TSTP Solution File: NUM637+4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM637+4 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 13:29:49 EDT 2022
% Result : Timeout 300.05s 300.31s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM637+4 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n013.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 : Wed Jul 6 03:00:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.94/1.24 ============================== Prover9 ===============================
% 0.94/1.24 Prover9 (32) version 2009-11A, November 2009.
% 0.94/1.24 Process 13930 was started by sandbox2 on n013.cluster.edu,
% 0.94/1.24 Wed Jul 6 03:00:45 2022
% 0.94/1.24 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_13777_n013.cluster.edu".
% 0.94/1.24 ============================== end of head ===========================
% 0.94/1.24
% 0.94/1.24 ============================== INPUT =================================
% 0.94/1.24
% 0.94/1.24 % Reading from file /tmp/Prover9_13777_n013.cluster.edu
% 0.94/1.24
% 0.94/1.24 set(prolog_style_variables).
% 0.94/1.24 set(auto2).
% 0.94/1.24 % set(auto2) -> set(auto).
% 0.94/1.24 % set(auto) -> set(auto_inference).
% 0.94/1.24 % set(auto) -> set(auto_setup).
% 0.94/1.24 % set(auto_setup) -> set(predicate_elim).
% 0.94/1.24 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.94/1.24 % set(auto) -> set(auto_limits).
% 0.94/1.24 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.94/1.24 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.94/1.24 % set(auto) -> set(auto_denials).
% 0.94/1.24 % set(auto) -> set(auto_process).
% 0.94/1.24 % set(auto2) -> assign(new_constants, 1).
% 0.94/1.24 % set(auto2) -> assign(fold_denial_max, 3).
% 0.94/1.24 % set(auto2) -> assign(max_weight, "200.000").
% 0.94/1.24 % set(auto2) -> assign(max_hours, 1).
% 0.94/1.24 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.94/1.24 % set(auto2) -> assign(max_seconds, 0).
% 0.94/1.24 % set(auto2) -> assign(max_minutes, 5).
% 0.94/1.24 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.94/1.24 % set(auto2) -> set(sort_initial_sos).
% 0.94/1.24 % set(auto2) -> assign(sos_limit, -1).
% 0.94/1.24 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.94/1.24 % set(auto2) -> assign(max_megs, 400).
% 0.94/1.24 % set(auto2) -> assign(stats, some).
% 0.94/1.24 % set(auto2) -> clear(echo_input).
% 0.94/1.24 % set(auto2) -> set(quiet).
% 0.94/1.24 % set(auto2) -> clear(print_initial_clauses).
% 0.94/1.24 % set(auto2) -> clear(print_given).
% 0.94/1.24 assign(lrs_ticks,-1).
% 0.94/1.24 assign(sos_limit,10000).
% 0.94/1.24 assign(order,kbo).
% 0.94/1.24 set(lex_order_vars).
% 0.94/1.24 clear(print_given).
% 0.94/1.24
% 0.94/1.24 % formulas(sos). % not echoed (290 formulas)
% 0.94/1.24
% 0.94/1.24 ============================== end of input ==========================
% 0.94/1.24
% 0.94/1.24 % From the command line: assign(max_seconds, 300).
% 0.94/1.24
% 0.94/1.24 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.94/1.24
% 0.94/1.24 % Formulas that are not ordinary clauses:
% 0.94/1.24 1 (all B_1 all B_2 gg_bool(scratc1874193181_amone(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__39548__11527_ONUM637__thf__4__p_Obnd__amone) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 2 (all B_1 all B_2 gg_bool(scratc95353584_d_and(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__39548__11527_ONUM637__thf__4__p_Obnd__d__and) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 3 (all B_1 gg_bool(scratc202818764_d_not(B_1))) # label(gsy_c_Scratch__tptp__translate__39548__11527_ONUM637__thf__4__p_Obnd__d__not) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 4 (all B_1 all B_2 all B_3 gg_bool(scratc1555627512nd_ec3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__39548__11527_ONUM637__thf__4__p_Obnd__ec3) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 5 (all B_1 all B_2 gg_TPTP_ind(scratc1555627577nd_ect(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__39548__11527_ONUM637__thf__4__p_Obnd__ect) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 6 (all B_1 gg_TPTP_ind(scratc1556480363nd_eps(B_1))) # label(gsy_c_Scratch__tptp__translate__39548__11527_ONUM637__thf__4__p_Obnd__eps) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 7 (all B_1 all B_2 gg_TPTP_ind(scratc1589395170nd_ind(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__39548__11527_ONUM637__thf__4__p_Obnd__ind) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 8 (all B_1 all B_2 gg_bool(scratc1200921453d_l_ec(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__39548__11527_ONUM637__thf__4__p_Obnd__l__ec) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 9 (all B_1 all B_2 all B_3 gg_bool(scratc1639226547nd_or3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__39548__11527_ONUM637__thf__4__p_Obnd__or3) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 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].
% 0.94/1.24 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].
% 0.94/1.24 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].
% 0.94/1.24 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].
% 0.94/1.24 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].
% 0.94/1.24 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].
% 0.94/1.24 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].
% 0.94/1.24 17 (all X (pp(aa_TPTP_ind_bool(scratc825655750_prop1,X)) <-> pp(aa_bool_bool(scratc1201577458d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1332828795d_n_is,X),scratc1886364608nd_n_1)),aa_fun171081125l_bool(scratc78565797n_some,aa_TPT43085870d_bool(aTP_Lamm_aa,X)))))) # label(fact_def__d__23__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 18 (all X (pp(aa_TPTP_ind_bool(scratc237293575_prop1,X)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1630374715nd_nis,aa_TPTP_ind_TPTP_ind(scratc1454189926rdsucc,X)),X)))) # label(fact_def__d__22__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 19 (all X (pp(aa_TPTP_ind_bool(scratc1410611315_cond2,X)) <-> pp(aa_fun171081125l_bool(scratc1667811056_n_all,aa_TPT43085870d_bool(aTP_Lamm_ac,X))))) # label(fact_def__cond2) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 20 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1630374715nd_nis,X),Xa)) <-> pp(scratc202818764_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1332828795d_n_is,X),Xa))))) # label(fact_def__nis) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 21 (all X all Xa all Xb all Xc all Xd scratc1510196356indeq2(X,Xa,Xb,Xc,Xd) = aa_TPT1424761345TP_ind(scratc942409518_indeq(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1266139010d_11_i(X,Xa,Xb),Xc),Xd))) # label(fact_def__indeq2) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 22 (all X all Xa all Xb scratc1266139010d_11_i(X,Xa,Xb) = scratc942409518_indeq(X,Xa,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc672964160d_d_Pi,X),aTP_Lamm_ae(Xb)))) # label(fact_def__d__11__i) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 23 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1726686507fixfu2(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc224080347all_of(aa_TPT43085870d_bool(aTP_Lamm_af,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_aj(X),Xa),Xb),Xc))))) # label(fact_def__fixfu2) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 24 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc942409518_indeq(X,Xa,Xb),Xc),Xd) = scratc1589395170nd_ind(Xb,aa_TPT43085870d_bool(scratc1395888178_prop2(X,Xa,Xb,Xc),Xd))) # label(fact_def__indeq) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 25 (all X all Xa all Xb all Xc all Xd all Xe (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1395888178_prop2(X,Xa,Xb,Xc),Xd),Xe)) <-> pp(aa_fun171081125l_bool(scratc1482224803l_some(X),aa_TPT43085870d_bool(scratc1961340552_prop1(X,Xa,Xb,Xc,Xd),Xe))))) # label(fact_def__prop2) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 26 (all X all Xa all Xb all Xc all Xd all Xe all Xf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1961340552_prop1(X,Xa,Xb,Xc,Xd),Xe),Xf)) <-> pp(scratc95353584_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1470138496d_esti(X),Xf),aa_TPTP_ind_TPTP_ind(scratc690725371_ecect(X,Xa),Xd)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1814168434d_e_is(Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc416169996bnd_ap,Xc),Xf)),Xe))))) # label(fact_def__d__10__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 27 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc228527303_fixfu(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc224080347all_of(aa_TPT43085870d_bool(aTP_Lamm_af,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_al(X),Xa),Xb),Xc))))) # label(fact_def__fixfu) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 28 (all X all Xa scratc690725371_ecect(X,Xa) = scratc1814168429d_e_in(aa_TPTP_ind_TPTP_ind(scratc1266980744_power,X),scratc452981832d_anec(X,Xa))) # label(fact_def__ecect) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 29 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc2123511156ectelt(X,Xa),Xb) = aa_TPTP_ind_TPTP_ind(scratc91229385ectset(X,Xa),aa_TPTP_ind_TPTP_ind(scratc691315762_ecelt(X,Xa),Xb))) # label(fact_def__ectelt) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 30 (all X all Xa scratc91229385ectset(X,Xa) = scratc1639423409nd_out(aa_TPTP_ind_TPTP_ind(scratc1266980744_power,X),scratc452981832d_anec(X,Xa))) # label(fact_def__ectset) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 31 (all X all Xa scratc1555627577nd_ect(X,Xa) = aa_fun1431113780TP_ind(scratc2126585783_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1266980744_power,X)),scratc452981832d_anec(X,Xa))) # label(fact_def__ect) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 32 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc452981832d_anec(X,Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1482224803l_some(X),aa_TPT43085870d_bool(scratc1555627573nd_ecp(X,Xa),Xb))))) # label(fact_def__anec) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 33 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1555627573nd_ecp(X,Xa),Xb),Xc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1814168434d_e_is(aa_TPTP_ind_TPTP_ind(scratc1266980744_power,X)),Xb),aa_TPTP_ind_TPTP_ind(scratc691315762_ecelt(X,Xa),Xc))))) # label(fact_def__ecp) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 34 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc691315762_ecelt(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc2126585783_d_Sep(X),aa_TPT43085870d_bool(Xa,Xb))) # label(fact_def__ecelt) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 35 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc197346731unmore(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc2126585783_d_Sep(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_an(X),Xa),Xb))) # label(fact_def__unmore) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 36 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc496865546etprop(X,Xa),Xb),Xc)) <-> pp(scratc95353584_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1470138496d_esti(X),Xc),Xa),scratc202818764_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1470138496d_esti(X),Xc),Xb)))))) # label(fact_def__nissetprop) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 37 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1767637626t_disj(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1523171940nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ao(X),Xa),Xb))))) # label(fact_def__st__disj) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 