0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.12/0.33 % Computer : n021.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 180 0.12/0.33 % DateTime : Thu Aug 29 14:05:04 EDT 2019 0.12/0.33 % CPUTime : 0.93/1.23 ============================== Prover9 =============================== 0.93/1.23 Prover9 (32) version 2009-11A, November 2009. 0.93/1.23 Process 10491 was started by sandbox on n021.cluster.edu, 0.93/1.23 Thu Aug 29 14:05:04 2019 0.93/1.23 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 180 -f /tmp/Prover9_10332_n021.cluster.edu". 0.93/1.23 ============================== end of head =========================== 0.93/1.23 0.93/1.23 ============================== INPUT ================================= 0.93/1.23 0.93/1.23 % Reading from file /tmp/Prover9_10332_n021.cluster.edu 0.93/1.23 0.93/1.23 set(prolog_style_variables). 0.93/1.23 set(auto2). 0.93/1.23 % set(auto2) -> set(auto). 0.93/1.23 % set(auto) -> set(auto_inference). 0.93/1.23 % set(auto) -> set(auto_setup). 0.93/1.23 % set(auto_setup) -> set(predicate_elim). 0.93/1.23 % set(auto_setup) -> assign(eq_defs, unfold). 0.93/1.23 % set(auto) -> set(auto_limits). 0.93/1.23 % set(auto_limits) -> assign(max_weight, "100.000"). 0.93/1.23 % set(auto_limits) -> assign(sos_limit, 20000). 0.93/1.23 % set(auto) -> set(auto_denials). 0.93/1.23 % set(auto) -> set(auto_process). 0.93/1.23 % set(auto2) -> assign(new_constants, 1). 0.93/1.23 % set(auto2) -> assign(fold_denial_max, 3). 0.93/1.23 % set(auto2) -> assign(max_weight, "200.000"). 0.93/1.23 % set(auto2) -> assign(max_hours, 1). 0.93/1.23 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.93/1.23 % set(auto2) -> assign(max_seconds, 0). 0.93/1.23 % set(auto2) -> assign(max_minutes, 5). 0.93/1.23 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.93/1.23 % set(auto2) -> set(sort_initial_sos). 0.93/1.23 % set(auto2) -> assign(sos_limit, -1). 0.93/1.23 % set(auto2) -> assign(lrs_ticks, 3000). 0.93/1.23 % set(auto2) -> assign(max_megs, 400). 0.93/1.23 % set(auto2) -> assign(stats, some). 0.93/1.23 % set(auto2) -> clear(echo_input). 0.93/1.23 % set(auto2) -> set(quiet). 0.93/1.23 % set(auto2) -> clear(print_initial_clauses). 0.93/1.23 % set(auto2) -> clear(print_given). 0.93/1.23 assign(lrs_ticks,-1). 0.93/1.23 assign(sos_limit,10000). 0.93/1.23 assign(order,kbo). 0.93/1.23 set(lex_order_vars). 0.93/1.23 clear(print_given). 0.93/1.23 0.93/1.23 % formulas(sos). % not echoed (322 formulas) 0.93/1.23 0.93/1.23 ============================== end of input ========================== 0.93/1.23 0.93/1.23 % From the command line: assign(max_seconds, 180). 0.93/1.23 0.93/1.23 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.93/1.23 0.93/1.23 % Formulas that are not ordinary clauses: 0.93/1.23 1 (all X0 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X0),scratc315931824_omega)) -> pp(aa_TPTP_ind_bool(scratc1337809184_nat_p,X0)))) # label(fact_omega__nat__p) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 2 (all X all Xa (scratc1451164978_is_of(X,Xa) <-> pp(aa_TPTP_ind_bool(Xa,X)))) # label(fact_def__is__of) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 3 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2035434666_image(aa_fun1431113780TP_ind(scratc322369131_d_Sep(Uu),Uua),Uu),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1709589394_Sigma,aa_fun1431113780TP_ind(scratc322369131_d_Sep(Uu),Uua)),scratc1564950457d_e_in(Uu,Uua))),Uub))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_db(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__54) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 4 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc153871017nd_ite(X,Xa,Xb),Xc) = scratc153477422nd_ind(Xa,aa_TPT43085870d_bool(scratc1146670205_prop1(X,Xa,Xb),Xc))) # label(fact_def__ite) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 5 (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]. 0.93/1.23 6 (all Uu all Uua all Uub all Uuc all Uud all Uue all Uuf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_ak(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)) <-> pp(aa_fun171081125l_bool(scratc1829701671all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_TPT125613450d_bool(aTP_Lamm_aj(Uua),Uub),Uuc),Uud),Uue),Uuf))))) # label(fact_ATP_Olambda__89) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 7 (all X scratc1550011574bnd_in = scratc1777039668d_esti(X)) # label(fact_def__esti) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 8 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc324534245hangef(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1709589394_Sigma,X),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aa_TPT1781712639TP_ind(aTP_Lamm_au(X),Xb),Xc),Xd))) # label(fact_def__changef) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 9 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1709589394_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,aa_TPTP_ind_TPTP_ind(scratc1146276611_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1146276610_proj0,X22)))) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,aa_TPTP_ind_TPTP_ind(scratc1146276610_proj0,X22)),X0)) & aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1624135595d_pair,aa_TPTP_ind_TPTP_ind(scratc1146276610_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1146276611_proj1,X22)) = X22))) # label(fact_k__Sigma__eta__proj0__proj1) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 10 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc957265209nunion(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1071331552d_repl,X),scratc1679165214d_Inj0)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1071331552d_repl,Xa),scratc1679165215d_Inj1)) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1624135595d_pair,X),Xa)) # label(fact_def__pair) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 11 (all X0 (scratc268548109nd_wel(X0) -> pp(X0))) # label(fact_l__et) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 12 (all X (pp(aa_TPTP_ind_bool(scratc1069222522_prop1,X)) <-> pp(aa_bool_bool(scratc952359486d_l_or(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610823d_n_is,X),scratc45782132nd_n_1)),aa_fun171081125l_bool(scratc1684187121n_some,aa_TPT43085870d_bool(aTP_Lamm_ae,X)))))) # label(fact_def__d__23__prop1) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 13 (all X (pp(aa_TPTP_ind_bool(scratc1146670208_prop4,X)) <-> pp(aa_fun171081125l_bool(scratc940362479l_some(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc423746188d_d_Pi,scratc193932176nd_nat),aTP_Lamm_ab)),aa_TPT43085870d_bool(scratc1657584698_prop2,X))))) # label(fact_def__prop4) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 14 (all Uu ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc194456967nd_nis,Uu),scratc45782132nd_n_1)) -> pp(aa_fun171081125l_bool(scratc1684187121n_some,aa_TPT43085870d_bool(aTP_Lamm_ae,Uu)))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cb,Uu)))) # label(fact_ATP_Olambda__1) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 15 (all X all Xa all Xb all Xc scratc153477422nd_ind(X,aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ax(Xa),Xb),Xc)) = aa_TPTP_ind_TPTP_ind(scratc1933877819d_soft(X,Xa,Xb),Xc)) # label(fact_def__soft) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 16 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610823d_n_is,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uua))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610823d_n_is,Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ci,Uu),Uua)))) # label(fact_ATP_Olambda__25) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 17 (all X all Xa scratc1061739109second(X,Xa) = scratc1146276611_proj1) # label(fact_def__second) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 18 (all Uu all Uua all Uub ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X3),Uu)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,Uub),X3)),aa_TPTP_ind_TPTP_ind(Uua,X3)))))) <-> pp(aa_TPTP_ind_bool(aa_fun1913827119d_bool(aTP_Lamm_be(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__66) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 19 (all X all Xa aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1017762772_power,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1709589394_Sigma,X),aTP_Lamm_bd(Xa)))),aa_fun1913827119d_bool(aTP_Lamm_be(X),Xa)) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc423746188d_d_Pi,X),Xa)) # label(fact_def__d__Pi) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 20 (all Uu all Uua all Uub all Uuc all Uud all Uue (pp(aa_fun171081125l_bool(scratc1829701671all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_TPT985247859d_bool(aa_fun1107270209d_bool(aTP_Lamm_ak(Uu),Uua),Uub),Uuc),Uud),Uue))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_al(Uu),Uua),Uub),Uuc),Uud),Uue)))) # label(fact_ATP_Olambda__87) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 21 (all Uu all Uua all Uub all Uuc (pp(aa_fun171081125l_bool(scratc940362479l_some(Uua),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ap(Uu),Uub),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aq(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__81) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 22 (all X all Xa (pp(scratc438620580_d_and(scratc1624975209_amone(X,Xa),aa_fun171081125l_bool(scratc940362479l_some(X),Xa))) <-> pp(aa_fun171081125l_bool(scratc203046453nd_one(X),Xa)))) # label(fact_def__one) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 23 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1829701671all_of(aa_TPT43085870d_bool(aTP_Lamm_cv(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_cx(X0),X12)))) # label(fact_second__p) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 24 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cn(Uu),Uua),Uub)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561998463d_incl(Uu),Uua),Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561998463d_incl(Uu),Uub),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_TPTP_ind_TPTP_ind(scratc1017762772_power,Uu)),Uua),Uub)))))) # label(fact_ATP_Olambda__48) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 25 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1071331552d_repl,aa_TPTP_ind_TPTP_ind(scratc1017762772_power,aa_TPTP_ind_TPTP_ind(scratc1017762772_power,scratc1745451206ptyset))),aa_TPT1424761345TP_ind(aTP_Lamm_bn(X),Xa)) = aa_TPTP_ind_TPTP_ind(scratc1604075772_UPair(X),Xa)) # label(fact_def__d__UPair) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 26 (all X all Xa all Xb all Xc (pp(aa_fun171081125l_bool(scratc1829701671all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_am(X),Xa),Xb),Xc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2069953503fixfu2(X,Xa),Xb),Xc)))) # label(fact_def__fixfu2) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 27 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(Uu),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,Uua),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,Uub),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dg(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__70) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 28 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc203046453nd_one(X0),X12)) -> pp(aa_TPTP_ind_bool(X12,scratc153477422nd_ind(X0,X12))))) # label(fact_oneax) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 29 (all X scratc952359486d_l_or(X) = aa_boo1142376798l_bool(scratc153411835nd_imp,scratc546085760_d_not(X))) # label(fact_def__l__or) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 30 (all