Z3---4.15.1.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : SWV926-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% Computer : n005.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sat Jun 21 05:36:21 AM UTC 2025

% Result   : Unsatisfiable 1.77s 1.98s
% Output   : Proof 1.93s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SWV926-1 : TPTP v9.0.0. Released v4.1.0.
% 0.07/0.13  % Command    : run_E %s %d THM
% 0.14/0.34  % Computer : n005.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Fri Jun 20 11:03:35 EDT 2025
% 0.14/0.34  % CPUTime    : 
% 1.77/1.98  % SZS status Unsatisfiable
% 1.77/1.98  % SZS output start Proof
% 1.77/1.98  tff(c_lessequals_type, type, (
% 1.77/1.98     c_lessequals: ( $i * $i * $i ) > $o)).
% 1.77/1.98  tff(tc_fun_type, type, (
% 1.77/1.98     tc_fun: ( $i * $i ) > $i)).
% 1.77/1.98  tff(tc_bool_type, type, (
% 1.77/1.98     tc_bool: $i)).
% 1.77/1.98  tff(tc_List_Olist_type, type, (
% 1.77/1.98     tc_List_Olist: $i > $i)).
% 1.77/1.98  tff(tc_String_Ochar_type, type, (
% 1.77/1.98     tc_String_Ochar: $i)).
% 1.77/1.98  tff(c_Lattices_Oupper__semilattice__class_Osup_type, type, (
% 1.77/1.98     c_Lattices_Oupper__semilattice__class_Osup: ( $i * $i * $i ) > $i)).
% 1.77/1.98  tff(v_x_type, type, (
% 1.77/1.98     v_x: $i)).
% 1.77/1.98  tff(v_ac_type, type, (
% 1.77/1.98     v_ac: $i)).
% 1.77/1.98  tff(c_Map_Odom_type, type, (
% 1.77/1.98     c_Map_Odom: ( $i * $i * $i ) > $i)).
% 1.77/1.98  tff(tc_Value_Oval_type, type, (
% 1.77/1.98     tc_Value_Oval: $i)).
% 1.77/1.98  tff(v_ba_type, type, (
% 1.77/1.98     v_ba: $i)).
% 1.77/1.98  tff(v_b_type, type, (
% 1.77/1.98     v_b: $i)).
% 1.77/1.98  tff(hBOOL_type, type, (
% 1.77/1.98     hBOOL: $i > $o)).
% 1.77/1.98  tff(hAPP_type, type, (
% 1.77/1.98     hAPP: ( $i * $i ) > $i)).
% 1.77/1.98  tff(c_SmallStep_Ored_type, type, (
% 1.77/1.98     c_SmallStep_Ored: $i > $i)).
% 1.77/1.98  tff(v_P_type, type, (
% 1.77/1.98     v_P: $i)).
% 1.77/1.98  tff(c_Pair_type, type, (
% 1.77/1.98     c_Pair: ( $i * $i * $i * $i ) > $i)).
% 1.77/1.98  tff(tc_prod_type, type, (
% 1.77/1.98     tc_prod: ( $i * $i ) > $i)).
% 1.77/1.98  tff(tc_Option_Ooption_type, type, (
% 1.77/1.98     tc_Option_Ooption: $i > $i)).
% 1.77/1.98  tff(tc_nat_type, type, (
% 1.77/1.98     tc_nat: $i)).
% 1.77/1.98  tff(tc_Expr_Oexp_type, type, (
% 1.77/1.98     tc_Expr_Oexp: $i > $i)).
% 1.77/1.98  tff(v_aa_type, type, (
% 1.77/1.98     v_aa: $i)).
% 1.77/1.98  tff(v_e_Ha_type, type, (
% 1.77/1.98     v_e_Ha: $i)).
% 1.77/1.98  tff(v_a_type, type, (
% 1.77/1.98     v_a: $i)).
% 1.77/1.98  tff(v_ea_type, type, (
% 1.77/1.98     v_ea: $i)).
% 1.77/1.98  tff(c_in_type, type, (
% 1.77/1.98     c_in: $i > $i)).
% 1.77/1.98  tff(class_Lattices_Oupper__semilattice_type, type, (
% 1.77/1.98     class_Lattices_Oupper__semilattice: $i > $o)).
% 1.77/1.98  tff(class_Lattices_Olattice_type, type, (
% 1.77/1.98     class_Lattices_Olattice: $i > $o)).
% 1.77/1.98  tff(class_Orderings_Oorder_type, type, (
% 1.77/1.98     class_Orderings_Oorder: $i > $o)).
% 1.77/1.98  tff(v_ae_type, type, (
% 1.77/1.98     v_ae: $i)).
% 1.77/1.98  tff(v_ab_type, type, (
% 1.77/1.98     v_ab: $i)).
% 1.77/1.98  tff(v_ad_type, type, (
% 1.77/1.98     v_ad: $i)).
% 1.77/1.98  tff(1,plain,
% 1.77/1.98      (hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))) <=> hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P)))),
% 1.77/1.98      inference(rewrite,[status(thm)],[])).
% 1.77/1.98  tff(2,axiom,(hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_1')).
% 1.77/1.98  tff(3,plain,
% 1.77/1.98      (hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P)))),
% 1.77/1.98      inference(modus_ponens,[status(thm)],[2, 1])).
% 1.77/1.98  tff(4,plain,
% 1.77/1.98      (^[V_e_H: $i, V_h_092_060_094isub_0621: $i, V_l_092_060_094isub_0620: $i, V_h_092_060_094isub_0620: $i, V_l_092_060_094isub_0621: $i, V_e: $i, V_P: $i] : refl((c_lessequals(c_Map_Odom(V_l_092_060_094isub_0620, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(V_l_092_060_094isub_0621, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(V_e, c_Pair(V_h_092_060_094isub_0620, V_l_092_060_094isub_0620, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(V_e_H, c_Pair(V_h_092_060_094isub_0621, V_l_092_060_094isub_0621, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(V_P))))) <=> (c_lessequals(c_Map_Odom(V_l_092_060_094isub_0620, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(V_l_092_060_094isub_0621, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(V_e, c_Pair(V_h_092_060_094isub_0620, V_l_092_060_094isub_0620, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(V_e_H, c_Pair(V_h_092_060_094isub_0621, V_l_092_060_094isub_0621, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(V_P))))))),
% 1.77/1.98      inference(bind,[status(th)],[])).
% 1.77/1.98  tff(5,plain,
% 1.77/1.98      (![V_e_H: $i, V_h_092_060_094isub_0621: $i, V_l_092_060_094isub_0620: $i, V_h_092_060_094isub_0620: $i, V_l_092_060_094isub_0621: $i, V_e: $i, V_P: $i] : (c_lessequals(c_Map_Odom(V_l_092_060_094isub_0620, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(V_l_092_060_094isub_0621, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(V_e, c_Pair(V_h_092_060_094isub_0620, V_l_092_060_094isub_0620, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(V_e_H, c_Pair(V_h_092_060_094isub_0621, V_l_092_060_094isub_0621, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(V_P))))) <=> ![V_e_H: $i, V_h_092_060_094isub_0621: $i, V_l_092_060_094isub_0620: $i, V_h_092_060_094isub_0620: $i, V_l_092_060_094isub_0621: $i, V_e: $i, V_P: $i] : (c_lessequals(c_Map_Odom(V_l_092_060_094isub_0620, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(V_l_092_060_094isub_0621, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(V_e, c_Pair(V_h_092_060_094isub_0620, V_l_092_060_094isub_0620, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(V_e_H, c_Pair(V_h_092_060_094isub_0621, V_l_092_060_094isub_0621, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(V_P)))))),
% 1.83/1.99      inference(quant_intro,[status(thm)],[4])).
% 1.83/1.99  tff(6,plain,
% 1.83/1.99      (![V_e_H: $i, V_h_092_060_094isub_0621: $i, V_l_092_060_094isub_0620: $i, V_h_092_060_094isub_0620: $i, V_l_092_060_094isub_0621: $i, V_e: $i, V_P: $i] : (c_lessequals(c_Map_Odom(V_l_092_060_094isub_0620, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(V_l_092_060_094isub_0621, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(V_e, c_Pair(V_h_092_060_094isub_0620, V_l_092_060_094isub_0620, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(V_e_H, c_Pair(V_h_092_060_094isub_0621, V_l_092_060_094isub_0621, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(V_P))))) <=> ![V_e_H: $i, V_h_092_060_094isub_0621: $i, V_l_092_060_094isub_0620: $i, V_h_092_060_094isub_0620: $i, V_l_092_060_094isub_0621: $i, V_e: $i, V_P: $i] : (c_lessequals(c_Map_Odom(V_l_092_060_094isub_0620, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(V_l_092_060_094isub_0621, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(V_e, c_Pair(V_h_092_060_094isub_0620, V_l_092_060_094isub_0620, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(V_e_H, c_Pair(V_h_092_060_094isub_0621, V_l_092_060_094isub_0621, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(V_P)))))),
% 1.83/1.99      inference(rewrite,[status(thm)],[])).
% 1.83/1.99  tff(7,axiom,(![V_e_H: $i, V_h_092_060_094isub_0621: $i, V_l_092_060_094isub_0620: $i, V_h_092_060_094isub_0620: $i, V_l_092_060_094isub_0621: $i, V_e: $i, V_P: $i] : (c_lessequals(c_Map_Odom(V_l_092_060_094isub_0620, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(V_l_092_060_094isub_0621, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(V_e, c_Pair(V_h_092_060_094isub_0620, V_l_092_060_094isub_0620, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(V_e_H, c_Pair(V_h_092_060_094isub_0621, V_l_092_060_094isub_0621, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(V_P)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_red__lcl__incr_0')).
% 1.83/1.99  tff(8,plain,
% 1.83/1.99      (![V_e_H: $i, V_h_092_060_094isub_0621: $i, V_l_092_060_094isub_0620: $i, V_h_092_060_094isub_0620: $i, V_l_092_060_094isub_0621: $i, V_e: $i, V_P: $i] : (c_lessequals(c_Map_Odom(V_l_092_060_094isub_0620, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(V_l_092_060_094isub_0621, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(V_e, c_Pair(V_h_092_060_094isub_0620, V_l_092_060_094isub_0620, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(V_e_H, c_Pair(V_h_092_060_094isub_0621, V_l_092_060_094isub_0621, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(V_P)))))),
% 1.83/1.99      inference(modus_ponens,[status(thm)],[7, 6])).
