TSTP Solution File: LCL817-1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : LCL817-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n028.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 : Thu Aug 31 06:51:09 EDT 2023
% Result : Unsatisfiable 0.75s 0.80s
% Output : CNFRefutation 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : LCL817-1 : TPTP v8.1.2. Released v4.1.0.
% 0.06/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.12/0.35 % Computer : n028.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Fri Aug 25 06:36:21 EDT 2023
% 0.12/0.35 % CPUTime :
% 0.20/0.58 start to proof:theBenchmark
% 0.20/0.77 %-------------------------------------------
% 0.20/0.77 % File :CSE---1.6
% 0.20/0.77 % Problem :theBenchmark
% 0.20/0.77 % Transform :cnf
% 0.20/0.77 % Format :tptp:raw
% 0.20/0.77 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.77
% 0.20/0.77 % Result :Theorem 0.070000s
% 0.20/0.77 % Output :CNFRefutation 0.070000s
% 0.20/0.77 %-------------------------------------------
% 0.20/0.77 %------------------------------------------------------------------------------
% 0.20/0.77 % File : LCL817-1 : TPTP v8.1.2. Released v4.1.0.
% 0.20/0.77 % Domain : Logic Calculi
% 0.20/0.77 % Problem : Strong normalization of typed lambda calculus 184_15
% 0.20/0.77 % Version : Especial.
% 0.20/0.77 % English :
% 0.20/0.77
% 0.20/0.77 % Refs : [vON99] von Oheimb & Nipkow (1999), Machine-Checking the Java
% 0.20/0.77 % : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe
% 0.20/0.77 % : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.20/0.77 % Source : [Nip10]
% 0.20/0.77 % Names : StrongNorm-184_15 [Nip10]
% 0.20/0.77
% 0.20/0.77 % Status : Unsatisfiable
% 0.20/0.77 % Rating : 0.05 v8.1.0, 0.11 v7.5.0, 0.05 v7.4.0, 0.12 v7.3.0, 0.00 v7.0.0, 0.13 v6.4.0, 0.07 v6.3.0, 0.00 v6.2.0, 0.10 v6.1.0, 0.00 v6.0.0, 0.10 v5.5.0, 0.30 v5.4.0, 0.25 v5.3.0, 0.28 v5.2.0, 0.31 v5.1.0, 0.41 v5.0.0, 0.29 v4.1.0
% 0.20/0.77 % Syntax : Number of clauses : 294 ( 99 unt; 20 nHn; 180 RR)
% 0.20/0.77 % Number of literals : 584 ( 194 equ; 290 neg)
% 0.20/0.77 % Maximal clause size : 6 ( 1 avg)
% 0.20/0.77 % Maximal term depth : 6 ( 2 avg)
% 0.20/0.77 % Number of predicates : 29 ( 28 usr; 0 prp; 1-4 aty)
% 0.20/0.77 % Number of functors : 48 ( 48 usr; 23 con; 0-5 aty)
% 0.20/0.77 % Number of variables : 865 ( 135 sgn)
% 0.20/0.77 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.20/0.77
% 0.20/0.77 % Comments :
% 0.20/0.77 %------------------------------------------------------------------------------
% 0.20/0.77 cnf(cls_append__eq__append__conv2_5,axiom,
% 0.20/0.77 c_List_Oappend(V_xs,c_List_Oappend(V_x,V_ts,T_a),T_a) = c_List_Oappend(c_List_Oappend(V_xs,V_x,T_a),V_ts,T_a) ).
% 0.20/0.77
% 0.20/0.77 cnf(cls_append__eq__append__conv2_4,axiom,
% 0.20/0.77 c_List_Oappend(c_List_Oappend(V_zs,V_x,T_a),V_ys,T_a) = c_List_Oappend(V_zs,c_List_Oappend(V_x,V_ys,T_a),T_a) ).
% 0.20/0.77
% 0.20/0.77 cnf(cls_append__eq__appendI_0,axiom,
% 0.20/0.77 c_List_Oappend(V_xs,c_List_Oappend(V_xs1,V_us,T_a),T_a) = c_List_Oappend(c_List_Oappend(V_xs,V_xs1,T_a),V_us,T_a) ).
% 0.20/0.77
% 0.20/0.77 cnf(cls_append__assoc_0,axiom,
% 0.20/0.77 c_List_Oappend(c_List_Oappend(V_xs,V_ys,T_a),V_zs,T_a) = c_List_Oappend(V_xs,c_List_Oappend(V_ys,V_zs,T_a),T_a) ).
% 0.20/0.77
% 0.20/0.77 cnf(cls_append__is__Nil__conv_2,axiom,
% 0.20/0.77 c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ).
% 0.20/0.77
% 0.20/0.77 cnf(cls_append1__eq__conv_1,axiom,
% 0.20/0.77 ( c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) != c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a)
% 0.20/0.77 | V_x = V_y ) ).
% 0.20/0.77
% 0.20/0.77 cnf(cls_append1__eq__conv_0,axiom,
% 0.20/0.77 ( c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) != c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a)
% 0.20/0.77 | V_xs = V_ys ) ).
% 0.20/0.77
% 0.20/0.77 cnf(cls_append__eq__Cons__conv_4,axiom,
% 0.20/0.77 c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,V_xs,T_a) ).
% 0.20/0.77
% 0.20/0.77 cnf(cls_self__append__conv2_0,axiom,
% 0.20/0.77 ( V_ys != c_List_Oappend(V_xs,V_ys,T_a)
% 0.20/0.77 | V_xs = c_List_Olist_ONil(T_a) ) ).
% 0.20/0.77
% 0.20/0.77 cnf(cls_append__self__conv2_0,axiom,
% 0.20/0.77 ( c_List_Oappend(V_xs,V_ys,T_a) != V_ys
% 0.20/0.77 | V_xs = c_List_Olist_ONil(T_a) ) ).
% 0.20/0.77
% 0.20/0.77 cnf(cls_self__append__conv_0,axiom,
% 0.20/0.77 ( V_xs != c_List_Oappend(V_xs,V_ys,T_a)
% 0.20/0.77 | V_ys = c_List_Olist_ONil(T_a) ) ).
% 0.20/0.77
% 0.20/0.77 cnf(cls_append__self__conv_0,axiom,
% 0.20/0.77 ( c_List_Oappend(V_xs,V_ys,T_a) != V_xs
% 0.20/0.77 | V_ys = c_List_Olist_ONil(T_a) ) ).
% 0.20/0.77
% 0.20/0.77 cnf(cls_append__in__listsp__conv_2,axiom,
% 0.20/0.77 ( c_List_Olistsp(V_A,c_List_Oappend(V_xs,V_ys,T_a),T_a)
% 0.20/0.77 | ~ c_List_Olistsp(V_A,V_ys,T_a)
% 0.20/0.77 | ~ c_List_Olistsp(V_A,V_xs,T_a) ) ).
% 0.69/0.77
% 0.69/0.77 cnf(cls_Snoc__step1__SnocD_2,axiom,
% 0.69/0.77 ( V_ys = V_xs
% 0.69/0.77 | V_y = V_x
% 0.69/0.77 | ~ c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a) ) ).
% 0.69/0.77
% 0.69/0.77 cnf(cls_append__is__Nil__conv_1,axiom,
% 0.69/0.77 ( c_List_Oappend(V_xs,V_ys,T_a) != c_List_Olist_ONil(T_a)
% 0.69/0.77 | V_ys = c_List_Olist_ONil(T_a) ) ).
% 0.69/0.77
% 0.69/0.77 cnf(cls_append__is__Nil__conv_0,axiom,
% 0.69/0.77 ( c_List_Oappend(V_xs,V_ys,T_a) != c_List_Olist_ONil(T_a)
% 0.69/0.77 | V_xs = c_List_Olist_ONil(T_a) ) ).
% 0.69/0.77
% 0.69/0.77 cnf(cls_Nil__is__append__conv_1,axiom,
% 0.69/0.77 ( c_List_Olist_ONil(T_a) != c_List_Oappend(V_xs,V_ys,T_a)
% 0.69/0.77 | V_ys = c_List_Olist_ONil(T_a) ) ).
% 0.69/0.77
% 0.69/0.77 cnf(cls_Nil__is__append__conv_0,axiom,
% 0.69/0.77 ( c_List_Olist_ONil(T_a) != c_List_Oappend(V_xs,V_ys,T_a)
% 0.69/0.77 | V_xs = c_List_Olist_ONil(T_a) ) ).
% 0.69/0.77
% 0.69/0.77 cnf(cls_Snoc__step1__SnocD_3,axiom,
% 0.69/0.77 ( hBOOL(hAPP(hAPP(V_r,V_y),V_x))
% 0.69/0.77 | V_y = V_x
% 0.69/0.77 | ~ c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a) ) ).
% 0.69/0.77
% 0.69/0.77 cnf(cls_foldr__append_0,axiom,
% 0.69/0.77 c_List_Ofoldr(V_f,c_List_Oappend(V_xs,V_ys,T_b),V_a,T_b,T_a) = c_List_Ofoldr(V_f,V_xs,c_List_Ofoldr(V_f,V_ys,V_a,T_b,T_a),T_b,T_a) ).
% 0.69/0.77
% 0.69/0.77 cnf(cls_self__append__conv2_1,axiom,
% 0.69/0.77 V_ys = c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a) ).
% 0.69/0.77
% 0.69/0.77 cnf(cls_append__Nil_0,axiom,
% 0.69/0.77 c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a) = V_ys ).
% 0.69/0.77
% 0.69/0.77 cnf(cls_self__append__conv_1,axiom,
% 0.69/0.78 V_xs = c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_eq__Nil__appendI_0,axiom,
% 0.69/0.78 V_x = c_List_Oappend(c_List_Olist_ONil(T_a),V_x,T_a) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_append__Nil2_0,axiom,
% 0.69/0.78 c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a) = V_xs ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_same__append__eq_0,axiom,
% 0.69/0.78 ( c_List_Oappend(V_xs,V_ys,T_a) != c_List_Oappend(V_xs,V_zs,T_a)
% 0.69/0.78 | V_ys = V_zs ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_append__same__eq_0,axiom,
% 0.69/0.78 ( c_List_Oappend(V_ys,V_xs,T_a) != c_List_Oappend(V_zs,V_xs,T_a)
% 0.69/0.78 | V_ys = V_zs ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_append__in__listsp__conv_1,axiom,
% 0.69/0.78 ( c_List_Olistsp(V_A,V_ys,T_a)
% 0.69/0.78 | ~ c_List_Olistsp(V_A,c_List_Oappend(V_xs,V_ys,T_a),T_a) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_append__in__listsp__conv_0,axiom,
% 0.69/0.78 ( c_List_Olistsp(V_A,V_xs,T_a)
% 0.69/0.78 | ~ c_List_Olistsp(V_A,c_List_Oappend(V_xs,V_ys,T_a),T_a) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_append__step1I_1,axiom,
% 0.69/0.78 ( c_ListOrder_Ostep1(V_r,c_List_Oappend(V_x,V_vs,T_a),c_List_Oappend(V_x,V_us,T_a),T_a)
% 0.69/0.78 | ~ c_ListOrder_Ostep1(V_r,V_vs,V_us,T_a) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_append__step1I_0,axiom,
% 0.69/0.78 ( ~ c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a)
% 0.69/0.78 | c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,V_x,T_a),c_List_Oappend(V_xs,V_x,T_a),T_a) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_Snoc__step1__SnocD_1,axiom,
% 0.69/0.78 ( hBOOL(hAPP(hAPP(V_r,V_y),V_x))
% 0.69/0.78 | c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a)
% 0.69/0.78 | ~ c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_types__snocE_2,axiom,
% 0.69/0.78 ( c_Type_Otyping(V_e,V_t,c_Type_Osko__Type__Xtypes__snocE__1__2(V_Ts,V_e,V_t,V_ts))
% 0.69/0.78 | ~ c_Type_Otypings(V_e,c_List_Oappend(V_ts,c_List_Olist_OCons(V_t,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),V_Ts) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_append__eq__Cons__conv_5,axiom,
% 0.69/0.78 c_List_Oappend(c_List_Olist_OCons(V_x,V_xa,T_a),V_zs,T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(V_xa,V_zs,T_a),T_a) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_append__Cons_0,axiom,
% 0.69/0.78 c_List_Oappend(c_List_Olist_OCons(V_x,V_xs,T_a),V_ys,T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(V_xs,V_ys,T_a),T_a) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_Cons__eq__append__conv_5,axiom,
% 0.69/0.78 c_List_Olist_OCons(V_x,c_List_Oappend(V_xa,V_zs,T_a),T_a) = c_List_Oappend(c_List_Olist_OCons(V_x,V_xa,T_a),V_zs,T_a) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_Cons__eq__appendI_0,axiom,
% 0.69/0.78 c_List_Olist_OCons(V_x,c_List_Oappend(V_xs1,V_zs,T_a),T_a) = c_List_Oappend(c_List_Olist_OCons(V_x,V_xs1,T_a),V_zs,T_a) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_Cons__eq__append__conv_4,axiom,
% 0.69/0.78 c_List_Olist_OCons(V_x,V_xs,T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_Snoc__step1__SnocD_0,axiom,
% 0.69/0.78 ( V_ys = V_xs
% 0.69/0.78 | c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a)
% 0.69/0.78 | ~ c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_Nil__is__append__conv_2,axiom,
% 0.69/0.78 c_List_Olist_ONil(T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_foldl__append_0,axiom,
% 0.69/0.78 c_List_Ofoldl(V_f,V_a,c_List_Oappend(V_xs,V_ys,T_b),T_a,T_b) = c_List_Ofoldl(V_f,c_List_Ofoldl(V_f,V_a,V_xs,T_a,T_b),V_ys,T_a,T_b) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_zero__less__double__add__iff__zero__less__single__add_1,axiom,
% 0.69/0.78 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
% 0.69/0.78 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a)
% 0.69/0.78 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_zero__less__double__add__iff__zero__less__single__add_0,axiom,
% 0.69/0.78 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
% 0.69/0.78 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
% 0.69/0.78 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom,
% 0.69/0.78 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.69/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
% 0.69/0.78 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.69/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_monoid__add__class_Oadd__0__right_0,axiom,
% 0.69/0.78 ( ~ class_OrderedGroup_Omonoid__add(T_a)
% 0.69/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_add__0__left_0,axiom,
% 0.69/0.78 ( ~ class_OrderedGroup_Omonoid__add(T_a)
% 0.69/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_comm__monoid__add_Omult__1__right_0,axiom,
% 0.69/0.78 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
% 0.69/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_class__ringb_Oadd__r0__iff_1,axiom,
% 0.69/0.78 ( ~ class_Ring__and__Field_Oidom(T_a)
% 0.69/0.78 | ~ class_Int_Onumber__ring(T_a)
% 0.69/0.78 | V_x = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_HOL_Ozero__class_Ozero(T_a)) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_comm__monoid__add_Omult__1_0,axiom,
% 0.69/0.78 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
% 0.69/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_class__semiring_Oadd__0_0,axiom,
% 0.69/0.78 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.69/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_x) = V_x ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_not__Cons__self_0,axiom,
% 0.69/0.78 V_xs != c_List_Olist_OCons(V_x,V_xs,T_a) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_not__Cons__self2_0,axiom,
% 0.69/0.78 c_List_Olist_OCons(V_x,V_t,T_a) != V_t ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_of__nat__less__0__iff_0,axiom,
% 0.69/0.78 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.69/0.78 | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom,
% 0.69/0.78 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.69/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d)) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_Cons__step1__Cons_0,axiom,
% 0.69/0.78 ( V_x = V_y
% 0.69/0.78 | hBOOL(hAPP(hAPP(V_r,V_y),V_x))
% 0.69/0.78 | ~ c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_list_Osimps_I3_J_0,axiom,
% 0.69/0.78 c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_neq__Nil__conv_1,axiom,
% 0.69/0.78 c_List_Olist_OCons(V_x,V_xa,T_a) != c_List_Olist_ONil(T_a) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_add__right__cancel_0,axiom,
% 0.69/0.78 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a)
% 0.69/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_a) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a)
% 0.69/0.78 | V_b = V_c ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_add__left__cancel_0,axiom,
% 0.69/0.78 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a)
% 0.69/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)
% 0.69/0.78 | V_b = V_c ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_add__imp__eq_0,axiom,
% 0.69/0.78 ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(T_a)
% 0.69/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)
% 0.69/0.78 | V_b = V_c ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_class__ringb_Oadd__cancel_0,axiom,
% 0.69/0.78 ( ~ class_Ring__and__Field_Oidom(T_a)
% 0.69/0.78 | ~ class_Int_Onumber__ring(T_a)
% 0.69/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z)
% 0.69/0.78 | V_y = V_z ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_add__neg__neg_0,axiom,
% 0.69/0.78 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
% 0.69/0.78 | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.69/0.78 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.69/0.78 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_of__nat__0_0,axiom,
% 0.69/0.78 ( ~ class_Ring__and__Field_Osemiring__1(T_a)
% 0.69/0.78 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_rtranclp__converseI_0,axiom,
% 0.69/0.78 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(V_r,T_a,T_a),T_a),V_x),V_y))
% 0.69/0.78 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_y),V_x)) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_rtranclp__converseD_0,axiom,
% 0.69/0.78 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_y),V_x))
% 0.69/0.78 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(V_r,T_a,T_a),T_a),V_x),V_y)) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_foldl__Cons_0,axiom,
% 0.69/0.78 c_List_Ofoldl(V_f,V_a,c_List_Olist_OCons(V_x,V_xs,T_b),T_a,T_b) = c_List_Ofoldl(V_f,hAPP(hAPP(V_f,V_a),V_x),V_xs,T_a,T_b) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_foldr_Osimps_I1_J_0,axiom,
% 0.69/0.78 c_List_Ofoldr(V_f,c_List_Olist_ONil(T_b),V_a,T_b,T_a) = V_a ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_add__cancel__21_0,axiom,
% 0.69/0.78 ( ~ class_OrderedGroup_Oab__group__add(T_a)
% 0.69/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_u)
% 0.69/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z) = V_u ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_conversepD_0,axiom,
% 0.69/0.78 ( hBOOL(hAPP(hAPP(V_r,V_b),V_a))
% 0.69/0.78 | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_a),V_b)) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_conversep__iff_1,axiom,
% 0.69/0.78 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_a),V_b))
% 0.69/0.78 | ~ hBOOL(hAPP(hAPP(V_r,V_b),V_a)) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_conversep_Ocases_0,axiom,
