0.02/0.06 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.02/0.07 % Command : tptp2X_and_run_prover9 %d %s 0.06/0.25 % Computer : n009.cluster.edu 0.06/0.25 % Model : x86_64 x86_64 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.06/0.25 % Memory : 8042.1875MB 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64 0.06/0.25 % CPULimit : 1440 0.06/0.25 % WCLimit : 180 0.06/0.25 % DateTime : Mon Jul 3 12:05:26 EDT 2023 0.06/0.25 % CPUTime : 0.74/1.03 ============================== Prover9 =============================== 0.74/1.03 Prover9 (32) version 2009-11A, November 2009. 0.74/1.03 Process 2305 was started by sandbox2 on n009.cluster.edu, 0.74/1.03 Mon Jul 3 12:05:27 2023 0.74/1.03 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1440 -f /tmp/Prover9_2047_n009.cluster.edu". 0.74/1.03 ============================== end of head =========================== 0.74/1.03 0.74/1.03 ============================== INPUT ================================= 0.74/1.03 0.74/1.03 % Reading from file /tmp/Prover9_2047_n009.cluster.edu 0.74/1.03 0.74/1.03 set(prolog_style_variables). 0.74/1.03 set(auto2). 0.74/1.03 % set(auto2) -> set(auto). 0.74/1.03 % set(auto) -> set(auto_inference). 0.74/1.03 % set(auto) -> set(auto_setup). 0.74/1.03 % set(auto_setup) -> set(predicate_elim). 0.74/1.03 % set(auto_setup) -> assign(eq_defs, unfold). 0.74/1.03 % set(auto) -> set(auto_limits). 0.74/1.03 % set(auto_limits) -> assign(max_weight, "100.000"). 0.74/1.03 % set(auto_limits) -> assign(sos_limit, 20000). 0.74/1.03 % set(auto) -> set(auto_denials). 0.74/1.03 % set(auto) -> set(auto_process). 0.74/1.03 % set(auto2) -> assign(new_constants, 1). 0.74/1.03 % set(auto2) -> assign(fold_denial_max, 3). 0.74/1.03 % set(auto2) -> assign(max_weight, "200.000"). 0.74/1.03 % set(auto2) -> assign(max_hours, 1). 0.74/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.74/1.03 % set(auto2) -> assign(max_seconds, 0). 0.74/1.03 % set(auto2) -> assign(max_minutes, 5). 0.74/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.74/1.03 % set(auto2) -> set(sort_initial_sos). 0.74/1.03 % set(auto2) -> assign(sos_limit, -1). 0.74/1.03 % set(auto2) -> assign(lrs_ticks, 3000). 0.74/1.03 % set(auto2) -> assign(max_megs, 400). 0.74/1.03 % set(auto2) -> assign(stats, some). 0.74/1.03 % set(auto2) -> clear(echo_input). 0.74/1.03 % set(auto2) -> set(quiet). 0.74/1.03 % set(auto2) -> clear(print_initial_clauses). 0.74/1.03 % set(auto2) -> clear(print_given). 0.74/1.03 assign(lrs_ticks,-1). 0.74/1.03 assign(sos_limit,10000). 0.74/1.03 assign(order,kbo). 0.74/1.03 set(lex_order_vars). 0.74/1.03 clear(print_given). 0.74/1.03 0.74/1.03 % formulas(sos). % not echoed (394 formulas) 0.74/1.03 0.74/1.03 ============================== end of input ========================== 0.74/1.03 0.74/1.03 % From the command line: assign(max_seconds, 1440). 0.74/1.03 0.74/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.74/1.03 0.74/1.03 % Formulas that are not ordinary clauses: 0.74/1.03 1 (all Uu all Uua aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1188233249d_repl,aa_TPTP_ind_TPTP_ind(Uu,Uua)),aa_TPT1424761345TP_ind(scratc1741037292d_pair,Uua)) = aa_TPTP_ind_TPTP_ind(aTP_Lamm_bh(Uu),Uua)) # label(fact_ATP_Olambda__63) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 2 (all Uu (pp(aa_fun171081125l_bool(scratc1809285542all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_by,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_bz,Uu)))) # label(fact_ATP_Olambda__32) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 3 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ej(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1809285542all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ei(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__101) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 4 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1034740847bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1034740855bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1188233249d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bn(X),Xa))),scratc350117639ptyset) = aa_fun1431113780TP_ind(scratc750595372_d_Sep(X),Xa)) # label(fact_def__d__Sep) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 5 (all Uu all Uua all Uub all Uuc (pp(scratc922017976d_l_ec(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1893941365d_esti(Uu),Uuc),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1893941365d_esti(Uu),Uuc),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_as(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__117) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 6 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(scratc1034740847bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,scratc350117639ptyset),Uub),Uu),Uua) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_bo(Uu),Uua),Uub)) # label(fact_ATP_Olambda__82) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 7 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1809285542all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bc(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bd(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__98) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 8 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc343180806nd_nis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc343180806nd_nis,aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_du,Uu),Uua)))) # label(fact_ATP_Olambda__54) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 9 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc678900160d_incl(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc235978031nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_at(X),Xa),Xb))))) # label(fact_def__incl) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 10 (all X0 all X12 scratc1879391219_is_of(aa_fun1431113780TP_ind(scratc750595372_d_Sep(X0),X12),aa_TPT43085870d_bool(aTP_Lamm_ed,X0))) # label(fact_setof__p) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 11 (all Uu (pp(aa_fun171081125l_bool(scratc1809285542all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dj,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_dk,Uu)))) # label(fact_ATP_Olambda__17) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 12 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cq(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(Uu),Uub))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,Uua),Uub))))) # label(fact_ATP_Olambda__91) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 13 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cy,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(Uua),Uu))))) # label(fact_ATP_Olambda__56) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 14 (all B_1 all B_2 gg_bool(scratc866846821_d_and(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__42811__30845_ONUM653__thf__4__p_Obnd__d__and) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 15 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1809285542all_of(aa_fun1584354236d_bool(aTP_Lamm_et(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_eu(X0),X12)))) # label(fact_e__inp) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 16 (all X (scratc417271948nd_wel(X) <-> pp(scratc974312001_d_not(scratc974312001_d_not(X))))) # label(fact_def__wel) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 17 (all Uu (pp(aa_fun171081125l_bool(scratc1809285542all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cg,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ch,Uu)))) # label(fact_ATP_Olambda__28) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 18 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cr,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1809285542all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cq(Uu),Uua))))) # label(fact_ATP_Olambda__76) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 19 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(Xa),X))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc505619704_prop1,X),Xa)))) # label(fact_def__d__26__prop1) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 20 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ek(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1535264957d_e_is(Uu),aa_TPTP_ind_TPTP_ind(scratc2048391230_first(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1929413676d_pair(Uu,Uua),Uub),Uuc))),Uub)))) # label(fact_ATP_Olambda__111) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 21 (all Uu (pp(aa_fun171081125l_bool(scratc1809285542all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cm,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cn,Uu)))) # label(fact_ATP_Olambda__26) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 22 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1625700832tminus(X),Xa) = aa_fun1431113780TP_ind(scratc750595372_d_Sep(X),aa_TPT43085870d_bool(aTP_Lamm_bm,Xa))) # label(fact_def__setminus) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 23 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc314255827_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,aa_TPTP_ind_TPTP_ind(scratc1116591105_proj0,X22)),X0)))) # label(fact_proj0__Sigma) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 24 (all X all Xa all Xb all Xc all Xd scratc134205945indeq2(X,Xa,Xb,Xc,Xd) = aa_TPT1424761345TP_ind(scratc663506041_indeq(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1541038711d_11_i(X,Xa,Xb),Xc),Xd))) # label(fact_def__indeq2) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 25 (all X ((all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,aa_TPTP_ind_TPTP_ind(scratc1495339133_union,X1)),X))))) <-> pp(aa_TPTP_ind_bool(scratc1527012265closed,X)))) # label(fact_def__d__Union__closed) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 26 (all X0 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X0),scratc286246319_omega)) -> pp(aa_TPTP_ind_bool(scratc1766035425_nat_p,X0)))) # label(fact_omega__nat__p) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 27 (all Uu all Uua all Uub all Uuc (gg_TPTP_ind(Uua) & gg_TPTP_ind(Uub) & gg_TPTP_ind(Uuc) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bp(Uu),Uua),Uub),Uuc)) <-> Uua = Uuc & pp(Uu) | -pp(Uu) & Uub = Uuc))) # label(fact_ATP_Olambda__120) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 28 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc343574395nd_non(X,Xa),Xb)) <-> pp(scratc974312001_d_not(aa_TPTP_ind_bool(Xa,Xb))))) # label(fact_def__non) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 29 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,X12) = aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,X0) -> X0 = X12))) # label(fact_ordsucc__inj) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 30 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cp,Uu)) <-> pp(aa_fun171081125l_bool(scratc1809285542all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_co,Uu))))) # label(fact_ATP_Olambda__25) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 31 (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(scratc804593329moreis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670609717lessis,Uua),Uu))))) # label(fact_ATP_Olambda__58) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 32 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_fun171081125l_bool(scratc1809285542all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_ao(Uua),Uub),Uuc),Uud))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ap(Uu),Uua),Uub),Uuc),Uud)))) # label(fact_ATP_Olambda__128) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 33 (all X all Xa (pp(aa_TPTP_ind_bool(Xa,X)) <-> scratc1879391219_is_of(X,Xa))) # label(fact_def__is__of) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 34 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_em(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,Uub),aa_TPTP_ind_TPTP_ind(scratc525834567etprod(Uu),Uua))))) # label(fact_ATP_Olambda__105) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 35 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301873271nd_iii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1663770992n_some,aa_TPT43085870d_bool(scratc1632014586ffprop(Xa),X))))) # label(fact_def__iii) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 36 (all Uu (pp(aa_fun171081125l_bool(scratc1809285542all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ce,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cf,Uu)))) # label(fact_ATP_Olambda__29) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 37 (all X scratc1893941365d_esti(X) = scratc1034740855bnd_in) # label(fact_def__esti) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 38 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1070076558ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc235978031nd_all(Xa),aa_TPT43085870d_bool(scratc2005749161_image(X,Xa),Xb))))) # label(fact_def__surjective) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 39 (all X all Xa (pp(scratc866846821_d_and(aa_bool_bool(scratc922673981d_l_or(X),Xa),scratc922017976d_l_ec(X,Xa))) <-> scratc1100633267d_orec(X,Xa))) # label(fact_def__orec) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 