TSTP Solution File: NUM655+4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM655+4 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 13:30:07 EDT 2022
% Result : Timeout 300.08s 300.42s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM655+4 : TPTP v8.1.0. Released v7.3.0.
% 0.13/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jul 5 14:10:57 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.97/1.27 ============================== Prover9 ===============================
% 0.97/1.27 Prover9 (32) version 2009-11A, November 2009.
% 0.97/1.27 Process 12671 was started by sandbox on n025.cluster.edu,
% 0.97/1.27 Tue Jul 5 14:10:58 2022
% 0.97/1.27 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_12518_n025.cluster.edu".
% 0.97/1.27 ============================== end of head ===========================
% 0.97/1.27
% 0.97/1.27 ============================== INPUT =================================
% 0.97/1.27
% 0.97/1.27 % Reading from file /tmp/Prover9_12518_n025.cluster.edu
% 0.97/1.27
% 0.97/1.27 set(prolog_style_variables).
% 0.97/1.27 set(auto2).
% 0.97/1.27 % set(auto2) -> set(auto).
% 0.97/1.27 % set(auto) -> set(auto_inference).
% 0.97/1.27 % set(auto) -> set(auto_setup).
% 0.97/1.27 % set(auto_setup) -> set(predicate_elim).
% 0.97/1.27 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.97/1.27 % set(auto) -> set(auto_limits).
% 0.97/1.27 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.97/1.27 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.97/1.27 % set(auto) -> set(auto_denials).
% 0.97/1.27 % set(auto) -> set(auto_process).
% 0.97/1.27 % set(auto2) -> assign(new_constants, 1).
% 0.97/1.27 % set(auto2) -> assign(fold_denial_max, 3).
% 0.97/1.27 % set(auto2) -> assign(max_weight, "200.000").
% 0.97/1.27 % set(auto2) -> assign(max_hours, 1).
% 0.97/1.27 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.97/1.27 % set(auto2) -> assign(max_seconds, 0).
% 0.97/1.27 % set(auto2) -> assign(max_minutes, 5).
% 0.97/1.27 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.97/1.27 % set(auto2) -> set(sort_initial_sos).
% 0.97/1.27 % set(auto2) -> assign(sos_limit, -1).
% 0.97/1.27 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.97/1.27 % set(auto2) -> assign(max_megs, 400).
% 0.97/1.27 % set(auto2) -> assign(stats, some).
% 0.97/1.27 % set(auto2) -> clear(echo_input).
% 0.97/1.27 % set(auto2) -> set(quiet).
% 0.97/1.27 % set(auto2) -> clear(print_initial_clauses).
% 0.97/1.27 % set(auto2) -> clear(print_given).
% 0.97/1.27 assign(lrs_ticks,-1).
% 0.97/1.27 assign(sos_limit,10000).
% 0.97/1.27 assign(order,kbo).
% 0.97/1.27 set(lex_order_vars).
% 0.97/1.27 clear(print_given).
% 0.97/1.27
% 0.97/1.27 % formulas(sos). % not echoed (400 formulas)
% 0.97/1.27
% 0.97/1.27 ============================== end of input ==========================
% 0.97/1.27
% 0.97/1.27 % From the command line: assign(max_seconds, 300).
% 0.97/1.27
% 0.97/1.27 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.97/1.27
% 0.97/1.27 % Formulas that are not ordinary clauses:
% 0.97/1.27 1 (all B_1 all B_2 gg_bool(scratc729570347_amone(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__43213__14863_ONUM655__thf__4__p_Obnd__amone) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 2 (all B_1 all B_2 gg_bool(scratc747818338_d_and(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__43213__14863_ONUM655__thf__4__p_Obnd__d__and) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 3 (all B_1 gg_bool(scratc855283518_d_not(B_1))) # label(gsy_c_Scratch__tptp__translate__43213__14863_ONUM655__thf__4__p_Obnd__d__not) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 4 (all B_1 all B_2 all B_3 gg_bool(scratc2129040902nd_ec3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__43213__14863_ONUM655__thf__4__p_Obnd__ec3) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 5 (all B_1 all B_2 gg_TPTP_ind(scratc2129040967nd_ect(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__43213__14863_ONUM655__thf__4__p_Obnd__ect) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 6 (all B_1 gg_TPTP_ind(scratc2129893753nd_eps(B_1))) # label(gsy_c_Scratch__tptp__translate__43213__14863_ONUM655__thf__4__p_Obnd__eps) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 7 (all B_1 all B_2 gg_TPTP_ind(scratc15324912nd_ind(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__43213__14863_ONUM655__thf__4__p_Obnd__ind) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 8 (all B_1 all B_2 gg_bool(scratc56298619d_l_ec(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__43213__14863_ONUM655__thf__4__p_Obnd__l__ec) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 9 (all B_1 all B_2 all B_3 gg_bool(scratc65156289nd_or3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__43213__14863_ONUM655__thf__4__p_Obnd__or3) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 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].
% 0.97/1.27 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].
% 0.97/1.27 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].
% 0.97/1.27 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].
% 0.97/1.27 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].
% 0.97/1.27 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].
% 0.97/1.27 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].
% 0.97/1.27 17 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc551581234lessis,X),Xa)) <-> pp(aa_bool_bool(scratc56954624d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc14996922nd_iii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,X),Xa))))) # label(fact_def__lessis) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 18 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc685564846moreis,X),Xa)) <-> pp(aa_bool_bool(scratc56954624d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1244405180_29_ii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,X),Xa))))) # label(fact_def__moreis) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 19 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1019720626_prop1,X),Xa)) <-> pp(scratc65156289nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1244405180_29_ii,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc14996922nd_iii,X),Xa))))) # label(fact_def__d__29__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 20 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc14996922nd_iii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1764858803n_some,aa_TPT43085870d_bool(scratc1461823351ffprop(Xa),X))))) # label(fact_def__iii) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 21 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1244405180_29_ii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1764858803n_some,aa_TPT43085870d_bool(scratc1461823351ffprop(X),Xa))))) # label(fact_def__d__29__ii) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 22 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1461823351ffprop(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,X),aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(Xa),Xb))))) # label(fact_def__diffprop) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 23 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc431358451_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc56304457nd_nis,aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(X),Xb))))) # label(fact_def__d__28__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 24 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1990479924_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc56304457nd_nis,Xa),aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(X),Xa))))) # label(fact_def__d__27__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 25 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1402117749_prop1,X),Xa)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(Xa),X))))) # label(fact_def__d__26__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 26 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc813755574_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(X),Xa)),Xb)),aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(X),aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(Xa),Xb)))))) # label(fact_def__d__25__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 27 (all X scratc188665147d_n_pl(X) = aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1430290409d_plus,X))) # label(fact_def__n__pl) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 28 (all X aa_TPTP_ind_TPTP_ind(scratc1430290409d_plus,X) = scratc15324912nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1675824974d_d_Pi,scratc55779666nd_nat),aTP_Lamm_ac),aa_TPT43085870d_bool(scratc225393400_prop2,X))) # label(fact_def__plus) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 29 (all X aa_TPTP_ind_TPTP_ind(scratc557206064d_24_g,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc144064592_Sigma,scratc55779666nd_nat),aTP_Lamm_ad(X))) # label(fact_def__d__24__g) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 30 (all X (pp(aa_TPTP_ind_bool(scratc251265346_prop4,X)) <-> pp(aa_fun171081125l_bool(scratc1021034161l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1675824974d_d_Pi,scratc55779666nd_nat),aTP_Lamm_ac)),aa_TPT43085870d_bool(scratc225393400_prop2,X))))) # label(fact_def__prop4) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 31 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc251265345_prop3(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,X),Xb)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,Xa),Xb))))) # label(fact_def__prop3) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 32 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc225393400_prop2,X),Xa)) <-> pp(scratc747818338_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,Xa),scratc1907756850nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,X)),aa_TPTP_ind_bool(scratc225393399_prop1,Xa))))) # label(fact_def__d__24__prop2) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 33 (all X (pp(aa_TPTP_ind_bool(scratc225393399_prop1,X)) <-> pp(aa_fun171081125l_bool(scratc172792162_n_all,aa_TPT43085870d_bool(aTP_Lamm_ae,X))))) # label(fact_def__d__24__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 34 (all X (pp(aa_TPTP_ind_bool(scratc1784514872_prop1,X)) <-> pp(aa_bool_bool(scratc56954624d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,X),scratc1907756850nd_n_1)),aa_fun171081125l_bool(scratc1764858803n_some,aa_TPT43085870d_bool(aTP_Lamm_af,X)))))) # label(fact_def__d__23__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 35 (all X (pp(aa_TPTP_ind_bool(scratc1196152697_prop1,X)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc56304457nd_nis,aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,X)),X)))) # label(fact_def__d__22__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 36 (all X (pp(aa_TPTP_ind_bool(scratc265988481_cond2,X)) <-> pp(aa_fun171081125l_bool(scratc172792162_n_all,aa_TPT43085870d_bool(aTP_Lamm_ag,X))))) # label(fact_def__cond2) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 37 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc56304457nd_nis,X),Xa)) <-> pp(scratc855283518_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,X),Xa))))) # label(fact_def__nis) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 38 (all X all Xa all Xb all Xc all Xd scratc15177462indeq2(X,Xa,Xb,Xc,Xd) = aa_TPT1424761345TP_ind(scratc1945270332_indeq(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1370847476d_11_i(X,Xa,Xb),Xc),Xd))) # label(fact_def__indeq2) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 39 (all X all Xa all Xb scratc1370847476d_11_i(X,Xa,Xb) = scratc1945270332_indeq(X,Xa,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1675824974d_d_Pi,X),aTP_Lamm_ai(Xb)))) # label(fact_def__d__11__i) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 40 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc231667613fixfu2(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_an(X),Xa),Xb),Xc))))) # label(fact_def__fixfu2) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 41 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1945270332_indeq(X,Xa,Xb),Xc),Xd) = scratc15324912nd_ind(Xb,aa_TPT43085870d_bool(scratc251265344_prop2(X,Xa,Xb,Xc),Xd))) # label(fact_def__indeq) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 42 (all X all Xa all Xb all Xc all Xd all Xe (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc251265344_prop2(X,Xa,Xb,Xc),Xd),Xe)) <-> pp(aa_fun171081125l_bool(scratc1021034161l_some(X),aa_TPT43085870d_bool(scratc772716026_prop1(X,Xa,Xb,Xc,Xd),Xe))))) # label(fact_def__prop2) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 