X0 (pp(aa_TPTP_ind_bool(scratc1337809184_nat_p,X0)) -> pp(aa_TPTP_ind_bool(scratc1337809184_nat_p,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,X0))))) # label(fact_nat__ordsucc) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 31 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ct(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(Uu),aa_TPTP_ind_TPTP_ind(scratc2078076735_first(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1949829805d_pair(Uu,Uua),Uub),Uuc))),Uub)))) # label(fact_ATP_Olambda__68) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 32 (all X0 pp(aa_fun171081125l_bool(scratc1829701671all_of(aa_TPT43085870d_bool(aTP_Lamm_cm,X0)),aa_TPT43085870d_bool(aTP_Lamm_co,X0)))) # label(fact_isseti) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 33 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1829701671all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cr(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cs(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__60) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 34 (all X ((all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,aa_TPTP_ind_TPTP_ind(scratc1017762772_power,X1)),X))))) <-> pp(aa_TPTP_ind_bool(scratc633591742closed,X)))) # label(fact_def__d__Power__closed) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 35 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2126792979_fixfu(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc1829701671all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,X)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ao(X),Xa),Xb),Xc))))) # label(fact_def__fixfu) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 36 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cf,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,Uu),aa_TPTP_ind_TPTP_ind(scratc1017762772_power,scratc193932176nd_nat))))) # label(fact_ATP_Olambda__12) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 37 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc1770865966univof,X0)))) # label(fact_k__UnivOf__In) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 38 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_bool_bool(aa_boo1142376798l_bool(scratc153411835nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,Uub),Uud))),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(Uu),Uuc),Uud))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_ay(Uu),Uua),Uub),Uuc),Uud)))) # label(fact_ATP_Olambda__82) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 39 (all X all Xa scratc434496381ectset(X,Xa) = scratc203505661nd_out(aa_TPTP_ind_TPTP_ind(scratc1017762772_power,X),scratc759883004d_anec(X,Xa))) # label(fact_def__ectset) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 40 (all X aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,X) = scratc153477422nd_ind(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc423746188d_d_Pi,scratc193932176nd_nat),aTP_Lamm_ab),aa_TPT43085870d_bool(scratc1657584698_prop2,X))) # label(fact_def__plus) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 41 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc952408420d_Subq,X12),X0)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1017762772_power,X0))))) # label(fact_k__PowerEq) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 42 (all Uu all Uua all Uub all Uuc ((pp(aa_fun171081125l_bool(scratc1829701671all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dg(Uua),Uub),Uuc))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc423746188d_d_Pi,Uu),aTP_Lamm_ah(Uua))),Uub),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dh(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__76) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 43 (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]. 0.93/1.23 44 (all X (gg_TPTP_ind(X) -> (pp(aa_TPTP_ind_bool(scratc769077573pair_p,X)) <-> X = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1624135595d_pair,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,X),scratc1745451206ptyset)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,X),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)))))) # label(fact_def__pair__p) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 45 (all X all Xa scratc566981369d_tofs(X,Xa) = scratc1549486784bnd_ap) # label(fact_def__tofs) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 46 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X33),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,aa_TPTP_ind_TPTP_ind(X22,X33)),aa_TPTP_ind_TPTP_ind(X12,X33)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1709589394_Sigma,X0),X22)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc423746188d_d_Pi,X0),X12))))) # label(fact_lam__Pi) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 47 (all X scratc1084070009d_n_pl(X) = aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1715799339d_plus,X))) # label(fact_def__n__pl) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 48 (all X (pp(aa_fun171081125l_bool(scratc2011078052_n_all,aa_TPT43085870d_bool(aTP_Lamm_af,X))) <-> pp(aa_TPTP_ind_bool(scratc1161393343_cond2,X)))) # label(fact_def__cond2) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 49 (all X all Xa all Xb aa_fun1431113780TP_ind(scratc322369131_d_Sep(X),aa_TPT43085870d_bool(Xa,Xb)) = aa_TPTP_ind_TPTP_ind(scratc442097790_ecelt(X,Xa),Xb)) # label(fact_def__ecelt) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 50 (all X0 all X12 all X22 ((all X33 (gg_TPTP_ind(X33) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X33),X0)) -> aa_TPTP_ind_TPTP_ind(X12,X33) = aa_TPTP_ind_TPTP_ind(X22,X33)))) -> aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1709589394_Sigma,X0),X22) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1709589394_Sigma,X0),X12))) # label(fact_xi__ext) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 51 (all Uu all Uua (pp(aa_fun171081125l_bool(scratc1829701671all_of(aa_TPT43085870d_bool(aTP_Lamm_cm,Uu)),aa_TPT43085870d_bool(aTP_Lamm_cn(Uu),Uua))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_co,Uu),Uua)))) # label(fact_ATP_Olambda__32) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 52 (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]. 0.93/1.23 53 (all Uu (gg_TPTP_ind(Uu) -> ((exists X2 (gg_TPTP_ind(X2) & Uu = aa_TPTP_ind_TPTP_ind(scratc1679165214d_Inj0,X2))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_bi,Uu))))) # label(fact_ATP_Olambda__22) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 54 (all Uu aa_TPT494704832TP_ind(scratc1071331552d_repl,aa_TPTP_ind_TPTP_ind(scratc873550751tminus(Uu),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset))) = aa_TPT494704832TP_ind(aTP_Lamm_bj,Uu)) # label(fact_ATP_Olambda__19) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 55 (all X (pp(scratc546085760_d_not(scratc546085760_d_not(X))) <-> scratc268548109nd_wel(X))) # label(fact_def__wel) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 56 (all X all Xa aa_fun1431113780TP_ind(scratc322369131_d_Sep(X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(fEx_TPTP_ind(cOMBS_2003118649l_bool(cOMBB_658106424TP_ind(fconj,aa_TPT43085870d_bool(cOMBC_1555011498d_bool(scratc1550011574bnd_in),X)),Xa)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1071331552d_repl,X),aa_fun1235454963TP_ind(aTP_Lamm_bm(X),Xa))),scratc1745451206ptyset)) # label(fact_def__d__Sep) # label(axiom) # label(non_clause). [assumption]. 0.93/1.23 57 (all X0 all X12 scratc1451164978_is_of(aa_fun1431113780TP_ind(scratc322369131_d_Sep(X0),X12),aa_TPT43085870d_bool(aTP_Lamm_cm,X0))) # label(fact_setof__p) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 58 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ap(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1777039668d_esti(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__71) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 59 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_bn(Uu),Uua),Uub) = aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,scratc1745451206ptyset),Uub),Uu),Uua)) # label(fact_ATP_Olambda__44) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 60 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1017762772_power,X0))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc952408420d_Subq,X12),X0)))) # label(fact_k__PowerE) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 61 (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_am(Uu),Uua),Uub),Uuc),Uud)) <-> pp(aa_fun171081125l_bool(scratc1829701671all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aa_fun845057962d_bool(aTP_Lamm_al(Uu),Uua),Uub),Uuc),Uud))))) # label(fact_ATP_Olambda__84) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 62 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_br,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610823d_n_is,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(Uu),scratc45782132nd_n_1))))) # label(fact_ATP_Olambda__7) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 63 (all X0 all X12 (pp(aa_fun171081125l_bool(scratc203046453nd_one(X0),X12)) -> scratc1451164978_is_of(scratc153477422nd_ind(X0,X12),aa_TPT43085870d_bool(aTP_Lamm_ai,X0)))) # label(fact_ind__p) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 64 (all X all Xa all Xb aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1709589394_Sigma,X),scratc1930628757sel_wb(X,Xa,Xb)) = aa_TPTP_ind_TPTP_ind(scratc302523178wissel(X,Xa),Xb)) # label(fact_def__wissel) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 65 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,X0) = aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,X12) -> X0 = X12))) # label(fact_ordsucc__inj) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 66 (all X all Xa all Xb (pp(scratc438620580_d_and(scratc203308799nd_or3(X,Xa,Xb),scratc119709764nd_ec3(X,Xa,Xb))) <-> scratc2071121729_orec3(X,Xa,Xb))) # label(fact_def__orec3) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 67 (all B_1 all B_2 gg_bool(scratc438620580_d_and(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__40362__32620_ONUM641__thf__4__p_Obnd__d__and) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 68 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_dd(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(Uua,aa_TPTP_ind_TPTP_ind(scratc1564950457d_e_in(Uu,Uua),Uub))))) # label(fact_ATP_Olambda__65) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 69 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_a,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,Uu),scratc193932176nd_nat)))) # label(fact_ATP_Olambda__13) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 70 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_TPTP_ind_TPTP_ind(scratc1017762772_power,X)),Xb),aa_TPTP_ind_TPTP_ind(scratc442097790_ecelt(X,Xa),Xc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc119709825nd_ecp(X,Xa),Xb),Xc)))) # label(fact_def__ecp) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 71 (all X all Xa all Xb aa_fun1431113780TP_ind(scratc322369131_d_Sep(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_aq(X),Xa),Xb)) = aa_TPTP_ind_TPTP_ind(scratc540613727unmore(X,Xa),Xb)) # label(fact_def__unmore) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 72 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610823d_n_is,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(Uu),Uua))),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bp,Uu),Uua)))) # label(fact_ATP_Olambda__33) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 73 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1376844911_rec_G(X),Xa),Xb)) <-> (all X3 ((all X4 all X5 (gg_TPTP_ind(X4) -> ((all X6 (gg_TPTP_ind(X6) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X6),X4)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(X3,X6),aa_TPTP_ind_TPTP_ind(X5,X6)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(X3,X4),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(X,X4),X5)))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(X3,Xa),Xb)))))) # label(fact_def__d__In__rec__G) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 74 (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]. 