38 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc255097291d_incl(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1523171940nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ap(X),Xa),Xb))))) # label(fact_def__incl) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 39 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc360812925nempty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1482224803l_some(X),aa_TPT43085870d_bool(aTP_Lamm_aq(X),Xa))))) # label(fact_def__nonempty) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 40 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2146138160_empty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc224080347all_of(aa_TPT43085870d_bool(aTP_Lamm_af,X)),scratc1630768304nd_non(X,aa_TPT43085870d_bool(aTP_Lamm_aq(X),Xa)))))) # label(fact_def__empty) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 41 (all X scratc1470138496d_esti(X) = scratc416694786bnd_in) # label(fact_def__esti) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 42 (all X all Xa (scratc1595856243d_r_ec(X,Xa) <-> (pp(X) -> pp(scratc202818764_d_not(Xa))))) # label(fact_def__r__ec) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 43 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc866396569hangef(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc39356126_Sigma,X),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_ar(X),Xb),Xc),Xd))) # label(fact_def__changef) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 44 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc2106739830wissel(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc39356126_Sigma,X),scratc436235233sel_wb(X,Xa,Xb))) # label(fact_def__wissel) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 45 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc436235233sel_wb(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc1589788765nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1814168434d_e_is(X),Xc),Xb),X,Xa),aa_TPTP_ind_TPTP_ind(scratc436235232sel_wa(X,Xa,Xb),Xc))) # label(fact_def__wissel__wb) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 46 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc436235232sel_wa(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc1589788765nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1814168434d_e_is(X),Xc),Xa),X,Xb),Xc)) # label(fact_def__wissel__wa) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 47 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1589788765nd_ite(X,Xa,Xb),Xc) = scratc1589395170nd_ind(Xa,aa_TPT43085870d_bool(scratc1395888177_prop1(X,Xa,Xb),Xc))) # label(fact_def__ite) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 48 (all X all Xa all Xb all Xc all Xd (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1395888177_prop1(X,Xa,Xb),Xc),Xd)) <-> pp(scratc95353584_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1589329583nd_imp,X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1814168434d_e_is(Xa),Xd),Xb)),aa_bool_bool(aa_boo1142376798l_bool(scratc1589329583nd_imp,scratc202818764_d_not(X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1814168434d_e_is(Xa),Xd),Xc)))))) # label(fact_def__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 49 (all X all Xa scratc718472113second(X,Xa) = scratc1395494583_proj1) # label(fact_def__second) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 50 (all X all Xa scratc179811059_first(X,Xa) = scratc1395494582_proj0) # label(fact_def__first) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 51 (all X all Xa scratc344208481d_pair(X,Xa) = scratc1317234423d_pair) # label(fact_def__d__pair) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 52 (all X all Xa scratc1639423409nd_out(X,Xa) = scratc1626976647d_soft(aa_fun1431113780TP_ind(scratc2126585783_d_Sep(X),Xa),X,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc39356126_Sigma,aa_fun1431113780TP_ind(scratc2126585783_d_Sep(X),Xa)),scratc1814168429d_e_in(X,Xa)))) # label(fact_def__out) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 53 (all X all Xa all Xb (gg_TPTP_ind(Xb) -> aa_TPTP_ind_TPTP_ind(scratc1814168429d_e_in(X,Xa),Xb) = Xb)) # label(fact_def__e__in) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 54 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc1848002496_inj_h(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc39356126_Sigma,X),aa_TPT1424761345TP_ind(aTP_Lamm_as(Xc),Xd))) # label(fact_def__inj__h) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 55 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc256343666d_invf(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc39356126_Sigma,Xa),scratc1626976647d_soft(X,Xa,Xb))) # label(fact_def__invf) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 56 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1502012232ective(X),Xa),Xb)) <-> pp(scratc95353584_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1318293002ective(X),Xa),Xb),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc32610841ective(X),Xa),Xb))))) # label(fact_def__bijective) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 57 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc32610841ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1523171940nd_all(Xa),aa_TPT43085870d_bool(scratc137168990_image(X,Xa),Xb))))) # label(fact_def__surjective) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 58 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc852437619nverse(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc39356126_Sigma,Xa),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_at(X),Xa),Xb))) # label(fact_def__inverse) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 59 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1626976647d_soft(X,Xa,Xb),Xc) = scratc1589395170nd_ind(X,aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_au(Xa),Xb),Xc))) # label(fact_def__soft) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 60 (all X all Xa scratc260080197d_tofs(X,Xa) = scratc416169996bnd_ap) # label(fact_def__tofs) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 61 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc137168990_image(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1482224803l_some(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_au(Xa),Xb),Xc))))) # label(fact_def__image) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 62 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1318293002ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1523171940nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aw(X),Xa),Xb))))) # label(fact_def__injective) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 63 (all X all Xa scratc1589395170nd_ind(X,Xa) = scratc1556480363nd_eps(aa_fun1584354236d_bool(aTP_Lamm_ax(X),Xa))) # label(fact_def__ind) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 64 (all X all Xa (pp(aa_fun171081125l_bool(scratc1638964201nd_one(X),Xa)) <-> pp(scratc95353584_d_and(scratc1874193181_amone(X,Xa),aa_fun171081125l_bool(scratc1482224803l_some(X),Xa))))) # label(fact_def__one) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 65 (all X all Xa (pp(scratc1874193181_amone(X,Xa)) <-> pp(aa_fun171081125l_bool(scratc224080347all_of(aa_TPT43085870d_bool(aTP_Lamm_af,X)),aa_fun1584354236d_bool(aTP_Lamm_az(X),Xa))))) # label(fact_def__amone) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 66 (all X scratc1814168434d_e_is(X) = fequal_TPTP_ind) # label(fact_def__e__is) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 67 (all X all Xa all Xb (scratc172856053_orec3(X,Xa,Xb) <-> pp(scratc95353584_d_and(scratc1639226547nd_or3(X,Xa,Xb),scratc1555627512nd_ec3(X,Xa,Xb))))) # label(fact_def__orec3) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 68 (all X all Xa all Xb (pp(scratc1555627512nd_ec3(X,Xa,Xb)) <-> scratc452916185d_and3(scratc1200921453d_l_ec(X,Xa),scratc1200921453d_l_ec(Xa,Xb),scratc1200921453d_l_ec(Xb,X)))) # label(fact_def__ec3) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 69 (all X all Xa all Xb (scratc452916185d_and3(X,Xa,Xb) <-> pp(scratc95353584_d_and(X,scratc95353584_d_and(Xa,Xb))))) # label(fact_def__and3) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 70 (all X all Xa all Xb (pp(scratc1639226547nd_or3(X,Xa,Xb)) <-> pp(aa_bool_bool(scratc1201577458d_l_or(X),aa_bool_bool(scratc1201577458d_l_or(Xa),Xb))))) # label(fact_def__or3) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 71 (all X all Xa (pp(aa_fun171081125l_bool(scratc1482224803l_some(X),Xa)) <-> pp(scratc202818764_d_not(aa_fun171081125l_bool(scratc224080347all_of(aa_TPT43085870d_bool(aTP_Lamm_af,X)),scratc1630768304nd_non(X,Xa)))))) # label(fact_def__l__some) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 72 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc1630768304nd_non(X,Xa),Xb)) <-> pp(scratc202818764_d_not(aa_TPTP_ind_bool(Xa,Xb))))) # label(fact_def__non) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 73 (all X scratc1523171940nd_all(X) = scratc224080347all_of(aa_TPT43085870d_bool(aTP_Lamm_af,X))) # label(fact_def__all) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 74 (all X all Xa (scratc989495034_l_iff(X,Xa) <-> pp(scratc95353584_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1589329583nd_imp,X),Xa),aa_bool_bool(aa_boo1142376798l_bool(scratc1589329583nd_imp,Xa),X))))) # label(fact_def__l__iff) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 75 (all X all Xa (scratc676830398d_orec(X,Xa) <-> pp(scratc95353584_d_and(aa_bool_bool(scratc1201577458d_l_or(X),Xa),scratc1200921453d_l_ec(X,Xa))))) # label(fact_def__orec) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 76 (all X scratc1201577458d_l_or(X) = aa_boo1142376798l_bool(scratc1589329583nd_imp,scratc202818764_d_not(X))) # label(fact_def__l__or) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 77 (all X all Xa (pp(scratc95353584_d_and(X,Xa)) <-> pp(scratc202818764_d_not(scratc1200921453d_l_ec(X,Xa))))) # label(fact_def__d__and) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 78 (all X all Xa (pp(scratc1200921453d_l_ec(X,Xa)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1589329583nd_imp,X),scratc202818764_d_not(Xa))))) # label(fact_def__l__ec) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 79 scratc1717520266bvious <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1589329583nd_imp,fFalse),fFalse)) # label(fact_def__obvious) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 80 (all X (scratc1704465857nd_wel(X) <-> pp(scratc202818764_d_not(scratc202818764_d_not(X))))) # label(fact_def__wel) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 81 (all X (pp(scratc202818764_d_not(X)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1589329583nd_imp,X),fFalse)))) # label(fact_def__d__not) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 82 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc672964160d_d_Pi,X),Xa) = aa_fun1431113780TP_ind(scratc2126585783_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1266980744_power,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc39356126_Sigma,X),aTP_Lamm_ba(Xa)))),aa_fun1913827119d_bool(aTP_Lamm_bb(X),Xa))) # label(fact_def__d__Pi) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 83 (all X (gg_TPTP_ind(X) -> (pp(aa_TPTP_ind_bool(scratc1310939897pair_p,X)) <-> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1317234423d_pair,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc416169996bnd_ap,X),scratc75217938ptyset)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc416169996bnd_ap,X),aa_TPTP_ind_TPTP_ind(scratc1454189926rdsucc,scratc75217938ptyset))) = X))) # label(fact_def__pair__p) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 