_of(aa_fun1431113780TP_ind(scratc1644457143_d_Sep(X0),X12),aa_TPT43085870d_bool(aTP_Lamm_cy,X0))) # label(fact_setof__p) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 126 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1206592731all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X0)),aa_TPT43085870d_bool(aTP_Lamm_de(X0),X12)))) # label(fact_secondis1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 127 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1206592731all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X0)),aa_TPT43085870d_bool(aTP_Lamm_dg(X0),X12)))) # label(fact_firstis1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 128 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1206592731all_of(aa_TPT43085870d_bool(aTP_Lamm_dh(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_di(X0),X12)))) # label(fact_pairis1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 129 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1206592731all_of(aa_TPT43085870d_bool(aTP_Lamm_dh(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_dj(X0),X12)))) # label(fact_second__p) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 130 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1206592731all_of(aa_TPT43085870d_bool(aTP_Lamm_dh(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_dk(X0),X12)))) # label(fact_first__p) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 131 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1206592731all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X0)),aa_TPT43085870d_bool(aTP_Lamm_dm(X0),X12)))) # label(fact_e__pair__p) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 132 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1206592731all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X0)),aa_fun1584354236d_bool(aTP_Lamm_dn(X0),X12)))) # label(fact_otax2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 133 (all X0 all X12 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1515847946ective(aa_fun1431113780TP_ind(scratc1644457143_d_Sep(X0),X12)),X0),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1589990366_Sigma,aa_fun1431113780TP_ind(scratc1644457143_d_Sep(X0),X12)),scratc37451373d_e_in(X0,X12))))) # label(fact_otax1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 134 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1206592731all_of(aa_fun1584354236d_bool(aTP_Lamm_do(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_dp(X0),X12)))) # label(fact_e__inp) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 135 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1206592731all_of(aa_fun1584354236d_bool(aTP_Lamm_do(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_dq(X0),X12)))) # label(fact_e__in__p) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 136 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1206592731all_of(aa_TPT43085870d_bool(aTP_Lamm_dr(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_du(X0),X12)))) # label(fact_e__fisi) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 137 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc1611894505nd_one(X0),X12)) -> pp(aa_TPTP_ind_bool(X12,scratc1562325474nd_ind(X0,X12))))) # label(fact_oneax) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 138 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc1611894505nd_one(X0),X12)) -> scratc625769342_is_of(scratc1562325474nd_ind(X0,X12),aa_TPT43085870d_bool(aTP_Lamm_ak,X0)))) # label(fact_ind__p) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 139 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1206592731all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X0)),aa_fun1584354236d_bool(aTP_Lamm_dw(X0),X12)))) # label(fact_e__isp) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 140 (all X0 pp(aa_fun171081125l_bool(scratc1206592731all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,X0)),aa_TPT43085870d_bool(aTP_Lamm_dx,X0)))) # label(fact_refis) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 141 (all X0 (scratc1677396161nd_wel(X0) -> pp(X0))) # label(fact_l__et) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 142 (all X0 all X12 all X22 all X32 (pp(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc327585530bnd_if(X0,X22),X32))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X12),X22))))) # label(fact_k__If__In__then__E) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 143 (all X0 all X12 all X22 ((pp(X0) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X12),X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,aa_TPTP_ind_TPTP_ind(scratc327585530bnd_if(X0,X12),scratc1625852178ptyset)),aa_TPTP_ind_TPTP_ind(scratc327585530bnd_if(X0,X22),aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,scratc1625852178ptyset)))))) # label(fact_k__If__In__01) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 144 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X33),X0)) -> aa_TPTP_ind_TPTP_ind(X12,X33) = aa_TPTP_ind_TPTP_ind(X22,X33)))) -> aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1589990366_Sigma,X0),X12) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1589990366_Sigma,X0),X22))) # label(fact_xi__ext) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 145 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1043730752d_d_Pi,X0),X12))) -> (all X32 (gg_TPTP_ind(X32) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X32),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1043730752d_d_Pi,X0),X12))) -> ((all X42 (gg_TPTP_ind(X42) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X42),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,X22),X42) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,X32),X42)))) -> X22 = X32))))))) # label(fact_k__Pi__ext) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 146 (all X0 all X12 all X22 all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1043730752d_d_Pi,X0),X12))) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X32),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,X22),X32)),aa_TPTP_ind_TPTP_ind(X12,X32)))))) # label(fact_ap__Pi) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 147 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X33),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,aa_TPTP_ind_TPTP_ind(X22,X33)),aa_TPTP_ind_TPTP_ind(X12,X33)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1589990366_Sigma,X0),X22)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1043730752d_d_Pi,X0),X12))))) # label(fact_lam__Pi) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 148 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X22),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1589990366_Sigma,X0),X12)),X22) = aa_TPTP_ind_TPTP_ind(X12,X22))) # label(fact_beta) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 149 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1589990366_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,aa_TPTP_ind_TPTP_ind(scratc1766261175_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1766261174_proj0,X22)))))) # label(fact_proj1__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 150 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1589990366_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,aa_TPTP_ind_TPTP_ind(scratc1766261174_proj0,X22)),X0)))) # label(fact_proj0__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 151 