43 (all X all Xa all Xb all Xc all Xd all Xe all Xf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc772716026_prop1(X,Xa,Xb,Xc,Xd),Xe),Xf)) <-> pp(scratc747818338_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1491530738d_esti(X),Xf),aa_TPTP_ind_TPTP_ind(scratc1693586185_ecect(X,Xa),Xd)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc669545600d_e_is(Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,Xc),Xf)),Xe))))) # label(fact_def__d__10__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 44 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1231388117_fixfu(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ap(X),Xa),Xb),Xc))))) # label(fact_def__fixfu) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 45 (all X all Xa scratc1693586185_ecect(X,Xa) = scratc669545595d_e_in(aa_TPTP_ind_TPTP_ind(scratc122357910_power,X),scratc474374074d_anec(X,Xa))) # label(fact_def__ecect) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 46 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc628492262ectelt(X,Xa),Xb) = aa_TPTP_ind_TPTP_ind(scratc743694139ectset(X,Xa),aa_TPTP_ind_TPTP_ind(scratc1694176576_ecelt(X,Xa),Xb))) # label(fact_def__ectelt) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 47 (all X all Xa scratc743694139ectset(X,Xa) = scratc65353151nd_out(aa_TPTP_ind_TPTP_ind(scratc122357910_power,X),scratc474374074d_anec(X,Xa))) # label(fact_def__ectset) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 48 (all X all Xa scratc2129040967nd_ect(X,Xa) = aa_fun1431113780TP_ind(scratc631566889_d_Sep(aa_TPTP_ind_TPTP_ind(scratc122357910_power,X)),scratc474374074d_anec(X,Xa))) # label(fact_def__ect) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 49 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc474374074d_anec(X,Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1021034161l_some(X),aa_TPT43085870d_bool(scratc2129040963nd_ecp(X,Xa),Xb))))) # label(fact_def__anec) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 50 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2129040963nd_ecp(X,Xa),Xb),Xc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc669545600d_e_is(aa_TPTP_ind_TPTP_ind(scratc122357910_power,X)),Xb),aa_TPTP_ind_TPTP_ind(scratc1694176576_ecelt(X,Xa),Xc))))) # label(fact_def__ecp) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 51 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1694176576_ecelt(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc631566889_d_Sep(X),aa_TPT43085870d_bool(Xa,Xb))) # label(fact_def__ecelt) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 52 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc849811485unmore(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc631566889_d_Sep(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ar(X),Xa),Xb))) # label(fact_def__unmore) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 53 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc649179516etprop(X,Xa),Xb),Xc)) <-> pp(scratc747818338_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1491530738d_esti(X),Xc),Xa),scratc855283518_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1491530738d_esti(X),Xc),Xb)))))) # label(fact_def__nissetprop) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 54 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1872346092t_disj(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc2096585330nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_as(X),Xa),Xb))))) # label(fact_def__st__disj) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 55 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc276489533d_incl(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc2096585330nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_at(X),Xa),Xb))))) # label(fact_def__incl) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 56 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc465521391nempty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1021034161l_some(X),aa_TPT43085870d_bool(aTP_Lamm_au(X),Xa))))) # label(fact_def__nonempty) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 57 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1001515326_empty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),scratc56698046nd_non(X,aa_TPT43085870d_bool(aTP_Lamm_au(X),Xa)))))) # label(fact_def__empty) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 58 (all X scratc1491530738d_esti(X) = scratc1685833332bnd_in) # label(fact_def__esti) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 59 (all X all Xa (scratc451233409d_r_ec(X,Xa) <-> (pp(X) -> pp(scratc855283518_d_not(Xa))))) # label(fact_def__r__ec) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 60 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc405205927hangef(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc144064592_Sigma,X),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_av(X),Xb),Xc),Xd))) # label(fact_def__changef) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 61 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc611720936wissel(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc144064592_Sigma,X),scratc588549203sel_wb(X,Xa,Xb))) # label(fact_def__wissel) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 62 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc588549203sel_wb(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc15718507nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc669545600d_e_is(X),Xc),Xb),X,Xa),aa_TPTP_ind_TPTP_ind(scratc588549202sel_wa(X,Xa,Xb),Xc))) # label(fact_def__wissel__wb) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 63 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc588549202sel_wa(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc15718507nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc669545600d_e_is(X),Xc),Xa),X,Xb),Xc)) # label(fact_def__wissel__wa) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 64 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc15718507nd_ite(X,Xa,Xb),Xc) = scratc15324912nd_ind(Xa,aa_TPT43085870d_bool(scratc251265343_prop1(X,Xa,Xb),Xc))) # label(fact_def__ite) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 65 (all X all Xa all Xb all Xc all Xd (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc251265343_prop1(X,Xa,Xb),Xc),Xd)) <-> pp(scratc747818338_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc15259325nd_imp,X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc669545600d_e_is(Xa),Xd),Xb)),aa_bool_bool(aa_boo1142376798l_bool(scratc15259325nd_imp,scratc855283518_d_not(X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc669545600d_e_is(Xa),Xd),Xc)))))) # label(fact_def__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 66 (all X all Xa scratc1370936867second(X,Xa) = scratc250871749_proj1) # label(fact_def__second) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 67 (all X all Xa scratc1182671873_first(X,Xa) = scratc250871748_proj0) # label(fact_def__first) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 68 (all X all Xa scratc2030501487d_pair(X,Xa) = scratc1338626665d_pair) # label(fact_def__d__pair) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 69 (all X all Xa scratc65353151nd_out(X,Xa) = scratc1648368889d_soft(aa_fun1431113780TP_ind(scratc631566889_d_Sep(X),Xa),X,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc144064592_Sigma,aa_fun1431113780TP_ind(scratc631566889_d_Sep(X),Xa)),scratc669545595d_e_in(X,Xa)))) # label(fact_def__out) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 70 (all X all Xa all Xb (gg_TPTP_ind(Xb) -> aa_TPTP_ind_TPTP_ind(scratc669545595d_e_in(X,Xa),Xb) = Xb)) # label(fact_def__e__in) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 71 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc352983602_inj_h(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc144064592_Sigma,X),aa_TPT1424761345TP_ind(aTP_Lamm_aw(Xc),Xd))) # label(fact_def__inj__h) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 72 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc277735908d_invf(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc144064592_Sigma,Xa),scratc1648368889d_soft(X,Xa,Xb))) # label(fact_def__invf) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 73 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc472483414ective(X),Xa),Xb)) <-> pp(scratc747818338_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc288764184ective(X),Xa),Xb),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc184924811ective(X),Xa),Xb))))) # label(fact_def__bijective) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 74 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc184924811ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc2096585330nd_all(Xa),aa_TPT43085870d_bool(scratc1140029804_image(X,Xa),Xb))))) # label(fact_def__surjective) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 75 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc391246977nverse(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc144064592_Sigma,Xa),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ax(X),Xa),Xb))) # label(fact_def__inverse) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 76 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1648368889d_soft(X,Xa,Xb),Xc) = scratc15324912nd_ind(X,aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(Xa),Xb),Xc))) # label(fact_def__soft) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 77 (all X all Xa scratc281472439d_tofs(X,Xa) = scratc1685308542bnd_ap) # label(fact_def__tofs) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 78 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1140029804_image(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1021034161l_some(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(Xa),Xb),Xc))))) # label(fact_def__image) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 79 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc288764184ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc2096585330nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ba(X),Xa),Xb))))) # label(fact_def__injective) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 80 (all X all Xa scratc15324912nd_ind(X,Xa) = scratc2129893753nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bb(X),Xa))) # label(fact_def__ind) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 81 (all X all Xa (pp(aa_fun171081125l_bool(scratc64893943nd_one(X),Xa)) <-> pp(scratc747818338_d_and(scratc729570347_amone(X,Xa),aa_fun171081125l_bool(scratc1021034161l_some(X),Xa))))) # label(fact_def__one) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 82 (all X all Xa (pp(scratc729570347_amone(X,Xa)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),aa_fun1584354236d_bool(aTP_Lamm_bd(X),Xa))))) # label(fact_def__amone) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 83 (all X scratc669545600d_e_is(X) = fequal_TPTP_ind) # label(fact_def__e__is) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 84 (all X all Xa all Xb (scratc1175716867_orec3(X,Xa,Xb) <-> pp(scratc747818338_d_and(scratc65156289nd_or3(X,Xa,Xb),scratc2129040902nd_ec3(X,Xa,Xb))))) # label(fact_def__orec3) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 85 (all X all Xa all Xb (pp(scratc2129040902nd_ec3(X,Xa,Xb)) <-> scratc474308427d_and3(scratc56298619d_l_ec(X,Xa),scratc56298619d_l_ec(Xa,Xb),scratc56298619d_l_ec(Xb,X)))) # label(fact_def__ec3) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 86 (all X all Xa all Xb (scratc474308427d_and3(X,Xa,Xb) <-> pp(scratc747818338_d_and(X,scratc747818338_d_and(Xa,Xb))))) # label(fact_def__and3) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 87 (all X all Xa all Xb (pp(scratc65156289nd_or3(X,Xa,Xb)) <-> pp(aa_bool_bool(scratc56954624d_l_or(X),aa_bool_bool(scratc56954624d_l_or(Xa),Xb))))) # label(fact_def__or3) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 88 (all X all Xa (pp(aa_fun171081125l_bool(scratc1021034161l_some(X),Xa)) <-> pp(scratc855283518_d_not(aa_fun171081125l_bool(scratc1910373353all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),scratc56698046nd_non(X,Xa)))))) # label(fact_def__l__some) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 89 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc56698046nd_non(X,Xa),Xb)) <-> pp(scratc855283518_d_not(aa_TPTP_ind_bool(Xa,Xb))))) # label(fact_def__non) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 90 (all X scratc2096585330nd_all(X) = scratc1910373353all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X))) # label(fact_def__all) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 91 (all X all Xa (scratc1641959788_l_iff(X,Xa) <-> pp(scratc747818338_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc15259325nd_imp,X),Xa),aa_bool_bool(aa_boo1142376798l_bool(scratc15259325nd_imp,Xa),X))))) # label(fact_def__l__iff) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 92 (all X all Xa (scratc698222640d_orec(X,Xa) <-> pp(scratc747818338_d_and(aa_bool_bool(scratc56954624d_l_or(X),Xa),scratc56298619d_l_ec(X,Xa))))) # label(fact_def__orec) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 93 (all X scratc56954624d_l_or(X) = aa_boo1142376798l_bool(scratc15259325nd_imp,scratc855283518_d_not(X))) # label(fact_def__l__or) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 94 (all X all Xa (pp(scratc747818338_d_and(X,Xa)) <-> pp(scratc855283518_d_not(scratc56298619d_l_ec(X,Xa))))) # label(fact_def__d__and) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 95 (all X all Xa (pp(scratc56298619d_l_ec(X,Xa)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc15259325nd_imp,X),scratc855283518_d_not(Xa))))) # label(fact_def__l__ec) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 96 scratc1256329624bvious <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc15259325nd_imp,fFalse),fFalse)) # label(fact_def__obvious) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 97 (all X (scratc130395599nd_wel(X) <-> pp(scratc855283518_d_not(scratc855283518_d_not(X))))) # label(fact_def__wel) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 98 (all X (pp(scratc855283518_d_not(X)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc15259325nd_imp,X),fFalse)))) # label(fact_def__d__not) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 99 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1675824974d_d_Pi,X),Xa) = aa_fun1431113780TP_ind(scratc631566889_d_Sep(aa_TPTP_ind_TPTP_ind(scratc122357910_power,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc144064592_Sigma,X),aTP_Lamm_be(Xa)))),aa_fun1913827119d_bool(aTP_Lamm_bf(X),Xa))) # label(fact_def__d__Pi) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 100 (all X (gg_TPTP_ind(X) -> (pp(aa_TPTP_ind_bool(scratc849749255pair_p,X)) <-> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1338626665d_pair,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,X),scratc179926404ptyset)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,X),aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,scratc179926404ptyset))) = X))) # label(fact_def__pair__p) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 101 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc1212640090eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bg,Xa)),scratc250871749_proj1)) # label(fact_def__ap) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 102 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc626922378etprod(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc144064592_Sigma,X),aTP_Lamm_ai(Xa))) # label(fact_def__setprod) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 103 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc144064592_Sigma,X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc545366956munion,X),aTP_Lamm_bh(Xa))) # label(fact_def__d__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 104 (all X aa_TPTP_ind_TPTP_ind(scratc250871749_proj1,X) = aa_fun277296641TP_ind(scratc1212640090eplSep(X,aTP_Lamm_bi),scratc648680284_d_Unj)) # label(fact_def__proj1) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 105 (all X aa_TPTP_ind_TPTP_ind(scratc250871748_proj0,X) = aa_fun277296641TP_ind(scratc1212640090eplSep(X,aTP_Lamm_bj),scratc648680284_d_Unj)) # label(fact_def__proj0) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 106 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1338626665d_pair,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1539224055nunion(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc785822622d_repl,X),scratc1759836896d_Inj0)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc785822622d_repl,Xa),scratc1759836897d_Inj1))) # label(fact_def__pair) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 107 (all X aa_TPTP_ind_TPTP_ind(scratc1759836896d_Inj0,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc785822622d_repl,X),scratc1759836897d_Inj1)) # label(fact_def__d__Inj0) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 108 (all X (pp(aa_TPTP_ind_bool(scratc1647006942_nat_p,X)) <-> (all X1 (pp(aa_TPTP_ind_bool(X1,scratc179926404ptyset)) -> ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(X1,X2)) -> pp(aa_TPTP_ind_bool(X1,aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,X2)))))) -> pp(aa_TPTP_ind_bool(X1,X))))))) # label(fact_def__nat__p) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 109 (all X aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1539224055nunion(X),aa_TPTP_ind_TPTP_ind(scratc934729220d_Sing,X))) # label(fact_def__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 110 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc940403670In_rec(X),Xa) = scratc2129893753nd_eps(aa_TPT43085870d_bool(scratc1322003761_rec_G(X),Xa))) # label(fact_def__d__In__rec) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 111 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1322003761_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(scratc1685833332bnd_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].
% 0.97/1.27 112 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1455509597tminus(X),Xa) = aa_fun1431113780TP_ind(scratc631566889_d_Sep(X),aa_TPT43085870d_bool(aTP_Lamm_bm,Xa))) # label(fact_def__setminus) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 113 (all X all Xa scratc1212640090eplSep(X,Xa) = aa_TPT494704832TP_ind(scratc785822622d_repl,aa_fun1431113780TP_ind(scratc631566889_d_Sep(X),Xa))) # label(fact_def__d__ReplSep) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 114 (all X all Xa aa_fun1431113780TP_ind(scratc631566889_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1685833324bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1685833332bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc785822622d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bn(X),Xa))),scratc179926404ptyset)) # label(fact_def__d__Sep) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 115 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc545366956munion,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc629619776_union,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc785822622d_repl,X),Xa))) # label(fact_def__famunion) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 116 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1539224055nunion(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc629619776_union,aa_TPTP_ind_TPTP_ind(scratc38550970_UPair(X),Xa))) # label(fact_def__binunion) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 117 (all X aa_TPTP_ind_TPTP_ind(scratc934729220d_Sing,X) = aa_TPTP_ind_TPTP_ind(scratc38550970_UPair(X),X)) # label(fact_def__d__Sing) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 118 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc38550970_UPair(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc785822622d_repl,aa_TPTP_ind_TPTP_ind(scratc122357910_power,aa_TPTP_ind_TPTP_ind(scratc122357910_power,scratc179926404ptyset))),aa_TPT1424761345TP_ind(aTP_Lamm_bo(X),Xa))) # label(fact_def__d__UPair) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 119 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc54205284nd_nIn,X),Xa)) <-> -pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X),Xa)))) # label(fact_def__nIn) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 120 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1685833324bnd_if(X,Xa),Xb) = scratc2129893753nd_eps(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bp(X),Xa),Xb))) # label(fact_def__if) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 121 (all X (pp(aa_TPTP_ind_bool(scratc1620527661closed,X)) <-> pp(aa_TPTP_ind_bool(scratc616904742closed,X)) & pp(aa_TPTP_ind_bool(scratc781637756closed,X)) & pp(aa_TPTP_ind_bool(scratc360512080closed,X)))) # label(fact_def__d__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 122 (all X (pp(aa_TPTP_ind_bool(scratc360512080closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X1),X)) -> (all X2 ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X3),X1)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,aa_TPTP_ind_TPTP_ind(X2,X3)),X))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc785822622d_repl,X1),X2)),X))))))))) # label(fact_def__d__Repl__closed) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 123 (all X (pp(aa_TPTP_ind_bool(scratc781637756closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,aa_TPTP_ind_TPTP_ind(scratc122357910_power,X1)),X))))))) # label(fact_def__d__Power__closed) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 124 (all X (pp(aa_TPTP_ind_bool(scratc616904742closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,aa_TPTP_ind_TPTP_ind(scratc629619776_union,X1)),X))))))) # label(fact_def__d__Union__closed) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 125 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1033080102d_Subq,X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X2),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X2),Xa))))))) # label(fact_def__d__Subq) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 126 (all X all Xa (pp(aa_fun171081125l_bool(scratc1910373353all_of(X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (scratc1760362736_is_of(X2,X) -> pp(aa_TPTP_ind_bool(Xa,X2))))))) # label(fact_def__all__of) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.27 127 (all X all Xa (scratc1760362736_is_of(X,Xa) <-> pp(aa_TPTP_ind_bool(Xa,X)))) # label(fact_def__is__of) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 128 (all X0 pp(aa_fun171081125l_bool(scratc1910373353all_of(aa_TPT43085870d_bool(aTP_Lamm_eh,X0)),aa_TPT43085870d_bool(aTP_Lamm_ej,X0)))) # label(fact_isseti) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 129 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1910373353all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_ek(X0),X12)))) # label(fact_estie) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 130 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1910373353all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_el(X0),X12)))) # label(fact_estii) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 131 (all X0 all X12 scratc1760362736_is_of(aa_fun1431113780TP_ind(scratc631566889_d_Sep(X0),X12),aa_TPT43085870d_bool(aTP_Lamm_eh,X0))) # label(fact_setof__p) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 132 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1910373353all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_en(X0),X12)))) # label(fact_secondis1) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 133 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1910373353all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_ep(X0),X12)))) # label(fact_firstis1) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 134 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1910373353all_of(aa_TPT43085870d_bool(aTP_Lamm_eq(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_er(X0),X12)))) # label(fact_pairis1) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 135 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1910373353all_of(aa_TPT43085870d_bool(aTP_Lamm_eq(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_es(X0),X12)))) # label(fact_second__p) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 136 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1910373353all_of(aa_TPT43085870d_bool(aTP_Lamm_eq(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_et(X0),X12)))) # label(fact_first__p) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 137 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1910373353all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_ev(X0),X12)))) # label(fact_e__pair__p) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 138 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1910373353all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_ew(X0),X12)))) # label(fact_otax2) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 139 (all X0 all X12 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc288764184ective(aa_fun1431113780TP_ind(scratc631566889_d_Sep(X0),X12)),X0),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc144064592_Sigma,aa_fun1431113780TP_ind(scratc631566889_d_Sep(X0),X12)),scratc669545595d_e_in(X0,X12))))) # label(fact_otax1) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 140 