TSTP Solution File: LCL854-1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : LCL854-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n001.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 06:51:23 EDT 2023
% Result : Unsatisfiable 0.21s 0.77s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL854-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.14/0.35 % Computer : n001.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 18:36:26 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.57 start to proof:theBenchmark
% 0.21/0.73 %-------------------------------------------
% 0.21/0.73 % File :CSE---1.6
% 0.21/0.73 % Problem :theBenchmark
% 0.21/0.73 % Transform :cnf
% 0.21/0.73 % Format :tptp:raw
% 0.21/0.73 % Command :java -jar mcs_scs.jar %d %s
% 0.21/0.73
% 0.21/0.73 % Result :Theorem 0.030000s
% 0.21/0.73 % Output :CNFRefutation 0.030000s
% 0.21/0.73 %-------------------------------------------
% 0.21/0.74 %------------------------------------------------------------------------------
% 0.21/0.74 % File : LCL854-1 : TPTP v8.1.2. Released v4.1.0.
% 0.21/0.74 % Domain : Logic Calculi
% 0.21/0.74 % Problem : Strong normalization of typed lambda calculus 274_26
% 0.21/0.74 % Version : Especial.
% 0.21/0.74 % English :
% 0.21/0.74
% 0.21/0.74 % Refs : [vON99] von Oheimb & Nipkow (1999), Machine-Checking the Java
% 0.21/0.74 % : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe
% 0.21/0.74 % : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.21/0.74 % Source : [Nip10]
% 0.21/0.74 % Names : StrongNorm-274_26 [Nip10]
% 0.21/0.74
% 0.21/0.74 % Status : Unsatisfiable
% 0.21/0.74 % Rating : 0.05 v7.4.0, 0.06 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 v5.5.0, 0.05 v5.3.0, 0.06 v5.1.0, 0.12 v5.0.0, 0.14 v4.1.0
% 0.21/0.74 % Syntax : Number of clauses : 296 ( 98 unt; 13 nHn; 179 RR)
% 0.21/0.74 % Number of literals : 606 ( 220 equ; 321 neg)
% 0.21/0.74 % Maximal clause size : 6 ( 2 avg)
% 0.21/0.74 % Maximal term depth : 6 ( 2 avg)
% 0.21/0.74 % Number of predicates : 36 ( 35 usr; 0 prp; 1-4 aty)
% 0.21/0.74 % Number of functors : 51 ( 51 usr; 14 con; 0-5 aty)
% 0.21/0.74 % Number of variables : 777 ( 137 sgn)
% 0.21/0.74 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.21/0.74
% 0.21/0.74 % Comments :
% 0.21/0.74 %------------------------------------------------------------------------------
% 0.21/0.74 cnf(cls_rtranclp__converseD_0,axiom,
% 0.21/0.74 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_y),V_x))
% 0.21/0.74 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(V_r,T_a,T_a),T_a),V_x),V_y)) ) ).
% 0.21/0.74
% 0.21/0.74 cnf(cls_rtranclp__converseI_0,axiom,
% 0.21/0.74 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(V_r,T_a,T_a),T_a),V_x),V_y))
% 0.21/0.74 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_y),V_x)) ) ).
% 0.21/0.74
% 0.21/0.74 cnf(cls_natgb_Oadd__cancel_0,axiom,
% 0.21/0.74 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_y) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_z)
% 0.21/0.74 | V_y = V_z ) ).
% 0.21/0.74
% 0.21/0.74 cnf(cls_nat__add__right__cancel_0,axiom,
% 0.21/0.74 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_k) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k)
% 0.21/0.74 | V_m = V_n ) ).
% 0.21/0.74
% 0.21/0.74 cnf(cls_nat__add__left__cancel_0,axiom,
% 0.21/0.74 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n)
% 0.21/0.74 | V_m = V_n ) ).
% 0.21/0.74
% 0.21/0.74 cnf(cls_class__ringb_Oadd__cancel_0,axiom,
% 0.21/0.74 ( ~ class_Ring__and__Field_Oidom(T_a)
% 0.21/0.74 | ~ class_Int_Onumber__ring(T_a)
% 0.21/0.74 | 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)
% 0.21/0.74 | V_y = V_z ) ).
% 0.21/0.74
% 0.21/0.74 cnf(cls_add__imp__eq_0,axiom,
% 0.21/0.74 ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(T_a)
% 0.21/0.74 | 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)
% 0.21/0.74 | V_b = V_c ) ).
% 0.21/0.74
% 0.21/0.74 cnf(cls_add__left__cancel_0,axiom,
% 0.21/0.74 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a)
% 0.21/0.74 | 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)
% 0.21/0.74 | V_b = V_c ) ).
% 0.21/0.74
% 0.21/0.74 cnf(cls_add__right__cancel_0,axiom,
% 0.21/0.74 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a)
% 0.21/0.74 | 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)
% 0.21/0.74 | V_b = V_c ) ).
% 0.21/0.74
% 0.21/0.74 cnf(cls_var__app__types_1,axiom,
% 0.21/0.74 ( c_Type_Otypings(V_e,V_us,c_Type_Osko__Type__Xvar__app__types__1__1(V_T,V_U,V_e,V_us))
% 0.21/0.74 | ~ 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)
% 0.21/0.74 | ~ c_Type_Otypings(V_e,V_ts,V_Ts)
% 0.21/0.74 | ~ 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) ) ).
% 0.21/0.74
% 0.21/0.74 cnf(cls_add__is__1_3,axiom,
% 0.21/0.74 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
% 0.21/0.74 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
% 0.21/0.74 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
% 0.21/0.74
% 0.21/0.74 cnf(cls_add__is__1_0,axiom,
% 0.21/0.74 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
% 0.21/0.74 | V_m = c_HOL_Ozero__class_Ozero(tc_nat)
% 0.21/0.74 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ).
% 0.21/0.74
% 0.21/0.74 cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom,
% 0.21/0.74 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.21/0.74 | 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)) ) ).
% 0.21/0.74
% 0.21/0.74 cnf(cls_of__nat__0__le__iff_0,axiom,
% 0.21/0.74 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.21/0.74 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ).
% 0.21/0.74
% 0.21/0.74 cnf(cls_zero__le__imp__of__nat_0,axiom,
% 0.21/0.74 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.21/0.74 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),T_a) ) ).
% 0.21/0.74
% 0.21/0.74 cnf(cls_class__semiring_Oadd__0_0,axiom,
% 0.21/0.74 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.21/0.74 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_x) = V_x ) ).