% 1.83/1.99  tff(9,plain,(
% 1.83/1.99      ![V_e_H: $i, V_h_092_060_094isub_0621: $i, V_l_092_060_094isub_0620: $i, V_h_092_060_094isub_0620: $i, V_l_092_060_094isub_0621: $i, V_e: $i, V_P: $i] : (c_lessequals(c_Map_Odom(V_l_092_060_094isub_0620, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(V_l_092_060_094isub_0621, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(V_e, c_Pair(V_h_092_060_094isub_0620, V_l_092_060_094isub_0620, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(V_e_H, c_Pair(V_h_092_060_094isub_0621, V_l_092_060_094isub_0621, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(V_P)))))),
% 1.83/1.99      inference(skolemize,[status(sab)],[8])).
% 1.83/1.99  tff(10,plain,
% 1.83/1.99      (![V_e_H: $i, V_h_092_060_094isub_0621: $i, V_l_092_060_094isub_0620: $i, V_h_092_060_094isub_0620: $i, V_l_092_060_094isub_0621: $i, V_e: $i, V_P: $i] : (c_lessequals(c_Map_Odom(V_l_092_060_094isub_0620, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(V_l_092_060_094isub_0621, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(V_e, c_Pair(V_h_092_060_094isub_0620, V_l_092_060_094isub_0620, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(V_e_H, c_Pair(V_h_092_060_094isub_0621, V_l_092_060_094isub_0621, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(V_P)))))),
% 1.83/1.99      inference(modus_ponens,[status(thm)],[9, 5])).
% 1.83/1.99  tff(11,plain,
% 1.83/1.99      (((~![V_e_H: $i, V_h_092_060_094isub_0621: $i, V_l_092_060_094isub_0620: $i, V_h_092_060_094isub_0620: $i, V_l_092_060_094isub_0621: $i, V_e: $i, V_P: $i] : (c_lessequals(c_Map_Odom(V_l_092_060_094isub_0620, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(V_l_092_060_094isub_0621, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(V_e, c_Pair(V_h_092_060_094isub_0620, V_l_092_060_094isub_0620, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(V_e_H, c_Pair(V_h_092_060_094isub_0621, V_l_092_060_094isub_0621, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(V_P)))))) | ((~hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P)))) | c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))) <=> ((~![V_e_H: $i, V_h_092_060_094isub_0621: $i, V_l_092_060_094isub_0620: $i, V_h_092_060_094isub_0620: $i, V_l_092_060_094isub_0621: $i, V_e: $i, V_P: $i] : (c_lessequals(c_Map_Odom(V_l_092_060_094isub_0620, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(V_l_092_060_094isub_0621, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(V_e, c_Pair(V_h_092_060_094isub_0620, V_l_092_060_094isub_0620, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(V_e_H, c_Pair(V_h_092_060_094isub_0621, V_l_092_060_094isub_0621, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(V_P)))))) | (~hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P)))) | c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))),
% 1.83/1.99      inference(rewrite,[status(thm)],[])).
% 1.83/1.99  tff(12,plain,
% 1.83/1.99      ((c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P))))) <=> ((~hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P)))) | c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))),
% 1.83/1.99      inference(rewrite,[status(thm)],[])).
% 1.83/1.99  tff(13,plain,
% 1.83/1.99      (((~![V_e_H: $i, V_h_092_060_094isub_0621: $i, V_l_092_060_094isub_0620: $i, V_h_092_060_094isub_0620: $i, V_l_092_060_094isub_0621: $i, V_e: $i, V_P: $i] : (c_lessequals(c_Map_Odom(V_l_092_060_094isub_0620, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(V_l_092_060_094isub_0621, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(V_e, c_Pair(V_h_092_060_094isub_0620, V_l_092_060_094isub_0620, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(V_e_H, c_Pair(V_h_092_060_094isub_0621, V_l_092_060_094isub_0621, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(V_P)))))) | (c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P)))))) <=> ((~![V_e_H: $i, V_h_092_060_094isub_0621: $i, V_l_092_060_094isub_0620: $i, V_h_092_060_094isub_0620: $i, V_l_092_060_094isub_0621: $i, V_e: $i, V_P: $i] : (c_lessequals(c_Map_Odom(V_l_092_060_094isub_0620, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(V_l_092_060_094isub_0621, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(V_e, c_Pair(V_h_092_060_094isub_0620, V_l_092_060_094isub_0620, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(V_e_H, c_Pair(V_h_092_060_094isub_0621, V_l_092_060_094isub_0621, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(V_P)))))) | ((~hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P)))) | c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))))),
% 1.83/2.00      inference(monotonicity,[status(thm)],[12])).
% 1.83/2.00  tff(14,plain,
% 1.83/2.00      (((~![V_e_H: $i, V_h_092_060_094isub_0621: $i, V_l_092_060_094isub_0620: $i, V_h_092_060_094isub_0620: $i, V_l_092_060_094isub_0621: $i, V_e: $i, V_P: $i] : (c_lessequals(c_Map_Odom(V_l_092_060_094isub_0620, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(V_l_092_060_094isub_0621, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(V_e, c_Pair(V_h_092_060_094isub_0620, V_l_092_060_094isub_0620, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(V_e_H, c_Pair(V_h_092_060_094isub_0621, V_l_092_060_094isub_0621, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(V_P)))))) | (c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P)))))) <=> ((~![V_e_H: $i, V_h_092_060_094isub_0621: $i, V_l_092_060_094isub_0620: $i, V_h_092_060_094isub_0620: $i, V_l_092_060_094isub_0621: $i, V_e: $i, V_P: $i] : (c_lessequals(c_Map_Odom(V_l_092_060_094isub_0620, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(V_l_092_060_094isub_0621, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(V_e, c_Pair(V_h_092_060_094isub_0620, V_l_092_060_094isub_0620, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(V_e_H, c_Pair(V_h_092_060_094isub_0621, V_l_092_060_094isub_0621, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(V_P)))))) | (~hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P)))) | c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))),
% 1.83/2.00      inference(transitivity,[status(thm)],[13, 11])).
% 1.83/2.00  tff(15,plain,
% 1.83/2.00      ((~![V_e_H: $i, V_h_092_060_094isub_0621: $i, V_l_092_060_094isub_0620: $i, V_h_092_060_094isub_0620: $i, V_l_092_060_094isub_0621: $i, V_e: $i, V_P: $i] : (c_lessequals(c_Map_Odom(V_l_092_060_094isub_0620, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(V_l_092_060_094isub_0621, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(V_e, c_Pair(V_h_092_060_094isub_0620, V_l_092_060_094isub_0620, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(V_e_H, c_Pair(V_h_092_060_094isub_0621, V_l_092_060_094isub_0621, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(V_P)))))) | (c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P)))))),
% 1.83/2.00      inference(quant_inst,[status(thm)],[])).
% 1.83/2.00  tff(16,plain,
% 1.83/2.00      ((~![V_e_H: $i, V_h_092_060_094isub_0621: $i, V_l_092_060_094isub_0620: $i, V_h_092_060_094isub_0620: $i, V_l_092_060_094isub_0621: $i, V_e: $i, V_P: $i] : (c_lessequals(c_Map_Odom(V_l_092_060_094isub_0620, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(V_l_092_060_094isub_0621, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(V_e, c_Pair(V_h_092_060_094isub_0620, V_l_092_060_094isub_0620, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(V_e_H, c_Pair(V_h_092_060_094isub_0621, V_l_092_060_094isub_0621, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(V_P)))))) | (~hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_Pair(c_Pair(v_ea, c_Pair(v_a, v_b, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), c_Pair(v_e_Ha, c_Pair(v_aa, v_ba, tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval))), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))), tc_prod(tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)), tc_prod(tc_fun(tc_nat, tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar), tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar), tc_List_Olist(tc_String_Ochar)), tc_Option_Ooption(tc_Value_Oval))))), tc_fun(tc_List_Olist(tc_String_Ochar), tc_Option_Ooption(tc_Value_Oval)))))), c_SmallStep_Ored(v_P)))) | c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.00      inference(modus_ponens,[status(thm)],[15, 14])).
% 1.83/2.00  tff(17,plain,
% 1.83/2.00      (c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.00      inference(unit_resolution,[status(thm)],[16, 10, 3])).
% 1.83/2.00  tff(18,plain,
% 1.83/2.00      (class_Lattices_Olattice(tc_bool) <=> class_Lattices_Olattice(tc_bool)),
% 1.83/2.00      inference(rewrite,[status(thm)],[])).
% 1.83/2.00  tff(19,axiom,(class_Lattices_Olattice(tc_bool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clsarity_bool__Lattices_Olattice')).
% 1.83/2.00  tff(20,plain,
% 1.83/2.00      (class_Lattices_Olattice(tc_bool)),
% 1.83/2.00      inference(modus_ponens,[status(thm)],[19, 18])).
% 1.83/2.00  tff(21,plain,
% 1.83/2.00      (^[T_1: $i, T_2: $i] : refl((class_Lattices_Oupper__semilattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1))) <=> (class_Lattices_Oupper__semilattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1))))),
% 1.83/2.00      inference(bind,[status(th)],[])).
% 1.83/2.00  tff(22,plain,
% 1.83/2.00      (![T_1: $i, T_2: $i] : (class_Lattices_Oupper__semilattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1))) <=> ![T_1: $i, T_2: $i] : (class_Lattices_Oupper__semilattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1)))),
% 1.83/2.00      inference(quant_intro,[status(thm)],[21])).
% 1.83/2.00  tff(23,plain,
% 1.83/2.00      (![T_1: $i, T_2: $i] : (class_Lattices_Oupper__semilattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1))) <=> ![T_1: $i, T_2: $i] : (class_Lattices_Oupper__semilattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1)))),
% 1.83/2.00      inference(rewrite,[status(thm)],[])).
% 1.83/2.00  tff(24,axiom,(![T_1: $i, T_2: $i] : (class_Lattices_Oupper__semilattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clsarity_fun__Lattices_Oupper__semilattice')).
% 1.83/2.00  tff(25,plain,
% 1.83/2.00      (![T_1: $i, T_2: $i] : (class_Lattices_Oupper__semilattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1)))),
% 1.83/2.00      inference(modus_ponens,[status(thm)],[24, 23])).
% 1.83/2.00  tff(26,plain,(
% 1.83/2.00      ![T_1: $i, T_2: $i] : (class_Lattices_Oupper__semilattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1)))),
% 1.83/2.00      inference(skolemize,[status(sab)],[25])).
% 1.83/2.00  tff(27,plain,
% 1.83/2.00      (![T_1: $i, T_2: $i] : (class_Lattices_Oupper__semilattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1)))),
% 1.83/2.00      inference(modus_ponens,[status(thm)],[26, 22])).