% 0.69/0.78 ( hBOOL(hAPP(hAPP(V_r,V_a2),V_a1))
% 0.69/0.78 | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_a1),V_a2)) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_conversep_Ointros_0,axiom,
% 0.69/0.78 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_b),V_a))
% 0.69/0.78 | ~ hBOOL(hAPP(hAPP(V_r,V_a),V_b)) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom,
% 0.69/0.78 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.69/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom,
% 0.69/0.78 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.69/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_d)) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom,
% 0.69/0.78 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.69/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),V_b) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom,
% 0.69/0.78 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.69/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),V_d) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom,
% 0.69/0.78 ( ~ class_OrderedGroup_Oab__semigroup__add(T_a)
% 0.69/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom,
% 0.69/0.78 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
% 0.69/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_comm__monoid__add_Omult__assoc_0,axiom,
% 0.69/0.78 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
% 0.69/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_add__cancel__21_1,axiom,
% 0.69/0.78 ( ~ class_OrderedGroup_Oab__group__add(T_a)
% 0.69/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z)) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_class__semiring_Oadd__a_0,axiom,
% 0.69/0.78 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.69/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y)),V_z) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_double__eq__0__iff_1,axiom,
% 0.69/0.78 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
% 0.69/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(T_a)) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_Var_I3_J_0,axiom,
% 0.69/0.78 hBOOL(hAPP(c_InductTermi_OIT,v_ua______)) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_Cons__step1__Cons_2,axiom,
% 0.69/0.78 ( V_x = V_y
% 0.69/0.78 | V_xs = V_ys
% 0.69/0.78 | ~ c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(cls_Cons__step1__Cons_4,axiom,
% 0.69/0.79 ( ~ hBOOL(hAPP(hAPP(V_r,V_y),V_xa))
% 0.69/0.79 | c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_x,T_a),c_List_Olist_OCons(V_xa,V_x,T_a),T_a) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_listsp_ONil_0,axiom,
% 0.69/0.79 c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_accp__downwards_0,axiom,
% 0.69/0.79 ( c_Wellfounded_Oaccp(V_r,V_b,T_a)
% 0.69/0.79 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_a))
% 0.69/0.79 | ~ c_Wellfounded_Oaccp(V_r,V_a,T_a) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_accp__downwards__aux_0,axiom,
% 0.69/0.79 ( c_Wellfounded_Oaccp(V_r,V_b,T_a)
% 0.69/0.79 | ~ c_Wellfounded_Oaccp(V_r,V_a,T_a)
% 0.69/0.79 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_a)) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_IT__implies__termi_0,axiom,
% 0.69/0.79 ( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB)
% 0.69/0.79 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_termi__implies__IT_0,axiom,
% 0.69/0.79 ( hBOOL(hAPP(c_InductTermi_OIT,V_r))
% 0.69/0.79 | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_r,tc_Lambda_OdB) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom,
% 0.69/0.79 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.69/0.79 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_comm__monoid__add_Omult__commute_0,axiom,
% 0.69/0.79 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
% 0.69/0.79 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_a) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_class__semiring_Oadd__c_0,axiom,
% 0.69/0.79 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.69/0.79 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_x) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_foldl__assoc_0,axiom,
% 0.69/0.79 ( ~ class_OrderedGroup_Osemigroup__add(T_a)
% 0.69/0.79 | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y),V_zs,T_a,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_y,V_zs,T_a,T_a)) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_of__nat__eq__iff_0,axiom,
% 0.69/0.79 ( ~ class_Nat_Osemiring__char__0(T_a)
% 0.69/0.79 | c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a) != c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)
% 0.69/0.79 | V_m = V_n ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_class__ringb_Oadd__r0__iff_0,axiom,
% 0.69/0.79 ( ~ class_Ring__and__Field_Oidom(T_a)
% 0.69/0.79 | ~ class_Int_Onumber__ring(T_a)
% 0.69/0.79 | V_x != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_a)
% 0.69/0.79 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_double__eq__0__iff_0,axiom,
% 0.69/0.79 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
% 0.69/0.79 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a) != c_HOL_Ozero__class_Ozero(T_a)
% 0.69/0.79 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_foldr__conv__foldl_0,axiom,
% 0.69/0.79 ( ~ class_OrderedGroup_Oab__semigroup__add(T_a)
% 0.69/0.79 | c_List_Ofoldr(c_HOL_Oplus__class_Oplus(T_a),V_xs,V_a,T_a,T_a) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_a,V_xs,T_a,T_a) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_not__Nil__step1_0,axiom,
% 0.69/0.79 ~ c_ListOrder_Ostep1(V_r,c_List_Olist_ONil(T_a),V_xs,T_a) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_not__step1__Nil_0,axiom,
% 0.69/0.79 ~ c_ListOrder_Ostep1(V_r,V_xs,c_List_Olist_ONil(T_a),T_a) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom,
% 0.69/0.79 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
% 0.69/0.79 | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.69/0.79 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_double__add__less__zero__iff__single__less__zero_0,axiom,
% 0.69/0.79 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
% 0.69/0.79 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.69/0.79 | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_even__less__0__iff_0,axiom,
% 0.69/0.79 ( ~ class_Ring__and__Field_Oordered__idom(T_a)
% 0.69/0.79 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.69/0.79 | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_even__less__0__iff_1,axiom,
% 0.69/0.79 ( ~ class_Ring__and__Field_Oordered__idom(T_a)
% 0.69/0.79 | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.69/0.79 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_foldl__absorb0_0,axiom,
% 0.69/0.79 ( ~ class_OrderedGroup_Omonoid__add(T_a)
% 0.69/0.79 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a),V_zs,T_a,T_a)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_x,V_zs,T_a,T_a) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_foldl__Nil_0,axiom,
% 0.69/0.79 c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_App__eq__foldl__conv_5,axiom,
% 0.69/0.79 ( V_r != c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s),V_xa,tc_Lambda_OdB,tc_Lambda_OdB)
% 0.69/0.79 | hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s),c_List_Oappend(V_xa,c_List_Olist_OCons(V_s,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_conversep__eq_0,axiom,
% 0.69/0.79 c_Predicate_Oconversep(c_fequal(T_a),T_a,T_a) = c_fequal(T_a) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_add__pos__pos_0,axiom,
% 0.69/0.79 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
% 0.69/0.79 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),T_a)
% 0.69/0.79 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
% 0.69/0.79 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_Cons__step1__Cons_3,axiom,
% 0.69/0.79 ( c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a)
% 0.69/0.79 | V_xs = V_ys
% 0.69/0.79 | ~ c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_add__strict__mono_0,axiom,
% 0.69/0.79 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
% 0.69/0.79 | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d),T_a)
% 0.69/0.79 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a)
% 0.69/0.79 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_list_Osimps_I2_J_0,axiom,
% 0.69/0.79 c_List_Olist_ONil(T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_of__nat__less__iff_1,axiom,
% 0.69/0.79 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.69/0.79 | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)
% 0.69/0.79 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_of__nat__less__iff_0,axiom,
% 0.69/0.79 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.69/0.79 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.69/0.79 | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_App__eq__foldl__conv_0,axiom,
% 0.69/0.79 ( hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
% 0.69/0.79 | hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) = V_t ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_pos__add__strict_0,axiom,
% 0.69/0.79 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.69/0.79 | c_HOL_Oord__class_Oless(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a)
% 0.69/0.79 | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a)
% 0.69/0.79 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_foldr_Osimps_I2_J_0,axiom,
% 0.69/0.79 c_List_Ofoldr(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),V_a,T_b,T_a) = hAPP(hAPP(V_f,V_x),c_List_Ofoldr(V_f,V_xs,V_a,T_b,T_a)) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_conversep__conversep_0,axiom,
% 0.69/0.79 c_Predicate_Oconversep(c_Predicate_Oconversep(V_r,T_a,T_b),T_b,T_a) = V_r ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_add__strict__right__mono_0,axiom,
% 0.69/0.79 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
% 0.69/0.79 | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a)
% 0.69/0.79 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_add__less__cancel__right_1,axiom,
% 0.69/0.79 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
% 0.69/0.79 | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a)
% 0.69/0.79 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_add__less__cancel__right_0,axiom,
% 0.69/0.79 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
% 0.69/0.79 | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
% 0.69/0.79 | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_add__strict__left__mono_0,axiom,
% 0.69/0.79 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
% 0.69/0.79 | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a)
% 0.69/0.79 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_add__less__cancel__left_1,axiom,
% 0.69/0.79 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
% 0.69/0.79 | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a)
% 0.69/0.79 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_add__less__cancel__left_0,axiom,
% 0.69/0.79 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
% 0.69/0.79 | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
% 0.69/0.79 | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_list_Oinject_0,axiom,
% 0.69/0.79 ( c_List_Olist_OCons(V_a,V_list,T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a)
% 0.69/0.79 | V_a = V_a_H ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_list_Oinject_1,axiom,
% 0.69/0.79 ( c_List_Olist_OCons(V_a,V_list,T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a)
% 0.69/0.79 | V_list = V_list_H ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_Cons__step1__Cons_1,axiom,
% 0.69/0.79 ( c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a)
% 0.69/0.79 | hBOOL(hAPP(hAPP(V_r,V_y),V_x))
% 0.69/0.79 | ~ c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_Cons__step1__Cons_5,axiom,
% 0.69/0.79 ( c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_x,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a)
% 0.69/0.79 | ~ c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_app__last_0,axiom,
% 0.69/0.79 hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_u) = c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_List_Oappend(V_ts,c_List_Olist_OCons(V_u,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_App__eq__foldl__conv_4,axiom,
% 0.69/0.79 hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_App__eq__foldl__conv_3,axiom,
% 0.69/0.79 ( c_List_Oappend(V_x,c_List_Olist_OCons(V_s,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) = c_List_Olist_ONil(tc_Lambda_OdB)
% 0.69/0.79 | hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_x,tc_Lambda_OdB,tc_Lambda_OdB)),V_s) = c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_List_Oappend(V_x,c_List_Olist_OCons(V_s,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_accp_Ocases_0,axiom,
% 0.69/0.79 ( c_Wellfounded_Oaccp(V_r,V_y,T_a)
% 0.69/0.79 | ~ hBOOL(hAPP(hAPP(V_r,V_y),V_a))
% 0.69/0.79 | ~ c_Wellfounded_Oaccp(V_r,V_a,T_a) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_accp__downward_0,axiom,
% 0.69/0.79 ( c_Wellfounded_Oaccp(V_r,V_a,T_a)
% 0.69/0.79 | ~ hBOOL(hAPP(hAPP(V_r,V_a),V_b))
% 0.69/0.79 | ~ c_Wellfounded_Oaccp(V_r,V_b,T_a) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_order__less__asym_H_0,axiom,
% 0.69/0.79 ( ~ class_Orderings_Opreorder(T_a)
% 0.69/0.79 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
% 0.69/0.79 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_order__less__asym_0,axiom,
% 0.69/0.79 ( ~ class_Orderings_Opreorder(T_a)
% 0.69/0.79 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
% 0.69/0.79 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_not__less__iff__gr__or__eq_1,axiom,
% 0.69/0.79 ( ~ class_Orderings_Olinorder(T_a)
% 0.69/0.79 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
% 0.69/0.79 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_rtranclp_Ortrancl__into__rtrancl_0,axiom,
% 0.69/0.79 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_c))
% 0.69/0.79 | ~ hBOOL(hAPP(hAPP(V_r,V_b),V_c))
% 0.69/0.79 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_b)) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_converse__rtranclp__into__rtranclp_0,axiom,
% 0.69/0.79 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_c))
% 0.69/0.79 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_c))
% 0.69/0.79 | ~ hBOOL(hAPP(hAPP(V_r,V_a),V_b)) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_xt1_I9_J_0,axiom,
% 0.69/0.79 ( ~ class_Orderings_Oorder(T_a)
% 0.69/0.79 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
% 0.69/0.79 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_dB_Osimps_I7_J_0,axiom,
% 0.69/0.79 c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_dB_Osimps_I8_J_0,axiom,
% 0.69/0.79 hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != c_Lambda_OdB_OAbs(V_dB_H) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_var__app__typesE_1,axiom,
% 0.69/0.79 ( c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xvar__app__typesE__1__1(V_T,V_e,V_i,V_ts))
% 0.69/0.79 | ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_dB_Osimps_I9_J_0,axiom,
% 0.69/0.79 c_Lambda_OdB_OAbs(V_dB_H) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_list__app__typeD_1,axiom,
% 0.69/0.79 ( c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts))
% 0.69/0.79 | ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_shift__gt_0,axiom,
% 0.69/0.79 ( hAPP(c_Type_Oshift(V_e,V_i,V_T,T_a),V_j) = hAPP(V_e,V_j)
% 0.69/0.79 | ~ c_HOL_Oord__class_Oless(V_j,V_i,tc_nat) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_neq0__conv_1,axiom,
% 0.69/0.79 ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_gr0I_0,axiom,
% 0.69/0.79 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
% 0.69/0.79 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_apps__preserves__beta2_0,axiom,
% 0.69/0.79 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)))
% 0.69/0.79 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)) ) ).