0.93/1.24 75 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1829701671all_of(aa_fun1584354236d_bool(aTP_Lamm_dc(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_dd(X0),X12)))) # label(fact_e__inp) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 76 (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]. 0.93/1.24 77 (all X0 all X12 (gg_TPTP_ind(X0) & gg_TPTP_ind(X12) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc952408420d_Subq,X0),X12)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc952408420d_Subq,X12),X0)) -> X12 = X0)))) # label(fact_set__ext) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 78 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ch,Uu)) <-> (pp(aa_TPTP_ind_bool(scratc1161393342_cond1,Uu)) -> (pp(aa_TPTP_ind_bool(scratc1161393343_cond2,Uu)) -> pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cg,Uu))))))) # label(fact_ATP_Olambda__6) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 79 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc1525024638_union,aa_TPTP_ind_TPTP_ind(scratc1604075772_UPair(X),Xa)) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(X),Xa)) # label(fact_def__binunion) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 80 (all Uu all Uua ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc194456967nd_nis,Uu),Uua)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc194456967nd_nis,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cd,Uu),Uua)))) # label(fact_ATP_Olambda__29) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 81 (all X all Xa (pp(aa_bool_bool(aa_boo1142376798l_bool(scratc153411835nd_imp,X),scratc546085760_d_not(Xa))) <-> pp(scratc951703481d_l_ec(X,Xa)))) # label(fact_def__l__ec) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 82 (all X all Xa (pp(scratc438620580_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc153411835nd_imp,X),Xa),aa_bool_bool(aa_boo1142376798l_bool(scratc153411835nd_imp,Xa),X))) <-> scratc1332762030_l_iff(X,Xa))) # label(fact_def__l__iff) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 83 (all X all Xa scratc1624135595d_pair = scratc1949829805d_pair(X,Xa)) # label(fact_def__d__pair) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 84 (all X all Xa (pp(aa_fun171081125l_bool(scratc940362479l_some(X),Xa)) <-> pp(scratc546085760_d_not(aa_fun171081125l_bool(scratc1829701671all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,X)),scratc194850556nd_non(X,Xa)))))) # label(fact_def__l__some) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 85 (all X0 (pp(aa_TPTP_ind_bool(X0,scratc1745451206ptyset)) -> ((all X13 (gg_TPTP_ind(X13) -> (pp(aa_TPTP_ind_bool(scratc1337809184_nat_p,X13)) -> (pp(aa_TPTP_ind_bool(X0,X13)) -> pp(aa_TPTP_ind_bool(X0,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,X13))))))) -> (all X12 (pp(aa_TPTP_ind_bool(scratc1337809184_nat_p,X12)) -> pp(aa_TPTP_ind_bool(X0,X12))))))) # label(fact_nat__ind) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 86 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cl,Uu)) <-> scratc1451164978_is_of(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu),aTP_Lamm_a))) # label(fact_ATP_Olambda__10) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 87 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1829701671all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cz(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_da(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__58) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 88 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc192357794nd_nIn,X),Xa)) <-> -pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X),Xa)))) # label(fact_def__nIn) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 89 (all B_1 all B_2 gg_TPTP_ind(scratc119709829nd_ect(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__40362__32620_ONUM641__thf__4__p_Obnd__ect) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 90 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610823d_n_is,aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(Uu),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bv,Uu),Uua)))) # label(fact_ATP_Olambda__27) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 91 (all B_1 gg_TPTP_ind(scratc120562615nd_eps(B_1))) # label(gsy_c_Scratch__tptp__translate__40362__32620_ONUM641__thf__4__p_Obnd__eps) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 92 (all X (pp(aa_TPTP_ind_bool(scratc1337809184_nat_p,X)) <-> (all X1 (pp(aa_TPTP_ind_bool(X1,scratc1745451206ptyset)) -> ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(X1,X2)) -> pp(aa_TPTP_ind_bool(X1,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,X2)))))) -> pp(aa_TPTP_ind_bool(X1,X))))))) # label(fact_def__nat__p) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 93 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(Uua,Uuc)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(Uu),Uub),Uuc)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bb(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__79) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 94 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_dc(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,Uub),aa_fun1431113780TP_ind(scratc322369131_d_Sep(Uu),Uua))))) # label(fact_ATP_Olambda__63) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 95 (all X all Xa aa_fun277296641TP_ind(scratc407235996eplSep(X,aa_TPT43085870d_bool(aTP_Lamm_bf,Xa)),scratc1146276611_proj1) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,X),Xa)) # label(fact_def__ap) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 96 (all Uu all Uua (gg_TPTP_ind(Uua) -> ((exists X3 (aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1624135595d_pair,Uu),X3) = Uua & gg_TPTP_ind(X3))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bf,Uu),Uua))))) # label(fact_ATP_Olambda__42) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 97 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X22),aa_fun1431113780TP_ind(scratc322369131_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(X12,X22)))) # label(fact_k__SepE2) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 98 (all X ((all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X1),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,aa_TPTP_ind_TPTP_ind(scratc1525024638_union,X1)),X))))) <-> pp(aa_TPTP_ind_bool(scratc468858728closed,X)))) # label(fact_def__d__Union__closed) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 99 (all X all Xa (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1896920188_empty,X),Xa)) <-> pp(aa_fun171081125l_bool(scratc1829701671all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,X)),scratc194850556nd_non(X,aa_TPT43085870d_bool(aTP_Lamm_at(X),Xa)))))) # label(fact_def__empty) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 100 (all X all Xa (pp(scratc1624975209_amone(X,Xa)) <-> pp(aa_fun171081125l_bool(scratc1829701671all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,X)),aa_fun1584354236d_bool(aTP_Lamm_bc(X),Xa))))) # label(fact_def__amone) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 101 (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(scratc1083610823d_n_is,Uu),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uua))))) # label(fact_ATP_Olambda__35) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 102 (all Uu all Uua all Uub all Uuc (gg_TPTP_ind(Uua) & gg_TPTP_ind(Uuc) & gg_TPTP_ind(Uub) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bo(Uu),Uua),Uub),Uuc)) <-> -pp(Uu) & Uub = Uuc | Uua = Uuc & pp(Uu)))) # label(fact_ATP_Olambda__77) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 103 (all X all Xa (pp(aa_fun171081125l_bool(scratc1829701671all_of(X),Xa)) <-> (all X2 (gg_TPTP_ind(X2) -> (scratc1451164978_is_of(X2,X) -> pp(aa_TPTP_ind_bool(Xa,X2))))))) # label(fact_def__all__of) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 104 (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]. 0.93/1.24 105 (all X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X0),aa_TPTP_ind_TPTP_ind(scratc1017762772_power,X0)))) # label(fact_k__Self__In__Power) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 106 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1829701671all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,X0)),aa_fun1584354236d_bool(aTP_Lamm_cq(X0),X12)))) # label(fact_estii) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 107 (all B_1 all B_2 gg_TPTP_ind(scratc153477422nd_ind(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__40362__32620_ONUM641__thf__4__p_Obnd__ind) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 108 (all X all Xa all Xb (gg_TPTP_ind(Xb) -> Xb = aa_TPTP_ind_TPTP_ind(scratc1564950457d_e_in(X,Xa),Xb))) # label(fact_def__e__in) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 109 (all X0 (pp(aa_TPTP_ind_bool(scratc1337809184_nat_p,X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X0),scratc315931824_omega)))) # label(fact_nat__p__omega) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 110 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1527004365ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc87254192nd_all(Xa),aa_TPT43085870d_bool(scratc2035434666_image(X,Xa),Xb))))) # label(fact_def__surjective) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 111 (all X all Xa all Xb all Xc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2035434666_image(X,Xa),Xb),Xc)) <-> pp(aa_fun171081125l_bool(scratc940362479l_some(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ax(Xa),Xb),Xc))))) # label(fact_def__image) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 112 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1709589394_Sigma,X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2110891758munion,X),aTP_Lamm_bg(Xa))) # label(fact_def__d__Sigma) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 113 (all X0 all X12 all X22 (gg_TPTP_ind(X12) -> (pp(X0) -> aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(X0,X12),X22) = X12))) # label(fact_if__i__1) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 114 (all Uu (pp(aa_fun171081125l_bool(scratc203046453nd_one(aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc423746188d_d_Pi,scratc193932176nd_nat),aTP_Lamm_ab)),aa_TPT43085870d_bool(aTP_Lamm_by,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_bz,Uu)))) # label(fact_ATP_Olambda__5) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 115 (all X0 pp(aa_TPTP_ind_bool(scratc1675368811closed,aa_TPTP_ind_TPTP_ind(scratc1770865966univof,X0)))) # label(fact_k__UnivOf__ZF__closed) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 116 (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]. 