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1589990366_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1541223415d_pair,aa_TPTP_ind_TPTP_ind(scratc1766261174_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1766261175_proj1,X22)) = X22))) # label(fact_proj__Sigma__eta) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 152 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1589990366_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1541223415d_pair,aa_TPTP_ind_TPTP_ind(scratc1766261174_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1766261175_proj1,X22)) = X22 & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,aa_TPTP_ind_TPTP_ind(scratc1766261174_proj0,X22)),X0)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,aa_TPTP_ind_TPTP_ind(scratc1766261175_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1766261174_proj0,X22))))))) # label(fact_k__Sigma__eta__proj0__proj1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 153 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X22),X0)) -> (all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X32),aa_TPTP_ind_TPTP_ind(X12,X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1541223415d_pair,X22),X32)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1589990366_Sigma,X0),X12))))))) # label(fact_pair__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 154 (all X0 all X12 (gg_TPTP_ind(X12) -> aa_TPTP_ind_TPTP_ind(scratc1766261175_proj1,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1541223415d_pair,X0),X12)) = X12)) # label(fact_proj1__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 155 (all X0 all X12 (gg_TPTP_ind(X0) -> aa_TPTP_ind_TPTP_ind(scratc1766261174_proj0,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1541223415d_pair,X0),X12)) = X0)) # label(fact_proj0__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 156 (all X0 (pp(aa_TPTP_ind_bool(scratc512413548_nat_p,X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X0),scratc935916388_omega)))) # label(fact_nat__p__omega) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 157 (all X0 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X0),scratc935916388_omega)) -> pp(aa_TPTP_ind_bool(scratc512413548_nat_p,X0)))) # label(fact_omega__nat__p) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 158 (all X0 (gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(scratc512413548_nat_p,X0)) -> X0 = scratc1625852178ptyset | (exists X13 (gg_TPTP_ind(X13) & pp(aa_TPTP_ind_bool(scratc512413548_nat_p,X13)) & X0 = aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,X13)))))) # label(fact_nat__inv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 159 (all X0 (pp(aa_TPTP_ind_bool(X0,scratc1625852178ptyset)) -> ((all X13 (gg_TPTP_ind(X13) -> (pp(aa_TPTP_ind_bool(scratc512413548_nat_p,X13)) -> (pp(aa_TPTP_ind_bool(X0,X13)) -> pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,X13))))))) -> (all X12 (pp(aa_TPTP_ind_bool(scratc512413548_nat_p,X12)) -> pp(aa_TPTP_ind_bool(X0,X12))))))) # label(fact_nat__ind) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 160 (all X0 (pp(aa_TPTP_ind_bool(scratc512413548_nat_p,X0)) -> pp(aa_TPTP_ind_bool(scratc512413548_nat_p,aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,X0))))) # label(fact_nat__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 161 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,X0) = aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,X12) -> X0 = X12))) # label(fact_ordsucc__inj) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 162 (all X0 aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,X0) != scratc1625852178ptyset) # label(fact_neq__ordsucc__0) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 163 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X22),aa_fun1431113780TP_ind(scratc1644457143_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(X12,X22)))) # label(fact_k__SepE2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 164 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X22),aa_fun1431113780TP_ind(scratc1644457143_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X22),X0)))) # label(fact_k__SepE1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 165 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X22),X0)) -> (pp(aa_TPTP_ind_bool(X12,X22)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X22),aa_fun1431113780TP_ind(scratc1644457143_d_Sep(X0),X12)))))) # label(fact_k__SepI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 166 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc1637747336_power,X0)))) # label(fact_k__Self__In__Power) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.26 167 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc329299480d_Subq,X12),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1637747336_power,X0))))) # label(fact_k__PowerI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 168 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1637747336_power,X0))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc329299480d_Subq,X12),X0)))) # label(fact_k__PowerE) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 169 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> aa_TPTP_ind_TPTP_ind(scratc327585530bnd_if(X0,X12),X22) = X12 | aa_TPTP_ind_TPTP_ind(scratc327585530bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__or) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 170 (all X0 all X12 all X22 (gg_TPTP_ind(X12) -> (pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc327585530bnd_if(X0,X12),X22) = X12))) # label(fact_if__i__1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 171 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (-pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc327585530bnd_if(X0,X12),X22) = X22))) # label(fact_if__i__0) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 172 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> pp(X0) & aa_TPTP_ind_TPTP_ind(scratc327585530bnd_if(X0,X12),X22) = X12 | -pp(X0) & aa_TPTP_ind_TPTP_ind(scratc327585530bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__correct) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 173 (all X0 pp(aa_TPTP_ind_bool(scratc2097014815closed,aa_TPTP_ind_TPTP_ind(scratc945470330univof,X0)))) # label(fact_k__UnivOf__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 174 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc945470330univof,X0)))) # label(fact_k__UnivOf__In) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 175 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc988419372d_repl,X0),X12))) <-> (exists X3 (gg_TPTP_ind(X3) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X3),X0)) & X22 = aa_TPTP_ind_TPTP_ind(X12,X3)))))) # label(fact_k__ReplEq) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 176 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1637747336_power,X0))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc329299480d_Subq,X12),X0)))) # label(fact_k__PowerEq) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 177 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc2145009202_union,X0))) <-> (exists X2 (gg_TPTP_ind(X2) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X12),X2)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X2),X0)))))) # label(fact_k__UnionEq) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 178 -(exists X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X0),scratc1625852178ptyset))) # label(fact_k__EmptyAx) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 179 (all X0 ((all X13 (gg_TPTP_ind(X13) -> ((all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_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].