% 1.83/2.00  tff(28,plain,
% 1.83/2.00      (((~![T_1: $i, T_2: $i] : (class_Lattices_Oupper__semilattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1)))) | (class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~class_Lattices_Olattice(tc_bool)))) <=> ((~![T_1: $i, T_2: $i] : (class_Lattices_Oupper__semilattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1)))) | class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~class_Lattices_Olattice(tc_bool)))),
% 1.83/2.00      inference(rewrite,[status(thm)],[])).
% 1.83/2.00  tff(29,plain,
% 1.83/2.00      ((~![T_1: $i, T_2: $i] : (class_Lattices_Oupper__semilattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1)))) | (class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~class_Lattices_Olattice(tc_bool)))),
% 1.83/2.00      inference(quant_inst,[status(thm)],[])).
% 1.83/2.00  tff(30,plain,
% 1.83/2.00      ((~![T_1: $i, T_2: $i] : (class_Lattices_Oupper__semilattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1)))) | class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~class_Lattices_Olattice(tc_bool))),
% 1.83/2.00      inference(modus_ponens,[status(thm)],[29, 28])).
% 1.83/2.00  tff(31,plain,
% 1.83/2.00      (class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.00      inference(unit_resolution,[status(thm)],[30, 27, 20])).
% 1.83/2.00  tff(32,assumption,(~c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), introduced(assumption)).
% 1.83/2.00  tff(33,plain,
% 1.83/2.00      (^[V_x: $i, V_b: $i, V_a: $i, T_a: $i] : refl(((~class_Lattices_Oupper__semilattice(T_a)) | (~c_lessequals(V_x, V_a, T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_a, V_b, T_a), T_a)) <=> ((~class_Lattices_Oupper__semilattice(T_a)) | (~c_lessequals(V_x, V_a, T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_a, V_b, T_a), T_a)))),
% 1.83/2.00      inference(bind,[status(th)],[])).
% 1.83/2.00  tff(34,plain,
% 1.83/2.00      (![V_x: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_Lattices_Oupper__semilattice(T_a)) | (~c_lessequals(V_x, V_a, T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_a, V_b, T_a), T_a)) <=> ![V_x: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_Lattices_Oupper__semilattice(T_a)) | (~c_lessequals(V_x, V_a, T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_a, V_b, T_a), T_a))),
% 1.83/2.00      inference(quant_intro,[status(thm)],[33])).
% 1.83/2.00  tff(35,plain,
% 1.83/2.00      (![V_x: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_Lattices_Oupper__semilattice(T_a)) | (~c_lessequals(V_x, V_a, T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_a, V_b, T_a), T_a)) <=> ![V_x: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_Lattices_Oupper__semilattice(T_a)) | (~c_lessequals(V_x, V_a, T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_a, V_b, T_a), T_a))),
% 1.83/2.00      inference(rewrite,[status(thm)],[])).
% 1.83/2.00  tff(36,plain,
% 1.83/2.00      (^[V_x: $i, V_b: $i, V_a: $i, T_a: $i] : rewrite((((~class_Lattices_Oupper__semilattice(T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_a, V_b, T_a), T_a)) | (~c_lessequals(V_x, V_a, T_a))) <=> ((~class_Lattices_Oupper__semilattice(T_a)) | (~c_lessequals(V_x, V_a, T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_a, V_b, T_a), T_a)))),
% 1.83/2.00      inference(bind,[status(th)],[])).
% 1.83/2.00  tff(37,plain,
% 1.83/2.00      (![V_x: $i, V_b: $i, V_a: $i, T_a: $i] : (((~class_Lattices_Oupper__semilattice(T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_a, V_b, T_a), T_a)) | (~c_lessequals(V_x, V_a, T_a))) <=> ![V_x: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_Lattices_Oupper__semilattice(T_a)) | (~c_lessequals(V_x, V_a, T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_a, V_b, T_a), T_a))),
% 1.83/2.00      inference(quant_intro,[status(thm)],[36])).
% 1.83/2.00  tff(38,axiom,(![V_x: $i, V_b: $i, V_a: $i, T_a: $i] : (((~class_Lattices_Oupper__semilattice(T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_a, V_b, T_a), T_a)) | (~c_lessequals(V_x, V_a, T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_le__supI1_0')).
% 1.83/2.00  tff(39,plain,
% 1.83/2.00      (![V_x: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_Lattices_Oupper__semilattice(T_a)) | (~c_lessequals(V_x, V_a, T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_a, V_b, T_a), T_a))),
% 1.83/2.00      inference(modus_ponens,[status(thm)],[38, 37])).
% 1.83/2.00  tff(40,plain,
% 1.83/2.00      (![V_x: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_Lattices_Oupper__semilattice(T_a)) | (~c_lessequals(V_x, V_a, T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_a, V_b, T_a), T_a))),
% 1.83/2.00      inference(modus_ponens,[status(thm)],[39, 35])).
% 1.83/2.00  tff(41,plain,(
% 1.83/2.00      ![V_x: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_Lattices_Oupper__semilattice(T_a)) | (~c_lessequals(V_x, V_a, T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_a, V_b, T_a), T_a))),
% 1.83/2.00      inference(skolemize,[status(sab)],[40])).
% 1.83/2.00  tff(42,plain,
% 1.83/2.00      (![V_x: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_Lattices_Oupper__semilattice(T_a)) | (~c_lessequals(V_x, V_a, T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_a, V_b, T_a), T_a))),
% 1.83/2.00      inference(modus_ponens,[status(thm)],[41, 34])).
% 1.83/2.00  tff(43,plain,
% 1.83/2.00      (((~![V_x: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_Lattices_Oupper__semilattice(T_a)) | (~c_lessequals(V_x, V_a, T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_a, V_b, T_a), T_a))) | ((~class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))) <=> ((~![V_x: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_Lattices_Oupper__semilattice(T_a)) | (~c_lessequals(V_x, V_a, T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_a, V_b, T_a), T_a))) | (~class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))),
% 1.83/2.00      inference(rewrite,[status(thm)],[])).
% 1.83/2.00  tff(44,plain,
% 1.83/2.00      ((~![V_x: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_Lattices_Oupper__semilattice(T_a)) | (~c_lessequals(V_x, V_a, T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_a, V_b, T_a), T_a))) | ((~class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))),
% 1.83/2.00      inference(quant_inst,[status(thm)],[])).
% 1.83/2.00  tff(45,plain,
% 1.83/2.00      ((~![V_x: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_Lattices_Oupper__semilattice(T_a)) | (~c_lessequals(V_x, V_a, T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_a, V_b, T_a), T_a))) | (~class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.00      inference(modus_ponens,[status(thm)],[44, 43])).
% 1.83/2.00  tff(46,plain,
% 1.83/2.00      ($false),
% 1.83/2.00      inference(unit_resolution,[status(thm)],[45, 42, 32, 31, 17])).
% 1.83/2.00  tff(47,plain,(c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), inference(lemma,lemma(discharge,[]))).
% 1.83/2.00  tff(48,plain,
% 1.83/2.00      (^[T_1: $i, T_2: $i] : refl((class_Lattices_Olattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1))) <=> (class_Lattices_Olattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1))))),
% 1.83/2.00      inference(bind,[status(th)],[])).
% 1.83/2.00  tff(49,plain,
% 1.83/2.00      (![T_1: $i, T_2: $i] : (class_Lattices_Olattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1))) <=> ![T_1: $i, T_2: $i] : (class_Lattices_Olattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1)))),
% 1.83/2.00      inference(quant_intro,[status(thm)],[48])).
% 1.83/2.00  tff(50,plain,
% 1.83/2.00      (![T_1: $i, T_2: $i] : (class_Lattices_Olattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1))) <=> ![T_1: $i, T_2: $i] : (class_Lattices_Olattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1)))),
% 1.83/2.00      inference(rewrite,[status(thm)],[])).
% 1.83/2.00  tff(51,axiom,(![T_1: $i, T_2: $i] : (class_Lattices_Olattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clsarity_fun__Lattices_Olattice')).
% 1.83/2.00  tff(52,plain,
% 1.83/2.00      (![T_1: $i, T_2: $i] : (class_Lattices_Olattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1)))),
% 1.83/2.00      inference(modus_ponens,[status(thm)],[51, 50])).
% 1.83/2.00  tff(53,plain,(
% 1.83/2.00      ![T_1: $i, T_2: $i] : (class_Lattices_Olattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1)))),
% 1.83/2.00      inference(skolemize,[status(sab)],[52])).
% 1.83/2.00  tff(54,plain,
% 1.83/2.00      (![T_1: $i, T_2: $i] : (class_Lattices_Olattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1)))),
% 1.83/2.01      inference(modus_ponens,[status(thm)],[53, 49])).
% 1.83/2.01  tff(55,plain,
% 1.83/2.01      (((~![T_1: $i, T_2: $i] : (class_Lattices_Olattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1)))) | ((~class_Lattices_Olattice(tc_bool)) | class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))) <=> ((~![T_1: $i, T_2: $i] : (class_Lattices_Olattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1)))) | (~class_Lattices_Olattice(tc_bool)) | class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))),
% 1.83/2.01      inference(rewrite,[status(thm)],[])).
% 1.83/2.01  tff(56,plain,
% 1.83/2.01      ((class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~class_Lattices_Olattice(tc_bool))) <=> ((~class_Lattices_Olattice(tc_bool)) | class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))),
% 1.83/2.01      inference(rewrite,[status(thm)],[])).
% 1.83/2.01  tff(57,plain,
% 1.83/2.01      (((~![T_1: $i, T_2: $i] : (class_Lattices_Olattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1)))) | (class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~class_Lattices_Olattice(tc_bool)))) <=> ((~![T_1: $i, T_2: $i] : (class_Lattices_Olattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1)))) | ((~class_Lattices_Olattice(tc_bool)) | class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))))),
% 1.83/2.01      inference(monotonicity,[status(thm)],[56])).
% 1.83/2.01  tff(58,plain,
% 1.83/2.01      (((~![T_1: $i, T_2: $i] : (class_Lattices_Olattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1)))) | (class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~class_Lattices_Olattice(tc_bool)))) <=> ((~![T_1: $i, T_2: $i] : (class_Lattices_Olattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1)))) | (~class_Lattices_Olattice(tc_bool)) | class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))),
% 1.83/2.01      inference(transitivity,[status(thm)],[57, 55])).
% 1.83/2.01  tff(59,plain,
% 1.83/2.01      ((~![T_1: $i, T_2: $i] : (class_Lattices_Olattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1)))) | (class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~class_Lattices_Olattice(tc_bool)))),
% 1.83/2.01      inference(quant_inst,[status(thm)],[])).