84 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc416169996bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc1060326120eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bc,Xa)),scratc1395494583_proj1)) # label(fact_def__ap) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 85 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1088113020etprod(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc39356126_Sigma,X),aTP_Lamm_ae(Xa))) # label(fact_def__setprod) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 86 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc39356126_Sigma,X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc440658490munion,X),aTP_Lamm_bd(Xa))) # label(fact_def__d__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 87 (all X aa_TPTP_ind_TPTP_ind(scratc1395494583_proj1,X) = aa_fun277296641TP_ind(scratc1060326120eplSep(X,aTP_Lamm_be),scratc2143699178_d_Unj)) # label(fact_def__proj1) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 88 (all X aa_TPTP_ind_TPTP_ind(scratc1395494582_proj0,X) = aa_fun277296641TP_ind(scratc1060326120eplSep(X,aTP_Lamm_bf),scratc2143699178_d_Unj)) # label(fact_def__proj0) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.24 89 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1317234423d_pair,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1434515589nunion(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc764430380d_repl,X),scratc73543890d_Inj0)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc764430380d_repl,Xa),scratc73543891d_Inj1))) # label(fact_def__pair) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 90 (all X aa_TPTP_ind_TPTP_ind(scratc73543890d_Inj0,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc764430380d_repl,X),scratc73543891d_Inj1)) # label(fact_def__d__Inj0) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 91 (all X (pp(aa_TPTP_ind_bool(scratc994542188_nat_p,X)) <-> (all X1 (pp(aa_TPTP_ind_bool(X1,scratc75217938ptyset)) -> ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(X1,X2)) -> pp(aa_TPTP_ind_bool(X1,aa_TPTP_ind_TPTP_ind(scratc1454189926rdsucc,X2)))))) -> pp(aa_TPTP_ind_bool(X1,X))))))) # label(fact_def__nat__p) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 92 (all X aa_TPTP_ind_TPTP_ind(scratc1454189926rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1434515589nunion(X),aa_TPTP_ind_TPTP_ind(scratc1395919862d_Sing,X))) # label(fact_def__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 93 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc788089700In_rec(X),Xa) = scratc1556480363nd_eps(aa_TPT43085870d_bool(scratc918509603_rec_G(X),Xa))) # label(fact_def__d__In__rec) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 94 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc918509603_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(scratc416694786bnd_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].
% 0.94/1.25 95 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1350801131tminus(X),Xa) = aa_fun1431113780TP_ind(scratc2126585783_d_Sep(X),aa_TPT43085870d_bool(aTP_Lamm_bi,Xa))) # label(fact_def__setminus) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 96 (all X all Xa scratc1060326120eplSep(X,Xa) = aa_TPT494704832TP_ind(scratc764430380d_repl,aa_fun1431113780TP_ind(scratc2126585783_d_Sep(X),Xa))) # label(fact_def__d__ReplSep) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 97 (all X all Xa aa_fun1431113780TP_ind(scratc2126585783_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc416694778bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc416694786bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc764430380d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bj(X),Xa))),scratc75217938ptyset)) # label(fact_def__d__Sep) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 98 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc440658490munion,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1774242610_union,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc764430380d_repl,X),Xa))) # label(fact_def__famunion) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 99 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1434515589nunion(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1774242610_union,aa_TPTP_ind_TPTP_ind(scratc2081326152_UPair(X),Xa))) # label(fact_def__binunion) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 100 (all X aa_TPTP_ind_TPTP_ind(scratc1395919862d_Sing,X) = aa_TPTP_ind_TPTP_ind(scratc2081326152_UPair(X),X)) # label(fact_def__d__Sing) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 101 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc2081326152_UPair(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc764430380d_repl,aa_TPTP_ind_TPTP_ind(scratc1266980744_power,aa_TPTP_ind_TPTP_ind(scratc1266980744_power,scratc75217938ptyset))),aa_TPT1424761345TP_ind(aTP_Lamm_bk(X),Xa))) # label(fact_def__d__UPair) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 102 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1628275542nd_nIn,X),Xa)) <-> -pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X),Xa)))) # label(fact_def__nIn) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 103 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc416694778bnd_if(X,Xa),Xb) = scratc1556480363nd_eps(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bl(X),Xa),Xb))) # label(fact_def__if) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 104 (all X (pp(aa_TPTP_ind_bool(scratc1217033503closed,X)) <-> pp(aa_TPTP_ind_bool(scratc1019404980closed,X)) & pp(aa_TPTP_ind_bool(scratc1184137994closed,X)) & pp(aa_TPTP_ind_bool(scratc1504037954closed,X)))) # label(fact_def__d__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 105 (all X (pp(aa_TPTP_ind_bool(scratc1504037954closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X1),X)) -> (all X2 ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X3),X1)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,aa_TPTP_ind_TPTP_ind(X2,X3)),X))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc764430380d_repl,X1),X2)),X))))))))) # label(fact_def__d__Repl__closed) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 106 (all X (pp(aa_TPTP_ind_bool(scratc1184137994closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,aa_TPTP_ind_TPTP_ind(scratc1266980744_power,X1)),X))))))) # label(fact_def__d__Power__closed) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 107 (all X (pp(aa_TPTP_ind_bool(scratc1019404980closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,aa_TPTP_ind_TPTP_ind(scratc1774242610_union,X1)),X))))))) # label(fact_def__d__Union__closed) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 108 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1494270744d_Subq,X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X2),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X2),Xa))))))) # label(fact_def__d__Subq) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 109 (all X all Xa (pp(aa_fun171081125l_bool(scratc224080347all_of(X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (scratc1107897982_is_of(X2,X) -> pp(aa_TPTP_ind_bool(Xa,X2))))))) # label(fact_def__all__of) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 110 (all X all Xa (scratc1107897982_is_of(X,Xa) <-> pp(aa_TPTP_ind_bool(Xa,X)))) # label(fact_def__is__of) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 111 (all X0 pp(aa_fun171081125l_bool(scratc224080347all_of(aa_TPT43085870d_bool(aTP_Lamm_bw,X0)),aa_TPT43085870d_bool(aTP_Lamm_by,X0)))) # label(fact_isseti) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 112 (all X0 all X12 pp(aa_fun171081125l_bool(scratc224080347all_of(aa_TPT43085870d_bool(aTP_Lamm_af,X0)),aa_fun1584354236d_bool(aTP_Lamm_bz(X0),X12)))) # label(fact_estie) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 113 (all X0 all X12 pp(aa_fun171081125l_bool(scratc224080347all_of(aa_TPT43085870d_bool(aTP_Lamm_af,X0)),aa_fun1584354236d_bool(aTP_Lamm_ca(X0),X12)))) # label(fact_estii) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 114 (all X0 all X12 scratc1107897982_is_of(aa_fun1431113780TP_ind(scratc2126585783_d_Sep(X0),X12),aa_TPT43085870d_bool(aTP_Lamm_bw,X0))) # label(fact_setof__p) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 115 (all X0 all X12 pp(aa_fun171081125l_bool(scratc224080347all_of(aa_TPT43085870d_bool(aTP_Lamm_af,X0)),aa_TPT43085870d_bool(aTP_Lamm_cc(X0),X12)))) # label(fact_secondis1) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 116 (all X0 all X12 pp(aa_fun171081125l_bool(scratc224080347all_of(aa_TPT43085870d_bool(aTP_Lamm_af,X0)),aa_TPT43085870d_bool(aTP_Lamm_ce(X0),X12)))) # label(fact_firstis1) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 117 (all X0 all X12 pp(aa_fun171081125l_bool(scratc224080347all_of(aa_TPT43085870d_bool(aTP_Lamm_cf(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_cg(X0),X12)))) # label(fact_pairis1) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 118 (all X0 all X12 pp(aa_fun171081125l_bool(scratc224080347all_of(aa_TPT43085870d_bool(aTP_Lamm_cf(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_ch(X0),X12)))) # label(fact_second__p) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 119 (all X0 all X12 pp(aa_fun171081125l_bool(scratc224080347all_of(aa_TPT43085870d_bool(aTP_Lamm_cf(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_ci(X0),X12)))) # label(fact_first__p) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 120 (all X0 all X12 pp(aa_fun171081125l_bool(scratc224080347all_of(aa_TPT43085870d_bool(aTP_Lamm_af,X0)),aa_TPT43085870d_bool(aTP_Lamm_ck(X0),X12)))) # label(fact_e__pair__p) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 121 (all X0 all X12 pp(aa_fun171081125l_bool(scratc224080347all_of(aa_TPT43085870d_bool(aTP_Lamm_af,X0)),aa_fun1584354236d_bool(aTP_Lamm_cl(X0),X12)))) # label(fact_otax2) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 122 (all X0 all X12 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1318293002ective(aa_fun1431113780TP_ind(scratc2126585783_d_Sep(X0),X12)),X0),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc39356126_Sigma,aa_fun1431113780TP_ind(scratc2126585783_d_Sep(X0),X12)),scratc1814168429d_e_in(X0,X12))))) # label(fact_otax1) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 123 (all X0 all X12 pp(aa_fun171081125l_bool(scratc224080347all_of(aa_fun1584354236d_bool(aTP_Lamm_cm(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_cn(X0),X12)))) # label(fact_e__inp) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 124 (all X0 all X12 pp(aa_fun171081125l_bool(scratc224080347all_of(aa_fun1584354236d_bool(aTP_Lamm_cm(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_co(X0),X12)))) # label(fact_e__in__p) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 125 (all X0 all X12 pp(aa_fun171081125l_bool(scratc224080347all_of(aa_TPT43085870d_bool(aTP_Lamm_cp(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_cs(X0),X12)))) # label(fact_e__fisi) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 126 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc1638964201nd_one(X0),X12)) -> pp(aa_TPTP_ind_bool(X12,scratc1589395170nd_ind(X0,X12))))) # label(fact_oneax) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 127 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc1638964201nd_one(X0),X12)) -> scratc1107897982_is_of(scratc1589395170nd_ind(X0,X12),aa_TPT43085870d_bool(aTP_Lamm_af,X0)))) # label(fact_ind__p) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 