TSTP Solution File: NUM636+4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM636+4 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n005.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 13:29:47 EDT 2022
% Result : Timeout 300.08s 300.39s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM636+4 : TPTP v8.1.0. Released v7.3.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n005.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Wed Jul 6 13:45:07 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.92/1.21 ============================== Prover9 ===============================
% 0.92/1.21 Prover9 (32) version 2009-11A, November 2009.
% 0.92/1.21 Process 2161 was started by sandbox on n005.cluster.edu,
% 0.92/1.21 Wed Jul 6 13:45:08 2022
% 0.92/1.21 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_2000_n005.cluster.edu".
% 0.92/1.21 ============================== end of head ===========================
% 0.92/1.21
% 0.92/1.21 ============================== INPUT =================================
% 0.92/1.21
% 0.92/1.21 % Reading from file /tmp/Prover9_2000_n005.cluster.edu
% 0.92/1.21
% 0.92/1.21 set(prolog_style_variables).
% 0.92/1.21 set(auto2).
% 0.92/1.21 % set(auto2) -> set(auto).
% 0.92/1.21 % set(auto) -> set(auto_inference).
% 0.92/1.21 % set(auto) -> set(auto_setup).
% 0.92/1.21 % set(auto_setup) -> set(predicate_elim).
% 0.92/1.21 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.92/1.21 % set(auto) -> set(auto_limits).
% 0.92/1.21 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.92/1.21 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.92/1.21 % set(auto) -> set(auto_denials).
% 0.92/1.21 % set(auto) -> set(auto_process).
% 0.92/1.21 % set(auto2) -> assign(new_constants, 1).
% 0.92/1.21 % set(auto2) -> assign(fold_denial_max, 3).
% 0.92/1.21 % set(auto2) -> assign(max_weight, "200.000").
% 0.92/1.21 % set(auto2) -> assign(max_hours, 1).
% 0.92/1.21 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.92/1.21 % set(auto2) -> assign(max_seconds, 0).
% 0.92/1.21 % set(auto2) -> assign(max_minutes, 5).
% 0.92/1.21 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.92/1.21 % set(auto2) -> set(sort_initial_sos).
% 0.92/1.21 % set(auto2) -> assign(sos_limit, -1).
% 0.92/1.21 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.92/1.21 % set(auto2) -> assign(max_megs, 400).
% 0.92/1.21 % set(auto2) -> assign(stats, some).
% 0.92/1.21 % set(auto2) -> clear(echo_input).
% 0.92/1.21 % set(auto2) -> set(quiet).
% 0.92/1.21 % set(auto2) -> clear(print_initial_clauses).
% 0.92/1.21 % set(auto2) -> clear(print_given).
% 0.92/1.21 assign(lrs_ticks,-1).
% 0.92/1.21 assign(sos_limit,10000).
% 0.92/1.21 assign(order,kbo).
% 0.92/1.21 set(lex_order_vars).
% 0.92/1.21 clear(print_given).
% 0.92/1.21
% 0.92/1.21 % formulas(sos). % not echoed (286 formulas)
% 0.92/1.21
% 0.92/1.21 ============================== end of input ==========================
% 0.92/1.21
% 0.92/1.21 % From the command line: assign(max_seconds, 300).
% 0.92/1.21
% 0.92/1.21 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.92/1.21
% 0.92/1.21 % Formulas that are not ordinary clauses:
% 0.92/1.21 1 (all B_1 all B_2 gg_bool(scratc369594977_amone(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__39347__27944_ONUM636__thf__4__p_Obnd__amone) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 2 (all B_1 all B_2 gg_bool(scratc453715116_d_and(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__39347__27944_ONUM636__thf__4__p_Obnd__d__and) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 3 (all B_1 gg_bool(scratc561180296_d_not(B_1))) # label(gsy_c_Scratch__tptp__translate__39347__27944_ONUM636__thf__4__p_Obnd__d__not) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 4 (all B_1 all B_2 all B_3 gg_bool(scratc2013464380nd_ec3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__39347__27944_ONUM636__thf__4__p_Obnd__ec3) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 5 (all B_1 all B_2 gg_TPTP_ind(scratc2013464445nd_ect(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__39347__27944_ONUM636__thf__4__p_Obnd__ect) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 6 (all B_1 gg_TPTP_ind(scratc2014317231nd_eps(B_1))) # label(gsy_c_Scratch__tptp__translate__39347__27944_ONUM636__thf__4__p_Obnd__eps) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 7 (all B_1 all B_2 gg_TPTP_ind(scratc2047232038nd_ind(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__39347__27944_ONUM636__thf__4__p_Obnd__ind) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 8 (all B_1 all B_2 gg_bool(scratc1843806897d_l_ec(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__39347__27944_ONUM636__thf__4__p_Obnd__l__ec) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 9 (all B_1 all B_2 all B_3 gg_bool(scratc2097063415nd_or3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__39347__27944_ONUM636__thf__4__p_Obnd__or3) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 10 (all B_1 all B_2 gg_bool(aa_bool_bool(B_1,B_2))) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 11 (all B_1 all B_2 gg_bool(aa_TPTP_ind_bool(B_1,B_2))) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 12 (all B_1 all B_2 gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(B_1,B_2))) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 13 (all B_1 all B_2 gg_bool(aa_fun171081125l_bool(B_1,B_2))) # label(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__HOL__Obool) # label(hypothesis) # label(non_clause). [assumption].
% 0.92/1.21 14 (all B_1 all B_2 gg_TPTP_ind(aa_fun1431113780TP_ind(B_1,B_2))) # label(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 15 (all B_1 all B_2 gg_TPTP_ind(aa_fun277296641TP_ind(B_1,B_2))) # label(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__TPTP____Interpret__Oind_J_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 16 (all B_1 gg_bool(fEx_TPTP_ind(B_1))) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 17 (all X (pp(aa_TPTP_ind_bool(scratc20619203_prop1,X)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2088211583nd_nis,aa_TPTP_ind_TPTP_ind(scratc1108832938rdsucc,X)),X)))) # label(fact_def__d__22__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 18 (all X (pp(aa_TPTP_ind_bool(scratc2053496759_cond2,X)) <-> pp(aa_fun171081125l_bool(scratc2026172588_n_all,aa_TPT43085870d_bool(aTP_Lamm_ab,X))))) # label(fact_def__cond2) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 19 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2088211583nd_nis,X),Xa)) <-> pp(scratc561180296_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1975714239d_n_is,X),Xa))))) # label(fact_def__nis) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 20 (all X all Xa all Xb all Xc all Xd scratc1868557888indeq2(X,Xa,Xb,Xc,Xd) = aa_TPT1424761345TP_ind(scratc1585294962_indeq(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2145569598d_11_i(X,Xa,Xb),Xc),Xd))) # label(fact_def__indeq2) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 21 (all X all Xa all Xb scratc2145569598d_11_i(X,Xa,Xb) = scratc1585294962_indeq(X,Xa,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1315849604d_d_Pi,X),aTP_Lamm_ad(Xb)))) # label(fact_def__d__11__i) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 22 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2085048039fixfu2(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc2026207007all_of(aa_TPT43085870d_bool(aTP_Lamm_ae,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ai(X),Xa),Xb),Xc))))) # label(fact_def__fixfu2) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 23 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1585294962_indeq(X,Xa,Xb),Xc),Xd) = scratc2047232038nd_ind(Xb,aa_TPT43085870d_bool(scratc2038773622_prop2(X,Xa,Xb,Xc),Xd))) # label(fact_def__indeq) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 24 (all X all Xa all Xb all Xc all Xd all Xe (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2038773622_prop2(X,Xa,Xb,Xc),Xd),Xe)) <-> pp(aa_fun171081125l_bool(scratc1136867815l_some(X),aa_TPT43085870d_bool(scratc1744666180_prop1(X,Xa,Xb,Xc,Xd),Xe))))) # label(fact_def__prop2) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 25 (all X all Xa all Xb all Xc all Xd all Xe all Xf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1744666180_prop1(X,Xa,Xb,Xc,Xd),Xe),Xf)) <-> pp(scratc453715116_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc404541500d_esti(X),Xf),aa_TPTP_ind_TPTP_ind(scratc1333610815_ecect(X,Xa),Xd)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc309570230d_e_is(Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc907650504bnd_ap,Xc),Xf)),Xe))))) # label(fact_def__d__10__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 26 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc871412747_fixfu(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc2026207007all_of(aa_TPT43085870d_bool(aTP_Lamm_ae,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ak(X),Xa),Xb),Xc))))) # label(fact_def__fixfu) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 27 (all X all Xa scratc1333610815_ecect(X,Xa) = scratc309570225d_e_in(aa_TPTP_ind_TPTP_ind(scratc1909866188_power,X),scratc1534868484d_anec(X,Xa))) # label(fact_def__ecect) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 28 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc334389040ectelt(X,Xa),Xb) = aa_TPTP_ind_TPTP_ind(scratc449590917ectset(X,Xa),aa_TPTP_ind_TPTP_ind(scratc1334201206_ecelt(X,Xa),Xb))) # label(fact_def__ectelt) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 29 (all X all Xa scratc449590917ectset(X,Xa) = scratc2097260277nd_out(aa_TPTP_ind_TPTP_ind(scratc1909866188_power,X),scratc1534868484d_anec(X,Xa))) # label(fact_def__ectset) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 30 (all X all Xa scratc2013464445nd_ect(X,Xa) = aa_fun1431113780TP_ind(scratc337463667_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1909866188_power,X)),scratc1534868484d_anec(X,Xa))) # label(fact_def__ect) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 31 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc1534868484d_anec(X,Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1136867815l_some(X),aa_TPT43085870d_bool(scratc2013464441nd_ecp(X,Xa),Xb))))) # label(fact_def__anec) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 32 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2013464441nd_ecp(X,Xa),Xb),Xc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc309570230d_e_is(aa_TPTP_ind_TPTP_ind(scratc1909866188_power,X)),Xb),aa_TPTP_ind_TPTP_ind(scratc1334201206_ecelt(X,Xa),Xc))))) # label(fact_def__ecp) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 33 