% 1.83/2.01  tff(60,plain,
% 1.83/2.01      ((~![T_1: $i, T_2: $i] : (class_Lattices_Olattice(tc_fun(T_2, T_1)) | (~class_Lattices_Olattice(T_1)))) | (~class_Lattices_Olattice(tc_bool)) | class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.01      inference(modus_ponens,[status(thm)],[59, 58])).
% 1.83/2.01  tff(61,plain,
% 1.83/2.01      (class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.01      inference(unit_resolution,[status(thm)],[60, 54, 20])).
% 1.83/2.01  tff(62,plain,
% 1.83/2.01      (^[V_x: $i, T_a: $i, V_y: $i] : refl(((~class_Lattices_Olattice(T_a)) | c_lessequals(V_y, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a)) <=> ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_y, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a)))),
% 1.83/2.01      inference(bind,[status(th)],[])).
% 1.83/2.01  tff(63,plain,
% 1.83/2.01      (![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_y, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a)) <=> ![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_y, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a))),
% 1.83/2.01      inference(quant_intro,[status(thm)],[62])).
% 1.83/2.01  tff(64,plain,
% 1.83/2.01      (![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_y, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a)) <=> ![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_y, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a))),
% 1.83/2.01      inference(rewrite,[status(thm)],[])).
% 1.83/2.01  tff(65,axiom,(![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_y, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_inf__sup__ord_I4_J_0')).
% 1.83/2.01  tff(66,plain,
% 1.83/2.01      (![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_y, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a))),
% 1.83/2.01      inference(modus_ponens,[status(thm)],[65, 64])).
% 1.83/2.01  tff(67,plain,(
% 1.83/2.01      ![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_y, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a))),
% 1.83/2.01      inference(skolemize,[status(sab)],[66])).
% 1.83/2.01  tff(68,plain,
% 1.83/2.01      (![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_y, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a))),
% 1.83/2.01      inference(modus_ponens,[status(thm)],[67, 63])).
% 1.83/2.01  tff(69,plain,
% 1.83/2.01      (((~![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_y, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a))) | ((~class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))) <=> ((~![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_y, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a))) | (~class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))),
% 1.83/2.01      inference(rewrite,[status(thm)],[])).
% 1.83/2.01  tff(70,plain,
% 1.83/2.01      ((~![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_y, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a))) | ((~class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))),
% 1.83/2.01      inference(quant_inst,[status(thm)],[])).
% 1.83/2.01  tff(71,plain,
% 1.83/2.01      ((~![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_y, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a))) | (~class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.01      inference(modus_ponens,[status(thm)],[70, 69])).
% 1.83/2.01  tff(72,plain,
% 1.83/2.01      (c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.01      inference(unit_resolution,[status(thm)],[71, 68, 61])).
% 1.83/2.01  tff(73,plain,
% 1.83/2.01      (((~![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_y, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a))) | ((~class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))) <=> ((~![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_y, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a))) | (~class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))),
% 1.83/2.01      inference(rewrite,[status(thm)],[])).
% 1.83/2.01  tff(74,plain,
% 1.83/2.01      ((~![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_y, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a))) | ((~class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))),
% 1.83/2.01      inference(quant_inst,[status(thm)],[])).
% 1.83/2.01  tff(75,plain,
% 1.83/2.01      ((~![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_y, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a))) | (~class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.01      inference(modus_ponens,[status(thm)],[74, 73])).
% 1.83/2.01  tff(76,plain,
% 1.83/2.01      (c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.01      inference(unit_resolution,[status(thm)],[75, 68, 61])).
% 1.83/2.01  tff(77,plain,
% 1.83/2.01      (class_Orderings_Oorder(tc_bool) <=> class_Orderings_Oorder(tc_bool)),
% 1.83/2.01      inference(rewrite,[status(thm)],[])).
% 1.83/2.01  tff(78,axiom,(class_Orderings_Oorder(tc_bool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clsarity_bool__Orderings_Oorder')).
% 1.83/2.01  tff(79,plain,
% 1.83/2.01      (class_Orderings_Oorder(tc_bool)),
% 1.83/2.01      inference(modus_ponens,[status(thm)],[78, 77])).
% 1.83/2.01  tff(80,plain,
% 1.83/2.01      (^[T_1: $i, T_2: $i] : refl((class_Orderings_Oorder(tc_fun(T_2, T_1)) | (~class_Orderings_Oorder(T_1))) <=> (class_Orderings_Oorder(tc_fun(T_2, T_1)) | (~class_Orderings_Oorder(T_1))))),
% 1.83/2.01      inference(bind,[status(th)],[])).
% 1.83/2.01  tff(81,plain,
% 1.83/2.01      (![T_1: $i, T_2: $i] : (class_Orderings_Oorder(tc_fun(T_2, T_1)) | (~class_Orderings_Oorder(T_1))) <=> ![T_1: $i, T_2: $i] : (class_Orderings_Oorder(tc_fun(T_2, T_1)) | (~class_Orderings_Oorder(T_1)))),
% 1.83/2.01      inference(quant_intro,[status(thm)],[80])).
% 1.83/2.01  tff(82,plain,
% 1.83/2.01      (![T_1: $i, T_2: $i] : (class_Orderings_Oorder(tc_fun(T_2, T_1)) | (~class_Orderings_Oorder(T_1))) <=> ![T_1: $i, T_2: $i] : (class_Orderings_Oorder(tc_fun(T_2, T_1)) | (~class_Orderings_Oorder(T_1)))),
% 1.83/2.01      inference(rewrite,[status(thm)],[])).
% 1.83/2.01  tff(83,axiom,(![T_1: $i, T_2: $i] : (class_Orderings_Oorder(tc_fun(T_2, T_1)) | (~class_Orderings_Oorder(T_1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clsarity_fun__Orderings_Oorder')).
% 1.83/2.01  tff(84,plain,
% 1.83/2.01      (![T_1: $i, T_2: $i] : (class_Orderings_Oorder(tc_fun(T_2, T_1)) | (~class_Orderings_Oorder(T_1)))),
% 1.83/2.01      inference(modus_ponens,[status(thm)],[83, 82])).
% 1.83/2.01  tff(85,plain,(
% 1.83/2.01      ![T_1: $i, T_2: $i] : (class_Orderings_Oorder(tc_fun(T_2, T_1)) | (~class_Orderings_Oorder(T_1)))),
% 1.83/2.01      inference(skolemize,[status(sab)],[84])).
% 1.83/2.01  tff(86,plain,
% 1.83/2.01      (![T_1: $i, T_2: $i] : (class_Orderings_Oorder(tc_fun(T_2, T_1)) | (~class_Orderings_Oorder(T_1)))),
% 1.83/2.01      inference(modus_ponens,[status(thm)],[85, 81])).
% 1.83/2.01  tff(87,plain,
% 1.83/2.01      (((~![T_1: $i, T_2: $i] : (class_Orderings_Oorder(tc_fun(T_2, T_1)) | (~class_Orderings_Oorder(T_1)))) | ((~class_Orderings_Oorder(tc_bool)) | class_Orderings_Oorder(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))) <=> ((~![T_1: $i, T_2: $i] : (class_Orderings_Oorder(tc_fun(T_2, T_1)) | (~class_Orderings_Oorder(T_1)))) | (~class_Orderings_Oorder(tc_bool)) | class_Orderings_Oorder(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))),
% 1.83/2.01      inference(rewrite,[status(thm)],[])).
% 1.83/2.01  tff(88,plain,
% 1.83/2.01      ((class_Orderings_Oorder(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~class_Orderings_Oorder(tc_bool))) <=> ((~class_Orderings_Oorder(tc_bool)) | class_Orderings_Oorder(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))),
% 1.83/2.01      inference(rewrite,[status(thm)],[])).
% 1.83/2.01  tff(89,plain,
% 1.83/2.01      (((~![T_1: $i, T_2: $i] : (class_Orderings_Oorder(tc_fun(T_2, T_1)) | (~class_Orderings_Oorder(T_1)))) | (class_Orderings_Oorder(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~class_Orderings_Oorder(tc_bool)))) <=> ((~![T_1: $i, T_2: $i] : (class_Orderings_Oorder(tc_fun(T_2, T_1)) | (~class_Orderings_Oorder(T_1)))) | ((~class_Orderings_Oorder(tc_bool)) | class_Orderings_Oorder(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))))),
% 1.83/2.01      inference(monotonicity,[status(thm)],[88])).
% 1.83/2.01  tff(90,plain,
% 1.83/2.01      (((~![T_1: $i, T_2: $i] : (class_Orderings_Oorder(tc_fun(T_2, T_1)) | (~class_Orderings_Oorder(T_1)))) | (class_Orderings_Oorder(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~class_Orderings_Oorder(tc_bool)))) <=> ((~![T_1: $i, T_2: $i] : (class_Orderings_Oorder(tc_fun(T_2, T_1)) | (~class_Orderings_Oorder(T_1)))) | (~class_Orderings_Oorder(tc_bool)) | class_Orderings_Oorder(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))),
% 1.83/2.01      inference(transitivity,[status(thm)],[89, 87])).
% 1.83/2.01  tff(91,plain,
% 1.83/2.01      ((~![T_1: $i, T_2: $i] : (class_Orderings_Oorder(tc_fun(T_2, T_1)) | (~class_Orderings_Oorder(T_1)))) | (class_Orderings_Oorder(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~class_Orderings_Oorder(tc_bool)))),
% 1.83/2.01      inference(quant_inst,[status(thm)],[])).
% 1.83/2.01  tff(92,plain,
% 1.83/2.01      ((~![T_1: $i, T_2: $i] : (class_Orderings_Oorder(tc_fun(T_2, T_1)) | (~class_Orderings_Oorder(T_1)))) | (~class_Orderings_Oorder(tc_bool)) | class_Orderings_Oorder(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.01      inference(modus_ponens,[status(thm)],[91, 90])).
% 1.83/2.01  tff(93,plain,
% 1.83/2.01      (class_Orderings_Oorder(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.01      inference(unit_resolution,[status(thm)],[92, 86, 79])).
% 1.83/2.01  tff(94,plain,
% 1.83/2.01      (^[V_x: $i, V_z: $i, T_a: $i, V_y: $i] : refl(((~c_lessequals(V_y, V_x, T_a)) | (~c_lessequals(V_z, V_y, T_a)) | c_lessequals(V_z, V_x, T_a) | (~class_Orderings_Oorder(T_a))) <=> ((~c_lessequals(V_y, V_x, T_a)) | (~c_lessequals(V_z, V_y, T_a)) | c_lessequals(V_z, V_x, T_a) | (~class_Orderings_Oorder(T_a))))),
% 1.83/2.01      inference(bind,[status(th)],[])).