0.93/1.24 117 (all Uu all Uua all Uub all Uuc (scratc1451164978_is_of(aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1949829805d_pair(Uu,Uua),Uub),Uuc),aa_TPT43085870d_bool(aTP_Lamm_cv(Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cz(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__73) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 118 (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(scratc951703481d_l_ec(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1777039668d_esti(Uu),Uuc),Uua),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1777039668d_esti(Uu),Uuc),Uub))))) # label(fact_ATP_Olambda__74) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 119 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_af,Uu),Uua)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc153411835nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610818d_n_in,Uua),Uu)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610818d_n_in,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uua)),Uu))))) # label(fact_ATP_Olambda__30) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 120 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1829701671all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,X0)),aa_fun1584354236d_bool(aTP_Lamm_cp(X0),X12)))) # label(fact_estie) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 121 (all X all Xa (scratc983731570d_orec(X,Xa) <-> pp(scratc438620580_d_and(aa_bool_bool(scratc952359486d_l_or(X),Xa),scratc951703481d_l_ec(X,Xa))))) # label(fact_def__orec) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 122 (all X all Xa (pp(aa_fun171081125l_bool(scratc940362479l_some(X),aa_TPT43085870d_bool(aTP_Lamm_at(X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2031046193nempty,X),Xa)))) # label(fact_def__nonempty) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 123 (all Uu all Uua (pp(scratc438620580_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610823d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,Uua),scratc45782132nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu)),aa_fun171081125l_bool(scratc2011078052_n_all,aa_TPT43085870d_bool(aTP_Lamm_ad,Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_by,Uu),Uua)))) # label(fact_ATP_Olambda__24) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 124 (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(scratc1083610823d_n_is,aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu)),Uua)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(Uu),Uua)))))) # label(fact_ATP_Olambda__26) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 125 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610818d_n_in,Uua),Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cg,Uu),Uua)))) # label(fact_ATP_Olambda__37) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 126 (all X all Xa scratc407235996eplSep(X,Xa) = aa_TPT494704832TP_ind(scratc1071331552d_repl,aa_fun1431113780TP_ind(scratc322369131_d_Sep(X),Xa))) # label(fact_def__d__ReplSep) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 127 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cv(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,Uub),aa_TPTP_ind_TPTP_ind(scratc546250696etprod(Uu),Uua))))) # label(fact_ATP_Olambda__62) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 128 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc423746188d_d_Pi,X0),X12))) -> (all X32 (gg_TPTP_ind(X32) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X32),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc423746188d_d_Pi,X0),X12))) -> ((all X42 (gg_TPTP_ind(X42) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X42),X0)) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,X32),X42) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,X22),X42)))) -> X32 = X22))))))) # label(fact_k__Pi__ext) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 129 (all P (gg_bool(P) -> fFalse = P | P = fTrue)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 130 (all P all Q all R aa_boo1142376798l_bool(P,aa_TPTP_ind_bool(Q,R)) = aa_TPT2142672771l_bool(cOMBB_658106424TP_ind(P,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]. 0.93/1.24 131 (all X all Xa all Xb all Xc all Xd aa_TPT1424761345TP_ind(scratc693191546_indeq(X,Xa,Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc788888630d_11_i(X,Xa,Xb),Xc),Xd)) = scratc1853463352indeq2(X,Xa,Xb,Xc,Xd)) # label(fact_def__indeq2) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 132 (all X all Xa scratc441507399_ecect(X,Xa) = scratc1564950457d_e_in(aa_TPTP_ind_TPTP_ind(scratc1017762772_power,X),scratc759883004d_anec(X,Xa))) # label(fact_def__ecect) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 133 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,Uu),Uub)) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aTP_Lamm_av(Uu),Uua),Uub)) # label(fact_ATP_Olambda__64) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 134 (all X all Xa (pp(scratc438620580_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610823d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,Xa),scratc45782132nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,X)),aa_TPTP_ind_bool(scratc1657584697_prop1,Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1657584698_prop2,X),Xa)))) # label(fact_def__d__24__prop2) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 135 (all Uu (gg_TPTP_ind(Uu) -> ((exists X2 (gg_TPTP_ind(X2) & Uu = aa_TPTP_ind_TPTP_ind(scratc1679165215d_Inj1,X2))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_bh,Uu))))) # label(fact_ATP_Olambda__21) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 136 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1709589394_Sigma,X0),X12))) -> aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1624135595d_pair,aa_TPTP_ind_TPTP_ind(scratc1146276610_proj0,X22)),aa_TPTP_ind_TPTP_ind(scratc1146276611_proj1,X22)) = X22))) # label(fact_proj__Sigma__eta) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 137 (all X aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,X) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(X),aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,X))) # label(fact_def__ordsucc) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 138 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ai,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,Uua),Uu)))) # label(fact_ATP_Olambda__39) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 139 (all Uu all Uua all Uub all Uuc (pp(aa_bool_bool(aa_boo1142376798l_bool(scratc153411835nd_imp,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1777039668d_esti(Uu),Uuc),Uua)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1777039668d_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__75) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 140 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> (-pp(X0) -> X22 = aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(X0,X12),X22)))) # label(fact_if__i__0) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 141 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1709589394_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,aa_TPTP_ind_TPTP_ind(scratc1146276610_proj0,X22)),X0)))) # label(fact_proj0__Sigma) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 142 (all X aa_TPTP_ind_TPTP_ind(scratc1146276610_proj0,X) = aa_fun277296641TP_ind(scratc407235996eplSep(X,aTP_Lamm_bi),scratc339482526_d_Unj)) # label(fact_def__proj0) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 143 (all X0 ((all X13 (gg_TPTP_ind(X13) -> ((all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_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]. 0.93/1.24 144 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc370955156ective(X),Xa),Xb)) <-> pp(scratc438620580_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc187235926ective(X),Xa),Xb),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1527004365ective(X),Xa),Xb))))) # label(fact_def__bijective) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 145 (all X all Xa (pp(scratc546085760_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610823d_n_is,X),Xa))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc194456967nd_nis,X),Xa)))) # label(fact_def__nis) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 146 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,Uua),aa_TPTP_ind_TPTP_ind(scratc1017762772_power,Uu))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cm,Uu),Uua)))) # label(fact_ATP_Olambda__36) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 147 (all X0 all X12 (gg_TPTP_ind(X12) -> aa_TPTP_ind_TPTP_ind(scratc1146276611_proj1,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1624135595d_pair,X0),X12)) = X12)) # label(fact_proj1__pair__eq) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 148 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc319294504ectelt(X,Xa),Xb) = aa_TPTP_ind_TPTP_ind(scratc434496381ectset(X,Xa),aa_TPTP_ind_TPTP_ind(scratc442097790_ecelt(X,Xa),Xb))) # label(fact_def__ectelt) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 149 (all P all Q all R aa_bool_bool(aa_TPT2142672771l_bool(P,R),aa_TPTP_ind_bool(Q,R)) = aa_TPTP_ind_bool(cOMBS_2003118649l_bool(P,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]. 0.93/1.24 150 (all X0 all X12 all X22 (gg_TPTP_ind(X22) -> ((exists X3 (gg_TPTP_ind(X3) & X22 = aa_TPTP_ind_TPTP_ind(X12,X3) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X3),X0)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1071331552d_repl,X0),X12)))))) # label(fact_k__ReplEq) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 151 (all Q all P (-pp(Q) | pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)))) # label(help_fimplies_2_1_U) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 152 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc187235926ective(X),Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc87254192nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_az(X),Xa),Xb))))) # label(fact_def__injective) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 153 (all P all Q (-pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)) | pp(P))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 154 (all B_1 all B_2 all B_3 gg_bool(scratc203308799nd_or3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__40362__32620_ONUM641__thf__4__p_Obnd__or3) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 155 (all Uu all Uua aa_fun277296641TP_ind(aa_TPT494704832TP_ind(aTP_Lamm_bk,Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc957265209nunion(aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,scratc1745451206ptyset)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1071331552d_repl,Uu),Uua))) # label(fact_ATP_Olambda__34) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 156 (all X aa_TPTP_ind_TPTP_ind(scratc1146276611_proj1,X) = aa_fun277296641TP_ind(scratc407235996eplSep(X,aTP_Lamm_bh),scratc339482526_d_Unj)) # label(fact_def__proj1) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 157 (all Uu all Uua all Uub (scratc1451164978_is_of(aa_TPTP_ind_TPTP_ind(scratc1061739109second(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_ai,Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cx(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__49) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 158 (all X all Xa aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc2110891758munion,X),Xa) = aa_TPTP_ind_TPTP_ind(scratc1525024638_union,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1071331552d_repl,X),Xa))) # label(fact_def__famunion) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 159 (all Uu (pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bv,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_bw,Uu)))) # label(fact_ATP_Olambda__16) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 160 (all Uu (gg_TPTP_ind(Uu) -> (Uu != scratc1745451206ptyset <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ag,Uu))))) # label(fact_ATP_Olambda__20) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 161 (all X0 all X12 all X22 (gg_TPTP_ind(X22) & gg_TPTP_ind(X12) -> aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(X0,X12),X22) = X22 | aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(X0,X12),X22) = X12)) # label(fact_if__i__or) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 162 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X22),X0)) -> aa_TPTP_ind_TPTP_ind(X12,X22) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1709589394_Sigma,X0),X12)),X22))) # label(fact_beta) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 163 (all X aa_TPTP_ind_TPTP_ind(scratc854057538d_Sing,X) = aa_TPTP_ind_TPTP_ind(scratc1604075772_UPair(X),X)) # label(fact_def__d__Sing) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 164 (all X7 all Y (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X7),Y)) | X7 != Y)) # label(help_fequal_2_1_fequal_001t__TPTP____Interpret__Oind_T) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 165 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ax(Uu),Uua),Uub),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(Uu),Uub),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,Uua),Uuc))))) # label(fact_ATP_Olambda__72) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 166 (all B_1 all B_2 all B_3 gg_bool(scratc119709764nd_ec3(B_1,B_2,B_3))) # label(gsy_c_Scratch__tptp__translate__40362__32620_ONUM641__thf__4__p_Obnd__ec3) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 167 (all X0 all X12 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc187235926ective(aa_fun1431113780TP_ind(scratc322369131_d_Sep(X0),X12)),X0),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1709589394_Sigma,aa_fun1431113780TP_ind(scratc322369131_d_Sep(X0),X12)),scratc1564950457d_e_in(X0,X12))))) # label(fact_otax1) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 168 (all X all Xa ((pp(X) -> pp(scratc546085760_d_not(Xa))) <-> scratc1346638271d_r_ec(X,Xa))) # label(fact_def__r__ec) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 169 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1829701671all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,X0)),aa_TPT43085870d_bool(aTP_Lamm_cu(X0),X12)))) # label(fact_firstis1) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 170 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_ba(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(Uua,Uub)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,Uub),Uu)))) # label(fact_ATP_Olambda__53) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 171 (all Uu all Uua all Uub (scratc1451164978_is_of(aa_TPTP_ind_TPTP_ind(scratc2078076735_first(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_ai,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cy(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__50) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 172 (all X all Xa (pp(scratc438620580_d_and(X,Xa)) <-> pp(scratc546085760_d_not(scratc951703481d_l_ec(X,Xa))))) # label(fact_def__d__and) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 173 (all X0 scratc1745451206ptyset != aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,X0)) # label(fact_neq__ordsucc__0) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 174 (all X0 all X12 ((exists X2 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X2),X0)) & pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X12),X2)) & gg_TPTP_ind(X2))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1525024638_union,X0))))) # label(fact_k__UnionEq) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 175 (all X all Xa scratc1933877819d_soft(aa_fun1431113780TP_ind(scratc322369131_d_Sep(X),Xa),X,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1709589394_Sigma,aa_fun1431113780TP_ind(scratc322369131_d_Sep(X),Xa)),scratc1564950457d_e_in(X,Xa))) = scratc203505661nd_out(X,Xa)) # label(fact_def__out) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 176 (all Uu all Uua all Uub all Uuc ((pp(aa_TPTP_ind_bool(Uua,Uub)) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_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_dj(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__78) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 177 (all Uu (pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_ci,Uu))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_cj,Uu)))) # label(fact_ATP_Olambda__14) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 178 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cw(Uu),Uua),Uub)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(aa_TPTP_ind_TPTP_ind(scratc546250696etprod(Uu),Uua)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1949829805d_pair(Uu,Uua),aa_TPTP_ind_TPTP_ind(scratc2078076735_first(Uu,Uua),Uub)),aa_TPTP_ind_TPTP_ind(scratc1061739109second(Uu,Uua),Uub))),Uub)))) # label(fact_ATP_Olambda__43) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 179 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610823d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,X),Xb)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1146670207_prop3(X),Xa),Xb)))) # label(fact_def__prop3) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 180 (all X all Xa ((all X2 (gg_TPTP_ind(X2) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X2),X)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X2),Xa))))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc952408420d_Subq,X),Xa)))) # label(fact_def__d__Subq) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 181 (all X all Xa all Xb (pp(aa_TPTP_ind_bool(scratc759883004d_anec(X,Xa),Xb)) <-> pp(aa_fun171081125l_bool(scratc940362479l_some(X),aa_TPT43085870d_bool(scratc119709825nd_ecp(X,Xa),Xb))))) # label(fact_def__anec) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 182 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1829701671all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,X0)),aa_fun1584354236d_bool(aTP_Lamm_db(X0),X12)))) # label(fact_otax2) # label(axiom) # label(non_clause). [assumption]. 0.93/1.24 183 (all X7 all Y (gg_TPTP_ind(X7) & gg_TPTP_ind(Y) -> X7 = Y | -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]. 0.93/1.25 184 (all X all Xa scratc120562615nd_eps(aa_TPT43085870d_bool(scratc1376844911_rec_G(X),Xa)) = aa_TPTP_ind_TPTP_ind(scratc134999576In_rec(X),Xa)) # label(fact_def__d__In__rec) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 185 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1777039668d_esti(Uu),Uub),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_at(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__46) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 186 (all X (pp(aa_TPTP_ind_bool(scratc480860347_prop1,X)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc194456967nd_nis,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,X)),X)))) # label(fact_def__d__22__prop1) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 187 (all Uu all Uua all Uub aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(aa_TPTP_ind_bool(Uua,Uub),Uub),scratc120562615nd_eps(aa_fun1584354236d_bool(aTP_Lamm_ba(Uu),Uua))) = aa_TPTP_ind_TPTP_ind(aa_fun1235454963TP_ind(aTP_Lamm_bm(Uu),Uua),Uub)) # label(fact_ATP_Olambda__45) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 188 (all B_1 all B_2 gg_bool(scratc951703481d_l_ec(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__40362__32620_ONUM641__thf__4__p_Obnd__l__ec) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 189 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_an(Uu),Uua),Uub),Uuc),Uud)) <-> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(Uu,Uuc),Uud)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,Uub),Uuc)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,Uub),Uud)))))) # label(fact_ATP_Olambda__83) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 190 (all X all Xa all Xb (pp(scratc438620580_d_and(X,scratc438620580_d_and(Xa,Xb))) <-> scratc759817357d_and3(X,Xa,Xb))) # label(fact_def__and3) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 191 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X22),X0)) -> (pp(aa_TPTP_ind_bool(X12,X22)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X22),aa_fun1431113780TP_ind(scratc322369131_d_Sep(X0),X12)))))) # label(fact_k__SepI) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 192 (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]. 0.93/1.25 193 (all X (pp(aa_TPTP_ind_bool(scratc1657584697_prop1,X)) <-> pp(aa_fun171081125l_bool(scratc2011078052_n_all,aa_TPT43085870d_bool(aTP_Lamm_ad,X))))) # label(fact_def__d__24__prop1) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 194 (all X all Xa scratc2078076735_first(X,Xa) = scratc1146276610_proj0) # label(fact_def__first) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 195 (all X scratc1829701671all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,X)) = scratc87254192nd_all(X)) # label(fact_def__all) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 196 scratc1175657942bvious <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc153411835nd_imp,fFalse),fFalse)) # label(fact_def__obvious) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 197 (all X0 pp(aa_fun171081125l_bool(scratc1829701671all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,X0)),aa_TPT43085870d_bool(aTP_Lamm_dl,X0)))) # label(fact_refis) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 198 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(Uua,Uub)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1777039668d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc322369131_d_Sep(Uu),Uua)))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_cq(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__55) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 199 (all X fequal_TPTP_ind = scratc1564950462d_e_is(X)) # label(fact_def__e__is) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 200 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bq,Uu)) <-> pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bp,Uu))))) # label(fact_ATP_Olambda__18) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 201 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_ad,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610823d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,Uu),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uua))),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,Uu),Uua)))))) # label(fact_ATP_Olambda__28) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 202 (all Uu all Uua all Uub all Uuc (pp(aa_fun171081125l_bool(scratc87254192nd_all(Uu),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_ay(Uu),Uua),Uub),Uuc))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_az(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__80) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 203 (all X (pp(aa_TPTP_ind_bool(scratc1675368811closed,X)) <-> pp(aa_TPTP_ind_bool(scratc1137838734closed,X)) & pp(aa_TPTP_ind_bool(scratc633591742closed,X)) & pp(aa_TPTP_ind_bool(scratc468858728closed,X)))) # label(fact_def__d__ZF__closed) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 204 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bx,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610823d_n_is,aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(Uu),scratc45782132nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu))))) # label(fact_ATP_Olambda__3) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 205 