% 0.21/0.74
% 0.21/0.74 cnf(cls_comm__monoid__add_Omult__1_0,axiom,
% 0.21/0.74 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
% 0.21/0.74 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 0.21/0.74
% 0.21/0.74 cnf(cls_natgb_Oadd__r0__iff_1,axiom,
% 0.21/0.74 V_x = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Ozero__class_Ozero(tc_nat)) ).
% 0.21/0.74
% 0.21/0.74 cnf(cls_plus__nat_Oadd__0_0,axiom,
% 0.21/0.74 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n) = V_n ).
% 0.21/0.74
% 0.21/0.74 cnf(cls_Nat_Oadd__0__right_0,axiom,
% 0.21/0.74 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Ozero__class_Ozero(tc_nat)) = V_m ).
% 0.21/0.74
% 0.21/0.74 cnf(cls_class__ringb_Oadd__r0__iff_1,axiom,
% 0.21/0.74 ( ~ class_Ring__and__Field_Oidom(T_a)
% 0.21/0.74 | ~ class_Int_Onumber__ring(T_a)
% 0.21/0.74 | V_x = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_HOL_Ozero__class_Ozero(T_a)) ) ).
% 0.21/0.74
% 0.21/0.74 cnf(cls_comm__monoid__add_Omult__1__right_0,axiom,
% 0.21/0.74 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
% 0.21/0.74 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a ) ).
% 0.21/0.74
% 0.21/0.74 cnf(cls_add__0__left_0,axiom,
% 0.21/0.74 ( ~ class_OrderedGroup_Omonoid__add(T_a)
% 0.21/0.74 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 0.21/0.74
% 0.21/0.74 cnf(cls_monoid__add__class_Oadd__0__right_0,axiom,
% 0.21/0.74 ( ~ class_OrderedGroup_Omonoid__add(T_a)
% 0.21/0.74 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a ) ).
% 0.21/0.74
% 0.21/0.74 cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
% 0.21/0.74 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.21/0.74 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a ) ).
% 0.21/0.74
% 0.21/0.74 cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom,
% 0.21/0.74 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.21/0.74 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 0.21/0.74
% 0.21/0.74 cnf(cls_add__Suc__shift_0,axiom,
% 0.21/0.74 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(V_m)),V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_Suc(V_n)) ).
% 0.21/0.74
% 0.21/0.74 cnf(cls_of__nat__Suc_0,axiom,
% 0.21/0.74 ( ~ class_Ring__and__Field_Osemiring__1(T_a)
% 0.21/0.74 | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(V_m),T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a)),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)) ) ).
% 0.21/0.74
% 0.21/0.74 cnf(cls_one__is__add_0,axiom,
% 0.21/0.74 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)
% 0.21/0.74 | V_m = c_HOL_Ozero__class_Ozero(tc_nat)
% 0.21/0.74 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ).
% 0.21/0.74
% 0.21/0.74 cnf(cls_one__is__add_3,axiom,
% 0.21/0.74 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)
% 0.21/0.74 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
% 0.21/0.74 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
% 0.21/0.74
% 0.21/0.74 cnf(cls_zero__neq__one_0,axiom,
% 0.21/0.74 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
% 0.21/0.74 | c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a) ) ).
% 0.21/0.74
% 0.21/0.74 cnf(cls_power__mono_0,axiom,
% 0.21/0.74 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.21/0.74 | c_lessequals(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a)
% 0.21/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
% 0.21/0.75 | ~ c_lessequals(V_a,V_b,T_a) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_one__is__add_5,axiom,
% 0.21/0.75 c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_foldr_Osimps_I1_J_0,axiom,
% 0.21/0.75 c_List_Ofoldr(V_f,c_List_Olist_ONil(T_b),V_a,T_b,T_a) = V_a ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_list__app__typeE_1,axiom,
% 0.21/0.75 ( c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeE__1__1(V_T,V_e,V_t,V_ts))
% 0.21/0.75 | ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_power__one_0,axiom,
% 0.21/0.75 ( ~ class_OrderedGroup_Omonoid__mult(T_a)
% 0.21/0.75 | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_add__cancel__21_0,axiom,
% 0.21/0.75 ( ~ class_OrderedGroup_Oab__group__add(T_a)
% 0.21/0.75 | 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)
% 0.21/0.75 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z) = V_u ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_conversepD_0,axiom,
% 0.21/0.75 ( hBOOL(hAPP(hAPP(V_r,V_b),V_a))
% 0.21/0.75 | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_a),V_b)) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_conversep__iff_1,axiom,
% 0.21/0.75 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_a),V_b))
% 0.21/0.75 | ~ hBOOL(hAPP(hAPP(V_r,V_b),V_a)) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_conversep_Ocases_0,axiom,
% 0.21/0.75 ( hBOOL(hAPP(hAPP(V_r,V_a2),V_a1))
% 0.21/0.75 | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_a1),V_a2)) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_conversep_Ointros_0,axiom,
% 0.21/0.75 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_b),V_a))
% 0.21/0.75 | ~ hBOOL(hAPP(hAPP(V_r,V_a),V_b)) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom,
% 0.21/0.75 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.21/0.75 | 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)) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom,
% 0.21/0.75 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.21/0.75 | 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)) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom,
% 0.21/0.75 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.21/0.75 | 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) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom,
% 0.21/0.75 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.21/0.75 | 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) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom,
% 0.21/0.75 ( ~ class_OrderedGroup_Oab__semigroup__add(T_a)
% 0.21/0.75 | 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)) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom,
% 0.21/0.75 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
% 0.21/0.75 | 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)) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_comm__monoid__add_Omult__assoc_0,axiom,
% 0.21/0.75 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
% 0.21/0.75 | 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)) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_nat__add__assoc_0,axiom,
% 0.21/0.75 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)),V_k) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k)) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_nat__add__left__commute_0,axiom,
% 0.21/0.75 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_z)) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_add__cancel__21_1,axiom,
% 0.21/0.75 ( ~ class_OrderedGroup_Oab__group__add(T_a)
% 0.21/0.75 | 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)) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_class__semiring_Oadd__a_0,axiom,
% 0.21/0.75 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.21/0.75 | 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) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_add__nonneg__nonneg_0,axiom,
% 0.21/0.75 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
% 0.21/0.75 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),T_a)
% 0.21/0.75 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
% 0.21/0.75 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_add__nonneg__eq__0__iff_2,axiom,
% 0.21/0.75 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
% 0.21/0.75 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.21/0.75 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.21/0.75 | 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) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_add__is__0_2,axiom,
% 0.21/0.75 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_double__eq__0__iff_1,axiom,
% 0.21/0.75 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
% 0.21/0.75 | 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) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_add__mono_0,axiom,
% 0.21/0.75 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a)
% 0.21/0.75 | c_lessequals(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)
% 0.21/0.75 | ~ c_lessequals(V_c,V_d,T_a)
% 0.21/0.75 | ~ c_lessequals(V_a,V_b,T_a) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_zero__le__double__add__iff__zero__le__single__add_1,axiom,
% 0.21/0.75 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
% 0.21/0.75 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a)
% 0.21/0.75 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_zero__le__double__add__iff__zero__le__single__add_0,axiom,