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1334201206_ecelt(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc337463667_d_Sep(X),aa_TPT43085870d_bool(Xa,Xb))) # label(fact_def__ecelt) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 34 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc555708263unmore(X,Xa),Xb) = aa_fun1431113780TP_ind(scratc337463667_d_Sep(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_am(X),Xa),Xb))) # label(fact_def__unmore) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 35 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc331775686etprop(X,Xa),Xb),Xc)) <-> pp(scratc453715116_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc404541500d_esti(X),Xc),Xa),scratc561180296_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc404541500d_esti(X),Xc),Xb)))))) # label(fact_def__nissetprop) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 36 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc499584566t_disj(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1981008808nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_an(X),Xa),Xb))))) # label(fact_def__st__disj) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 37 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1336983943d_incl(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1981008808nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ao(X),Xa),Xb))))) # label(fact_def__incl) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 38 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1240243513nempty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1136867815l_some(X),aa_TPT43085870d_bool(aTP_Lamm_ap(X),Xa))))) # label(fact_def__nonempty) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 39 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc641539956_empty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc2026207007all_of(aa_TPT43085870d_bool(aTP_Lamm_ae,X)),scratc2088605172nd_non(X,aa_TPT43085870d_bool(aTP_Lamm_ap(X),Xa)))))) # label(fact_def__empty) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 40 (all X scratc404541500d_esti(X) = scratc908175294bnd_in) # label(fact_def__esti) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 41 (all X all Xa (scratc91258039d_r_ec(X,Xa) <-> (pp(X) -> pp(scratc561180296_d_not(Xa))))) # label(fact_def__r__ec) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 42 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc521039581hangef(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc918786714_Sigma,X),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_aq(X),Xb),Xc),Xd))) # label(fact_def__changef) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 43 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc317617714wissel(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc918786714_Sigma,X),scratc271145373sel_wb(X,Xa,Xb))) # label(fact_def__wissel) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 44 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc271145373sel_wb(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc2047625633nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc309570230d_e_is(X),Xc),Xb),X,Xa),aa_TPTP_ind_TPTP_ind(scratc271145372sel_wa(X,Xa,Xb),Xc))) # label(fact_def__wissel__wb) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 45 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc271145372sel_wa(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc2047625633nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc309570230d_e_is(X),Xc),Xa),X,Xb),Xc)) # label(fact_def__wissel__wa) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 46 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc2047625633nd_ite(X,Xa,Xb),Xc) = scratc2047232038nd_ind(Xa,aa_TPT43085870d_bool(scratc2038773621_prop1(X,Xa,Xb),Xc))) # label(fact_def__ite) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 47 (all X all Xa all Xb all Xc all Xd (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2038773621_prop1(X,Xa,Xb),Xc),Xd)) <-> pp(scratc453715116_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc2047166451nd_imp,X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc309570230d_e_is(Xa),Xd),Xb)),aa_bool_bool(aa_boo1142376798l_bool(scratc2047166451nd_imp,scratc561180296_d_not(X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc309570230d_e_is(Xa),Xd),Xc)))))) # label(fact_def__prop1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 48 (all X all Xa scratc1076833645second(X,Xa) = scratc2038380027_proj1) # label(fact_def__second) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 49 (all X all Xa scratc822696503_first(X,Xa) = scratc2038380026_proj0) # label(fact_def__first) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 50 (all X all Xa scratc2146335141d_pair(X,Xa) = scratc251637427d_pair) # label(fact_def__d__pair) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 51 (all X all Xa scratc2097260277nd_out(X,Xa) = scratc561379651d_soft(aa_fun1431113780TP_ind(scratc337463667_d_Sep(X),Xa),X,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc918786714_Sigma,aa_fun1431113780TP_ind(scratc337463667_d_Sep(X),Xa)),scratc309570225d_e_in(X,Xa)))) # label(fact_def__out) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 52 (all X all Xa all Xb (gg_TPTP_ind(Xb) -> aa_TPTP_ind_TPTP_ind(scratc309570225d_e_in(X,Xa),Xb) = Xb)) # label(fact_def__e__in) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 53 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc58880380_inj_h(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc918786714_Sigma,X),aa_TPT1424761345TP_ind(aTP_Lamm_ar(Xc),Xd))) # label(fact_def__inj__h) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 54 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1338230318d_invf(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc918786714_Sigma,Xa),scratc561379651d_soft(X,Xa,Xb))) # label(fact_def__invf) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 55 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1268434572ective(X),Xa),Xb)) <-> pp(scratc453715116_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1084715342ective(X),Xa),Xb),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2015004629ective(X),Xa),Xb))))) # label(fact_def__bijective) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 56 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2015004629ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1981008808nd_all(Xa),aa_TPT43085870d_bool(scratc780054434_image(X,Xa),Xb))))) # label(fact_def__surjective) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 57 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc507080631nverse(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc918786714_Sigma,Xa),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_as(X),Xa),Xb))) # label(fact_def__inverse) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 58 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc561379651d_soft(X,Xa,Xb),Xc) = scratc2047232038nd_ind(X,aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_at(Xa),Xb),Xc))) # label(fact_def__soft) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 59 (all X all Xa scratc1341966849d_tofs(X,Xa) = scratc907650504bnd_ap) # label(fact_def__tofs) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 60 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc780054434_image(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1136867815l_some(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_at(Xa),Xb),Xc))))) # label(fact_def__image) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 61 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1084715342ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc1981008808nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_av(X),Xa),Xb))))) # label(fact_def__injective) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 62 (all X all Xa scratc2047232038nd_ind(X,Xa) = scratc2014317231nd_eps(aa_fun1584354236d_bool(aTP_Lamm_aw(X),Xa))) # label(fact_def__ind) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 63 (all X all Xa (pp(aa_fun171081125l_bool(scratc2096801069nd_one(X),Xa)) <-> pp(scratc453715116_d_and(scratc369594977_amone(X,Xa),aa_fun171081125l_bool(scratc1136867815l_some(X),Xa))))) # label(fact_def__one) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 64 (all X all Xa (pp(scratc369594977_amone(X,Xa)) <-> pp(aa_fun171081125l_bool(scratc2026207007all_of(aa_TPT43085870d_bool(aTP_Lamm_ae,X)),aa_fun1584354236d_bool(aTP_Lamm_ay(X),Xa))))) # label(fact_def__amone) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 65 (all X scratc309570230d_e_is(X) = fequal_TPTP_ind) # label(fact_def__e__is) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 66 (all X all Xa all Xb (scratc815741497_orec3(X,Xa,Xb) <-> pp(scratc453715116_d_and(scratc2097063415nd_or3(X,Xa,Xb),scratc2013464380nd_ec3(X,Xa,Xb))))) # label(fact_def__orec3) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 67 (all X all Xa all Xb (pp(scratc2013464380nd_ec3(X,Xa,Xb)) <-> scratc1534802837d_and3(scratc1843806897d_l_ec(X,Xa),scratc1843806897d_l_ec(Xa,Xb),scratc1843806897d_l_ec(Xb,X)))) # label(fact_def__ec3) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 68 (all X all Xa all Xb (scratc1534802837d_and3(X,Xa,Xb) <-> pp(scratc453715116_d_and(X,scratc453715116_d_and(Xa,Xb))))) # label(fact_def__and3) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 69 (all X all Xa all Xb (pp(scratc2097063415nd_or3(X,Xa,Xb)) <-> pp(aa_bool_bool(scratc1844462902d_l_or(X),aa_bool_bool(scratc1844462902d_l_or(Xa),Xb))))) # label(fact_def__or3) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 70 (all X all Xa (pp(aa_fun171081125l_bool(scratc1136867815l_some(X),Xa)) <-> pp(scratc561180296_d_not(aa_fun171081125l_bool(scratc2026207007all_of(aa_TPT43085870d_bool(aTP_Lamm_ae,X)),scratc2088605172nd_non(X,Xa)))))) # label(fact_def__l__some) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 71 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc2088605172nd_non(X,Xa),Xb)) <-> pp(scratc561180296_d_not(aa_TPTP_ind_bool(Xa,Xb))))) # label(fact_def__non) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 72 (all X scratc1981008808nd_all(X) = scratc2026207007all_of(aa_TPT43085870d_bool(aTP_Lamm_ae,X))) # label(fact_def__all) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 73 (all X all Xa (scratc1347856566_l_iff(X,Xa) <-> pp(scratc453715116_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc2047166451nd_imp,X),Xa),aa_bool_bool(aa_boo1142376798l_bool(scratc2047166451nd_imp,Xa),X))))) # label(fact_def__l__iff) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 74 (all X all Xa (scratc1758717050d_orec(X,Xa) <-> pp(scratc453715116_d_and(aa_bool_bool(scratc1844462902d_l_or(X),Xa),scratc1843806897d_l_ec(X,Xa))))) # label(fact_def__orec) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 