40 (all X aa_boo1142376798l_bool(scratc302135674nd_imp,scratc974312001_d_not(X)) = scratc922673981d_l_or(X)) # label(fact_def__l__or) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 41 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1535264957d_e_is(Uu),Uub),Uuc)) -> pp(aa_TPTP_ind_bool(Uua,Uuc)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_fa(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__121) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 42 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X33),X0)) -> aa_TPTP_ind_TPTP_ind(X22,X33) = aa_TPTP_ind_TPTP_ind(X12,X33)))) -> aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc314255827_Sigma,X0),X12) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc314255827_Sigma,X0),X22))) # label(fact_xi__ext) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 43 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2097107474_fixfu(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1809285542all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ap(X),Xa),Xb),Xc))))) # label(fact_def__fixfu) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 44 (all Uu (pp(aa_fun171081125l_bool(scratc1809285542all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bq,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_br,Uu)))) # label(fact_ATP_Olambda__36) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 45 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dt,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc343180806nd_nis,aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__9) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 46 (all X all Xa all 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(scratc1034740855bnd_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)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc786450286_rec_G(X),Xa),Xb)))) # label(fact_def__d__In__rec__G) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 47 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_da(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(Uu),Uua)),Uub)),aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(Uua),Uub)))))) # label(fact_ATP_Olambda__92) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 48 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc715558191munion,X),aTP_Lamm_bh(Xa)) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc314255827_Sigma,X),Xa)) # label(fact_def__d__Sigma) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 49 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1809285542all_of(aa_fun1584354236d_bool(aTP_Lamm_et(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_ev(X0),X12)))) # label(fact_e__in__p) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 50 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_fun1235454963TP_ind(aTP_Lamm_bn(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc1034740847bnd_if(aa_TPTP_ind_bool(Uua,Uub),Uub),scratc269286454nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bb(Uu),Uua)))) # label(fact_ATP_Olambda__83) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 51 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X33),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,aa_TPTP_ind_TPTP_ind(X22,X33)),aa_TPTP_ind_TPTP_ind(X12,X33)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc314255827_Sigma,X0),X22)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc394060683d_d_Pi,X0),X12))))) # label(fact_lam__Pi) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 52 (all X all Xa scratc1116591105_proj0 = scratc2048391230_first(X,Xa)) # label(fact_def__first) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 53 (all X all Xa (pp(aa_fun171081125l_bool(scratc919946350l_some(X),Xa)) <-> pp(scratc974312001_d_not(aa_fun171081125l_bool(scratc1809285542all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),scratc343574395nd_non(X,Xa)))))) # label(fact_def__l__some) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 54 (all X (pp(aa_TPTP_ind_bool(scratc1116984703_prop4,X)) <-> pp(aa_fun171081125l_bool(scratc919946350l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc394060683d_d_Pi,scratc342656015nd_nat),aTP_Lamm_ac)),aa_TPT43085870d_bool(scratc1476379003_prop2,X))))) # label(fact_def__prop4) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 55 (all X aa_fun277296641TP_ind(scratc2097791837eplSep(X,aTP_Lamm_bi),scratc767708767_d_Unj) = aa_TPTP_ind_TPTP_ind(scratc1116591106_proj1,X)) # label(fact_def__proj1) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 56 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_eq(Uu),Uua),Uub),Uuc)) <-> scratc1879391219_is_of(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1929413676d_pair(Uu,Uua),Uub),Uuc),aa_TPT43085870d_bool(aTP_Lamm_em(Uu),Uua)))) # label(fact_ATP_Olambda__116) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 57 (all X0 all X12 all X22 all X32 (pp(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1034740847bnd_if(X0,X22),X32))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X12),X22))))) # label(fact_k__If__In__then__E) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 58 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1535264957d_e_is(aa_TPTP_ind_TPTP_ind(scratc988077267_power,X)),Xb),aa_TPTP_ind_TPTP_ind(scratc412412285_ecelt(X,Xa),Xc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc268433664nd_ecp(X,Xa),Xb),Xc)))) # label(fact_def__ecp) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 59 (all B_1 all B_2 all B_3 gg_bool(scratc352032638nd_or3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__42811__30845_ONUM653__thf__4__p_Obnd__or3) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 60 (all Uu aa_TPTP_ind_TPTP_ind(aTP_Lamm_ac,Uu) = scratc342656015nd_nat) # label(fact_ATP_Olambda__134) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 61 (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]. 0.74/1.03 62 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1495339133_union,X0))) <-> (exists X2 (gg_TPTP_ind(X2) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X2),X0)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X12),X2)))))) # label(fact_k__UnionEq) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 63 (all Uu all Uua (scratc2041436224_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc851743993_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301873271nd_iii,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ce,Uu),Uua)))) # label(fact_ATP_Olambda__42) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 64 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dc,Uu)) <-> pp(aa_fun171081125l_bool(scratc1809285542all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_db,Uu))))) # label(fact_ATP_Olambda__20) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 65 pp(aa_bool_bool(aa_boo1142376798l_bool(scratc302135674nd_imp,fFalse),fFalse)) <-> scratc1155241813bvious # label(fact_def__obvious) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 66 (all Uu (pp(aa_fun171081125l_bool(scratc1809285542all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bu,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_bv,Uu)))) # label(fact_ATP_Olambda__34) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 67 (all X all Xa all Xb all Xc (pp(aa_fun171081125l_bool(scratc919946350l_some(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(Xa),Xb),Xc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2005749161_image(X,Xa),Xb),Xc)))) # label(fact_def__image) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 68 (all X all Xa all Xb (pp(aa_bool_bool(scratc922673981d_l_or(X),aa_bool_bool(scratc922673981d_l_or(Xa),Xb))) <-> pp(scratc352032638nd_or3(X,Xa,Xb)))) # label(fact_def__or3) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 69 (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]. 0.74/1.03 70 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dh,Uu)) <-> pp(aa_fun171081125l_bool(scratc1809285542all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dg,Uu))))) # label(fact_ATP_Olambda__18) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 71 (all X ((all X1 (pp(aa_TPTP_ind_bool(X1,scratc350117639ptyset)) -> ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(X1,X2)) -> pp(aa_TPTP_ind_bool(X1,aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,X2)))))) -> pp(aa_TPTP_ind_bool(X1,X))))) <-> pp(aa_TPTP_ind_bool(scratc1766035425_nat_p,X)))) # label(fact_def__nat__p) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 72 (all Uu all Uua all Uub (scratc1879391219_is_of(aa_TPTP_ind_TPTP_ind(scratc2048391230_first(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ep(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__88) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 73 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,Uu)),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dd,Uu),Uua)))) # label(fact_ATP_Olambda__65) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 74 (all X all Xa all Xb scratc269286454nd_eps(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bp(X),Xa),Xb)) = aa_TPTP_ind_TPTP_ind(scratc1034740847bnd_if(X,Xa),Xb)) # label(fact_def__if) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 75 (all B_1 gg_bool(fEx_TPTP_ind(B_1))) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 76 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_ad(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,Uu),Uua))) # label(fact_ATP_Olambda__78) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 77 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_an(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_fun171081125l_bool(scratc1809285542all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_am(Uu),Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__127) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 78 (all X7 all Y (gg_TPTP_ind(Y) & gg_TPTP_ind(X7) -> Y = X7 | -pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)))) # label(help_fequal_1_1_fequal_001t__TPTP____Interpret__Oind_T) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 79 (all X all Xa all Xb aa_fun1431113780TP_ind(scratc750595372_d_Sep(X),aa_TPT43085870d_bool(Xa,Xb)) = aa_TPTP_ind_TPTP_ind(scratc412412285_ecelt(X,Xa),Xb)) # label(fact_def__ecelt) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 80 (all X (pp(aa_fun171081125l_bool(scratc291820645_n_all,aa_TPT43085870d_bool(aTP_Lamm_ae,X))) <-> pp(aa_TPTP_ind_bool(scratc1476379002_prop1,X)))) # label(fact_def__d__24__prop1) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 81 (all X0 all X12 (gg_TPTP_ind(X12) -> X12 = aa_TPTP_ind_TPTP_ind(scratc1116591106_proj1,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1741037292d_pair,X0),X12)))) # label(fact_proj1__pair__eq) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 82 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ck(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__103) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 83 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1535264957d_e_is(Uua),aa_TPTP_ind_TPTP_ind(scratc1489965350second(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1929413676d_pair(Uu,Uua),Uub),Uuc))),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ei(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__112) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 84 (all X (pp(aa_bool_bool(scratc922673981d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,X),scratc162683829nd_n_1)),aa_fun171081125l_bool(scratc1663770992n_some,aa_TPT43085870d_bool(aTP_Lamm_af,X)))) <-> pp(aa_TPTP_ind_bool(scratc888016827_prop1,X)))) # label(fact_def__d__23__prop1) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 85 (all B_1 all B_2 gg_TPTP_ind(scratc268433668nd_ect(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__42811__30845_ONUM653__thf__4__p_Obnd__ect) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 86 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc343180806nd_nis,Uua),Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc343180806nd_nis,aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(Uu),Uua)),aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(Uu),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ct(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__93) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 87 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1809285542all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_ej(X0),X12)))) # label(fact_secondis1) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 88 (all X all Xa all Xb (gg_TPTP_ind(Xb) -> aa_TPTP_ind_TPTP_ind(scratc1535264952d_e_in(X,Xa),Xb) = Xb)) # label(fact_def__e__in) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 89 (all X all Xa all Xb all Xc all Xd all Xe (pp(aa_fun171081125l_bool(scratc919946350l_some(X),aa_TPT43085870d_bool(scratc2023701629_prop1(X,Xa,Xb,Xc,Xd),Xe))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1116984701_prop2(X,Xa,Xb,Xc),Xd),Xe)))) # label(fact_def__prop2) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 90 (all Uu (pp(aa_fun171081125l_bool(scratc1809285542all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ab,Uu)))) # label(fact_ATP_Olambda__37) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 91 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dm,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__52) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 92 (all P all X7 (pp(fEx_TPTP_ind(P)) | -pp(aa_TPTP_ind_bool(P,X7)))) # label(help_fEx_1_1_fEx_001t__TPTP____Interpret__Oind_U) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 93 (all Uu all Uua all Uub all Uuc all Uud all Uue (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_am(Uu),Uua),Uub),Uuc),Uud),Uue)) <-> pp(aa_fun171081125l_bool(scratc1809285542all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_al(Uu),Uua),Uub),Uuc),Uud),Uue))))) # label(fact_ATP_Olambda__130) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 94 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,Uub),Uu)) & pp(aa_TPTP_ind_bool(Uua,Uub)) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bb(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__94) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 95 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1534331263etprop(X,Xa),Xb),Xc)) <-> pp(scratc866846821_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1893941365d_esti(X),Xc),Xa),scratc974312001_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1893941365d_esti(X),Xc),Xb)))))) # label(fact_def__nissetprop) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 96 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_es(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2005749161_image(aa_fun1431113780TP_ind(scratc750595372_d_Sep(Uu),Uua),Uu),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc314255827_Sigma,aa_fun1431113780TP_ind(scratc750595372_d_Sep(Uu),Uua)),scratc1535264952d_e_in(Uu,Uua))),Uub))))) # label(fact_ATP_Olambda__95) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 97 (all P all Q (pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) | pp(P))) # label(help_fimplies_1_1_U) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 98 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_bi,Uu)) <-> (exists X2 (Uu = aa_TPTP_ind_TPTP_ind(scratc1658749086d_Inj1,X2) & gg_TPTP_ind(X2)))))) # label(fact_ATP_Olambda__40) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 99 (all B_1 all B_2 gg_bool(scratc922017976d_l_ec(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__42811__30845_ONUM653__thf__4__p_Obnd__l__ec) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 100 (all X (gg_TPTP_ind(X) -> (aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1741037292d_pair,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,X),scratc350117639ptyset)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,X),aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,scratc350117639ptyset))) = X <-> pp(aa_TPTP_ind_bool(scratc748661444pair_p,X))))) # label(fact_def__pair__p) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 101 (all X ((all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X1),X)) -> (all X2 ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X3),X1)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,aa_TPTP_ind_TPTP_ind(X2,X3)),X))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1188233249d_repl,X1),X2)),X))))))) <-> pp(aa_TPTP_ind_bool(scratc388875789closed,X)))) # label(fact_def__d__Repl__closed) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 102 (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]. 0.74/1.04 103 (all X0 (scratc417271948nd_wel(X0) -> pp(X0))) # label(fact_l__et) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 104 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(scratc162683829nd_n_1),Uu)),aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_dl,Uu)))) # label(fact_ATP_Olambda__4) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 105 (all X all Xa scratc269286454nd_eps(aa_TPT43085870d_bool(scratc786450286_rec_G(X),Xa)) = aa_TPTP_ind_TPTP_ind(scratc1825555417In_rec(X),Xa)) # label(fact_def__d__In__rec) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 106 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_co,Uu),Uua)) <-> pp(scratc1595289704_amone(scratc342656015nd_nat,aa_TPT43085870d_bool(aTP_Lamm_ck(Uu),Uua))))) # label(fact_ATP_Olambda__77) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 107 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,X),aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1632014586ffprop(X),Xa),Xb)))) # label(fact_def__diffprop) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 108 (all Uu (pp(aa_fun171081125l_bool(scratc1809285542all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dm,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_dn,Uu)))) # label(fact_ATP_Olambda__16) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 109 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1893941365d_esti(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,Uua),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aq(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__114) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 110 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bt,Uu)) <-> pp(aa_fun171081125l_bool(scratc1809285542all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bs,Uu))))) # label(fact_ATP_Olambda__35) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 111 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1535264957d_e_is(Uu),Uua),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_fc,Uu),Uua)))) # label(fact_ATP_Olambda__48) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 112 (all X0 (pp(aa_TPTP_ind_bool(scratc1766035425_nat_p,X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X0),scratc286246319_omega)))) # label(fact_nat__p__omega) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 113 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc851743993_29_ii,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1663770992n_some,aa_TPT43085870d_bool(scratc1632014586ffprop(X),Xa))))) # label(fact_def__d__29__ii) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 114 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,Uu),Uub)) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_aw(Uu),Uua),Uub)) # label(fact_ATP_Olambda__107) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 115 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc208742205_UPair(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1188233249d_repl,aa_TPTP_ind_TPTP_ind(scratc988077267_power,aa_TPTP_ind_TPTP_ind(scratc988077267_power,scratc350117639ptyset))),aa_TPT1424761345TP_ind(aTP_Lamm_bo(X),Xa))) # label(fact_def__d__UPair) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 116 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_bool_bool(aa_boo1142376798l_bool(scratc302135674nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1535264957d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,Uub),Uud))),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1535264957d_e_is(Uu),Uuc),Uud))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_az(Uu),Uua),Uub),Uuc),Uud)))) # label(fact_ATP_Olambda__125) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 117 -(exists X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X0),scratc350117639ptyset))) # label(fact_k__EmptyAx) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 118 (all X all Xa all Xb aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc314255827_Sigma,X),scratc1473700950sel_wb(X,Xa,Xb)) = aa_TPTP_ind_TPTP_ind(scratc730749419wissel(X,Xa),Xb)) # label(fact_def__wissel) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 119 (all X0 scratc350117639ptyset != aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,X0)) # label(fact_neq__ordsucc__0) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 120 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_er(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1809285542all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_eq(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__99) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 121 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X22),X0)) -> (all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X32),aa_TPTP_ind_TPTP_ind(X12,X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1741037292d_pair,X22),X32)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc314255827_Sigma,X0),X12))))))) # label(fact_pair__Sigma) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 122 (all Uu all Uua all Uub (scratc1879391219_is_of(aa_TPTP_ind_TPTP_ind(scratc1535264952d_e_in(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ev(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__89) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 123 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1809285542all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_el(X0),X12)))) # label(fact_firstis1) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 124 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dg,Uu),Uua)))) # label(fact_ATP_Olambda__66) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 125 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1809285542all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_eg(X0),X12)))) # label(fact_estie) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 126 (all X all Xa scratc268433668nd_ect(X,Xa) = aa_fun1431113780TP_ind(scratc750595372_d_Sep(aa_TPTP_ind_TPTP_ind(scratc988077267_power,X)),scratc876784701d_anec(X,Xa))) # label(fact_def__ect) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 127 (all X (pp(aa_TPTP_ind_bool(scratc1131707838_cond2,X)) <-> pp(aa_fun171081125l_bool(scratc291820645_n_all,aa_TPT43085870d_bool(aTP_Lamm_ag,X))))) # label(fact_def__cond2) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 128 (all X all Xa scratc411821894_ecect(X,Xa) = scratc1535264952d_e_in(aa_TPTP_ind_TPTP_ind(scratc988077267_power,X),scratc876784701d_anec(X,Xa))) # label(fact_def__ecect) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 129 (all Uu all Uua aa_TPTP_ind_TPTP_ind(scratc1709415290nunion(aa_TPTP_ind_TPTP_ind(scratc833641409d_Sing,scratc350117639ptyset)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1188233249d_repl,Uu),Uua)) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(aTP_Lamm_bl,Uu),Uua)) # label(fact_ATP_Olambda__67) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 130 (all X (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc343180806nd_nis,aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,X)),X)) <-> pp(aa_TPTP_ind_bool(scratc299654652_prop1,X)))) # label(fact_def__d__22__prop1) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 131 (all X all Xa all Xb (scratc876719054d_and3(scratc922017976d_l_ec(X,Xa),scratc922017976d_l_ec(Xa,Xb),scratc922017976d_l_ec(Xb,X)) <-> pp(scratc268433603nd_ec3(X,Xa,Xb)))) # label(fact_def__ec3) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 132 (all Uu all Uua all Uub all Uuc all Uud all Uue all Uuf (pp(aa_fun171081125l_bool(scratc1809285542all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_ak(Uua),Uub),Uuc),Uud),Uue),Uuf))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_al(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)))) # label(fact_ATP_Olambda__132) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 133 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc931992291d_Subq,X0),X12)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc931992291d_Subq,X12),X0)) -> X0 = X12)))) # label(fact_set__ext) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 134 (all X all Xa (pp(aa_fun171081125l_bool(scratc919946350l_some(X),aa_TPT43085870d_bool(aTP_Lamm_au(X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc635712626nempty,X),Xa)))) # label(fact_def__nonempty) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 135 (all X aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc1709415290nunion(X),aa_TPTP_ind_TPTP_ind(scratc833641409d_Sing,X))) # label(fact_def__ordsucc) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 136 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1476379003_prop2,X),Xa)) <-> pp(scratc866846821_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,Xa),scratc162683829nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,X)),aa_TPTP_ind_bool(scratc1476379002_prop1,Xa))))) # label(fact_def__d__24__prop2) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 137 (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(scratc1053925318d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,Uu),aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,Uu),Uua)))))) # label(fact_ATP_Olambda__53) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 138 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1809285542all_of(aa_TPT43085870d_bool(aTP_Lamm_ew(Uu),Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ey(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ez(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__90) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 139 