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,Uub),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc423746188d_d_Pi,Uu),aTP_Lamm_ah(Uua)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_df(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__61) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 206 (all Uu all Uua all Uub all Uuc (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(Uua),aa_TPTP_ind_TPTP_ind(scratc1061739109second(Uu,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1949829805d_pair(Uu,Uua),Uub),Uuc))),Uuc)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_cr(Uu),Uua),Uub),Uuc)))) # label(fact_ATP_Olambda__69) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 207 (all X0 all X12 all X22 all X32 (pp(X0) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(X0,X22),X32))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X12),X22))))) # label(fact_k__If__In__then__E) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 208 (all P all Q (-pp(P) | -pp(Q) | pp(aa_bool_bool(aa_boo1142376798l_bool(fconj,P),Q)))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 209 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_bc(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1829701671all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_bb(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__57) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 210 (all X0 (gg_TPTP_ind(X0) -> (pp(aa_TPTP_ind_bool(scratc1337809184_nat_p,X0)) -> scratc1745451206ptyset = X0 | (exists X13 (gg_TPTP_ind(X13) & pp(aa_TPTP_ind_bool(scratc1337809184_nat_p,X13)) & aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,X13) = X0))))) # label(fact_nat__inv) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 211 (all B_1 gg_bool(scratc546085760_d_not(B_1))) # label(gsy_c_Scratch__tptp__translate__40362__32620_ONUM641__thf__4__p_Obnd__d__not) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 212 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1829701671all_of(aa_TPT43085870d_bool(aTP_Lamm_df(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_di(X0),X12)))) # label(fact_e__fisi) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 213 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1829701671all_of(aa_TPT43085870d_bool(aTP_Lamm_cv(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_cw(X0),X12)))) # label(fact_pairis1) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 214 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1829701671all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,X0)),aa_fun1584354236d_bool(aTP_Lamm_dk(X0),X12)))) # label(fact_e__isp) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 215 (all X all Xa all Xb (scratc759817357d_and3(scratc951703481d_l_ec(X,Xa),scratc951703481d_l_ec(Xa,Xb),scratc951703481d_l_ec(Xb,X)) <-> pp(scratc119709764nd_ec3(X,Xa,Xb)))) # label(fact_def__ec3) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 216 (all X all Xa all Xb (pp(scratc203308799nd_or3(X,Xa,Xb)) <-> pp(aa_bool_bool(scratc952359486d_l_or(X),aa_bool_bool(scratc952359486d_l_or(Xa),Xb))))) # label(fact_def__or3) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 217 (all X aa_TPTP_ind_TPTP_ind(scratc1679165214d_Inj0,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1071331552d_repl,X),scratc1679165215d_Inj1)) # label(fact_def__d__Inj0) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 218 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_cc,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc194456967nd_nis,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu)),Uu)))) # label(fact_ATP_Olambda__9) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 219 (all X all Xa all Xb all Xc all Xd all Xe all Xf (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc57423676_prop1(X,Xa,Xb,Xc,Xd),Xe),Xf)) <-> pp(scratc438620580_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1777039668d_esti(X),Xf),aa_TPTP_ind_TPTP_ind(scratc441507399_ecect(X,Xa),Xd)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(Xb),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,Xc),Xf)),Xe))))) # label(fact_def__d__10__prop1) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 220 (all X all Xa all Xb aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(X,Xa),Xb) = scratc120562615nd_eps(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_bo(X),Xa),Xb))) # label(fact_def__if) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 221 (all X0 all X12 all X22 ((pp(X0) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X12),X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(X0,X12),scratc1745451206ptyset)),aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(X0,X22),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,scratc1745451206ptyset)))))) # label(fact_k__If__In__01) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 222 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1829701671all_of(aa_TPT43085870d_bool(aTP_Lamm_df(Uu),Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_dh(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_di(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__52) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 223 -(exists X0 pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X0),scratc1745451206ptyset))) # label(fact_k__EmptyAx) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 224 (all P all Q (-pp(P) | pp(Q) | -pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,P),Q)))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 225 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1829701671all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,X0)),aa_TPT43085870d_bool(aTP_Lamm_da(X0),X12)))) # label(fact_e__pair__p) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 226 (all X all Xa all Xb all Xc (pp(scratc438620580_d_and(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1777039668d_esti(X),Xc),Xa),scratc546085760_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1777039668d_esti(X),Xc),Xb)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1991259070etprop(X,Xa),Xb),Xc)))) # label(fact_def__nissetprop) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 227 (all X (pp(scratc546085760_d_not(X)) <-> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc153411835nd_imp,X),fFalse)))) # label(fact_def__d__not) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 228 (all X all Xa all Xb aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1709589394_Sigma,Xa),scratc1933877819d_soft(X,Xa,Xb)) = aa_TPTP_ind_TPTP_ind(scratc563244838d_invf(X,Xa),Xb)) # label(fact_def__invf) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 229 (all Uu ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc194456967nd_nis,Uu),scratc45782132nd_n_1)) -> pp(aa_fun171081125l_bool(scratc2126870313_n_one,aa_TPT43085870d_bool(aTP_Lamm_ae,Uu)))) <-> pp(aa_TPTP_ind_bool(aTP_Lamm_ca,Uu)))) # label(fact_ATP_Olambda__2) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 230 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_aa,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610823d_n_is,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu)),aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(scratc45782132nd_n_1),Uu))))) # label(fact_ATP_Olambda__8) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 231 (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]. 0.93/1.25 232 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X22),X0)) -> (all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X32),aa_TPTP_ind_TPTP_ind(X12,X22))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1624135595d_pair,X22),X32)),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1709589394_Sigma,X0),X12))))))) # label(fact_pair__Sigma) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 233 (all X all Xa all Xb aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1709589394_Sigma,Xa),aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_aw(X),Xa),Xb)) = aa_TPTP_ind_TPTP_ind(scratc310575295nverse(X,Xa),Xb)) # label(fact_def__inverse) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 234 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bg(Uu),Uua) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1071331552d_repl,aa_TPTP_ind_TPTP_ind(Uu,Uua)),aa_TPT1424761345TP_ind(scratc1624135595d_pair,Uua))) # label(fact_ATP_Olambda__31) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 235 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ck,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc194456967nd_nis,aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu)),scratc45782132nd_n_1)))) # label(fact_ATP_Olambda__11) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 236 (all X all Xa all Xb scratc788888630d_11_i(X,Xa,Xb) = scratc693191546_indeq(X,Xa,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc423746188d_d_Pi,X),aTP_Lamm_ah(Xb)))) # label(fact_def__d__11__i) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 237 (all Uu all Uua all Uub all Uuc aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc2035434666_image(Uu,Uua),Uub),Uuc),aa_TPTP_ind_TPTP_ind(scratc1933877819d_soft(Uu,Uua,Uub),Uuc)),scratc1745451206ptyset) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(aa_TPT1791839040TP_ind(aTP_Lamm_aw(Uu),Uua),Uub),Uuc)) # label(fact_ATP_Olambda__67) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 238 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_dk(Uu),Uua),Uub)) <-> pp(aa_fun171081125l_bool(scratc1829701671all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,Uu)),aa_TPT43085870d_bool(aa_fun1212484691d_bool(aTP_Lamm_dj(Uu),Uua),Uub))))) # label(fact_ATP_Olambda__56) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 239 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1829701671all_of(aa_TPT43085870d_bool(aTP_Lamm_cv(X0),X12)),aa_TPT43085870d_bool(aTP_Lamm_cy(X0),X12)))) # label(fact_first__p) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 240 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_ac(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,Uu),Uua))) # label(fact_ATP_Olambda__40) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 241 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(scratc43785844_inj_h(X,Xa,Xb,Xc),Xd) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1709589394_Sigma,X),aa_TPT1424761345TP_ind(aTP_Lamm_av(Xc),Xd))) # label(fact_def__inj__h) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 242 (all X ((all X1 (gg_TPTP_ind(X1) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X1),X)) -> (all X2 ((all X3 (gg_TPTP_ind(X3) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X3),X1)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,aa_TPTP_ind_TPTP_ind(X2,X3)),X))))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1071331552d_repl,X1),X2)),X))))))) <-> pp(aa_TPTP_ind_bool(scratc1137838734closed,X)))) # label(fact_def__d__Repl__closed) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 243 (all Uu all Uua all Uub ((pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1777039668d_esti(Uu),Uub),aa_fun1431113780TP_ind(scratc322369131_d_Sep(Uu),Uua))) -> pp(aa_TPTP_ind_bool(Uua,Uub))) <-> pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_cp(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__47) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 244 (all B_1 gg_bool(fEx_TPTP_ind(B_1))) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 245 (all X aa_TPTP_ind_TPTP_ind(scratc2122730866d_24_g,X) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1709589394_Sigma,scratc193932176nd_nat),aTP_Lamm_ac(X))) # label(fact_def__d__24__g) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 