75 (all X scratc1844462902d_l_or(X) = aa_boo1142376798l_bool(scratc2047166451nd_imp,scratc561180296_d_not(X))) # label(fact_def__l__or) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 76 (all X all Xa (pp(scratc453715116_d_and(X,Xa)) <-> pp(scratc561180296_d_not(scratc1843806897d_l_ec(X,Xa))))) # label(fact_def__d__and) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 77 (all X all Xa (pp(scratc1843806897d_l_ec(X,Xa)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc2047166451nd_imp,X),scratc561180296_d_not(Xa))))) # label(fact_def__l__ec) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 78 scratc1372163278bvious <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc2047166451nd_imp,fFalse),fFalse)) # label(fact_def__obvious) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 79 (all X (scratc14819077nd_wel(X) <-> pp(scratc561180296_d_not(scratc561180296_d_not(X))))) # label(fact_def__wel) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 80 (all X (pp(scratc561180296_d_not(X)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc2047166451nd_imp,X),fFalse)))) # label(fact_def__d__not) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 81 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1315849604d_d_Pi,X),Xa) = aa_fun1431113780TP_ind(scratc337463667_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1909866188_power,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc918786714_Sigma,X),aTP_Lamm_az(Xa)))),aa_fun1913827119d_bool(aTP_Lamm_ba(X),Xa))) # label(fact_def__d__Pi) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 82 (all X (gg_TPTP_ind(X) -> (pp(aa_TPTP_ind_bool(scratc965582909pair_p,X)) <-> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc251637427d_pair,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc907650504bnd_ap,X),scratc954648526ptyset)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc907650504bnd_ap,X),aa_TPTP_ind_TPTP_ind(scratc1108832938rdsucc,scratc954648526ptyset))) = X))) # label(fact_def__pair__p) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 83 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc907650504bnd_ap,X),Xa) = aa_fun277296641TP_ind(scratc895236260eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bb,Xa)),scratc2038380027_proj1)) # label(fact_def__ap) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 84 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc742756032etprod(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc918786714_Sigma,X),aTP_Lamm_ad(Xa))) # label(fact_def__setprod) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 85 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc918786714_Sigma,X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1320089078munion,X),aTP_Lamm_bc(Xa))) # label(fact_def__d__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 86 (all X aa_TPTP_ind_TPTP_ind(scratc2038380027_proj1,X) = aa_fun277296641TP_ind(scratc895236260eplSep(X,aTP_Lamm_bd),scratc354577062_d_Unj)) # label(fact_def__proj1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 87 (all X aa_TPTP_ind_TPTP_ind(scratc2038380026_proj0,X) = aa_fun277296641TP_ind(scratc895236260eplSep(X,aTP_Lamm_be),scratc354577062_d_Unj)) # label(fact_def__proj0) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 88 (all X all Xa aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc251637427d_pair,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc166462529nunion(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1846317032d_repl,X),scratc1875670550d_Inj0)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1846317032d_repl,Xa),scratc1875670551d_Inj1))) # label(fact_def__pair) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 89 (all X aa_TPTP_ind_TPTP_ind(scratc1875670550d_Inj0,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1846317032d_repl,X),scratc1875670551d_Inj1)) # label(fact_def__d__Inj0) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 90 (all X (pp(aa_TPTP_ind_bool(scratc1352903720_nat_p,X)) <-> (all X1 (pp(aa_TPTP_ind_bool(X1,scratc954648526ptyset)) -> ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(X1,X2)) -> pp(aa_TPTP_ind_bool(X1,aa_TPTP_ind_TPTP_ind(scratc1108832938rdsucc,X2)))))) -> pp(aa_TPTP_ind_bool(X1,X))))))) # label(fact_def__nat__p) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 91 (all X aa_TPTP_ind_TPTP_ind(scratc1108832938rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc166462529nunion(X),aa_TPTP_ind_TPTP_ind(scratc1050562874d_Sing,X))) # label(fact_def__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 92 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc622999840In_rec(X),Xa) = scratc2014317231nd_eps(aa_TPT43085870d_bool(scratc1490646887_rec_G(X),Xa))) # label(fact_def__d__In__rec) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 93 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1490646887_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(scratc908175294bnd_in,X6),X4)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(X3,X6),aa_TPTP_ind_TPTP_ind(X5,X6)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(X3,X4),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(X,X4),X5)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(X3,Xa),Xb)))))) # label(fact_def__d__In__rec__G) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 94 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc82748071tminus(X),Xa) = aa_fun1431113780TP_ind(scratc337463667_d_Sep(X),aa_TPT43085870d_bool(aTP_Lamm_bh,Xa))) # label(fact_def__setminus) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 95 (all X all Xa scratc895236260eplSep(X,Xa) = aa_TPT494704832TP_ind(scratc1846317032d_repl,aa_fun1431113780TP_ind(scratc337463667_d_Sep(X),Xa))) # label(fact_def__d__ReplSep) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 96 (all X all Xa aa_fun1431113780TP_ind(scratc337463667_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc908175286bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc908175294bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1846317032d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bi(X),Xa))),scratc954648526ptyset)) # label(fact_def__d__Sep) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 97 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1320089078munion,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc269644406_union,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1846317032d_repl,X),Xa))) # label(fact_def__famunion) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 98 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc166462529nunion(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc269644406_union,aa_TPTP_ind_TPTP_ind(scratc813273092_UPair(X),Xa))) # label(fact_def__binunion) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 99 (all X aa_TPTP_ind_TPTP_ind(scratc1050562874d_Sing,X) = aa_TPTP_ind_TPTP_ind(scratc813273092_UPair(X),X)) # label(fact_def__d__Sing) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 100 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc813273092_UPair(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1846317032d_repl,aa_TPTP_ind_TPTP_ind(scratc1909866188_power,aa_TPTP_ind_TPTP_ind(scratc1909866188_power,scratc954648526ptyset))),aa_TPT1424761345TP_ind(aTP_Lamm_bj(X),Xa))) # label(fact_def__d__UPair) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 101 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2086112410nd_nIn,X),Xa)) <-> -pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X),Xa)))) # label(fact_def__nIn) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 102 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc908175286bnd_if(X,Xa),Xb) = scratc2014317231nd_eps(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bk(X),Xa),Xb))) # label(fact_def__if) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 103 (all X (pp(aa_TPTP_ind_bool(scratc1789170787closed,X)) <-> pp(aa_TPTP_ind_bool(scratc2101311088closed,X)) & pp(aa_TPTP_ind_bool(scratc118560454closed,X)) & pp(aa_TPTP_ind_bool(scratc1948027270closed,X)))) # label(fact_def__d__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 104 (all X (pp(aa_TPTP_ind_bool(scratc1948027270closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X1),X)) -> (all X2 ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X3),X1)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,aa_TPTP_ind_TPTP_ind(X2,X3)),X))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1846317032d_repl,X1),X2)),X))))))))) # label(fact_def__d__Repl__closed) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 105 (all X (pp(aa_TPTP_ind_bool(scratc118560454closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,aa_TPTP_ind_TPTP_ind(scratc1909866188_power,X1)),X))))))) # label(fact_def__d__Power__closed) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 106 (all X (pp(aa_TPTP_ind_bool(scratc2101311088closed,X)) <-> (all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,aa_TPTP_ind_TPTP_ind(scratc269644406_union,X1)),X))))))) # label(fact_def__d__Union__closed) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 107 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1148913756d_Subq,X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X2),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X2),Xa))))))) # label(fact_def__d__Subq) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 108 (all X all Xa (pp(aa_fun171081125l_bool(scratc2026207007all_of(X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (scratc1466259514_is_of(X2,X) -> pp(aa_TPTP_ind_bool(Xa,X2))))))) # label(fact_def__all__of) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 109 (all X all Xa (scratc1466259514_is_of(X,Xa) <-> pp(aa_TPTP_ind_bool(Xa,X)))) # label(fact_def__is__of) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 110 (all X0 pp(aa_fun171081125l_bool(scratc2026207007all_of(aa_TPT43085870d_bool(aTP_Lamm_bu,X0)),aa_TPT43085870d_bool(aTP_Lamm_bw,X0)))) # label(fact_isseti) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 111 (all X0 all X12 pp(aa_fun171081125l_bool(scratc2026207007all_of(aa_TPT43085870d_bool(aTP_Lamm_ae,X0)),aa_fun1584354236d_bool(aTP_Lamm_bx(X0),X12)))) # label(fact_estie) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 112 (all X0 all X12 pp(aa_fun171081125l_bool(scratc2026207007all_of(aa_TPT43085870d_bool(aTP_Lamm_ae,X0)),aa_fun1584354236d_bool(aTP_Lamm_by(X0),X12)))) # label(fact_estii) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 113 (all X0 all X12 scratc1466259514_is_of(aa_fun1431113780TP_ind(scratc337463667_d_Sep(X0),X12),aa_TPT43085870d_bool(aTP_Lamm_bu,X0))) # label(fact_setof__p) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 