% 0.96/1.27 180 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc329299480d_Subq,X0),X12)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc329299480d_Subq,X12),X0)) -> X0 = X12)))) # label(fact_set__ext) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 181 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cn,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1603305019nd_nis,Uu),scratc2110353600nd_n_1)) -> pp(aa_fun171081125l_bool(scratc1061078181n_some,aa_TPT43085870d_bool(aTP_Lamm_ag,Uu)))))) # label(fact_ATP_Olambda__1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 182 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cm,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1603305019nd_nis,Uu),scratc2110353600nd_n_1)) -> pp(aa_fun171081125l_bool(scratc1301474677_n_one,aa_TPT43085870d_bool(aTP_Lamm_ag,Uu)))))) # label(fact_ATP_Olambda__2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 183 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cj,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1703595387d_n_is,aa_TPTP_ind_TPTP_ind(scratc1704054573d_n_pl(Uu),scratc2110353600nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,Uu))))) # label(fact_ATP_Olambda__3) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 184 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cg,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1703595387d_n_is,aa_TPTP_ind_TPTP_ind(scratc1704054573d_n_pl(scratc2110353600nd_n_1),Uu)),aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,Uu))))) # label(fact_ATP_Olambda__4) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 185 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cl,Uu)) <-> pp(aa_fun171081125l_bool(scratc1611894505nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1043730752d_d_Pi,scratc1602780228nd_nat),aTP_Lamm_ad)),aa_TPT43085870d_bool(aTP_Lamm_ck,Uu))))) # label(fact_ATP_Olambda__5) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 186 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ct,Uu)) <-> (pp(aa_TPTP_ind_bool(scratc1781377906_cond1,Uu)) -> (pp(aa_TPTP_ind_bool(scratc1781377907_cond2,Uu)) -> pp(aa_fun171081125l_bool(scratc1206592731all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cs,Uu))))))) # label(fact_ATP_Olambda__6) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 187 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cd,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1703595387d_n_is,aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1704054573d_n_pl(Uu),scratc2110353600nd_n_1))))) # label(fact_ATP_Olambda__7) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 188 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ca,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1703595387d_n_is,aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1704054573d_n_pl(scratc2110353600nd_n_1),Uu))))) # label(fact_ATP_Olambda__8) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 189 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_co,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1603305019nd_nis,aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__9) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 190 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cx,Uu)) <-> scratc625769342_is_of(aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,Uu),aTP_Lamm_a))) # label(fact_ATP_Olambda__10) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 191 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cw,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1603305019nd_nis,aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,Uu)),scratc2110353600nd_n_1)))) # label(fact_ATP_Olambda__11) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 192 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cr,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,Uu),aa_TPTP_ind_TPTP_ind(scratc1637747336_power,scratc1602780228nd_nat))))) # label(fact_ATP_Olambda__12) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 193 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_a,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,Uu),scratc1602780228nd_nat)))) # label(fact_ATP_Olambda__13) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 194 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cv,Uu)) <-> pp(aa_fun171081125l_bool(scratc1206592731all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cu,Uu))))) # label(fact_ATP_Olambda__14) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 195 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cq,Uu)) <-> pp(aa_fun171081125l_bool(scratc1206592731all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cp,Uu))))) # label(fact_ATP_Olambda__15) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 196 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ci,Uu)) <-> pp(aa_fun171081125l_bool(scratc1206592731all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ch,Uu))))) # label(fact_ATP_Olambda__16) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 197 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cf,Uu)) <-> pp(aa_fun171081125l_bool(scratc1206592731all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ce,Uu))))) # label(fact_ATP_Olambda__17) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 198 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cc,Uu)) <-> pp(aa_fun171081125l_bool(scratc1206592731all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cb,Uu))))) # label(fact_ATP_Olambda__18) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 199 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bz,Uu)) <-> pp(aa_fun171081125l_bool(scratc1206592731all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_by,Uu))))) # label(fact_ATP_Olambda__19) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 200 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu)) <-> pp(aa_fun171081125l_bool(scratc1206592731all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bw,Uu))))) # label(fact_ATP_Olambda__20) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 201 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu)) <-> pp(aa_fun171081125l_bool(scratc1206592731all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bt,Uu))))) # label(fact_ATP_Olambda__21) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 202 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bs,Uu)) <-> pp(aa_fun171081125l_bool(scratc1206592731all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_br,Uu))))) # label(fact_ATP_Olambda__22) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 203 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ac,Uu)) <-> pp(aa_fun171081125l_bool(scratc1206592731all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ab,Uu))))) # label(fact_ATP_Olambda__23) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 204 (all Uu aa_TPT494704832TP_ind(aTP_Lamm_bl,Uu) = aa_TPT494704832TP_ind(scratc988419372d_repl,aa_TPTP_ind_TPTP_ind(scratc753951723tminus(Uu),aa_TPTP_ind_TPTP_ind(scratc230948598d_Sing,scratc1625852178ptyset)))) # label(fact_ATP_Olambda__24) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 205 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_ai,Uu)) <-> Uu != scratc1625852178ptyset))) # label(fact_ATP_Olambda__25) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 206 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_bj,Uu)) <-> (exists X2 (gg_TPTP_ind(X2) & aa_TPTP_ind_TPTP_ind(scratc1056056275d_Inj1,X2) = Uu))))) # label(fact_ATP_Olambda__26) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 207 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_bk,Uu)) <-> (exists X2 (gg_TPTP_ind(X2) & aa_TPTP_ind_TPTP_ind(scratc1056056274d_Inj0,X2) = Uu))))) # label(fact_ATP_Olambda__27) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 208 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dx,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc37451378d_e_is(Uu),Uua),Uua)))) # label(fact_ATP_Olambda__28) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 209 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ck,Uu),Uua)) <-> pp(scratc1760708592_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1703595387d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,Uua),scratc2110353600nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,Uu)),aa_fun171081125l_bool(scratc1185682416_n_all,aa_TPT43085870d_bool(aTP_Lamm_af,Uua)))))) # label(fact_ATP_Olambda__29) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 210 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cu,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1703595387d_n_is,aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1703595387d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__30) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 211 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ce,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1703595387d_n_is,aa_TPTP_ind_TPTP_ind(scratc1704054573d_n_pl(aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,aa_TPTP_ind_TPTP_ind(scratc1704054573d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__31) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 212 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ch,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1703595387d_n_is,aa_TPTP_ind_TPTP_ind(scratc1704054573d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,aa_TPTP_ind_TPTP_ind(scratc1704054573d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__32) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 213 (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(scratc1703595387d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,Uu),aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,Uu),Uua)))))) # label(fact_ATP_Olambda__33) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 214 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cp,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1603305019nd_nis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1603305019nd_nis,aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,Uua)))))) # label(fact_ATP_Olambda__34) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 215 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ah,Uu),Uua)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1562259887nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1703595382d_n_in,Uua),Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1703595382d_n_in,aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,Uua)),Uu))))) # label(fact_ATP_Olambda__35) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 