128 (all X0 all X12 pp(aa_fun171081125l_bool(scratc224080347all_of(aa_TPT43085870d_bool(aTP_Lamm_af,X0)),aa_fun1584354236d_bool(aTP_Lamm_cu(X0),X12)))) # label(fact_e__isp) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 129 (all X0 pp(aa_fun171081125l_bool(scratc224080347all_of(aa_TPT43085870d_bool(aTP_Lamm_af,X0)),aa_TPT43085870d_bool(aTP_Lamm_cv,X0)))) # label(fact_refis) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 130 (all X0 (scratc1704465857nd_wel(X0) -> pp(X0))) # label(fact_l__et) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 131 (all X0 all X12 all X22 all X32 (pp(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc416694778bnd_if(X0,X22),X32))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X12),X22))))) # label(fact_k__If__In__then__E) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 132 (all X0 all X12 all X22 ((pp(X0) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X12),X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,aa_TPTP_ind_TPTP_ind(scratc416694778bnd_if(X0,X12),scratc75217938ptyset)),aa_TPTP_ind_TPTP_ind(scratc416694778bnd_if(X0,X22),aa_TPTP_ind_TPTP_ind(scratc1454189926rdsucc,scratc75217938ptyset)))))) # label(fact_k__If__In__01) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 133 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X33),X0)) -> aa_TPTP_ind_TPTP_ind(X12,X33) = aa_TPTP_ind_TPTP_ind(X22,X33)))) -> aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc39356126_Sigma,X0),X12) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc39356126_Sigma,X0),X22))) # label(fact_xi__ext) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 134 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc672964160d_d_Pi,X0),X12))) -> (all X32 (gg_TPTP_ind(X32) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X32),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc672964160d_d_Pi,X0),X12))) -> ((all X42 (gg_TPTP_ind(X42) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X42),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc416169996bnd_ap,X22),X42) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc416169996bnd_ap,X32),X42)))) -> X22 = X32))))))) # label(fact_k__Pi__ext) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 135 (all X0 all X12 all X22 all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc672964160d_d_Pi,X0),X12))) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X32),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc416169996bnd_ap,X22),X32)),aa_TPTP_ind_TPTP_ind(X12,X32)))))) # label(fact_ap__Pi) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 136 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X33),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,aa_TPTP_ind_TPTP_ind(X22,X33)),aa_TPTP_ind_TPTP_ind(X12,X33)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc39356126_Sigma,X0),X22)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc672964160d_d_Pi,X0),X12))))) # label(fact_lam__Pi) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 137 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X22),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc416169996bnd_ap,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc39356126_Sigma,X0),X12)),X22) = aa_TPTP_ind_TPTP_ind(X12,X22))) # label(fact_beta) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 138 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc39356126_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,aa_TPTP_ind_TPTP_ind(scratc1395494583_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1395494582_proj0,X22)))))) # label(fact_proj1__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 139 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc39356126_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,aa_TPTP_ind_TPTP_ind(scratc1395494582_proj0,X22)),X0)))) # label(fact_proj0__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 140 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc39356126_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1317234423d_pair,aa_TPTP_ind_TPTP_ind(scratc1395494582_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1395494583_proj1,X22)) = X22))) # label(fact_proj__Sigma__eta) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 141 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc39356126_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1317234423d_pair,aa_TPTP_ind_TPTP_ind(scratc1395494582_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1395494583_proj1,X22)) = X22 & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,aa_TPTP_ind_TPTP_ind(scratc1395494582_proj0,X22)),X0)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,aa_TPTP_ind_TPTP_ind(scratc1395494583_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1395494582_proj0,X22))))))) # label(fact_k__Sigma__eta__proj0__proj1) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 142 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X22),X0)) -> (all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X32),aa_TPTP_ind_TPTP_ind(X12,X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1317234423d_pair,X22),X32)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc39356126_Sigma,X0),X12))))))) # label(fact_pair__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 143 (all X0 all X12 (gg_TPTP_ind(X12) -> aa_TPTP_ind_TPTP_ind(scratc1395494583_proj1,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1317234423d_pair,X0),X12)) = X12)) # label(fact_proj1__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 144 (all X0 all X12 (gg_TPTP_ind(X0) -> aa_TPTP_ind_TPTP_ind(scratc1395494582_proj0,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1317234423d_pair,X0),X12)) = X0)) # label(fact_proj0__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 145 (all X0 (pp(aa_TPTP_ind_bool(scratc994542188_nat_p,X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X0),scratc565149796_omega)))) # label(fact_nat__p__omega) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 146 (all X0 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X0),scratc565149796_omega)) -> pp(aa_TPTP_ind_bool(scratc994542188_nat_p,X0)))) # label(fact_omega__nat__p) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 147 (all X0 (gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(scratc994542188_nat_p,X0)) -> X0 = scratc75217938ptyset | (exists X13 (gg_TPTP_ind(X13) & pp(aa_TPTP_ind_bool(scratc994542188_nat_p,X13)) & X0 = aa_TPTP_ind_TPTP_ind(scratc1454189926rdsucc,X13)))))) # label(fact_nat__inv) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 148 (all X0 (pp(aa_TPTP_ind_bool(X0,scratc75217938ptyset)) -> ((all X13 (gg_TPTP_ind(X13) -> (pp(aa_TPTP_ind_bool(scratc994542188_nat_p,X13)) -> (pp(aa_TPTP_ind_bool(X0,X13)) -> pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc1454189926rdsucc,X13))))))) -> (all X12 (pp(aa_TPTP_ind_bool(scratc994542188_nat_p,X12)) -> pp(aa_TPTP_ind_bool(X0,X12))))))) # label(fact_nat__ind) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 149 (all X0 (pp(aa_TPTP_ind_bool(scratc994542188_nat_p,X0)) -> pp(aa_TPTP_ind_bool(scratc994542188_nat_p,aa_TPTP_ind_TPTP_ind(scratc1454189926rdsucc,X0))))) # label(fact_nat__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 150 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (aa_TPTP_ind_TPTP_ind(scratc1454189926rdsucc,X0) = aa_TPTP_ind_TPTP_ind(scratc1454189926rdsucc,X12) -> X0 = X12))) # label(fact_ordsucc__inj) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 151 (all X0 aa_TPTP_ind_TPTP_ind(scratc1454189926rdsucc,X0) != scratc75217938ptyset) # label(fact_neq__ordsucc__0) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 152 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X22),aa_fun1431113780TP_ind(scratc2126585783_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(X12,X22)))) # label(fact_k__SepE2) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 153 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X22),aa_fun1431113780TP_ind(scratc2126585783_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X22),X0)))) # label(fact_k__SepE1) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 154 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X22),X0)) -> (pp(aa_TPTP_ind_bool(X12,X22)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X22),aa_fun1431113780TP_ind(scratc2126585783_d_Sep(X0),X12)))))) # label(fact_k__SepI) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 155 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc1266980744_power,X0)))) # label(fact_k__Self__In__Power) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 156 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1494270744d_Subq,X12),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1266980744_power,X0))))) # label(fact_k__PowerI) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 157 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1266980744_power,X0))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1494270744d_Subq,X12),X0)))) # label(fact_k__PowerE) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 158 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> aa_TPTP_ind_TPTP_ind(scratc416694778bnd_if(X0,X12),X22) = X12 | aa_TPTP_ind_TPTP_ind(scratc416694778bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__or) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 159 (all X0 all X12 all X22 (gg_TPTP_ind(X12) -> (pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc416694778bnd_if(X0,X12),X22) = X12))) # label(fact_if__i__1) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 160 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (-pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc416694778bnd_if(X0,X12),X22) = X22))) # label(fact_if__i__0) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 161 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> pp(X0) & aa_TPTP_ind_TPTP_ind(scratc416694778bnd_if(X0,X12),X22) = X12 | -pp(X0) & aa_TPTP_ind_TPTP_ind(scratc416694778bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__correct) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 162 (all X0 pp(aa_TPTP_ind_bool(scratc1217033503closed,aa_TPTP_ind_TPTP_ind(scratc1427598970univof,X0)))) # label(fact_k__UnivOf__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 163 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc1427598970univof,X0)))) # label(fact_k__UnivOf__In) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 164 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc764430380d_repl,X0),X12))) <-> (exists X3 (gg_TPTP_ind(X3) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X3),X0)) & X22 = aa_TPTP_ind_TPTP_ind(X12,X3)))))) # label(fact_k__ReplEq) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 165 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1266980744_power,X0))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1494270744d_Subq,X12),X0)))) # label(fact_k__PowerEq) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 166 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1774242610_union,X0))) <-> (exists X2 (gg_TPTP_ind(X2) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X12),X2)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X2),X0)))))) # label(fact_k__UnionEq) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 167 -(exists X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X0),scratc75217938ptyset))) # label(fact_k__EmptyAx) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 168 (all X0 ((all X13 (gg_TPTP_ind(X13) -> ((all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_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].