114 (all X0 all X12 pp(aa_fun171081125l_bool(scratc2026207007all_of(aa_TPT43085870d_bool(aTP_Lamm_ae,X0)),aa_TPT43085870d_bool(aTP_Lamm_ca(X0),X12)))) # label(fact_secondis1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 115 (all X0 all X12 pp(aa_fun171081125l_bool(scratc2026207007all_of(aa_TPT43085870d_bool(aTP_Lamm_ae,X0)),aa_TPT43085870d_bool(aTP_Lamm_cc(X0),X12)))) # label(fact_firstis1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 116 (all X0 all X12 pp(aa_fun171081125l_bool(scratc2026207007all_of(aa_TPT43085870d_bool(aTP_Lamm_cd(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_ce(X0),X12)))) # label(fact_pairis1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 117 (all X0 all X12 pp(aa_fun171081125l_bool(scratc2026207007all_of(aa_TPT43085870d_bool(aTP_Lamm_cd(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_cf(X0),X12)))) # label(fact_second__p) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 118 (all X0 all X12 pp(aa_fun171081125l_bool(scratc2026207007all_of(aa_TPT43085870d_bool(aTP_Lamm_cd(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_cg(X0),X12)))) # label(fact_first__p) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 119 (all X0 all X12 pp(aa_fun171081125l_bool(scratc2026207007all_of(aa_TPT43085870d_bool(aTP_Lamm_ae,X0)),aa_TPT43085870d_bool(aTP_Lamm_ci(X0),X12)))) # label(fact_e__pair__p) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 120 (all X0 all X12 pp(aa_fun171081125l_bool(scratc2026207007all_of(aa_TPT43085870d_bool(aTP_Lamm_ae,X0)),aa_fun1584354236d_bool(aTP_Lamm_cj(X0),X12)))) # label(fact_otax2) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 121 (all X0 all X12 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1084715342ective(aa_fun1431113780TP_ind(scratc337463667_d_Sep(X0),X12)),X0),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc918786714_Sigma,aa_fun1431113780TP_ind(scratc337463667_d_Sep(X0),X12)),scratc309570225d_e_in(X0,X12))))) # label(fact_otax1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 122 (all X0 all X12 pp(aa_fun171081125l_bool(scratc2026207007all_of(aa_fun1584354236d_bool(aTP_Lamm_ck(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_cl(X0),X12)))) # label(fact_e__inp) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 123 (all X0 all X12 pp(aa_fun171081125l_bool(scratc2026207007all_of(aa_fun1584354236d_bool(aTP_Lamm_ck(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_cm(X0),X12)))) # label(fact_e__in__p) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 124 (all X0 all X12 pp(aa_fun171081125l_bool(scratc2026207007all_of(aa_TPT43085870d_bool(aTP_Lamm_cn(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_cq(X0),X12)))) # label(fact_e__fisi) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 125 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc2096801069nd_one(X0),X12)) -> pp(aa_TPTP_ind_bool(X12,scratc2047232038nd_ind(X0,X12))))) # label(fact_oneax) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 126 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc2096801069nd_one(X0),X12)) -> scratc1466259514_is_of(scratc2047232038nd_ind(X0,X12),aa_TPT43085870d_bool(aTP_Lamm_ae,X0)))) # label(fact_ind__p) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 127 (all X0 all X12 pp(aa_fun171081125l_bool(scratc2026207007all_of(aa_TPT43085870d_bool(aTP_Lamm_ae,X0)),aa_fun1584354236d_bool(aTP_Lamm_cs(X0),X12)))) # label(fact_e__isp) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 128 (all X0 pp(aa_fun171081125l_bool(scratc2026207007all_of(aa_TPT43085870d_bool(aTP_Lamm_ae,X0)),aa_TPT43085870d_bool(aTP_Lamm_ct,X0)))) # label(fact_refis) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 129 (all X0 (scratc14819077nd_wel(X0) -> pp(X0))) # label(fact_l__et) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 130 (all X0 all X12 all X22 all X32 (pp(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc908175286bnd_if(X0,X22),X32))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X12),X22))))) # label(fact_k__If__In__then__E) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 131 (all X0 all X12 all X22 ((pp(X0) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X12),X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,aa_TPTP_ind_TPTP_ind(scratc908175286bnd_if(X0,X12),scratc954648526ptyset)),aa_TPTP_ind_TPTP_ind(scratc908175286bnd_if(X0,X22),aa_TPTP_ind_TPTP_ind(scratc1108832938rdsucc,scratc954648526ptyset)))))) # label(fact_k__If__In__01) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 132 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X33),X0)) -> aa_TPTP_ind_TPTP_ind(X12,X33) = aa_TPTP_ind_TPTP_ind(X22,X33)))) -> aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc918786714_Sigma,X0),X12) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc918786714_Sigma,X0),X22))) # label(fact_xi__ext) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 133 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1315849604d_d_Pi,X0),X12))) -> (all X32 (gg_TPTP_ind(X32) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X32),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1315849604d_d_Pi,X0),X12))) -> ((all X42 (gg_TPTP_ind(X42) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X42),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc907650504bnd_ap,X22),X42) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc907650504bnd_ap,X32),X42)))) -> X22 = X32))))))) # label(fact_k__Pi__ext) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 134 (all X0 all X12 all X22 all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1315849604d_d_Pi,X0),X12))) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X32),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc907650504bnd_ap,X22),X32)),aa_TPTP_ind_TPTP_ind(X12,X32)))))) # label(fact_ap__Pi) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 135 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X33),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,aa_TPTP_ind_TPTP_ind(X22,X33)),aa_TPTP_ind_TPTP_ind(X12,X33)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc918786714_Sigma,X0),X22)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1315849604d_d_Pi,X0),X12))))) # label(fact_lam__Pi) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 136 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X22),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc907650504bnd_ap,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc918786714_Sigma,X0),X12)),X22) = aa_TPTP_ind_TPTP_ind(X12,X22))) # label(fact_beta) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 137 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc918786714_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,aa_TPTP_ind_TPTP_ind(scratc2038380027_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc2038380026_proj0,X22)))))) # label(fact_proj1__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 138 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc918786714_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,aa_TPTP_ind_TPTP_ind(scratc2038380026_proj0,X22)),X0)))) # label(fact_proj0__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 139 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc918786714_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc251637427d_pair,aa_TPTP_ind_TPTP_ind(scratc2038380026_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc2038380027_proj1,X22)) = X22))) # label(fact_proj__Sigma__eta) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 140 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc918786714_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc251637427d_pair,aa_TPTP_ind_TPTP_ind(scratc2038380026_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc2038380027_proj1,X22)) = X22 & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,aa_TPTP_ind_TPTP_ind(scratc2038380026_proj0,X22)),X0)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,aa_TPTP_ind_TPTP_ind(scratc2038380027_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc2038380026_proj0,X22))))))) # label(fact_k__Sigma__eta__proj0__proj1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 141 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X22),X0)) -> (all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X32),aa_TPTP_ind_TPTP_ind(X12,X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc251637427d_pair,X22),X32)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc918786714_Sigma,X0),X12))))))) # label(fact_pair__Sigma) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 142 (all X0 all X12 (gg_TPTP_ind(X12) -> aa_TPTP_ind_TPTP_ind(scratc2038380027_proj1,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc251637427d_pair,X0),X12)) = X12)) # label(fact_proj1__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 143 (all X0 all X12 (gg_TPTP_ind(X0) -> aa_TPTP_ind_TPTP_ind(scratc2038380026_proj0,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc251637427d_pair,X0),X12)) = X0)) # label(fact_proj0__pair__eq) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 144 (all X0 (pp(aa_TPTP_ind_bool(scratc1352903720_nat_p,X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X0),scratc1208035240_omega)))) # label(fact_nat__p__omega) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 145 (all X0 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X0),scratc1208035240_omega)) -> pp(aa_TPTP_ind_bool(scratc1352903720_nat_p,X0)))) # label(fact_omega__nat__p) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 146 (all X0 (gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(scratc1352903720_nat_p,X0)) -> X0 = scratc954648526ptyset | (exists X13 (gg_TPTP_ind(X13) & pp(aa_TPTP_ind_bool(scratc1352903720_nat_p,X13)) & X0 = aa_TPTP_ind_TPTP_ind(scratc1108832938rdsucc,X13)))))) # label(fact_nat__inv) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 147 (all X0 (pp(aa_TPTP_ind_bool(X0,scratc954648526ptyset)) -> ((all X13 (gg_TPTP_ind(X13) -> (pp(aa_TPTP_ind_bool(scratc1352903720_nat_p,X13)) -> (pp(aa_TPTP_ind_bool(X0,X13)) -> pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc1108832938rdsucc,X13))))))) -> (all X12 (pp(aa_TPTP_ind_bool(scratc1352903720_nat_p,X12)) -> pp(aa_TPTP_ind_bool(X0,X12))))))) # label(fact_nat__ind) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 148 (all X0 (pp(aa_TPTP_ind_bool(scratc1352903720_nat_p,X0)) -> pp(aa_TPTP_ind_bool(scratc1352903720_nat_p,aa_TPTP_ind_TPTP_ind(scratc1108832938rdsucc,X0))))) # label(fact_nat__ordsucc) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 149 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (aa_TPTP_ind_TPTP_ind(scratc1108832938rdsucc,X0) = aa_TPTP_ind_TPTP_ind(scratc1108832938rdsucc,X12) -> X0 = X12))) # label(fact_ordsucc__inj) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 150 (all X0 aa_TPTP_ind_TPTP_ind(scratc1108832938rdsucc,X0) != scratc954648526ptyset) # label(fact_neq__ordsucc__0) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 151 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X22),aa_fun1431113780TP_ind(scratc337463667_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(X12,X22)))) # label(fact_k__SepE2) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 152 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X22),aa_fun1431113780TP_ind(scratc337463667_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X22),X0)))) # label(fact_k__SepE1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 153 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X22),X0)) -> (pp(aa_TPTP_ind_bool(X12,X22)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X22),aa_fun1431113780TP_ind(scratc337463667_d_Sep(X0),X12)))))) # label(fact_k__SepI) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 154 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc1909866188_power,X0)))) # label(fact_k__Self__In__Power) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 155 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1148913756d_Subq,X12),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1909866188_power,X0))))) # label(fact_k__PowerI) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 156 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1909866188_power,X0))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1148913756d_Subq,X12),X0)))) # label(fact_k__PowerE) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 157 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> aa_TPTP_ind_TPTP_ind(scratc908175286bnd_if(X0,X12),X22) = X12 | aa_TPTP_ind_TPTP_ind(scratc908175286bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__or) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 158 (all X0 all X12 all X22 (gg_TPTP_ind(X12) -> (pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc908175286bnd_if(X0,X12),X22) = X12))) # label(fact_if__i__1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 159 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (-pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc908175286bnd_if(X0,X12),X22) = X22))) # label(fact_if__i__0) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 160 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> pp(X0) & aa_TPTP_ind_TPTP_ind(scratc908175286bnd_if(X0,X12),X22) = X12 | -pp(X0) & aa_TPTP_ind_TPTP_ind(scratc908175286bnd_if(X0,X12),X22) = X22)) # label(fact_if__i__correct) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 161 (all X0 pp(aa_TPTP_ind_bool(scratc1789170787closed,aa_TPTP_ind_TPTP_ind(scratc1785960502univof,X0)))) # label(fact_k__UnivOf__ZF__closed) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 162 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc1785960502univof,X0)))) # label(fact_k__UnivOf__In) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 163 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1846317032d_repl,X0),X12))) <-> (exists X3 (gg_TPTP_ind(X3) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X3),X0)) & X22 = aa_TPTP_ind_TPTP_ind(X12,X3)))))) # label(fact_k__ReplEq) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 164 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1909866188_power,X0))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1148913756d_Subq,X12),X0)))) # label(fact_k__PowerEq) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 165 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc269644406_union,X0))) <-> (exists X2 (gg_TPTP_ind(X2) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X12),X2)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X2),X0)))))) # label(fact_k__UnionEq) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 166 -(exists X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X0),scratc954648526ptyset))) # label(fact_k__EmptyAx) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 167 (all X0 ((all X13 (gg_TPTP_ind(X13) -> ((all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X22),X13)) -> pp(aa_TPTP_ind_bool(X0,X22)))) -> pp(aa_TPTP_ind_bool(X0,X13))))) -> (all X14 pp(aa_TPTP_ind_bool(X0,X14))))) # label(fact_k__In__ind) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 168 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1148913756d_Subq,X0),X12)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1148913756d_Subq,X12),X0)) -> X0 = X12)))) # label(fact_set__ext) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 169 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bp,Uu)) <-> (pp(aa_TPTP_ind_bool(scratc2053496758_cond1,Uu)) -> (pp(aa_TPTP_ind_bool(scratc2053496759_cond2,Uu)) -> pp(aa_fun171081125l_bool(scratc2026207007all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bo,Uu))))))) # label(fact_ATP_Olambda__1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 170 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2088211583nd_nis,aa_TPTP_ind_TPTP_ind(scratc1108832938rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__2) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 171 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bt,Uu)) <-> scratc1466259514_is_of(aa_TPTP_ind_TPTP_ind(scratc1108832938rdsucc,Uu),aTP_Lamm_a))) # label(fact_ATP_Olambda__3) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 172 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bs,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2088211583nd_nis,aa_TPTP_ind_TPTP_ind(scratc1108832938rdsucc,Uu)),scratc820767612nd_n_1)))) # label(fact_ATP_Olambda__4) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 173 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bn,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,Uu),aa_TPTP_ind_TPTP_ind(scratc1909866188_power,scratc2087686792nd_nat))))) # label(fact_ATP_Olambda__5) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 174 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_a,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,Uu),scratc2087686792nd_nat)))) # label(fact_ATP_Olambda__6) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 175 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_br,Uu)) <-> pp(aa_fun171081125l_bool(scratc2026207007all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bq,Uu))))) # label(fact_ATP_Olambda__7) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 176 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bm,Uu)) <-> pp(aa_fun171081125l_bool(scratc2026207007all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bl,Uu))))) # label(fact_ATP_Olambda__8) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 177 (all Uu aa_TPT494704832TP_ind(aTP_Lamm_bf,Uu) = aa_TPT494704832TP_ind(scratc1846317032d_repl,aa_TPTP_ind_TPTP_ind(scratc82748071tminus(Uu),aa_TPTP_ind_TPTP_ind(scratc1050562874d_Sing,scratc954648526ptyset)))) # label(fact_ATP_Olambda__9) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 178 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_ac,Uu)) <-> Uu != scratc954648526ptyset))) # label(fact_ATP_Olambda__10) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 179 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_bd,Uu)) <-> (exists X2 (gg_TPTP_ind(X2) & aa_TPTP_ind_TPTP_ind(scratc1875670551d_Inj1,X2) = Uu))))) # label(fact_ATP_Olambda__11) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 180 (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(scratc1875670550d_Inj0,X2) = Uu))))) # label(fact_ATP_Olambda__12) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 181 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ct,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc309570230d_e_is(Uu),Uua),Uua)))) # label(fact_ATP_Olambda__13) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 182 (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(scratc1975714239d_n_is,aa_TPTP_ind_TPTP_ind(scratc1108832938rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1108832938rdsucc,Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1975714239d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__14) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 183 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bl,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2088211583nd_nis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2088211583nd_nis,aa_TPTP_ind_TPTP_ind(scratc1108832938rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1108832938rdsucc,Uua)))))) # label(fact_ATP_Olambda__15) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 184 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ab,Uu),Uua)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc2047166451nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1975714234d_n_in,Uua),Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1975714234d_n_in,aa_TPTP_ind_TPTP_ind(scratc1108832938rdsucc,Uua)),Uu))))) # label(fact_ATP_Olambda__16) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 185 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bc(Uu),Uua) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1846317032d_repl,aa_TPTP_ind_TPTP_ind(Uu,Uua)),aa_TPT1424761345TP_ind(scratc251637427d_pair,Uua))) # label(fact_ATP_Olambda__17) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 186 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bw,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc2026207007all_of(aa_TPT43085870d_bool(aTP_Lamm_bu,Uu)),aa_TPT43085870d_bool(aTP_Lamm_bv(Uu),Uua))))) # label(fact_ATP_Olambda__18) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 187 (all Uu all Uua aa_fun277296641TP_ind(aa_TPT494704832TP_ind(aTP_Lamm_bg,Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc166462529nunion(aa_TPTP_ind_TPTP_ind(scratc1050562874d_Sing,scratc954648526ptyset)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1846317032d_repl,Uu),Uua))) # label(fact_ATP_Olambda__19) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 188 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bu,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,Uua),aa_TPTP_ind_TPTP_ind(scratc1909866188_power,Uu))))) # label(fact_ATP_Olambda__20) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 189 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bo,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1975714234d_n_in,Uua),Uu)))) # label(fact_ATP_Olambda__21) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 190 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bh,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2086112410nd_nIn,Uua),Uu)))) # label(fact_ATP_Olambda__22) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 191 