% 0.69/0.79
% 0.69/0.79 cnf(cls_of__nat__0__less__iff_0,axiom,
% 0.69/0.79 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.75/0.79 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
% 0.75/0.79 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_of__nat__0__less__iff_1,axiom,
% 0.75/0.79 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.75/0.79 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)
% 0.75/0.79 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_foldl__foldr1_0,axiom,
% 0.75/0.79 ( ~ class_OrderedGroup_Omonoid__add(T_a)
% 0.75/0.79 | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a),V_xs,T_a,T_a) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(T_a),V_xs,c_HOL_Ozero__class_Ozero(T_a),T_a,T_a) ) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_apps__eq__Abs__conv_0,axiom,
% 0.75/0.79 ( c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(V_r)
% 0.75/0.79 | V_s = c_Lambda_OdB_OAbs(V_r) ) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_Abs__apps__eq__Abs__apps__conv_0,axiom,
% 0.75/0.79 ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_rs,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)
% 0.75/0.79 | V_r = V_s ) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_Abs__apps__eq__Abs__apps__conv_1,axiom,
% 0.75/0.79 ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_rs,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)
% 0.75/0.79 | V_rs = V_ss ) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_linorder__antisym__conv3_0,axiom,
% 0.75/0.79 ( ~ class_Orderings_Olinorder(T_a)
% 0.75/0.79 | V_x = V_y
% 0.75/0.79 | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
% 0.75/0.79 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_linorder__less__linear_0,axiom,
% 0.75/0.79 ( ~ class_Orderings_Olinorder(T_a)
% 0.75/0.79 | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
% 0.75/0.79 | V_x = V_y
% 0.75/0.79 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_linorder__neqE_0,axiom,
% 0.75/0.79 ( ~ class_Orderings_Olinorder(T_a)
% 0.75/0.79 | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
% 0.75/0.79 | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
% 0.75/0.79 | V_x = V_y ) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_linorder__neqE__nat_0,axiom,
% 0.75/0.79 ( c_HOL_Oord__class_Oless(V_y,V_x,tc_nat)
% 0.75/0.79 | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)
% 0.75/0.79 | V_x = V_y ) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_nat__less__cases_0,axiom,
% 0.75/0.79 ( hBOOL(hAPP(hAPP(V_P,V_n),V_m))
% 0.75/0.79 | c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
% 0.75/0.79 | V_m = V_n
% 0.75/0.79 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_nat__neq__iff_0,axiom,
% 0.75/0.79 ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
% 0.75/0.79 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.75/0.79 | V_m = V_n ) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_not__less__iff__gr__or__eq_0,axiom,
% 0.75/0.79 ( ~ class_Orderings_Olinorder(T_a)
% 0.75/0.79 | V_x = V_y
% 0.75/0.79 | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
% 0.75/0.79 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_linorder__neqE__ordered__idom_0,axiom,
% 0.75/0.79 ( ~ class_Ring__and__Field_Oordered__idom(T_a)
% 0.75/0.79 | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
% 0.75/0.79 | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
% 0.75/0.79 | V_x = V_y ) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_apps__preserves__betas_0,axiom,
% 0.75/0.79 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)))
% 0.75/0.79 | ~ c_ListOrder_Ostep1(c_Lambda_Obeta,V_rs,V_ss,tc_Lambda_OdB) ) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_order__less__irrefl_0,axiom,
% 0.75/0.79 ( ~ class_Orderings_Opreorder(T_a)
% 0.75/0.79 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_linorder__neq__iff_1,axiom,
% 0.75/0.79 ( ~ class_Orderings_Olinorder(T_a)
% 0.75/0.79 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_order__less__le_1,axiom,
% 0.75/0.79 ( ~ class_Orderings_Oorder(T_a)
% 0.75/0.79 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_less__not__refl_0,axiom,
% 0.75/0.79 ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_nat__less__le_1,axiom,
% 0.75/0.79 ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_Abs__eq__apps__conv_1,axiom,
% 0.75/0.79 ( c_Lambda_OdB_OAbs(V_r) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)
% 0.75/0.79 | V_ss = c_List_Olist_ONil(tc_Lambda_OdB) ) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_dB_Osimps_I3_J_0,axiom,
% 0.75/0.79 ( c_Lambda_OdB_OAbs(V_dB) != c_Lambda_OdB_OAbs(V_dB_H)
% 0.75/0.79 | V_dB = V_dB_H ) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_Var__apps__neq__Abs__apps_0,axiom,
% 0.75/0.79 c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ts,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_ss,tc_Lambda_OdB,tc_Lambda_OdB) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_Beta_0,axiom,
% 0.75/0.79 ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r)),V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)))
% 0.75/0.79 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_s))
% 0.75/0.79 | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(V_r,V_s,c_HOL_Ozero__class_Ozero(tc_nat)),V_ss,tc_Lambda_OdB,tc_Lambda_OdB))) ) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_r__into__rtranclp_0,axiom,
% 0.75/0.79 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_y))
% 0.75/0.79 | ~ hBOOL(hAPP(hAPP(V_r,V_x),V_y)) ) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_dB_Osimps_I6_J_0,axiom,
% 0.75/0.79 c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_rtranclp__trans_0,axiom,
% 0.75/0.79 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_z))
% 0.75/0.79 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_y),V_z))
% 0.75/0.79 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_y)) ) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_Nitpick_Ortranclp__def_1,axiom,
% 0.75/0.79 hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_x)) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_rtranclp_Ortrancl__refl_0,axiom,
% 0.75/0.79 hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_a)) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_Var_I4_J_0,axiom,
% 0.75/0.79 c_Type_Otyping(v_ea______,v_ua______,v_T____) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_rtrancl__beta__Abs_0,axiom,
% 0.75/0.79 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(V_s)),c_Lambda_OdB_OAbs(V_s_H)))
% 0.75/0.79 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H)) ) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_double__induction__lemma_0,axiom,
% 0.75/0.79 ( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(V_r,V_s,c_HOL_Ozero__class_Ozero(tc_nat)),V_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
% 0.75/0.79 | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_s,tc_Lambda_OdB)
% 0.75/0.79 | c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r)),V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_order__less__trans_0,axiom,
% 0.75/0.79 ( ~ class_Orderings_Opreorder(T_a)
% 0.75/0.79 | c_HOL_Oord__class_Oless(V_x,V_z,T_a)
% 0.75/0.79 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
% 0.75/0.79 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_xt1_I10_J_0,axiom,
% 0.75/0.79 ( ~ class_Orderings_Oorder(T_a)
% 0.75/0.79 | c_HOL_Oord__class_Oless(V_z,V_x,T_a)
% 0.75/0.79 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a)
% 0.75/0.79 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_Var__eq__apps__conv_2,axiom,
% 0.75/0.79 c_Lambda_OdB_OVar(V_m) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_gr__implies__not0_0,axiom,
% 0.75/0.79 ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_not__less0_0,axiom,
% 0.75/0.79 ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_list__app__typeE_1,axiom,
% 0.75/0.79 ( c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeE__1__1(V_T,V_e,V_t,V_ts))
% 0.75/0.79 | ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T) ) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_Abs__eq__apps__conv_2,axiom,
% 0.75/0.79 c_Lambda_OdB_OAbs(V_r) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ).