% 0.94/1.25 169 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1494270744d_Subq,X0),X12)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1494270744d_Subq,X12),X0)) -> X0 = X12)))) # label(fact_set__ext) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 170 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ab,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1630374715nd_nis,Uu),scratc1886364608nd_n_1)) -> pp(aa_fun171081125l_bool(scratc78565797n_some,aa_TPT43085870d_bool(aTP_Lamm_aa,Uu)))))) # label(fact_ATP_Olambda__1) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 171 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_br,Uu)) <-> (pp(aa_TPTP_ind_bool(scratc1410611314_cond1,Uu)) -> (pp(aa_TPTP_ind_bool(scratc1410611315_cond2,Uu)) -> pp(aa_fun171081125l_bool(scratc224080347all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bq,Uu))))))) # label(fact_ATP_Olambda__2) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 172 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bm,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1630374715nd_nis,aa_TPTP_ind_TPTP_ind(scratc1454189926rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__3) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 173 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bv,Uu)) <-> scratc1107897982_is_of(aa_TPTP_ind_TPTP_ind(scratc1454189926rdsucc,Uu),aTP_Lamm_a))) # label(fact_ATP_Olambda__4) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 174 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1630374715nd_nis,aa_TPTP_ind_TPTP_ind(scratc1454189926rdsucc,Uu)),scratc1886364608nd_n_1)))) # label(fact_ATP_Olambda__5) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 175 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bp,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,Uu),aa_TPTP_ind_TPTP_ind(scratc1266980744_power,scratc1629849924nd_nat))))) # label(fact_ATP_Olambda__6) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 176 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_a,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,Uu),scratc1629849924nd_nat)))) # label(fact_ATP_Olambda__7) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 177 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bt,Uu)) <-> pp(aa_fun171081125l_bool(scratc224080347all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bs,Uu))))) # label(fact_ATP_Olambda__8) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 178 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bo,Uu)) <-> pp(aa_fun171081125l_bool(scratc224080347all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bn,Uu))))) # label(fact_ATP_Olambda__9) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 179 (all Uu aa_TPT494704832TP_ind(aTP_Lamm_bg,Uu) = aa_TPT494704832TP_ind(scratc764430380d_repl,aa_TPTP_ind_TPTP_ind(scratc1350801131tminus(Uu),aa_TPTP_ind_TPTP_ind(scratc1395919862d_Sing,scratc75217938ptyset)))) # label(fact_ATP_Olambda__10) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 180 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_ad,Uu)) <-> Uu != scratc75217938ptyset))) # label(fact_ATP_Olambda__11) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 181 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_be,Uu)) <-> (exists X2 (gg_TPTP_ind(X2) & aa_TPTP_ind_TPTP_ind(scratc73543891d_Inj1,X2) = Uu))))) # label(fact_ATP_Olambda__12) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 182 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_bf,Uu)) <-> (exists X2 (gg_TPTP_ind(X2) & aa_TPTP_ind_TPTP_ind(scratc73543890d_Inj0,X2) = Uu))))) # label(fact_ATP_Olambda__13) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 183 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cv,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1814168434d_e_is(Uu),Uua),Uua)))) # label(fact_ATP_Olambda__14) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 184 (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(scratc1332828795d_n_is,aa_TPTP_ind_TPTP_ind(scratc1454189926rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1454189926rdsucc,Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1332828795d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__15) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 185 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bn,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1630374715nd_nis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1630374715nd_nis,aa_TPTP_ind_TPTP_ind(scratc1454189926rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1454189926rdsucc,Uua)))))) # label(fact_ATP_Olambda__16) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 186 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ac,Uu),Uua)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1589329583nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1332828790d_n_in,Uua),Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1332828790d_n_in,aa_TPTP_ind_TPTP_ind(scratc1454189926rdsucc,Uua)),Uu))))) # label(fact_ATP_Olambda__17) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 187 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bd(Uu),Uua) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc764430380d_repl,aa_TPTP_ind_TPTP_ind(Uu,Uua)),aa_TPT1424761345TP_ind(scratc1317234423d_pair,Uua))) # label(fact_ATP_Olambda__18) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 188 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_by,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc224080347all_of(aa_TPT43085870d_bool(aTP_Lamm_bw,Uu)),aa_TPT43085870d_bool(aTP_Lamm_bx(Uu),Uua))))) # label(fact_ATP_Olambda__19) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 189 (all Uu all Uua aa_fun277296641TP_ind(aa_TPT494704832TP_ind(aTP_Lamm_bh,Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1434515589nunion(aa_TPTP_ind_TPTP_ind(scratc1395919862d_Sing,scratc75217938ptyset)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc764430380d_repl,Uu),Uua))) # label(fact_ATP_Olambda__20) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 190 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1332828795d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1454189926rdsucc,Uua))))) # label(fact_ATP_Olambda__21) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 191 (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(scratc416694786bnd_in,Uua),aa_TPTP_ind_TPTP_ind(scratc1266980744_power,Uu))))) # label(fact_ATP_Olambda__22) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 192 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bq,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1332828790d_n_in,Uua),Uu)))) # label(fact_ATP_Olambda__23) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 193 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bi,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1628275542nd_nIn,Uua),Uu)))) # label(fact_ATP_Olambda__24) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 194 (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(scratc416694786bnd_in,Uua),Uu)))) # label(fact_ATP_Olambda__25) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 195 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_ba(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1774242610_union,aa_TPTP_ind_TPTP_ind(Uu,Uua))) # label(fact_ATP_Olambda__26) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 196 (all Uu all Uua (gg_TPTP_ind(Uua) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bc,Uu),Uua)) <-> (exists X3 (gg_TPTP_ind(X3) & Uua = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1317234423d_pair,Uu),X3)))))) # label(fact_ATP_Olambda__27) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 197 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cg(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1814168434d_e_is(aa_TPTP_ind_TPTP_ind(scratc1088113020etprod(Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc344208481d_pair(Uu,Uua),aa_TPTP_ind_TPTP_ind(scratc179811059_first(Uu,Uua),Uub)),aa_TPTP_ind_TPTP_ind(scratc718472113second(Uu,Uua),Uub))),Uub)))) # label(fact_ATP_Olambda__28) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 198 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_bk(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc416694778bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,scratc75217938ptyset),Uub),Uu),Uua)) # label(fact_ATP_Olambda__29) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 199 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_fun1235454963TP_ind(aTP_Lamm_bj(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc416694778bnd_if(aa_TPTP_ind_bool(Uua,Uub),Uub),scratc1556480363nd_eps(aa_fun1584354236d_bool(aTP_Lamm_ax(Uu),Uua)))) # label(fact_ATP_Olambda__30) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 200 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aq(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1470138496d_esti(Uu),Uub),Uua)))) # label(fact_ATP_Olambda__31) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 201 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bz(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1470138496d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc2126585783_d_Sep(Uu),Uua))) -> pp(aa_TPTP_ind_bool(Uua,Uub))))) # label(fact_ATP_Olambda__32) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 202 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bx(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc255097291d_incl(Uu),Uua),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc255097291d_incl(Uu),Uub),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1814168434d_e_is(aa_TPTP_ind_TPTP_ind(scratc1266980744_power,Uu)),Uua),Uub)))))) # label(fact_ATP_Olambda__33) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 203 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ch(Uu),Uua),Uub)) <-> scratc1107897982_is_of(aa_TPTP_ind_TPTP_ind(scratc718472113second(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_af,Uua)))) # label(fact_ATP_Olambda__34) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 204 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ci(Uu),Uua),Uub)) <-> scratc1107897982_is_of(aa_TPTP_ind_TPTP_ind(scratc179811059_first(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_af,Uu)))) # label(fact_ATP_Olambda__35) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 205 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_co(Uu),Uua),Uub)) <-> scratc1107897982_is_of(aa_TPTP_ind_TPTP_ind(scratc1814168429d_e_in(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_af,Uu)))) # label(fact_ATP_Olambda__36) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 206 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cs(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc224080347all_of(aa_TPT43085870d_bool(aTP_Lamm_cp(Uu),Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cr(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__37) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 207 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ax(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,Uub),Uu)) & pp(aa_TPTP_ind_bool(Uua,Uub)))) # label(fact_ATP_Olambda__38) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 208 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_cl(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc137168990_image(aa_fun1431113780TP_ind(scratc2126585783_d_Sep(Uu),Uua),Uu),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc39356126_Sigma,aa_fun1431113780TP_ind(scratc2126585783_d_Sep(Uu),Uua)),scratc1814168429d_e_in(Uu,Uua))),Uub))))) # label(fact_ATP_Olambda__39) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.25 209 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ca(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1470138496d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc2126585783_d_Sep(Uu),Uua)))))) # label(fact_ATP_Olambda__40) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 210 