246 (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_au(Uu),Uua),Uub),Uuc),Uud) = aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,aa_TPTP_ind_TPTP_ind(scratc302523178wissel(Uu,Uub),Uuc)),Uud))) # label(fact_ATP_Olambda__86) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 247 (all X all Xa all Xb all Xc all Xd aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc693191546_indeq(X,Xa,Xb),Xc),Xd) = scratc153477422nd_ind(Xb,aa_TPT43085870d_bool(scratc1146670206_prop2(X,Xa,Xb,Xc),Xd))) # label(fact_def__indeq) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 248 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_dl,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(Uu),Uua),Uua)))) # label(fact_ATP_Olambda__23) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 249 (all Uu all Uua all Uub (pp(aa_fun171081125l_bool(scratc1829701671all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,Uua)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ct(Uu),Uua),Uub))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cu(Uu),Uua),Uub)))) # label(fact_ATP_Olambda__59) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 250 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc153871017nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(X),Xc),Xb),X,Xa),aa_TPTP_ind_TPTP_ind(scratc1930628756sel_wa(X,Xa,Xb),Xc)) = aa_TPTP_ind_TPTP_ind(scratc1930628757sel_wb(X,Xa,Xb),Xc)) # label(fact_def__wissel__wb) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 251 (all X all Xa all Xb (pp(aa_fun171081125l_bool(scratc87254192nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_as(X),Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc561998463d_incl(X),Xa),Xb)))) # label(fact_def__incl) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 252 (all Uu all Uua all Uub all Uuc all Uud (pp(aa_fun171081125l_bool(scratc1829701671all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,Uu)),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_TPT1123896796d_bool(aTP_Lamm_an(Uua),Uub),Uuc),Uud))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aa_TPT60673477d_bool(aa_fun987228051d_bool(aTP_Lamm_ao(Uu),Uua),Uub),Uuc),Uud)))) # label(fact_ATP_Olambda__85) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 253 (all Uu all Uua aa_TPTP_ind_TPTP_ind(aTP_Lamm_bd(Uu),Uua) = aa_TPTP_ind_TPTP_ind(scratc1525024638_union,aa_TPTP_ind_TPTP_ind(Uu,Uua))) # label(fact_ATP_Olambda__41) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 254 (all X0 all X12 all X22 all X32 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc423746188d_d_Pi,X0),X12))) -> (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X32),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,X22),X32)),aa_TPTP_ind_TPTP_ind(X12,X32)))))) # label(fact_ap__Pi) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 255 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1829701671all_of(aa_fun1584354236d_bool(aTP_Lamm_dc(X0),X12)),aa_fun1584354236d_bool(aTP_Lamm_de(X0),X12)))) # label(fact_e__in__p) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 256 (all X all Xa all Xb all Xc aa_TPTP_ind_TPTP_ind(scratc153871017nd_ite(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(X),Xc),Xa),X,Xb),Xc) = aa_TPTP_ind_TPTP_ind(scratc1930628756sel_wa(X,Xa,Xb),Xc)) # label(fact_def__wissel__wa) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 257 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X22),aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1709589394_Sigma,X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,aa_TPTP_ind_TPTP_ind(scratc1146276611_proj1,X22)),aa_TPTP_ind_TPTP_ind(X12,aa_TPTP_ind_TPTP_ind(scratc1146276610_proj0,X22)))))) # label(fact_proj1__Sigma) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 258 (all B_1 all B_2 gg_bool(scratc1624975209_amone(B_1,B_2))) # label(gsy_c_Scratch__tptp__translate__40362__32620_ONUM641__thf__4__p_Obnd__amone) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 259 (all X0 all X12 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc952408420d_Subq,X12),X0)) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X12),aa_TPTP_ind_TPTP_ind(scratc1017762772_power,X0))))) # label(fact_k__PowerI) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 260 (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(scratc1564950462d_e_is(Uua),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,Uub),Uuc)),Uue)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_ap,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1549486784bnd_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_aj(Uu),Uua),Uub),Uuc),Uud),Uue),Uuf)))) # label(fact_ATP_Olambda__88) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 261 (all X0 all X12 all X22 (gg_TPTP_ind(X22) & gg_TPTP_ind(X12) -> -pp(X0) & aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(X0,X12),X22) = X22 | X12 = aa_TPTP_ind_TPTP_ind(scratc1550011566bnd_if(X0,X12),X22) & pp(X0))) # label(fact_if__i__correct) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 262 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bt,Uu)) <-> pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_bs,Uu))))) # label(fact_ATP_Olambda__17) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 263 (all Uu all Uua (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_bl,Uu),Uua)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc192357794nd_nIn,Uua),Uu)))) # label(fact_ATP_Olambda__38) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 264 (all X0 all X12 (gg_TPTP_ind(X0) -> X0 = aa_TPTP_ind_TPTP_ind(scratc1146276610_proj0,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc1624135595d_pair,X0),X12)))) # label(fact_proj0__pair__eq) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 265 (all X all Xa all Xb (pp(aa_fun171081125l_bool(scratc87254192nd_all(X),aa_TPT43085870d_bool(aa_TPT60673477d_bool(aTP_Lamm_ar(X),Xa),Xb))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1290387246t_disj(X),Xa),Xb)))) # label(fact_def__st__disj) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 266 (all X0 all X12 all X22 (pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X22),aa_fun1431113780TP_ind(scratc322369131_d_Sep(X0),X12))) -> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1550011574bnd_in,X22),X0)))) # label(fact_k__SepE1) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 267 (all X0 all X12 pp(aa_fun171081125l_bool(scratc1829701671all_of(aa_TPT43085870d_bool(aTP_Lamm_ai,X0)),aa_TPT43085870d_bool(aTP_Lamm_cs(X0),X12)))) # label(fact_secondis1) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 268 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_ce,Uu)) <-> pp(aa_fun171081125l_bool(scratc1829701671all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cd,Uu))))) # label(fact_ATP_Olambda__15) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 269 (all X all Xa all Xb all Xc all Xd all Xe (pp(aa_fun171081125l_bool(scratc940362479l_some(X),aa_TPT43085870d_bool(scratc57423676_prop1(X,Xa,Xb,Xc,Xd),Xe))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1146670206_prop2(X,Xa,Xb,Xc),Xd),Xe)))) # label(fact_def__prop2) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 270 (all Uu all Uua all Uub (pp(aa_TPTP_ind_bool(aa_fun1584354236d_bool(aTP_Lamm_de(Uu),Uua),Uub)) <-> scratc1451164978_is_of(aa_TPTP_ind_TPTP_ind(scratc1564950457d_e_in(Uu,Uua),Uub),aa_TPT43085870d_bool(aTP_Lamm_ai,Uu)))) # label(fact_ATP_Olambda__51) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 271 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc873550751tminus(X),Xa) = aa_fun1431113780TP_ind(scratc322369131_d_Sep(X),aa_TPT43085870d_bool(aTP_Lamm_bl,Xa))) # label(fact_def__setminus) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 272 (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]. 0.93/1.25 273 (all X all Xa aa_TPTP_ind_TPTP_ind(scratc546250696etprod(X),Xa) = aa_fun277296641TP_ind(aa_TPT494704832TP_ind(scratc1709589394_Sigma,X),aTP_Lamm_ah(Xa))) # label(fact_def__setprod) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 274 (all X all Xa all Xb (pp(scratc546085760_d_not(aa_TPTP_ind_bool(Xa,Xb))) <-> pp(aa_TPTP_ind_bool(scratc194850556nd_non(X,Xa),Xb)))) # label(fact_def__non) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 275 (all X all Xa all Xb all Xc all Xd (pp(scratc438620580_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc153411835nd_imp,X),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(Xa),Xd),Xb)),aa_bool_bool(aa_boo1142376798l_bool(scratc153411835nd_imp,scratc546085760_d_not(X)),aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1564950462d_e_is(Xa),Xd),Xc)))) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1146670205_prop1(X,Xa,Xb),Xc),Xd)))) # label(fact_def__prop1) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 276 (all Uu aa_TPTP_ind_TPTP_ind(aTP_Lamm_ab,Uu) = scratc193932176nd_nat) # label(fact_ATP_Olambda__91) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 277 (all Uu (pp(aa_TPTP_ind_bool(aTP_Lamm_bu,Uu)) <-> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1083610823d_n_is,aa_TPTP_ind_TPTP_ind(scratc1084070009d_n_pl(scratc45782132nd_n_1),Uu)),aa_TPTP_ind_TPTP_ind(scratc912327602rdsucc,Uu))))) # label(fact_ATP_Olambda__4) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 278 (all X all Xa scratc153477422nd_ind(X,Xa) = scratc120562615nd_eps(aa_fun1584354236d_bool(aTP_Lamm_ba(X),Xa))) # label(fact_def__ind) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 279 (all X all Xa aa_fun1431113780TP_ind(scratc322369131_d_Sep(aa_TPTP_ind_TPTP_ind(scratc1017762772_power,X)),scratc759883004d_anec(X,Xa)) = scratc119709829nd_ect(X,Xa)) # label(fact_def__ect) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 280 (all Uu all Uua (gg_TPTP_ind(Uu) -> aa_TPTP_ind_TPTP_ind(aTP_Lamm_ah(Uu),Uua) = Uu)) # label(fact_ATP_Olambda__90) # label(axiom) # label(non_clause). [assumption]. 0.93/1.25 0.93/1.25 ============================== end of process non-clausal formulas === 0.93/1.29 0.93/1.29 ============================== PROCESS INITIAL CLAUSES =============== 0.93/1.29 0.93/1.29 ============================== PREDICATE ELIMINATION ================= 0.93/1.29 281 -pp(scratc546085760_d_not(scratc546085760_d_not(A))) | scratc268548109nd_wel(A) # label(fact_def__wel) # label(axiom). [clausify(55)]. 0.93/1.29 282 -scratc268548109nd_wel(A) | pp(A) # label(fact_l__et) # label(axiom). [clausify(11)]. 0.93/1.29 Derived: -pp(scratc546085760_d_not(scratc546085760_d_not(A))) | pp(A). [resolve(281,b,282,a)]. 0.93/1.29 283 pp(scratc546085760_d_not(scratc546085760_d_not(A))) | -scratc268548109nd_wel(A) # label(fact_def__wel) # label(axiom). [clausify(55)]. 0.93/1.29 284 -gg_bool(A) | fFalse = A | fTrue = A # label(help_fFalse_1_1_T) # label(axiom). [clausify(129)]. 0.93/1.29 285 gg_bool(aa_TPTP_ind_bool(A,B)) # label(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) # label(axiom). [clausify(43)]. 0.93/1.29 286 gg_bool(fFalse) # label(gsy_c_fFalse) # label(axiom). [assumption]. 0.93/1.29 287 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(52)]. 0.93/1.29 288 gg_bool(scratc438620580_d_and(A,B)) # label(gsy_c_Scratch__tptp__translate__40362__32620_ONUM641__thf__4__p_Obnd__d__and) # label(axiom). [clausify(67)]. 0.93/1.29 289 gg_bool(fTrue) # label(gsy_c_fTrue) # label(axiom). [assumption]. 0.93/1.29 290 gg_bool(aa_bool_bool(A,B)) # label(gsy_c_aa_001t__HOL__Obool_001t__HOL__Obool) # label(axiom). [clausify(104)]. 0.93/1.29 Derived: fFalse = aa_TPTP_ind_bool(A,B) | fTrue = aa_TPTP_ind_bool(A,B). [resolve(284,a,285,a)]. 0.93/1.29 Derived: fFalse = fFalse | fTrue = fFalse. [resolve(284,a,286,a)]. 