% 1.83/2.01  tff(95,plain,
% 1.83/2.01      (![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~c_lessequals(V_z, V_y, T_a)) | c_lessequals(V_z, V_x, T_a) | (~class_Orderings_Oorder(T_a))) <=> ![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~c_lessequals(V_z, V_y, T_a)) | c_lessequals(V_z, V_x, T_a) | (~class_Orderings_Oorder(T_a)))),
% 1.83/2.01      inference(quant_intro,[status(thm)],[94])).
% 1.83/2.01  tff(96,plain,
% 1.83/2.01      (![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~c_lessequals(V_z, V_y, T_a)) | c_lessequals(V_z, V_x, T_a) | (~class_Orderings_Oorder(T_a))) <=> ![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~c_lessequals(V_z, V_y, T_a)) | c_lessequals(V_z, V_x, T_a) | (~class_Orderings_Oorder(T_a)))),
% 1.83/2.01      inference(rewrite,[status(thm)],[])).
% 1.83/2.01  tff(97,plain,
% 1.83/2.01      (^[V_x: $i, V_z: $i, T_a: $i, V_y: $i] : trans(monotonicity(rewrite((((~class_Orderings_Oorder(T_a)) | c_lessequals(V_z, V_x, T_a)) | (~c_lessequals(V_z, V_y, T_a))) <=> ((~c_lessequals(V_z, V_y, T_a)) | c_lessequals(V_z, V_x, T_a) | (~class_Orderings_Oorder(T_a)))), (((((~class_Orderings_Oorder(T_a)) | c_lessequals(V_z, V_x, T_a)) | (~c_lessequals(V_z, V_y, T_a))) | (~c_lessequals(V_y, V_x, T_a))) <=> (((~c_lessequals(V_z, V_y, T_a)) | c_lessequals(V_z, V_x, T_a) | (~class_Orderings_Oorder(T_a))) | (~c_lessequals(V_y, V_x, T_a))))), rewrite((((~c_lessequals(V_z, V_y, T_a)) | c_lessequals(V_z, V_x, T_a) | (~class_Orderings_Oorder(T_a))) | (~c_lessequals(V_y, V_x, T_a))) <=> ((~c_lessequals(V_y, V_x, T_a)) | (~c_lessequals(V_z, V_y, T_a)) | c_lessequals(V_z, V_x, T_a) | (~class_Orderings_Oorder(T_a)))), (((((~class_Orderings_Oorder(T_a)) | c_lessequals(V_z, V_x, T_a)) | (~c_lessequals(V_z, V_y, T_a))) | (~c_lessequals(V_y, V_x, T_a))) <=> ((~c_lessequals(V_y, V_x, T_a)) | (~c_lessequals(V_z, V_y, T_a)) | c_lessequals(V_z, V_x, T_a) | (~class_Orderings_Oorder(T_a)))))),
% 1.83/2.01      inference(bind,[status(th)],[])).
% 1.83/2.01  tff(98,plain,
% 1.83/2.01      (![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : ((((~class_Orderings_Oorder(T_a)) | c_lessequals(V_z, V_x, T_a)) | (~c_lessequals(V_z, V_y, T_a))) | (~c_lessequals(V_y, V_x, T_a))) <=> ![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~c_lessequals(V_z, V_y, T_a)) | c_lessequals(V_z, V_x, T_a) | (~class_Orderings_Oorder(T_a)))),
% 1.83/2.01      inference(quant_intro,[status(thm)],[97])).
% 1.83/2.01  tff(99,axiom,(![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : ((((~class_Orderings_Oorder(T_a)) | c_lessequals(V_z, V_x, T_a)) | (~c_lessequals(V_z, V_y, T_a))) | (~c_lessequals(V_y, V_x, T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_xt1_I6_J_0')).
% 1.83/2.01  tff(100,plain,
% 1.83/2.01      (![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~c_lessequals(V_z, V_y, T_a)) | c_lessequals(V_z, V_x, T_a) | (~class_Orderings_Oorder(T_a)))),
% 1.83/2.01      inference(modus_ponens,[status(thm)],[99, 98])).
% 1.83/2.01  tff(101,plain,
% 1.83/2.01      (![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~c_lessequals(V_z, V_y, T_a)) | c_lessequals(V_z, V_x, T_a) | (~class_Orderings_Oorder(T_a)))),
% 1.83/2.01      inference(modus_ponens,[status(thm)],[100, 96])).
% 1.83/2.01  tff(102,plain,(
% 1.83/2.01      ![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~c_lessequals(V_z, V_y, T_a)) | c_lessequals(V_z, V_x, T_a) | (~class_Orderings_Oorder(T_a)))),
% 1.83/2.01      inference(skolemize,[status(sab)],[101])).
% 1.83/2.01  tff(103,plain,
% 1.83/2.01      (![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~c_lessequals(V_z, V_y, T_a)) | c_lessequals(V_z, V_x, T_a) | (~class_Orderings_Oorder(T_a)))),
% 1.83/2.01      inference(modus_ponens,[status(thm)],[102, 95])).
% 1.83/2.01  tff(104,plain,
% 1.83/2.01      (((~![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~c_lessequals(V_z, V_y, T_a)) | c_lessequals(V_z, V_x, T_a) | (~class_Orderings_Oorder(T_a)))) | (c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~class_Orderings_Oorder(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))))) <=> ((~![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~c_lessequals(V_z, V_y, T_a)) | c_lessequals(V_z, V_x, T_a) | (~class_Orderings_Oorder(T_a)))) | c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~class_Orderings_Oorder(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))))),
% 1.83/2.01      inference(rewrite,[status(thm)],[])).
% 1.83/2.01  tff(105,plain,
% 1.83/2.01      (((~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~class_Orderings_Oorder(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))) <=> (c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~class_Orderings_Oorder(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))))),
% 1.83/2.01      inference(rewrite,[status(thm)],[])).
% 1.83/2.01  tff(106,plain,
% 1.83/2.01      (((~![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~c_lessequals(V_z, V_y, T_a)) | c_lessequals(V_z, V_x, T_a) | (~class_Orderings_Oorder(T_a)))) | ((~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~class_Orderings_Oorder(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))))) <=> ((~![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~c_lessequals(V_z, V_y, T_a)) | c_lessequals(V_z, V_x, T_a) | (~class_Orderings_Oorder(T_a)))) | (c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~class_Orderings_Oorder(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))))),
% 1.83/2.01      inference(monotonicity,[status(thm)],[105])).
% 1.83/2.01  tff(107,plain,
% 1.83/2.01      (((~![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~c_lessequals(V_z, V_y, T_a)) | c_lessequals(V_z, V_x, T_a) | (~class_Orderings_Oorder(T_a)))) | ((~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~class_Orderings_Oorder(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))))) <=> ((~![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~c_lessequals(V_z, V_y, T_a)) | c_lessequals(V_z, V_x, T_a) | (~class_Orderings_Oorder(T_a)))) | c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~class_Orderings_Oorder(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))))),
% 1.83/2.01      inference(transitivity,[status(thm)],[106, 104])).
% 1.83/2.01  tff(108,plain,
% 1.83/2.01      ((~![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~c_lessequals(V_z, V_y, T_a)) | c_lessequals(V_z, V_x, T_a) | (~class_Orderings_Oorder(T_a)))) | ((~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~class_Orderings_Oorder(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))))),
% 1.83/2.01      inference(quant_inst,[status(thm)],[])).
% 1.83/2.01  tff(109,plain,
% 1.83/2.01      ((~![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~c_lessequals(V_z, V_y, T_a)) | c_lessequals(V_z, V_x, T_a) | (~class_Orderings_Oorder(T_a)))) | c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~class_Orderings_Oorder(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))),
% 1.83/2.01      inference(modus_ponens,[status(thm)],[108, 107])).
% 1.83/2.01  tff(110,plain,
% 1.83/2.01      (c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.01      inference(unit_resolution,[status(thm)],[109, 103, 93, 76, 72])).
% 1.83/2.01  tff(111,plain,
% 1.83/2.01      ((c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = v_ab) <=> (c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = v_ab)),
% 1.83/2.01      inference(rewrite,[status(thm)],[])).
% 1.83/2.01  tff(112,axiom,(c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = v_ab), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_3')).
% 1.83/2.01  tff(113,plain,
% 1.83/2.01      (c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = v_ab),
% 1.83/2.01      inference(modus_ponens,[status(thm)],[112, 111])).
% 1.83/2.01  tff(114,plain,
% 1.83/2.01      (v_ab = c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.01      inference(symmetry,[status(thm)],[113])).
% 1.83/2.01  tff(115,plain,
% 1.83/2.01      ((c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = v_ad) <=> (c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = v_ad)),
% 1.83/2.01      inference(rewrite,[status(thm)],[])).
% 1.83/2.01  tff(116,axiom,(c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = v_ad), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_5')).
% 1.83/2.01  tff(117,plain,
% 1.83/2.01      (c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = v_ad),
% 1.83/2.01      inference(modus_ponens,[status(thm)],[116, 115])).
% 1.83/2.01  tff(118,plain,
% 1.83/2.01      (c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) <=> c_lessequals(v_ad, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.01      inference(monotonicity,[status(thm)],[117])).
% 1.83/2.01  tff(119,plain,
% 1.83/2.01      (c_lessequals(v_ad, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) <=> c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.01      inference(symmetry,[status(thm)],[118])).
% 1.83/2.01  tff(120,plain,
% 1.83/2.01      (c_lessequals(v_ad, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) <=> c_lessequals(v_ad, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.01      inference(rewrite,[status(thm)],[])).
% 1.83/2.01  tff(121,axiom,(c_lessequals(v_ad, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_0')).
% 1.83/2.01  tff(122,plain,
% 1.83/2.01      (c_lessequals(v_ad, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.01      inference(modus_ponens,[status(thm)],[121, 120])).
% 1.83/2.01  tff(123,plain,
% 1.83/2.01      (c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.01      inference(modus_ponens,[status(thm)],[122, 119])).
% 1.83/2.01  tff(124,plain,
% 1.83/2.01      (^[V_x: $i, V_z: $i, T_a: $i, V_y: $i] : refl((c_lessequals(V_y, V_z, T_a) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), V_z, T_a)) | (~class_Lattices_Oupper__semilattice(T_a))) <=> (c_lessequals(V_y, V_z, T_a) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), V_z, T_a)) | (~class_Lattices_Oupper__semilattice(T_a))))),
% 1.83/2.01      inference(bind,[status(th)],[])).
% 1.83/2.01  tff(125,plain,
% 1.83/2.01      (![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_y, V_z, T_a) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), V_z, T_a)) | (~class_Lattices_Oupper__semilattice(T_a))) <=> ![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_y, V_z, T_a) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), V_z, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)))),
% 1.83/2.01      inference(quant_intro,[status(thm)],[124])).