216 (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(scratc1703595387d_n_is,aa_TPTP_ind_TPTP_ind(scratc1704054573d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1704054573d_n_pl(Uua),Uu))))) # label(fact_ATP_Olambda__36) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 217 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bi(Uu),Uua) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc988419372d_repl,aa_TPTP_ind_TPTP_ind(Uu,Uua)),aa_TPT1424761345TP_ind(scratc1541223415d_pair,Uua))) # label(fact_ATP_Olambda__37) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 218 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_da,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1206592731all_of(aa_TPT43085870d_bool(aTP_Lamm_cy,Uu)),aa_TPT43085870d_bool(aTP_Lamm_cz(Uu),Uua))))) # label(fact_ATP_Olambda__38) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 219 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_by,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1703595387d_n_is,aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,aa_TPTP_ind_TPTP_ind(scratc1704054573d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc1704054573d_n_pl(aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,Uu)),Uua))))) # label(fact_ATP_Olambda__39) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 220 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cb,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1703595387d_n_is,aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,aa_TPTP_ind_TPTP_ind(scratc1704054573d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc1704054573d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,Uua)))))) # label(fact_ATP_Olambda__40) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 221 (all Uu all Uua aa_fun277296641TP_ind(aa_TPT494704832TP_ind(aTP_Lamm_bm,Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc837666181nunion(aa_TPTP_ind_TPTP_ind(scratc230948598d_Sing,scratc1625852178ptyset)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc988419372d_repl,Uu),Uua))) # label(fact_ATP_Olambda__41) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 222 (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(scratc1603305019nd_nis,Uua),aa_TPTP_ind_TPTP_ind(scratc1704054573d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__42) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 223 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ag,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1703595387d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,Uua))))) # label(fact_ATP_Olambda__43) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 224 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cy,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,Uua),aa_TPTP_ind_TPTP_ind(scratc1637747336_power,Uu))))) # label(fact_ATP_Olambda__44) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 225 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cs,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1703595382d_n_in,Uua),Uu)))) # label(fact_ATP_Olambda__45) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 226 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bn,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1601205846nd_nIn,Uua),Uu)))) # label(fact_ATP_Olambda__46) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 227 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ak,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,Uua),Uu)))) # label(fact_ATP_Olambda__47) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 228 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bw,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1206592731all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bv(Uu),Uua))))) # label(fact_ATP_Olambda__48) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 229 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ab,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1206592731all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa(Uu),Uua))))) # label(fact_ATP_Olambda__49) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 230 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_ae(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc289218662rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,Uu),Uua))) # label(fact_ATP_Olambda__50) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 231 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bf(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc2145009202_union,aa_TPTP_ind_TPTP_ind(Uu,Uua))) # label(fact_ATP_Olambda__51) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 232 (all Uu all Uua (gg_TPTP_ind(Uua) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bh,Uu),Uua)) <-> (exists X3 (gg_TPTP_ind(X3) & Uua = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1541223415d_pair,Uu),X3)))))) # label(fact_ATP_Olambda__52) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 233 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_di(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc37451378d_e_is(aa_TPTP_ind_TPTP_ind(scratc2070625404etprod(Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1326720865d_pair(Uu,Uua),aa_TPTP_ind_TPTP_ind(scratc550577651_first(Uu,Uua),Uub)),aa_TPTP_ind_TPTP_ind(scratc236343473second(Uu,Uua),Uub))),Uub)))) # label(fact_ATP_Olambda__53) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 234 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_bp(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc327585530bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,scratc1625852178ptyset),Uub),Uu),Uua)) # label(fact_ATP_Olambda__54) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 235 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_fun1235454963TP_ind(aTP_Lamm_bo(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc327585530bnd_if(aa_TPTP_ind_bool(Uua,Uub),Uub),scratc1529410667nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bc(Uu),Uua)))) # label(fact_ATP_Olambda__55) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 236 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_av(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1694127488d_esti(Uu),Uub),Uua)))) # label(fact_ATP_Olambda__56) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 237 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_db(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1694127488d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc1644457143_d_Sep(Uu),Uua))) -> pp(aa_TPTP_ind_bool(Uua,Uub))))) # label(fact_ATP_Olambda__57) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 238 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cz(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc479086283d_incl(Uu),Uua),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc479086283d_incl(Uu),Uub),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc37451378d_e_is(aa_TPTP_ind_TPTP_ind(scratc1637747336_power,Uu)),Uua),Uub)))))) # label(fact_ATP_Olambda__58) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 239 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dj(Uu),Uua),Uub)) <-> scratc625769342_is_of(aa_TPTP_ind_TPTP_ind(scratc236343473second(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_ak,Uua)))) # label(fact_ATP_Olambda__59) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 240 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dk(Uu),Uua),Uub)) <-> scratc625769342_is_of(aa_TPTP_ind_TPTP_ind(scratc550577651_first(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_ak,Uu)))) # label(fact_ATP_Olambda__60) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 241 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_dq(Uu),Uua),Uub)) <-> scratc625769342_is_of(aa_TPTP_ind_TPTP_ind(scratc37451373d_e_in(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_ak,Uu)))) # label(fact_ATP_Olambda__61) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 242 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_du(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1206592731all_of(aa_TPT43085870d_bool(aTP_Lamm_dr(Uu),Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dt(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__62) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 243 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bv(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1703595387d_n_is,aa_TPTP_ind_TPTP_ind(scratc1704054573d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1704054573d_n_pl(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc1704054573d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc1704054573d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__63) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 244 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1603305019nd_nis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1603305019nd_nis,aa_TPTP_ind_TPTP_ind(scratc1704054573d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1704054573d_n_pl(Uu),Uub)))))) # label(fact_ATP_Olambda__64) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 245 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bc(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,Uub),Uu)) & pp(aa_TPTP_ind_bool(Uua,Uub)))) # label(fact_ATP_Olambda__65) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 246 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_dn(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc507935582_image(aa_fun1431113780TP_ind(scratc1644457143_d_Sep(Uu),Uua),Uu),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1589990366_Sigma,aa_fun1431113780TP_ind(scratc1644457143_d_Sep(Uu),Uua)),scratc37451373d_e_in(Uu,Uua))),Uub))))) # label(fact_ATP_Olambda__66) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 247 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_dc(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1694127488d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc1644457143_d_Sep(Uu),Uua)))))) # label(fact_ATP_Olambda__67) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 248 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_dw(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1206592731all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_dv(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__68) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 249 