% 0.21/0.75 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
% 0.21/0.75 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
% 0.21/0.75 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_add__is__1_4,axiom,
% 0.21/0.75 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_listsp_ONil_0,axiom,
% 0.21/0.75 c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_zero__le__power_0,axiom,
% 0.21/0.75 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.21/0.75 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
% 0.21/0.75 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_accp__downwards_0,axiom,
% 0.21/0.75 ( c_Wellfounded_Oaccp(V_r,V_b,T_a)
% 0.21/0.75 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_a))
% 0.21/0.75 | ~ c_Wellfounded_Oaccp(V_r,V_a,T_a) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_accp__downwards__aux_0,axiom,
% 0.21/0.75 ( c_Wellfounded_Oaccp(V_r,V_b,T_a)
% 0.21/0.75 | ~ c_Wellfounded_Oaccp(V_r,V_a,T_a)
% 0.21/0.75 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_a)) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_IT__implies__termi_0,axiom,
% 0.21/0.75 ( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB)
% 0.21/0.75 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_termi__implies__IT_0,axiom,
% 0.21/0.75 ( hBOOL(hAPP(c_InductTermi_OIT,V_r))
% 0.21/0.75 | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_r,tc_Lambda_OdB) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_one__le__power_0,axiom,
% 0.21/0.75 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.21/0.75 | c_lessequals(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
% 0.21/0.75 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_add__Suc__right_0,axiom,
% 0.21/0.75 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_Suc(V_n)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_add__Suc_0,axiom,
% 0.21/0.75 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(V_m)),V_n) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_add__increasing_0,axiom,
% 0.21/0.75 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
% 0.21/0.75 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
% 0.21/0.75 | c_lessequals(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a)
% 0.21/0.75 | ~ c_lessequals(V_b,V_c,T_a)
% 0.21/0.75 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_add__increasing2_0,axiom,
% 0.21/0.75 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
% 0.21/0.75 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
% 0.21/0.75 | c_lessequals(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a)
% 0.21/0.75 | ~ c_lessequals(V_b,V_a,T_a)
% 0.21/0.75 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom,
% 0.21/0.75 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.21/0.75 | 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) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_comm__monoid__add_Omult__commute_0,axiom,
% 0.21/0.75 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
% 0.21/0.75 | 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) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_nat__add__commute_0,axiom,
% 0.21/0.75 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_class__semiring_Oadd__c_0,axiom,
% 0.21/0.75 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.21/0.75 | 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) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_foldl__assoc_0,axiom,
% 0.21/0.75 ( ~ class_OrderedGroup_Osemigroup__add(T_a)
% 0.21/0.75 | 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)) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_class__ringb_Oadd__r0__iff_0,axiom,
% 0.21/0.75 ( ~ class_Ring__and__Field_Oidom(T_a)
% 0.21/0.75 | ~ class_Int_Onumber__ring(T_a)
% 0.21/0.75 | V_x != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_a)
% 0.21/0.75 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_add__eq__self__zero_0,axiom,
% 0.21/0.75 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != V_m
% 0.21/0.75 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_natgb_Oadd__r0__iff_0,axiom,
% 0.21/0.75 ( V_x != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_a)
% 0.21/0.75 | V_a = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_add__nonneg__eq__0__iff_1,axiom,
% 0.21/0.75 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
% 0.21/0.75 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y) != c_HOL_Ozero__class_Ozero(T_a)
% 0.21/0.75 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
% 0.21/0.75 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
% 0.21/0.75 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_add__nonneg__eq__0__iff_0,axiom,
% 0.21/0.75 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
% 0.21/0.75 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y) != c_HOL_Ozero__class_Ozero(T_a)
% 0.21/0.75 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
% 0.21/0.75 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
% 0.21/0.75 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_add__is__0_0,axiom,
% 0.21/0.75 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_HOL_Ozero__class_Ozero(tc_nat)
% 0.21/0.75 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_add__is__0_1,axiom,
% 0.21/0.75 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_HOL_Ozero__class_Ozero(tc_nat)
% 0.21/0.75 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_double__eq__0__iff_0,axiom,
% 0.21/0.75 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
% 0.21/0.75 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a) != c_HOL_Ozero__class_Ozero(T_a)
% 0.21/0.75 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_foldr__conv__foldl_0,axiom,
% 0.21/0.75 ( ~ class_OrderedGroup_Oab__semigroup__add(T_a)
% 0.21/0.75 | 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) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_not__Nil__step1_0,axiom,
% 0.21/0.75 ~ c_ListOrder_Ostep1(V_r,c_List_Olist_ONil(T_a),V_xs,T_a) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_not__step1__Nil_0,axiom,
% 0.21/0.75 ~ c_ListOrder_Ostep1(V_r,V_xs,c_List_Olist_ONil(T_a),T_a) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_one__is__add_1,axiom,
% 0.21/0.75 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)
% 0.21/0.75 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
% 0.21/0.75 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_one__is__add_2,axiom,
% 0.21/0.75 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)
% 0.21/0.75 | V_m = c_HOL_Ozero__class_Ozero(tc_nat)
% 0.21/0.75 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_foldl__absorb0_0,axiom,
% 0.21/0.75 ( ~ class_OrderedGroup_Omonoid__add(T_a)
% 0.21/0.75 | 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) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_foldl__Nil_0,axiom,
% 0.21/0.75 c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_one__neq__zero_0,axiom,
% 0.21/0.75 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
% 0.21/0.75 | c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_conversep__eq_0,axiom,
% 0.21/0.75 c_Predicate_Oconversep(c_fequal(T_a),T_a,T_a) = c_fequal(T_a) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_zero__le__one_0,axiom,
% 0.21/0.75 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.21/0.75 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_one__is__add_4,axiom,
% 0.21/0.75 c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_not__one__le__zero_0,axiom,
% 0.21/0.75 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.21/0.75 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_order__eq__iff_2,axiom,
% 0.21/0.75 ( ~ class_Orderings_Oorder(T_a)
% 0.21/0.75 | V_x = V_y
% 0.21/0.75 | ~ c_lessequals(V_y,V_x,T_a)
% 0.21/0.75 | ~ c_lessequals(V_x,V_y,T_a) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_order__antisym_0,axiom,
% 0.21/0.75 ( ~ class_Orderings_Oorder(T_a)
% 0.21/0.75 | V_x = V_y
% 0.21/0.75 | ~ c_lessequals(V_y,V_x,T_a)
% 0.21/0.75 | ~ c_lessequals(V_x,V_y,T_a) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_order__antisym__conv_0,axiom,
% 0.21/0.75 ( ~ class_Orderings_Oorder(T_a)
% 0.21/0.75 | V_x = V_y
% 0.21/0.75 | ~ c_lessequals(V_x,V_y,T_a)
% 0.21/0.75 | ~ c_lessequals(V_y,V_x,T_a) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_add__le__cancel__right_1,axiom,
% 0.21/0.75 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
% 0.21/0.75 | c_lessequals(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)
% 0.21/0.75 | ~ c_lessequals(V_a,V_b,T_a) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_add__le__cancel__right_0,axiom,
% 0.21/0.75 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
% 0.21/0.75 | c_lessequals(V_a,V_b,T_a)
% 0.21/0.75 | ~ c_lessequals(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) ) ).