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1910373353all_of(aa_fun1584354236d_bool(aTP_Lamm_ex(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_ey(X0),X12)))) # label(fact_e__inp) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 141 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1910373353all_of(aa_fun1584354236d_bool(aTP_Lamm_ex(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_ez(X0),X12)))) # label(fact_e__in__p) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 142 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1910373353all_of(aa_TPT43085870d_bool(aTP_Lamm_fa(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_fd(X0),X12)))) # label(fact_e__fisi) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 143 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc64893943nd_one(X0),X12)) -> pp(aa_TPTP_ind_bool(X12,scratc15324912nd_ind(X0,X12))))) # label(fact_oneax) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 144 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc64893943nd_one(X0),X12)) -> scratc1760362736_is_of(scratc15324912nd_ind(X0,X12),aa_TPT43085870d_bool(aTP_Lamm_aj,X0)))) # label(fact_ind__p) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 145 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1910373353all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_ff(X0),X12)))) # label(fact_e__isp) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 146 (all X0 pp(aa_fun171081125l_bool(scratc1910373353all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_fg,X0)))) # label(fact_refis) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 147 (all X0 (scratc130395599nd_wel(X0) -> pp(X0))) # label(fact_l__et) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 148 (all X0 all X12 all X22 all X32 (pp(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1685833324bnd_if(X0,X22),X32))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X12),X22))))) # label(fact_k__If__In__then__E) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 149 (all X0 all X12 all X22 ((pp(X0) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X12),X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,aa_TPTP_ind_TPTP_ind(scratc1685833324bnd_if(X0,X12),scratc179926404ptyset)),aa_TPTP_ind_TPTP_ind(scratc1685833324bnd_if(X0,X22),aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,scratc179926404ptyset)))))) # label(fact_k__If__In__01) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 150 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X33),X0)) -> aa_TPTP_ind_TPTP_ind(X12,X33) = aa_TPTP_ind_TPTP_ind(X22,X33)))) -> aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc144064592_Sigma,X0),X12) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc144064592_Sigma,X0),X22))) # label(fact_xi__ext) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 151 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1675824974d_d_Pi,X0),X12))) -> (all X32 (gg_TPTP_ind(X32) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X32),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1675824974d_d_Pi,X0),X12))) -> ((all X42 (gg_TPTP_ind(X42) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X42),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,X22),X42) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,X32),X42)))) -> X22 = X32))))))) # label(fact_k__Pi__ext) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 152 (all X0 all X12 all X22 all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1675824974d_d_Pi,X0),X12))) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X32),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,X22),X32)),aa_TPTP_ind_TPTP_ind(X12,X32)))))) # label(fact_ap__Pi) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 153 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X33),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,aa_TPTP_ind_TPTP_ind(X22,X33)),aa_TPTP_ind_TPTP_ind(X12,X33)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc144064592_Sigma,X0),X22)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1675824974d_d_Pi,X0),X12))))) # label(fact_lam__Pi) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 154 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X22),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc144064592_Sigma,X0),X12)),X22) = aa_TPTP_ind_TPTP_ind(X12,X22))) # label(fact_beta) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 155 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc144064592_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,aa_TPTP_ind_TPTP_ind(scratc250871749_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc250871748_proj0,X22)))))) # label(fact_proj1__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 156 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc144064592_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,aa_TPTP_ind_TPTP_ind(scratc250871748_proj0,X22)),X0)))) # label(fact_proj0__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 157 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc144064592_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1338626665d_pair,aa_TPTP_ind_TPTP_ind(scratc250871748_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc250871749_proj1,X22)) = X22))) # label(fact_proj__Sigma__eta) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 158 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc144064592_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1338626665d_pair,aa_TPTP_ind_TPTP_ind(scratc250871748_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc250871749_proj1,X22)) = X22 & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,aa_TPTP_ind_TPTP_ind(scratc250871748_proj0,X22)),X0)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,aa_TPTP_ind_TPTP_ind(scratc250871749_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc250871748_proj0,X22))))))) # label(fact_k__Sigma__eta__proj0__proj1) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 159 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X22),X0)) -> (all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X32),aa_TPTP_ind_TPTP_ind(X12,X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1338626665d_pair,X22),X32)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc144064592_Sigma,X0),X12))))))) # label(fact_pair__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 160 (all X0 all X12 (gg_TPTP_ind(X12) -> aa_TPTP_ind_TPTP_ind(scratc250871749_proj1,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1338626665d_pair,X0),X12)) = X12)) # label(fact_proj1__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 161 (all X0 all X12 (gg_TPTP_ind(X0) -> aa_TPTP_ind_TPTP_ind(scratc250871748_proj0,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1338626665d_pair,X0),X12)) = X0)) # label(fact_proj0__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 162 (all X0 (pp(aa_TPTP_ind_bool(scratc1647006942_nat_p,X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X0),scratc1568010610_omega)))) # label(fact_nat__p__omega) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 163 (all X0 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X0),scratc1568010610_omega)) -> pp(aa_TPTP_ind_bool(scratc1647006942_nat_p,X0)))) # label(fact_omega__nat__p) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 164 (all X0 (gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(scratc1647006942_nat_p,X0)) -> X0 = scratc179926404ptyset | (exists X13 (gg_TPTP_ind(X13) & pp(aa_TPTP_ind_bool(scratc1647006942_nat_p,X13)) & X0 = aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,X13)))))) # label(fact_nat__inv) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 165 (all X0 (pp(aa_TPTP_ind_bool(X0,scratc179926404ptyset)) -> ((all X13 (gg_TPTP_ind(X13) -> (pp(aa_TPTP_ind_bool(scratc1647006942_nat_p,X13)) -> (pp(aa_TPTP_ind_bool(X0,X13)) -> pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,X13))))))) -> (all X12 (pp(aa_TPTP_ind_bool(scratc1647006942_nat_p,X12)) -> pp(aa_TPTP_ind_bool(X0,X12))))))) # label(fact_nat__ind) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 166 (all X0 (pp(aa_TPTP_ind_bool(scratc1647006942_nat_p,X0)) -> pp(aa_TPTP_ind_bool(scratc1647006942_nat_p,aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,X0))))) # label(fact_nat__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 167 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,X0) = aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,X12) -> X0 = X12))) # label(fact_ordsucc__inj) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 168 (all X0 aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,X0) != scratc179926404ptyset) # label(fact_neq__ordsucc__0) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 169 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X22),aa_fun1431113780TP_ind(scratc631566889_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(X12,X22)))) # label(fact_k__SepE2) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 170 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X22),aa_fun1431113780TP_ind(scratc631566889_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X22),X0)))) # label(fact_k__SepE1) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 171 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X22),X0)) -> (pp(aa_TPTP_ind_bool(X12,X22)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X22),aa_fun1431113780TP_ind(scratc631566889_d_Sep(X0),X12)))))) # label(fact_k__SepI) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 172 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc122357910_power,X0)))) # label(fact_k__Self__In__Power) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 173 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1033080102d_Subq,X12),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc122357910_power,X0))))) # label(fact_k__PowerI) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 174 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc122357910_power,X0))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1033080102d_Subq,X12),X0)))) # label(fact_k__PowerE) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 175 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> aa_TPTP_ind_TPTP_ind(scratc1685833324bnd_if(X0,X12),X22) = X12 | aa_TPTP_ind_TPTP_ind(scratc1685833324bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__or) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 176 (all X0 all X12 all X22 (gg_TPTP_ind(X12) -> (pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc1685833324bnd_if(X0,X12),X22) = X12))) # label(fact_if__i__1) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 177 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (-pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc1685833324bnd_if(X0,X12),X22) = X22))) # label(fact_if__i__0) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 178 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> pp(X0) & aa_TPTP_ind_TPTP_ind(scratc1685833324bnd_if(X0,X12),X22) = X12 | -pp(X0) & aa_TPTP_ind_TPTP_ind(scratc1685833324bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__correct) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 179 (all X0 pp(aa_TPTP_ind_bool(scratc1620527661closed,aa_TPTP_ind_TPTP_ind(scratc2080063724univof,X0)))) # label(fact_k__UnivOf__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 180 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc2080063724univof,X0)))) # label(fact_k__UnivOf__In) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 181 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc785822622d_repl,X0),X12))) <-> (exists X3 (gg_TPTP_ind(X3) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X3),X0)) & X22 = aa_TPTP_ind_TPTP_ind(X12,X3)))))) # label(fact_k__ReplEq) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 182 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc122357910_power,X0))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1033080102d_Subq,X12),X0)))) # label(fact_k__PowerEq) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 183 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc629619776_union,X0))) <-> (exists X2 (gg_TPTP_ind(X2) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X12),X2)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X2),X0)))))) # label(fact_k__UnionEq) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 184 -(exists X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X0),scratc179926404ptyset))) # label(fact_k__EmptyAx) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 185 (all X0 ((all X13 (gg_TPTP_ind(X13) -> ((all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_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].