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_be(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1206592731all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bd(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__69) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 250 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dm(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1206592731all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dl(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__70) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 251 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dg(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1206592731all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_df(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__71) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 252 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_de(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1206592731all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dd(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__72) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 253 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dr(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,Uub),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1043730752d_d_Pi,Uu),aTP_Lamm_aj(Uua)))))) # label(fact_ATP_Olambda__73) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 254 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dh(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,Uub),aa_TPTP_ind_TPTP_ind(scratc2070625404etprod(Uu),Uua))))) # label(fact_ATP_Olambda__74) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 255 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_do(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,Uub),aa_fun1431113780TP_ind(scratc1644457143_d_Sep(Uu),Uua))))) # label(fact_ATP_Olambda__75) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 256 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_ax(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,Uu),Uub))) # label(fact_ATP_Olambda__76) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 257 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_dp(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(Uua,aa_TPTP_ind_TPTP_ind(scratc37451373d_e_in(Uu,Uua),Uub))))) # label(fact_ATP_Olambda__77) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 258 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1913827119d_bool(aTP_Lamm_bg(Uu),Uua),Uub)) <-> (all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,X3),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc327585538bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,Uub),X3)),aa_TPTP_ind_TPTP_ind(Uua,X3)))))))) # label(fact_ATP_Olambda__78) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 259 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ay(Uu),Uua),Uub),Uuc) = aa_TPTP_ind_TPTP_ind(scratc327585530bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc507935582_image(Uu,Uua),Uub),Uuc),aa_TPTP_ind_TPTP_ind(scratc1850965639d_soft(Uu,Uua,Uub),Uuc)),scratc1625852178ptyset)) # label(fact_ATP_Olambda__79) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 260 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_df(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc37451378d_e_is(Uu),aa_TPTP_ind_TPTP_ind(scratc550577651_first(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1326720865d_pair(Uu,Uua),Uub),Uuc))),Uub)))) # label(fact_ATP_Olambda__80) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 261 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dd(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc37451378d_e_is(Uua),aa_TPTP_ind_TPTP_ind(scratc236343473second(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1326720865d_pair(Uu,Uua),Uub),Uuc))),Uuc)))) # label(fact_ATP_Olambda__81) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 262 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ds(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc37451378d_e_is(Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,Uua),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,Uub),Uuc))))) # label(fact_ATP_Olambda__82) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 263 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ar(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1694127488d_esti(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__83) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 264 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_az(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc37451378d_e_is(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__84) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 265 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dl(Uu),Uua),Uub),Uuc)) <-> scratc625769342_is_of(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1326720865d_pair(Uu,Uua),Uub),Uuc),aa_TPT43085870d_bool(aTP_Lamm_dh(Uu),Uua)))) # label(fact_ATP_Olambda__85) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 266 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_at(Uu),Uua),Uub),Uuc)) <-> pp(scratc1571688045d_l_ec(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1694127488d_esti(Uu),Uuc),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1694127488d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__86) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 267 (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_bool_bool(aa_boo1142376798l_bool(scratc1562259887nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1694127488d_esti(Uu),Uuc),Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1694127488d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__87) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 268 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dt(Uu),Uua),Uub),Uuc)) <-> (pp(aa_fun171081125l_bool(scratc1206592731all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ds(Uua),Uub),Uuc))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc37451378d_e_is(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1043730752d_d_Pi,Uu),aTP_Lamm_aj(Uua))),Uub),Uuc))))) # label(fact_ATP_Olambda__88) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 269 (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_bq(Uu),Uua),Uub),Uuc)) <-> pp(Uu) & Uuc = Uua | -pp(Uu) & Uuc = Uub))) # label(fact_ATP_Olambda__89) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 270 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_dv(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc37451378d_e_is(Uu),Uub),Uuc)) -> pp(aa_TPTP_ind_bool(Uua,Uuc)))))) # label(fact_ATP_Olambda__90) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 271 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bd(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(scratc37451378d_e_is(Uu),Uub),Uuc)))))) # label(fact_ATP_Olambda__91) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 272 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bb(Uu),Uua),Uub),Uuc)) <-> pp(aa_fun171081125l_bool(scratc1496102244nd_all(Uu),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_ba(Uu),Uua),Uub),Uuc))))) # label(fact_ATP_Olambda__92) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 273 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_as(Uu),Uua),Uub),Uuc)) <-> pp(aa_fun171081125l_bool(scratc317253539l_some(Uua),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ar(Uu),Uub),Uuc))))) # label(fact_ATP_Olambda__93) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 274 (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_ba(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1562259887nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc37451378d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,Uub),Uud))),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc37451378d_e_is(Uu),Uuc),Uud))))) # label(fact_ATP_Olambda__94) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 275 (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_ap(Uu),Uua),Uub),Uuc),Uud)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc37451378d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,Uub),Uud)))))) # label(fact_ATP_Olambda__95) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 276 (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_ao(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_fun171081125l_bool(scratc1206592731all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_an(Uu),Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__96) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 277 (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_aq(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_fun171081125l_bool(scratc1206592731all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_ap(Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__97) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.27 278 (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_aw(Uu),Uua),Uub),Uuc),Uud) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1624611190wissel(Uu,Uub),Uuc)),Uud))) # label(fact_ATP_Olambda__98) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 279 (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_an(Uu),Uua),Uub),Uuc),Uud),Uue)) <-> pp(aa_fun171081125l_bool(scratc1206592731all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_am(Uu),Uua),Uub),Uuc),Uud),Uue))))) # label(fact_ATP_Olambda__99) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 280 (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_al(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(scratc37451378d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,Uub),Uuc)),Uue)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc327060748bnd_ap,Uub),Uud)),Uuf))))))) # label(fact_ATP_Olambda__100) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 281 (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_am(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)) <-> pp(aa_fun171081125l_bool(scratc1206592731all_of(aa_TPT43085870d_bool(aTP_Lamm_ak,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_al(Uua),Uub),Uuc),Uud),Uue),Uuf))))) # label(fact_ATP_Olambda__101) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 282 (all Uu all Uua (gg_TPTP_ind(Uu) -> aa_TPTP_ind_TPTP_ind(aTP_Lamm_aj(Uu),Uua) = Uu)) # label(fact_ATP_Olambda__102) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 283 (all Uu aa_TPTP_ind_TPTP_ind(aTP_Lamm_ad,Uu) = scratc1602780228nd_nat) # label(fact_ATP_Olambda__103) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 284 (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].
