TSTP Solution File: SWW478+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW478+1 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 01:17:16 EDT 2022
% Result : Theorem 0.90s 1.26s
% Output : Refutation 0.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWW478+1 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n019.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 : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 5 22:15:10 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.90/1.18 ============================== Prover9 ===============================
% 0.90/1.18 Prover9 (32) version 2009-11A, November 2009.
% 0.90/1.18 Process 24455 was started by sandbox on n019.cluster.edu,
% 0.90/1.18 Sun Jun 5 22:15:11 2022
% 0.90/1.18 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_24302_n019.cluster.edu".
% 0.90/1.18 ============================== end of head ===========================
% 0.90/1.18
% 0.90/1.18 ============================== INPUT =================================
% 0.90/1.18
% 0.90/1.18 % Reading from file /tmp/Prover9_24302_n019.cluster.edu
% 0.90/1.18
% 0.90/1.18 set(prolog_style_variables).
% 0.90/1.18 set(auto2).
% 0.90/1.18 % set(auto2) -> set(auto).
% 0.90/1.18 % set(auto) -> set(auto_inference).
% 0.90/1.18 % set(auto) -> set(auto_setup).
% 0.90/1.18 % set(auto_setup) -> set(predicate_elim).
% 0.90/1.18 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.90/1.18 % set(auto) -> set(auto_limits).
% 0.90/1.18 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.90/1.18 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.90/1.18 % set(auto) -> set(auto_denials).
% 0.90/1.18 % set(auto) -> set(auto_process).
% 0.90/1.18 % set(auto2) -> assign(new_constants, 1).
% 0.90/1.18 % set(auto2) -> assign(fold_denial_max, 3).
% 0.90/1.18 % set(auto2) -> assign(max_weight, "200.000").
% 0.90/1.18 % set(auto2) -> assign(max_hours, 1).
% 0.90/1.18 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.90/1.18 % set(auto2) -> assign(max_seconds, 0).
% 0.90/1.18 % set(auto2) -> assign(max_minutes, 5).
% 0.90/1.18 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.90/1.18 % set(auto2) -> set(sort_initial_sos).
% 0.90/1.18 % set(auto2) -> assign(sos_limit, -1).
% 0.90/1.18 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.90/1.18 % set(auto2) -> assign(max_megs, 400).
% 0.90/1.18 % set(auto2) -> assign(stats, some).
% 0.90/1.18 % set(auto2) -> clear(echo_input).
% 0.90/1.18 % set(auto2) -> set(quiet).
% 0.90/1.18 % set(auto2) -> clear(print_initial_clauses).
% 0.90/1.18 % set(auto2) -> clear(print_given).
% 0.90/1.18 assign(lrs_ticks,-1).
% 0.90/1.18 assign(sos_limit,10000).
% 0.90/1.18 assign(order,kbo).
% 0.90/1.18 set(lex_order_vars).
% 0.90/1.18 clear(print_given).
% 0.90/1.18
% 0.90/1.18 % formulas(sos). % not echoed (213 formulas)
% 0.90/1.18
% 0.90/1.18 ============================== end of input ==========================
% 0.90/1.18
% 0.90/1.18 % From the command line: assign(max_seconds, 300).
% 0.90/1.18
% 0.90/1.18 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.90/1.18
% 0.90/1.18 % Formulas that are not ordinary clauses:
% 0.90/1.18 1 (all B_1_1 all B_2_1 is_bool(assigned(B_1_1,B_2_1))) # label(gsy_c_SmallStep_Oassigned) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 2 (all B_1_1 all B_2_1 all B_3 is_bool(widen_2090681816t_char(B_1_1,B_2_1,B_3))) # label(gsy_c_TypeRel_Owiden_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 3 (all B_1_1 all B_2_1 is_bool(wf_pro755087577t_char(B_1_1,B_2_1))) # label(gsy_c_WellForm_Owf__prog_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Stri) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 4 (all B_1_1 all B_2_1 all B_3 all B_4 all B_5 is_bool(wTrt(B_1_1,B_2_1,B_3,B_4,B_5))) # label(gsy_c_WellTypeRT_OWTrt) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 5 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_bool(hAPP_bool_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 6 (all B_1_1 all B_2_1 is_bool(hAPP_f1001225811y_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 7 (all B_1_1 all B_2_1 is_bool(hAPP_f1033709212l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption_001) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 8 (all B_1_1 all B_2_1 is_bool(hAPP_f61040418l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__O) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 9 (all B_1_1 all B_2_1 is_bool(hAPP_P1708370145l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_M) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 10 (all B_1_1 all B_2_1 is_bool(hAPP_P159683425l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 11 (all B_1_1 all B_2_1 is_bool(hAPP_P282169671l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 12 (all B_1_1 all B_2_1 is_bool(member840932460on_val(B_1_1,B_2_1))) # label(gsy_c_member_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 13 (all B_1_1 all B_2_1 is_bool(member763590124on_val(B_1_1,B_2_1))) # label(gsy_c_member_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 14 (all B_1_1 all B_2_1 is_bool(member773094996on_val(B_1_1,B_2_1))) # label(gsy_c_member_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String_) # label(hypothesis) # label(non_clause). [assumption].
% 0.90/1.18 15 (all F all X_1 fun_up1149430426on_val(F,X_1,hAPP_l207779698on_val(F,X_1)) = F) # label(fact_2_fun__upd__triv) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 16 (all F all X_1 fun_up424764369ion_ty(F,X_1,hAPP_l512744617ion_ty(F,X_1)) = F) # label(fact_3_fun__upd__triv) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 17 (all M all A_10 all B_1 all X_1 all Y_1 (hAPP_l207779698on_val(fun_up1149430426on_val(M,A_10,some_val(B_1)),X_1) = some_val(Y_1) <-> X_1 = A_10 & B_1 = Y_1 | X_1 != A_10 & hAPP_l207779698on_val(M,X_1) = some_val(Y_1))) # label(fact_5_map__upd__Some__unfold) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 18 (all M all A_10 all B_1 all X_1 all Y_1 (hAPP_l512744617ion_ty(fun_up424764369ion_ty(M,A_10,some_ty(B_1)),X_1) = some_ty(Y_1) <-> X_1 = A_10 & B_1 = Y_1 | X_1 != A_10 & hAPP_l512744617ion_ty(M,X_1) = some_ty(Y_1))) # label(fact_6_map__upd__Some__unfold) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 19 (all T all K all X_1 (hAPP_l207779698on_val(T,K) = some_val(X_1) -> fun_up1149430426on_val(T,K,some_val(X_1)) = T)) # label(fact_7_map__upd__triv) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 20 (all T all K all X_1 (hAPP_l512744617ion_ty(T,K) = some_ty(X_1) -> fun_up424764369ion_ty(T,K,some_ty(X_1)) = T)) # label(fact_8_map__upd__triv) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 21 (all M all A_10 all X_1 all N all Y_1 (fun_up1149430426on_val(M,A_10,some_val(X_1)) = fun_up1149430426on_val(N,A_10,some_val(Y_1)) -> X_1 = Y_1)) # label(fact_9_map__upd__eqD1) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 22 (all M all A_10 all X_1 all N all Y_1 (fun_up424764369ion_ty(M,A_10,some_ty(X_1)) = fun_up424764369ion_ty(N,A_10,some_ty(Y_1)) -> X_1 = Y_1)) # label(fact_10_map__upd__eqD1) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 23 (all Ta all Ea (hBOOL(hAPP_P159683425l_bool(typeSa1234865140_sconf(p,Ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,ha),fun_up1149430426on_val(la,v_1,some_val(v))))) -> (hBOOL(wTrt(p,ha,Ea,ea,Ta)) -> (exists T_5 (hBOOL(wTrt(p,h_a,Ea,e_a,T_5)) & hBOOL(widen_2090681816t_char(p,T_5,Ta))))))) # label(fact_11_InitBlockRed_I2_J) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 24 (all X_1 all Pa ((all A_15 all B all C_1 all D_1 hBOOL(hAPP_P282169671l_bool(Pa,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,C_1),D_1)))))) -> hBOOL(hAPP_P282169671l_bool(Pa,X_1)))) # label(fact_12_prod__induct4) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 25 (all Y_1 -(all A_15 all B all C_1 all D_1 Y_1 != hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,C_1),D_1))))) # label(fact_13_prod__cases4) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 26 (all A_10 all B_1 all A_9 all B_2 (hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_10),B_1) = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_9),B_2) -> -(A_10 = A_9 -> B_1 != B_2))) # label(fact_15_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 27 (all A_10 all B_1 all A_9 all B_2 (hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_10),B_1) = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_9),B_2) -> -(A_10 = A_9 -> B_1 != B_2))) # label(fact_16_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 28 (all A_10 all B_1 all A_9 all B_2 (hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_10),B_1) = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_9),B_2) -> -(A_10 = A_9 -> B_1 != B_2))) # label(fact_17_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 29 (all A_10 all B_1 all A_9 all B_2 (hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_10),B_1) = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_9),B_2) <-> A_10 = A_9 & B_1 = B_2)) # label(fact_18_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 30 (all A_10 all B_1 all A_9 all B_2 (hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_10),B_1) = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_9),B_2) <-> A_10 = A_9 & B_1 = B_2)) # label(fact_19_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 31 (all A_10 all B_1 all A_9 all B_2 (hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_10),B_1) = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_9),B_2) <-> A_10 = A_9 & B_1 = B_2)) # label(fact_20_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 32 (all Pa ((all X1 hBOOL(hAPP_P282169671l_bool(Pa,X1))) <-> (all A_15 all B hBOOL(hAPP_P282169671l_bool(Pa,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),B)))))) # label(fact_21_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 33 (all Pa ((all X1 hBOOL(hAPP_P1708370145l_bool(Pa,X1))) <-> (all A_15 all B hBOOL(hAPP_P1708370145l_bool(Pa,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_15),B)))))) # label(fact_22_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 34 (all Pa ((all X1 hBOOL(hAPP_P159683425l_bool(Pa,X1))) <-> (all A_15 all B hBOOL(hAPP_P159683425l_bool(Pa,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_15),B)))))) # label(fact_23_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 35 (all F all B_1 all A_10 all X ((X = A_10 -> hAPP_l207779698on_val(fun_up1149430426on_val(F,A_10,B_1),X) = B_1) & (X != A_10 -> hAPP_l207779698on_val(fun_up1149430426on_val(F,A_10,B_1),X) = hAPP_l207779698on_val(F,X)))) # label(fact_24_fun__upd__def) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 36 (all F all B_1 all A_10 all X ((X = A_10 -> hAPP_l512744617ion_ty(fun_up424764369ion_ty(F,A_10,B_1),X) = B_1) & (X != A_10 -> hAPP_l512744617ion_ty(fun_up424764369ion_ty(F,A_10,B_1),X) = hAPP_l512744617ion_ty(F,X)))) # label(fact_25_fun__upd__def) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 37 (all F all X_1 all Y_1 (hAPP_l207779698on_val(F,X_1) = Y_1 -> fun_up1149430426on_val(F,X_1,Y_1) = F)) # label(fact_26_fun__upd__idem) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 38 (all F all X_1 all Y_1 (hAPP_l512744617ion_ty(F,X_1) = Y_1 -> fun_up424764369ion_ty(F,X_1,Y_1) = F)) # label(fact_27_fun__upd__idem) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 39 (all F all Y_1 all Z all X_1 (Z != X_1 -> hAPP_l207779698on_val(fun_up1149430426on_val(F,X_1,Y_1),Z) = hAPP_l207779698on_val(F,Z))) # label(fact_28_fun__upd__other) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 40 (all F all Y_1 all Z all X_1 (Z != X_1 -> hAPP_l512744617ion_ty(fun_up424764369ion_ty(F,X_1,Y_1),Z) = hAPP_l512744617ion_ty(F,Z))) # label(fact_29_fun__upd__other) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 41 (all M all B_1 all D all A_10 all C (A_10 != C -> fun_up1149430426on_val(fun_up1149430426on_val(M,A_10,B_1),C,D) = fun_up1149430426on_val(fun_up1149430426on_val(M,C,D),A_10,B_1))) # label(fact_30_fun__upd__twist) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 42 (all M all B_1 all D all A_10 all C (A_10 != C -> fun_up424764369ion_ty(fun_up424764369ion_ty(M,A_10,B_1),C,D) = fun_up424764369ion_ty(fun_up424764369ion_ty(M,C,D),A_10,B_1))) # label(fact_31_fun__upd__twist) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 43 (all F all Y_1 all Z all X_1 ((Z = X_1 -> hAPP_l207779698on_val(fun_up1149430426on_val(F,X_1,Y_1),Z) = Y_1) & (Z != X_1 -> hAPP_l207779698on_val(fun_up1149430426on_val(F,X_1,Y_1),Z) = hAPP_l207779698on_val(F,Z)))) # label(fact_32_fun__upd__apply) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 44 (all F all Y_1 all Z all X_1 ((Z = X_1 -> hAPP_l512744617ion_ty(fun_up424764369ion_ty(F,X_1,Y_1),Z) = Y_1) & (Z != X_1 -> hAPP_l512744617ion_ty(fun_up424764369ion_ty(F,X_1,Y_1),Z) = hAPP_l512744617ion_ty(F,Z)))) # label(fact_33_fun__upd__apply) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 45 (all F all X_1 all Y_1 hAPP_l207779698on_val(fun_up1149430426on_val(F,X_1,Y_1),X_1) = Y_1) # label(fact_34_fun__upd__same) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 46 (all F all X_1 all Y_1 hAPP_l512744617ion_ty(fun_up424764369ion_ty(F,X_1,Y_1),X_1) = Y_1) # label(fact_35_fun__upd__same) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 47 (all F all X_1 all Y_1 all Z fun_up1149430426on_val(fun_up1149430426on_val(F,X_1,Y_1),X_1,Z) = fun_up1149430426on_val(F,X_1,Z)) # label(fact_36_fun__upd__upd) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 48 (all F all X_1 all Y_1 all Z fun_up424764369ion_ty(fun_up424764369ion_ty(F,X_1,Y_1),X_1,Z) = fun_up424764369ion_ty(F,X_1,Z)) # label(fact_37_fun__upd__upd) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 49 (all F all X_1 all Y_1 (fun_up1149430426on_val(F,X_1,Y_1) = F <-> hAPP_l207779698on_val(F,X_1) = Y_1)) # label(fact_38_fun__upd__idem__iff) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 50 (all F all X_1 all Y_1 (fun_up424764369ion_ty(F,X_1,Y_1) = F <-> hAPP_l512744617ion_ty(F,X_1) = Y_1)) # label(fact_39_fun__upd__idem__iff) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 51 (all P_3 all T_4 hBOOL(widen_2090681816t_char(P_3,T_4,T_4))) # label(fact_40_widen__refl) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 52 (all Ea all Ta all Eb all Hb all Lb all E_b all H_b all L_b all Pa (hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))),red(Pa))) -> (hBOOL(wTrt(Pa,Hb,Ea,Eb,Ta)) -> (hBOOL(hAPP_f61040418l_bool(hconf_97414254t_char(Pa),Hb)) -> hBOOL(hAPP_f61040418l_bool(hconf_97414254t_char(Pa),H_b)))))) # label(fact_41_red__preserves__hconf) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 53 (all Ea all Ta all Eb all Hb all Lb all E_b all H_b all L_b all Pa (hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))),red(Pa))) -> (hBOOL(wTrt(Pa,Hb,Ea,Eb,Ta)) -> (hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),Hb),Lb),Ea)) -> hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),H_b),L_b),Ea)))))) # label(fact_42_red__preserves__lconf) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 54 (all Y_1 -(all A_15 all B all C_1 Y_1 != hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B),C_1)))) # label(fact_43_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 55 (all Y_1 -(all A_15 all B all C_1 Y_1 != hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_15),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,B),C_1)))) # label(fact_44_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 56 (all X_1 all Pa ((all A_15 all B all C_1 hBOOL(hAPP_P282169671l_bool(Pa,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B),C_1))))) -> hBOOL(hAPP_P282169671l_bool(Pa,X_1)))) # label(fact_45_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 57 (all X_1 all Pa ((all A_15 all B all C_1 hBOOL(hAPP_P1708370145l_bool(Pa,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_15),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,B),C_1))))) -> hBOOL(hAPP_P1708370145l_bool(Pa,X_1)))) # label(fact_46_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 58 (all Ea all Ta all Eb all S all E_b all S_1 all Pa (hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_1)),red(Pa))) -> (hBOOL(wTrt(Pa,hp(S),Ea,Eb,Ta)) -> (hBOOL(hAPP_P159683425l_bool(typeSa1234865140_sconf(Pa,Ea),S)) -> hBOOL(hAPP_P159683425l_bool(typeSa1234865140_sconf(Pa,Ea),S_1)))))) # label(fact_47_red__preserves__sconf) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 59 (all S_3 all R_1 ((all X all Xa (hBOOL(member840932460on_val(hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X),Xa),R_1)) <-> hBOOL(member840932460on_val(hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X),Xa),S_3)))) <-> R_1 = S_3)) # label(fact_48_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 60 (all S_3 all R_1 ((all X all Xa (hBOOL(member763590124on_val(hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X),Xa),R_1)) <-> hBOOL(member763590124on_val(hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X),Xa),S_3)))) <-> R_1 = S_3)) # label(fact_49_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 61 (all S_3 all R_1 ((all X all Xa (hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X),Xa),R_1)) <-> hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X),Xa),S_3)))) <-> R_1 = S_3)) # label(fact_50_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 62 (all Y_1 -(all A_15 all B Y_1 != hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),B))) # label(fact_51_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 63 (all Y_1 -(all A_15 all B Y_1 != hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_15),B))) # label(fact_52_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 64 (all Y_1 -(all A_15 all B Y_1 != hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_15),B))) # label(fact_53_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 65 (all T_3 all P_2 all S_2 all U_1 (hBOOL(widen_2090681816t_char(P_2,S_2,U_1)) -> (hBOOL(widen_2090681816t_char(P_2,U_1,T_3)) -> hBOOL(widen_2090681816t_char(P_2,S_2,T_3))))) # label(fact_54_widen__trans) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 66 (all Pa ((exists X1 hBOOL(hAPP_P282169671l_bool(Pa,X1))) <-> (exists A_15 exists B hBOOL(hAPP_P282169671l_bool(Pa,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),B)))))) # label(fact_56_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 67 (all Pa ((exists X1 hBOOL(hAPP_P1708370145l_bool(Pa,X1))) <-> (exists A_15 exists B hBOOL(hAPP_P1708370145l_bool(Pa,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_15),B)))))) # label(fact_57_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 68 (all Pa ((exists X1 hBOOL(hAPP_P159683425l_bool(Pa,X1))) <-> (exists A_15 exists B hBOOL(hAPP_P159683425l_bool(Pa,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_15),B)))))) # label(fact_58_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 69 (all P_1 -(all X all Y P_1 != hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X),Y))) # label(fact_59_PairE) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 70 (all P_1 -(all X all Y P_1 != hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X),Y))) # label(fact_60_PairE) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 71 (all P_1 -(all X all Y P_1 != hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X),Y))) # label(fact_61_PairE) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 72 (all C all A_10 all B_1 (hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc2128769400l_bool,C),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_10),B_1))) <-> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(C,A_10),B_1)))) # label(fact_62_internal__split__conv) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 73 (all Pa all Ea all S (hBOOL(hAPP_P159683425l_bool(typeSa1234865140_sconf(Pa,Ea),S)) <-> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,cOMBS_570216337l_bool(hAPP_f1523875321l_bool(hAPP_f592397849l_bool(cOMBB_1718333400on_val,cOMBB_383678192on_val),hAPP_f1452292669l_bool(hAPP_f1977633121l_bool(cOMBB_1303934920on_val,fconj),hconf_97414254t_char(Pa))),hAPP_f550652027l_bool(hAPP_f838396643l_bool(cOMBC_2027949654l_bool,hAPP_f857351829l_bool(hAPP_f348318673l_bool(cOMBB_1518282696on_val,cOMBC_832625297y_bool),lconf_496643946t_char(Pa))),Ea))),S)))) # label(fact_63_sconf__def) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 74 (all F1 all A_10 all B_1 (hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(F1,A_10),B_1)) -> hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,F1),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_10),B_1))))) # label(fact_64_prod__caseI) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 75 (all F1 all A_10 all B_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(F1,A_10),B_1)) -> hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,F1),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_10),B_1))))) # label(fact_65_prod__caseI) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 76 (all F1 all A_10 all B_1 (hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F1,A_10),B_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_10),B_1))))) # label(fact_66_prod__caseI) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 77 (all F all A_10 all B_1 (hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(F,A_10),B_1)) -> hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,F),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_10),B_1))))) # label(fact_67_splitI) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 78 (all F all A_10 all B_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(F,A_10),B_1)) -> hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,F),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_10),B_1))))) # label(fact_68_splitI) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 79 (all F all A_10 all B_1 (hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F,A_10),B_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_10),B_1))))) # label(fact_69_splitI) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 80 (all F all A_10 all B_1 (hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,F),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_10),B_1))) -> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(F,A_10),B_1)))) # label(fact_70_splitD) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 81 (all F all A_10 all B_1 (hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,F),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_10),B_1))) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(F,A_10),B_1)))) # label(fact_71_splitD) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 82 (all F all A_10 all B_1 (hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_10),B_1))) -> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F,A_10),B_1)))) # label(fact_72_splitD) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 83 (all C all P_1 all Q_2 (P_1 = Q_2 -> (hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,C),P_1)) <-> hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,C),Q_2))))) # label(fact_73_split__weak__cong) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 84 (all C all P_1 all Q_2 (P_1 = Q_2 -> (hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,C),P_1)) <-> hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,C),Q_2))))) # label(fact_74_split__weak__cong) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 85 (all C all P_1 all Q_2 (P_1 = Q_2 -> (hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,C),P_1)) <-> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,C),Q_2))))) # label(fact_75_split__weak__cong) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 86 (all F all G all P_1 (hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F),hAPP_P789556885on_val(hAPP_f1520199827on_val(produc1174947465on_val,G),P_1))) <-> hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,hAPP_f653692369l_bool(hAPP_f516738477l_bool(cOMBB_819439237t_char,hAPP_f1825030711l_bool(cOMBB_877741809on_val,hAPP_f2121594859l_bool(produc1958875245l_bool,F))),G)),P_1)))) # label(fact_79_split__twice) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 87 (all F all G all P_1 (hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F),hAPP_P1760219823on_val(hAPP_f394183983on_val(produc1003071703on_val,G),P_1))) <-> hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,hAPP_f1241216909l_bool(hAPP_f1438732387l_bool(cOMBB_635947099on_val,hAPP_f881985847l_bool(cOMBB_1083177073on_val,hAPP_f2121594859l_bool(produc1958875245l_bool,F))),G)),P_1)))) # label(fact_80_split__twice) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 88 (all F all G all P_1 (hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,F),hAPP_P604205461on_val(hAPP_f1309113673on_val(produc901351817on_val,G),P_1))) <-> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f850751421l_bool(hAPP_f399538905l_bool(cOMBB_1466889536on_val,hAPP_f1233687287l_bool(cOMBB_171276332on_val,hAPP_f1930574389l_bool(produc1815960045l_bool,F))),G)),P_1)))) # label(fact_81_split__twice) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 89 (all F all G all P_1 (hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,F),hAPP_P2024243179on_val(hAPP_f204556415on_val(produc1148763895on_val,G),P_1))) <-> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f927043595l_bool(hAPP_f1043869573l_bool(cOMBB_1259202826on_val,hAPP_f2052660463l_bool(cOMBB_1292453606on_val,hAPP_f635218277l_bool(produc1911463199l_bool,F))),G)),P_1)))) # label(fact_82_split__twice) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 90 (all Pa all Q_1 all X (hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,hAPP_f546724245l_bool(hAPP_f917296015l_bool(cOMBB_740252943t_char,hAPP_f1308714617l_bool(cOMBB_338347573on_val,hAPP_b589554111l_bool(fconj,Pa))),Q_1)),X)) <-> hBOOL(Pa) & hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,Q_1),X)))) # label(fact_83_split__part) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 91 (all Pa all Q_1 all X (hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,hAPP_f641257349l_bool(hAPP_f2032347769l_bool(cOMBB_466903633on_val,hAPP_f1560238713l_bool(cOMBB_672625589on_val,hAPP_b589554111l_bool(fconj,Pa))),Q_1)),X)) <-> hBOOL(Pa) & hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,Q_1),X)))) # label(fact_84_split__part) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 92 (all Pa all Q_1 all X (hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f555424277l_bool(hAPP_f1734879897l_bool(cOMBB_1522540928on_val,hAPP_f1863694447l_bool(cOMBB_383678192on_val,hAPP_b589554111l_bool(fconj,Pa))),Q_1)),X)) <-> hBOOL(Pa) & hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,Q_1),X)))) # label(fact_85_split__part) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 93 (all F1 all A_10 all B_1 (hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_10),B_1))) <-> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F1,A_10),B_1)))) # label(fact_86_prod_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 94 (all F1 all A_10 all B_1 (hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,F1),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_10),B_1))) <-> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(F1,A_10),B_1)))) # label(fact_87_prod_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 95 (all F1 all A_10 all B_1 (hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,F1),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_10),B_1))) <-> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(F1,A_10),B_1)))) # label(fact_88_prod_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 96 (all F all A_10 all B_1 (hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_10),B_1))) <-> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F,A_10),B_1)))) # label(fact_89_split__conv) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 97 (all F all A_10 all B_1 (hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,F),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_10),B_1))) <-> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(F,A_10),B_1)))) # label(fact_90_split__conv) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 98 (all F all A_10 all B_1 (hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,F),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_10),B_1))) <-> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(F,A_10),B_1)))) # label(fact_91_split__conv) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 99 (all F hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f1363667773l_bool(hAPP_f1050935001l_bool(cOMBB_1153617344on_val,hAPP_f2057883639l_bool(cOMBB_1750801836on_val,F)),produc899768717on_val)) = F) # label(fact_92_split__eta) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 100 (all F hAPP_f635218277l_bool(produc1911463199l_bool,hAPP_f1342895119l_bool(hAPP_f639265145l_bool(cOMBB_364363975on_val,hAPP_f365540729l_bool(cOMBB_1466662571on_val,F)),produc1441475159on_val)) = F) # label(fact_93_split__eta) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 101 (all F hAPP_f1930574389l_bool(produc1815960045l_bool,hAPP_f439412817l_bool(hAPP_f1725502637l_bool(cOMBB_1027621637t_char,hAPP_f10074679l_bool(cOMBB_1759207793on_val,F)),produc1259058957on_val)) = F) # label(fact_94_split__eta) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 102 (all Ta all V_a all Eb all Hb all Lb all Va_1 all Va all E_b all H_b all L_b all Pa (hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,Va_1,some_val(Va))))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))),red(Pa))) -> (hAPP_l207779698on_val(L_b,Va_1) = some_val(V_a) -> hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,val_list_char(Va)),Eb))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,val_list_char(V_a)),E_b))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,Va_1,hAPP_l207779698on_val(Lb,Va_1))))),red(Pa)))))) # label(fact_95_red__reds_OInitBlockRed) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 103 (all Va_1 all Ta all Va all U all S all Pa hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,val_list_char(Va)),val_list_char(U)))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,val_list_char(U)),S)),red(Pa)))) # label(fact_96_red__reds_ORedInitBlock) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 104 (all C all P_1 ((all A_15 all B (P_1 = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),B) -> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(C,A_15),B)))) -> hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,C),P_1)))) # label(fact_97_splitI2) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 105 (all C all P_1 ((all A_15 all B (P_1 = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_15),B) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(C,A_15),B)))) -> hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,C),P_1)))) # label(fact_98_splitI2) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 106 (all C all P_1 ((all A_15 all B (P_1 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_15),B) -> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(C,A_15),B)))) -> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,C),P_1)))) # label(fact_99_splitI2) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 107 (all C all P_1 (hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,C),P_1)) -> -(all X all Y (P_1 = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X),Y) -> -hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(C,X),Y)))))) # label(fact_100_splitE) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 108 (all C all P_1 (hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,C),P_1)) -> -(all X all Y (P_1 = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X),Y) -> -hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(C,X),Y)))))) # label(fact_101_splitE) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 109 (all C all P_1 (hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,C),P_1)) -> -(all X all Y (P_1 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X),Y) -> -hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(C,X),Y)))))) # label(fact_102_splitE) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 110 (all Pa all Hb all Ea all Va_1 all Ta all Eb all T_a (hBOOL(wTrt(Pa,Hb,fun_up424764369ion_ty(Ea,Va_1,some_ty(Ta)),Eb,T_a)) -> hBOOL(wTrt(Pa,Hb,Ea,block_list_char(Va_1,Ta,Eb),T_a)))) # label(fact_103_WTrtBlock) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.18 111 (all Z all C all A_10 all B_1 (hBOOL(member763590124on_val(Z,hAPP_P595502227l_bool(hAPP_P1134042693l_bool(C,A_10),B_1))) -> hBOOL(member763590124on_val(Z,hAPP_P1826803705l_bool(hAPP_f444383845l_bool(produc376702929l_bool,C),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_10),B_1)))))) # label(fact_104_mem__splitI) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 112 (all Z all C all A_10 all B_1 (hBOOL(member840932460on_val(Z,hAPP_P1116729363l_bool(hAPP_P1953518277l_bool(C,A_10),B_1))) -> hBOOL(member840932460on_val(Z,hAPP_P678729081l_bool(hAPP_f1591648613l_bool(produc20018513l_bool,C),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_10),B_1)))))) # label(fact_105_mem__splitI) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 113 (all Z all C all A_10 all B_1 (hBOOL(member763590124on_val(Z,hAPP_P1988153107l_bool(hAPP_e500528395l_bool(C,A_10),B_1))) -> hBOOL(member763590124on_val(Z,hAPP_P595502227l_bool(hAPP_f468299289l_bool(produc2036005791l_bool,C),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_10),B_1)))))) # label(fact_106_mem__splitI) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 114 (all Z all C all A_10 all B_1 (hBOOL(member840932460on_val(Z,hAPP_P1638898323l_bool(hAPP_e592495499l_bool(C,A_10),B_1))) -> hBOOL(member840932460on_val(Z,hAPP_P1116729363l_bool(hAPP_f1760682521l_bool(produc1275132703l_bool,C),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_10),B_1)))))) # label(fact_107_mem__splitI) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 115 (all Z all C all A_10 all B_1 (hBOOL(member763590124on_val(Z,hAPP_f396019662l_bool(hAPP_f2135509569l_bool(C,A_10),B_1))) -> hBOOL(member763590124on_val(Z,hAPP_P1988153107l_bool(hAPP_f1276548047l_bool(produc121041439l_bool,C),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_10),B_1)))))) # label(fact_108_mem__splitI) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 