% 1.83/2.01  tff(126,plain,
% 1.83/2.01      (![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_y, V_z, T_a) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), V_z, T_a)) | (~class_Lattices_Oupper__semilattice(T_a))) <=> ![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_y, V_z, T_a) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), V_z, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)))),
% 1.83/2.01      inference(rewrite,[status(thm)],[])).
% 1.83/2.01  tff(127,plain,
% 1.83/2.01      (^[V_x: $i, V_z: $i, T_a: $i, V_y: $i] : rewrite((((~class_Lattices_Oupper__semilattice(T_a)) | c_lessequals(V_y, V_z, T_a)) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), V_z, T_a))) <=> (c_lessequals(V_y, V_z, T_a) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), V_z, T_a)) | (~class_Lattices_Oupper__semilattice(T_a))))),
% 1.83/2.01      inference(bind,[status(th)],[])).
% 1.83/2.01  tff(128,plain,
% 1.83/2.01      (![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (((~class_Lattices_Oupper__semilattice(T_a)) | c_lessequals(V_y, V_z, T_a)) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), V_z, T_a))) <=> ![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_y, V_z, T_a) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), V_z, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)))),
% 1.83/2.01      inference(quant_intro,[status(thm)],[127])).
% 1.83/2.01  tff(129,axiom,(![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (((~class_Lattices_Oupper__semilattice(T_a)) | c_lessequals(V_y, V_z, T_a)) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), V_z, T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_le__sup__iff_1')).
% 1.83/2.01  tff(130,plain,
% 1.83/2.01      (![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_y, V_z, T_a) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), V_z, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)))),
% 1.83/2.01      inference(modus_ponens,[status(thm)],[129, 128])).
% 1.83/2.01  tff(131,plain,
% 1.83/2.01      (![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_y, V_z, T_a) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), V_z, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)))),
% 1.83/2.01      inference(modus_ponens,[status(thm)],[130, 126])).
% 1.83/2.01  tff(132,plain,(
% 1.83/2.01      ![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_y, V_z, T_a) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), V_z, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)))),
% 1.83/2.01      inference(skolemize,[status(sab)],[131])).
% 1.83/2.01  tff(133,plain,
% 1.83/2.01      (![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_y, V_z, T_a) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), V_z, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)))),
% 1.83/2.01      inference(modus_ponens,[status(thm)],[132, 125])).
% 1.83/2.01  tff(134,plain,
% 1.83/2.01      (((~![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_y, V_z, T_a) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), V_z, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)))) | (c_lessequals(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))))) <=> ((~![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_y, V_z, T_a) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), V_z, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)))) | c_lessequals(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))))),
% 1.83/2.01      inference(rewrite,[status(thm)],[])).
% 1.83/2.01  tff(135,plain,
% 1.83/2.01      ((~![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_y, V_z, T_a) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), V_z, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)))) | (c_lessequals(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))))),
% 1.83/2.01      inference(quant_inst,[status(thm)],[])).
% 1.83/2.01  tff(136,plain,
% 1.83/2.01      ((~![V_x: $i, V_z: $i, T_a: $i, V_y: $i] : (c_lessequals(V_y, V_z, T_a) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), V_z, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)))) | c_lessequals(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))),
% 1.83/2.01      inference(modus_ponens,[status(thm)],[135, 134])).
% 1.83/2.01  tff(137,plain,
% 1.83/2.01      (c_lessequals(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ae, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))),
% 1.83/2.01      inference(unit_resolution,[status(thm)],[136, 133])).
% 1.83/2.01  tff(138,plain,
% 1.83/2.01      (c_lessequals(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.01      inference(unit_resolution,[status(thm)],[137, 123, 31])).
% 1.83/2.01  tff(139,plain,
% 1.83/2.01      (^[V_x: $i, T_a: $i, V_y: $i] : refl(((~c_lessequals(V_x, V_y, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_y)) <=> ((~c_lessequals(V_x, V_y, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_y)))),
% 1.83/2.01      inference(bind,[status(th)],[])).
% 1.83/2.01  tff(140,plain,
% 1.83/2.01      (![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_x, V_y, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_y)) <=> ![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_x, V_y, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_y))),
% 1.83/2.01      inference(quant_intro,[status(thm)],[139])).
% 1.83/2.01  tff(141,plain,
% 1.83/2.01      (![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_x, V_y, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_y)) <=> ![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_x, V_y, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_y))),
% 1.83/2.01      inference(rewrite,[status(thm)],[])).
% 1.83/2.01  tff(142,plain,
% 1.83/2.01      (^[V_x: $i, T_a: $i, V_y: $i] : rewrite((((~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_y)) | (~c_lessequals(V_x, V_y, T_a))) <=> ((~c_lessequals(V_x, V_y, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_y)))),
% 1.83/2.01      inference(bind,[status(th)],[])).
% 1.83/2.01  tff(143,plain,
% 1.83/2.01      (![V_x: $i, T_a: $i, V_y: $i] : (((~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_y)) | (~c_lessequals(V_x, V_y, T_a))) <=> ![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_x, V_y, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_y))),
% 1.83/2.01      inference(quant_intro,[status(thm)],[142])).
% 1.83/2.01  tff(144,axiom,(![V_x: $i, T_a: $i, V_y: $i] : (((~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_y)) | (~c_lessequals(V_x, V_y, T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_le__iff__sup_0')).
% 1.83/2.01  tff(145,plain,
% 1.83/2.01      (![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_x, V_y, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_y))),
% 1.83/2.01      inference(modus_ponens,[status(thm)],[144, 143])).
% 1.83/2.01  tff(146,plain,
% 1.83/2.01      (![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_x, V_y, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_y))),
% 1.83/2.01      inference(modus_ponens,[status(thm)],[145, 141])).
% 1.83/2.01  tff(147,plain,(
% 1.83/2.01      ![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_x, V_y, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_y))),
% 1.83/2.01      inference(skolemize,[status(sab)],[146])).
% 1.83/2.01  tff(148,plain,
% 1.83/2.01      (![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_x, V_y, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_y))),
% 1.83/2.01      inference(modus_ponens,[status(thm)],[147, 140])).
% 1.83/2.01  tff(149,plain,
% 1.83/2.01      (((~![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_x, V_y, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_y))) | ((~class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (c_Lattices_Oupper__semilattice__class_Osup(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = v_ab))) <=> ((~![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_x, V_y, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_y))) | (~class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (c_Lattices_Oupper__semilattice__class_Osup(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = v_ab))),
% 1.83/2.02      inference(rewrite,[status(thm)],[])).
% 1.83/2.02  tff(150,plain,
% 1.83/2.02      (((~c_lessequals(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (c_Lattices_Oupper__semilattice__class_Osup(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = v_ab)) <=> ((~class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (c_Lattices_Oupper__semilattice__class_Osup(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = v_ab))),
% 1.83/2.02      inference(rewrite,[status(thm)],[])).
% 1.83/2.02  tff(151,plain,
% 1.83/2.02      (((~![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_x, V_y, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_y))) | ((~c_lessequals(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (c_Lattices_Oupper__semilattice__class_Osup(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = v_ab))) <=> ((~![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_x, V_y, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_y))) | ((~class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (c_Lattices_Oupper__semilattice__class_Osup(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = v_ab)))),
% 1.83/2.02      inference(monotonicity,[status(thm)],[150])).
% 1.83/2.02  tff(152,plain,
% 1.83/2.02      (((~![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_x, V_y, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_y))) | ((~c_lessequals(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (c_Lattices_Oupper__semilattice__class_Osup(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = v_ab))) <=> ((~![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_x, V_y, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_y))) | (~class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (c_Lattices_Oupper__semilattice__class_Osup(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = v_ab))),
% 1.83/2.02      inference(transitivity,[status(thm)],[151, 149])).
% 1.83/2.02  tff(153,plain,
% 1.83/2.02      ((~![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_x, V_y, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_y))) | ((~c_lessequals(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (c_Lattices_Oupper__semilattice__class_Osup(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = v_ab))),
% 1.83/2.02      inference(quant_inst,[status(thm)],[])).
% 1.83/2.02  tff(154,plain,
% 1.83/2.02      ((~![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_x, V_y, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_y))) | (~class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (c_Lattices_Oupper__semilattice__class_Osup(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = v_ab)),
% 1.83/2.02      inference(modus_ponens,[status(thm)],[153, 152])).
% 1.83/2.02  tff(155,plain,
% 1.83/2.02      (c_Lattices_Oupper__semilattice__class_Osup(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = v_ab),
% 1.83/2.02      inference(unit_resolution,[status(thm)],[154, 148, 138, 31])).
% 1.83/2.02  tff(156,plain,
% 1.83/2.02      (c_Lattices_Oupper__semilattice__class_Osup(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.02      inference(transitivity,[status(thm)],[155, 114])).
% 1.83/2.02  tff(157,plain,
% 1.83/2.02      (c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) <=> c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.02      inference(monotonicity,[status(thm)],[156])).
% 1.83/2.02  tff(158,plain,
% 1.83/2.02      (c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) <=> c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.02      inference(symmetry,[status(thm)],[157])).
% 1.83/2.02  tff(159,plain,
% 1.83/2.02      (^[V_x: $i, T_a: $i, V_y: $i] : refl(((~class_Lattices_Olattice(T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a)) <=> ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a)))),
% 1.83/2.02      inference(bind,[status(th)],[])).
% 1.83/2.02  tff(160,plain,
% 1.83/2.02      (![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a)) <=> ![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a))),
% 1.83/2.02      inference(quant_intro,[status(thm)],[159])).
% 1.83/2.02  tff(161,plain,
% 1.83/2.02      (![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a)) <=> ![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a))),
% 1.83/2.02      inference(rewrite,[status(thm)],[])).
% 1.83/2.02  tff(162,axiom,(![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_inf__sup__ord_I3_J_0')).
% 1.83/2.02  tff(163,plain,
% 1.83/2.02      (![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a))),
% 1.83/2.02      inference(modus_ponens,[status(thm)],[162, 161])).
% 1.83/2.02  tff(164,plain,(
% 1.83/2.02      ![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a))),
% 1.83/2.02      inference(skolemize,[status(sab)],[163])).
% 1.83/2.02  tff(165,plain,
% 1.83/2.02      (![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a))),
% 1.83/2.02      inference(modus_ponens,[status(thm)],[164, 160])).
% 1.83/2.02  tff(166,plain,
% 1.83/2.02      (((~![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a))) | ((~class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | c_lessequals(v_ac, c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))) <=> ((~![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a))) | (~class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | c_lessequals(v_ac, c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))),
% 1.83/2.02      inference(rewrite,[status(thm)],[])).