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ae,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,Uua),Uu)))) # label(fact_ATP_Olambda__23) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 192 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_az(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc269644406_union,aa_TPTP_ind_TPTP_ind(Uu,Uua))) # label(fact_ATP_Olambda__24) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 193 (all Uu all Uua (gg_TPTP_ind(Uua) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bb,Uu),Uua)) <-> (exists X3 (gg_TPTP_ind(X3) & Uua = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc251637427d_pair,Uu),X3)))))) # label(fact_ATP_Olambda__25) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 194 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ce(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc309570230d_e_is(aa_TPTP_ind_TPTP_ind(scratc742756032etprod(Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2146335141d_pair(Uu,Uua),aa_TPTP_ind_TPTP_ind(scratc822696503_first(Uu,Uua),Uub)),aa_TPTP_ind_TPTP_ind(scratc1076833645second(Uu,Uua),Uub))),Uub)))) # label(fact_ATP_Olambda__26) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 195 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_bj(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc908175286bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,scratc954648526ptyset),Uub),Uu),Uua)) # label(fact_ATP_Olambda__27) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 196 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_fun1235454963TP_ind(aTP_Lamm_bi(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc908175286bnd_if(aa_TPTP_ind_bool(Uua,Uub),Uub),scratc2014317231nd_eps(aa_fun1584354236d_bool(aTP_Lamm_aw(Uu),Uua)))) # label(fact_ATP_Olambda__28) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 197 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ap(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc404541500d_esti(Uu),Uub),Uua)))) # label(fact_ATP_Olambda__29) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 198 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bx(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc404541500d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc337463667_d_Sep(Uu),Uua))) -> pp(aa_TPTP_ind_bool(Uua,Uub))))) # label(fact_ATP_Olambda__30) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 199 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bv(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1336983943d_incl(Uu),Uua),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1336983943d_incl(Uu),Uub),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc309570230d_e_is(aa_TPTP_ind_TPTP_ind(scratc1909866188_power,Uu)),Uua),Uub)))))) # label(fact_ATP_Olambda__31) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 200 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cf(Uu),Uua),Uub)) <-> scratc1466259514_is_of(aa_TPTP_ind_TPTP_ind(scratc1076833645second(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_ae,Uua)))) # label(fact_ATP_Olambda__32) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 201 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cg(Uu),Uua),Uub)) <-> scratc1466259514_is_of(aa_TPTP_ind_TPTP_ind(scratc822696503_first(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_ae,Uu)))) # label(fact_ATP_Olambda__33) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 202 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_cm(Uu),Uua),Uub)) <-> scratc1466259514_is_of(aa_TPTP_ind_TPTP_ind(scratc309570225d_e_in(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_ae,Uu)))) # label(fact_ATP_Olambda__34) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 203 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cq(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc2026207007all_of(aa_TPT43085870d_bool(aTP_Lamm_cn(Uu),Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cp(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__35) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 204 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_aw(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,Uub),Uu)) & pp(aa_TPTP_ind_bool(Uua,Uub)))) # label(fact_ATP_Olambda__36) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 205 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_cj(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc780054434_image(aa_fun1431113780TP_ind(scratc337463667_d_Sep(Uu),Uua),Uu),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc918786714_Sigma,aa_fun1431113780TP_ind(scratc337463667_d_Sep(Uu),Uua)),scratc309570225d_e_in(Uu,Uua))),Uub))))) # label(fact_ATP_Olambda__37) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 206 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_by(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc404541500d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc337463667_d_Sep(Uu),Uua)))))) # label(fact_ATP_Olambda__38) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 207 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_cs(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc2026207007all_of(aa_TPT43085870d_bool(aTP_Lamm_ae,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_cr(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__39) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 208 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ay(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc2026207007all_of(aa_TPT43085870d_bool(aTP_Lamm_ae,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_ax(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__40) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 209 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ci(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc2026207007all_of(aa_TPT43085870d_bool(aTP_Lamm_ae,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ch(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__41) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 210 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cc(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc2026207007all_of(aa_TPT43085870d_bool(aTP_Lamm_ae,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cb(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__42) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 211 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ca(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc2026207007all_of(aa_TPT43085870d_bool(aTP_Lamm_ae,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bz(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__43) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 212 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cn(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,Uub),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1315849604d_d_Pi,Uu),aTP_Lamm_ad(Uua)))))) # label(fact_ATP_Olambda__44) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 213 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cd(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,Uub),aa_TPTP_ind_TPTP_ind(scratc742756032etprod(Uu),Uua))))) # label(fact_ATP_Olambda__45) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 214 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ck(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,Uub),aa_fun1431113780TP_ind(scratc337463667_d_Sep(Uu),Uua))))) # label(fact_ATP_Olambda__46) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 215 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_ar(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc907650504bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc907650504bnd_ap,Uu),Uub))) # label(fact_ATP_Olambda__47) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 216 (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,aa_TPTP_ind_TPTP_ind(scratc309570225d_e_in(Uu,Uua),Uub))))) # label(fact_ATP_Olambda__48) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 217 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1913827119d_bool(aTP_Lamm_ba(Uu),Uua),Uub)) <-> (all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,X3),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc908175294bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc907650504bnd_ap,Uub),X3)),aa_TPTP_ind_TPTP_ind(Uua,X3)))))))) # label(fact_ATP_Olambda__49) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 218 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_as(Uu),Uua),Uub),Uuc) = aa_TPTP_ind_TPTP_ind(scratc908175286bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc780054434_image(Uu,Uua),Uub),Uuc),aa_TPTP_ind_TPTP_ind(scratc561379651d_soft(Uu,Uua,Uub),Uuc)),scratc954648526ptyset)) # label(fact_ATP_Olambda__50) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 219 (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(scratc309570230d_e_is(Uu),aa_TPTP_ind_TPTP_ind(scratc822696503_first(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2146335141d_pair(Uu,Uua),Uub),Uuc))),Uub)))) # label(fact_ATP_Olambda__51) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 220 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bz(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc309570230d_e_is(Uua),aa_TPTP_ind_TPTP_ind(scratc1076833645second(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2146335141d_pair(Uu,Uua),Uub),Uuc))),Uuc)))) # label(fact_ATP_Olambda__52) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 221 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_co(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc309570230d_e_is(Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc907650504bnd_ap,Uua),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc907650504bnd_ap,Uub),Uuc))))) # label(fact_ATP_Olambda__53) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 222 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_al(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc404541500d_esti(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc907650504bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__54) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 223 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_at(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc309570230d_e_is(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc907650504bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__55) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 224 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ch(Uu),Uua),Uub),Uuc)) <-> scratc1466259514_is_of(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc2146335141d_pair(Uu,Uua),Uub),Uuc),aa_TPT43085870d_bool(aTP_Lamm_cd(Uu),Uua)))) # label(fact_ATP_Olambda__56) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 