116 (all Z all C all A_10 all B_1 (hBOOL(member840932460on_val(Z,hAPP_f2011777102l_bool(hAPP_f2144092865l_bool(C,A_10),B_1))) -> hBOOL(member840932460on_val(Z,hAPP_P1638898323l_bool(hAPP_f833559503l_bool(produc334393759l_bool,C),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_10),B_1)))))) # label(fact_109_mem__splitI) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 117 (all E_2 all T_2 all Pa all Hb all Ea all E_1 all T_1 (hBOOL(wTrt(Pa,Hb,Ea,E_1,T_1)) -> (hBOOL(wTrt(Pa,Hb,Ea,E_2,T_2)) -> hBOOL(wTrt(Pa,Hb,Ea,seq_list_char(E_1,E_2),T_2))))) # label(fact_110_WTrtSeq) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 118 (all E_2 all Eb all S all E_b all S_1 all Pa (hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_1)),red(Pa))) -> hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,seq_list_char(Eb,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,seq_list_char(E_b,E_2)),S_1)),red(Pa))))) # label(fact_111_red__reds_OSeqRed) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 119 (all Va_1 all Eb all S all E_b all S_1 all Pa (hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_1)),red(Pa))) -> hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(Va_1,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(Va_1,E_b)),S_1)),red(Pa))))) # label(fact_112_red__reds_OLAssRed) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 120 (all Va all E_2 all S all Pa hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,seq_list_char(val_list_char(Va),E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),S)),red(Pa)))) # label(fact_113_red__reds_ORedSeq) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 121 (all Va_1 all Ta all U all S all Pa hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,val_list_char(U))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,val_list_char(U)),S)),red(Pa)))) # label(fact_114_red__reds_ORedBlock) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 122 (all Z all C all P_1 (hBOOL(member763590124on_val(Z,hAPP_P1826803705l_bool(hAPP_f444383845l_bool(produc376702929l_bool,C),P_1))) -> -(all X all Y (P_1 = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X),Y) -> -hBOOL(member763590124on_val(Z,hAPP_P595502227l_bool(hAPP_P1134042693l_bool(C,X),Y))))))) # label(fact_115_mem__splitE) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 123 (all Z all C all P_1 (hBOOL(member840932460on_val(Z,hAPP_P678729081l_bool(hAPP_f1591648613l_bool(produc20018513l_bool,C),P_1))) -> -(all X all Y (P_1 = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X),Y) -> -hBOOL(member840932460on_val(Z,hAPP_P1116729363l_bool(hAPP_P1953518277l_bool(C,X),Y))))))) # label(fact_116_mem__splitE) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 124 (all Z all C all P_1 (hBOOL(member763590124on_val(Z,hAPP_P595502227l_bool(hAPP_f468299289l_bool(produc2036005791l_bool,C),P_1))) -> -(all X all Y (P_1 = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X),Y) -> -hBOOL(member763590124on_val(Z,hAPP_P1988153107l_bool(hAPP_e500528395l_bool(C,X),Y))))))) # label(fact_117_mem__splitE) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 125 (all Z all C all P_1 (hBOOL(member840932460on_val(Z,hAPP_P1116729363l_bool(hAPP_f1760682521l_bool(produc1275132703l_bool,C),P_1))) -> -(all X all Y (P_1 = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X),Y) -> -hBOOL(member840932460on_val(Z,hAPP_P1638898323l_bool(hAPP_e592495499l_bool(C,X),Y))))))) # label(fact_118_mem__splitE) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 126 (all Z all C all P_1 (hBOOL(member763590124on_val(Z,hAPP_P1988153107l_bool(hAPP_f1276548047l_bool(produc121041439l_bool,C),P_1))) -> -(all X all Y (P_1 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X),Y) -> -hBOOL(member763590124on_val(Z,hAPP_f396019662l_bool(hAPP_f2135509569l_bool(C,X),Y))))))) # label(fact_119_mem__splitE) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 127 (all Z all C all P_1 (hBOOL(member840932460on_val(Z,hAPP_P1638898323l_bool(hAPP_f833559503l_bool(produc334393759l_bool,C),P_1))) -> -(all X all Y (P_1 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X),Y) -> -hBOOL(member840932460on_val(Z,hAPP_f2011777102l_bool(hAPP_f2144092865l_bool(C,X),Y))))))) # label(fact_120_mem__splitE) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 128 (all Z all C all P_1 ((all A_15 all B (P_1 = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),B) -> hBOOL(member763590124on_val(Z,hAPP_P595502227l_bool(hAPP_P1134042693l_bool(C,A_15),B))))) -> hBOOL(member763590124on_val(Z,hAPP_P1826803705l_bool(hAPP_f444383845l_bool(produc376702929l_bool,C),P_1))))) # label(fact_121_mem__splitI2) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 129 (all Z all C all P_1 ((all A_15 all B (P_1 = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),B) -> hBOOL(member840932460on_val(Z,hAPP_P1116729363l_bool(hAPP_P1953518277l_bool(C,A_15),B))))) -> hBOOL(member840932460on_val(Z,hAPP_P678729081l_bool(hAPP_f1591648613l_bool(produc20018513l_bool,C),P_1))))) # label(fact_122_mem__splitI2) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 130 (all Z all C all P_1 ((all A_15 all B (P_1 = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_15),B) -> hBOOL(member763590124on_val(Z,hAPP_P1988153107l_bool(hAPP_e500528395l_bool(C,A_15),B))))) -> hBOOL(member763590124on_val(Z,hAPP_P595502227l_bool(hAPP_f468299289l_bool(produc2036005791l_bool,C),P_1))))) # label(fact_123_mem__splitI2) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 131 (all Z all C all P_1 ((all A_15 all B (P_1 = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_15),B) -> hBOOL(member840932460on_val(Z,hAPP_P1638898323l_bool(hAPP_e592495499l_bool(C,A_15),B))))) -> hBOOL(member840932460on_val(Z,hAPP_P1116729363l_bool(hAPP_f1760682521l_bool(produc1275132703l_bool,C),P_1))))) # label(fact_124_mem__splitI2) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 132 (all Z all C all P_1 ((all A_15 all B (P_1 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_15),B) -> hBOOL(member763590124on_val(Z,hAPP_f396019662l_bool(hAPP_f2135509569l_bool(C,A_15),B))))) -> hBOOL(member763590124on_val(Z,hAPP_P1988153107l_bool(hAPP_f1276548047l_bool(produc121041439l_bool,C),P_1))))) # label(fact_125_mem__splitI2) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 133 (all Z all C all P_1 ((all A_15 all B (P_1 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_15),B) -> hBOOL(member840932460on_val(Z,hAPP_f2011777102l_bool(hAPP_f2144092865l_bool(C,A_15),B))))) -> hBOOL(member840932460on_val(Z,hAPP_P1638898323l_bool(hAPP_f833559503l_bool(produc334393759l_bool,C),P_1))))) # label(fact_126_mem__splitI2) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 134 (all Va_1 all Va all Hb all Lb all Pa hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(Va_1,val_list_char(Va))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,val_list_char(unit)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,Va_1,some_val(Va))))),red(Pa)))) # label(fact_127_red__reds_ORedLAss) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 135 (all G all F ((all X all Y (hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F,X),Y)) <-> hBOOL(hAPP_P159683425l_bool(G,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X),Y))))) -> hAPP_f2121594859l_bool(produc1958875245l_bool,F) = G)) # label(fact_128_cond__split__eta) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 136 (all G all F ((all X all Y (hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(F,X),Y)) <-> hBOOL(hAPP_P282169671l_bool(G,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X),Y))))) -> hAPP_f635218277l_bool(produc1911463199l_bool,F) = G)) # label(fact_129_cond__split__eta) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 137 (all G all F ((all X all Y (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(F,X),Y)) <-> hBOOL(hAPP_P1708370145l_bool(G,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X),Y))))) -> hAPP_f1930574389l_bool(produc1815960045l_bool,F) = G)) # label(fact_130_cond__split__eta) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 138 (all Q_1 all Pa all Z (hBOOL(hAPP_bool_bool(Q_1,hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,Pa),Z))) -> -(all X all Y (Z = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X),Y) -> -hBOOL(hAPP_bool_bool(Q_1,hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,X),Y))))))) # label(fact_131_splitE2) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 139 (all Q_1 all Pa all Z (hBOOL(hAPP_bool_bool(Q_1,hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,Pa),Z))) -> -(all X all Y (Z = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X),Y) -> -hBOOL(hAPP_bool_bool(Q_1,hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,X),Y))))))) # label(fact_132_splitE2) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 140 (all Q_1 all Pa all Z (hBOOL(hAPP_bool_bool(Q_1,hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,Pa),Z))) -> -(all X all Y (Z = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X),Y) -> -hBOOL(hAPP_bool_bool(Q_1,hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,X),Y))))))) # label(fact_133_splitE2) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 141 (all A_14 all Ty_7 all Exp_13 all A_13 all Exp_12 block_list_char(A_14,Ty_7,Exp_13) != lAss_list_char(A_13,Exp_12)) # label(fact_134_exp_Osimps_I143_J) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 142 (all A_12 all Ty_6 all Exp_11 all Exp1_7 all Exp2_7 block_list_char(A_12,Ty_6,Exp_11) != seq_list_char(Exp1_7,Exp2_7)) # label(fact_135_exp_Osimps_I196_J) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 143 (all Val_7 all Val_6 (val_list_char(Val_7) = val_list_char(Val_6) <-> Val_7 = Val_6)) # label(fact_136_exp_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 144 (all Exp1_6 all Exp2_6 all Exp1_5 all Exp2_5 (seq_list_char(Exp1_6,Exp2_6) = seq_list_char(Exp1_5,Exp2_5) <-> Exp1_6 = Exp1_5 & Exp2_6 = Exp2_5)) # label(fact_137_exp_Osimps_I11_J) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 145 (all A_10 all Exp_10 all A_9 all Exp_9 (lAss_list_char(A_10,Exp_10) = lAss_list_char(A_9,Exp_9) <-> A_10 = A_9 & Exp_10 = Exp_9)) # label(fact_138_exp_Osimps_I6_J) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 146 (all X_1 all A_11 (hBOOL(member763590124on_val(X_1,A_11)) <-> hBOOL(hAPP_P159683425l_bool(A_11,X_1)))) # label(fact_139_mem__def) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 147 (all X_1 all A_11 (hBOOL(member840932460on_val(X_1,A_11)) <-> hBOOL(hAPP_P1708370145l_bool(A_11,X_1)))) # label(fact_140_mem__def) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 148 (all X_1 all A_11 (hBOOL(member773094996on_val(X_1,A_11)) <-> hBOOL(hAPP_P282169671l_bool(A_11,X_1)))) # label(fact_141_mem__def) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 149 (all A_10 all Ty_5 all Exp_10 all A_9 all Ty_4 all Exp_9 (block_list_char(A_10,Ty_5,Exp_10) = block_list_char(A_9,Ty_4,Exp_9) <-> A_10 = A_9 & Ty_5 = Ty_4 & Exp_10 = Exp_9)) # label(fact_142_exp_Osimps_I10_J) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 150 (all Val_5 all Exp1_4 all Exp2_4 val_list_char(Val_5) != seq_list_char(Exp1_4,Exp2_4)) # label(fact_143_exp_Osimps_I84_J) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 151 (all Val_4 all A_8 all Exp_8 val_list_char(Val_4) != lAss_list_char(A_8,Exp_8)) # label(fact_144_exp_Osimps_I74_J) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 152 (all Exp1_3 all Exp2_3 all Val_3 seq_list_char(Exp1_3,Exp2_3) != val_list_char(Val_3)) # label(fact_145_exp_Osimps_I85_J) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 153 (all A_7 all Exp_7 all Val_2 lAss_list_char(A_7,Exp_7) != val_list_char(Val_2)) # label(fact_146_exp_Osimps_I75_J) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 154 (all Val_1 all A_6 all Ty_3 all Exp_6 val_list_char(Val_1) != block_list_char(A_6,Ty_3,Exp_6)) # label(fact_147_exp_Osimps_I82_J) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 155 (all A_5 all Ty_2 all Exp_5 all Val block_list_char(A_5,Ty_2,Exp_5) != val_list_char(Val)) # label(fact_148_exp_Osimps_I83_J) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 156 (all Exp1_2 all Exp2_2 all A_4 all Exp_4 seq_list_char(Exp1_2,Exp2_2) != lAss_list_char(A_4,Exp_4)) # label(fact_149_exp_Osimps_I145_J) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 157 (all A_3 all Exp_3 all Exp1_1 all Exp2_1 lAss_list_char(A_3,Exp_3) != seq_list_char(Exp1_1,Exp2_1)) # label(fact_150_exp_Osimps_I144_J) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 158 (all Exp1 all Exp2 all A_2 all Ty_1 all Exp_2 seq_list_char(Exp1,Exp2) != block_list_char(A_2,Ty_1,Exp_2)) # label(fact_151_exp_Osimps_I197_J) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 159 (all A_1 all Exp_1 all A all Ty all Exp lAss_list_char(A_1,Exp_1) != block_list_char(A,Ty,Exp)) # label(fact_152_exp_Osimps_I142_J) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 160 (all Ta all V_a all Pa all Eb all Hb all Lb all Va_1 all Va all E_b all H_b all L_b (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,Va_1,some_val(Va)))),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))) -> (hAPP_l207779698on_val(L_b,Va_1) = some_val(V_a) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,val_list_char(Va)),Eb)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,val_list_char(V_a)),E_b))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,Va_1,hAPP_l207779698on_val(Lb,Va_1)))))))) # label(fact_153_redp__redsp_OInitBlockRed) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 161 (all Ta all Va all Eb all Hb all Lb all Va_1 all E_b all H_b all L_b all Pa (hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,Va_1,none_val)))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))),red(Pa))) -> (hAPP_l207779698on_val(L_b,Va_1) = some_val(Va) -> (-hBOOL(assigned(Va_1,Eb)) -> hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,Eb)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,val_list_char(Va)),E_b))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,Va_1,hAPP_l207779698on_val(Lb,Va_1))))),red(Pa))))))) # label(fact_154_red__reds_OBlockRedSome) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 162 (all E_2 all Pa all Eb all S all E_b all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,seq_list_char(Eb,E_2),S),seq_list_char(E_b,E_2)),S_1)))) # label(fact_155_redp__redsp_OSeqRed) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 163 (all Va_1 all Pa all Eb all S all E_b all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,lAss_list_char(Va_1,Eb),S),lAss_list_char(Va_1,E_b)),S_1)))) # label(fact_156_redp__redsp_OLAssRed) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 164 (all Ta all Pa all Eb all Hb all Lb all Va_1 all E_b all H_b all L_b (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,Va_1,none_val))),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))) -> (hAPP_l207779698on_val(L_b,Va_1) = none_val -> (-hBOOL(assigned(Va_1,Eb)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(Va_1,Ta,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),block_list_char(Va_1,Ta,E_b)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,Va_1,hAPP_l207779698on_val(Lb,Va_1))))))))) # label(fact_157_redp__redsp_OBlockRedNone) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 165 (all Pa all Va all E_2 all S hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,seq_list_char(val_list_char(Va),E_2),S),E_2),S))) # label(fact_158_redp__redsp_ORedSeq) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 166 (all T all K all X_1 -(all X hAPP_l207779698on_val(fun_up1149430426on_val(T,K,some_val(X_1)),X) = none_val)) # label(fact_159_map__upd__nonempty) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 167 (all T all K all X_1 -(all X hAPP_l512744617ion_ty(fun_up424764369ion_ty(T,K,some_ty(X_1)),X) = none_ty)) # label(fact_160_map__upd__nonempty) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 168 (all Pa all Va_1 all Ta all U all S hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(Va_1,Ta,val_list_char(U)),S),val_list_char(U)),S))) # label(fact_161_redp__redsp_ORedBlock) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 169 (all X_1 all X hAPP_l207779698on_val(fun_up1149430426on_val(cOMBK_1097134891t_char(none_val),X_1,none_val),X) = none_val) # label(fact_162_empty__upd__none) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 170 (all X_1 all X hAPP_l512744617ion_ty(fun_up424764369ion_ty(cOMBK_1294242658t_char(none_ty),X_1,none_ty),X) = none_ty) # label(fact_163_empty__upd__none) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 171 (all Ta all Va all Pa all Eb all Hb all Lb all Va_1 all E_b all H_b all L_b (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,Va_1,none_val))),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))) -> (hAPP_l207779698on_val(L_b,Va_1) = some_val(Va) -> (-hBOOL(assigned(Va_1,Eb)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(Va_1,Ta,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,val_list_char(Va)),E_b))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,Va_1,hAPP_l207779698on_val(Lb,Va_1))))))))) # label(fact_164_redp__redsp_OBlockRedSome) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 