% 1.83/2.02  tff(167,plain,
% 1.83/2.02      ((~![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a))) | ((~class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | c_lessequals(v_ac, c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))),
% 1.83/2.02      inference(quant_inst,[status(thm)],[])).
% 1.83/2.02  tff(168,plain,
% 1.83/2.02      ((~![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a))) | (~class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | c_lessequals(v_ac, c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.02      inference(modus_ponens,[status(thm)],[167, 166])).
% 1.83/2.02  tff(169,plain,
% 1.83/2.02      (c_lessequals(v_ac, c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.02      inference(unit_resolution,[status(thm)],[168, 165, 61])).
% 1.83/2.02  tff(170,plain,
% 1.83/2.02      (^[V_x: $i, T_a: $i, V_y: $i] : refl(((~c_lessequals(V_y, V_x, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_x)) <=> ((~c_lessequals(V_y, V_x, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_x)))),
% 1.83/2.02      inference(bind,[status(th)],[])).
% 1.83/2.02  tff(171,plain,
% 1.83/2.02      (![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_x)) <=> ![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_x))),
% 1.83/2.02      inference(quant_intro,[status(thm)],[170])).
% 1.83/2.02  tff(172,plain,
% 1.83/2.02      (![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_x)) <=> ![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_x))),
% 1.83/2.02      inference(rewrite,[status(thm)],[])).
% 1.83/2.02  tff(173,plain,
% 1.83/2.02      (^[V_x: $i, T_a: $i, V_y: $i] : rewrite((((~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_x)) | (~c_lessequals(V_y, V_x, T_a))) <=> ((~c_lessequals(V_y, V_x, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_x)))),
% 1.83/2.02      inference(bind,[status(th)],[])).
% 1.83/2.02  tff(174,plain,
% 1.83/2.02      (![V_x: $i, T_a: $i, V_y: $i] : (((~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_x)) | (~c_lessequals(V_y, V_x, T_a))) <=> ![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_x))),
% 1.83/2.02      inference(quant_intro,[status(thm)],[173])).
% 1.83/2.02  tff(175,axiom,(![V_x: $i, T_a: $i, V_y: $i] : (((~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_x)) | (~c_lessequals(V_y, V_x, T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_sup__absorb1_0')).
% 1.83/2.02  tff(176,plain,
% 1.83/2.02      (![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_x))),
% 1.83/2.02      inference(modus_ponens,[status(thm)],[175, 174])).
% 1.83/2.02  tff(177,plain,
% 1.83/2.02      (![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_x))),
% 1.83/2.02      inference(modus_ponens,[status(thm)],[176, 172])).
% 1.83/2.02  tff(178,plain,(
% 1.83/2.02      ![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_x))),
% 1.83/2.02      inference(skolemize,[status(sab)],[177])).
% 1.83/2.02  tff(179,plain,
% 1.83/2.02      (![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_x))),
% 1.83/2.02      inference(modus_ponens,[status(thm)],[178, 171])).
% 1.83/2.02  tff(180,plain,
% 1.83/2.02      (((~![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_x))) | ((~class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval)))) <=> ((~![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_x))) | (~class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval)))),
% 1.83/2.02      inference(rewrite,[status(thm)],[])).
% 1.83/2.02  tff(181,plain,
% 1.83/2.02      (((~c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval))) <=> ((~class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval)))),
% 1.83/2.02      inference(rewrite,[status(thm)],[])).
% 1.83/2.02  tff(182,plain,
% 1.83/2.02      (((~![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_x))) | ((~c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval)))) <=> ((~![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_x))) | ((~class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval))))),
% 1.83/2.02      inference(monotonicity,[status(thm)],[181])).
% 1.83/2.02  tff(183,plain,
% 1.83/2.02      (((~![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_x))) | ((~c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval)))) <=> ((~![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_x))) | (~class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval)))),
% 1.83/2.02      inference(transitivity,[status(thm)],[182, 180])).
% 1.83/2.02  tff(184,plain,
% 1.83/2.02      ((~![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_x))) | ((~c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval)))),
% 1.83/2.02      inference(quant_inst,[status(thm)],[])).
% 1.83/2.02  tff(185,plain,
% 1.83/2.02      ((~![V_x: $i, T_a: $i, V_y: $i] : ((~c_lessequals(V_y, V_x, T_a)) | (~class_Lattices_Oupper__semilattice(T_a)) | (c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a) = V_x))) | (~class_Lattices_Oupper__semilattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval))),
% 1.83/2.02      inference(modus_ponens,[status(thm)],[184, 183])).
% 1.83/2.02  tff(186,plain,
% 1.83/2.02      (c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) = c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval)),
% 1.83/2.02      inference(unit_resolution,[status(thm)],[185, 179, 31, 17])).
% 1.83/2.02  tff(187,plain,
% 1.83/2.02      (c_lessequals(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) <=> c_lessequals(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.02      inference(monotonicity,[status(thm)],[186])).
% 1.83/2.02  tff(188,plain,
% 1.83/2.02      (((~![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a))) | ((~class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | c_lessequals(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))) <=> ((~![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a))) | (~class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | c_lessequals(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))),
% 1.83/2.02      inference(rewrite,[status(thm)],[])).
% 1.83/2.02  tff(189,plain,
% 1.83/2.02      ((~![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a))) | ((~class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | c_lessequals(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))),
% 1.83/2.02      inference(quant_inst,[status(thm)],[])).
% 1.83/2.02  tff(190,plain,
% 1.83/2.02      ((~![V_x: $i, T_a: $i, V_y: $i] : ((~class_Lattices_Olattice(T_a)) | c_lessequals(V_x, c_Lattices_Oupper__semilattice__class_Osup(V_x, V_y, T_a), T_a))) | (~class_Lattices_Olattice(tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | c_lessequals(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.02      inference(modus_ponens,[status(thm)],[189, 188])).
% 1.83/2.02  tff(191,plain,
% 1.83/2.02      (c_lessequals(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.02      inference(unit_resolution,[status(thm)],[190, 165, 61])).
% 1.83/2.02  tff(192,plain,
% 1.83/2.02      (c_lessequals(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.02      inference(modus_ponens,[status(thm)],[191, 187])).
% 1.83/2.02  tff(193,plain,
% 1.83/2.02      (^[V_D: $i, T_a: $i, V_B: $i, V_A: $i, V_C: $i] : refl(((~c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool))) | (~c_lessequals(V_B, V_D, tc_fun(T_a, tc_bool))) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(V_C, V_D, tc_fun(T_a, tc_bool)), tc_fun(T_a, tc_bool))) <=> ((~c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool))) | (~c_lessequals(V_B, V_D, tc_fun(T_a, tc_bool))) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(V_C, V_D, tc_fun(T_a, tc_bool)), tc_fun(T_a, tc_bool))))),
% 1.83/2.02      inference(bind,[status(th)],[])).
% 1.83/2.02  tff(194,plain,
% 1.83/2.02      (![V_D: $i, T_a: $i, V_B: $i, V_A: $i, V_C: $i] : ((~c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool))) | (~c_lessequals(V_B, V_D, tc_fun(T_a, tc_bool))) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(V_C, V_D, tc_fun(T_a, tc_bool)), tc_fun(T_a, tc_bool))) <=> ![V_D: $i, T_a: $i, V_B: $i, V_A: $i, V_C: $i] : ((~c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool))) | (~c_lessequals(V_B, V_D, tc_fun(T_a, tc_bool))) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(V_C, V_D, tc_fun(T_a, tc_bool)), tc_fun(T_a, tc_bool)))),
% 1.83/2.02      inference(quant_intro,[status(thm)],[193])).
% 1.83/2.02  tff(195,plain,
% 1.83/2.02      (![V_D: $i, T_a: $i, V_B: $i, V_A: $i, V_C: $i] : ((~c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool))) | (~c_lessequals(V_B, V_D, tc_fun(T_a, tc_bool))) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(V_C, V_D, tc_fun(T_a, tc_bool)), tc_fun(T_a, tc_bool))) <=> ![V_D: $i, T_a: $i, V_B: $i, V_A: $i, V_C: $i] : ((~c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool))) | (~c_lessequals(V_B, V_D, tc_fun(T_a, tc_bool))) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(V_C, V_D, tc_fun(T_a, tc_bool)), tc_fun(T_a, tc_bool)))),
% 1.83/2.02      inference(rewrite,[status(thm)],[])).
% 1.83/2.02  tff(196,plain,
% 1.83/2.02      (^[V_D: $i, T_a: $i, V_B: $i, V_A: $i, V_C: $i] : trans(monotonicity(rewrite((c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(V_C, V_D, tc_fun(T_a, tc_bool)), tc_fun(T_a, tc_bool)) | (~c_lessequals(V_B, V_D, tc_fun(T_a, tc_bool)))) <=> ((~c_lessequals(V_B, V_D, tc_fun(T_a, tc_bool))) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(V_C, V_D, tc_fun(T_a, tc_bool)), tc_fun(T_a, tc_bool)))), (((c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(V_C, V_D, tc_fun(T_a, tc_bool)), tc_fun(T_a, tc_bool)) | (~c_lessequals(V_B, V_D, tc_fun(T_a, tc_bool)))) | (~c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool)))) <=> (((~c_lessequals(V_B, V_D, tc_fun(T_a, tc_bool))) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(V_C, V_D, tc_fun(T_a, tc_bool)), tc_fun(T_a, tc_bool))) | (~c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool)))))), rewrite((((~c_lessequals(V_B, V_D, tc_fun(T_a, tc_bool))) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(V_C, V_D, tc_fun(T_a, tc_bool)), tc_fun(T_a, tc_bool))) | (~c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool)))) <=> ((~c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool))) | (~c_lessequals(V_B, V_D, tc_fun(T_a, tc_bool))) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(V_C, V_D, tc_fun(T_a, tc_bool)), tc_fun(T_a, tc_bool)))), (((c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(V_C, V_D, tc_fun(T_a, tc_bool)), tc_fun(T_a, tc_bool)) | (~c_lessequals(V_B, V_D, tc_fun(T_a, tc_bool)))) | (~c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool)))) <=> ((~c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool))) | (~c_lessequals(V_B, V_D, tc_fun(T_a, tc_bool))) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(V_C, V_D, tc_fun(T_a, tc_bool)), tc_fun(T_a, tc_bool)))))),
% 1.83/2.02      inference(bind,[status(th)],[])).