% 0.75/0.79
% 0.75/0.79 cnf(cls_Abs__eq__apps__conv_0,axiom,
% 0.75/0.80 ( c_Lambda_OdB_OAbs(V_r) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)
% 0.75/0.80 | c_Lambda_OdB_OAbs(V_r) = V_s ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_foldl__foldr1__lemma_0,axiom,
% 0.75/0.80 ( ~ class_OrderedGroup_Omonoid__add(T_a)
% 0.75/0.80 | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_a,V_xs,T_a,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(T_a),V_xs,c_HOL_Ozero__class_Ozero(T_a),T_a,T_a)) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_apps__eq__Abs__conv_1,axiom,
% 0.75/0.80 ( c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(V_r)
% 0.75/0.80 | V_ss = c_List_Olist_ONil(tc_Lambda_OdB) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_apps__eq__tail__conv_0,axiom,
% 0.75/0.80 ( c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ts,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)
% 0.75/0.80 | V_r = V_s ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_var__app__types_1,axiom,
% 0.75/0.80 ( c_Type_Otypings(V_e,V_us,c_Type_Osko__Type__Xvar__app__types__1__1(V_T,V_U,V_e,V_us))
% 0.75/0.80 | ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_U)
% 0.75/0.80 | ~ c_Type_Otypings(V_e,V_ts,V_Ts)
% 0.75/0.80 | ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_us,tc_Lambda_OdB,tc_Lambda_OdB),V_T) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_Lambda_0,axiom,
% 0.75/0.80 ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(V_r)))
% 0.75/0.80 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_r)) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_Cons_0,axiom,
% 0.75/0.80 v_rs____ = c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_apps__eq__Abs__conv_2,axiom,
% 0.75/0.80 c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(V_r) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_Var__eq__apps__conv_1,axiom,
% 0.75/0.80 ( c_Lambda_OdB_OVar(V_m) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)
% 0.75/0.80 | V_ss = c_List_Olist_ONil(tc_Lambda_OdB) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_head__Var__reduction_0,axiom,
% 0.75/0.80 ( c_ListOrder_Ostep1(c_Lambda_Obeta,V_rs,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(V_n,V_rs,V_v),tc_Lambda_OdB)
% 0.75/0.80 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_v)) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_Abs__App__neq__Var__apps_0,axiom,
% 0.75/0.80 hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_rtranclp__idemp_0,axiom,
% 0.75/0.80 c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(V_r,T_a),T_a) = c_Transitive__Closure_Ortranclp(V_r,T_a) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_abs_0,axiom,
% 0.75/0.80 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(V_s)),c_Lambda_OdB_OAbs(V_t)))
% 0.75/0.80 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t)) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_dB_Osimps_I5_J_0,axiom,
% 0.75/0.80 hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) != c_Lambda_OdB_OVar(V_nat) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_typing__elims_I2_J_0,axiom,
% 0.75/0.80 ( c_Type_Otyping(V_e,V_t,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u)),V_T))
% 0.75/0.80 | ~ c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_app__Var__IT_0,axiom,
% 0.75/0.80 ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),c_Lambda_OdB_OVar(V_i))))
% 0.75/0.80 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_list__app__typeD_0,axiom,
% 0.75/0.80 ( c_Type_Otyping(V_e,V_t,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts),V_T,tc_Type_Otype,tc_Type_Otype))
% 0.75/0.80 | ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_lift__preserves__beta_0,axiom,
% 0.75/0.80 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(V_r,V_i)),c_Lambda_Olift(V_s,V_i)))
% 0.75/0.80 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_lift_Osimps_I1_J_0,axiom,
% 0.75/0.80 ( c_Lambda_Olift(c_Lambda_OdB_OVar(V_i),V_k) = c_Lambda_OdB_OVar(V_i)
% 0.75/0.80 | ~ c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_subject__reduction_H_0,axiom,
% 0.75/0.80 ( c_Type_Otyping(V_e,V_t_H,V_T)
% 0.75/0.80 | ~ c_Type_Otyping(V_e,V_t,V_T)
% 0.75/0.80 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H)) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_appL_0,axiom,
% 0.75/0.80 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_u)),hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u)))
% 0.75/0.80 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t)) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_appR_0,axiom,
% 0.75/0.80 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,V_u),V_s)),hAPP(hAPP(c_Lambda_OdB_OApp,V_u),V_t)))
% 0.75/0.80 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t)) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_rtrancl__beta__App_0,axiom,
% 0.75/0.80 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),hAPP(hAPP(c_Lambda_OdB_OApp,V_s_H),V_t_H)))
% 0.75/0.80 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H))
% 0.75/0.80 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H)) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_rtrancl__beta__AppL_0,axiom,
% 0.75/0.80 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),hAPP(hAPP(c_Lambda_OdB_OApp,V_s_H),V_t)))
% 0.75/0.80 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H)) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_rtrancl__beta__AppR_0,axiom,
% 0.75/0.80 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t_H)))
% 0.75/0.80 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H)) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_T_0,axiom,
% 0.75/0.80 v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_subst__Var_1,axiom,
% 0.75/0.80 ( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)
% 0.75/0.80 | c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x),V_s,V_x) = V_s ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_typing__elims_I2_J_1,axiom,
% 0.75/0.80 ( c_Type_Otyping(V_e,V_u,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u))
% 0.75/0.80 | ~ c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_head__Var__reduction_1,axiom,
% 0.75/0.80 ( V_v = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(V_n,V_rs,V_v),tc_Lambda_OdB,tc_Lambda_OdB)
% 0.75/0.80 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_v)) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_list__app__typeI_0,axiom,
% 0.75/0.80 ( c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T)
% 0.75/0.80 | ~ c_Type_Otypings(V_e,V_ts,V_Ts)
% 0.75/0.80 | ~ c_Type_Otyping(V_e,V_t,c_List_Ofoldr(c_Type_Otype_OFun,V_Ts,V_T,tc_Type_Otype,tc_Type_Otype)) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_nT_0,axiom,
% 0.75/0.80 c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_var__app__typesE_0,axiom,
% 0.75/0.80 ( c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(V_T,V_e,V_i,V_ts),V_T,tc_Type_Otype,tc_Type_Otype))
% 0.75/0.80 | ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_subst__Var_2,axiom,
% 0.75/0.80 ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_i),V_s,V_k) = c_Lambda_OdB_OVar(V_i)
% 0.75/0.80 | V_i = V_k
% 0.75/0.80 | c_HOL_Oord__class_Oless(V_k,V_i,tc_nat) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_list__app__typeE_0,axiom,
% 0.75/0.80 ( c_Type_Otyping(V_e,V_t,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(V_T,V_e,V_t,V_ts),V_T,tc_Type_Otype,tc_Type_Otype))
% 0.75/0.80 | ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_argsT_0,axiom,
% 0.75/0.80 c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_headT_0,axiom,
% 0.75/0.80 c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_varT_0,axiom,
% 0.75/0.80 c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_subst__preserves__beta2_0,axiom,
% 0.75/0.80 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(V_t,V_r,V_i)),c_Lambda_Osubst(V_t,V_s,V_i)))
% 0.75/0.80 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_Var_I2_J_0,axiom,
% 0.75/0.80 c_Type_Otyping(c_Type_Oshift(v_ea______,v_ia______,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_Ha______) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_lift_Osimps_I2_J_0,axiom,
% 0.75/0.80 c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(V_s,V_k)),c_Lambda_Olift(V_t,V_k)) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_subst__preserves__beta_H_0,axiom,
% 0.75/0.80 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(V_r,V_t,V_i)),c_Lambda_Osubst(V_s,V_t,V_i)))
% 0.75/0.80 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_subst__preserves__beta2_H_0,axiom,
% 0.75/0.80 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(V_t,V_r,V_i)),c_Lambda_Osubst(V_t,V_s,V_i)))
% 0.75/0.80 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_Var__IT_0,axiom,
% 0.75/0.80 hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n))) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_Abs_0,axiom,
% 0.75/0.80 ( c_Type_Otyping(V_env,c_Lambda_OdB_OAbs(V_t),hAPP(hAPP(c_Type_Otype_OFun,V_T),V_U))
% 0.75/0.80 | ~ c_Type_Otyping(c_Type_Oshift(V_env,c_HOL_Ozero__class_Ozero(tc_nat),V_T,tc_Type_Otype),V_t,V_U) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_shift__eq_0,axiom,
% 0.75/0.80 hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_MI1_0,axiom,
% 0.75/0.80 ( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,V_T1),V_T2)
% 0.75/0.80 | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(V_t,V_u,V_i)))
% 0.75/0.80 | ~ c_Type_Otyping(V_e,V_u,V_T1)
% 0.75/0.80 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
% 0.75/0.80 | ~ c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_T1,tc_Type_Otype),V_t,V_Ta)
% 0.75/0.80 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_MI2_0,axiom,
% 0.75/0.80 ( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,V_T1),V_T2)
% 0.75/0.80 | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(V_t,V_u,V_i)))
% 0.75/0.80 | ~ c_Type_Otyping(V_e,V_u,V_T2)
% 0.75/0.80 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
% 0.75/0.80 | ~ c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_T2,tc_Type_Otype),V_t,V_Ta)
% 0.75/0.80 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_lift__IT_0,axiom,
% 0.75/0.80 ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(V_t,V_i)))
% 0.75/0.80 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_dB_Osimps_I4_J_0,axiom,
% 0.75/0.80 c_Lambda_OdB_OVar(V_nat) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_Var__eq__apps__conv_0,axiom,
% 0.75/0.80 ( c_Lambda_OdB_OVar(V_m) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)
% 0.75/0.80 | c_Lambda_OdB_OVar(V_m) = V_s ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_apps__preserves__beta_0,axiom,
% 0.75/0.80 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)))
% 0.75/0.80 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_beta_0,axiom,
% 0.75/0.80 hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t)),c_Lambda_Osubst(V_s,V_t,c_HOL_Ozero__class_Ozero(tc_nat)))) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_lift__preserves__beta_H_0,axiom,
% 0.75/0.80 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(V_r,V_i)),c_Lambda_Olift(V_s,V_i)))
% 0.75/0.80 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_var__app__type__eq_0,axiom,
% 0.75/0.80 ( V_T = V_U
% 0.75/0.80 | ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_U)
% 0.75/0.80 | ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_dB_Osimps_I2_J_1,axiom,
% 0.75/0.80 ( hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H)
% 0.75/0.80 | V_dB2 = V_dB2_H ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_dB_Osimps_I2_J_0,axiom,
% 0.75/0.80 ( hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H)
% 0.75/0.80 | V_dB1 = V_dB1_H ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_IT_OVar_0,axiom,
% 0.75/0.80 ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)))
% 0.75/0.80 | ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_App_0,axiom,
% 0.75/0.80 ( c_Type_Otyping(V_env,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_U)
% 0.75/0.80 | ~ c_Type_Otyping(V_env,V_t,V_T)
% 0.75/0.80 | ~ c_Type_Otyping(V_env,V_s,hAPP(hAPP(c_Type_Otype_OFun,V_T),V_U)) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_beta__cases_I1_J_0,axiom,
% 0.75/0.80 ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_var__app__types_0,axiom,
% 0.75/0.80 ( V_U = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(V_T,V_U,V_e,V_us),V_T,tc_Type_Otype,tc_Type_Otype)
% 0.75/0.80 | ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_U)
% 0.75/0.80 | ~ c_Type_Otypings(V_e,V_ts,V_Ts)
% 0.75/0.80 | ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_us,tc_Lambda_OdB,tc_Lambda_OdB),V_T) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_subst__lt_0,axiom,
% 0.75/0.80 ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_j),V_u,V_i) = c_Lambda_OdB_OVar(V_j)
% 0.75/0.80 | ~ c_HOL_Oord__class_Oless(V_j,V_i,tc_nat) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_subst__Var__IT_0,axiom,
% 0.75/0.80 ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j)))
% 0.75/0.80 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_r)) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_type_Osimps_I2_J_1,axiom,
% 0.75/0.80 ( hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2) != hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H)
% 0.75/0.80 | V_type2 = V_type2_H ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_type_Osimps_I2_J_0,axiom,
% 0.75/0.80 ( hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2) != hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H)
% 0.75/0.80 | V_type1 = V_type1_H ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_Var__apps__eq__Var__apps__conv_1,axiom,
% 0.75/0.80 ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),V_rs,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)
% 0.75/0.80 | V_rs = V_ss ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_Var__apps__eq__Var__apps__conv_0,axiom,
% 0.75/0.80 ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),V_rs,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)
% 0.75/0.80 | V_m = V_n ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_dB_Osimps_I1_J_0,axiom,
% 0.75/0.80 ( c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OVar(V_nat_H)
% 0.75/0.80 | V_nat = V_nat_H ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_lift__type_0,axiom,
% 0.75/0.80 ( c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_U,tc_Type_Otype),c_Lambda_Olift(V_t,V_i),V_T)
% 0.75/0.80 | ~ c_Type_Otyping(V_e,V_t,V_T) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_uT_0,axiom,
% 0.75/0.80 c_Type_Otyping(v_e____,v_u____,v_T____) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_subst__App_0,axiom,
% 0.75/0.80 c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_s,V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(V_t,V_s,V_k)),c_Lambda_Osubst(V_u,V_s,V_k)) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_subject__reduction_0,axiom,
% 0.75/0.80 ( c_Type_Otyping(V_e,V_t_H,V_T)
% 0.75/0.80 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H))
% 0.75/0.80 | ~ c_Type_Otyping(V_e,V_t,V_T) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_subst__eq_0,axiom,
% 0.75/0.80 c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k) = V_u ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_uT_H_0,axiom,
% 0.75/0.80 c_Type_Otyping(v_e____,v_u____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_argT_0,axiom,
% 0.75/0.80 c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_True_0,axiom,
% 0.75/0.80 v_n____ = v_i____ ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_typing__elims_I1_J_0,axiom,
% 0.75/0.80 ( hAPP(V_e,V_i) = V_T
% 0.75/0.80 | ~ c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_subst__preserves__beta_0,axiom,
% 0.75/0.80 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(V_r,V_t,V_i)),c_Lambda_Osubst(V_s,V_t,V_i)))
% 0.75/0.80 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_typing_OVar_0,axiom,
% 0.75/0.80 c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_uIT_0,axiom,
% 0.75/0.80 hBOOL(hAPP(c_InductTermi_OIT,v_u____)) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_subst__lift_0,axiom,
% 0.75/0.80 c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_subst__lemma_0,axiom,
% 0.75/0.80 ( ~ c_Type_Otyping(V_e_H,V_u,V_U)
% 0.75/0.80 | ~ c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)
% 0.75/0.80 | c_Type_Otyping(V_e_H,c_Lambda_Osubst(V_t,V_u,V_i),V_T) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_CHAINED_0,axiom,
% 0.75/0.80 c_Type_Otyping(v_e____,v_u____,v_T____) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_CHAINED_0_01,axiom,
% 0.75/0.80 c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_conjecture_0,negated_conjecture,
% 0.75/0.80 ~ c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____) ).
% 0.75/0.80
% 0.75/0.80 cnf(clsarity_fun__Orderings_Opreorder,axiom,
% 0.75/0.80 ( class_Orderings_Opreorder(tc_fun(T_2,T_1))
% 0.75/0.80 | ~ class_Orderings_Opreorder(T_1) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(clsarity_fun__Orderings_Oorder,axiom,
% 0.75/0.80 ( class_Orderings_Oorder(tc_fun(T_2,T_1))
% 0.75/0.80 | ~ class_Orderings_Oorder(T_1) ) ).
% 0.75/0.80
% 0.75/0.80 cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
% 0.75/0.80 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ).
% 0.75/0.80
% 0.75/0.80 cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
% 0.75/0.80 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ).
% 0.75/0.80
% 0.75/0.80 cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom,
% 0.75/0.80 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ).
% 0.75/0.80
% 0.75/0.80 cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
% 0.75/0.80 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ).
% 0.75/0.80
% 0.75/0.80 cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom,
% 0.75/0.80 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ).
% 0.75/0.80
% 0.75/0.80 cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom,
% 0.75/0.80 class_Ring__and__Field_Oordered__semidom(tc_nat) ).
% 0.75/0.80
% 0.75/0.80 cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
% 0.75/0.80 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ).
% 0.75/0.80
% 0.75/0.80 cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom,
% 0.75/0.80 class_OrderedGroup_Oab__semigroup__add(tc_nat) ).
% 0.75/0.80
% 0.75/0.80 cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom,
% 0.75/0.80 class_OrderedGroup_Ocomm__monoid__add(tc_nat) ).
% 0.75/0.80
% 0.75/0.80 cnf(clsarity_nat__OrderedGroup_Osemigroup__add,axiom,
% 0.75/0.80 class_OrderedGroup_Osemigroup__add(tc_nat) ).
% 0.75/0.80
% 0.75/0.80 cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom,
% 0.75/0.80 class_Ring__and__Field_Osemiring__1(tc_nat) ).
% 0.75/0.80
% 0.75/0.80 cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom,
% 0.75/0.80 class_OrderedGroup_Omonoid__add(tc_nat) ).
% 0.75/0.80
% 0.75/0.80 cnf(clsarity_nat__Nat_Osemiring__char__0,axiom,
% 0.75/0.80 class_Nat_Osemiring__char__0(tc_nat) ).
% 0.75/0.80
% 0.75/0.80 cnf(clsarity_nat__Orderings_Opreorder,axiom,
% 0.75/0.80 class_Orderings_Opreorder(tc_nat) ).
% 0.75/0.80
% 0.75/0.80 cnf(clsarity_nat__Orderings_Olinorder,axiom,
% 0.75/0.80 class_Orderings_Olinorder(tc_nat) ).
% 0.75/0.80
% 0.75/0.80 cnf(clsarity_nat__Orderings_Oorder,axiom,
% 0.75/0.80 class_Orderings_Oorder(tc_nat) ).
% 0.75/0.80
% 0.75/0.80 cnf(clsarity_bool__Orderings_Opreorder,axiom,
% 0.75/0.80 class_Orderings_Opreorder(tc_bool) ).
% 0.75/0.80
% 0.75/0.80 cnf(clsarity_bool__Orderings_Oorder,axiom,
% 0.75/0.80 class_Orderings_Oorder(tc_bool) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
% 0.75/0.80 hBOOL(hAPP(hAPP(c_fequal(T_a),V_x),V_x)) ).
% 0.75/0.80
% 0.75/0.80 cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom,
% 0.75/0.80 ( V_X = V_Y
% 0.75/0.80 | ~ hBOOL(hAPP(hAPP(c_fequal(T_a),V_X),V_Y)) ) ).