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_cu(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc224080347all_of(aa_TPT43085870d_bool(aTP_Lamm_af,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_ct(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__41) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 211 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_az(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc224080347all_of(aa_TPT43085870d_bool(aTP_Lamm_af,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_ay(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__42) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 212 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ck(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc224080347all_of(aa_TPT43085870d_bool(aTP_Lamm_af,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cj(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__43) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 213 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ce(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc224080347all_of(aa_TPT43085870d_bool(aTP_Lamm_af,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cd(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__44) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 214 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cc(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc224080347all_of(aa_TPT43085870d_bool(aTP_Lamm_af,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cb(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__45) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 215 (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(scratc416694786bnd_in,Uub),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc672964160d_d_Pi,Uu),aTP_Lamm_ae(Uua)))))) # label(fact_ATP_Olambda__46) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 216 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cf(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,Uub),aa_TPTP_ind_TPTP_ind(scratc1088113020etprod(Uu),Uua))))) # label(fact_ATP_Olambda__47) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 217 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_cm(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,Uub),aa_fun1431113780TP_ind(scratc2126585783_d_Sep(Uu),Uua))))) # label(fact_ATP_Olambda__48) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 218 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_as(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc416169996bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc416169996bnd_ap,Uu),Uub))) # label(fact_ATP_Olambda__49) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 219 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_cn(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(Uua,aa_TPTP_ind_TPTP_ind(scratc1814168429d_e_in(Uu,Uua),Uub))))) # label(fact_ATP_Olambda__50) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 220 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1913827119d_bool(aTP_Lamm_bb(Uu),Uua),Uub)) <-> (all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,X3),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc416694786bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc416169996bnd_ap,Uub),X3)),aa_TPTP_ind_TPTP_ind(Uua,X3)))))))) # label(fact_ATP_Olambda__51) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 221 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_at(Uu),Uua),Uub),Uuc) = aa_TPTP_ind_TPTP_ind(scratc416694778bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc137168990_image(Uu,Uua),Uub),Uuc),aa_TPTP_ind_TPTP_ind(scratc1626976647d_soft(Uu,Uua,Uub),Uuc)),scratc75217938ptyset)) # label(fact_ATP_Olambda__52) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 222 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cd(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1814168434d_e_is(Uu),aa_TPTP_ind_TPTP_ind(scratc179811059_first(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc344208481d_pair(Uu,Uua),Uub),Uuc))),Uub)))) # label(fact_ATP_Olambda__53) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 223 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cb(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1814168434d_e_is(Uua),aa_TPTP_ind_TPTP_ind(scratc718472113second(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc344208481d_pair(Uu,Uua),Uub),Uuc))),Uuc)))) # label(fact_ATP_Olambda__54) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 224 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cq(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1814168434d_e_is(Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc416169996bnd_ap,Uua),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc416169996bnd_ap,Uub),Uuc))))) # label(fact_ATP_Olambda__55) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 225 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_am(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1470138496d_esti(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc416169996bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__56) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 226 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_au(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1814168434d_e_is(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc416169996bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__57) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 227 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cj(Uu),Uua),Uub),Uuc)) <-> scratc1107897982_is_of(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc344208481d_pair(Uu,Uua),Uub),Uuc),aa_TPT43085870d_bool(aTP_Lamm_cf(Uu),Uua)))) # label(fact_ATP_Olambda__58) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 228 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ao(Uu),Uua),Uub),Uuc)) <-> pp(scratc1200921453d_l_ec(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1470138496d_esti(Uu),Uuc),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1470138496d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__59) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 229 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ap(Uu),Uua),Uub),Uuc)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1589329583nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1470138496d_esti(Uu),Uuc),Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1470138496d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__60) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 230 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cr(Uu),Uua),Uub),Uuc)) <-> (pp(aa_fun171081125l_bool(scratc224080347all_of(aa_TPT43085870d_bool(aTP_Lamm_af,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cq(Uua),Uub),Uuc))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1814168434d_e_is(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc672964160d_d_Pi,Uu),aTP_Lamm_ae(Uua))),Uub),Uuc))))) # label(fact_ATP_Olambda__61) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 231 (all Uu all Uua all Uub all Uuc (gg_TPTP_ind(Uua) & gg_TPTP_ind(Uub) & gg_TPTP_ind(Uuc) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bl(Uu),Uua),Uub),Uuc)) <-> pp(Uu) & Uuc = Uua | -pp(Uu) & Uuc = Uub))) # label(fact_ATP_Olambda__62) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 232 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_ct(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1814168434d_e_is(Uu),Uub),Uuc)) -> pp(aa_TPTP_ind_bool(Uua,Uuc)))))) # label(fact_ATP_Olambda__63) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 233 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_ay(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(Uua,Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1814168434d_e_is(Uu),Uub),Uuc)))))) # label(fact_ATP_Olambda__64) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 234 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aw(Uu),Uua),Uub),Uuc)) <-> pp(aa_fun171081125l_bool(scratc1523171940nd_all(Uu),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_av(Uu),Uua),Uub),Uuc))))) # label(fact_ATP_Olambda__65) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 235 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_an(Uu),Uua),Uub),Uuc)) <-> pp(aa_fun171081125l_bool(scratc1482224803l_some(Uua),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_am(Uu),Uub),Uuc))))) # label(fact_ATP_Olambda__66) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 236 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_av(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1589329583nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1814168434d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc416169996bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc416169996bnd_ap,Uub),Uud))),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1814168434d_e_is(Uu),Uuc),Uud))))) # label(fact_ATP_Olambda__67) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 237 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_ak(Uu),Uua),Uub),Uuc),Uud)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1814168434d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc416169996bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc416169996bnd_ap,Uub),Uud)))))) # label(fact_ATP_Olambda__68) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 238 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_aj(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_fun171081125l_bool(scratc224080347all_of(aa_TPT43085870d_bool(aTP_Lamm_af,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_ai(Uu),Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__69) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 239 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_al(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_fun171081125l_bool(scratc224080347all_of(aa_TPT43085870d_bool(aTP_Lamm_af,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_ak(Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__70) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 240 (all Uu all Uua all Uub all Uuc all Uud aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_ar(Uu),Uua),Uub),Uuc),Uud) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc416169996bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc416169996bnd_ap,aa_TPTP_ind_TPTP_ind(scratc2106739830wissel(Uu,Uub),Uuc)),Uud))) # label(fact_ATP_Olambda__71) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 241 (all Uu all Uua all Uub all Uuc all Uud all Uue (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_ai(Uu),Uua),Uub),Uuc),Uud),Uue)) <-> pp(aa_fun171081125l_bool(scratc224080347all_of(aa_TPT43085870d_bool(aTP_Lamm_af,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_ah(Uu),Uua),Uub),Uuc),Uud),Uue))))) # label(fact_ATP_Olambda__72) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 242 (all Uu all Uua all Uub all Uuc all Uud all Uue all Uuf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_ag(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uue),Uuf)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1814168434d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc416169996bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc416169996bnd_ap,Uub),Uuc)),Uue)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc416169996bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc416169996bnd_ap,Uub),Uud)),Uuf))))))) # label(fact_ATP_Olambda__73) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 243 (all Uu all Uua all Uub all Uuc all Uud all Uue all Uuf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_ah(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)) <-> pp(aa_fun171081125l_bool(scratc224080347all_of(aa_TPT43085870d_bool(aTP_Lamm_af,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_ag(Uua),Uub),Uuc),Uud),Uue),Uuf))))) # label(fact_ATP_Olambda__74) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 244 (all Uu all Uua (gg_TPTP_ind(Uu) -> aa_TPTP_ind_TPTP_ind(aTP_Lamm_ae(Uu),Uua) = Uu)) # label(fact_ATP_Olambda__75) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 245 (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].