% 0.96/1.28 285 (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].
% 0.96/1.28 286 (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].
% 0.96/1.28 287 (all P (gg_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 288 (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].
% 0.96/1.28 289 (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].
% 0.96/1.28 290 (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].
% 0.96/1.28 291 (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].
% 0.96/1.28 292 (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].
% 0.96/1.28 293 (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].
% 0.96/1.29 294 (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].
% 0.96/1.29 295 (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].
% 0.96/1.29 296 (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].
% 0.96/1.29
% 0.96/1.29 ============================== end of process non-clausal formulas ===
% 0.96/1.29
% 0.96/1.29 ============================== PROCESS INITIAL CLAUSES ===============
% 0.96/1.29
% 0.96/1.29 ============================== PREDICATE ELIMINATION =================
% 0.96/1.29 297 -gg_bool(A) | A = fTrue | A = fFalse # label(help_fFalse_1_1_T) # label(axiom). [clausify(287)].
% 0.96/1.29 298 gg_bool(undefined_bool(bool)) # label(gsy_c_HOL_Oundefined_001t__HOL__Obool) # label(axiom). [assumption].
% 0.96/1.29 299 gg_bool(scratc97476125_amone(A,B)) # label(gsy_c_Scratch__tptp__translate__41368__4731_ONUM646__thf__4__p_Obnd__amone) # label(axiom). [clausify(1)].
% 0.96/1.29 300 gg_bool(scratc1760708592_d_and(A,B)) # label(gsy_c_Scratch__tptp__translate__41368__4731_ONUM646__thf__4__p_Obnd__d__and) # label(axiom). [clausify(2)].
% 0.96/1.29 301 gg_bool(scratc1868173772_d_not(A)) # label(gsy_c_Scratch__tptp__translate__41368__4731_ONUM646__thf__4__p_Obnd__d__not) # label(axiom). [clausify(3)].
% 0.96/1.29 302 gg_bool(scratc1528557816nd_ec3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__41368__4731_ONUM646__thf__4__p_Obnd__ec3) # label(axiom). [clausify(4)].
% 0.96/1.29 303 gg_bool(scratc1571688045d_l_ec(A,B)) # label(gsy_c_Scratch__tptp__translate__41368__4731_ONUM646__thf__4__p_Obnd__l__ec) # label(axiom). [clausify(8)].
% 0.96/1.29 304 gg_bool(scratc1612156851nd_or3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__41368__4731_ONUM646__thf__4__p_Obnd__or3) # label(axiom). [clausify(9)].
% 0.96/1.29 305 gg_bool(aa_bool_bool(A,B)) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom). [clausify(10)].
% 0.96/1.29 306 gg_bool(aa_TPTP_ind_bool(A,B)) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom). [clausify(11)].
% 0.96/1.29 307 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)].
% 0.96/1.29 308 gg_bool(fEx_TPTP_ind(A)) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom). [clausify(16)].
% 0.96/1.29 309 gg_bool(fFalse) # label(gsy_c_fFalse) # label(axiom). [assumption].
% 0.96/1.29 310 gg_bool(fTrue) # label(gsy_c_fTrue) # label(axiom). [assumption].
% 0.96/1.29 Derived: undefined_bool(bool) = fTrue | undefined_bool(bool) = fFalse. [resolve(297,a,298,a)].
% 0.96/1.29 Derived: scratc97476125_amone(A,B) = fTrue | scratc97476125_amone(A,B) = fFalse. [resolve(297,a,299,a)].
% 0.96/1.29 Derived: scratc1760708592_d_and(A,B) = fTrue | scratc1760708592_d_and(A,B) = fFalse. [resolve(297,a,300,a)].
% 0.96/1.29 Derived: scratc1868173772_d_not(A) = fTrue | scratc1868173772_d_not(A) = fFalse. [resolve(297,a,301,a)].
% 0.96/1.29 Derived: scratc1528557816nd_ec3(A,B,C) = fTrue | scratc1528557816nd_ec3(A,B,C) = fFalse. [resolve(297,a,302,a)].
% 0.96/1.29 Derived: scratc1571688045d_l_ec(A,B) = fTrue | scratc1571688045d_l_ec(A,B) = fFalse. [resolve(297,a,303,a)].
% 0.96/1.29 Derived: scratc1612156851nd_or3(A,B,C) = fTrue | scratc1612156851nd_or3(A,B,C) = fFalse. [resolve(297,a,304,a)].
% 0.96/1.29 Derived: aa_bool_bool(A,B) = fTrue | aa_bool_bool(A,B) = fFalse. [resolve(297,a,305,a)].
% 0.96/1.29 Derived: aa_TPTP_ind_bool(A,B) = fTrue | aa_TPTP_ind_bool(A,B) = fFalse. [resolve(297,a,306,a)].
% 0.96/1.29 Derived: aa_fun171081125l_bool(A,B) = fTrue | aa_fun171081125l_bool(A,B) = fFalse. [resolve(297,a,307,a)].
% 0.96/1.54 Derived: fEx_TPTP_ind(A) = fTrue | fEx_TPTP_ind(A) = fFalse. [resolve(297,a,308,a)].
% 0.96/1.54 Derived: fFalse = fTrue | fFalse = fFalse. [resolve(297,a,309,a)].
% 0.96/1.54 Derived: fTrue = fTrue | fTrue = fFalse. [resolve(297,a,310,a)].
% 0.96/1.54 311 scratc1966622835d_r_ec(A,B) | pp(A) # label(fact_def__r__ec) # label(axiom). [clausify(53)].