% 0.21/0.75
% 0.21/0.75 cnf(cls_add__le__cancel__left_1,axiom,
% 0.21/0.75 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
% 0.21/0.75 | c_lessequals(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)
% 0.21/0.75 | ~ c_lessequals(V_a,V_b,T_a) ) ).
% 0.21/0.75
% 0.21/0.76 cnf(cls_add__le__cancel__left_0,axiom,
% 0.21/0.76 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
% 0.21/0.76 | c_lessequals(V_a,V_b,T_a)
% 0.21/0.76 | ~ c_lessequals(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) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_add__right__mono_0,axiom,
% 0.21/0.76 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a)
% 0.21/0.76 | c_lessequals(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)
% 0.21/0.76 | ~ c_lessequals(V_a,V_b,T_a) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_add__left__mono_0,axiom,
% 0.21/0.76 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a)
% 0.21/0.76 | c_lessequals(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)
% 0.21/0.76 | ~ c_lessequals(V_a,V_b,T_a) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_App__eq__foldl__conv_0,axiom,
% 0.21/0.76 ( 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)
% 0.21/0.76 | hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) = V_t ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_power__0_0,axiom,
% 0.21/0.76 ( ~ class_Power_Opower(T_a)
% 0.21/0.76 | c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_class__semiring_Opwr__0_0,axiom,
% 0.21/0.76 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
% 0.21/0.76 | c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_list__app__typeD_1,axiom,
% 0.21/0.76 ( c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts))
% 0.21/0.76 | ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_conversep__conversep_0,axiom,
% 0.21/0.76 c_Predicate_Oconversep(c_Predicate_Oconversep(V_r,T_a,T_b),T_b,T_a) = V_r ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_double__add__le__zero__iff__single__add__le__zero_1,axiom,
% 0.21/0.76 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
% 0.21/0.76 | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.21/0.76 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_double__add__le__zero__iff__single__add__le__zero_0,axiom,
% 0.21/0.76 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
% 0.21/0.76 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.21/0.76 | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_xt1_I6_J_0,axiom,
% 0.21/0.76 ( ~ class_Orderings_Oorder(T_a)
% 0.21/0.76 | c_lessequals(V_z,V_x,T_a)
% 0.21/0.76 | ~ c_lessequals(V_z,V_y,T_a)
% 0.21/0.76 | ~ c_lessequals(V_y,V_x,T_a) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_add__nonpos__nonpos_0,axiom,
% 0.21/0.76 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
% 0.21/0.76 | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.21/0.76 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
% 0.21/0.76 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_order__trans_0,axiom,
% 0.21/0.76 ( ~ class_Orderings_Opreorder(T_a)
% 0.21/0.76 | c_lessequals(V_x,V_z,T_a)
% 0.21/0.76 | ~ c_lessequals(V_y,V_z,T_a)
% 0.21/0.76 | ~ c_lessequals(V_x,V_y,T_a) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_order__eq__iff_0,axiom,
% 0.21/0.76 ( ~ class_Orderings_Oorder(T_a)
% 0.21/0.76 | c_lessequals(V_x,V_x,T_a) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_order__eq__refl_0,axiom,
% 0.21/0.76 ( ~ class_Orderings_Opreorder(T_a)
% 0.21/0.76 | c_lessequals(V_x,V_x,T_a) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_le__add__right__mono_0,axiom,
% 0.21/0.76 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
% 0.21/0.76 | c_lessequals(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d),T_a)
% 0.21/0.76 | ~ c_lessequals(V_c,V_d,T_a)
% 0.21/0.76 | ~ c_lessequals(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_add__is__1_5,axiom,
% 0.21/0.76 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_of__nat__add_0,axiom,
% 0.21/0.76 ( ~ class_Ring__and__Field_Osemiring__1(T_a)
% 0.21/0.76 | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_App__eq__foldl__conv_4,axiom,
% 0.21/0.76 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) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_add__is__1_1,axiom,
% 0.21/0.76 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
% 0.21/0.76 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
% 0.21/0.76 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_add__is__1_2,axiom,
% 0.21/0.76 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
% 0.21/0.76 | V_m = c_HOL_Ozero__class_Ozero(tc_nat)
% 0.21/0.76 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_accp_Ocases_0,axiom,
% 0.21/0.76 ( c_Wellfounded_Oaccp(V_r,V_y,T_a)
% 0.21/0.76 | ~ hBOOL(hAPP(hAPP(V_r,V_y),V_a))
% 0.21/0.76 | ~ c_Wellfounded_Oaccp(V_r,V_a,T_a) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_linorder__linear_0,axiom,
% 0.21/0.76 ( ~ class_Orderings_Olinorder(T_a)
% 0.21/0.76 | c_lessequals(V_y,V_x,T_a)
% 0.21/0.76 | c_lessequals(V_x,V_y,T_a) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_accp__downward_0,axiom,
% 0.21/0.76 ( c_Wellfounded_Oaccp(V_r,V_a,T_a)
% 0.21/0.76 | ~ hBOOL(hAPP(hAPP(V_r,V_a),V_b))
% 0.21/0.76 | ~ c_Wellfounded_Oaccp(V_r,V_b,T_a) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_rtranclp_Ortrancl__into__rtrancl_0,axiom,
% 0.21/0.76 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_c))
% 0.21/0.76 | ~ hBOOL(hAPP(hAPP(V_r,V_b),V_c))
% 0.21/0.76 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_b)) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_converse__rtranclp__into__rtranclp_0,axiom,
% 0.21/0.76 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_c))
% 0.21/0.76 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_c))
% 0.21/0.76 | ~ hBOOL(hAPP(hAPP(V_r,V_a),V_b)) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_dB_Osize_I3_J_0,axiom,
% 0.21/0.76 c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(V_dB)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(V_dB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_dB_Osize_I2_J_0,axiom,
% 0.21/0.76 c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(V_dB1)),c_Lambda_OdB_OdB__size(V_dB2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_subst__App_0,axiom,
% 0.21/0.76 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)) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_var__app__typesE_1,axiom,
% 0.21/0.76 ( c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xvar__app__typesE__1__1(V_T,V_e,V_i,V_ts))
% 0.21/0.76 | ~ 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) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_type_Osize_I4_J_0,axiom,
% 0.21/0.76 c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2),tc_Type_Otype) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(V_type1,tc_Type_Otype)),c_Nat_Osize__class_Osize(V_type2,tc_Type_Otype))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_subst__eq_0,axiom,
% 0.21/0.76 c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k) = V_u ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_n__not__Suc__n_0,axiom,
% 0.21/0.76 V_n != c_Suc(V_n) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_Suc__n__not__n_0,axiom,
% 0.21/0.76 c_Suc(V_n) != V_n ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_var__app__types_0,axiom,
% 0.21/0.76 ( 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)
% 0.21/0.76 | ~ 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)
% 0.21/0.76 | ~ c_Type_Otypings(V_e,V_ts,V_Ts)