% 0.94/1.26 246 (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].
% 0.94/1.26 247 (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].
% 0.94/1.26 248 (all P (gg_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 0.94/1.26 249 (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].
% 0.94/1.26 250 (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].
% 0.94/1.26 251 (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].
% 0.94/1.26 252 (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].
% 0.94/1.26 253 (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].
% 0.94/1.26 254 (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].
% 0.94/1.26 255 (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].
% 0.94/1.26 256 (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].
% 0.94/1.28 257 (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].
% 0.94/1.28
% 0.94/1.28 ============================== end of process non-clausal formulas ===
% 0.94/1.28
% 0.94/1.28 ============================== PROCESS INITIAL CLAUSES ===============
% 0.94/1.28
% 0.94/1.28 ============================== PREDICATE ELIMINATION =================
% 0.94/1.28 258 -gg_bool(A) | A = fTrue | A = fFalse # label(help_fFalse_1_1_T) # label(axiom). [clausify(248)].
% 0.94/1.28 259 gg_bool(undefined_bool(bool)) # label(gsy_c_HOL_Oundefined_001t__HOL__Obool) # label(axiom). [assumption].
% 0.94/1.28 260 gg_bool(scratc1874193181_amone(A,B)) # label(gsy_c_Scratch__tptp__translate__39548__11527_ONUM637__thf__4__p_Obnd__amone) # label(axiom). [clausify(1)].
% 0.94/1.28 261 gg_bool(scratc95353584_d_and(A,B)) # label(gsy_c_Scratch__tptp__translate__39548__11527_ONUM637__thf__4__p_Obnd__d__and) # label(axiom). [clausify(2)].
% 0.94/1.28 262 gg_bool(scratc202818764_d_not(A)) # label(gsy_c_Scratch__tptp__translate__39548__11527_ONUM637__thf__4__p_Obnd__d__not) # label(axiom). [clausify(3)].
% 0.94/1.28 263 gg_bool(scratc1555627512nd_ec3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__39548__11527_ONUM637__thf__4__p_Obnd__ec3) # label(axiom). [clausify(4)].
% 0.94/1.28 264 gg_bool(scratc1200921453d_l_ec(A,B)) # label(gsy_c_Scratch__tptp__translate__39548__11527_ONUM637__thf__4__p_Obnd__l__ec) # label(axiom). [clausify(8)].
% 0.94/1.28 265 gg_bool(scratc1639226547nd_or3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__39548__11527_ONUM637__thf__4__p_Obnd__or3) # label(axiom). [clausify(9)].
% 0.94/1.28 266 gg_bool(aa_bool_bool(A,B)) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom). [clausify(10)].
% 0.94/1.28 267 gg_bool(aa_TPTP_ind_bool(A,B)) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom). [clausify(11)].
% 0.94/1.28 268 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)].
% 0.94/1.28 269 gg_bool(fEx_TPTP_ind(A)) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom). [clausify(16)].
% 0.94/1.28 270 gg_bool(fFalse) # label(gsy_c_fFalse) # label(axiom). [assumption].
% 0.94/1.28 271 gg_bool(fTrue) # label(gsy_c_fTrue) # label(axiom). [assumption].
% 0.94/1.28 Derived: undefined_bool(bool) = fTrue | undefined_bool(bool) = fFalse. [resolve(258,a,259,a)].
% 0.94/1.28 Derived: scratc1874193181_amone(A,B) = fTrue | scratc1874193181_amone(A,B) = fFalse. [resolve(258,a,260,a)].
% 0.94/1.28 Derived: scratc95353584_d_and(A,B) = fTrue | scratc95353584_d_and(A,B) = fFalse. [resolve(258,a,261,a)].
% 0.94/1.28 Derived: scratc202818764_d_not(A) = fTrue | scratc202818764_d_not(A) = fFalse. [resolve(258,a,262,a)].
% 0.94/1.28 Derived: scratc1555627512nd_ec3(A,B,C) = fTrue | scratc1555627512nd_ec3(A,B,C) = fFalse. [resolve(258,a,263,a)].
% 0.94/1.28 Derived: scratc1200921453d_l_ec(A,B) = fTrue | scratc1200921453d_l_ec(A,B) = fFalse. [resolve(258,a,264,a)].
% 0.94/1.28 Derived: scratc1639226547nd_or3(A,B,C) = fTrue | scratc1639226547nd_or3(A,B,C) = fFalse. [resolve(258,a,265,a)].
% 0.94/1.28 Derived: aa_bool_bool(A,B) = fTrue | aa_bool_bool(A,B) = fFalse. [resolve(258,a,266,a)].
% 0.94/1.28 Derived: aa_TPTP_ind_bool(A,B) = fTrue | aa_TPTP_ind_bool(A,B) = fFalse. [resolve(258,a,267,a)].
% 0.94/1.28 Derived: aa_fun171081125l_bool(A,B) = fTrue | aa_fun171081125l_bool(A,B) = fFalse. [resolve(258,a,268,a)].
% 0.94/1.28 Derived: fEx_TPTP_ind(A) = fTrue | fEx_TPTP_ind(A) = fFalse. [resolve(258,a,269,a)].
% 0.94/1.28 Derived: fFalse = fTrue | fFalse = fFalse. [resolve(258,a,270,a)].
% 0.94/1.28 Derived: fTrue = fTrue | fTrue = fFalse. [resolve(258,a,271,a)].
% 0.94/1.28 272 scratc1595856243d_r_ec(A,B) | pp(A) # label(fact_def__r__ec) # label(axiom). [clausify(42)].
% 0.94/1.28 273 -scratc1595856243d_r_ec(A,B) | -pp(A) | pp(scratc202818764_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(42)].
% 0.94/1.46 274 scratc1595856243d_r_ec(A,B) | -pp(scratc202818764_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(42)].
% 0.94/1.46 275 scratc172856053_orec3(A,B,C) | -pp(scratc95353584_d_and(scratc1639226547nd_or3(A,B,C),scratc1555627512nd_ec3(A,B,C))) # label(fact_def__orec3) # label(axiom). [clausify(67)].
% 0.94/1.46 276 -scratc172856053_orec3(A,B,C) | pp(scratc95353584_d_and(scratc1639226547nd_or3(A,B,C),scratc1555627512nd_ec3(A,B,C))) # label(fact_def__orec3) # label(axiom). [clausify(67)].
% 0.94/1.46 277 scratc989495034_l_iff(A,B) | -pp(scratc95353584_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1589329583nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc1589329583nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(74)].
% 0.94/1.46 278 -scratc989495034_l_iff(A,B) | pp(scratc95353584_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc1589329583nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc1589329583nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(74)].
% 0.94/1.46 279 scratc676830398d_orec(A,B) | -pp(scratc95353584_d_and(aa_bool_bool(scratc1201577458d_l_or(A),B),scratc1200921453d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(75)].
% 0.94/1.46 280 -scratc676830398d_orec(A,B) | pp(scratc95353584_d_and(aa_bool_bool(scratc1201577458d_l_or(A),B),scratc1200921453d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(75)].
% 0.94/1.46 281 scratc1704465857nd_wel(A) | -pp(scratc202818764_d_not(scratc202818764_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(80)].
% 0.94/1.46 282 -scratc1704465857nd_wel(A) | pp(scratc202818764_d_not(scratc202818764_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(80)].
% 0.94/1.46 283 -scratc1704465857nd_wel(A) | pp(A) # label(fact_l__et) # label(axiom). [clausify(130)].
% 0.94/1.46 Derived: pp(A) | -pp(scratc202818764_d_not(scratc202818764_d_not(A))). [resolve(283,a,281,a)].
% 0.94/1.46
% 0.94/1.46 ============================== end predicate elimination =============
% 0.94/1.46
% 0.94/1.46 Auto_denials: (non-Horn, no changes).