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X22),aa_fun1431113780TP_ind(scratc750595372_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(X12,X22)))) # label(fact_k__SepE2) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 140 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,Uua),aa_TPTP_ind_TPTP_ind(scratc988077267_power,Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ed,Uu),Uua)))) # label(fact_ATP_Olambda__70) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 141 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc341081633nd_nIn,X),Xa)) <-> -pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X),Xa)))) # label(fact_def__nIn) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 142 (all X all Xa all Xb scratc663506041_indeq(X,Xa,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc394060683d_d_Pi,X),aTP_Lamm_ai(Xb))) = scratc1541038711d_11_i(X,Xa,Xb)) # label(fact_def__d__11__i) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 143 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bc(Uu),Uua),Uub),Uuc)) <-> (pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(Uua,Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1535264957d_e_is(Uu),Uub),Uuc)))))) # label(fact_ATP_Olambda__122) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 144 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> ((exists X3 (gg_TPTP_ind(X3) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X3),X0)) & X22 = aa_TPTP_ind_TPTP_ind(X12,X3))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1188233249d_repl,X0),X12)))))) # label(fact_k__ReplEq) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 145 (all X aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1832701036d_plus,X)) = scratc1054384504d_n_pl(X)) # label(fact_def__n__pl) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 146 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670609717lessis,Uu),Uua)) -> pp(scratc974312001_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc851743993_29_ii,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,Uu),Uua)))) # label(fact_ATP_Olambda__62) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 147 (all X0 all X12 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2043586645ective(aa_fun1431113780TP_ind(scratc750595372_d_Sep(X0),X12)),X0),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc314255827_Sigma,aa_fun1431113780TP_ind(scratc750595372_d_Sep(X0),X12)),scratc1535264952d_e_in(X0,X12))))) # label(fact_otax1) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 148 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_eb,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc343180806nd_nis,aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,Uu)),scratc162683829nd_n_1)))) # label(fact_ATP_Olambda__11) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 149 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cj,Uu)) <-> pp(aa_fun171081125l_bool(scratc1809285542all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ci,Uu))))) # label(fact_ATP_Olambda__27) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 150 (all B_1 all B_2 gg_bool(scratc1595289704_amone(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__42811__30845_ONUM653__thf__4__p_Obnd__amone) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 151 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc2050779516d_soft(X,Xa,Xb),Xc) = scratc302201261nd_ind(X,aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(Xa),Xb),Xc))) # label(fact_def__soft) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 152 (all X0 pp(aa_fun171081125l_bool(scratc1809285542all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_fc,X0)))) # label(fact_refis) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 153 (all X aa_fun277296641TP_ind(scratc2097791837eplSep(X,aTP_Lamm_bj),scratc767708767_d_Unj) = aa_TPTP_ind_TPTP_ind(scratc1116591105_proj0,X)) # label(fact_def__proj0) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 154 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(scratc162683829nd_n_1),Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_df,Uu)))) # label(fact_ATP_Olambda__8) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 155 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cu,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1809285542all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ct(Uu),Uua))))) # label(fact_ATP_Olambda__75) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 156 (all P all Q (pp(Q) | -pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 157 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1809285542all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_eh(X0),X12)))) # label(fact_estii) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 158 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cw,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc343180806nd_nis,Uua),aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(Uu),Uua))))) # label(fact_ATP_Olambda__68) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 159 (all B_1 gg_bool(scratc974312001_d_not(B_1))) # label(gsy_c_Scratch__tptp__translate__42811__30845_ONUM653__thf__4__p_Obnd__d__not) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 160 (all Uu ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc343180806nd_nis,Uu),scratc162683829nd_n_1)) -> pp(aa_fun171081125l_bool(scratc407612906_n_one,aa_TPT43085870d_bool(aTP_Lamm_af,Uu)))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_dr,Uu)))) # label(fact_ATP_Olambda__2) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 161 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dz,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,Uu),Uua))))) # label(fact_ATP_Olambda__50) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 162 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc314255827_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,aa_TPTP_ind_TPTP_ind(scratc1116591105_proj0,X22)),X0)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,aa_TPTP_ind_TPTP_ind(scratc1116591106_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1116591105_proj0,X22)))) & X22 = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1741037292d_pair,aa_TPTP_ind_TPTP_ind(scratc1116591105_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1116591106_proj1,X22))))) # label(fact_k__Sigma__eta__proj0__proj1) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 163 (all X0 all X12 all X22 (gg_TPTP_ind(X12) & gg_TPTP_ind(X22) -> -pp(X0) & X22 = aa_TPTP_ind_TPTP_ind(scratc1034740847bnd_if(X0,X12),X22) | X12 = aa_TPTP_ind_TPTP_ind(scratc1034740847bnd_if(X0,X12),X22) & pp(X0))) # label(fact_if__i__correct) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 164 (all X0 ((all X13 (gg_TPTP_ind(X13) -> ((all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_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]. 0.74/1.04 165 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(Uua,aa_TPTP_ind_TPTP_ind(scratc1535264952d_e_in(Uu,Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_eu(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__108) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 166 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ax(Uu),Uua),Uub),Uuc) = aa_TPTP_ind_TPTP_ind(scratc1034740847bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2005749161_image(Uu,Uua),Uub),Uuc),aa_TPTP_ind_TPTP_ind(scratc2050779516d_soft(Uu,Uua,Uub),Uuc)),scratc350117639ptyset)) # label(fact_ATP_Olambda__110) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 167 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1809285542all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_es(X0),X12)))) # label(fact_otax2) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 168 (all Uu aa_TPT494704832TP_ind(scratc1188233249d_repl,aa_TPTP_ind_TPTP_ind(scratc1625700832tminus(Uu),aa_TPTP_ind_TPTP_ind(scratc833641409d_Sing,scratc350117639ptyset))) = aa_TPT494704832TP_ind(aTP_Lamm_bk,Uu)) # label(fact_ATP_Olambda__38) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 169 (all X all Xa all Xb aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc314255827_Sigma,Xa),scratc2050779516d_soft(X,Xa,Xb)) = aa_TPTP_ind_TPTP_ind(scratc680146535d_invf(X,Xa),Xb)) # label(fact_def__invf) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 170 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2064741177_prop1(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(X),Xa)),Xb)),aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(X),aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(Xa),Xb)))))) # label(fact_def__d__25__prop1) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 171 (all X all Xa (pp(scratc922017976d_l_ec(X,Xa)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc302135674nd_imp,X),scratc974312001_d_not(Xa))))) # label(fact_def__l__ec) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 172 (all X all Xa all Xb all Xc all Xd all Xe all Xf (pp(scratc866846821_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1893941365d_esti(X),Xf),aa_TPTP_ind_TPTP_ind(scratc411821894_ecect(X,Xa),Xd)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1535264957d_e_is(Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,Xc),Xf)),Xe))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2023701629_prop1(X,Xa,Xb,Xc,Xd),Xe),Xf)))) # label(fact_def__d__10__prop1) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 173 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1473700949sel_wa(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc302594856nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1535264957d_e_is(X),Xc),Xa),X,Xb),Xc)) # label(fact_def__wissel__wa) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 174 (all X all Xa (pp(aa_fun171081125l_bool(scratc351770292nd_one(X),Xa)) <-> pp(scratc866846821_d_and(scratc1595289704_amone(X,Xa),aa_fun171081125l_bool(scratc919946350l_some(X),Xa))))) # label(fact_def__one) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 175 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1116984702_prop3(X),Xa),Xb)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,X),Xb)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,Xa),Xb))))) # label(fact_def__prop3) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 176 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1809285542all_of(aa_TPT43085870d_bool(aTP_Lamm_em(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_en(X0),X12)))) # label(fact_pairis1) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 177 (all Uu all Uua (gg_TPTP_ind(Uu) -> Uu = aa_TPTP_ind_TPTP_ind(aTP_Lamm_ai(Uu),Uua))) # label(fact_ATP_Olambda__133) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 178 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,Uub),aa_fun1431113780TP_ind(scratc750595372_d_Sep(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_et(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__106) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 179 (all X all Xa scratc1741037292d_pair = scratc1929413676d_pair(X,Xa)) # label(fact_def__d__pair) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 180 (all X0 pp(aa_fun171081125l_bool(scratc1809285542all_of(aa_TPT43085870d_bool(aTP_Lamm_ed,X0)),aa_TPT43085870d_bool(aTP_Lamm_ef,X0)))) # label(fact_isseti) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 181 (all X all Xa (pp(scratc352032638nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc851743993_29_ii,X),Xa),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301873271nd_iii,X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc123222581_prop1,X),Xa)))) # label(fact_def__d__29__prop1) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 182 (all Uu (pp(aa_fun171081125l_bool(scratc1809285542all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cy,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cz,Uu)))) # label(fact_ATP_Olambda__21) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 183 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_db,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1809285542all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_da(Uu),Uua))))) # label(fact_ATP_Olambda__74) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 184 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X22),aa_fun1431113780TP_ind(scratc750595372_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X22),X0)))) # label(fact_k__SepE1) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 185 (all X all Xa scratc352229500nd_out(X,Xa) = scratc2050779516d_soft(aa_fun1431113780TP_ind(scratc750595372_d_Sep(X),Xa),X,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc314255827_Sigma,aa_fun1431113780TP_ind(scratc750595372_d_Sep(X),Xa)),scratc1535264952d_e_in(X,Xa)))) # label(fact_def__out) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 186 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ey(Uu),Uua),Uub),Uuc)) <-> (pp(aa_fun171081125l_bool(scratc1809285542all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ex(Uua),Uub),Uuc))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1535264957d_e_is(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc394060683d_d_Pi,Uu),aTP_Lamm_ai(Uua))),Uub),Uuc))))) # label(fact_ATP_Olambda__119) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 