172 (all Pa all X all Xa all Xb all Xc (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,X,Xa),Xb),Xc)) <-> hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X),Xa)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Xb),Xc)),red(Pa))))) # label(fact_165_redp__red__eq) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 173 (all Pa all Va_1 all Ta all Va all U all S hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,val_list_char(Va)),val_list_char(U))),S),val_list_char(U)),S))) # label(fact_166_redp__redsp_ORedInitBlock) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 174 (all Q all P (-hBOOL(P) | -hBOOL(Q) | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 175 (all P all Q (-hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) | hBOOL(P))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 176 (all P all Q (-hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) | hBOOL(Q))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 177 (all P all Q hAPP_l512744617ion_ty(cOMBK_1294242658t_char(P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__List__Olist_) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 178 (all P all Q hAPP_l207779698on_val(cOMBK_1097134891t_char(P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__List__Olis) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 179 (all P all Q all R hAPP_f1033709212l_bool(hAPP_f1074020887l_bool(hAPP_f1863694447l_bool(cOMBB_383678192on_val,P),Q),R) = hAPP_bool_bool(P,hAPP_f1033709212l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__List__O) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 180 (all P all Q all R hAPP_f1033709212l_bool(hAPP_f603925568l_bool(hAPP_f181262431l_bool(cOMBC_832625297y_bool,P),Q),R) = hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Optio) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 181 (all P all Q all R hAPP_f1145256474l_bool(hAPP_f1452292669l_bool(hAPP_f1977633121l_bool(cOMBB_1303934920on_val,P),Q),R) = hAPP_b589554111l_bool(P,hAPP_f61040418l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 182 (all P all Q all R hAPP_P159683425l_bool(hAPP_f2134824737l_bool(hAPP_f1308714617l_bool(cOMBB_338347573on_val,P),Q),R) = hAPP_bool_bool(P,hAPP_P159683425l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__prod_Itc__fun_It) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 183 (all P all Q all R hAPP_P1708370145l_bool(hAPP_f926562337l_bool(hAPP_f1560238713l_bool(cOMBB_672625589on_val,P),Q),R) = hAPP_bool_bool(P,hAPP_P1708370145l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__prod_Itc__Expr__) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 184 (all P all Q all R hAPP_f1175813647l_bool(hAPP_f550652027l_bool(hAPP_f838396643l_bool(cOMBC_2027949654l_bool,P),Q),R) = hAPP_f603925568l_bool(hAPP_f1617787571l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 185 (all P all Q all R hAPP_f1033709212l_bool(hAPP_f1008932791l_bool(hAPP_f2057883639l_bool(cOMBB_1750801836on_val,P),Q),R) = hAPP_P159683425l_bool(P,hAPP_f1727192346on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 186 (all P all Q all R hAPP_f1175813647l_bool(hAPP_f555424277l_bool(hAPP_f1734879897l_bool(cOMBB_1522540928on_val,P),Q),R) = hAPP_f1074020887l_bool(P,hAPP_f1175813647l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 187 (all P all Q all R hAPP_f1175813647l_bool(cOMBS_570216337l_bool(P,Q),R) = hAPP_f1074020887l_bool(hAPP_f1492320500l_bool(P,R),hAPP_f1175813647l_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 188 (all P all Q all R hAPP_f1033709212l_bool(hAPP_f318082871l_bool(hAPP_f1233687287l_bool(cOMBB_171276332on_val,P),Q),R) = hAPP_P1708370145l_bool(P,hAPP_f1926378906on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 189 (all P all Q all R hAPP_f1492320500l_bool(hAPP_f1523875321l_bool(hAPP_f592397849l_bool(cOMBB_1718333400on_val,P),Q),R) = hAPP_f1863694447l_bool(P,hAPP_f1145256474l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 190 (all P all Q all R hAPP_f1617787571l_bool(hAPP_f857351829l_bool(hAPP_f348318673l_bool(cOMBB_1518282696on_val,P),Q),R) = hAPP_f181262431l_bool(P,hAPP_f1213370163y_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_002) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 191 (all P all Q all R hAPP_P159683425l_bool(hAPP_f1301559543l_bool(hAPP_f1825030711l_bool(cOMBB_877741809on_val,P),Q),R) = hAPP_P159683425l_bool(P,hAPP_P1776198677on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_003) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 192 (all P all Q all R hAPP_P159683425l_bool(hAPP_f489055607l_bool(hAPP_f10074679l_bool(cOMBB_1759207793on_val,P),Q),R) = hAPP_P1708370145l_bool(P,hAPP_P604205461on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O_004) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 193 (all P all Q all R hAPP_P1708370145l_bool(hAPP_f1712766199l_bool(hAPP_f881985847l_bool(cOMBB_1083177073on_val,P),Q),R) = hAPP_P159683425l_bool(P,hAPP_P789556885on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_005) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.19 194 (all P all Q all R hAPP_e1833980889l_bool(hAPP_f546724245l_bool(hAPP_f917296015l_bool(cOMBB_740252943t_char,P),Q),R) = hAPP_f2134824737l_bool(P,hAPP_e1833980889l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.26 195 (all P all Q all R hAPP_f1175813647l_bool(hAPP_f1363667773l_bool(hAPP_f1050935001l_bool(cOMBB_1153617344on_val,P),Q),R) = hAPP_f1008932791l_bool(P,hAPP_f1849790461on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_006) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.26 196 (all P all Q all R hAPP_f1175813647l_bool(hAPP_f850751421l_bool(hAPP_f399538905l_bool(cOMBB_1466889536on_val,P),Q),R) = hAPP_f318082871l_bool(P,hAPP_f1840640125on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_007) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.26 197 (all P all Q all R hAPP_f1033709212l_bool(hAPP_f524589473l_bool(hAPP_f2052660463l_bool(cOMBB_1292453606on_val,P),Q),R) = hAPP_P282169671l_bool(P,hAPP_f602593190on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.26 198 (all P all Q all R hAPP_e1833980889l_bool(hAPP_f653692369l_bool(hAPP_f516738477l_bool(cOMBB_819439237t_char,P),Q),R) = hAPP_f1301559543l_bool(P,hAPP_e108155315on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_008) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.26 199 (all P all Q all R hAPP_e1833980889l_bool(hAPP_f439412817l_bool(hAPP_f1725502637l_bool(cOMBB_1027621637t_char,P),Q),R) = hAPP_f489055607l_bool(P,hAPP_e1659493427on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_009) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.26 200 (all P all Q all R hAPP_P1708370145l_bool(hAPP_f204771371l_bool(hAPP_f365540729l_bool(cOMBB_1466662571on_val,P),Q),R) = hAPP_P282169671l_bool(P,hAPP_P1886180715on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__010) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.26 201 (all P all Q all R hAPP_P1116729363l_bool(hAPP_f641257349l_bool(hAPP_f2032347769l_bool(cOMBB_466903633on_val,P),Q),R) = hAPP_f926562337l_bool(P,hAPP_P1116729363l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.26 202 (all P all Q all R hAPP_f1175813647l_bool(hAPP_f927043595l_bool(hAPP_f1043869573l_bool(cOMBB_1259202826on_val,P),Q),R) = hAPP_f524589473l_bool(P,hAPP_f600512025on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_011) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.26 203 (all P all Q all R hAPP_P1116729363l_bool(hAPP_f1241216909l_bool(hAPP_f1438732387l_bool(cOMBB_635947099on_val,P),Q),R) = hAPP_f1712766199l_bool(P,hAPP_P2083594489on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc___012) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.26 204 (all P all Q all R hAPP_P1116729363l_bool(hAPP_f1342895119l_bool(hAPP_f639265145l_bool(cOMBB_364363975on_val,P),Q),R) = hAPP_f204771371l_bool(P,hAPP_P1870962205on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc___013) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.26
% 0.90/1.26 ============================== end of process non-clausal formulas ===
% 0.90/1.26
% 0.90/1.26 ============================== PROCESS INITIAL CLAUSES ===============
% 0.90/1.26
% 0.90/1.26 ============================== PREDICATE ELIMINATION =================
% 0.90/1.26
% 0.90/1.26 ============================== end predicate elimination =============
% 0.90/1.26
% 0.90/1.26 Auto_denials: (non-Horn, no changes).