% 0.21/0.76 | ~ 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) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_apps__preserves__beta2_0,axiom,
% 0.21/0.76 ( 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)))
% 0.21/0.76 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_power__eq__0__iff_0,axiom,
% 0.21/0.76 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
% 0.21/0.76 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
% 0.21/0.76 | ~ class_Ring__and__Field_Omult__zero(T_a)
% 0.21/0.76 | ~ class_Power_Opower(T_a)
% 0.21/0.76 | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a)
% 0.21/0.76 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_field__power__not__zero_0,axiom,
% 0.21/0.76 ( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(T_a)
% 0.21/0.76 | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a)
% 0.21/0.76 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_type_Osize_I2_J_0,axiom,
% 0.21/0.76 c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(V_type1)),c_Type_Otype_Otype__size(V_type2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_power__le__imp__le__base_0,axiom,
% 0.21/0.76 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.21/0.76 | c_lessequals(V_a,V_b,T_a)
% 0.21/0.76 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
% 0.21/0.76 | ~ c_lessequals(c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a),c_Power_Opower__class_Opower(V_b,c_Suc(V_n),T_a),T_a) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_foldl__foldr1_0,axiom,
% 0.21/0.76 ( ~ class_OrderedGroup_Omonoid__add(T_a)
% 0.21/0.76 | 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) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_Suc__neq__Zero_0,axiom,
% 0.21/0.76 c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_nat_Osimps_I3_J_0,axiom,
% 0.21/0.76 c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_apps__preserves__betas_0,axiom,
% 0.21/0.76 ( 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)))
% 0.21/0.76 | ~ c_ListOrder_Ostep1(c_Lambda_Obeta,V_rs,V_ss,tc_Lambda_OdB) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_lift__preserves__beta_H_0,axiom,
% 0.21/0.76 ( 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)))
% 0.21/0.76 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_Abs__eq__apps__conv_1,axiom,
% 0.21/0.76 ( c_Lambda_OdB_OAbs(V_r) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)
% 0.21/0.76 | V_ss = c_List_Olist_ONil(tc_Lambda_OdB) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_lift__IT_0,axiom,
% 0.21/0.76 ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(V_t,V_i)))
% 0.21/0.76 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_r__into__rtranclp_0,axiom,
% 0.21/0.76 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_y))
% 0.21/0.76 | ~ hBOOL(hAPP(hAPP(V_r,V_x),V_y)) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_nat_Oinject_0,axiom,
% 0.21/0.76 ( c_Suc(V_nat) != c_Suc(V_nat_H)
% 0.21/0.76 | V_nat = V_nat_H ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_Suc__inject_0,axiom,
% 0.21/0.76 ( c_Suc(V_x) != c_Suc(V_y)
% 0.21/0.76 | V_x = V_y ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_subst__preserves__beta2_H_0,axiom,
% 0.21/0.76 ( 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)))
% 0.21/0.76 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_subst__preserves__beta_H_0,axiom,
% 0.21/0.76 ( 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)))
% 0.21/0.76 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_of__nat__eq__iff_0,axiom,
% 0.21/0.76 ( ~ class_Nat_Osemiring__char__0(T_a)
% 0.21/0.76 | c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a) != c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)
% 0.21/0.76 | V_m = V_n ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_lift_Osimps_I2_J_0,axiom,
% 0.21/0.76 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)) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_subst__preserves__beta2_0,axiom,
% 0.21/0.76 ( 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)))
% 0.21/0.76 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_Zero__neq__Suc_0,axiom,
% 0.21/0.76 c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_nat_Osimps_I2_J_0,axiom,
% 0.21/0.76 c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_power__0__Suc_0,axiom,
% 0.21/0.76 ( ~ class_Ring__and__Field_Osemiring__0(T_a)
% 0.21/0.76 | ~ class_Power_Opower(T_a)
% 0.21/0.76 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Suc(V_n),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_list__app__typeE_0,axiom,
% 0.21/0.76 ( 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))
% 0.21/0.76 | ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_rtranclp__trans_0,axiom,
% 0.21/0.76 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_z))
% 0.21/0.76 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_y),V_z))
% 0.21/0.76 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_y)) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_Nitpick_Ortranclp__def_1,axiom,
% 0.21/0.76 hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_x)) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_rtranclp_Ortrancl__refl_0,axiom,
% 0.21/0.76 hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_a)) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_subst__preserves__beta_0,axiom,
% 0.21/0.76 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(V_r,V_t,V_i)),c_Lambda_Osubst(V_s,V_t,V_i)))
% 0.21/0.76 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_power__0__left_0,axiom,
% 0.21/0.76 ( ~ class_Ring__and__Field_Osemiring__0(T_a)
% 0.21/0.76 | ~ class_Power_Opower(T_a)
% 0.21/0.76 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_double__induction__lemma_0,axiom,
% 0.21/0.76 ( ~ 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)
% 0.21/0.76 | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_s,tc_Lambda_OdB)
% 0.21/0.76 | 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) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_list__app__typeI_0,axiom,
% 0.21/0.76 ( c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T)
% 0.21/0.76 | ~ c_Type_Otypings(V_e,V_ts,V_Ts)
% 0.21/0.76 | ~ c_Type_Otyping(V_e,V_t,c_List_Ofoldr(c_Type_Otype_OFun,V_Ts,V_T,tc_Type_Otype,tc_Type_Otype)) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_Var__eq__apps__conv_2,axiom,
% 0.21/0.76 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) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_dB_Osize_I5_J_0,axiom,
% 0.21/0.76 c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(V_dB1,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(V_dB2,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_Abs__eq__apps__conv_2,axiom,
% 0.21/0.76 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) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_foldl__foldr1__lemma_0,axiom,
% 0.21/0.76 ( ~ class_OrderedGroup_Omonoid__add(T_a)
% 0.21/0.76 | 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)) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_apps__eq__Abs__conv_1,axiom,
% 0.21/0.76 ( c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(V_r)
% 0.21/0.76 | V_ss = c_List_Olist_ONil(tc_Lambda_OdB) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_apps__eq__tail__conv_0,axiom,
% 0.21/0.76 ( 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)
% 0.21/0.76 | V_r = V_s ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_dB_Osize_I6_J_0,axiom,