% 0.75/0.80
% 0.75/0.80 %------------------------------------------------------------------------------
% 0.75/0.80 %-------------------------------------------
% 0.75/0.80 % Proof found
% 0.75/0.80 % SZS status Theorem for theBenchmark
% 0.75/0.80 % SZS output start Proof
% 0.75/0.80 %ClaNum:407(EqnAxiom:113)
% 0.75/0.80 %VarNum:1694(SingletonVarNum:741)
% 0.75/0.80 %MaxLitNum:6
% 0.75/0.80 %MaxfuncDepth:5
% 0.75/0.80 %SharedTerms:74
% 0.75/0.80 %goalClause: 208
% 0.75/0.80 %singleGoalClaCount:1
% 0.75/0.80 [114]E(a1,a2)
% 0.75/0.80 [115]P1(a3)
% 0.75/0.80 [116]P2(a3)
% 0.75/0.80 [117]P3(a3)
% 0.75/0.80 [118]P24(a3)
% 0.75/0.80 [119]P4(a3)
% 0.75/0.80 [120]P5(a3)
% 0.75/0.80 [121]P17(a3)
% 0.75/0.80 [122]P27(a3)
% 0.75/0.80 [123]P6(a3)
% 0.75/0.80 [124]P20(a3)
% 0.75/0.80 [125]P7(a3)
% 0.75/0.80 [126]P18(a3)
% 0.75/0.80 [127]P19(a3)
% 0.75/0.80 [128]P21(a3)
% 0.75/0.80 [129]P21(a4)
% 0.75/0.80 [130]P22(a3)
% 0.75/0.80 [131]P23(a3)
% 0.75/0.80 [132]P23(a4)
% 0.75/0.80 [137]P8(a43,a46,a37)
% 0.75/0.80 [139]P8(a44,a47,a37)
% 0.75/0.80 [133]P28(f8(a5,a46))
% 0.75/0.80 [134]P28(f8(a5,a47))
% 0.75/0.80 [136]E(f13(a36,a42,a33),a48)
% 0.75/0.80 [171]P8(f25(a44,a2,a37,a34),a36,a38)
% 0.75/0.80 [172]P12(f25(a44,a2,a37,a34),a42,a41)
% 0.75/0.80 [208]~P8(a44,f15(a36,a47,a2),a38)
% 0.75/0.80 [180]E(f8(f8(a26,a38),f19(a26,a41,a39,a34,a34)),a37)
% 0.75/0.80 [182]P8(f25(a43,a45,a37,a34),f18(a10,f9(a1),a48,a33,a33),a40)
% 0.75/0.80 [183]P8(f25(a44,a2,a37,a34),f18(a10,f9(a1),a48,a33,a33),a39)
% 0.75/0.80 [186]P8(a44,a47,f8(f8(a26,a38),f19(a26,a41,a39,a34,a34)))
% 0.75/0.80 [189]P8(f25(a44,a2,a37,a34),f9(a1),f8(f8(a26,a38),f19(a26,a41,a39,a34,a34)))
% 0.75/0.80 [184]P8(f25(a44,a2,a37,a34),f8(f8(a10,f9(a1)),a36),f19(a26,a41,a39,a34,a34))
% 0.75/0.80 [198]~P10(x1981,x1981,a3)
% 0.75/0.80 [202]~P10(x2021,f6(a3),a3)
% 0.75/0.80 [135]P28(f8(a5,f9(x1351)))
% 0.75/0.80 [148]E(f22(f24(x1481),x1481,x1481),f24(x1481))
% 0.75/0.80 [141]P9(x1411,f21(x1412),x1412)
% 0.75/0.80 [152]P8(x1521,f9(x1522),f8(x1521,x1522))
% 0.75/0.80 [192]~E(f9(x1921),f12(x1922))
% 0.75/0.80 [140]E(f20(f20(x1401,x1402),x1402),f20(x1401,x1402))
% 0.75/0.80 [145]E(f14(x1451,f21(x1452),x1452),x1451)
% 0.75/0.80 [146]E(f14(f21(x1461),x1462,x1461),x1462)
% 0.75/0.80 [147]E(f15(f9(x1471),x1472,x1471),x1472)
% 0.75/0.80 [153]P28(f8(f8(f24(x1531),x1532),x1532))
% 0.75/0.80 [173]P28(f8(f8(a11,f8(f8(a10,f12(x1731)),x1732)),f15(x1731,x1732,f6(a3))))
% 0.75/0.80 [207]~P28(f8(f8(a11,f9(x2071)),x2072))
% 0.75/0.80 [200]~E(f13(x2001,x2002,x2003),x2002)
% 0.75/0.80 [205]~E(f13(x2051,x2052,x2053),f21(x2053))
% 0.75/0.80 [209]~P11(x2091,x2092,f21(x2093),x2093)
% 0.75/0.80 [210]~P11(x2101,f21(x2102),x2103,x2102)
% 0.75/0.80 [151]E(f15(f16(x1511,x1512),x1513,x1512),x1511)
% 0.75/0.80 [154]E(f22(f22(x1541,x1542,x1543),x1543,x1542),x1541)
% 0.75/0.80 [193]~E(f12(x1931),f8(f8(a10,x1932),x1933))
% 0.75/0.80 [194]~E(f9(x1941),f8(f8(a10,x1942),x1943))
% 0.75/0.80 [195]~E(f8(f8(a10,x1951),x1952),f12(x1953))
% 0.75/0.80 [196]~E(f8(f8(a10,x1961),x1962),f9(x1963))
% 0.75/0.80 [156]P28(f8(f8(f20(x1561,x1562),x1563),x1563))
% 0.75/0.80 [157]E(f8(f8(a10,f16(x1571,x1572)),f16(x1573,x1572)),f16(f8(f8(a10,x1571),x1573),x1572))
% 0.75/0.80 [190]E(f18(a10,x1901,f14(x1902,f13(x1903,f21(a33),a33),a33),a33,a33),f8(f8(a10,f18(a10,x1901,x1902,a33,a33)),x1903))
% 0.75/0.80 [165]E(f14(f14(x1651,x1652,x1653),x1654,x1653),f14(x1651,f14(x1652,x1654,x1653),x1653))
% 0.75/0.80 [167]E(f13(x1671,f14(x1672,x1673,x1674),x1674),f14(f13(x1671,x1672,x1674),x1673,x1674))
% 0.75/0.80 [169]E(f8(f25(x1691,x1692,x1693,x1694),x1692),x1693)
% 0.75/0.80 [174]E(f18(x1741,x1742,f21(x1743),x1744,x1743),x1742)
% 0.75/0.80 [175]E(f19(x1751,f21(x1752),x1753,x1752,x1754),x1753)
% 0.75/0.80 [212]~E(f18(a10,f9(x2121),x2122,a33,a33),f18(a10,f12(x2123),x2124,a33,a33))
% 0.75/0.80 [168]E(f8(f8(a10,f15(x1681,x1682,x1683)),f15(x1684,x1682,x1683)),f15(f8(f8(a10,x1681),x1684),x1682,x1683))
% 0.75/0.80 [211]~E(f8(f8(a10,f12(x2111)),x2112),f18(a10,f9(x2113),x2114,a33,a33))
% 0.75/0.80 [185]E(f19(x1851,f13(x1852,x1853,x1854),x1855,x1854,x1856),f8(f8(x1851,x1852),f19(x1851,x1853,x1855,x1854,x1856)))
% 0.75/0.80 [187]E(f18(x1871,f18(x1871,x1872,x1873,x1874,x1875),x1876,x1874,x1875),f18(x1871,x1872,f14(x1873,x1876,x1875),x1874,x1875))
% 0.75/0.80 [188]E(f19(x1881,x1882,f19(x1881,x1883,x1884,x1885,x1886),x1885,x1886),f19(x1881,f14(x1882,x1883,x1885),x1884,x1885,x1886))
% 0.75/0.80 [181]E(f18(x1811,x1812,f13(x1813,x1814,x1815),x1816,x1815),f18(x1811,f8(f8(x1811,x1812),x1813),x1814,x1816,x1815))
% 0.75/0.80 [219]E(x2191,f6(a3))+P10(f6(a3),x2191,a3)
% 0.75/0.80 [279]P14(f22(a11,a33,a33),x2791,a33)+~P28(f8(a5,x2791))
% 0.75/0.80 [288]~P14(f22(a11,a33,a33),x2881,a33)+P28(f8(a5,x2881))
% 0.75/0.80 [215]~P27(x2151)+E(f23(f6(a3),x2151),f6(x2151))
% 0.75/0.80 [228]~P16(x2281)+E(f8(f8(f7(x2281),f6(x2281)),f6(x2281)),f6(x2281))
% 0.75/0.80 [229]~P28(f8(a5,x2291))+P28(f8(a5,f12(x2291)))
% 0.75/0.80 [234]~P10(x2342,x2342,x2341)+~P21(x2341)
% 0.75/0.80 [235]~P10(x2352,x2352,x2351)+~P22(x2351)
% 0.75/0.80 [236]~P10(x2362,x2362,x2361)+~P23(x2361)
% 0.75/0.80 [213]E(x2131,x2132)+~E(f12(x2131),f12(x2132))
% 0.75/0.80 [214]E(x2141,x2142)+~E(f9(x2141),f9(x2142))
% 0.75/0.80 [216]~P21(x2162)+P21(f35(x2161,x2162))
% 0.75/0.80 [217]~P23(x2172)+P23(f35(x2171,x2172))
% 0.75/0.80 [262]~P24(x2621)+~P10(f23(x2622,x2621),f6(x2621),x2621)
% 0.75/0.80 [220]~P1(x2201)+E(f8(f8(f7(x2201),x2202),f6(x2201)),x2202)
% 0.75/0.80 [221]~P2(x2211)+E(f8(f8(f7(x2211),x2212),f6(x2211)),x2212)
% 0.75/0.80 [222]~P3(x2221)+E(f8(f8(f7(x2221),x2222),f6(x2221)),x2222)
% 0.75/0.80 [243]~P10(x2431,x2432,a3)+E(f16(f9(x2431),x2432),f9(x2431))
% 0.75/0.80 [261]~P28(f8(a5,x2611))+P28(f8(a5,f16(x2611,x2612)))
% 0.75/0.80 [283]~P28(f8(f8(a11,x2831),x2832))+P28(f8(f8(a11,f12(x2831)),f12(x2832)))
% 0.75/0.80 [379]~P2(x3791)+E(f19(f7(x3791),x3792,f6(x3791),x3791,x3791),f18(f7(x3791),f6(x3791),x3792,x3791,x3791))
% 0.75/0.80 [224]~P1(x2241)+E(f8(f8(f7(x2241),f6(x2241)),x2242),x2242)
% 0.75/0.80 [225]~P2(x2251)+E(f8(f8(f7(x2251),f6(x2251)),x2252),x2252)
% 0.75/0.80 [226]~P3(x2261)+E(f8(f8(f7(x2261),f6(x2261)),x2262),x2262)
% 0.75/0.80 [286]~P28(f8(a5,x2861))+P28(f8(a5,f8(f8(a10,x2861),f9(x2862))))
% 0.75/0.80 [324]P28(f8(f8(f20(a11,a33),f12(x3241)),f12(x3242)))+~P28(f8(f8(f20(a11,a33),x3241),x3242))
% 0.75/0.80 [392]~P9(a5,x3922,a33)+P28(f8(a5,f18(a10,f9(x3921),x3922,a33,a33)))
% 0.75/0.80 [232]~E(f14(x2323,x2321,x2322),x2323)+E(x2321,f21(x2322))
% 0.75/0.80 [233]~E(f14(x2331,x2333,x2332),x2333)+E(x2331,f21(x2332))
% 0.75/0.80 [239]~E(f14(x2393,x2391,x2392),f21(x2392))+E(x2391,f21(x2392))
% 0.75/0.80 [240]~E(f14(x2401,x2403,x2402),f21(x2402))+E(x2401,f21(x2402))
% 0.75/0.80 [246]~P8(x2461,f9(x2462),x2463)+E(f8(x2461,x2462),x2463)
% 0.75/0.80 [370]~E(f12(x3702),f18(a10,x3703,x3701,a33,a33))+E(x3701,f21(a33))
% 0.75/0.80 [371]~E(f9(x3712),f18(a10,x3713,x3711,a33,a33))+E(x3711,f21(a33))
% 0.75/0.80 [372]~E(f18(a10,x3722,x3721,a33,a33),f12(x3723))+E(x3721,f21(a33))
% 0.75/0.80 [373]E(x3731,f12(x3732))+~E(f18(a10,x3731,x3733,a33,a33),f12(x3732))
% 0.75/0.80 [374]E(f12(x3741),x3742)+~E(f12(x3741),f18(a10,x3742,x3743,a33,a33))
% 0.75/0.80 [375]E(f9(x3751),x3752)+~E(f9(x3751),f18(a10,x3752,x3753,a33,a33))
% 0.75/0.80 [383]E(x3831,x3832)+~E(f18(a10,x3831,x3833,a33,a33),f18(a10,x3832,x3833,a33,a33))
% 0.75/0.80 [263]~P10(x2631,x2633,a3)+E(f15(f9(x2631),x2632,x2633),f9(x2631))
% 0.75/0.80 [306]~P28(f8(f8(a11,x3061),x3063))+P28(f8(f8(a11,f16(x3061,x3062)),f16(x3063,x3062)))
% 0.75/0.80 [376]E(f8(f8(a10,x3761),x3762),x3763)+~E(f8(f8(a10,x3761),x3762),f18(a10,x3763,f21(a33),a33,a33))
% 0.75/0.80 [378]~P6(x3781)+E(f19(f7(x3781),x3782,x3783,x3781,x3781),f18(f7(x3781),x3783,x3782,x3781,x3781))
% 0.75/0.80 [401]~P28(f8(f8(a11,x4011),x4013))+P28(f8(f8(a11,f18(a10,x4011,x4012,a33,a33)),f18(a10,x4013,x4012,a33,a33)))
% 0.75/0.80 [403]~P11(a11,x4032,x4033,a33)+P28(f8(f8(a11,f18(a10,x4031,x4032,a33,a33)),f18(a10,x4031,x4033,a33,a33)))
% 0.75/0.80 [248]~P1(x2481)+E(f8(f8(f7(x2481),x2482),x2483),f8(f8(f7(x2481),x2483),x2482))
% 0.75/0.80 [249]~P3(x2491)+E(f8(f8(f7(x2491),x2492),x2493),f8(f8(f7(x2491),x2493),x2492))
% 0.75/0.80 [264]E(x2641,x2642)+~P28(f8(f8(f24(x2643),x2641),x2642))