% 1.83/2.02  tff(197,plain,
% 1.83/2.02      (![V_D: $i, T_a: $i, V_B: $i, V_A: $i, V_C: $i] : ((c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(V_C, V_D, tc_fun(T_a, tc_bool)), tc_fun(T_a, tc_bool)) | (~c_lessequals(V_B, V_D, tc_fun(T_a, tc_bool)))) | (~c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool)))) <=> ![V_D: $i, T_a: $i, V_B: $i, V_A: $i, V_C: $i] : ((~c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool))) | (~c_lessequals(V_B, V_D, tc_fun(T_a, tc_bool))) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(V_C, V_D, tc_fun(T_a, tc_bool)), tc_fun(T_a, tc_bool)))),
% 1.83/2.02      inference(quant_intro,[status(thm)],[196])).
% 1.83/2.02  tff(198,axiom,(![V_D: $i, T_a: $i, V_B: $i, V_A: $i, V_C: $i] : ((c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(V_C, V_D, tc_fun(T_a, tc_bool)), tc_fun(T_a, tc_bool)) | (~c_lessequals(V_B, V_D, tc_fun(T_a, tc_bool)))) | (~c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Un__mono_0')).
% 1.83/2.02  tff(199,plain,
% 1.83/2.02      (![V_D: $i, T_a: $i, V_B: $i, V_A: $i, V_C: $i] : ((~c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool))) | (~c_lessequals(V_B, V_D, tc_fun(T_a, tc_bool))) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(V_C, V_D, tc_fun(T_a, tc_bool)), tc_fun(T_a, tc_bool)))),
% 1.83/2.02      inference(modus_ponens,[status(thm)],[198, 197])).
% 1.83/2.02  tff(200,plain,
% 1.83/2.02      (![V_D: $i, T_a: $i, V_B: $i, V_A: $i, V_C: $i] : ((~c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool))) | (~c_lessequals(V_B, V_D, tc_fun(T_a, tc_bool))) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(V_C, V_D, tc_fun(T_a, tc_bool)), tc_fun(T_a, tc_bool)))),
% 1.83/2.02      inference(modus_ponens,[status(thm)],[199, 195])).
% 1.83/2.02  tff(201,plain,(
% 1.83/2.02      ![V_D: $i, T_a: $i, V_B: $i, V_A: $i, V_C: $i] : ((~c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool))) | (~c_lessequals(V_B, V_D, tc_fun(T_a, tc_bool))) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(V_C, V_D, tc_fun(T_a, tc_bool)), tc_fun(T_a, tc_bool)))),
% 1.83/2.02      inference(skolemize,[status(sab)],[200])).
% 1.83/2.02  tff(202,plain,
% 1.83/2.02      (![V_D: $i, T_a: $i, V_B: $i, V_A: $i, V_C: $i] : ((~c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool))) | (~c_lessequals(V_B, V_D, tc_fun(T_a, tc_bool))) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(V_C, V_D, tc_fun(T_a, tc_bool)), tc_fun(T_a, tc_bool)))),
% 1.83/2.02      inference(modus_ponens,[status(thm)],[201, 194])).
% 1.83/2.02  tff(203,plain,
% 1.83/2.02      (((~![V_D: $i, T_a: $i, V_B: $i, V_A: $i, V_C: $i] : ((~c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool))) | (~c_lessequals(V_B, V_D, tc_fun(T_a, tc_bool))) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(V_C, V_D, tc_fun(T_a, tc_bool)), tc_fun(T_a, tc_bool)))) | ((~c_lessequals(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_ac, c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))) <=> ((~![V_D: $i, T_a: $i, V_B: $i, V_A: $i, V_C: $i] : ((~c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool))) | (~c_lessequals(V_B, V_D, tc_fun(T_a, tc_bool))) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(V_C, V_D, tc_fun(T_a, tc_bool)), tc_fun(T_a, tc_bool)))) | (~c_lessequals(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_ac, c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))),
% 1.83/2.02      inference(rewrite,[status(thm)],[])).
% 1.83/2.02  tff(204,plain,
% 1.83/2.02      ((~![V_D: $i, T_a: $i, V_B: $i, V_A: $i, V_C: $i] : ((~c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool))) | (~c_lessequals(V_B, V_D, tc_fun(T_a, tc_bool))) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(V_C, V_D, tc_fun(T_a, tc_bool)), tc_fun(T_a, tc_bool)))) | ((~c_lessequals(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_ac, c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))),
% 1.83/2.02      inference(quant_inst,[status(thm)],[])).
% 1.83/2.02  tff(205,plain,
% 1.83/2.02      ((~![V_D: $i, T_a: $i, V_B: $i, V_A: $i, V_C: $i] : ((~c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool))) | (~c_lessequals(V_B, V_D, tc_fun(T_a, tc_bool))) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(V_C, V_D, tc_fun(T_a, tc_bool)), tc_fun(T_a, tc_bool)))) | (~c_lessequals(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_ac, c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.02      inference(modus_ponens,[status(thm)],[204, 203])).
% 1.83/2.02  tff(206,plain,
% 1.83/2.02      ((~c_lessequals(v_ac, c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.02      inference(unit_resolution,[status(thm)],[205, 202, 192])).
% 1.83/2.02  tff(207,plain,
% 1.83/2.02      (c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), v_ac, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.02      inference(unit_resolution,[status(thm)],[206, 169])).
% 1.83/2.02  tff(208,plain,
% 1.83/2.02      (c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.02      inference(modus_ponens,[status(thm)],[207, 158])).
% 1.83/2.02  tff(209,plain,
% 1.83/2.02      (^[T_a: $i, V_B: $i, V_A: $i, V_C: $i] : refl((c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool)) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), V_C, tc_fun(T_a, tc_bool)))) <=> (c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool)) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), V_C, tc_fun(T_a, tc_bool)))))),
% 1.83/2.03      inference(bind,[status(th)],[])).
% 1.83/2.03  tff(210,plain,
% 1.83/2.03      (![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool)) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), V_C, tc_fun(T_a, tc_bool)))) <=> ![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool)) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), V_C, tc_fun(T_a, tc_bool))))),
% 1.83/2.03      inference(quant_intro,[status(thm)],[209])).
% 1.83/2.03  tff(211,plain,
% 1.83/2.03      (![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool)) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), V_C, tc_fun(T_a, tc_bool)))) <=> ![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool)) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), V_C, tc_fun(T_a, tc_bool))))),
% 1.83/2.03      inference(rewrite,[status(thm)],[])).
% 1.83/2.03  tff(212,axiom,(![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool)) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), V_C, tc_fun(T_a, tc_bool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Un__subset__iff_0')).
% 1.83/2.03  tff(213,plain,
% 1.83/2.03      (![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool)) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), V_C, tc_fun(T_a, tc_bool))))),
% 1.83/2.03      inference(modus_ponens,[status(thm)],[212, 211])).
% 1.83/2.03  tff(214,plain,(
% 1.83/2.03      ![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool)) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), V_C, tc_fun(T_a, tc_bool))))),
% 1.83/2.03      inference(skolemize,[status(sab)],[213])).
% 1.83/2.03  tff(215,plain,
% 1.83/2.03      (![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool)) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), V_C, tc_fun(T_a, tc_bool))))),
% 1.83/2.03      inference(modus_ponens,[status(thm)],[214, 210])).
% 1.83/2.03  tff(216,plain,
% 1.83/2.03      (((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool)) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), V_C, tc_fun(T_a, tc_bool))))) | (c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool)) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), V_C, tc_fun(T_a, tc_bool))))) | c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))))),
% 1.83/2.03      inference(rewrite,[status(thm)],[])).
% 1.83/2.03  tff(217,plain,
% 1.83/2.03      ((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool)) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), V_C, tc_fun(T_a, tc_bool))))) | (c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))))),
% 1.83/2.03      inference(quant_inst,[status(thm)],[])).
% 1.83/2.03  tff(218,plain,
% 1.83/2.03      ((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_fun(T_a, tc_bool)) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), V_C, tc_fun(T_a, tc_bool))))) | c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)) | (~c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(v_ae, v_ab, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))),
% 1.83/2.03      inference(modus_ponens,[status(thm)],[217, 216])).
% 1.83/2.03  tff(219,plain,
% 1.83/2.03      (c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))),
% 1.83/2.03      inference(unit_resolution,[status(thm)],[218, 215, 208])).
% 1.83/2.03  tff(220,plain,
% 1.83/2.03      (((~c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))) <=> ((~c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))))),
% 1.83/2.03      inference(rewrite,[status(thm)],[])).
% 1.83/2.03  tff(221,plain,
% 1.83/2.03      ((((~c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))) | (~c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))) <=> ((~c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))))),
% 1.83/2.03      inference(rewrite,[status(thm)],[])).
% 1.83/2.03  tff(222,plain,
% 1.83/2.03      (((~c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))) <=> ((~c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))))),
% 1.83/2.03      inference(rewrite,[status(thm)],[])).
% 1.83/2.03  tff(223,plain,
% 1.83/2.03      ((((~c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))) | (~c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))) <=> (((~c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))) | (~c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))))),
% 1.83/2.03      inference(monotonicity,[status(thm)],[222])).
% 1.83/2.03  tff(224,plain,
% 1.83/2.03      ((((~c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))) | (~c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))) <=> ((~c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))))),
% 1.83/2.03      inference(transitivity,[status(thm)],[223, 221])).
% 1.83/2.03  tff(225,axiom,(((~c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))) | (~c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_7')).
% 1.83/2.03  tff(226,plain,
% 1.83/2.03      ((~c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))),
% 1.83/2.03      inference(modus_ponens,[status(thm)],[225, 224])).
% 1.83/2.03  tff(227,plain,
% 1.83/2.03      ((~c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))),
% 1.93/2.09      inference(modus_ponens,[status(thm)],[226, 220])).
% 1.93/2.09  tff(228,plain,
% 1.93/2.09      ((~c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))),
% 1.93/2.09      inference(modus_ponens,[status(thm)],[227, 220])).
% 1.93/2.09  tff(229,plain,
% 1.93/2.09      ((~c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))),
% 1.93/2.09      inference(modus_ponens,[status(thm)],[228, 220])).
% 1.93/2.09  tff(230,plain,
% 1.93/2.09      ((~c_lessequals(v_x, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(v_ae, c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool))) | (~c_lessequals(c_Map_Odom(v_b, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(v_ba, tc_List_Olist(tc_String_Ochar), tc_Value_Oval), c_Lattices_Oupper__semilattice__class_Osup(v_ac, v_x, tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)), tc_fun(tc_List_Olist(tc_String_Ochar), tc_bool)))),
% 1.93/2.09      inference(modus_ponens,[status(thm)],[229, 220])).
% 1.93/2.09  tff(231,plain,
% 1.93/2.09      ($false),
% 1.93/2.09      inference(unit_resolution,[status(thm)],[230, 219, 110, 47])).
% 1.93/2.09  % SZS output end Proof
% 1.93/2.10  % E exiting
%------------------------------------------------------------------------------