% 0.21/0.76 c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(V_dB),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(V_dB,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_subst__lift_0,axiom,
% 0.21/0.76 c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_apps__eq__Abs__conv_2,axiom,
% 0.21/0.76 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) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_lift__preserves__beta_0,axiom,
% 0.21/0.76 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(V_r,V_i)),c_Lambda_Olift(V_s,V_i)))
% 0.21/0.76 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_Var__eq__apps__conv_1,axiom,
% 0.21/0.76 ( c_Lambda_OdB_OVar(V_m) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)
% 0.21/0.76 | V_ss = c_List_Olist_ONil(tc_Lambda_OdB) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_list__app__typeD_0,axiom,
% 0.21/0.76 ( 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))
% 0.21/0.76 | ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_head__Var__reduction_0,axiom,
% 0.21/0.76 ( 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)
% 0.21/0.76 | ~ 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)) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_power__inject__base_0,axiom,
% 0.21/0.76 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.21/0.76 | c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) != c_Power_Opower__class_Opower(V_b,c_Suc(V_n),T_a)
% 0.21/0.76 | V_a = V_b
% 0.21/0.76 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
% 0.21/0.76 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_rtranclp__idemp_0,axiom,
% 0.21/0.76 c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(V_r,T_a),T_a) = c_Transitive__Closure_Ortranclp(V_r,T_a) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_dB_Osimps_I5_J_0,axiom,
% 0.21/0.76 hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) != c_Lambda_OdB_OVar(V_nat) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_type_Osimps_I5_J_0,axiom,
% 0.21/0.76 c_Type_Otype_Otype__case(V_f1,V_f2,c_Type_Otype_OAtom(V_nat),T_a) = hAPP(V_f1,V_nat) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_abs_0,axiom,
% 0.21/0.76 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(V_s)),c_Lambda_OdB_OAbs(V_t)))
% 0.21/0.76 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t)) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_beta__cases_I2_J_0,axiom,
% 0.21/0.76 ( V_s = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(V_r,V_s))
% 0.21/0.76 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(V_r)),V_s)) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_Abs__App__neq__Var__apps_0,axiom,
% 0.21/0.76 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) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_subst__lemma_0,axiom,
% 0.21/0.76 ( ~ c_Type_Otyping(V_e_H,V_u,V_U)
% 0.21/0.76 | ~ c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)
% 0.21/0.76 | c_Type_Otyping(V_e_H,c_Lambda_Osubst(V_t,V_u,V_i),V_T) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_app__Var__IT_0,axiom,
% 0.21/0.76 ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),c_Lambda_OdB_OVar(V_i))))
% 0.21/0.76 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_subject__reduction_H_0,axiom,
% 0.21/0.76 ( c_Type_Otyping(V_e,V_t_H,V_T)
% 0.21/0.76 | ~ c_Type_Otyping(V_e,V_t,V_T)
% 0.21/0.76 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H)) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_type_Osize_I1_J_0,axiom,
% 0.21/0.76 c_Type_Otype_Otype__size(c_Type_Otype_OAtom(V_nat)) = c_HOL_Ozero__class_Ozero(tc_nat) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_appL_0,axiom,
% 0.21/0.76 ( 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)))
% 0.21/0.76 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t)) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_appR_0,axiom,
% 0.21/0.76 ( 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)))
% 0.21/0.76 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t)) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_rtrancl__beta__App_0,axiom,
% 0.21/0.76 ( 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)))
% 0.21/0.76 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H))
% 0.21/0.76 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H)) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_Lambda_0,axiom,
% 0.21/0.76 ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(V_r)))
% 0.21/0.76 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_r)) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_type_Osplit_0,axiom,
% 0.21/0.76 ( ~ hBOOL(hAPP(V_P,c_Type_Otype_Otype__case(V_f1,V_f2,c_Type_Otype_OAtom(V_nat),t_a)))
% 0.21/0.76 | hBOOL(hAPP(V_P,hAPP(V_f1,V_nat))) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_type_Osplit__asm_0,axiom,
% 0.21/0.76 ( ~ hBOOL(hAPP(V_P,c_Type_Otype_Otype__case(V_f1,V_f2,c_Type_Otype_OAtom(V_xc),t_a)))
% 0.21/0.76 | hBOOL(hAPP(V_P,hAPP(V_f1,V_xc))) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_rtrancl__beta__AppL_0,axiom,
% 0.21/0.76 ( 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)))
% 0.21/0.76 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H)) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_rtrancl__beta__AppR_0,axiom,
% 0.21/0.76 ( 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)))
% 0.21/0.76 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H)) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_Abs__eq__apps__conv_0,axiom,
% 0.21/0.76 ( c_Lambda_OdB_OAbs(V_r) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)
% 0.21/0.76 | c_Lambda_OdB_OAbs(V_r) = V_s ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_of__nat__0_0,axiom,
% 0.21/0.76 ( ~ class_Ring__and__Field_Osemiring__1(T_a)
% 0.21/0.76 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_type__induct_2,axiom,
% 0.21/0.76 ( hBOOL(hAPP(V_P,V_T))
% 0.21/0.76 | ~ hBOOL(hAPP(V_P,c_Type_Osko__Type__Xtype__induct__1__1(V_P))) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_power__eq__0__iff_1,axiom,
% 0.21/0.76 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
% 0.21/0.76 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
% 0.21/0.76 | ~ class_Ring__and__Field_Omult__zero(T_a)
% 0.21/0.76 | ~ class_Power_Opower(T_a)
% 0.21/0.76 | c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_typing__elims_I2_J_1,axiom,
% 0.21/0.76 ( c_Type_Otyping(V_e,V_u,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u))
% 0.21/0.76 | ~ c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_typing__elims_I3_J_1,axiom,
% 0.21/0.76 ( c_Type_Otyping(c_Type_Oshift(V_e,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xtyping__elims__3__1(V_T,V_e,V_t),tc_Type_Otype),V_t,c_Type_Osko__Type__Xtyping__elims__3__2(V_T,V_e,V_t))
% 0.21/0.76 | ~ c_Type_Otyping(V_e,c_Lambda_OdB_OAbs(V_t),V_T) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_App_I4_J_0,axiom,
% 0.21/0.76 hBOOL(hAPP(c_InductTermi_OIT,v_ta____)) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_head__Var__reduction_1,axiom,
% 0.21/0.76 ( 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)
% 0.21/0.76 | ~ 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)) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_rtrancl__beta__Abs_0,axiom,
% 0.21/0.76 ( 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)))
% 0.21/0.76 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H)) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_var__app__typesE_0,axiom,
% 0.21/0.76 ( 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))
% 0.21/0.76 | ~ 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) ) ).