% 0.75/0.80 [294]~P28(f8(a5,x2941))+P28(f8(a5,f15(x2941,f9(x2942),x2943)))
% 0.75/0.80 [330]P28(f8(f8(f20(a11,a33),f16(x3301,x3302)),f16(x3303,x3302)))+~P28(f8(f8(f20(a11,a33),x3301),x3303))
% 0.75/0.80 [335]~P28(f8(f8(a11,x3351),x3353))+P28(f8(f8(a11,f8(f8(a10,x3351),x3352)),f8(f8(a10,x3353),x3352)))
% 0.75/0.80 [336]~P28(f8(f8(a11,x3362),x3363))+P28(f8(f8(a11,f8(f8(a10,x3361),x3362)),f8(f8(a10,x3361),x3363)))
% 0.75/0.80 [346]~P28(f8(f8(f20(a11,a33),x3461),x3463))+P28(f8(f8(f20(a11,a33),f8(f8(a10,x3461),x3462)),f8(f8(a10,x3463),x3462)))
% 0.75/0.80 [347]~P28(f8(f8(f20(a11,a33),x3472),x3473))+P28(f8(f8(f20(a11,a33),f8(f8(a10,x3471),x3472)),f8(f8(a10,x3471),x3473)))
% 0.75/0.80 [381]~P2(x3811)+E(f8(f8(f7(x3811),x3812),f19(f7(x3811),x3813,f6(x3811),x3811,x3811)),f18(f7(x3811),x3812,x3813,x3811,x3811))
% 0.75/0.80 [382]~P2(x3821)+E(f8(f8(f7(x3821),x3822),f18(f7(x3821),f6(x3821),x3823,x3821,x3821)),f18(f7(x3821),x3822,x3823,x3821,x3821))
% 0.75/0.80 [402]P28(f8(f8(f20(a11,a33),f18(a10,x4021,x4022,a33,a33)),f18(a10,x4023,x4022,a33,a33)))+~P28(f8(f8(f20(a11,a33),x4021),x4023))
% 0.75/0.80 [380]~E(f18(a10,f8(f8(a10,x3801),x3802),x3803,a33,a33),x3801)+E(f18(a10,f8(f8(a10,x3801),x3802),f14(x3803,f13(x3802,f21(a33),a33),a33),a33,a33),f8(f8(a10,x3801),x3802))
% 0.75/0.80 [404]P11(a11,x4041,f17(x4042,x4041,x4043),a33)+~P28(f8(f8(a11,f18(a10,f9(x4042),x4041,a33,a33)),x4043))
% 0.75/0.80 [406]E(f18(a10,f9(x4061),f17(x4061,x4062,x4063),a33,a33),x4063)+~P28(f8(f8(a11,f18(a10,f9(x4061),x4062,a33,a33)),x4063))
% 0.75/0.80 [266]E(x2661,x2662)+~E(f14(x2663,x2661,x2664),f14(x2663,x2662,x2664))
% 0.75/0.80 [267]E(x2671,x2672)+~E(f14(x2671,x2673,x2674),f14(x2672,x2673,x2674))
% 0.75/0.80 [295]P9(x2951,x2952,x2953)+~P9(x2951,f14(x2954,x2952,x2953),x2953)
% 0.75/0.80 [296]P9(x2961,x2962,x2963)+~P9(x2961,f14(x2962,x2964,x2963),x2963)
% 0.75/0.80 [389]P12(x3891,x3892,f29(x3893,x3891,x3894,x3892))+~P8(x3891,f18(a10,x3894,x3892,a33,a33),x3893)
% 0.75/0.80 [390]P12(x3901,x3902,f30(x3903,x3901,x3904,x3902))+~P8(x3901,f18(a10,x3904,x3902,a33,a33),x3903)
% 0.75/0.80 [251]E(x2511,x2512)+~E(f8(f8(a10,x2513),x2511),f8(f8(a10,x2514),x2512))
% 0.75/0.80 [252]E(x2521,x2522)+~E(f8(f8(a26,x2523),x2521),f8(f8(a26,x2524),x2522))
% 0.75/0.80 [253]E(x2531,x2532)+~E(f8(f8(a10,x2531),x2533),f8(f8(a10,x2532),x2534))
% 0.75/0.80 [254]E(x2541,x2542)+~E(f8(f8(a26,x2541),x2543),f8(f8(a26,x2542),x2544))
% 0.75/0.80 [342]P8(x3421,x3422,f27(x3423,x3421,x3424,x3422))+~P8(x3421,f8(f8(a10,x3424),x3422),x3423)
% 0.75/0.80 [345]~P28(f8(f8(a11,x3451),x3454))+P28(f8(f8(a11,f15(x3451,x3452,x3453)),f15(x3454,x3452,x3453)))
% 0.75/0.80 [353]P28(f8(f8(f20(a11,a33),f15(x3531,x3532,x3533)),f15(x3531,x3534,x3533)))+~P28(f8(f8(a11,x3532),x3534))
% 0.75/0.80 [355]P8(x3551,f12(x3552),f8(f8(a26,x3553),x3554))+~P8(f25(x3551,f6(a3),x3553,a34),x3552,x3554)
% 0.75/0.80 [385]E(x3851,x3852)+~E(f18(a10,f12(x3853),x3851,a33,a33),f18(a10,f12(x3854),x3852,a33,a33))
% 0.75/0.80 [386]E(x3861,x3862)+~E(f18(a10,f9(x3863),x3861,a33,a33),f18(a10,f9(x3864),x3862,a33,a33))
% 0.75/0.80 [387]E(x3871,x3872)+~E(f18(a10,f12(x3871),x3873,a33,a33),f18(a10,f12(x3872),x3874,a33,a33))
% 0.75/0.80 [388]E(x3881,x3882)+~E(f18(a10,f9(x3881),x3883,a33,a33),f18(a10,f9(x3882),x3884,a33,a33))
% 0.75/0.80 [391]P12(x3911,x3912,f31(x3913,x3911,x3914,x3912))+~P8(x3911,f18(a10,f9(x3914),x3912,a33,a33),x3913)
% 0.75/0.80 [395]~P8(x3951,f18(a10,x3952,x3954,a33,a33),x3953)+P8(x3951,x3952,f19(a26,f29(x3953,x3951,x3952,x3954),x3953,a34,a34))
% 0.75/0.80 [396]~P8(x3961,f18(a10,x3962,x3964,a33,a33),x3963)+P8(x3961,x3962,f19(a26,f30(x3963,x3961,x3962,x3964),x3963,a34,a34))
% 0.75/0.80 [397]~P8(x3971,f18(a10,f9(x3972),x3974,a33,a33),x3973)+P8(x3971,f9(x3972),f19(a26,f31(x3973,x3971,x3972,x3974),x3973,a34,a34))
% 0.75/0.80 [297]~P28(f8(f8(x2971,x2973),x2974))+P28(f8(f8(f20(x2971,x2972),x2973),x2974))
% 0.75/0.80 [357]P28(f8(f8(f20(a11,a33),f15(x3571,x3572,x3573)),f15(x3574,x3572,x3573)))+~P28(f8(f8(f20(a11,a33),x3571),x3574))
% 0.75/0.80 [358]P28(f8(f8(f20(a11,a33),f15(x3581,x3582,x3583)),f15(x3581,x3584,x3583)))+~P28(f8(f8(f20(a11,a33),x3582),x3584))
% 0.75/0.80 [361]P8(x3611,x3612,f28(x3613,x3611,x3612,x3614))+~P12(x3611,f14(x3614,f13(x3612,f21(a33),a33),a33),x3613)
% 0.75/0.80 [377]~P8(x3771,f8(f8(a10,x3772),x3774),x3773)+P8(x3771,x3772,f8(f8(a26,f27(x3773,x3771,x3772,x3774)),x3773))
% 0.75/0.80 [298]~P1(x2981)+E(f8(f8(f7(x2981),x2982),f8(f8(f7(x2981),x2983),x2984)),f8(f8(f7(x2981),x2983),f8(f8(f7(x2981),x2982),x2984)))
% 0.75/0.80 [299]~P3(x2991)+E(f8(f8(f7(x2991),x2992),f8(f8(f7(x2991),x2993),x2994)),f8(f8(f7(x2991),x2993),f8(f8(f7(x2991),x2992),x2994)))
% 0.75/0.80 [300]~P15(x3001)+E(f8(f8(f7(x3001),x3002),f8(f8(f7(x3001),x3003),x3004)),f8(f8(f7(x3001),x3003),f8(f8(f7(x3001),x3002),x3004)))
% 0.75/0.80 [364]~P28(f8(f8(f20(x3641,x3642),x3644),x3643))+P28(f8(f8(f20(f22(x3641,x3642,x3642),x3642),x3643),x3644))
% 0.75/0.80 [369]P28(f8(f8(f20(x3691,x3692),x3693),x3694))+~P28(f8(f8(f20(f22(x3691,x3692,x3692),x3692),x3694),x3693))
% 0.75/0.80 [384]~P20(x3841)+E(f18(f7(x3841),f8(f8(f7(x3841),x3842),x3843),x3844,x3841,x3841),f8(f8(f7(x3841),x3842),f18(f7(x3841),x3843,x3844,x3841,x3841)))
% 0.75/0.80 [318]~P1(x3181)+E(f8(f8(f7(x3181),f8(f8(f7(x3181),x3182),x3183)),x3184),f8(f8(f7(x3181),x3182),f8(f8(f7(x3181),x3183),x3184)))
% 0.75/0.80 [319]~P3(x3191)+E(f8(f8(f7(x3191),f8(f8(f7(x3191),x3192),x3193)),x3194),f8(f8(f7(x3191),x3192),f8(f8(f7(x3191),x3193),x3194)))
% 0.75/0.80 [320]~P6(x3201)+E(f8(f8(f7(x3201),f8(f8(f7(x3201),x3202),x3203)),x3204),f8(f8(f7(x3201),x3202),f8(f8(f7(x3201),x3203),x3204)))
% 0.75/0.80 [327]~P1(x3271)+E(f8(f8(f7(x3271),f8(f8(f7(x3271),x3272),x3273)),x3274),f8(f8(f7(x3271),f8(f8(f7(x3271),x3272),x3274)),x3273))
% 0.75/0.80 [265]E(x2651,x2652)+~E(f13(x2653,x2651,x2654),f13(x2655,x2652,x2654))
% 0.75/0.80 [268]E(x2681,x2682)+~E(f13(x2681,x2683,x2684),f13(x2682,x2685,x2684))
% 0.75/0.80 [339]~P8(x3391,x3394,x3395)+P8(f25(x3391,x3392,x3393,a34),f16(x3394,x3392),x3395)
% 0.75/0.80 [348]~P11(x3481,x3482,x3485,x3484)+P11(x3481,f14(x3482,x3483,x3484),f14(x3485,x3483,x3484),x3484)
% 0.75/0.80 [349]~P11(x3491,x3493,x3495,x3494)+P11(x3491,f14(x3492,x3493,x3494),f14(x3492,x3495,x3494),x3494)
% 0.75/0.80 [350]~P11(x3501,x3503,x3505,x3504)+P11(x3501,f13(x3502,x3503,x3504),f13(x3502,x3505,x3504),x3504)
% 0.75/0.80 [331]P11(x3311,f13(x3312,x3313,x3314),f13(x3315,x3313,x3314),x3314)+~P28(f8(f8(x3311,x3312),x3315))
% 0.75/0.80 [332]~P10(x3325,x3322,a3)+E(f8(f25(x3321,x3322,x3323,x3324),x3325),f8(x3321,x3325))
% 0.75/0.80 [328]E(x3281,x3282)+~E(f14(x3283,f13(x3281,f21(x3284),x3284),x3284),f14(x3285,f13(x3282,f21(x3284),x3284),x3284))
% 0.75/0.80 [329]E(x3291,x3292)+~E(f14(x3291,f13(x3293,f21(x3294),x3294),x3294),f14(x3292,f13(x3295,f21(x3294),x3294),x3294))
% 0.75/0.80 [338]~P28(f8(f8(x3381,x3385),x3384))+P28(f8(f8(f22(x3381,x3382,x3383),x3384),x3385))
% 0.75/0.80 [352]P28(f8(f8(x3521,x3522),x3523))+~P28(f8(f8(f22(x3521,x3524,x3525),x3523),x3522))
% 0.75/0.80 [340]~P1(x3401)+E(f8(f8(f7(x3401),f8(f8(f7(x3401),x3402),x3403)),f8(f8(f7(x3401),x3404),x3405)),f8(f8(f7(x3401),f8(f8(f7(x3401),x3402),x3404)),f8(f8(f7(x3401),x3403),x3405)))
% 0.75/0.80 [245]E(x2451,x2452)+P10(x2452,x2451,a3)+P10(x2451,x2452,a3)
% 0.75/0.80 [277]~P24(x2771)+P10(f6(x2771),f23(x2772,x2771),x2771)+~P10(f6(a3),x2772,a3)
% 0.75/0.80 [281]~P24(x2812)+~P10(f6(x2812),f23(x2811,x2812),x2812)+P10(f6(a3),x2811,a3)
% 0.75/0.80 [227]~P25(x2271)+~P13(x2271)+E(f8(f8(f7(x2271),x2272),f6(x2271)),x2272)
% 0.75/0.80 [241]~P16(x2412)+E(x2411,f6(x2412))+~E(f8(f8(f7(x2412),x2411),x2411),f6(x2412))
% 0.75/0.80 [289]~P16(x2891)+~P10(f6(x2891),x2892,x2891)+P10(f6(x2891),f8(f8(f7(x2891),x2892),x2892),x2891)
% 0.75/0.80 [290]~P16(x2901)+~P10(x2902,f6(x2901),x2901)+P10(f8(f8(f7(x2901),x2902),x2902),f6(x2901),x2901)
% 0.75/0.80 [291]~P26(x2911)+~P10(x2912,f6(x2911),x2911)+P10(f8(f8(f7(x2911),x2912),x2912),f6(x2911),x2911)
% 0.75/0.80 [301]~P16(x3012)+P10(x3011,f6(x3012),x3012)+~P10(f8(f8(f7(x3012),x3011),x3011),f6(x3012),x3012)
% 0.75/0.80 [302]~P26(x3022)+P10(x3021,f6(x3022),x3022)+~P10(f8(f8(f7(x3022),x3021),x3021),f6(x3022),x3022)
% 0.75/0.80 [303]~P16(x3031)+P10(f6(x3031),x3032,x3031)+~P10(f6(x3031),f8(f8(f7(x3031),x3032),x3032),x3031)