% 0.96/1.54 312 -scratc1966622835d_r_ec(A,B) | -pp(A) | pp(scratc1868173772_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(53)].
% 0.96/1.54 313 scratc1966622835d_r_ec(A,B) | -pp(scratc1868173772_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(53)].
% 0.96/1.54 314 scratc543622645_orec3(A,B,C) | -pp(scratc1760708592_d_and(scratc1612156851nd_or3(A,B,C),scratc1528557816nd_ec3(A,B,C))) # label(fact_def__orec3) # label(axiom). [clausify(78)].
% 0.96/1.54 315 -scratc543622645_orec3(A,B,C) | pp(scratc1760708592_d_and(scratc1612156851nd_or3(A,B,C),scratc1528557816nd_ec3(A,B,C))) # label(fact_def__orec3) # label(axiom). [clausify(78)].
% 0.96/1.54 316 scratc507366394_l_iff(A,B) | -pp(scratc1760708592_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1562259887nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc1562259887nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(85)].
% 0.96/1.54 317 -scratc507366394_l_iff(A,B) | pp(scratc1760708592_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1562259887nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc1562259887nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(85)].
% 0.96/1.54 318 scratc900819390d_orec(A,B) | -pp(scratc1760708592_d_and(aa_bool_bool(scratc1572344050d_l_or(A),B),scratc1571688045d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(86)].
% 0.96/1.54 319 -scratc900819390d_orec(A,B) | pp(scratc1760708592_d_and(aa_bool_bool(scratc1572344050d_l_or(A),B),scratc1571688045d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(86)].
% 0.96/1.54 320 scratc1677396161nd_wel(A) | -pp(scratc1868173772_d_not(scratc1868173772_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(91)].
% 0.96/1.54 321 -scratc1677396161nd_wel(A) | pp(scratc1868173772_d_not(scratc1868173772_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(91)].
% 0.96/1.54 322 -scratc1677396161nd_wel(A) | pp(A) # label(fact_l__et) # label(axiom). [clausify(141)].
% 0.96/1.54 Derived: pp(A) | -pp(scratc1868173772_d_not(scratc1868173772_d_not(A))). [resolve(322,a,320,a)].
% 0.96/1.54
% 0.96/1.54 ============================== end predicate elimination =============
% 0.96/1.54
% 0.96/1.54 Auto_denials: (non-Horn, no changes).
% 0.96/1.54
% 0.96/1.54 Term ordering decisions:
% 0.96/1.54 Function symbol KB weights: scratc327585538bnd_in=1. scratc289218662rdsucc=1. scratc327060748bnd_ap=1. aTP_Lamm_a=1. aTP_Lamm_ak=1. scratc1703595387d_n_is=1. scratc1625852178ptyset=1. scratc1589990366_Sigma=1. scratc1603305019nd_nis=1. scratc2110353600nd_n_1=1. fFalse=1. scratc1043730752d_d_Pi=1. scratc1637747336_power=1. scratc512413548_nat_p=1. scratc1602780228nd_nat=1. scratc1562259887nd_imp=1. scratc988419372d_repl=1. fTrue=1. scratc1541223415d_pair=1. scratc329299480d_Subq=1. scratc1766261174_proj0=1. scratc2145009202_union=1. scratc630177602closed=1. aTP_Lamm_ag=1. scratc1703595382d_n_in=1. scratc1766261175_proj1=1. scratc1185682416_n_all=1. aTP_Lamm_ad=1. aTP_Lamm_af=1. aTP_Lamm_cy=1. scratc1582673844closed=1. scratc1747406858closed=1. aTP_Lamm_cp=1. aTP_Lamm_ct=1. aTP_Lamm_cu=1. scratc1056056275d_Inj1=1. scratc1061078181n_some=1. scratc2097014815closed=1. scratc214433926_prop2=1. scratc935916388_omega=1. aTP_Lamm_ab=1. aTP_Lamm_ah=1. aTP_Lamm_bh=1. aTP_Lamm_bj=1. aTP_Lamm_bk=1. aTP_Lamm_br=1. aTP_Lamm_bt=1. aTP_Lamm_bw=1. aTP_Lamm_by=1. aTP_Lamm_cb=1. aTP_Lamm_ce=1. aTP_Lamm_ch=1. aTP_Lamm_ck=1. aTP_Lamm_cm=1. aTP_Lamm_cn=1. aTP_Lamm_cs=1. fconj=1. fimplies=1. scratc1056056274d_Inj0=1. scratc1781377907_cond2=1. scratc214433925_prop1=1. scratc230948598d_Sing=1. aTP_Lamm_bn=1. aTP_Lamm_bs=1. aTP_Lamm_bu=1. aTP_Lamm_bx=1. aTP_Lamm_bz=1. aTP_Lamm_ca=1. aTP_Lamm_cc=1. aTP_Lamm_cd=1. aTP_Lamm_cf=1. aTP_Lamm_cg=1. aTP_Lamm_ci=1. aTP_Lamm_cj=1. aTP_Lamm_cl=1. aTP_Lamm_co=1. aTP_Lamm_cq=1. aTP_Lamm_cr=1. aTP_Lamm_cv=1. aTP_Lamm_cw=1. aTP_Lamm_cx=1. aTP_Lamm_da=1. aTP_Lamm_dx=1. fequal_TPTP_ind=1. scratc1301474677_n_one=1. scratc1601205846nd_nIn=1. scratc1661570538_d_Unj=1. scratc1781377906_cond1=1. scratc945470330univof=1. aTP_Lamm_ac=1. aTP_Lamm_ai=1. aTP_Lamm_bl=1. aTP_Lamm_bm=1. bool=1. scratc1185193223_prop1=1. scratc1391158275_prop1=1. scratc145968633pair_p=1. scratc1632887159d_plus=1. scratc1766654772_prop4=1. scratc1773555398_prop1=1. scratc1911447165nempty=1. scratc1979520450_prop1=1. scratc1991292730munion=1. scratc369421104_empty=1. scratc2003131838d_24_g=1. scratc900296110d_i1_s=1. tPTP_ind=1. aa_TPTP_ind_bool=1. aa_TPT43085870d_bool=1. aa_TPTP_ind_TPTP_ind=1. aa_fun171081125l_bool=1. aa_TPT1424761345TP_ind=1. aa_TPT60673477d_bool=1. aa_fun277296641TP_ind=1. aa_TPT494704832TP_ind=1. aa_fun1584354236d_bool=1. aa_bool_bool=1. aa_fun1431113780TP_ind=1. aa_boo1142376798l_bool=1. aa_TPT1123896796d_bool=1. scratc1760708592_d_and=1. scratc327585530bnd_if=1. scratc1571688045d_l_ec=1. aa_fun1212484691d_bool=1. aa_TPT985247859d_bool=1. scratc37451373d_e_in=1. scratc1326720865d_pair=1. aa_fun987228051d_bool=1. scratc1562325474nd_ind=1. scratc236343473second=1. scratc507935582_image=1. scratc550577651_first=1. aa_TPT125613450d_bool=1. scratc1603698608nd_non=1. scratc97476125_amone=1. aa_fun1913827119d_bool=1. scratc676970824d_anec=1. aa_TPT1791839040TP_ind=1. aa_fun1107270209d_bool=1. aa_fun845057962d_bool=1. scratc1062082354_ecelt=1. scratc1528557877nd_ecp=1. scratc403281896eplSep=1. scratc1061491963_ecect=1. aa_TPT1781712639TP_ind=1. aa_TPT2142672771l_bool=1. aa_fun1235454963TP_ind=1. cOMBB_658106424TP_ind=1. cOMBS_2003118649l_bool=1. scratc1244557867fixfu2=1. scratc1528557881nd_ect=1. scratc1612353713nd_out=1. scratc1624611190wissel=1. scratc1756584393ectset=1. scratc1987304970etprop=1. scratc599293895_fixfu=1. scratc1641382516ectelt=1. scratc1834950003nverse=1. scratc1862701739unmore=1. scratc480332658d_invf=1. scratc484069189d_tofs=1. f1=1. f12=1. f13=1. f20=1. f24=1. scratc1206592731all_of=1. scratc1704054573d_n_pl=1. scratc37451378d_e_is=1. scratc1644457143_d_Sep=1. scratc1694127488d_esti=1. scratc1868173772_d_not=1. scratc317253539l_some=1. scratc1496102244nd_all=1. scratc1798490915_rec_G=1. aTP_Lamm_aj=1. aTP_Lamm_dh=1. scratc1572344050d_l_or=1. scratc1611894505nd_one=1. aTP_Lamm_al=1. aTP_Lamm_av=1. aTP_Lamm_bd=1. aTP_Lamm_bq=1. aTP_Lamm_cz=1. aTP_Lamm_dv=1. scratc479086283d_incl=1. aTP_Lamm_aa=1. aTP_Lamm_ap=1. aTP_Lamm_az=1. aTP_Lamm_bc=1. aTP_Lamm_bg=1. aTP_Lamm_dr=1. aTP_Lamm_dt=1. scratc1515847946ective=1. scratc1529410667nd_eps=1. scratc2070625404etprod=1. aTP_Lamm_am=1. aTP_Lamm_an=1. aTP_Lamm_ao=1. aTP_Lamm_aq=1. aTP_Lamm_ar=1. aTP_Lamm_at=1. aTP_Lamm_au=1. aTP_Lamm_ba=1. aTP_Lamm_bb=1. aTP_Lamm_be=1. aTP_Lamm_bv=1. aTP_Lamm_db=1. aTP_Lamm_dc=1. aTP_Lamm_dd=1. aTP_Lamm_df=1. aTP_Lamm_dl=1. aTP_Lamm_dn=1. aTP_Lamm_do=1. aTP_Lamm_ds=1. fEx_TPTP_ind=1. scratc1523050265ective=1. scratc837666181nunion=1. aTP_Lamm_as=1. aTP_Lamm_de=1. aTP_Lamm_dg=1. aTP_Lamm_di=1. aTP_Lamm_dj=1. aTP_Lamm_dk=1. aTP_Lamm_dm=1. aTP_Lamm_dp=1. aTP_Lamm_dq=1. aTP_Lamm_du=1. aTP_Lamm_dw=1. scratc131045476In_rec=1. scratc1484476744_UPair=1. aTP_Lamm_ae=1. aTP_Lamm_aw=1. aTP_Lamm_ax=1. aTP_Lamm_ay=1. aTP_Lamm_bf=1. aTP_Lamm_bi=1. aTP_Lamm_bo=1. aTP_Lamm_bp=1. cOMBC_1555011498d_bool=1. scratc1170788218t_disj=1. scratc1699567176ective=1. scratc1766654771_prop3=1. scratc420398977_prop1=1. scratc753951723tminus=1. scratc802796100_prop1=1. undefined_bool=1. undefined_TPTP_ind=1. f2=1. f8=1. f9=1. f10=1. f11=1. f17=1. f18=1. f21=1. f22=1. f23=1. scratc1528557816nd_ec3=1. scratc1612156851nd_or3=1. scratc1850965639d_soft=1. scratc1313176110_indeq=1. scratc1562719069nd_ite=1. scratc1766654769_prop1=1. scratc1926674656sel_wa=1. scratc1926674657sel_wb=1. scratc669289602d_11_i=1. f5=1. f7=1. f14=1. f16=1. f19=1. f25=1. scratc1766654770_prop2=1. scratc1365873856_inj_h=1. scratc1848908953hangef=1. f3=1. f4=1. f15=1. scratc761756552_prop1=1. scratc1028067716indeq2=1. f6=1.
% 0.96/1.54
% 0.96/1.54 ============================== end of process initial clauses ========
% 0.96/1.54
% 0.96/1.54 ============================== CLAUSES FOR SEARCH ====================
% 0.96/1.54
% 0.96/1.54 ============================== end of clauses for sCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------