% 0.21/0.76
% 0.21/0.76 cnf(cls_dB_Osize_I1_J_0,axiom,
% 0.21/0.77 c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(V_nat)) = c_HOL_Ozero__class_Ozero(tc_nat) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_abs__typeE_0,axiom,
% 0.21/0.77 ( c_Type_Otyping(c_Type_Oshift(V_e,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xabs__typeE__1__1(V_e,V_t),tc_Type_Otype),V_t,c_Type_Osko__Type__Xabs__typeE__1__2(V_e,V_t))
% 0.21/0.77 | ~ c_Type_Otyping(V_e,c_Lambda_OdB_OAbs(V_t),V_T) ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_type_Osimps_I1_J_0,axiom,
% 0.21/0.77 ( c_Type_Otype_OAtom(V_nat) != c_Type_Otype_OAtom(V_nat_H)
% 0.21/0.77 | V_nat = V_nat_H ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_Var__IT_0,axiom,
% 0.21/0.77 hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n))) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_shift__commute_0,axiom,
% 0.21/0.77 c_Type_Oshift(c_Type_Oshift(V_e,V_i,V_U,T_a),c_HOL_Ozero__class_Ozero(tc_nat),V_T,T_a) = c_Type_Oshift(c_Type_Oshift(V_e,c_HOL_Ozero__class_Ozero(tc_nat),V_T,T_a),c_Suc(V_i),V_U,T_a) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_dB_Osimps_I6_J_0,axiom,
% 0.21/0.77 c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_Beta_0,axiom,
% 0.21/0.77 ( 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)))
% 0.21/0.77 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_s))
% 0.21/0.77 | ~ 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))) ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_shift__eq_0,axiom,
% 0.21/0.77 hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_Var__apps__neq__Abs__apps_0,axiom,
% 0.21/0.77 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) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_dB_Osimps_I3_J_0,axiom,
% 0.21/0.77 ( c_Lambda_OdB_OAbs(V_dB) != c_Lambda_OdB_OAbs(V_dB_H)
% 0.21/0.77 | V_dB = V_dB_H ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_dB_Osimps_I4_J_0,axiom,
% 0.21/0.77 c_Lambda_OdB_OVar(V_nat) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_Var__eq__apps__conv_0,axiom,
% 0.21/0.77 ( c_Lambda_OdB_OVar(V_m) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)
% 0.21/0.77 | c_Lambda_OdB_OVar(V_m) = V_s ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_type_Orecs_I1_J_0,axiom,
% 0.21/0.77 c_Type_Otype_Otype__rec(V_f1,V_f2,c_Type_Otype_OAtom(V_nat),T_a) = hAPP(V_f1,V_nat) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_apps__preserves__beta_0,axiom,
% 0.21/0.77 ( 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)))
% 0.21/0.77 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)) ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_beta_0,axiom,
% 0.21/0.77 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)))) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_var__app__type__eq_0,axiom,
% 0.21/0.77 ( V_T = V_U
% 0.21/0.77 | ~ 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)
% 0.21/0.77 | ~ 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) ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_dB_Osimps_I2_J_1,axiom,
% 0.21/0.77 ( hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H)
% 0.21/0.77 | V_dB2 = V_dB2_H ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_dB_Osimps_I2_J_0,axiom,
% 0.21/0.77 ( hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H)
% 0.21/0.77 | V_dB1 = V_dB1_H ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_IT_OVar_0,axiom,
% 0.21/0.77 ( 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)))
% 0.21/0.77 | ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB) ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_Abs__apps__eq__Abs__apps__conv_1,axiom,
% 0.21/0.77 ( 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)
% 0.21/0.77 | V_rs = V_ss ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_Abs__apps__eq__Abs__apps__conv_0,axiom,
% 0.21/0.77 ( 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)
% 0.21/0.77 | V_r = V_s ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_apps__eq__Abs__conv_0,axiom,
% 0.21/0.77 ( c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(V_r)
% 0.21/0.77 | V_s = c_Lambda_OdB_OAbs(V_r) ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_beta__cases_I1_J_0,axiom,
% 0.21/0.77 ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_beta__cases_I2_J_1,axiom,
% 0.21/0.77 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),c_Lambda_Osko__Lambda__Xbeta__cases__2__1(V_r,V_s)))
% 0.21/0.77 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(V_r)),V_s)) ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_type_Osize_I3_J_0,axiom,
% 0.21/0.77 c_Nat_Osize__class_Osize(c_Type_Otype_OAtom(V_nat),tc_Type_Otype) = c_HOL_Ozero__class_Ozero(tc_nat) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_power__0__left_1,axiom,
% 0.21/0.77 ( ~ class_Ring__and__Field_Osemiring__0(T_a)
% 0.21/0.77 | ~ class_Power_Opower(T_a)
% 0.21/0.77 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a)
% 0.21/0.77 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_power__eq__0__iff_2,axiom,
% 0.21/0.77 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
% 0.21/0.77 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
% 0.21/0.77 | ~ class_Ring__and__Field_Omult__zero(T_a)
% 0.21/0.77 | ~ class_Power_Opower(T_a)
% 0.21/0.77 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a)
% 0.21/0.77 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_subst__Var__IT_0,axiom,
% 0.21/0.77 ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j)))