% 0.75/0.80 [273]~P10(x2733,x2732,x2731)+~P21(x2731)+~P10(x2732,x2733,x2731)
% 0.75/0.80 [274]~P10(x2743,x2742,x2741)+~P22(x2741)+~P10(x2742,x2743,x2741)
% 0.75/0.80 [275]~P10(x2753,x2752,x2751)+~P23(x2751)+~P10(x2752,x2753,x2751)
% 0.75/0.80 [218]~P7(x2183)+E(x2181,x2182)+~E(f23(x2181,x2183),f23(x2182,x2183))
% 0.75/0.80 [280]~P24(x2802)+~P10(x2801,x2803,a3)+P10(f23(x2801,x2802),f23(x2803,x2802),x2802)
% 0.75/0.80 [282]~P24(x2823)+~P10(f23(x2821,x2823),f23(x2822,x2823),x2823)+P10(x2821,x2822,a3)
% 0.75/0.80 [260]E(x2601,x2602)+P10(x2602,x2601,a3)+E(f15(f9(x2601),x2603,x2602),f9(x2601))
% 0.75/0.80 [398]~P14(f22(a11,a33,a33),x3982,a33)+~P14(f22(a11,a33,a33),f18(a10,f15(x3981,x3982,f6(a3)),x3983,a33,a33),a33)+P14(f22(a11,a33,a33),f18(a10,f8(f8(a10,f12(x3981)),x3982),x3983,a33,a33),a33)
% 0.75/0.80 [400]~P28(f8(a5,x4002))+~P28(f8(a5,f18(a10,f15(x4001,x4002,f6(a3)),x4003,a33,a33)))+P28(f8(a5,f18(a10,f8(f8(a10,f12(x4001)),x4002),x4003,a33,a33)))
% 0.75/0.80 [304]~P9(x3041,x3043,x3044)+~P9(x3041,x3042,x3044)+P9(x3041,f14(x3042,x3043,x3044),x3044)
% 0.75/0.80 [287]P8(x2871,x2872,x2873)+~P8(x2871,x2874,x2873)+~P28(f8(f8(a11,x2874),x2872))
% 0.75/0.80 [293]P14(x2931,x2932,x2933)+~P14(x2931,x2934,x2933)+~P28(f8(f8(x2931,x2932),x2934))
% 0.75/0.80 [269]~P4(x2693)+E(x2691,x2692)+~E(f8(f8(f7(x2693),x2694),x2691),f8(f8(f7(x2693),x2694),x2692))
% 0.75/0.80 [270]~P5(x2703)+E(x2701,x2702)+~E(f8(f8(f7(x2703),x2704),x2701),f8(f8(f7(x2703),x2704),x2702))
% 0.75/0.80 [271]~P4(x2713)+E(x2711,x2712)+~E(f8(f8(f7(x2713),x2711),x2714),f8(f8(f7(x2713),x2712),x2714))
% 0.75/0.80 [307]~P18(x3071)+~P10(x3072,x3074,x3071)+P10(f8(f8(f7(x3071),x3072),x3073),f8(f8(f7(x3071),x3074),x3073),x3071)
% 0.75/0.80 [308]~P19(x3081)+~P10(x3082,x3084,x3081)+P10(f8(f8(f7(x3081),x3082),x3083),f8(f8(f7(x3081),x3084),x3083),x3081)
% 0.75/0.80 [309]~P18(x3091)+~P10(x3093,x3094,x3091)+P10(f8(f8(f7(x3091),x3092),x3093),f8(f8(f7(x3091),x3092),x3094),x3091)
% 0.75/0.80 [310]~P19(x3101)+~P10(x3103,x3104,x3101)+P10(f8(f8(f7(x3101),x3102),x3103),f8(f8(f7(x3101),x3102),x3104),x3101)
% 0.75/0.80 [314]P8(x3141,x3142,x3143)+~P8(x3141,x3144,x3143)+~P28(f8(f8(f20(a11,a33),x3144),x3142))
% 0.75/0.80 [322]P14(x3221,x3222,x3223)+~P14(x3221,x3224,x3223)+~P28(f8(f8(f20(x3221,x3223),x3222),x3224))
% 0.75/0.80 [325]~P19(x3253)+P10(x3251,x3252,x3253)+~P10(f8(f8(f7(x3253),x3254),x3251),f8(f8(f7(x3253),x3254),x3252),x3253)
% 0.75/0.80 [326]~P19(x3263)+P10(x3261,x3262,x3263)+~P10(f8(f8(f7(x3263),x3261),x3264),f8(f8(f7(x3263),x3262),x3264),x3263)
% 0.75/0.80 [359]~P28(f8(f8(f20(a11,a33),x3591),x3593))+~P28(f8(f8(f20(a11,a33),x3592),x3594))+P28(f8(f8(f20(a11,a33),f8(f8(a10,x3591),x3592)),f8(f8(a10,x3593),x3594)))
% 0.75/0.80 [393]~P12(x3931,x3933,x3935)+~P8(x3931,x3932,f19(a26,x3935,x3934,a34,a34))+P8(x3931,f18(a10,x3932,x3933,a33,a33),x3934)
% 0.75/0.81 [315]~P8(x3151,x3153,x3155)+~P8(x3151,x3152,f8(f8(a26,x3155),x3154))+P8(x3151,f8(f8(a10,x3152),x3153),x3154)
% 0.75/0.81 [399]E(x3991,x3992)+~P8(x3993,f18(a10,f9(x3994),x3995,a33,a33),x3991)+~P8(x3993,f18(a10,f9(x3994),x3995,a33,a33),x3992)
% 0.75/0.81 [333]~P28(f8(f8(x3331,x3335),x3334))+~P28(f8(f8(f20(x3331,x3332),x3333),x3335))+P28(f8(f8(f20(x3331,x3332),x3333),x3334))
% 0.75/0.81 [334]~P28(f8(f8(x3341,x3343),x3345))+~P28(f8(f8(f20(x3341,x3342),x3345),x3344))+P28(f8(f8(f20(x3341,x3342),x3343),x3344))
% 0.75/0.81 [343]~P28(f8(f8(f20(x3431,x3432),x3433),x3435))+P28(f8(f8(f20(x3431,x3432),x3433),x3434))+~P28(f8(f8(f20(x3431,x3432),x3435),x3434))
% 0.75/0.81 [313]~P15(x3131)+E(f8(f8(f7(x3131),x3132),x3133),x3134)+~E(f8(f8(f7(x3131),x3132),f8(f8(f7(x3131),x3135),x3133)),f8(f8(f7(x3131),x3135),x3134))
% 0.75/0.81 [341]E(x3411,x3412)+E(x3413,x3414)+~P11(x3415,f13(x3414,x3412,x3416),f13(x3413,x3411,x3416),x3416)
% 0.75/0.81 [354]E(x3541,x3542)+P11(x3543,x3541,x3542,x3544)+~P11(x3543,f13(x3545,x3541,x3544),f13(x3546,x3542,x3544),x3544)
% 0.75/0.81 [360]~P8(x3601,x3603,x3606)+P8(x3601,f15(x3602,x3603,x3604),x3605)+~P8(f25(x3601,x3604,x3606,a34),x3602,x3605)
% 0.75/0.81 [344]E(x3441,x3442)+~P11(x3443,f13(x3442,x3444,x3445),f13(x3441,x3446,x3445),x3445)+P28(f8(f8(x3443,x3442),x3441))
% 0.75/0.81 [356]P11(x3561,x3562,x3563,x3564)+~P11(x3561,f13(x3565,x3562,x3564),f13(x3566,x3563,x3564),x3564)+P28(f8(f8(x3561,x3565),x3566))
% 0.75/0.81 [365]E(x3651,x3652)+E(x3653,x3654)+~P11(x3655,f14(x3653,f13(x3651,f21(x3656),x3656),x3656),f14(x3654,f13(x3652,f21(x3656),x3656),x3656),x3656)
% 0.75/0.81 [366]E(x3661,x3662)+~P11(x3663,f14(x3664,f13(x3661,f21(x3665),x3665),x3665),f14(x3666,f13(x3662,f21(x3665),x3665),x3665),x3665)+P28(f8(f8(x3663,x3661),x3662))
% 0.75/0.81 [367]E(x3671,x3672)+P11(x3673,x3671,x3672,x3674)+~P11(x3673,f14(x3671,f13(x3675,f21(x3674),x3674),x3674),f14(x3672,f13(x3676,f21(x3674),x3674),x3674),x3674)
% 0.75/0.81 [368]P11(x3681,x3682,x3683,x3684)+~P11(x3681,f14(x3682,f13(x3685,f21(x3684),x3684),x3684),f14(x3683,f13(x3686,f21(x3684),x3684),x3684),x3684)+P28(f8(f8(x3681,x3685),x3686))
% 0.75/0.81 [255]P10(x2551,x2552,x2553)+~P26(x2553)+E(x2551,x2552)+P10(x2552,x2551,x2553)
% 0.75/0.81 [259]P10(x2591,x2592,x2593)+~P22(x2593)+E(x2591,x2592)+P10(x2592,x2591,x2593)
% 0.75/0.81 [242]~P25(x2422)+~P13(x2422)+E(x2421,f6(x2422))+~E(f8(f8(f7(x2422),x2423),x2421),x2423)
% 0.75/0.81 [311]~P17(x3111)+~P10(f6(x3111),x3113,x3111)+~P10(f6(x3111),x3112,x3111)+P10(f6(x3111),f8(f8(f7(x3111),x3112),x3113),x3111)
% 0.75/0.81 [312]~P17(x3121)+~P10(x3123,f6(x3121),x3121)+~P10(x3122,f6(x3121),x3121)+P10(f8(f8(f7(x3121),x3122),x3123),f6(x3121),x3121)
% 0.75/0.81 [284]~P21(x2843)+~P10(x2841,x2844,x2843)+P10(x2841,x2842,x2843)+~P10(x2844,x2842,x2843)
% 0.75/0.81 [285]~P23(x2853)+~P10(x2851,x2854,x2853)+P10(x2851,x2852,x2853)+~P10(x2854,x2852,x2853)
% 0.75/0.81 [276]~P25(x2763)+~P13(x2763)+E(x2761,x2762)+~E(f8(f8(f7(x2763),x2764),x2761),f8(f8(f7(x2763),x2764),x2762))
% 0.75/0.81 [305]~P24(x3052)+~P10(x3051,x3054,x3052)+~P10(f6(x3052),x3053,x3052)+P10(x3051,f8(f8(f7(x3052),x3053),x3054),x3052)
% 0.75/0.81 [323]~P18(x3231)+~P10(x3233,x3235,x3231)+~P10(x3232,x3234,x3231)+P10(f8(f8(f7(x3231),x3232),x3233),f8(f8(f7(x3231),x3234),x3235),x3231)
% 0.75/0.81 [405]~P12(x4051,x4055,x4056)+P12(x4051,x4052,f32(x4053,x4054,x4051,x4052))+~P8(x4051,f18(a10,f9(x4057),x4055,a33,a33),x4054)+~P8(x4051,f18(a10,f18(a10,f9(x4057),x4055,a33,a33),x4052,a33,a33),x4053)
% 0.75/0.81 [407]~P12(x4073,x4075,x4076)+~P8(x4073,f18(a10,f9(x4077),x4075,a33,a33),x4072)+~P8(x4073,f18(a10,f18(a10,f9(x4077),x4075,a33,a33),x4074,a33,a33),x4071)+E(f19(a26,f32(x4071,x4072,x4073,x4074),x4071,a34,a34),x4072)
% 0.75/0.81 [362]~P8(x3626,x3622,x3625)+~P8(f25(x3626,x3623,x3625,a34),x3621,x3627)+~P28(f8(a5,x3622))+~P28(f8(a5,x3621))+~E(f8(f8(a26,x3624),x3625),a37)+P28(f8(a5,f15(x3621,x3622,x3623)))
% 0.75/0.81 [363]~P8(x3636,x3632,x3634)+~P8(f25(x3636,x3633,x3634,a34),x3631,x3637)+~P28(f8(a5,x3632))+~P28(f8(a5,x3631))+~E(f8(f8(a26,x3634),x3635),a37)+P28(f8(a5,f15(x3631,x3632,x3633)))
% 0.75/0.81 %EqnAxiom
% 0.75/0.81 [1]E(x11,x11)
% 0.75/0.81 [2]E(x22,x21)+~E(x21,x22)
% 0.75/0.81 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.75/0.81 [4]~E(x41,x42)+E(f8(x41,x43),f8(x42,x43))
% 0.75/0.81 [5]~E(x51,x52)+E(f8(x53,x51),f8(x53,x52))
% 0.75/0.81 [6]~E(x61,x62)+E(f18(x61,x63,x64,x65,x66),f18(x62,x63,x64,x65,x66))
% 0.75/0.81 [7]~E(x71,x72)+E(f18(x73,x71,x74,x75,x76),f18(x73,x72,x74,x75,x76))
% 0.75/0.81 [8]~E(x81,x82)+E(f18(x83,x84,x81,x85,x86),f18(x83,x84,x82,x85,x86))
% 0.75/0.81 [9]~E(x91,x92)+E(f18(x93,x94,x95,x91,x96),f18(x93,x94,x95,x92,x96))
% 0.75/0.81 [10]~E(x101,x102)+E(f18(x103,x104,x105,x106,x101),f18(x103,x104,x105,x106,x102))
% 0.75/0.81 [11]~E(x111,x112)+E(f9(x111),f9(x112))
% 0.75/0.81 [12]~E(x121,x122)+E(f12(x121),f12(x122))
% 0.75/0.81 [13]~E(x131,x132)+E(f13(x131,x133,x134),f13(x132,x133,x134))
% 0.75/0.81 [14]~E(x141,x142)+E(f13(x143,x141,x144),f13(x143,x142,x144))
% 0.75/0.81 [15]~E(x151,x152)+E(f13(x153,x154,x151),f13(x153,x154,x152))
% 0.75/0.81 [16]~E(x161,x162)+E(f20(x161,x163),f20(x162,x163))
% 0.75/0.81 [17]~E(x171,x172)+E(f20(x173,x171),f20(x173,x172))
% 0.75/0.81 [18]~E(x181,x182)+E(f15(x181,x183,x184),f15(x182,x183,x184))
% 0.75/0.81 [19]~E(x191,x192)+E(f15(x193,x191,x194),f15(x193,x192,x194))
% 0.75/0.81 [20]~E(x201,x202)+E(f15(x203,x204,x201),f15(x203,x204,x202))