187 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1893941365d_esti(Uu),Uub),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_au(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__84) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 188 (all X scratc1535264957d_e_is(X) = fequal_TPTP_ind) # label(fact_def__e__is) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 189 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc350696096fixfu2(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1809285542all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_an(X),Xa),Xb),Xc))))) # label(fact_def__fixfu2) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 190 (all Q all P (pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)) | -pp(Q))) # label(help_fimplies_2_1_U) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 191 (all P (gg_bool(P) -> P = fFalse | fTrue = P)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 192 (all X all Xa all Xb (pp(scratc866846821_d_and(X,scratc866846821_d_and(Xa,Xb))) <-> scratc876719054d_and3(X,Xa,Xb))) # label(fact_def__and3) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 193 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1867234683_empty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1809285542all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),scratc343574395nd_non(X,aa_TPT43085870d_bool(aTP_Lamm_au(X),Xa)))))) # label(fact_def__empty) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 194 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,Uub),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc394060683d_d_Pi,Uu),aTP_Lamm_ai(Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ew(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__102) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 195 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1809285542all_of(aa_TPT43085870d_bool(aTP_Lamm_em(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_eo(X0),X12)))) # label(fact_second__p) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 196 (all X all Xa scratc1489965350second(X,Xa) = scratc1116591106_proj1) # label(fact_def__second) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 197 (all Uu all Uua (gg_TPTP_ind(Uua) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bg,Uu),Uua)) <-> (exists X3 (Uua = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1741037292d_pair,Uu),X3) & gg_TPTP_ind(X3)))))) # label(fact_ATP_Olambda__80) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 198 (all P all Q (-pp(P) | pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)) | -pp(Q))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 199 (all X all Xa scratc1034216065bnd_ap = scratc683883066d_tofs(X,Xa)) # label(fact_def__tofs) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 200 (all X all Xa all Xb all Xc all Xd aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc314255827_Sigma,X),aa_TPT1424761345TP_ind(aTP_Lamm_aw(Xc),Xd)) = aa_TPTP_ind_TPTP_ind(scratc472012085_inj_h(X,Xa,Xb,Xc),Xd)) # label(fact_def__inj__h) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 201 (all Uu all Uua all Uub all Uuc all Uud ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1535264957d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,Uub),Uud)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_ao(Uu),Uua),Uub),Uuc),Uud)))) # label(fact_ATP_Olambda__126) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 202 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1495339133_union,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1188233249d_repl,X),Xa)) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc715558191munion,X),Xa)) # label(fact_def__famunion) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 203 (all X0 all X12 all X22 ((pp(X0) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X12),X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,aa_TPTP_ind_TPTP_ind(scratc1034740847bnd_if(X0,X12),scratc350117639ptyset)),aa_TPTP_ind_TPTP_ind(scratc1034740847bnd_if(X0,X22),aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,scratc350117639ptyset)))))) # label(fact_k__If__In__01) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 204 (all B_1 all B_2 gg_TPTP_ind(scratc302201261nd_ind(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__42811__30845_ONUM653__thf__4__p_Obnd__ind) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 205 (all X0 pp(aa_TPTP_ind_bool(scratc1084974186closed,aa_TPTP_ind_TPTP_ind(scratc51608559univof,X0)))) # label(fact_k__UnivOf__ZF__closed) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 206 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc314255827_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1741037292d_pair,aa_TPTP_ind_TPTP_ind(scratc1116591105_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1116591106_proj1,X22)) = X22))) # label(fact_proj__Sigma__eta) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 207 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc804593329moreis,X),Xa)) <-> pp(aa_bool_bool(scratc922673981d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc851743993_29_ii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,X),Xa))))) # label(fact_def__moreis) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 208 (all X all Xa (pp(scratc1595289704_amone(X,Xa)) <-> pp(aa_fun171081125l_bool(scratc1809285542all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)),aa_fun1584354236d_bool(aTP_Lamm_bd(X),Xa))))) # label(fact_def__amone) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 209 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cc,Uu),Uua)) <-> pp(scratc352032638nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc851743993_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301873271nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__43) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 210 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cg,Uu),Uua)) <-> pp(scratc268433603nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1663770992n_some,aa_TPT43085870d_bool(scratc1632014586ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc1663770992n_some,aa_TPT43085870d_bool(scratc1632014586ffprop(Uua),Uu)))))) # label(fact_ATP_Olambda__47) # label(axiom) # label(non_clause). [assumption]. 0.74/1.04 211 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X22),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc314255827_Sigma,X0),X12)),X22) = aa_TPTP_ind_TPTP_ind(X12,X22))) # label(fact_beta) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 212 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1809285542all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ek(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_el(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__100) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 213 (all X all Xa all Xb all Xc scratc302201261nd_ind(Xa,aa_TPT43085870d_bool(scratc1116984700_prop1(X,Xa,Xb),Xc)) = aa_TPTP_ind_TPTP_ind(scratc302594856nd_ite(X,Xa,Xb),Xc)) # label(fact_def__ite) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 214 (all X all Xa all Xb all Xc all Xd aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc314255827_Sigma,X),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_av(X),Xb),Xc),Xd)) = aa_TPTP_ind_TPTP_ind(scratc304118116hangef(X,Xa,Xb,Xc),Xd)) # label(fact_def__changef) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 215 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dq,Uu)) <-> pp(aa_fun171081125l_bool(scratc351770292nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc394060683d_d_Pi,scratc342656015nd_nat),aTP_Lamm_ac)),aa_TPT43085870d_bool(aTP_Lamm_dp,Uu))))) # label(fact_ATP_Olambda__5) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 216 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ea,Uu)) <-> pp(aa_fun171081125l_bool(scratc1809285542all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dz,Uu))))) # label(fact_ATP_Olambda__14) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 217 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2042537327t_disj(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc235978031nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_as(X),Xa),Xb))))) # label(fact_def__st__disj) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 218 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ar(Uu),Uua),Uub),Uuc)) <-> pp(aa_fun171081125l_bool(scratc919946350l_some(Uua),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aq(Uu),Uub),Uuc))))) # label(fact_ATP_Olambda__124) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 219 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,Uu),scratc342656015nd_nat)) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_a,Uu)))) # label(fact_ATP_Olambda__13) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 220 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc351770292nd_one(X0),X12)) -> scratc1879391219_is_of(scratc302201261nd_ind(X0,X12),aa_TPT43085870d_bool(aTP_Lamm_aj,X0)))) # label(fact_ind__p) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 221 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_be(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1495339133_union,aa_TPTP_ind_TPTP_ind(Uu,Uua))) # label(fact_ATP_Olambda__79) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 222 (all X all Xa ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X2),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X2),Xa))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc931992291d_Subq,X),Xa)))) # label(fact_def__d__Subq) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 223 (all X all Xa ((all X2 (gg_TPTP_ind(X2) -> (scratc1879391219_is_of(X2,X) -> pp(aa_TPTP_ind_bool(Xa,X2))))) <-> pp(aa_fun171081125l_bool(scratc1809285542all_of(X),Xa)))) # label(fact_def__all__of) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 224 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc290159166nverse(X,Xa),Xb) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc314255827_Sigma,Xa),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_ax(X),Xa),Xb))) # label(fact_def__inverse) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 225 (all Uu (pp(aa_fun171081125l_bool(scratc1809285542all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dd,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_de,Uu)))) # label(fact_ATP_Olambda__19) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 226 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1809285542all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_TPT43085870d_bool(aTP_Lamm_er(X0),X12)))) # label(fact_e__pair__p) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 227 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2043586645ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc235978031nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ba(X),Xa),Xb))))) # label(fact_def__injective) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 228 (all X (pp(aa_TPTP_ind_bool(scratc1084974186closed,X)) <-> pp(aa_TPTP_ind_bool(scratc1527012265closed,X)) & pp(aa_TPTP_ind_bool(scratc388875789closed,X)) & pp(aa_TPTP_ind_bool(scratc1691745279closed,X)))) # label(fact_def__d__ZF__closed) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 229 (all X ((all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,aa_TPTP_ind_TPTP_ind(scratc988077267_power,X1)),X))))) <-> pp(aa_TPTP_ind_bool(scratc1691745279closed,X)))) # label(fact_def__d__Power__closed) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 230 (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]. 