% 0.97/1.28 186 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1033080102d_Subq,X0),X12)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1033080102d_Subq,X12),X0)) -> X0 = X12)))) # label(fact_set__ext) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 187 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dw,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc56304457nd_nis,Uu),scratc1907756850nd_n_1)) -> pp(aa_fun171081125l_bool(scratc1764858803n_some,aa_TPT43085870d_bool(aTP_Lamm_af,Uu)))))) # label(fact_ATP_Olambda__1) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 188 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dv,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc56304457nd_nis,Uu),scratc1907756850nd_n_1)) -> pp(aa_fun171081125l_bool(scratc288584423_n_one,aa_TPT43085870d_bool(aTP_Lamm_af,Uu)))))) # label(fact_ATP_Olambda__2) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 189 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ds,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(Uu),scratc1907756850nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,Uu))))) # label(fact_ATP_Olambda__3) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 190 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dp,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(scratc1907756850nd_n_1),Uu)),aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,Uu))))) # label(fact_ATP_Olambda__4) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 191 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_du,Uu)) <-> pp(aa_fun171081125l_bool(scratc64893943nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1675824974d_d_Pi,scratc55779666nd_nat),aTP_Lamm_ac)),aa_TPT43085870d_bool(aTP_Lamm_dt,Uu))))) # label(fact_ATP_Olambda__5) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 192 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ec,Uu)) <-> (pp(aa_TPTP_ind_bool(scratc265988480_cond1,Uu)) -> (pp(aa_TPTP_ind_bool(scratc265988481_cond2,Uu)) -> pp(aa_fun171081125l_bool(scratc1910373353all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_eb,Uu))))))) # label(fact_ATP_Olambda__6) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 193 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dm,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(Uu),scratc1907756850nd_n_1))))) # label(fact_ATP_Olambda__7) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 194 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dj,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(scratc1907756850nd_n_1),Uu))))) # label(fact_ATP_Olambda__8) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 195 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dx,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc56304457nd_nis,aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__9) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 196 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_eg,Uu)) <-> scratc1760362736_is_of(aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,Uu),aTP_Lamm_a))) # label(fact_ATP_Olambda__10) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 197 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ef,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc56304457nd_nis,aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,Uu)),scratc1907756850nd_n_1)))) # label(fact_ATP_Olambda__11) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 198 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ea,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,Uu),aa_TPTP_ind_TPTP_ind(scratc122357910_power,scratc55779666nd_nat))))) # label(fact_ATP_Olambda__12) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 199 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_a,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,Uu),scratc55779666nd_nat)))) # label(fact_ATP_Olambda__13) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 200 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ee,Uu)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ed,Uu))))) # label(fact_ATP_Olambda__14) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 201 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dz,Uu)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dy,Uu))))) # label(fact_ATP_Olambda__15) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 202 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dr,Uu)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dq,Uu))))) # label(fact_ATP_Olambda__16) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 203 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_do,Uu)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dn,Uu))))) # label(fact_ATP_Olambda__17) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 204 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dl,Uu)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dk,Uu))))) # label(fact_ATP_Olambda__18) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 205 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_di,Uu)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dh,Uu))))) # label(fact_ATP_Olambda__19) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 206 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dg,Uu)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_df,Uu))))) # label(fact_ATP_Olambda__20) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 207 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dd,Uu)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dc,Uu))))) # label(fact_ATP_Olambda__21) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 208 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_db,Uu)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_da,Uu))))) # label(fact_ATP_Olambda__22) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 209 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cz,Uu)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cy,Uu))))) # label(fact_ATP_Olambda__23) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 210 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cw,Uu)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cv,Uu))))) # label(fact_ATP_Olambda__24) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 211 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ct,Uu)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cs,Uu))))) # label(fact_ATP_Olambda__25) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 212 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cr,Uu)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cq,Uu))))) # label(fact_ATP_Olambda__26) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 213 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cn,Uu)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cm,Uu))))) # label(fact_ATP_Olambda__27) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 214 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cl,Uu)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ck,Uu))))) # label(fact_ATP_Olambda__28) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 215 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cj,Uu)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ci,Uu))))) # label(fact_ATP_Olambda__29) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 216 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ch,Uu)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cg,Uu))))) # label(fact_ATP_Olambda__30) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 217 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cf,Uu)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ce,Uu))))) # label(fact_ATP_Olambda__31) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 218 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cd,Uu)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cc,Uu))))) # label(fact_ATP_Olambda__32) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 219 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cb,Uu)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ca,Uu))))) # label(fact_ATP_Olambda__33) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 220 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bz,Uu)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_by,Uu))))) # label(fact_ATP_Olambda__34) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 221 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bw,Uu))))) # label(fact_ATP_Olambda__35) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 222 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bv,Uu)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bu,Uu))))) # label(fact_ATP_Olambda__36) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 223 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bt,Uu)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bs,Uu))))) # label(fact_ATP_Olambda__37) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 224 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_br,Uu)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bq,Uu))))) # label(fact_ATP_Olambda__38) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 225 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ab,Uu)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,Uu))))) # label(fact_ATP_Olambda__39) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 226 (all Uu aa_TPT494704832TP_ind(aTP_Lamm_bk,Uu) = aa_TPT494704832TP_ind(scratc785822622d_repl,aa_TPTP_ind_TPTP_ind(scratc1455509597tminus(Uu),aa_TPTP_ind_TPTP_ind(scratc934729220d_Sing,scratc179926404ptyset)))) # label(fact_ATP_Olambda__40) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 227 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_ah,Uu)) <-> Uu != scratc179926404ptyset))) # label(fact_ATP_Olambda__41) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 228 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_bi,Uu)) <-> (exists X2 (gg_TPTP_ind(X2) & aa_TPTP_ind_TPTP_ind(scratc1759836897d_Inj1,X2) = Uu))))) # label(fact_ATP_Olambda__42) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 229 (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(scratc1759836896d_Inj0,X2) = Uu))))) # label(fact_ATP_Olambda__43) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 230 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ci,Uu),Uua)) <-> scratc1175716867_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1244405180_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc14996922nd_iii,Uu),Uua)))) # label(fact_ATP_Olambda__44) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 231 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cg,Uu),Uua)) <-> pp(scratc65156289nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1244405180_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc14996922nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__45) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 232 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ce,Uu),Uua)) <-> pp(scratc2129040902nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1244405180_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc14996922nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__46) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 233 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cq,Uu),Uua)) <-> scratc1175716867_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1764858803n_some,aa_TPT43085870d_bool(aTP_Lamm_co(Uu),Uua)),aa_fun171081125l_bool(scratc1764858803n_some,aa_TPT43085870d_bool(aTP_Lamm_cp(Uu),Uua))))) # label(fact_ATP_Olambda__47) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 234 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cm,Uu),Uua)) <-> pp(scratc65156289nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1764858803n_some,aa_TPT43085870d_bool(scratc1461823351ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc1764858803n_some,aa_TPT43085870d_bool(scratc1461823351ffprop(Uua),Uu)))))) # label(fact_ATP_Olambda__48) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 235 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ck,Uu),Uua)) <-> pp(scratc2129040902nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1764858803n_some,aa_TPT43085870d_bool(scratc1461823351ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc1764858803n_some,aa_TPT43085870d_bool(scratc1461823351ffprop(Uua),Uu)))))) # label(fact_ATP_Olambda__49) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 236 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fg,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc669545600d_e_is(Uu),Uua),Uua)))) # label(fact_ATP_Olambda__50) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 237 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dt,Uu),Uua)) <-> pp(scratc747818338_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,Uua),scratc1907756850nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,Uu)),aa_fun171081125l_bool(scratc172792162_n_all,aa_TPT43085870d_bool(aTP_Lamm_ae,Uua)))))) # label(fact_ATP_Olambda__51) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 238 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ed,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__52) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 239 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dn,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__53) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 240 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dq,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__54) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 241 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ae,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,Uu),aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,Uu),Uua)))))) # label(fact_ATP_Olambda__55) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 242 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dy,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc56304457nd_nis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc56304457nd_nis,aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,Uua)))))) # label(fact_ATP_Olambda__56) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 243 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ag,Uu),Uua)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc15259325nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205956d_n_in,Uua),Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205956d_n_in,aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,Uua)),Uu))))) # label(fact_ATP_Olambda__57) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 244 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dc,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(Uua),Uu))))) # label(fact_ATP_Olambda__58) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 245 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cc,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1244405180_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc14996922nd_iii,Uua),Uu))))) # label(fact_ATP_Olambda__59) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 246 (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(scratc685564846moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc551581234lessis,Uua),Uu))))) # label(fact_ATP_Olambda__60) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 247 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bw,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc551581234lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc685564846moreis,Uua),Uu))))) # label(fact_ATP_Olambda__61) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 248 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ca,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc14996922nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1244405180_29_ii,Uua),Uu))))) # label(fact_ATP_Olambda__62) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 249 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bu,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc685564846moreis,Uu),Uua)) -> pp(scratc855283518_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc14996922nd_iii,Uu),Uua)))))) # label(fact_ATP_Olambda__63) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 250 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bs,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc551581234lessis,Uu),Uua)) -> pp(scratc855283518_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1244405180_29_ii,Uu),Uua)))))) # label(fact_ATP_Olambda__64) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 251 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bh(Uu),Uua) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc785822622d_repl,aa_TPTP_ind_TPTP_ind(Uu,Uua)),aa_TPT1424761345TP_ind(scratc1338626665d_pair,Uua))) # label(fact_ATP_Olambda__65) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 252 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ej,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aa_TPT43085870d_bool(aTP_Lamm_eh,Uu)),aa_TPT43085870d_bool(aTP_Lamm_ei(Uu),Uua))))) # label(fact_ATP_Olambda__66) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 253 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dh,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,Uu)),Uua))))) # label(fact_ATP_Olambda__67) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 254 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dk,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,Uua)))))) # label(fact_ATP_Olambda__68) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 255 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bq,Uu),Uua)) <-> (pp(scratc855283518_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1244405180_29_ii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc551581234lessis,Uu),Uua))))) # label(fact_ATP_Olambda__69) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 256 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,Uu),Uua)) <-> (pp(scratc855283518_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc14996922nd_iii,Uu),Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc685564846moreis,Uu),Uua))))) # label(fact_ATP_Olambda__70) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 257 (all Uu all Uua aa_fun277296641TP_ind(aa_TPT494704832TP_ind(aTP_Lamm_bl,Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1539224055nunion(aa_TPTP_ind_TPTP_ind(scratc934729220d_Sing,scratc179926404ptyset)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc785822622d_repl,Uu),Uua))) # label(fact_ATP_Olambda__71) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 258 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_da,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc56304457nd_nis,Uua),aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__72) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 259 (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(scratc188205961d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,Uua))))) # label(fact_ATP_Olambda__73) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 