% 0.90/1.26
% 0.90/1.26 Term ordering decisions:
% 0.90/1.26 Function symbol KB weights: produc1259058957on_val=1. produc899768717on_val=1. produc1441475159on_val=1. produc1958875245l_bool=1. produc1815960045l_bool=1. produc1911463199l_bool=1. fconj=1. p=1. ha=1. none_val=1. cOMBB_383678192on_val=1. v_1=1. produc121041439l_bool=1. produc1275132703l_bool=1. produc20018513l_bool=1. produc2036005791l_bool=1. produc334393759l_bool=1. produc376702929l_bool=1. cOMBB_1522540928on_val=1. cOMBB_338347573on_val=1. cOMBB_466903633on_val=1. cOMBB_672625589on_val=1. cOMBB_740252943t_char=1. ea=1. la=1. v=1. cOMBB_1083177073on_val=1. cOMBB_1259202826on_val=1. cOMBB_1292453606on_val=1. cOMBB_1303934920on_val=1. cOMBB_1466889536on_val=1. cOMBB_1518282696on_val=1. cOMBB_171276332on_val=1. cOMBB_1718333400on_val=1. cOMBB_635947099on_val=1. cOMBB_819439237t_char=1. cOMBB_877741809on_val=1. cOMBC_2027949654l_bool=1. cOMBC_832625297y_bool=1. none_ty=1. produc2128769400l_bool=1. cOMBB_1027621637t_char=1. cOMBB_1153617344on_val=1. cOMBB_1466662571on_val=1. cOMBB_1750801836on_val=1. cOMBB_1759207793on_val=1. cOMBB_364363975on_val=1. e=1. e_a=1. h_a=1. l_a=1. produc1003071703on_val=1. produc1148763895on_val=1. produc1174947465on_val=1. produc901351817on_val=1. produc1988544340l_bool=1. produc399384568l_bool=1. t=1. t_1=1. unit=1. v_2=1. wf_J_mdecl=1. hAPP_P159683425l_bool=1. hAPP_P604205461on_val=1. hAPP_e1659493427on_val=1. hAPP_f1727192346on_val=1. hAPP_f1849790461on_val=1. hAPP_P1870962205on_val=1. hAPP_P1886180715on_val=1. hAPP_P1708370145l_bool=1. hAPP_P282169671l_bool=1. hAPP_f2121594859l_bool=1. hAPP_l207779698on_val=1. member763590124on_val=1. member840932460on_val=1. hAPP_e1833980889l_bool=1. hAPP_f1930574389l_bool=1. hAPP_f635218277l_bool=1. member773094996on_val=1. hAPP_P1116729363l_bool=1. hAPP_l512744617ion_ty=1. hAPP_f1175813647l_bool=1. seq_list_char=1. hAPP_f1033709212l_bool=1. lAss_list_char=1. hAPP_bool_bool=1. hAPP_b589554111l_bool=1. hAPP_P1638898323l_bool=1. hAPP_P1988153107l_bool=1. hAPP_P595502227l_bool=1. typeSa1234865140_sconf=1. hAPP_P1826803705l_bool=1. hAPP_P678729081l_bool=1. hAPP_f1276548047l_bool=1. hAPP_f1591648613l_bool=1. hAPP_f1760682521l_bool=1. hAPP_f1863694447l_bool=1. hAPP_f444383845l_bool=1. hAPP_f468299289l_bool=1. hAPP_f833559503l_bool=1. assigned=1. hAPP_f1001225811y_bool=1. hAPP_f1308714617l_bool=1. hAPP_f1560238713l_bool=1. hAPP_f1734879897l_bool=1. hAPP_f2032347769l_bool=1. hAPP_f546724245l_bool=1. hAPP_f555424277l_bool=1. hAPP_f61040418l_bool=1. hAPP_f641257349l_bool=1. hAPP_f917296015l_bool=1. cOMBS_570216337l_bool=1. hAPP_P1134042693l_bool=1. hAPP_P1953518277l_bool=1. hAPP_P789556885on_val=1. hAPP_e500528395l_bool=1. hAPP_e592495499l_bool=1. hAPP_f1043869573l_bool=1. hAPP_f1074020887l_bool=1. hAPP_f1213370163y_bool=1. hAPP_f1233687287l_bool=1. hAPP_f1241216909l_bool=1. hAPP_f1438732387l_bool=1. hAPP_f1452292669l_bool=1. hAPP_f1523875321l_bool=1. hAPP_f1825030711l_bool=1. hAPP_f1977633121l_bool=1. hAPP_f2011777102l_bool=1. hAPP_f2052660463l_bool=1. hAPP_f2060496320y_bool=1. hAPP_f2135509569l_bool=1. hAPP_f2144092865l_bool=1. hAPP_f348318673l_bool=1. hAPP_f396019662l_bool=1. hAPP_f399538905l_bool=1. hAPP_f516738477l_bool=1. hAPP_f550652027l_bool=1. hAPP_f592397849l_bool=1. hAPP_f653692369l_bool=1. hAPP_f838396643l_bool=1. hAPP_f850751421l_bool=1. hAPP_f857351829l_bool=1. hAPP_f881985847l_bool=1. hAPP_f927043595l_bool=1. hAPP_P1760219823on_val=1. hAPP_P2024243179on_val=1. hAPP_f10074679l_bool=1. hAPP_f1008932791l_bool=1. hAPP_f1050935001l_bool=1. hAPP_f1145256474l_bool=1. hAPP_f1301559543l_bool=1. hAPP_f1309113673on_val=1. hAPP_f1342895119l_bool=1. hAPP_f1363667773l_bool=1. hAPP_f1492320500l_bool=1. hAPP_f1520199827on_val=1. hAPP_f1617787571l_bool=1. hAPP_f1712766199l_bool=1. hAPP_f1725502637l_bool=1. hAPP_f181262431l_bool=1. hAPP_f204556415on_val=1. hAPP_f204771371l_bool=1. hAPP_f2057883639l_bool=1. hAPP_f2134824737l_bool=1. hAPP_f318082871l_bool=1. hAPP_f365540729l_bool=1. hAPP_f394183983on_val=1. hAPP_f439412817l_bool=1. hAPP_f489055607l_bool=1. hAPP_f524589473l_bool=1. hAPP_f603925568l_bool=1. hAPP_f639265145l_bool=1. hAPP_f926562337l_bool=1. wf_pro755087577t_char=1. hAPP_P1776198677on_val=1. hAPP_P2083594489on_val=1. hAPP_e108155315on_val=1. hAPP_f1840640125on_val=1. hAPP_f1926378906on_val=1. hAPP_f600512025on_val=1. hAPP_f602593190on_val=1. f1=1. f2=1. f3=1. f4=1. f5=1. f25=1. f26=1. f27=1. f28=1. f29=1. f30=1. f31=1. f32=1. f33=1. f34=1. f35=1. f36=1. f58=1. f59=1. f60=1. f61=1. f62=1. f63=1. f64=1. f65=1. f66=1. f67=1. f68=1. f69=1. f94=1. f95=1. f96=1. f97=1. f98=1. f99=1. some_val=1. val_list_char=1. red=1. some_ty=1. hconf_97414254t_char=1. lconf_496643946t_char=1. cOMBK_1097134891t_char=1. cOMBK_1294242658t_char=1. hp=1. f6=1. f7=1. f8=1. f9=1. f10=1. f11=1. f12=1. f13=1. f14=1. f15=1. f16=1. f17=1. f18=1. f19=1. f20=1. f21=1. f22=1. f23=1. f24=1. f37=1. f38=1. f39=1. f40=1. f41=1. f42=1. f43=1. f44=1. f45=1. f46=1. f47=1. f48=1. f49=1. f50=1. f51=1. f52=1. f53=1. f54=1. f55=1. f56=1. f57=1. fun_up1149430426on_val=1. fun_up424764369ion_ty=1. block_list_char=1. redp=1. widen_2090681816t_char=1. f70=1. f71=1. f72=1. f73=1. f74=1. f75=1. f76=1. f77=1. f78=1. f79=1. f80=1. f81=1. f82=1. f83=1. f84=1. f85=1. f86=1. f87=1. f88=1. f89=1. f90=1. f91=1. f92=1. f93=1. f100=1. f101=1. f102=1. f103=1. f104=1. f105=1. f106=1. f107=1. wTrt=1.
% 0.90/1.26
% 0.90/1.26 ============================== PROOF =================================
% 0.90/1.26 % SZS status Theorem
% 0.90/1.26 % SZS output start Refutation
% 0.90/1.26
% 0.90/1.26 % Proof 1 at 0.12 (+ 0.01) seconds.
% 0.90/1.26 % Length of proof is 3.
% 0.90/1.26 % Level of proof is 1.
% 0.90/1.26 % Maximum clause weight is 29.000.
% 0.90/1.26 % Given clauses 0.
% 0.90/1.26
% 0.90/1.26 220 hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,ha),fun_up1149430426on_val(la,v_1,some_val(v))))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,e_a),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,h_a),l_a))),red(p))) # label(fact_1_InitBlockRed_I1_J) # label(axiom). [assumption].
% 0.90/1.26 494 -hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,ha),fun_up1149430426on_val(la,v_1,some_val(v))))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,e_a),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,h_a),l_a))),red(p))) # label(conj_0) # label(negated_conjecture). [assumption].
% 0.90/1.26 495 $F. [copy(494),unit_del(a,220)].
% 0.90/1.26
% 0.90/1.26 % SZS output end Refutation
% 0.90/1.26 ============================== end of proof ==========================
% 0.90/1.26
% 0.90/1.26 ============================== STATISTICS ============================
% 0.90/1.26
% 0.90/1.26 Given=0. Generated=309. Kept=273. proofs=1.
% 0.90/1.26 Usable=0. Sos=0. Demods=52. Limbo=273, Disabled=309. Hints=0.
% 0.90/1.26 Megabytes=2.97.
% 0.90/1.26 User_CPU=0.12, System_CPU=0.01, Wall_clock=0.
% 0.90/1.26
% 0.90/1.26 ============================== end of statistics =====================
% 0.90/1.26
% 0.90/1.26 ============================== end of search =========================
% 0.90/1.26
% 0.90/1.26 THEOREM PROVED
% 0.90/1.26 % SZS status Theorem
% 0.90/1.26
% 0.90/1.26 Exiting with 1 proof.
% 0.90/1.26
% 0.90/1.26 Process 24455 exit (max_proofs) Sun Jun 5 22:15:11 2022
% 0.90/1.26 Prover9 interrupted
%------------------------------------------------------------------------------