225 (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(scratc1843806897d_l_ec(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc404541500d_esti(Uu),Uuc),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc404541500d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__57) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 226 (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(aa_bool_bool(aa_boo1142376798l_bool(scratc2047166451nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc404541500d_esti(Uu),Uuc),Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc404541500d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__58) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 227 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cp(Uu),Uua),Uub),Uuc)) <-> (pp(aa_fun171081125l_bool(scratc2026207007all_of(aa_TPT43085870d_bool(aTP_Lamm_ae,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_co(Uua),Uub),Uuc))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc309570230d_e_is(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1315849604d_d_Pi,Uu),aTP_Lamm_ad(Uua))),Uub),Uuc))))) # label(fact_ATP_Olambda__59) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 228 (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_bk(Uu),Uua),Uub),Uuc)) <-> pp(Uu) & Uuc = Uua | -pp(Uu) & Uuc = Uub))) # label(fact_ATP_Olambda__60) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 229 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_cr(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc309570230d_e_is(Uu),Uub),Uuc)) -> pp(aa_TPTP_ind_bool(Uua,Uuc)))))) # label(fact_ATP_Olambda__61) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 230 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_ax(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(scratc309570230d_e_is(Uu),Uub),Uuc)))))) # label(fact_ATP_Olambda__62) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 231 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_av(Uu),Uua),Uub),Uuc)) <-> pp(aa_fun171081125l_bool(scratc1981008808nd_all(Uu),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_au(Uu),Uua),Uub),Uuc))))) # label(fact_ATP_Olambda__63) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 232 (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_fun171081125l_bool(scratc1136867815l_some(Uua),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_al(Uu),Uub),Uuc))))) # label(fact_ATP_Olambda__64) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 233 (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_au(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc2047166451nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc309570230d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc907650504bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc907650504bnd_ap,Uub),Uud))),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc309570230d_e_is(Uu),Uuc),Uud))))) # label(fact_ATP_Olambda__65) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 234 (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_aj(Uu),Uua),Uub),Uuc),Uud)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc309570230d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc907650504bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc907650504bnd_ap,Uub),Uud)))))) # label(fact_ATP_Olambda__66) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 235 (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_ai(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_fun171081125l_bool(scratc2026207007all_of(aa_TPT43085870d_bool(aTP_Lamm_ae,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_ah(Uu),Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__67) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 236 (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_ak(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_fun171081125l_bool(scratc2026207007all_of(aa_TPT43085870d_bool(aTP_Lamm_ae,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_aj(Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__68) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 237 (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_aq(Uu),Uua),Uub),Uuc),Uud) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc907650504bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc907650504bnd_ap,aa_TPTP_ind_TPTP_ind(scratc317617714wissel(Uu,Uub),Uuc)),Uud))) # label(fact_ATP_Olambda__69) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 238 (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_ah(Uu),Uua),Uub),Uuc),Uud),Uue)) <-> pp(aa_fun171081125l_bool(scratc2026207007all_of(aa_TPT43085870d_bool(aTP_Lamm_ae,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_ag(Uu),Uua),Uub),Uuc),Uud),Uue))))) # label(fact_ATP_Olambda__70) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 239 (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_af(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(scratc309570230d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc907650504bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc907650504bnd_ap,Uub),Uuc)),Uue)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc907650504bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc907650504bnd_ap,Uub),Uud)),Uuf))))))) # label(fact_ATP_Olambda__71) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 240 (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_ag(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)) <-> pp(aa_fun171081125l_bool(scratc2026207007all_of(aa_TPT43085870d_bool(aTP_Lamm_ae,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_af(Uua),Uub),Uuc),Uud),Uue),Uuf))))) # label(fact_ATP_Olambda__72) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 241 (all Uu all Uua (gg_TPTP_ind(Uu) -> aa_TPTP_ind_TPTP_ind(aTP_Lamm_ad(Uu),Uua) = Uu)) # label(fact_ATP_Olambda__73) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 242 (all P all Q (-pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)) | pp(Q))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 243 (all P all Q (-pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)) | pp(P))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 244 (all P all Q (-pp(P) | -pp(Q) | pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 245 (all P (gg_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 246 (all P all Q (-pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) | -pp(P) | pp(Q))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 247 (all Q all P (-pp(Q) | pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)))) # label(help_fimplies_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 248 (all P all Q (pp(P) | pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)))) # label(help_fimplies_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 249 (all P all X7 (-pp(aa_TPTP_ind_bool(P,X7)) | pp(fEx_TPTP_ind(P)))) # label(help_fEx_1_1_fEx_001t__TPTP____Interpret__Oind_U) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 250 (all X7 all Y (X7 != Y | pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)))) # label(help_fequal_2_1_fequal_001t__TPTP____Interpret__Oind_T) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 251 (all X7 all Y (gg_TPTP_ind(X7) & gg_TPTP_ind(Y) -> -pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) | X7 = Y)) # label(help_fequal_1_1_fequal_001t__TPTP____Interpret__Oind_T) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 252 (all P all Q all R aa_TPTP_ind_bool(cOMBS_2003118649l_bool(P,Q),R) = aa_bool_bool(aa_TPT2142672771l_bool(P,R),aa_TPTP_ind_bool(Q,R))) # label(help_COMBS_1_1_COMBS_001t__TPTP____Interpret__Oind_001t__HOL__Obool_001t__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 253 (all P all Q all R aa_TPTP_ind_bool(aa_TPT43085870d_bool(cOMBC_1555011498d_bool(P),Q),R) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind_001t__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 254 (all P all Q all R aa_TPT2142672771l_bool(cOMBB_658106424TP_ind(P,Q),R) = aa_boo1142376798l_bool(P,aa_TPTP_ind_bool(Q,R))) # label(help_COMBB_1_1_COMBB_001t__HOL__Obool_001t__fun_It__HOL__Obool_Mt__HOL__Obool_J_001t__TPTP____Interpret__Oind_U) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24
% 0.92/1.24 ============================== end of process non-clausal formulas ===
% 0.92/1.24
% 0.92/1.24 ============================== PROCESS INITIAL CLAUSES ===============
% 0.92/1.24
% 0.92/1.24 ============================== PREDICATE ELIMINATION =================
% 0.92/1.24 255 -gg_bool(A) | A = fTrue | A = fFalse # label(help_fFalse_1_1_T) # label(axiom). [clausify(245)].
% 0.92/1.24 256 gg_bool(undefined_bool(bool)) # label(gsy_c_HOL_Oundefined_001t__HOL__Obool) # label(axiom). [assumption].
% 0.92/1.27 257 gg_bool(scratc369594977_amone(A,B)) # label(gsy_c_Scratch__tptp__translate__39347__27944_ONUM636__thf__4__p_Obnd__amone) # label(axiom). [clausify(1)].
% 0.92/1.27 258 gg_bool(scratc453715116_d_and(A,B)) # label(gsy_c_Scratch__tptp__translate__39347__27944_ONUM636__thf__4__p_Obnd__d__and) # label(axiom). [clausify(2)].
% 0.92/1.27 259 gg_bool(scratc561180296_d_not(A)) # label(gsy_c_Scratch__tptp__translate__39347__27944_ONUM636__thf__4__p_Obnd__d__not) # label(axiom). [clausify(3)].
% 0.92/1.27 260 gg_bool(scratc2013464380nd_ec3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__39347__27944_ONUM636__thf__4__p_Obnd__ec3) # label(axiom). [clausify(4)].
% 0.92/1.27 261 gg_bool(scratc1843806897d_l_ec(A,B)) # label(gsy_c_Scratch__tptp__translate__39347__27944_ONUM636__thf__4__p_Obnd__l__ec) # label(axiom). [clausify(8)].
% 0.92/1.27 262 gg_bool(scratc2097063415nd_or3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__39347__27944_ONUM636__thf__4__p_Obnd__or3) # label(axiom). [clausify(9)].
% 0.92/1.27 263 gg_bool(aa_bool_bool(A,B)) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom). [clausify(10)].
% 0.92/1.27 264 gg_bool(aa_TPTP_ind_bool(A,B)) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom). [clausify(11)].
% 0.92/1.27 265 gg_bool(aa_fun171081125l_bool(A,B)) # label(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__HOL__Obool) # label(hypothesis). [clausify(13)].
% 0.92/1.27 266 gg_bool(fEx_TPTP_ind(A)) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom). [clausify(16)].
% 0.92/1.27 267 gg_bool(fFalse) # label(gsy_c_fFalse) # label(axiom). [assumption].
% 0.92/1.27 268 gg_bool(fTrue) # label(gsy_c_fTrue) # label(axiom). [assumption].
% 0.92/1.27 Derived: undefined_bool(bool) = fTrue | undefined_bool(bool) = fFalse. [resolve(255,a,256,a)].
% 0.92/1.27 Derived: scratc369594977_amone(A,B) = fTrue | scratc369594977_amone(A,B) = fFalse. [resolve(255,a,257,a)].