260 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eh,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,Uua),aa_TPTP_ind_TPTP_ind(scratc122357910_power,Uu))))) # label(fact_ATP_Olambda__74) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 261 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eb,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205956d_n_in,Uua),Uu)))) # label(fact_ATP_Olambda__75) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 262 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bm,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc54205284nd_nIn,Uua),Uu)))) # label(fact_ATP_Olambda__76) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.28 263 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,Uua),Uu)))) # label(fact_ATP_Olambda__77) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 264 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_df,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_de(Uu),Uua))))) # label(fact_ATP_Olambda__78) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 265 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cy,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cx(Uu),Uua))))) # label(fact_ATP_Olambda__79) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 266 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cv,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cu(Uu),Uua))))) # label(fact_ATP_Olambda__80) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 267 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cs,Uu),Uua)) <-> pp(scratc729570347_amone(scratc55779666nd_nat,aa_TPT43085870d_bool(aTP_Lamm_co(Uu),Uua))))) # label(fact_ATP_Olambda__81) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 268 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_ad(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc992999284rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,Uu),Uua))) # label(fact_ATP_Olambda__82) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 269 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_be(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc629619776_union,aa_TPTP_ind_TPTP_ind(Uu,Uua))) # label(fact_ATP_Olambda__83) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 270 (all Uu all Uua (gg_TPTP_ind(Uua) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bg,Uu),Uua)) <-> (exists X3 (gg_TPTP_ind(X3) & Uua = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1338626665d_pair,Uu),X3)))))) # label(fact_ATP_Olambda__84) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 271 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_er(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc669545600d_e_is(aa_TPTP_ind_TPTP_ind(scratc626922378etprod(Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2030501487d_pair(Uu,Uua),aa_TPTP_ind_TPTP_ind(scratc1182671873_first(Uu,Uua),Uub)),aa_TPTP_ind_TPTP_ind(scratc1370936867second(Uu,Uua),Uub))),Uub)))) # label(fact_ATP_Olambda__85) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 272 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_bo(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc1685833324bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,scratc179926404ptyset),Uub),Uu),Uua)) # label(fact_ATP_Olambda__86) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 273 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_fun1235454963TP_ind(aTP_Lamm_bn(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc1685833324bnd_if(aa_TPTP_ind_bool(Uua,Uub),Uub),scratc2129893753nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bb(Uu),Uua)))) # label(fact_ATP_Olambda__87) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 274 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_au(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1491530738d_esti(Uu),Uub),Uua)))) # label(fact_ATP_Olambda__88) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 275 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ek(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1491530738d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc631566889_d_Sep(Uu),Uua))) -> pp(aa_TPTP_ind_bool(Uua,Uub))))) # label(fact_ATP_Olambda__89) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 276 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ei(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc276489533d_incl(Uu),Uua),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc276489533d_incl(Uu),Uub),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc669545600d_e_is(aa_TPTP_ind_TPTP_ind(scratc122357910_power,Uu)),Uua),Uub)))))) # label(fact_ATP_Olambda__90) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 277 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_es(Uu),Uua),Uub)) <-> scratc1760362736_is_of(aa_TPTP_ind_TPTP_ind(scratc1370936867second(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)))) # label(fact_ATP_Olambda__91) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 278 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_et(Uu),Uua),Uub)) <-> scratc1760362736_is_of(aa_TPTP_ind_TPTP_ind(scratc1182671873_first(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)))) # label(fact_ATP_Olambda__92) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 279 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ez(Uu),Uua),Uub)) <-> scratc1760362736_is_of(aa_TPTP_ind_TPTP_ind(scratc669545595d_e_in(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)))) # label(fact_ATP_Olambda__93) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 280 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fd(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aa_TPT43085870d_bool(aTP_Lamm_fa(Uu),Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fc(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__94) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 281 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cu(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(Uu),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,Uua),Uub))))) # label(fact_ATP_Olambda__95) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 282 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_de(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__96) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 283 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cx(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc56304457nd_nis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc56304457nd_nis,aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(Uu),Uub)))))) # label(fact_ATP_Olambda__97) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 284 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bb(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,Uub),Uu)) & pp(aa_TPTP_ind_bool(Uua,Uub)))) # label(fact_ATP_Olambda__98) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 285 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ew(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1140029804_image(aa_fun1431113780TP_ind(scratc631566889_d_Sep(Uu),Uua),Uu),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc144064592_Sigma,aa_fun1431113780TP_ind(scratc631566889_d_Sep(Uu),Uua)),scratc669545595d_e_in(Uu,Uua))),Uub))))) # label(fact_ATP_Olambda__99) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 286 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_el(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1491530738d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc631566889_d_Sep(Uu),Uua)))))) # label(fact_ATP_Olambda__100) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 287 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ff(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_fe(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__101) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 288 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bd(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bc(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__102) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 289 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ev(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_eu(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__103) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 290 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ep(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_eo(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__104) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 291 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_en(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_em(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__105) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 292 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fa(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,Uub),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1675824974d_d_Pi,Uu),aTP_Lamm_ai(Uua)))))) # label(fact_ATP_Olambda__106) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 293 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_co(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(Uua),Uub))))) # label(fact_ATP_Olambda__107) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 294 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cp(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc188205961d_n_is,Uua),aa_TPTP_ind_TPTP_ind(scratc188665147d_n_pl(Uu),Uub))))) # label(fact_ATP_Olambda__108) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 295 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eq(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,Uub),aa_TPTP_ind_TPTP_ind(scratc626922378etprod(Uu),Uua))))) # label(fact_ATP_Olambda__109) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 296 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ex(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,Uub),aa_fun1431113780TP_ind(scratc631566889_d_Sep(Uu),Uua))))) # label(fact_ATP_Olambda__110) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 297 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_aw(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,Uu),Uub))) # label(fact_ATP_Olambda__111) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 298 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ey(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(Uua,aa_TPTP_ind_TPTP_ind(scratc669545595d_e_in(Uu,Uua),Uub))))) # label(fact_ATP_Olambda__112) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 299 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1913827119d_bool(aTP_Lamm_bf(Uu),Uua),Uub)) <-> (all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,X3),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1685833332bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,Uub),X3)),aa_TPTP_ind_TPTP_ind(Uua,X3)))))))) # label(fact_ATP_Olambda__113) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 300 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ax(Uu),Uua),Uub),Uuc) = aa_TPTP_ind_TPTP_ind(scratc1685833324bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1140029804_image(Uu,Uua),Uub),Uuc),aa_TPTP_ind_TPTP_ind(scratc1648368889d_soft(Uu,Uua,Uub),Uuc)),scratc179926404ptyset)) # label(fact_ATP_Olambda__114) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 301 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_eo(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc669545600d_e_is(Uu),aa_TPTP_ind_TPTP_ind(scratc1182671873_first(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2030501487d_pair(Uu,Uua),Uub),Uuc))),Uub)))) # label(fact_ATP_Olambda__115) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 302 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_em(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc669545600d_e_is(Uua),aa_TPTP_ind_TPTP_ind(scratc1370936867second(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2030501487d_pair(Uu,Uua),Uub),Uuc))),Uuc)))) # label(fact_ATP_Olambda__116) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 303 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fb(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc669545600d_e_is(Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,Uua),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,Uub),Uuc))))) # label(fact_ATP_Olambda__117) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 304 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aq(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1491530738d_esti(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__118) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 305 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc669545600d_e_is(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__119) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 306 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_eu(Uu),Uua),Uub),Uuc)) <-> scratc1760362736_is_of(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2030501487d_pair(Uu,Uua),Uub),Uuc),aa_TPT43085870d_bool(aTP_Lamm_eq(Uu),Uua)))) # label(fact_ATP_Olambda__120) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 307 (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(scratc56298619d_l_ec(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1491530738d_esti(Uu),Uuc),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1491530738d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__121) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 308 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_at(Uu),Uua),Uub),Uuc)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc15259325nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1491530738d_esti(Uu),Uuc),Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1491530738d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__122) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 309 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fc(Uu),Uua),Uub),Uuc)) <-> (pp(aa_fun171081125l_bool(scratc1910373353all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_fb(Uua),Uub),Uuc))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc669545600d_e_is(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1675824974d_d_Pi,Uu),aTP_Lamm_ai(Uua))),Uub),Uuc))))) # label(fact_ATP_Olambda__123) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 310 (all Uu all Uua all Uub all Uuc (gg_TPTP_ind(Uua) & gg_TPTP_ind(Uub) & gg_TPTP_ind(Uuc) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bp(Uu),Uua),Uub),Uuc)) <-> pp(Uu) & Uuc = Uua | -pp(Uu) & Uuc = Uub))) # label(fact_ATP_Olambda__124) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 311 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_fe(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc669545600d_e_is(Uu),Uub),Uuc)) -> pp(aa_TPTP_ind_bool(Uua,Uuc)))))) # label(fact_ATP_Olambda__125) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 312 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bc(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(Uua,Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc669545600d_e_is(Uu),Uub),Uuc)))))) # label(fact_ATP_Olambda__126) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 313 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ba(Uu),Uua),Uub),Uuc)) <-> pp(aa_fun171081125l_bool(scratc2096585330nd_all(Uu),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_az(Uu),Uua),Uub),Uuc))))) # label(fact_ATP_Olambda__127) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 314 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ar(Uu),Uua),Uub),Uuc)) <-> pp(aa_fun171081125l_bool(scratc1021034161l_some(Uua),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aq(Uu),Uub),Uuc))))) # label(fact_ATP_Olambda__128) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 315 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_az(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc15259325nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc669545600d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,Uub),Uud))),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc669545600d_e_is(Uu),Uuc),Uud))))) # label(fact_ATP_Olambda__129) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 316 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_ao(Uu),Uua),Uub),Uuc),Uud)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc669545600d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,Uub),Uud)))))) # label(fact_ATP_Olambda__130) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 317 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_an(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_am(Uu),Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__131) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 318 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ap(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_ao(Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__132) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 319 (all Uu all Uua all Uub all Uuc all Uud aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_av(Uu),Uua),Uub),Uuc),Uud) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,aa_TPTP_ind_TPTP_ind(scratc611720936wissel(Uu,Uub),Uuc)),Uud))) # label(fact_ATP_Olambda__133) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 320 (all Uu all Uua all Uub all Uuc all Uud all Uue (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_am(Uu),Uua),Uub),Uuc),Uud),Uue)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_al(Uu),Uua),Uub),Uuc),Uud),Uue))))) # label(fact_ATP_Olambda__134) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 321 (all Uu all Uua all Uub all Uuc all Uud all Uue all Uuf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_ak(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uue),Uuf)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc669545600d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,Uub),Uuc)),Uue)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1685308542bnd_ap,Uub),Uud)),Uuf))))))) # label(fact_ATP_Olambda__135) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 322 (all Uu all Uua all Uub all Uuc all Uud all Uue all Uuf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_al(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)) <-> pp(aa_fun171081125l_bool(scratc1910373353all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_ak(Uua),Uub),Uuc),Uud),Uue),Uuf))))) # label(fact_ATP_Olambda__136) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 323 (all Uu all Uua (gg_TPTP_ind(Uu) -> aa_TPTP_ind_TPTP_ind(aTP_Lamm_ai(Uu),Uua) = Uu)) # label(fact_ATP_Olambda__137) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 324 (all Uu aa_TPTP_ind_TPTP_ind(aTP_Lamm_ac,Uu) = scratc55779666nd_nat) # label(fact_ATP_Olambda__138) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 325 (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].