0.93/1.29 Derived: fFalse = aa_fun171081125l_bool(A,B) | fTrue = aa_fun171081125l_bool(A,B). [resolve(284,a,287,a)]. 0.93/1.29 Derived: fFalse = scratc438620580_d_and(A,B) | fTrue = scratc438620580_d_and(A,B). [resolve(284,a,288,a)]. 0.93/1.29 Derived: fFalse = fTrue | fTrue = fTrue. [resolve(284,a,289,a)]. 0.93/1.29 Derived: fFalse = aa_bool_bool(A,B) | fTrue = aa_bool_bool(A,B). [resolve(284,a,290,a)]. 0.93/1.29 291 gg_bool(scratc203308799nd_or3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__40362__32620_ONUM641__thf__4__p_Obnd__or3) # label(axiom). [clausify(154)]. 0.93/1.29 Derived: fFalse = scratc203308799nd_or3(A,B,C) | fTrue = scratc203308799nd_or3(A,B,C). [resolve(291,a,284,a)]. 0.93/1.29 292 gg_bool(scratc119709764nd_ec3(A,B,C)) # label(gsy_c_Scratch__tptp__translate__40362__32620_ONUM641__thf__4__p_Obnd__ec3) # label(axiom). [clausify(166)]. 0.93/1.29 Derived: fFalse = scratc119709764nd_ec3(A,B,C) | fTrue = scratc119709764nd_ec3(A,B,C). [resolve(292,a,284,a)]. 0.93/1.29 293 gg_bool(scratc951703481d_l_ec(A,B)) # label(gsy_c_Scratch__tptp__translate__40362__32620_ONUM641__thf__4__p_Obnd__l__ec) # label(axiom). [clausify(188)]. 0.93/1.29 Derived: fFalse = scratc951703481d_l_ec(A,B) | fTrue = scratc951703481d_l_ec(A,B). [resolve(293,a,284,a)]. 0.93/1.29 294 gg_bool(scratc546085760_d_not(A)) # label(gsy_c_Scratch__tptp__translate__40362__32620_ONUM641__thf__4__p_Obnd__d__not) # label(axiom). [clausify(211)]. 0.93/1.29 Derived: fFalse = scratc546085760_d_not(A) | fTrue = scratc546085760_d_not(A). [resolve(294,a,284,a)]. 0.93/1.29 295 gg_bool(undefined_bool(bool)) # label(gsy_c_HOL_Oundefined_001t__HOL__Obool) # label(axiom). [assumption]. 0.93/1.29 Derived: fFalse = undefined_bool(bool) | fTrue = undefined_bool(bool). [resolve(295,a,284,a)]. 0.93/1.29 296 gg_bool(fEx_TPTP_ind(A)) # label(gsy_c_fEx_001t__TPTP____Interpret__Oind) # label(axiom). [clausify(244)]. 0.93/1.29 Derived: fFalse = fEx_TPTP_ind(A) | fTrue = fEx_TPTP_ind(A). [resolve(296,a,284,a)]. 0.93/1.29 297 gg_bool(scratc1624975209_amone(A,B)) # label(gsy_c_Scratch__tptp__translate__40362__32620_ONUM641__thf__4__p_Obnd__amone) # label(axiom). [clausify(258)]. 0.93/1.29 Derived: fFalse = scratc1624975209_amone(A,B) | fTrue = scratc1624975209_amone(A,B). [resolve(297,a,284,a)]. 0.93/1.29 298 pp(scratc438620580_d_and(scratc203308799nd_or3(A,B,C),scratc119709764nd_ec3(A,B,C))) | -scratc2071121729_orec3(A,B,C) # label(fact_def__orec3) # label(axiom). [clausify(66)]. 0.93/1.29 299 -pp(scratc438620580_d_and(scratc203308799nd_or3(A,B,C),scratc119709764nd_ec3(A,B,C))) | scratc2071121729_orec3(A,B,C) # label(fact_def__orec3) # label(axiom). [clausify(66)]. 0.93/1.48 300 pp(scratc438620580_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc153411835nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc153411835nd_imp,B),A))) | -scratc1332762030_l_iff(A,B) # label(fact_def__l__iff) # label(axiom). [clausify(82)]. 0.93/1.48 301 -pp(scratc438620580_d_and(aa_bool_bool(aa_boo1142376798l_bool(scratc153411835nd_imp,A),B),aa_bool_bool(aa_boo1142376798l_bool(scratc153411835nd_imp,B),A))) | scratc1332762030_l_iff(A,B) # label(fact_def__l__iff) # label(axiom). [clausify(82)]. 0.93/1.48 302 scratc983731570d_orec(A,B) | -pp(scratc438620580_d_and(aa_bool_bool(scratc952359486d_l_or(A),B),scratc951703481d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(121)]. 0.93/1.48 303 -scratc983731570d_orec(A,B) | pp(scratc438620580_d_and(aa_bool_bool(scratc952359486d_l_or(A),B),scratc951703481d_l_ec(A,B))) # label(fact_def__orec) # label(axiom). [clausify(121)]. 0.93/1.48 304 -pp(A) | pp(scratc546085760_d_not(B)) | -scratc1346638271d_r_ec(A,B) # label(fact_def__r__ec) # label(axiom). [clausify(168)]. 0.93/1.48 305 pp(A) | scratc1346638271d_r_ec(A,B) # label(fact_def__r__ec) # label(axiom). [clausify(168)]. 0.93/1.48 306 -pp(scratc546085760_d_not(A)) | scratc1346638271d_r_ec(B,A) # label(fact_def__r__ec) # label(axiom). [clausify(168)]. 0.93/1.48 0.93/1.48 ============================== end predicate elimination ============= 0.93/1.48 0.93/1.48 Auto_denials: (non-Horn, no changes). 0.93/1.48 0.93/1.48 Term ordering decisions: 0.93/1.48 Function symbol KB weights: scratc1550011574bnd_in=1. scratc912327602rdsucc=1. scratc1549486784bnd_ap=1. aTP_Lamm_ai=1. scratc1083610823d_n_is=1. scratc1745451206ptyset=1. aTP_Lamm_a=1. scratc1709589394_Sigma=1. scratc45782132nd_n_1=1. fFalse=1. scratc1017762772_power=1. scratc1337809184_nat_p=1. scratc423746188d_d_Pi=1. scratc193932176nd_nat=1. scratc1071331552d_repl=1. scratc153411835nd_imp=1. fTrue=1. scratc194456967nd_nis=1. scratc1624135595d_pair=1. scratc952408420d_Subq=1. scratc1137838734closed=1. scratc1146276610_proj0=1. scratc1525024638_union=1. aTP_Lamm_ae=1. scratc1083610818d_n_in=1. scratc1146276611_proj1=1. scratc2011078052_n_all=1. aTP_Lamm_ab=1. aTP_Lamm_ad=1. aTP_Lamm_cm=1. scratc468858728closed=1. scratc633591742closed=1. aTP_Lamm_cd=1. aTP_Lamm_ch=1. aTP_Lamm_ci=1. scratc1657584698_prop2=1. scratc1675368811closed=1. scratc1679165215d_Inj1=1. scratc1684187121n_some=1. scratc315931824_omega=1. aTP_Lamm_af=1. aTP_Lamm_bf=1. aTP_Lamm_bh=1. aTP_Lamm_bi=1. aTP_Lamm_bp=1. aTP_Lamm_bs=1. aTP_Lamm_bv=1. aTP_Lamm_by=1. aTP_Lamm_ca=1. aTP_Lamm_cb=1. aTP_Lamm_cg=1. fconj=1. fimplies=1. scratc1161393343_cond2=1. scratc1657584697_prop1=1. scratc1679165214d_Inj0=1. scratc854057538d_Sing=1. aTP_Lamm_bl=1. aTP_Lamm_bq=1. aTP_Lamm_br=1. aTP_Lamm_bt=1. aTP_Lamm_bu=1. aTP_Lamm_bw=1. aTP_Lamm_bx=1. aTP_Lamm_bz=1. aTP_Lamm_cc=1. aTP_Lamm_ce=1. aTP_Lamm_cf=1. aTP_Lamm_cj=1. aTP_Lamm_ck=1. aTP_Lamm_cl=1. aTP_Lamm_co=1. aTP_Lamm_dl=1. fequal_TPTP_ind=1. scratc1161393342_cond1=1. scratc1770865966univof=1. scratc192357794nd_nIn=1. scratc2126870313_n_one=1. scratc339482526_d_Unj=1. aTP_Lamm_aa=1. aTP_Lamm_ag=1. aTP_Lamm_bj=1. aTP_Lamm_bk=1. bool=1. scratc1069222522_prop1=1. scratc1146670208_prop4=1. scratc1715799339d_plus=1. scratc1896920188_empty=1. scratc2031046193nempty=1. scratc2110891758munion=1. scratc480860347_prop1=1. scratc769077573pair_p=1. scratc2122730866d_24_g=1. scratc280311546d_i1_s=1. tPTP_ind=1. aa_TPTP_ind_bool=1. aa_TPT43085870d_bool=1. aa_TPTP_ind_TPTP_ind=1. aa_fun171081125l_bool=1. aa_TPT1424761345TP_ind=1. aa_TPT60673477d_bool=1. aa_fun277296641TP_ind=1. aa_TPT494704832TP_ind=1. aa_fun1584354236d_bool=1. aa_bool_bool=1. aa_fun1431113780TP_ind=1. aa_boo1142376798l_bool=1. aa_TPT1123896796d_bool=1. scratc438620580_d_and=1. scratc1550011566bnd_if=1. scratc951703481d_l_ec=1. aa_fun1212484691d_bool=1. aa_TPT985247859d_bool=1. scratc1564950457d_e_in=1. scratc1949829805d_pair=1. aa_fun987228051d_bool=1. scratc153477422nd_ind=1. scratc1061739109second=1. scratc2035434666_image=1. scratc2078076735_first=1. aa_TPT125613450d_bool=1. scratc1624975209_amone=1. scratc194850556nd_non=1. aa_fun1913827119d_bool=1. scratc759883004d_anec=1. aa_TPT1791839040TP_ind=1. aa_fun1107270209d_bool=1. aa_fun845057962d_bool=1. scratc119709825nd_ecp=1. scratc407235996eplSep=1. scratc442097790_ecelt=1. scratc441507399_ecect=1. aa_TPT1781712639TP_ind=1. aa_TPT2142672771l_bool=1. aa_fun1235454963TP_ind=1. cOMBB_658106424TP_ind=1. cOMBS_2003118649l_bool=1. scratc119709829nd_ect=1. scratc1991259070etprop=1. scratc203505661nd_out=1. scratc2069953503fixfu2=1. scratc2126792979_fixfu=1. scratc302523178wissel=1. scratc434496381ectset=1. scratc310575295nverse=1. scratc319294504ectelt=1. scratc540613727unmore=1. scratc563244838d_invf=1. scratc566981369d_tofs=1. f11=1. f13=1. f15=1. f20=1. f21=1. scratc1829701671all_of=1. scratc1564950462d_e_is=1. scratc322369131_d_Sep=1. scratc1777039668d_esti=1. scratc1084070009d_n_pl=1. scratc546085760_d_not=1. scratc940362479l_some=1. scratc87254192nd_all=1. scratc1376844911_rec_G=1. aTP_Lamm_ah=1. aTP_Lamm_cv=1. scratc203046453nd_one=1. scratc952359486d_l_or=1. aTP_Lamm_aj=1. aTP_Lamm_at=1. aTP_Lamm_bb=1. aTP_Lamm_bo=1. aTP_Lamm_cn=1. aTP_Lamm_dj=1. scratc561998463d_incl=1. aTP_Lamm_an=1. aTP_Lamm_ax=1. aTP_Lamm_ba=1. aTP_Lamm_be=1. aTP_Lamm_df=1. aTP_Lamm_dh=1. scratc120562615nd_eps=1. scratc187235926ective=1. scratc546250696etprod=1. aTP_Lamm_ak=1. aTP_Lamm_al=1. aTP_Lamm_am=1. aTP_Lamm_ao=1. aTP_Lamm_ap=1. aTP_Lamm_ar=1. aTP_Lamm_as=1. aTP_Lamm_ay=1. aTP_Lamm_az=1. aTP_Lamm_bc=1. aTP_Lamm_cp=1. aTP_Lamm_cq=1. aTP_Lamm_cr=1. aTP_Lamm_ct=1. aTP_Lamm_cz=1. aTP_Lamm_db=1. aTP_Lamm_dc=1. aTP_Lamm_dg=1. fEx_TPTP_ind=1. scratc1527004365ective=1. scratc957265209nunion=1. aTP_Lamm_aq=1. aTP_Lamm_cs=1. aTP_Lamm_cu=1. aTP_Lamm_cw=1. aTP_Lamm_cx=1. aTP_Lamm_cy=1. aTP_Lamm_da=1. aTP_Lamm_dd=1. aTP_Lamm_de=1. aTP_Lamm_di=1. aTP_Lamm_dk=1. scratc134999576In_rec=1. scratc1604075772_UPair=1. aTP_Lamm_ac=1. aTP_Lamm_au=1. aTP_Lamm_av=1. aTP_Lamm_aw=1. aTP_Lamm_bd=1. aTP_Lamm_bg=1. aTP_Lamm_bm=1. aTP_Lamm_bn=1. cOMBC_1555011498d_bool=1. scratc1146670207_prop3=1. scratc1290387246t_disj=1. scratc370955156ective=1. scratc873550751tminus=1. undefined_bool=1. undefined_TPTP_ind=1. f2=1. f5=1. f10=1. f12=1. f14=1. f17=1. f18=1. f22=1. f23=1. f24=1. scratc119709764nd_ec3=1. scratc1933877819d_soft=1. scratc203308799nd_or3=1. scratc1146670205_prop1=1. scratc153871017nd_ite=1. scratc693191546_indeq=1. scratc1930628756sel_wa=1. scratc1930628757sel_wb=1. scratc788888630d_11_i=1. f1=1. f3=1. f4=1. f8=1. f19=1. f25=1. scratc1146670206_prop2=1. scratc324534245hangef=1. scratc43785844_inj_h=1. f6=1. f7=1. f16=1. scratc57423676_prop1=1. scratc1853463352indeq2=1. f9=1. 3.35/3.64 3.35/3.64 ============================== end of process initial clauses ======== 3.35/3.64 3.35/3.64 ============================== CLAUSES FOR SEARCH ==================== 3.35/3.64 3.35/3.64 ============================== end of clauses for search ============= 3.35/3.64 3.35/3.64 ============================== SEARCH ================================ 3.35/3.64 3.35/3.64 % Starting search at 0.29 seconds. 3.35/3.64 3.35/3.64 Low Water (keep): wt=36.000, iters=3388 3.35/3.64 3.35/3.64 Low Water (keep): wt=35.000, iters=3351 3.35/3.64 3.35/3.64 Low Water (keep): wt=34.000, iters=3381 3.35/3.64 3.35/3.64 Low Water (keep): wt=33.000, iters=3357 3.35/3.64 3.35/3.64 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 67 (0.00 of 1.21 sec). 3.35/3.64 3.35/3.64 Low Water (keep): wt=32.000, iters=3385 3.35/3.64 3.35/3.64 Low Water (keep): wt=30.000, iters=3405 3.35/3.64 3.35/3.64 Low Water (keep): wt=28.000, iters=3435 3.35/3.64 3.35/3.64 Low Water (keep): wt=27.000, iters=3335 3.35/3.64 3.35/3.64 Low Water (keep): wt=26.000, iters=4635 3.35/3.64 3.35/3.64 Low Water (keep): wt=23.000, iters=4190 3.35/3.64 3.35/3.64 Low Water (keep): wt=22.000, iters=3976 3.35/3.64 3.35/3.64 Low Water (keep): wt=21.000, iters=3717 3.35/3.64 3.35/3.64 Low Water (keep): wt=20.000, iters=3550 3.35/3.64 3.35/3.64 Low Water (keep): wt=19.000, iters=3340 3.35/3.64 3.35/3.64 Low Water (keep): wt=18.000, iters=3346 3.35/3.64 3.35/3.64 Low Water (keep): wt=17.000, iters=3358 3.35/3.64 3.35/3.64 Low Water (keep): wt=16.000, iters=3485 3.35/3.64 3.35/3.64 Low Water (displace): id=5765, wt=122.000 3.35/3.64 3.35/3.64 Low Water (displace): id=4368, wt=84.000 3.35/3.64 3.35/3.64 Low Water (displace): id=5908, wt=79.000 3.35/3.64 3.35/3.64 Low Water (displace): id=5766, wt=76.000 3.35/3.64 3.35/3.64 Low Water (displace): id=6261, wt=73.000 3.35/3.64 3.35/3.64 Low Water (displace): id=12137, wt=15.000 3.35/3.64 3.35/3.64 Low Water (displace): id=12138, wt=13.000 3.35/3.64 3.35/3.64 Low Water (displace): id=12150, wt=12.000 3.35/3.64 3.35/3.64 Low Water (keep): wt=15.000, iters=3385 3.35/3.64 3.35/3.64 Low Water (displace): id=12515, wt=10.000 3.35/3.64 3.35/3.64 LCputime limit exceeded (core dumped) 180.01/180.32 EOF