0.74/1.05 231 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1809285542all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_fa(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_fb(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__97) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 232 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ef,Uu),Uua)) <-> pp(aa_fun171081125l_bool(scratc1809285542all_of(aa_TPT43085870d_bool(aTP_Lamm_ed,Uu)),aa_TPT43085870d_bool(aTP_Lamm_ee(Uu),Uua))))) # label(fact_ATP_Olambda__64) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 233 (all X aa_TPTP_ind_TPTP_ind(scratc1658749085d_Inj0,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1188233249d_repl,X),scratc1658749086d_Inj1)) # label(fact_def__d__Inj0) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 234 (all Uu all Uua all Uub all Uuc (pp(aa_fun171081125l_bool(scratc235978031nd_all(Uu),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_az(Uu),Uua),Uub),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ba(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__123) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 235 (all X all Xa scratc302201261nd_ind(X,Xa) = scratc269286454nd_eps(aa_fun1584354236d_bool(aTP_Lamm_bb(X),Xa))) # label(fact_def__ind) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 236 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc862722622ectset(X,Xa),aa_TPTP_ind_TPTP_ind(scratc412412285_ecelt(X,Xa),Xb)) = aa_TPTP_ind_TPTP_ind(scratc747520745ectelt(X,Xa),Xb)) # label(fact_def__ectelt) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 237 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1809285542all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X0)),aa_fun1584354236d_bool(aTP_Lamm_fb(X0),X12)))) # label(fact_e__isp) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 238 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(Uu),scratc162683829nd_n_1))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_di,Uu)))) # label(fact_ATP_Olambda__7) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 239 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc670609717lessis,X),Xa)) <-> pp(aa_bool_bool(scratc922673981d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301873271nd_iii,X),Xa)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,X),Xa))))) # label(fact_def__lessis) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 240 (all Uu (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(Uu),scratc162683829nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_do,Uu)))) # label(fact_ATP_Olambda__3) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 241 (all X0 all X12 all X22 (gg_TPTP_ind(X22) & gg_TPTP_ind(X12) -> aa_TPTP_ind_TPTP_ind(scratc1034740847bnd_if(X0,X12),X22) = X12 | X22 = aa_TPTP_ind_TPTP_ind(scratc1034740847bnd_if(X0,X12),X22))) # label(fact_if__i__or) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 242 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aj,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,Uua),Uu)))) # label(fact_ATP_Olambda__73) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 243 (all X all Xa all Xb aa_fun1431113780TP_ind(scratc750595372_d_Sep(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ar(X),Xa),Xb)) = aa_TPTP_ind_TPTP_ind(scratc968839968unmore(X,Xa),Xb)) # label(fact_def__unmore) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 244 (all X aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc314255827_Sigma,scratc342656015nd_nat),aTP_Lamm_ad(X)) = aa_TPTP_ind_TPTP_ind(scratc727397299d_24_g,X)) # label(fact_def__d__24__g) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 245 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dj,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__51) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 246 (all B_1 gg_TPTP_ind(scratc269286454nd_eps(B_1))) # label(gsy_c_Scratch__tptp__translate__42811__30845_ONUM653__thf__4__p_Obnd__eps) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 247 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1809285542all_of(aa_TPT43085870d_bool(aTP_Lamm_ew(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_ez(X0),X12)))) # label(fact_e__fisi) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 248 (all X0 (gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(scratc1766035425_nat_p,X0)) -> X0 = scratc350117639ptyset | (exists X13 (gg_TPTP_ind(X13) & aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,X13) = X0 & pp(aa_TPTP_ind_bool(scratc1766035425_nat_p,X13))))))) # label(fact_nat__inv) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 249 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc988077267_power,X0))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc931992291d_Subq,X12),X0)))) # label(fact_k__PowerE) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 250 (all X all Xa scratc2097791837eplSep(X,Xa) = aa_TPT494704832TP_ind(scratc1188233249d_repl,aa_fun1431113780TP_ind(scratc750595372_d_Sep(X),Xa))) # label(fact_def__d__ReplSep) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 251 (all X aa_TPTP_ind_TPTP_ind(scratc1832701036d_plus,X) = scratc302201261nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc394060683d_d_Pi,scratc342656015nd_nat),aTP_Lamm_ac),aa_TPT43085870d_bool(scratc1476379003_prop2,X))) # label(fact_def__plus) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 252 (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]. 0.74/1.05 253 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ex(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1535264957d_e_is(Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,Uua),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,Uub),Uuc))))) # label(fact_ATP_Olambda__113) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 254 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cm,Uu),Uua)) <-> scratc2041436224_orec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1663770992n_some,aa_TPT43085870d_bool(aTP_Lamm_ck(Uu),Uua)),aa_fun171081125l_bool(scratc1663770992n_some,aa_TPT43085870d_bool(aTP_Lamm_cl(Uu),Uua))))) # label(fact_ATP_Olambda__45) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 255 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1709415290nunion(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1188233249d_repl,X),scratc1658749085d_Inj0)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1188233249d_repl,Xa),scratc1658749086d_Inj1)) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1741037292d_pair,X),Xa)) # label(fact_def__pair) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 256 (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]. 0.74/1.05 257 (all X all Xa all Xb all Xc all Xd scratc302201261nd_ind(Xb,aa_TPT43085870d_bool(scratc1116984701_prop2(X,Xa,Xb,Xc),Xd)) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc663506041_indeq(X,Xa,Xb),Xc),Xd)) # label(fact_def__indeq) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 258 (all Uu all Uua all Uub all Uuc all Uud all Uue all 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(scratc1535264957d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,Uub),Uuc)),Uue)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,Uub),Uud)),Uuf))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_ak(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)))) # label(fact_ATP_Olambda__131) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 259 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc314255827_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,aa_TPTP_ind_TPTP_ind(scratc1116591106_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1116591105_proj0,X22)))))) # label(fact_proj1__Sigma) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 260 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc931992291d_Subq,X12),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc988077267_power,X0))))) # label(fact_k__PowerI) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 261 (all X all Xa all Xb (pp(scratc866846821_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2043586645ective(X),Xa),Xb),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1070076558ective(X),Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79822227ective(X),Xa),Xb)))) # label(fact_def__bijective) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 262 (all P all Q all R aa_TPTP_ind_bool(aa_TPT43085870d_bool(P,R),Q) = aa_TPTP_ind_bool(aa_TPT43085870d_bool(cOMBC_1555011498d_bool(P),Q),R)) # label(help_COMBC_1_1_COMBC_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind_001t__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 263 (all P all Q (pp(P) | -pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 264 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc51608559univof,X0)))) # label(fact_k__UnivOf__In) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 265 (all X0 (pp(aa_TPTP_ind_bool(X0,scratc350117639ptyset)) -> ((all X13 (gg_TPTP_ind(X13) -> (pp(aa_TPTP_ind_bool(scratc1766035425_nat_p,X13)) -> (pp(aa_TPTP_ind_bool(X0,X13)) -> pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,X13))))))) -> (all X12 (pp(aa_TPTP_ind_bool(scratc1766035425_nat_p,X12)) -> pp(aa_TPTP_ind_bool(X0,X12))))))) # label(fact_nat__ind) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 266 (all X all Xa all Xb (pp(scratc866846821_d_and(scratc352032638nd_or3(X,Xa,Xb),scratc268433603nd_ec3(X,Xa,Xb))) <-> scratc2041436224_orec3(X,Xa,Xb))) # label(fact_def__orec3) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 267 (all X all Xa (pp(scratc974312001_d_not(scratc922017976d_l_ec(X,Xa))) <-> pp(scratc866846821_d_and(X,Xa)))) # label(fact_def__d__and) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 268 (all X0 all X12 all X22 (gg_TPTP_ind(X12) -> (pp(X0) -> X12 = aa_TPTP_ind_TPTP_ind(scratc1034740847bnd_if(X0,X12),X22)))) # label(fact_if__i__1) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 269 (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]. 0.74/1.05 270 (all Uu all Uua all Uub (scratc1879391219_is_of(aa_TPTP_ind_TPTP_ind(scratc1489965350second(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_aj,Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_eo(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__87) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 271 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc876784701d_anec(X,Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc919946350l_some(X),aa_TPT43085870d_bool(scratc268433664nd_ecp(X,Xa),Xb))))) # label(fact_def__anec) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 272 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (-pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc1034740847bnd_if(X0,X12),X22) = X22))) # label(fact_if__i__0) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 273 (all X (pp(scratc974312001_d_not(X)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc302135674nd_imp,X),fFalse)))) # label(fact_def__d__not) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 274 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_en(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1535264957d_e_is(aa_TPTP_ind_TPTP_ind(scratc525834567etprod(Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1929413676d_pair(Uu,Uua),aa_TPTP_ind_TPTP_ind(scratc2048391230_first(Uu,Uua),Uub)),aa_TPTP_ind_TPTP_ind(scratc1489965350second(Uu,Uua),Uub))),Uub)))) # label(fact_ATP_Olambda__81) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 275 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cd,Uu)) <-> pp(aa_fun171081125l_bool(scratc1809285542all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cc,Uu))))) # label(fact_ATP_Olambda__30) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 276 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ca,Uu),Uua)) <-> pp(scratc268433603nd_ec3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc851743993_29_ii,Uu),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301873271nd_iii,Uu),Uua))))) # label(fact_ATP_Olambda__44) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 277 (all X all Xa aa_fun277296641TP_ind(scratc2097791837eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bg,Xa)),scratc1116591106_proj1) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,X),Xa)) # label(fact_def__ap) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 278 (all Uu (pp(aa_fun171081125l_bool(scratc1809285542all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bw,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu)))) # label(fact_ATP_Olambda__33) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 279 (all Uu (gg_TPTP_ind(Uu) -> (pp(aa_TPTP_ind_bool(aTP_Lamm_ah,Uu)) <-> scratc350117639ptyset != Uu))) # label(fact_ATP_Olambda__39) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 280 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc988077267_power,X0)))) # label(fact_k__Self__In__Power) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 281 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_by,Uu),Uua)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc851743993_29_ii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301873271nd_iii,Uua),Uu))))) # label(fact_ATP_Olambda__57) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 282 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1495339133_union,aa_TPTP_ind_TPTP_ind(scratc208742205_UPair(X),Xa)) = aa_TPTP_ind_TPTP_ind(scratc1709415290nunion(X),Xa)) # label(fact_def__binunion) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 283 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X22),X0)) -> (pp(aa_TPTP_ind_bool(X12,X22)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X22),aa_fun1431113780TP_ind(scratc750595372_d_Sep(X0),X12)))))) # label(fact_k__SepI) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 284 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_eg(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1893941365d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc750595372_d_Sep(Uu),Uua))) -> pp(aa_TPTP_ind_bool(Uua,Uub))))) # label(fact_ATP_Olambda__85) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 285 (all X all Xa all Xb all Xc all Xd (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1116984700_prop1(X,Xa,Xb),Xc),Xd)) <-> pp(scratc866846821_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc302135674nd_imp,X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1535264957d_e_is(Xa),Xd),Xb)),aa_bool_bool(aa_boo1142376798l_bool(scratc302135674nd_imp,scratc974312001_d_not(X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1535264957d_e_is(Xa),Xd),Xc)))))) # label(fact_def__prop1) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 