% 0.97/1.29 326 (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].
% 0.97/1.29 327 (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].
% 0.97/1.29 328 (all P (gg_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 0.97/1.29 329 (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].
% 0.97/1.29 330 (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].
% 0.97/1.29 331 (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].
% 0.97/1.29 332 (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].
% 0.97/1.29 333 (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].
% 0.97/1.31 334 (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].
% 0.97/1.31 335 (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].
% 0.97/1.31 336 (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].
% 0.97/1.31 337 (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].
% 0.97/1.31
% 0.97/1.31 ============================== end of process non-clausal formulas ===
% 0.97/1.31
% 0.97/1.31 ============================== PROCESS INITIAL CLAUSES ===============
% 0.97/1.31
% 0.97/1.31 ============================== PREDICATE ELIMINATION =================
% 0.97/1.31 338 -gg_bool(A) | A = fTrue | A = fFalse # label(help_fFalse_1_1_T) # label(axiom). [clausify(328)].
% 0.97/1.31 339 gg_bool(undefined_bool(bool)) # label(gsy_c_HOL_Oundefined_001t__HOL__Obool) # label(axiom). [assumption].
% 0.97/1.31 340 gg_bool(scratc729570347_amone(A,B)) # label(gsy_c_Scratch__tptp__translate__43213__14863_ONUM655__thf__4__p_Obnd__amone) # label(axiom). [clausify(1)].
% 0.97/1.31 341 gg_bool(scratc747818338_d_and(A,B)) # label(gsy_c_Scratch__tptp__translate__43213__14863_ONUM655__thf__4__p_Obnd__d__and) # label(axiom). [clausify(2)].
% 0.97/1.31 342 gg_bool(scratc855283518_d_not(A)) # label(gsy_c_Scratch__tptp__translate__43213__14863_ONUM655__thf__4__p_Obnd__d__not) # label(axiom). [clausify(3)].
% 0.97/1.31 343 gg_bool(scratc2129040902nd_ec3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__43213__14863_ONUM655__thf__4__p_Obnd__ec3) # label(axiom). [clausify(4)].
% 0.97/1.31 344 gg_bool(scratc56298619d_l_ec(A,B)) # label(gsy_c_Scratch__tptp__translate__43213__14863_ONUM655__thf__4__p_Obnd__l__ec) # label(axiom). [clausify(8)].
% 0.97/1.31 345 gg_bool(scratc65156289nd_or3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__43213__14863_ONUM655__thf__4__p_Obnd__or3) # label(axiom). [clausify(9)].
% 0.97/1.31 346 gg_bool(aa_bool_bool(A,B)) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom). [clausify(10)].
% 0.97/1.31 347 gg_bool(aa_TPTP_ind_bool(A,B)) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom). [clausify(11)].
% 0.97/1.31 348 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)].
% 0.97/1.31 349 gg_bool(fEx_TPTP_ind(A)) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom). [clausify(16)].
% 0.97/1.31 350 gg_bool(fFalse) # label(gsy_c_fFalse) # label(axiom). [assumption].
% 0.97/1.31 351 gg_bool(fTrue) # label(gsy_c_fTrue) # label(axiom). [assumption].
% 0.97/1.31 Derived: undefined_bool(bool) = fTrue | undefined_bool(bool) = fFalse. [resolve(338,a,339,a)].
% 0.97/1.31 Derived: scratc729570347_amone(A,B) = fTrue | scratc729570347_amone(A,B) = fFalse. [resolve(338,a,340,a)].
% 0.97/1.31 Derived: scratc747818338_d_and(A,B) = fTrue | scratc747818338_d_and(A,B) = fFalse. [resolve(338,a,341,a)].
% 0.97/1.31 Derived: scratc855283518_d_not(A) = fTrue | scratc855283518_d_not(A) = fFalse. [resolve(338,a,342,a)].
% 0.97/1.31 Derived: scratc2129040902nd_ec3(A,B,C) = fTrue | scratc2129040902nd_ec3(A,B,C) = fFalse. [resolve(338,a,343,a)].
% 0.97/1.31 Derived: scratc56298619d_l_ec(A,B) = fTrue | scratc56298619d_l_ec(A,B) = fFalse. [resolve(338,a,344,a)].
% 0.97/1.31 Derived: scratc65156289nd_or3(A,B,C) = fTrue | scratc65156289nd_or3(A,B,C) = fFalse. [resolve(338,a,345,a)].
% 0.97/1.31 Derived: aa_bool_bool(A,B) = fTrue | aa_bool_bool(A,B) = fFalse. [resolve(338,a,346,a)].
% 0.97/1.31 Derived: aa_TPTP_ind_bool(A,B) = fTrue | aa_TPTP_ind_bool(A,B) = fFalse. [resolve(338,a,347,a)].
% 0.97/1.64 Derived: aa_fun171081125l_bool(A,B) = fTrue | aa_fun171081125l_bool(A,B) = fFalse. [resolve(338,a,348,a)].
% 0.97/1.64 Derived: fEx_TPTP_ind(A) = fTrue | fEx_TPTP_ind(A) = fFalse. [resolve(338,a,349,a)].
% 0.97/1.64 Derived: fFalse = fTrue | fFalse = fFalse. [resolve(338,a,350,a)].
% 0.97/1.64 Derived: fTrue = fTrue | fTrue = fFalse. [resolve(338,a,351,a)].
% 0.97/1.64 352 scratc451233409d_r_ec(A,B) | pp(A) # label(fact_def__r__ec) # label(axiom). [clausify(59)].
% 0.97/1.64 353 -scratc451233409d_r_ec(A,B) | -pp(A) | pp(scratc855283518_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(59)].
% 0.97/1.64 354 scratc451233409d_r_ec(A,B) | -pp(scratc855283518_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(59)].
% 0.97/1.64 355 scratc1641959788_l_iff(A,B) | -pp(scratc747818338_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc15259325nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc15259325nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(91)].
% 0.97/1.64 356 -scratc1641959788_l_iff(A,B) | pp(scratc747818338_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc15259325nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc15259325nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(91)].
% 0.97/1.64 357 scratc698222640d_orec(A,B) | -pp(scratc747818338_d_and(aa_bool_bool(scratc56954624d_l_or(A),B),scratc56298619d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(92)].
% 0.97/1.64 358 -scratc698222640d_orec(A,B) | pp(scratc747818338_d_and(aa_bool_bool(scratc56954624d_l_or(A),B),scratc56298619d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(92)].
% 0.97/1.64 359 scratc130395599nd_wel(A) | -pp(scratc855283518_d_not(scratc855283518_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(97)].
% 0.97/1.64 360 -scratc130395599nd_wel(A) | pp(scratc855283518_d_not(scratc855283518_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(97)].
% 0.97/1.64 361 -scratc130395599nd_wel(A) | pp(A) # label(fact_l__et) # label(axiom). [clausify(147)].
% 0.97/1.64 Derived: pp(A) | -pp(scratc855283518_d_not(scratc855283518_d_not(A))). [resolve(361,a,359,a)].
% 0.97/1.64
% 0.97/1.64 ============================== end predicate elimination =============
% 0.97/1.64
% 0.97/1.64 Auto_denials: (non-Horn, no changes).