% 0.94/1.46
% 0.94/1.46 Term ordering decisions:
% 0.94/1.46 Function symbol KB weights: scratc416694786bnd_in=1. aTP_Lamm_af=1. scratc416169996bnd_ap=1. scratc1454189926rdsucc=1. scratc75217938ptyset=1. scratc39356126_Sigma=1. fFalse=1. scratc1266980744_power=1. scratc994542188_nat_p=1. scratc1589329583nd_imp=1. scratc764430380d_repl=1. aTP_Lamm_a=1. fTrue=1. scratc672964160d_d_Pi=1. scratc1630374715nd_nis=1. scratc1317234423d_pair=1. scratc1629849924nd_nat=1. scratc1332828795d_n_is=1. scratc1494270744d_Subq=1. scratc1886364608nd_n_1=1. scratc1395494582_proj0=1. scratc1504037954closed=1. scratc1774242610_union=1. scratc1332828790d_n_in=1. scratc1395494583_proj1=1. aTP_Lamm_aa=1. aTP_Lamm_bw=1. scratc1019404980closed=1. scratc1184137994closed=1. aTP_Lamm_bn=1. aTP_Lamm_br=1. aTP_Lamm_bs=1. scratc1217033503closed=1. scratc565149796_omega=1. scratc73543891d_Inj1=1. scratc78565797n_some=1. aTP_Lamm_ac=1. aTP_Lamm_bc=1. aTP_Lamm_be=1. aTP_Lamm_bf=1. aTP_Lamm_bq=1. fconj=1. fimplies=1. scratc1395919862d_Sing=1. scratc1410611315_cond2=1. scratc73543890d_Inj0=1. aTP_Lamm_ab=1. aTP_Lamm_bi=1. aTP_Lamm_bm=1. aTP_Lamm_bo=1. aTP_Lamm_bp=1. aTP_Lamm_bt=1. aTP_Lamm_bu=1. aTP_Lamm_bv=1. aTP_Lamm_by=1. aTP_Lamm_cv=1. fequal_TPTP_ind=1. scratc1410611314_cond1=1. scratc1427598970univof=1. scratc1628275542nd_nIn=1. scratc1667811056_n_all=1. scratc2143699178_d_Unj=1. aTP_Lamm_ad=1. aTP_Lamm_bg=1. aTP_Lamm_bh=1. bool=1. scratc1310939897pair_p=1. scratc2146138160_empty=1. scratc237293575_prop1=1. scratc360812925nempty=1. scratc440658490munion=1. scratc825655750_prop1=1. scratc1783603317_n_one=1. scratc529529518d_i1_s=1. tPTP_ind=1. aa_TPTP_ind_bool=1. aa_TPT43085870d_bool=1. aa_TPTP_ind_TPTP_ind=1. aa_fun171081125l_bool=1. aa_TPT60673477d_bool=1. aa_fun277296641TP_ind=1. aa_TPT1424761345TP_ind=1. aa_TPT494704832TP_ind=1. aa_fun1584354236d_bool=1. aa_bool_bool=1. aa_fun1431113780TP_ind=1. aa_boo1142376798l_bool=1. aa_TPT1123896796d_bool=1. scratc416694778bnd_if=1. scratc95353584_d_and=1. scratc1200921453d_l_ec=1. aa_fun1212484691d_bool=1. aa_TPT985247859d_bool=1. scratc1814168429d_e_in=1. scratc344208481d_pair=1. aa_fun987228051d_bool=1. scratc137168990_image=1. scratc1589395170nd_ind=1. scratc179811059_first=1. scratc718472113second=1. aa_TPT125613450d_bool=1. scratc1630768304nd_non=1. scratc1874193181_amone=1. aa_fun1913827119d_bool=1. scratc452981832d_anec=1. aa_TPT1791839040TP_ind=1. aa_fun1107270209d_bool=1. aa_fun845057962d_bool=1. scratc1060326120eplSep=1. scratc1555627573nd_ecp=1. scratc691315762_ecelt=1. scratc690725371_ecect=1. aa_TPT1781712639TP_ind=1. aa_TPT2142672771l_bool=1. aa_fun1235454963TP_ind=1. cOMBB_658106424TP_ind=1. cOMBS_2003118649l_bool=1. scratc1555627577nd_ect=1. scratc1639423409nd_out=1. scratc1726686507fixfu2=1. scratc2106739830wissel=1. scratc228527303_fixfu=1. scratc496865546etprop=1. scratc91229385ectset=1. scratc197346731unmore=1. scratc2123511156ectelt=1. scratc256343666d_invf=1. scratc260080197d_tofs=1. scratc852437619nverse=1. f1=1. f12=1. f13=1. f20=1. f24=1. scratc224080347all_of=1. scratc1814168434d_e_is=1. scratc2126585783_d_Sep=1. scratc1470138496d_esti=1. scratc202818764_d_not=1. scratc1482224803l_some=1. scratc1523171940nd_all=1. scratc918509603_rec_G=1. aTP_Lamm_ae=1. aTP_Lamm_cf=1. scratc1201577458d_l_or=1. aTP_Lamm_ag=1. aTP_Lamm_aq=1. aTP_Lamm_ay=1. aTP_Lamm_bl=1. aTP_Lamm_bx=1. aTP_Lamm_ct=1. scratc255097291d_incl=1. aTP_Lamm_ak=1. aTP_Lamm_au=1. aTP_Lamm_ax=1. aTP_Lamm_bb=1. aTP_Lamm_cp=1. aTP_Lamm_cr=1. scratc1088113020etprod=1. scratc1318293002ective=1. scratc1556480363nd_eps=1. scratc1638964201nd_one=1. aTP_Lamm_ah=1. aTP_Lamm_ai=1. aTP_Lamm_aj=1. aTP_Lamm_al=1. aTP_Lamm_am=1. aTP_Lamm_ao=1. aTP_Lamm_ap=1. aTP_Lamm_av=1. aTP_Lamm_aw=1. aTP_Lamm_az=1. aTP_Lamm_bz=1. aTP_Lamm_ca=1. aTP_Lamm_cb=1. aTP_Lamm_cd=1. aTP_Lamm_cj=1. aTP_Lamm_cl=1. aTP_Lamm_cm=1. aTP_Lamm_cq=1. fEx_TPTP_ind=1. scratc1434515589nunion=1. scratc32610841ective=1. aTP_Lamm_an=1. aTP_Lamm_cc=1. aTP_Lamm_ce=1. aTP_Lamm_cg=1. aTP_Lamm_ch=1. aTP_Lamm_ci=1. aTP_Lamm_ck=1. aTP_Lamm_cn=1. aTP_Lamm_co=1. aTP_Lamm_cs=1. aTP_Lamm_cu=1. scratc2081326152_UPair=1. scratc788089700In_rec=1. aTP_Lamm_ar=1. aTP_Lamm_as=1. aTP_Lamm_at=1. aTP_Lamm_ba=1. aTP_Lamm_bd=1. aTP_Lamm_bj=1. aTP_Lamm_bk=1. cOMBC_1555011498d_bool=1. scratc1350801131tminus=1. scratc1502012232ective=1. scratc1767637626t_disj=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. scratc1555627512nd_ec3=1. scratc1626976647d_soft=1. scratc1639226547nd_or3=1. scratc1395888177_prop1=1. scratc1589788765nd_ite=1. scratc942409518_indeq=1. scratc1266139010d_11_i=1. scratc436235232sel_wa=1. scratc436235233sel_wb=1. f5=1. f7=1. f14=1. f16=1. f19=1. f25=1. scratc1395888178_prop2=1. scratc1848002496_inj_h=1. scratc866396569hangef=1. f3=1. f4=1. f15=1. scratc1961340552_prop1=1. scratc1510196356indeq2=1. f6=1.
% 3.24/3.57
% 3.24/3.57 ============================== end of process initial clauses ========
% 3.24/3.57
% 3.24/3.57 ============================== CLAUSES FOR SEARCH ====================
% 3.24/3.57
% 3.24/3.57 ============================== end of clauses for search =============
% 3.24/3.57
% 3.24/3.57 ============================== SEARCH ================================
% 3.24/3.57
% 3.24/3.57 % Starting search at 0.27 seconds.
% 3.24/3.57
% 3.24/3.57 Low Water (keep): wt=64.000, iters=3765
% 3.24/3.57
% 3.24/3.57 Low Water (keep): wt=40.000, iters=3518
% 3.24/3.57
% 3.24/3.57 Low Water (keep): wt=36.000, iters=3378
% 3.24/3.57
% 3.24/3.57 Low Water (keep): wt=35.000, iters=3369
% 3.24/3.57
% 3.24/3.57 Low Water (keep): wt=34.000, iters=3348
% 3.24/3.57
% 3.24/3.57 Low Water (keep): wt=33.000, iters=3358
% 3.24/3.57
% 3.24/3.57 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 28 (0.00 of 1.18 sec).
% 3.24/3.57
% 3.24/3.57 Low Water (keep): wt=24.000, iters=3386
% 3.24/3.57
% 3.24/3.57 Low Water (keep): wt=23.000, iters=3340
% 3.24/3.57
% 3.24/3.57 Low Water (keep): wt=22.000, iters=3346
% 3.24/3.57
% 3.24/3.57 Low Water (keep): wt=21.000, iters=3335
% 3.24/3.57
% 3.24/3.57 Low Water (keep): wt=20.000, iters=3391
% 3.24/3.57
% 3.24/3.57 Low Water (keep): wt=19.000, iters=3443
% 3.24/3.57
% 3.24/3.57 Low Water (keep): wt=18.000, iters=3575
% 3.24/3.57
% 3.24/3.57 Low Water (keep): wt=16.000, iters=3342
% 3.24/3.57
% 3.24/3.57 Low Water (displace): id=6673, wt=107.000
% 3.24/3.57
% 3.24/3.57 Low Water (displace): id=6779, wt=103.000
% 3.24/3.57
% 3.24/3.57 Low Water (displace): id=6791, wt=93.000
% 3.24/3.57
% 3.24/3.57 Low Water (displace): id=6669, wt=86.000
% 3.24/3.57
% 3.24/3.57 Low Water (displace): id=3813, wt=84.000
% 3.24/3.57
% 3.24/3.57 Low Water (displace): id=6792, wt=83.000
% 3.24/3.57
% 3.24/3.57 Low Water (displace): id=6789, wt=81.000
% 3.24/3.57
% 3.24/3.57 Low Water (displace): id=6794, wt=80.000
% 3.24/3.57
% 3.24/3.57 Low Water (displace): id=6672, wt=77.000
% 3.24/3.57
% 3.24/3.57 Low Water (displace): id=6Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------