286 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dw,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,Uu),aa_TPTP_ind_TPTP_ind(scratc988077267_power,scratc342656015nd_nat))))) # label(fact_ATP_Olambda__12) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 287 (all B_1 all B_2 all B_3 gg_bool(scratc268433603nd_ec3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__42811__30845_ONUM653__thf__4__p_Obnd__ec3) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 288 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,Uua),aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(Uu),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cl(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__104) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 289 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ci,Uu),Uua)) <-> pp(scratc352032638nd_or3(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,Uu),Uua),aa_fun171081125l_bool(scratc1663770992n_some,aa_TPT43085870d_bool(scratc1632014586ffprop(Uu),Uua)),aa_fun171081125l_bool(scratc1663770992n_some,aa_TPT43085870d_bool(scratc1632014586ffprop(Uua),Uu)))))) # label(fact_ATP_Olambda__46) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 290 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc351770292nd_one(X0),X12)) -> pp(aa_TPTP_ind_bool(X12,scratc302201261nd_ind(X0,X12))))) # label(fact_oneax) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 291 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_dv,Uu)) <-> pp(aa_fun171081125l_bool(scratc1809285542all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_du,Uu))))) # label(fact_ATP_Olambda__15) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 292 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ds,Uu)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc343180806nd_nis,Uu),scratc162683829nd_n_1)) -> pp(aa_fun171081125l_bool(scratc1663770992n_some,aa_TPT43085870d_bool(aTP_Lamm_af,Uu)))))) # label(fact_ATP_Olambda__1) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 293 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ay(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1535264957d_e_is(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__115) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 294 (all Uu ((pp(aa_TPTP_ind_bool(scratc1131707837_cond1,Uu)) -> (pp(aa_TPTP_ind_bool(scratc1131707838_cond2,Uu)) -> pp(aa_fun171081125l_bool(scratc1809285542all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_dx,Uu))))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_dy,Uu)))) # label(fact_ATP_Olambda__6) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 295 (all Uu (scratc1879391219_is_of(aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,Uu),aTP_Lamm_a) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ec,Uu)))) # label(fact_ATP_Olambda__10) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 296 (all Uu (gg_TPTP_ind(Uu) -> ((exists X2 (Uu = aa_TPTP_ind_TPTP_ind(scratc1658749085d_Inj0,X2) & gg_TPTP_ind(X2))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_bj,Uu))))) # label(fact_ATP_Olambda__41) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 297 (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]. 0.74/1.05 298 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925313d_n_in,Uua),Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dx,Uu),Uua)))) # label(fact_ATP_Olambda__71) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 299 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc314255827_Sigma,X),aTP_Lamm_ai(Xa)) = aa_TPTP_ind_TPTP_ind(scratc525834567etprod(X),Xa)) # label(fact_def__setprod) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 300 (all X all Xa (scratc1316952766d_r_ec(X,Xa) <-> (pp(X) -> pp(scratc974312001_d_not(Xa))))) # label(fact_def__r__ec) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 301 (all Uu all Uua all Uub all Uuc all Uud aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_av(Uu),Uua),Uub),Uuc),Uud) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,aa_TPTP_ind_TPTP_ind(scratc730749419wissel(Uu,Uub),Uuc)),Uud))) # label(fact_ATP_Olambda__129) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 302 (all X scratc1809285542all_of(aa_TPT43085870d_bool(aTP_Lamm_aj,X)) = scratc235978031nd_all(X)) # label(fact_def__all) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 303 (all X0 all X12 all X22 all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc394060683d_d_Pi,X0),X12))) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X32),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,X22),X32)),aa_TPTP_ind_TPTP_ind(X12,X32)))))) # label(fact_ap__Pi) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 304 (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(scratc670609717lessis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc804593329moreis,Uua),Uu))))) # label(fact_ATP_Olambda__59) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 305 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc343180806nd_nis,Xa),aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1093981879_prop1,X),Xa)))) # label(fact_def__d__27__prop1) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 306 (all X0 (pp(aa_TPTP_ind_bool(scratc1766035425_nat_p,X0)) -> pp(aa_TPTP_ind_bool(scratc1766035425_nat_p,aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,X0))))) # label(fact_nat__ordsucc) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 307 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc1473700950sel_wb(X,Xa,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc302594856nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1535264957d_e_is(X),Xc),Xb),X,Xa),aa_TPTP_ind_TPTP_ind(scratc1473700949sel_wa(X,Xa,Xb),Xc))) # label(fact_def__wissel__wb) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 308 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc343180806nd_nis,aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(X),Xa)),aa_TPTP_ind_TPTP_ind(scratc1054384504d_n_pl(X),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1682344054_prop1(X),Xa),Xb)))) # label(fact_def__d__28__prop1) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 309 (all X all Xa scratc352229500nd_out(aa_TPTP_ind_TPTP_ind(scratc988077267_power,X),scratc876784701d_anec(X,Xa)) = scratc862722622ectset(X,Xa)) # label(fact_def__ectset) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 310 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301873271nd_iii,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc851743993_29_ii,Uua),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bw,Uu),Uua)))) # label(fact_ATP_Olambda__60) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 311 (all X aa_TPTP_ind_TPTP_ind(scratc833641409d_Sing,X) = aa_TPTP_ind_TPTP_ind(scratc208742205_UPair(X),X)) # label(fact_def__d__Sing) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 312 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc394060683d_d_Pi,X0),X12))) -> (all X32 (gg_TPTP_ind(X32) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X32),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc394060683d_d_Pi,X0),X12))) -> ((all X42 (gg_TPTP_ind(X42) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X42),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,X32),X42) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,X22),X42)))) -> X22 = X32))))))) # label(fact_k__Pi__ext) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 313 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc343180806nd_nis,X),Xa)) <-> pp(scratc974312001_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,X),Xa))))) # label(fact_def__nis) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 314 (all Uu all Uua (pp(aa_bool_bool(aa_boo1142376798l_bool(scratc302135674nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925313d_n_in,Uua),Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925313d_n_in,aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,Uua)),Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ag,Uu),Uua)))) # label(fact_ATP_Olambda__55) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 315 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_af,Uu),Uua)))) # label(fact_ATP_Olambda__69) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 316 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cb,Uu)) <-> pp(aa_fun171081125l_bool(scratc1809285542all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ca,Uu))))) # label(fact_ATP_Olambda__31) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 317 (all Uu all Uua all Uub all Uuc (pp(aa_bool_bool(aa_boo1142376798l_bool(scratc302135674nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1893941365d_esti(Uu),Uuc),Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1893941365d_esti(Uu),Uuc),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_at(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__118) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 318 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1893941365d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc750595372_d_Sep(Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_eh(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__96) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 319 (all P all Q (pp(Q) | -pp(P) | -pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 320 (all Uu all Uua all Uub ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X3),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,Uub),X3)),aa_TPTP_ind_TPTP_ind(Uua,X3)))))) <-> pp(aa_TPTP_ind_bool(aa_fun1913827119d_bool(aTP_Lamm_bf(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__109) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 321 (all Uu (pp(aa_fun171081125l_bool(scratc1809285542all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cr,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cs,Uu)))) # label(fact_ATP_Olambda__24) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 322 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cx,Uu)) <-> pp(aa_fun171081125l_bool(scratc1809285542all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cw,Uu))))) # label(fact_ATP_Olambda__22) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 323 (all X all Xa aa_fun1431113780TP_ind(scratc750595372_d_Sep(aa_TPTP_ind_TPTP_ind(scratc988077267_power,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc314255827_Sigma,X),aTP_Lamm_be(Xa)))),aa_fun1913827119d_bool(aTP_Lamm_bf(X),Xa)) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc394060683d_d_Pi,X),Xa)) # label(fact_def__d__Pi) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 324 (all Uu all Uua (pp(scratc866846821_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1053925318d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1034216065bnd_ap,Uua),scratc162683829nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc891911473rdsucc,Uu)),aa_fun171081125l_bool(scratc291820645_n_all,aa_TPT43085870d_bool(aTP_Lamm_ae,Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dp,Uu),Uua)))) # label(fact_ATP_Olambda__49) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 325 (all X0 all X12 (gg_TPTP_ind(X0) -> aa_TPTP_ind_TPTP_ind(scratc1116591105_proj0,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1741037292d_pair,X0),X12)) = X0)) # label(fact_proj0__pair__eq) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 326 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bm,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc341081633nd_nIn,Uua),Uu)))) # label(fact_ATP_Olambda__72) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 327 (all X all Xa (pp(scratc866846821_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc302135674nd_imp,X),Xa),aa_bool_bool(aa_boo1142376798l_bool(scratc302135674nd_imp,Xa),X))) <-> scratc1760988271_l_iff(X,Xa))) # label(fact_def__l__iff) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 328 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc804593329moreis,Uu),Uua)) -> pp(scratc974312001_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301873271nd_iii,Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bq,Uu),Uua)))) # label(fact_ATP_Olambda__61) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 329 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1034740855bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc988077267_power,X0))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc931992291d_Subq,X12),X0)))) # label(fact_k__PowerEq) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 330 (all Uu (pp(aa_fun171081125l_bool(scratc1809285542all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cu,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cv,Uu)))) # label(fact_ATP_Olambda__23) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 331 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1809285542all_of(aa_TPT43085870d_bool(aTP_Lamm_em(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_ep(X0),X12)))) # label(fact_first__p) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 332 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc678900160d_incl(Uu),Uua),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc678900160d_incl(Uu),Uub),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1535264957d_e_is(aa_TPTP_ind_TPTP_ind(scratc988077267_power,Uu)),Uua),Uub)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ee(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__86) # label(axiom) # label(non_clause). [assumption]. 