% 0.97/1.64
% 0.97/1.64 Term ordering decisions:
% 0.97/1.64 Function symbol KB weights: scratc1685833332bnd_in=1. aTP_Lamm_a=1. scratc188205961d_n_is=1. scratc992999284rdsucc=1. scratc1685308542bnd_ap=1. aTP_Lamm_aj=1. scratc179926404ptyset=1. scratc144064592_Sigma=1. scratc56304457nd_nis=1. scratc1907756850nd_n_1=1. fFalse=1. scratc122357910_power=1. scratc1647006942_nat_p=1. scratc1675824974d_d_Pi=1. scratc1764858803n_some=1. scratc55779666nd_nat=1. scratc1244405180_29_ii=1. scratc14996922nd_iii=1. scratc15259325nd_imp=1. scratc785822622d_repl=1. fTrue=1. scratc1338626665d_pair=1. scratc1033080102d_Subq=1. scratc551581234lessis=1. scratc685564846moreis=1. scratc250871748_proj0=1. scratc360512080closed=1. scratc629619776_union=1. aTP_Lamm_af=1. scratc188205956d_n_in=1. scratc250871749_proj1=1. scratc172792162_n_all=1. aTP_Lamm_ac=1. aTP_Lamm_ae=1. aTP_Lamm_eh=1. scratc616904742closed=1. scratc781637756closed=1. aTP_Lamm_aa=1. aTP_Lamm_bq=1. aTP_Lamm_bs=1. aTP_Lamm_bu=1. aTP_Lamm_bw=1. aTP_Lamm_by=1. aTP_Lamm_ca=1. aTP_Lamm_cc=1. aTP_Lamm_dy=1. aTP_Lamm_ec=1. aTP_Lamm_ed=1. scratc1568010610_omega=1. scratc1620527661closed=1. scratc1759836897d_Inj1=1. scratc225393400_prop2=1. aTP_Lamm_ag=1. aTP_Lamm_bg=1. aTP_Lamm_bi=1. aTP_Lamm_bj=1. aTP_Lamm_ce=1. aTP_Lamm_cg=1. aTP_Lamm_ci=1. aTP_Lamm_ck=1. aTP_Lamm_cm=1. aTP_Lamm_cq=1. aTP_Lamm_cs=1. aTP_Lamm_cv=1. aTP_Lamm_cy=1. aTP_Lamm_da=1. aTP_Lamm_dc=1. aTP_Lamm_df=1. aTP_Lamm_dh=1. aTP_Lamm_dk=1. aTP_Lamm_dn=1. aTP_Lamm_dq=1. aTP_Lamm_dt=1. aTP_Lamm_dv=1. aTP_Lamm_dw=1. aTP_Lamm_eb=1. fconj=1. fimplies=1. scratc1759836896d_Inj0=1. scratc225393399_prop1=1. scratc265988481_cond2=1. scratc934729220d_Sing=1. aTP_Lamm_bm=1. aTP_Lamm_br=1. aTP_Lamm_bt=1. aTP_Lamm_bv=1. aTP_Lamm_bx=1. aTP_Lamm_bz=1. aTP_Lamm_cb=1. aTP_Lamm_cd=1. aTP_Lamm_cf=1. aTP_Lamm_ch=1. aTP_Lamm_cj=1. aTP_Lamm_cl=1. aTP_Lamm_cn=1. aTP_Lamm_cr=1. aTP_Lamm_ct=1. aTP_Lamm_cw=1. aTP_Lamm_cz=1. aTP_Lamm_db=1. aTP_Lamm_dd=1. aTP_Lamm_dg=1. aTP_Lamm_di=1. aTP_Lamm_dj=1. aTP_Lamm_dl=1. aTP_Lamm_dm=1. aTP_Lamm_do=1. aTP_Lamm_dp=1. aTP_Lamm_dr=1. aTP_Lamm_ds=1. aTP_Lamm_du=1. aTP_Lamm_dx=1. aTP_Lamm_dz=1. aTP_Lamm_ea=1. aTP_Lamm_ee=1. aTP_Lamm_ef=1. aTP_Lamm_eg=1. aTP_Lamm_ej=1. aTP_Lamm_fg=1. fequal_TPTP_ind=1. scratc2080063724univof=1. scratc265988480_cond1=1. scratc288584423_n_one=1. scratc54205284nd_nIn=1. scratc648680284_d_Unj=1. aTP_Lamm_ab=1. aTP_Lamm_ah=1. aTP_Lamm_bk=1. aTP_Lamm_bl=1. bool=1. scratc1001515326_empty=1. scratc1019720626_prop1=1. scratc1196152697_prop1=1. scratc1402117749_prop1=1. scratc1430290409d_plus=1. scratc1784514872_prop1=1. scratc1990479924_prop1=1. scratc251265346_prop4=1. scratc465521391nempty=1. scratc545366956munion=1. scratc849749255pair_p=1. scratc1532390332d_i1_s=1. scratc557206064d_24_g=1. tPTP_ind=1. aa_TPTP_ind_bool=1. aa_TPT43085870d_bool=1. aa_TPTP_ind_TPTP_ind=1. aa_fun171081125l_bool=1. aa_TPT1424761345TP_ind=1. aa_TPT60673477d_bool=1. aa_fun277296641TP_ind=1. aa_TPT494704832TP_ind=1. aa_bool_bool=1. aa_fun1584354236d_bool=1. aa_fun1431113780TP_ind=1. aa_boo1142376798l_bool=1. scratc747818338_d_and=1. aa_TPT1123896796d_bool=1. scratc1685833324bnd_if=1. scratc56298619d_l_ec=1. aa_fun1212484691d_bool=1. aa_TPT985247859d_bool=1. scratc669545595d_e_in=1. scratc2030501487d_pair=1. aa_fun987228051d_bool=1. scratc15324912nd_ind=1. scratc729570347_amone=1. scratc1140029804_image=1. scratc1182671873_first=1. scratc1370936867second=1. aa_TPT125613450d_bool=1. scratc56698046nd_non=1. aa_fun1913827119d_bool=1. scratc474374074d_anec=1. aa_TPT1791839040TP_ind=1. aa_fun1107270209d_bool=1. aa_fun845057962d_bool=1. scratc1212640090eplSep=1. scratc1694176576_ecelt=1. scratc2129040963nd_ecp=1. scratc1693586185_ecect=1. aa_TPT1781712639TP_ind=1. aa_TPT2142672771l_bool=1. aa_fun1235454963TP_ind=1. cOMBB_658106424TP_ind=1. cOMBS_2003118649l_bool=1. scratc1231388117_fixfu=1. scratc2129040967nd_ect=1. scratc231667613fixfu2=1. scratc611720936wissel=1. scratc649179516etprop=1. scratc65353151nd_out=1. scratc743694139ectset=1. scratc277735908d_invf=1. scratc281472439d_tofs=1. scratc391246977nverse=1. scratc628492262ectelt=1. scratc849811485unmore=1. f1=1. f12=1. f13=1. f20=1. f24=1. scratc1910373353all_of=1. scratc188665147d_n_pl=1. scratc669545600d_e_is=1. scratc855283518_d_not=1. scratc631566889_d_Sep=1. scratc1491530738d_esti=1. scratc1021034161l_some=1. scratc1461823351ffprop=1. scratc2096585330nd_all=1. scratc56954624d_l_or=1. scratc1322003761_rec_G=1. aTP_Lamm_ai=1. aTP_Lamm_eq=1. scratc64893943nd_one=1. aTP_Lamm_ak=1. aTP_Lamm_au=1. aTP_Lamm_bc=1. aTP_Lamm_bp=1. aTP_Lamm_co=1. aTP_Lamm_ei=1. aTP_Lamm_fe=1. scratc276489533d_incl=1. aTP_Lamm_ao=1. aTP_Lamm_ay=1. aTP_Lamm_bb=1. aTP_Lamm_bf=1. aTP_Lamm_cu=1. aTP_Lamm_cx=1. aTP_Lamm_fa=1. aTP_Lamm_fc=1. scratc2129893753nd_eps=1. scratc288764184ective=1. scratc626922378etprod=1. aTP_Lamm_al=1. aTP_Lamm_am=1. aTP_Lamm_an=1. aTP_Lamm_ap=1. aTP_Lamm_aq=1. aTP_Lamm_as=1. aTP_Lamm_at=1. aTP_Lamm_az=1. aTP_Lamm_ba=1. aTP_Lamm_bd=1. aTP_Lamm_cp=1. aTP_Lamm_de=1. aTP_Lamm_ek=1. aTP_Lamm_el=1. aTP_Lamm_em=1. aTP_Lamm_eo=1. aTP_Lamm_eu=1. aTP_Lamm_ew=1. aTP_Lamm_ex=1. aTP_Lamm_fb=1. fEx_TPTP_ind=1. scratc1539224055nunion=1. scratc184924811ective=1. aTP_Lamm_ar=1. aTP_Lamm_en=1. aTP_Lamm_ep=1. aTP_Lamm_er=1. aTP_Lamm_es=1. aTP_Lamm_et=1. aTP_Lamm_ev=1. aTP_Lamm_ey=1. aTP_Lamm_ez=1. aTP_Lamm_fd=1. aTP_Lamm_ff=1. scratc38550970_UPair=1. scratc940403670In_rec=1. aTP_Lamm_ad=1. aTP_Lamm_av=1. aTP_Lamm_aw=1. aTP_Lamm_ax=1. aTP_Lamm_be=1. aTP_Lamm_bh=1. aTP_Lamm_bn=1. aTP_Lamm_bo=1. cOMBC_1555011498d_bool=1. scratc1455509597tminus=1. scratc1872346092t_disj=1. scratc251265345_prop3=1. scratc431358451_prop1=1. scratc472483414ective=1. scratc813755574_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. scratc65156289nd_or3=1. scratc2129040902nd_ec3=1. scratc1648368889d_soft=1. scratc15718507nd_ite=1. scratc1945270332_indeq=1. scratc251265343_prop1=1. scratc1370847476d_11_i=1. scratc588549202sel_wa=1. scratc588549203sel_wb=1. fCputime limit exceeded (core dumped)
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