% 0.75/0.81 [21]~E(x211,x212)+E(f23(x211,x213),f23(x212,x213))
% 0.75/0.81 [22]~E(x221,x222)+E(f23(x223,x221),f23(x223,x222))
% 0.75/0.81 [23]~E(x231,x232)+E(f21(x231),f21(x232))
% 0.75/0.81 [24]~E(x241,x242)+E(f7(x241),f7(x242))
% 0.75/0.81 [25]~E(x251,x252)+E(f14(x251,x253,x254),f14(x252,x253,x254))
% 0.75/0.81 [26]~E(x261,x262)+E(f14(x263,x261,x264),f14(x263,x262,x264))
% 0.75/0.81 [27]~E(x271,x272)+E(f14(x273,x274,x271),f14(x273,x274,x272))
% 0.75/0.81 [28]~E(x281,x282)+E(f27(x281,x283,x284,x285),f27(x282,x283,x284,x285))
% 0.75/0.81 [29]~E(x291,x292)+E(f27(x293,x291,x294,x295),f27(x293,x292,x294,x295))
% 0.75/0.81 [30]~E(x301,x302)+E(f27(x303,x304,x301,x305),f27(x303,x304,x302,x305))
% 0.75/0.81 [31]~E(x311,x312)+E(f27(x313,x314,x315,x311),f27(x313,x314,x315,x312))
% 0.75/0.81 [32]~E(x321,x322)+E(f6(x321),f6(x322))
% 0.75/0.81 [33]~E(x331,x332)+E(f19(x331,x333,x334,x335,x336),f19(x332,x333,x334,x335,x336))
% 0.75/0.81 [34]~E(x341,x342)+E(f19(x343,x341,x344,x345,x346),f19(x343,x342,x344,x345,x346))
% 0.75/0.81 [35]~E(x351,x352)+E(f19(x353,x354,x351,x355,x356),f19(x353,x354,x352,x355,x356))
% 0.75/0.81 [36]~E(x361,x362)+E(f19(x363,x364,x365,x361,x366),f19(x363,x364,x365,x362,x366))
% 0.75/0.81 [37]~E(x371,x372)+E(f19(x373,x374,x375,x376,x371),f19(x373,x374,x375,x376,x372))
% 0.75/0.81 [38]~E(x381,x382)+E(f22(x381,x383,x384),f22(x382,x383,x384))
% 0.75/0.81 [39]~E(x391,x392)+E(f22(x393,x391,x394),f22(x393,x392,x394))
% 0.75/0.81 [40]~E(x401,x402)+E(f22(x403,x404,x401),f22(x403,x404,x402))
% 0.75/0.81 [41]~E(x411,x412)+E(f25(x411,x413,x414,x415),f25(x412,x413,x414,x415))
% 0.75/0.81 [42]~E(x421,x422)+E(f25(x423,x421,x424,x425),f25(x423,x422,x424,x425))
% 0.75/0.81 [43]~E(x431,x432)+E(f25(x433,x434,x431,x435),f25(x433,x434,x432,x435))
% 0.75/0.81 [44]~E(x441,x442)+E(f25(x443,x444,x445,x441),f25(x443,x444,x445,x442))
% 0.75/0.81 [45]~E(x451,x452)+E(f32(x451,x453,x454,x455),f32(x452,x453,x454,x455))
% 0.75/0.81 [46]~E(x461,x462)+E(f32(x463,x461,x464,x465),f32(x463,x462,x464,x465))
% 0.75/0.81 [47]~E(x471,x472)+E(f32(x473,x474,x471,x475),f32(x473,x474,x472,x475))
% 0.75/0.81 [48]~E(x481,x482)+E(f32(x483,x484,x485,x481),f32(x483,x484,x485,x482))
% 0.75/0.81 [49]~E(x491,x492)+E(f24(x491),f24(x492))
% 0.75/0.81 [50]~E(x501,x502)+E(f30(x501,x503,x504,x505),f30(x502,x503,x504,x505))
% 0.75/0.81 [51]~E(x511,x512)+E(f30(x513,x511,x514,x515),f30(x513,x512,x514,x515))
% 0.75/0.81 [52]~E(x521,x522)+E(f30(x523,x524,x521,x525),f30(x523,x524,x522,x525))
% 0.75/0.81 [53]~E(x531,x532)+E(f30(x533,x534,x535,x531),f30(x533,x534,x535,x532))
% 0.75/0.81 [54]~E(x541,x542)+E(f31(x541,x543,x544,x545),f31(x542,x543,x544,x545))
% 0.75/0.81 [55]~E(x551,x552)+E(f31(x553,x551,x554,x555),f31(x553,x552,x554,x555))
% 0.75/0.81 [56]~E(x561,x562)+E(f31(x563,x564,x561,x565),f31(x563,x564,x562,x565))
% 0.75/0.81 [57]~E(x571,x572)+E(f31(x573,x574,x575,x571),f31(x573,x574,x575,x572))
% 0.75/0.81 [58]~E(x581,x582)+E(f29(x581,x583,x584,x585),f29(x582,x583,x584,x585))
% 0.75/0.81 [59]~E(x591,x592)+E(f29(x593,x591,x594,x595),f29(x593,x592,x594,x595))
% 0.75/0.81 [60]~E(x601,x602)+E(f29(x603,x604,x601,x605),f29(x603,x604,x602,x605))
% 0.75/0.81 [61]~E(x611,x612)+E(f29(x613,x614,x615,x611),f29(x613,x614,x615,x612))
% 0.75/0.81 [62]~E(x621,x622)+E(f35(x621,x623),f35(x622,x623))
% 0.75/0.81 [63]~E(x631,x632)+E(f35(x633,x631),f35(x633,x632))
% 0.75/0.81 [64]~E(x641,x642)+E(f28(x641,x643,x644,x645),f28(x642,x643,x644,x645))
% 0.75/0.81 [65]~E(x651,x652)+E(f28(x653,x651,x654,x655),f28(x653,x652,x654,x655))
% 0.75/0.81 [66]~E(x661,x662)+E(f28(x663,x664,x661,x665),f28(x663,x664,x662,x665))
% 0.75/0.81 [67]~E(x671,x672)+E(f28(x673,x674,x675,x671),f28(x673,x674,x675,x672))
% 0.75/0.81 [68]~E(x681,x682)+E(f17(x681,x683,x684),f17(x682,x683,x684))
% 0.75/0.81 [69]~E(x691,x692)+E(f17(x693,x691,x694),f17(x693,x692,x694))
% 0.75/0.81 [70]~E(x701,x702)+E(f17(x703,x704,x701),f17(x703,x704,x702))
% 0.75/0.81 [71]~E(x711,x712)+E(f16(x711,x713),f16(x712,x713))
% 0.75/0.81 [72]~E(x721,x722)+E(f16(x723,x721),f16(x723,x722))
% 0.75/0.81 [73]~P1(x731)+P1(x732)+~E(x731,x732)
% 0.75/0.81 [74]~P2(x741)+P2(x742)+~E(x741,x742)
% 0.75/0.81 [75]~P3(x751)+P3(x752)+~E(x751,x752)
% 0.75/0.81 [76]~P24(x761)+P24(x762)+~E(x761,x762)
% 0.75/0.81 [77]~P4(x771)+P4(x772)+~E(x771,x772)
% 0.75/0.81 [78]~P5(x781)+P5(x782)+~E(x781,x782)
% 0.75/0.81 [79]~P17(x791)+P17(x792)+~E(x791,x792)
% 0.75/0.81 [80]~P27(x801)+P27(x802)+~E(x801,x802)
% 0.75/0.81 [81]~P6(x811)+P6(x812)+~E(x811,x812)
% 0.75/0.81 [82]~P20(x821)+P20(x822)+~E(x821,x822)
% 0.75/0.81 [83]~P7(x831)+P7(x832)+~E(x831,x832)
% 0.75/0.81 [84]~P18(x841)+P18(x842)+~E(x841,x842)
% 0.75/0.81 [85]~P19(x851)+P19(x852)+~E(x851,x852)
% 0.75/0.81 [86]~P21(x861)+P21(x862)+~E(x861,x862)
% 0.75/0.81 [87]~P28(x871)+P28(x872)+~E(x871,x872)
% 0.75/0.81 [88]~P22(x881)+P22(x882)+~E(x881,x882)
% 0.75/0.81 [89]~P23(x891)+P23(x892)+~E(x891,x892)
% 0.75/0.81 [90]P14(x902,x903,x904)+~E(x901,x902)+~P14(x901,x903,x904)
% 0.75/0.81 [91]P14(x913,x912,x914)+~E(x911,x912)+~P14(x913,x911,x914)
% 0.75/0.81 [92]P14(x923,x924,x922)+~E(x921,x922)+~P14(x923,x924,x921)
% 0.75/0.81 [93]P11(x932,x933,x934,x935)+~E(x931,x932)+~P11(x931,x933,x934,x935)
% 0.75/0.81 [94]P11(x943,x942,x944,x945)+~E(x941,x942)+~P11(x943,x941,x944,x945)
% 0.75/0.81 [95]P11(x953,x954,x952,x955)+~E(x951,x952)+~P11(x953,x954,x951,x955)
% 0.75/0.81 [96]P11(x963,x964,x965,x962)+~E(x961,x962)+~P11(x963,x964,x965,x961)
% 0.75/0.81 [97]P10(x972,x973,x974)+~E(x971,x972)+~P10(x971,x973,x974)
% 0.75/0.81 [98]P10(x983,x982,x984)+~E(x981,x982)+~P10(x983,x981,x984)
% 0.75/0.81 [99]P10(x993,x994,x992)+~E(x991,x992)+~P10(x993,x994,x991)
% 0.75/0.81 [100]P9(x1002,x1003,x1004)+~E(x1001,x1002)+~P9(x1001,x1003,x1004)
% 0.75/0.81 [101]P9(x1013,x1012,x1014)+~E(x1011,x1012)+~P9(x1013,x1011,x1014)
% 0.75/0.81 [102]P9(x1023,x1024,x1022)+~E(x1021,x1022)+~P9(x1023,x1024,x1021)
% 0.75/0.81 [103]P8(x1032,x1033,x1034)+~E(x1031,x1032)+~P8(x1031,x1033,x1034)
% 0.75/0.81 [104]P8(x1043,x1042,x1044)+~E(x1041,x1042)+~P8(x1043,x1041,x1044)
% 0.75/0.81 [105]P8(x1053,x1054,x1052)+~E(x1051,x1052)+~P8(x1053,x1054,x1051)
% 0.75/0.81 [106]~P13(x1061)+P13(x1062)+~E(x1061,x1062)
% 0.75/0.81 [107]P12(x1072,x1073,x1074)+~E(x1071,x1072)+~P12(x1071,x1073,x1074)
% 0.75/0.81 [108]P12(x1083,x1082,x1084)+~E(x1081,x1082)+~P12(x1083,x1081,x1084)
% 0.75/0.81 [109]P12(x1093,x1094,x1092)+~E(x1091,x1092)+~P12(x1093,x1094,x1091)
% 0.75/0.81 [110]~P26(x1101)+P26(x1102)+~E(x1101,x1102)
% 0.75/0.81 [111]~P15(x1111)+P15(x1112)+~E(x1111,x1112)
% 0.75/0.81 [112]~P16(x1121)+P16(x1122)+~E(x1121,x1122)
% 0.75/0.81 [113]~P25(x1131)+P25(x1132)+~E(x1131,x1132)
% 0.75/0.81
% 0.75/0.81 %-------------------------------------------
% 0.75/0.81 cnf(412,plain,
% 0.75/0.81 (~E(f13(x4121,x4122,x4123),x4122)),
% 0.75/0.81 inference(rename_variables,[],[200])).
% 0.75/0.81 cnf(417,plain,
% 0.75/0.81 (~E(f13(x4171,x4172,x4173),x4172)),
% 0.75/0.81 inference(rename_variables,[],[200])).
% 0.75/0.81 cnf(420,plain,
% 0.75/0.81 (~E(f13(x4201,x4202,x4203),x4202)),
% 0.75/0.81 inference(rename_variables,[],[200])).
% 0.75/0.81 cnf(425,plain,
% 0.75/0.81 (~E(f13(x4251,x4252,x4253),x4252)),
% 0.75/0.81 inference(rename_variables,[],[200])).
% 0.75/0.81 cnf(428,plain,
% 0.75/0.81 (~E(f13(x4281,x4282,x4283),x4282)),
% 0.75/0.81 inference(rename_variables,[],[200])).
% 0.75/0.81 cnf(437,plain,
% 0.75/0.81 (~E(f13(x4371,x4372,x4373),x4372)),
% 0.75/0.81 inference(rename_variables,[],[200])).
% 0.75/0.81 cnf(440,plain,
% 0.75/0.81 (~E(f13(x4401,x4402,x4403),x4402)),
% 0.75/0.81 inference(rename_variables,[],[200])).
% 0.75/0.81 cnf(443,plain,
% 0.75/0.81 (P8(x4431,f9(x4432),f8(x4431,x4432))),
% 0.75/0.81 inference(rename_variables,[],[152])).
% 0.75/0.81 cnf(470,plain,
% 0.75/0.81 ($false),
% 0.75/0.81 inference(scs_inference,[],[208,198,114,118,132,139,202,171,133,183,180,189,184,209,141,200,412,417,420,425,428,437,440,152,443,145,195,153,207,173,2,236,372,279,371,370,246,233,232,353,330,324,240,239,355,331,391,390,389,342,105,103,102,96,95,87,3,281,282,360]),
% 0.75/0.81 ['proof']).
% 0.75/0.81 % SZS output end Proof
% 0.75/0.81 % Total time :0.070000s
%------------------------------------------------------------------------------