0.74/1.05 333 (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]. 0.84/1.10 0.84/1.10 ============================== end of process non-clausal formulas === 0.84/1.10 0.84/1.10 ============================== PROCESS INITIAL CLAUSES =============== 0.84/1.10 0.84/1.10 ============================== PREDICATE ELIMINATION ================= 0.84/1.10 334 -gg_bool(A) | A = fFalse | A = fTrue # label(help_fFalse_1_1_T) # label(axiom). [clausify(191)]. 0.84/1.10 335 gg_bool(scratc866846821_d_and(A,B)) # label(gsy_c_Scratch__tptp__translate__42811__30845_ONUM653__thf__4__p_Obnd__d__and) # label(axiom). [clausify(14)]. 0.84/1.10 336 gg_bool(fFalse) # label(gsy_c_fFalse) # label(axiom). [assumption]. 0.84/1.10 337 gg_bool(fTrue) # label(gsy_c_fTrue) # label(axiom). [assumption]. 0.84/1.10 338 gg_bool(scratc352032638nd_or3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__42811__30845_ONUM653__thf__4__p_Obnd__or3) # label(axiom). [clausify(59)]. 0.84/1.10 339 gg_bool(aa_bool_bool(A,B)) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom). [clausify(61)]. 0.84/1.10 340 gg_bool(fEx_TPTP_ind(A)) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom). [clausify(75)]. 0.84/1.10 341 gg_bool(scratc922017976d_l_ec(A,B)) # label(gsy_c_Scratch__tptp__translate__42811__30845_ONUM653__thf__4__p_Obnd__l__ec) # label(axiom). [clausify(99)]. 0.84/1.10 342 gg_bool(scratc1595289704_amone(A,B)) # label(gsy_c_Scratch__tptp__translate__42811__30845_ONUM653__thf__4__p_Obnd__amone) # label(axiom). [clausify(150)]. 0.84/1.10 343 gg_bool(scratc974312001_d_not(A)) # label(gsy_c_Scratch__tptp__translate__42811__30845_ONUM653__thf__4__p_Obnd__d__not) # label(axiom). [clausify(159)]. 0.84/1.10 Derived: scratc866846821_d_and(A,B) = fFalse | scratc866846821_d_and(A,B) = fTrue. [resolve(334,a,335,a)]. 0.84/1.10 Derived: fFalse = fFalse | fFalse = fTrue. [resolve(334,a,336,a)]. 0.84/1.10 Derived: fTrue = fFalse | fTrue = fTrue. [resolve(334,a,337,a)]. 0.84/1.10 Derived: scratc352032638nd_or3(A,B,C) = fFalse | scratc352032638nd_or3(A,B,C) = fTrue. [resolve(334,a,338,a)]. 0.84/1.10 Derived: aa_bool_bool(A,B) = fFalse | aa_bool_bool(A,B) = fTrue. [resolve(334,a,339,a)]. 0.84/1.10 Derived: fEx_TPTP_ind(A) = fFalse | fEx_TPTP_ind(A) = fTrue. [resolve(334,a,340,a)]. 0.84/1.10 Derived: scratc922017976d_l_ec(A,B) = fFalse | scratc922017976d_l_ec(A,B) = fTrue. [resolve(334,a,341,a)]. 0.84/1.10 Derived: scratc1595289704_amone(A,B) = fFalse | scratc1595289704_amone(A,B) = fTrue. [resolve(334,a,342,a)]. 0.84/1.10 Derived: scratc974312001_d_not(A) = fFalse | scratc974312001_d_not(A) = fTrue. [resolve(334,a,343,a)]. 0.84/1.10 344 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(252)]. 0.84/1.10 Derived: aa_fun171081125l_bool(A,B) = fFalse | aa_fun171081125l_bool(A,B) = fTrue. [resolve(344,a,334,a)]. 0.84/1.10 345 gg_bool(scratc268433603nd_ec3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__42811__30845_ONUM653__thf__4__p_Obnd__ec3) # label(axiom). [clausify(287)]. 0.84/1.10 Derived: scratc268433603nd_ec3(A,B,C) = fFalse | scratc268433603nd_ec3(A,B,C) = fTrue. [resolve(345,a,334,a)]. 0.84/1.10 346 gg_bool(undefined_bool(bool)) # label(gsy_c_HOL_Oundefined_001t__HOL__Obool) # label(axiom). [assumption]. 0.84/1.10 Derived: undefined_bool(bool) = fFalse | undefined_bool(bool) = fTrue. [resolve(346,a,334,a)]. 0.84/1.10 347 gg_bool(aa_TPTP_ind_bool(A,B)) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom). [clausify(297)]. 0.84/1.10 Derived: aa_TPTP_ind_bool(A,B) = fFalse | aa_TPTP_ind_bool(A,B) = fTrue. [resolve(347,a,334,a)]. 0.84/1.10 348 scratc417271948nd_wel(A) | -pp(scratc974312001_d_not(scratc974312001_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(16)]. 0.84/1.10 349 -scratc417271948nd_wel(A) | pp(scratc974312001_d_not(scratc974312001_d_not(A))) # label(fact_def__wel) # label(axiom). [clausify(16)]. 0.84/1.10 350 -scratc417271948nd_wel(A) | pp(A) # label(fact_l__et) # label(axiom). [clausify(103)]. 0.84/1.10 Derived: pp(A) | -pp(scratc974312001_d_not(scratc974312001_d_not(A))). [resolve(350,a,348,a)]. 0.84/1.10 351 pp(scratc866846821_d_and(aa_bool_bool(scratc922673981d_l_or(A),B),scratc922017976d_l_ec(A,B))) | -scratc1100633267d_orec(A,B) # label(fact_def__orec) # label(axiom). [clausify(39)]. 0.98/1.29 352 -pp(scratc866846821_d_and(aa_bool_bool(scratc922673981d_l_or(A),B),scratc922017976d_l_ec(A,B))) | scratc1100633267d_orec(A,B) # label(fact_def__orec) # label(axiom). [clausify(39)]. 0.98/1.29 353 scratc1316952766d_r_ec(A,B) | pp(A) # label(fact_def__r__ec) # label(axiom). [clausify(300)]. 0.98/1.29 354 -scratc1316952766d_r_ec(A,B) | -pp(A) | pp(scratc974312001_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(300)]. 0.98/1.29 355 scratc1316952766d_r_ec(A,B) | -pp(scratc974312001_d_not(B)) # label(fact_def__r__ec) # label(axiom). [clausify(300)]. 0.98/1.29 356 pp(scratc866846821_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc302135674nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc302135674nd_imp,B),A))) | -scratc1760988271_l_iff(A,B) # label(fact_def__l__iff) # label(axiom). [clausify(327)]. 0.98/1.29 357 -pp(scratc866846821_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc302135674nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc302135674nd_imp,B),A))) | scratc1760988271_l_iff(A,B) # label(fact_def__l__iff) # label(axiom). [clausify(327)]. 0.98/1.29 0.98/1.29 ============================== end predicate elimination ============= 0.98/1.29 0.98/1.29 Auto_denials: (non-Horn, no changes). 0.98/1.29 0.98/1.29 Term ordering decisions: 0.98/1.29 Function symbol KB weights: scratc1034740855bnd_in=1. aTP_Lamm_a=1. scratc1053925318d_n_is=1. scratc891911473rdsucc=1. scratc1034216065bnd_ap=1. aTP_Lamm_aj=1. scratc350117639ptyset=1. scratc314255827_Sigma=1. scratc343180806nd_nis=1. scratc162683829nd_n_1=1. fFalse=1. scratc1663770992n_some=1. scratc1766035425_nat_p=1. scratc342656015nd_nat=1. scratc394060683d_d_Pi=1. scratc988077267_power=1. scratc1188233249d_repl=1. scratc301873271nd_iii=1. scratc302135674nd_imp=1. scratc851743993_29_ii=1. fTrue=1. scratc1741037292d_pair=1. scratc931992291d_Subq=1. scratc1116591105_proj0=1. scratc1495339133_union=1. scratc388875789closed=1. aTP_Lamm_af=1. scratc1053925313d_n_in=1. scratc1116591106_proj1=1. scratc670609717lessis=1. scratc804593329moreis=1. scratc291820645_n_all=1. aTP_Lamm_ac=1. aTP_Lamm_ae=1. aTP_Lamm_ed=1. scratc1527012265closed=1. scratc1691745279closed=1. aTP_Lamm_aa=1. aTP_Lamm_bq=1. aTP_Lamm_bs=1. aTP_Lamm_bu=1. aTP_Lamm_bw=1. aTP_Lamm_by=1. aTP_Lamm_du=1. aTP_Lamm_dy=1. aTP_Lamm_dz=1. scratc1084974186closed=1. scratc1476379003_prop2=1. scratc1658749086d_Inj1=1. scratc286246319_omega=1. aTP_Lamm_ag=1. aTP_Lamm_bg=1. aTP_Lamm_bi=1. aTP_Lamm_bj=1. aTP_Lamm_ca=1. aTP_Lamm_cc=1. aTP_Lamm_ce=1. aTP_Lamm_cg=1. aTP_Lamm_ci=1. aTP_Lamm_cm=1. aTP_Lamm_co=1. aTP_Lamm_cr=1. aTP_Lamm_cu=1. aTP_Lamm_cw=1. aTP_Lamm_cy=1. aTP_Lamm_db=1. aTP_Lamm_dd=1. aTP_Lamm_dg=1. aTP_Lamm_dj=1. aTP_Lamm_dm=1. aTP_Lamm_dp=1. aTP_Lamm_dr=1. aTP_Lamm_ds=1. aTP_Lamm_dx=1. fconj=1. fimplies=1. scratc1131707838_cond2=1. scratc1476379002_prop1=1. scratc1658749085d_Inj0=1. scratc833641409d_Sing=1. aTP_Lamm_bm=1. aTP_Lamm_br=1. aTP_Lamm_bt=1. aTP_Lamm_bv=1. aTP_Lamm_bx=1. aTP_Lamm_bz=1. aTP_Lamm_cb=1. aTP_Lamm_cd=1. aTP_Lamm_cf=1. aTP_Lamm_ch=1. aTP_Lamm_cj=1. aTP_Lamm_cn=1. aTP_Lamm_cp=1. aTP_Lamm_cs=1. aTP_Lamm_cv=1. aTP_Lamm_cx=1. aTP_Lamm_cz=1. aTP_Lamm_dc=1. aTP_Lamm_de=1. aTP_Lamm_df=1. aTP_Lamm_dh=1. aTP_Lamm_di=1. aTP_Lamm_dk=1. aTP_Lamm_dl=1. aTP_Lamm_dn=1. aTP_Lamm_do=1. aTP_Lamm_dq=1. aTP_Lamm_dt=1. aTP_Lamm_dv=1. aTP_Lamm_dw=1. aTP_Lamm_ea=1. aTP_Lamm_eb=1. aTP_Lamm_ec=1. aTP_Lamm_ef=1. aTP_Lamm_fc=1. fequal_TPTP_ind=1. scratc1131707837_cond1=1. scratc341081633nd_nIn=1. scratc407612906_n_one=1. scratc51608559univof=1. scratc767708767_d_Unj=1. aTP_Lamm_ab=1. aTP_Lamm_ah=1. aTP_Lamm_bk=1. aTP_Lamm_bl=1. bool=1. scratc1093981879_prop1=1. scratc1116984703_prop4=1. scratc123222581_prop1=1. scratc1832701036d_plus=1. scratc1867234683_empty=1. scratc299654652_prop1=1. scratc505619704_prop1=1. scratc635712626nempty=1. scratc715558191munion=1. scratc748661444pair_p=1. scratc888016827_prop1=1. scratc250626041d_i1_s=1. scratc727397299d_24_g=1. tPTP_ind=1. aa_TPTP_ind_bool=1. aa_TPT43085870d_bool=1. aa_TPTP_ind_TPTP_ind=1. aa_fun171081125l_bool=1. aa_TPT1424761345TP_ind=1. aa_TPT60673477d_bool=1. aa_fun277296641TP_ind=1. aa_TPT494704832TP_ind=1. aa_bool_bool=1. aa_fun1584354236d_bool=1. aa_fun1431113780TP_ind=1. aa_boo1142376798l_bool=1. scratc866846821_d_and=1. aa_TPT1123896796d_bool=1. scratc1034740847bnd_if=1. scratc922017976d_l_ec=1. aa_fun1212484691d_bool=1. aa_TPT985247859d_bool=1. scratc1535264952d_e_in=1. scratc1929413676d_pair=1. aa_fun987228051d_bool=1. scratc1595289704_amone=1. scratc302201261nd_ind=1. scratc1489965350second=1. scratc2005749161_image=1. scratc2048391230_first=1. aa_TPT125613450d_bool=1. scratc343574395nd_non=1. aa_fun1913827119d_bool=1. scratc876784701d_anec=1. aa_TPT1791839040TP_ind=1. aa_fun1107270209d_bool=1. aa_fun845057962d_bool=1. scratc2097791837eplSep=1. scratc268433664nd_ecp=1. scratc412412285_ecelt=1. scratc411821894_ecect=1. aa_TPT1781712639TP_ind=1. aa_TPT2142672771l_bool=1. aa_fun1235454963TP_ind=1. cOMBB_658106424TP_ind=1. cOMBS_2003118649l_bool=1. scratc1534331263etprop=1. scratc2097107474_fixfu=1. scratc268433668nd_ect=1. scratc350696096fixfu2=1. scratc352229500nd_out=1. scratc730749419wissel=1. scratc862722622ectset=1. scratc290159166nverse=1. scratc680146535d_invf=1. scratc683883066d_tofs=1. scratc747520745ectelt=1. scratc968839968unmore=1. f8=1. f10=1. f17=1. f18=1. f19=1. scratc1809285542all_of=1. scratc1054384504d_n_pl=1. scratc1535264957d_e_is=1. scratc750595372_d_Sep=1. scratc974312001_d_not=1. scratc1893941365d_esti=1. scratc919946350l_some=1. scratc1632014586ffprop=1. scratc235978031nd_all=1. scratc922673981d_l_or=1. scratc786450286_rec_G=1. aTP_Lamm_ai=1. aTP_Lamm_em=1. scratc351770292nd_one=1. aTP_Lamm_ak=1. aTP_Lamm_au=1. aTP_Lamm_bc=1. aTP_Lamm_bp=1. aTP_Lamm_ck=1. aTP_Lamm_ee=1. aTP_Lamm_fa=1. scratc678900160d_incl=1. aTP_Lamm_ao=1. aTP_Lamm_ay=1. aTP_Lamm_bb=1. aTP_Lamm_bf=1. aTP_Lamm_cq=1. aTP_Lamm_ct=1. aTP_Lamm_ew=1. aTP_Lamm_ey=1. scratc2043586645ective=1. scratc269286454nd_eps=1. scratc525834567etprod=1. aTP_Lamm_al=1. aTP_Lamm_am=1. aTP_Lamm_an=1. aTP_Lamm_ap=1. aTP_Lamm_aq=1. aTP_Lamm_as=1. aTP_Lamm_at=1. aTP_Lamm_az=1. aTP_Lamm_ba=1. aTP_Lamm_bd=1. aTP_Lamm_cl=1. aTP_Lamm_da=1. aTP_Lamm_eg=1. aTP_Lamm_eh=1. aTP_Lamm_ei=1. aTP_Lamm_ek=1. aTP_Lamm_eq=1. aTP_Lamm_es=1. aTP_Lamm_et=1. aTP_Lamm_ex=1. fEx_TPTP_ind=1. scratc1070076558ective=1. scratc1709415290nunion=1. aTP_Lamm_ar=1. aTP_Lamm_ej=1. aTP_Lamm_el=1. aTP_Lamm_en=1. aTP_Lamm_eo=1. aTP_Lamm_ep=1. aTP_Lamm_er=1. aTP_Lamm_eu=1. aTP_Lamm_ev=1. aTP_Lamm_ez=1. aTP_Lamm_fb=1. scratc1825555417In_rec=1. scratc208742205_UPair=1. aTP_Lamm_ad=1. aTP_Lamm_av=1. aTP_Lamm_aw=1. aTP_Lamm_ax=1. aTP_Lamm_be=1. aTP_Lamm_bh=1. aTP_Lamm_bn=1. aTP_Lamm_bo=1. cOMBC_1555011498d_bool=1. scratc1116984702_prop3=1. scratc1625700832tminus=1. scratc1682344054_prop1=1. scratc2042537327t_disj=1. scratc2064741177_prop1=1. scratc79822227ective=1. undefined_bool=1. undefined_TPTP_ind=1. f1=1. f9=1. f11=1. f12=1. f13=1. f16=1. f20=1. f21=1. f22=1. f23=1. scratc352032638nd_or3=1. scratc268433603nd_ec3=1. scratc2050779516d_soft=1. scratc1116984700_prop1=1. scratc302594856nd_ite=1. scratc663506041_indeq=1. scratc1473700949sel_wa=1. scratc1473700950sel_wb=1. scratc1541038711d_11_i=1. f2=1. f3=1. f7=1. f14=1. f15=1. f25=1. scratc1116984701_prop2=1. scratc304118116hangef=1. scratc472012085_inj_h=1. f5=1. f6=1. f24=1. scratc2023701629_prop1=1. scratc134205945indeq2=1. f4=1. 1.86/2.16 1.86/2.16 ============================== end of process initial clauses ======== 1.86/2.16 1.86/2.16 ============================== CLAUSES FOR SEARCH ==================== 1.86/2.16 1.86/2.16 ============================== end of clauses for search ============= 1.86/2.16 1.86/2.16 ============================== SEARCH ================================ 1.86/2.16 1.86/2.16 % Starting search at 0.31 seconds. 1.86/2.16 1.86/2.16 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 83 (0.00 of 0.95 sec). 1.86/2.16 1.86/2.16 Low Water (keep): wt=37.000, iters=3417 1.86/2.16 1.86/2.16 Low Water (keep): wt=36.000, iters=3400 1.86/2.16 1.86/2.16 Low Water (keep): wt=35.000, iters=3373 1.86/2.16 1.86/2.16 Low Water (keep): wt=33.000, iters=3342 1.86/2.16 1.86/2.16 Low Water (keep): wt=32.000, iters=3342 1.86/2.16 1.86/2.16 Low Water (keep): wt=31.000, iters=3357 1.86/2.16 1.86/2.16 Low Water (keep): wt=30.000, iters=3338 1.86/2.16 1.86/2.16 Low Water (keep): wt=29.000, iters=3340 1.86/2.16 1.86/2.16 Low Water (keep): wt=28.000, iters=3349 1.86/2.16 1.86/2.16 Low Water (keep): Alarm clock 179.77/180.03 Prover9 interrupted 179.77/180.03 EOF