% 0.92/1.27 Derived: scratc453715116_d_and(A,B) = fTrue | scratc453715116_d_and(A,B) = fFalse. [resolve(255,a,258,a)].
% 0.92/1.27 Derived: scratc561180296_d_not(A) = fTrue | scratc561180296_d_not(A) = fFalse. [resolve(255,a,259,a)].
% 0.92/1.27 Derived: scratc2013464380nd_ec3(A,B,C) = fTrue | scratc2013464380nd_ec3(A,B,C) = fFalse. [resolve(255,a,260,a)].
% 0.92/1.27 Derived: scratc1843806897d_l_ec(A,B) = fTrue | scratc1843806897d_l_ec(A,B) = fFalse. [resolve(255,a,261,a)].
% 0.92/1.27 Derived: scratc2097063415nd_or3(A,B,C) = fTrue | scratc2097063415nd_or3(A,B,C) = fFalse. [resolve(255,a,262,a)].
% 0.92/1.27 Derived: aa_bool_bool(A,B) = fTrue | aa_bool_bool(A,B) = fFalse. [resolve(255,a,263,a)].
% 0.92/1.27 Derived: aa_TPTP_ind_bool(A,B) = fTrue | aa_TPTP_ind_bool(A,B) = fFalse. [resolve(255,a,264,a)].
% 0.92/1.27 Derived: aa_fun171081125l_bool(A,B) = fTrue | aa_fun171081125l_bool(A,B) = fFalse. [resolve(255,a,265,a)].
% 0.92/1.27 Derived: fEx_TPTP_ind(A) = fTrue | fEx_TPTP_ind(A) = fFalse. [resolve(255,a,266,a)].
% 0.92/1.27 Derived: fFalse = fTrue | fFalse = fFalse. [resolve(255,a,267,a)].
% 0.92/1.27 Derived: fTrue = fTrue | fTrue = fFalse. [resolve(255,a,268,a)].
% 0.92/1.27 269 scratc91258039d_r_ec(A,B) | pp(A) # label(fact_def__r__ec) # label(axiom). [clausify(41)].
% 0.92/1.27 270 -scratc91258039d_r_ec(A,B) | -pp(A) | pp(scratc561180296_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(41)].
% 0.92/1.27 271 scratc91258039d_r_ec(A,B) | -pp(scratc561180296_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(41)].
% 0.92/1.27 272 scratc815741497_orec3(A,B,C) | -pp(scratc453715116_d_and(scratc2097063415nd_or3(A,B,C),scratc2013464380nd_ec3(A,B,C))) # label(fact_def__orec3) # label(axiom). [clausify(66)].
% 0.92/1.27 273 -scratc815741497_orec3(A,B,C) | pp(scratc453715116_d_and(scratc2097063415nd_or3(A,B,C),scratc2013464380nd_ec3(A,B,C))) # label(fact_def__orec3) # label(axiom). [clausify(66)].
% 0.92/1.27 274 scratc1347856566_l_iff(A,B) | -pp(scratc453715116_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc2047166451nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc2047166451nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(73)].
% 0.92/1.27 275 -scratc1347856566_l_iff(A,B) | pp(scratc453715116_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc2047166451nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc2047166451nd_imp,B),A))) # label(fact_def__l__iff) # label(axiom). [clausify(73)].
% 0.92/1.43 276 scratc1758717050d_orec(A,B) | -pp(scratc453715116_d_and(aa_bool_bool(scratc1844462902d_l_or(A),B),scratc1843806897d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(74)].
% 0.92/1.43 277 -scratc1758717050d_orec(A,B) | pp(scratc453715116_d_and(aa_bool_bool(scratc1844462902d_l_or(A),B),scratc1843806897d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(74)].
% 0.92/1.43 278 scratc14819077nd_wel(A) | -pp(scratc561180296_d_not(scratc561180296_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(79)].
% 0.92/1.43 279 -scratc14819077nd_wel(A) | pp(scratc561180296_d_not(scratc561180296_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(79)].
% 0.92/1.43 280 -scratc14819077nd_wel(A) | pp(A) # label(fact_l__et) # label(axiom). [clausify(129)].
% 0.92/1.43 Derived: pp(A) | -pp(scratc561180296_d_not(scratc561180296_d_not(A))). [resolve(280,a,278,a)].
% 0.92/1.43
% 0.92/1.43 ============================== end predicate elimination =============
% 0.92/1.43
% 0.92/1.43 Auto_denials: (non-Horn, no changes).
% 0.92/1.43
% 0.92/1.43 Term ordering decisions:
% 0.92/1.43 Function symbol KB weights: scratc908175294bnd_in=1. aTP_Lamm_ae=1. scratc907650504bnd_ap=1. scratc1108832938rdsucc=1. scratc954648526ptyset=1. scratc918786714_Sigma=1. fFalse=1. scratc1352903720_nat_p=1. scratc1909866188_power=1. scratc1846317032d_repl=1. scratc2047166451nd_imp=1. fTrue=1. scratc1315849604d_d_Pi=1. aTP_Lamm_a=1. scratc2087686792nd_nat=1. scratc2088211583nd_nis=1. scratc251637427d_pair=1. scratc1148913756d_Subq=1. scratc1948027270closed=1. scratc2038380026_proj0=1. scratc269644406_union=1. scratc1975714234d_n_in=1. scratc2038380027_proj1=1. scratc1975714239d_n_is=1. aTP_Lamm_bu=1. scratc118560454closed=1. scratc2101311088closed=1. scratc820767612nd_n_1=1. aTP_Lamm_bl=1. aTP_Lamm_bp=1. aTP_Lamm_bq=1. scratc1208035240_omega=1. scratc1789170787closed=1. scratc1875670551d_Inj1=1. aTP_Lamm_ab=1. aTP_Lamm_bb=1. aTP_Lamm_bd=1. aTP_Lamm_be=1. aTP_Lamm_bo=1. fconj=1. fimplies=1. scratc1050562874d_Sing=1. scratc1875670550d_Inj0=1. scratc2053496759_cond2=1. aTP_Lamm_bh=1. aTP_Lamm_bm=1. aTP_Lamm_bn=1. aTP_Lamm_br=1. aTP_Lamm_bs=1. aTP_Lamm_bt=1. aTP_Lamm_bw=1. aTP_Lamm_ct=1. fequal_TPTP_ind=1. scratc1785960502univof=1. scratc2026172588_n_all=1. scratc2053496758_cond1=1. scratc2086112410nd_nIn=1. scratc354577062_d_Unj=1. aTP_Lamm_aa=1. aTP_Lamm_ac=1. aTP_Lamm_bf=1. aTP_Lamm_bg=1. bool=1. scratc1240243513nempty=1. scratc1320089078munion=1. scratc20619203_prop1=1. scratc641539956_empty=1. scratc965582909pair_p=1. scratc1172414962d_i1_s=1. scratc1880692457n_some=1. scratc2141964849_n_one=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. scratc453715116_d_and=1. scratc908175286bnd_if=1. scratc1843806897d_l_ec=1. aa_fun1212484691d_bool=1. aa_TPT985247859d_bool=1. scratc309570225d_e_in=1. scratc2146335141d_pair=1. aa_fun987228051d_bool=1. scratc1076833645second=1. scratc2047232038nd_ind=1. scratc780054434_image=1. scratc822696503_first=1. aa_TPT125613450d_bool=1. scratc2088605172nd_non=1. scratc369594977_amone=1. aa_fun1913827119d_bool=1. scratc1534868484d_anec=1. aa_TPT1791839040TP_ind=1. aa_fun1107270209d_bool=1. aa_fun845057962d_bool=1. scratc1334201206_ecelt=1. scratc2013464441nd_ecp=1. scratc895236260eplSep=1. scratc1333610815_ecect=1. aa_TPT1781712639TP_ind=1. aa_TPT2142672771l_bool=1. aa_fun1235454963TP_ind=1. cOMBB_658106424TP_ind=1. cOMBS_2003118649l_bool=1. scratc2013464445nd_ect=1. scratc2085048039fixfu2=1. scratc2097260277nd_out=1. scratc317617714wissel=1. scratc331775686etprop=1. scratc449590917ectset=1. scratc871412747_fixfu=1. scratc1338230318d_invf=1. scratc1341966849d_tofs=1. scratc334389040ectelt=1. scratc507080631nverse=1. scratc555708263unmore=1. f1=1. f12=1. f13=1. f20=1. f24=1. scratc2026207007all_of=1. scratc309570230d_e_is=1. scratc337463667_d_Sep=1. scratc404541500d_esti=1. scratc561180296_d_not=1. scratcCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------