% 0.21/0.77 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_r)) ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_Var__apps__eq__Var__apps__conv_1,axiom,
% 0.21/0.77 ( 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)
% 0.21/0.77 | V_rs = V_ss ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_Var__apps__eq__Var__apps__conv_0,axiom,
% 0.21/0.77 ( 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)
% 0.21/0.77 | V_m = V_n ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_dB_Osimps_I9_J_0,axiom,
% 0.21/0.77 c_Lambda_OdB_OAbs(V_dB_H) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_dB_Osimps_I1_J_0,axiom,
% 0.21/0.77 ( c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OVar(V_nat_H)
% 0.21/0.77 | V_nat = V_nat_H ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_dB_Osimps_I8_J_0,axiom,
% 0.21/0.77 hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != c_Lambda_OdB_OAbs(V_dB_H) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_dB_Osimps_I7_J_0,axiom,
% 0.21/0.77 c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_dB_Osize_I4_J_0,axiom,
% 0.21/0.77 c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(V_nat),tc_Lambda_OdB) = c_HOL_Ozero__class_Ozero(tc_nat) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_subst__type__IT_0,axiom,
% 0.21/0.77 ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(V_t,V_u,V_i)))
% 0.21/0.77 | ~ c_Type_Otyping(V_e,V_u,V_U)
% 0.21/0.77 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
% 0.21/0.77 | ~ c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_U,tc_Type_Otype),V_t,V_T)
% 0.21/0.77 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_lift__type_0,axiom,
% 0.21/0.77 ( c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_U,tc_Type_Otype),c_Lambda_Olift(V_t,V_i),V_T)
% 0.21/0.77 | ~ c_Type_Otyping(V_e,V_t,V_T) ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_type_Osimps_I4_J_0,axiom,
% 0.21/0.77 hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H) != c_Type_Otype_OAtom(V_nat) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_typing__elims_I3_J_0,axiom,
% 0.21/0.77 ( V_T = hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(V_T,V_e,V_t)),c_Type_Osko__Type__Xtyping__elims__3__2(V_T,V_e,V_t))
% 0.21/0.77 | ~ c_Type_Otyping(V_e,c_Lambda_OdB_OAbs(V_t),V_T) ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_subject__reduction_0,axiom,
% 0.21/0.77 ( c_Type_Otyping(V_e,V_t_H,V_T)
% 0.21/0.77 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H))
% 0.21/0.77 | ~ c_Type_Otyping(V_e,V_t,V_T) ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_type_Osimps_I2_J_0,axiom,
% 0.21/0.77 ( hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2) != hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H)
% 0.21/0.77 | V_type1 = V_type1_H ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_type_Osimps_I2_J_1,axiom,
% 0.21/0.77 ( hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2) != hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H)
% 0.21/0.77 | V_type2 = V_type2_H ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_type__induct_1,axiom,
% 0.21/0.77 ( c_Type_Osko__Type__Xtype__induct__1__1(V_P) != hAPP(hAPP(c_Type_Otype_OFun,V_T1),V_T2)
% 0.21/0.77 | hBOOL(hAPP(V_P,V_T))
% 0.21/0.77 | hBOOL(hAPP(V_P,V_T2)) ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_type__induct_0,axiom,
% 0.21/0.77 ( c_Type_Osko__Type__Xtype__induct__1__1(V_P) != hAPP(hAPP(c_Type_Otype_OFun,V_T1a),V_x)
% 0.21/0.77 | hBOOL(hAPP(V_P,V_T))
% 0.21/0.77 | hBOOL(hAPP(V_P,V_T1a)) ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_typing_OApp_0,axiom,
% 0.21/0.77 ( c_Type_Otyping(V_env,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_U)
% 0.21/0.77 | ~ c_Type_Otyping(V_env,V_t,V_T)
% 0.21/0.77 | ~ c_Type_Otyping(V_env,V_s,hAPP(hAPP(c_Type_Otype_OFun,V_T),V_U)) ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_App_I2_J_0,axiom,
% 0.21/0.77 hBOOL(hAPP(c_InductTermi_OIT,v_s____)) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_Abs_0,axiom,
% 0.21/0.77 ( c_Type_Otyping(V_env,c_Lambda_OdB_OAbs(V_t),hAPP(hAPP(c_Type_Otype_OFun,V_T),V_U))
% 0.21/0.77 | ~ c_Type_Otyping(c_Type_Oshift(V_env,c_HOL_Ozero__class_Ozero(tc_nat),V_T,tc_Type_Otype),V_t,V_U) ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_typing__elims_I1_J_0,axiom,
% 0.21/0.77 ( hAPP(V_e,V_i) = V_T
% 0.21/0.77 | ~ c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T) ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_App_I3_J_0,axiom,
% 0.21/0.77 c_Type_Otyping(v_ea____,v_ta____,v_Ta____) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_type_Orecs_I2_J_0,axiom,
% 0.21/0.77 c_Type_Otype_Otype__rec(V_f1,V_f2,hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2),T_a) = hAPP(hAPP(hAPP(hAPP(V_f2,V_type1),V_type2),c_Type_Otype_Otype__rec(V_f1,V_f2,V_type1,T_a)),c_Type_Otype_Otype__rec(V_f1,V_f2,V_type2,T_a)) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_type_Osimps_I6_J_0,axiom,
% 0.21/0.77 c_Type_Otype_Otype__case(V_f1,V_f2,hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2),T_a) = hAPP(hAPP(V_f2,V_type1),V_type2) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_App_I1_J_0,axiom,
% 0.21/0.77 c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_typing_OVar_0,axiom,
% 0.21/0.77 c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_type_Osplit__asm_1,axiom,
% 0.21/0.77 ( ~ hBOOL(hAPP(V_P,c_Type_Otype_Otype__case(V_f1,V_f2,hAPP(hAPP(c_Type_Otype_OFun,V_xa),V_xb),t_a)))
% 0.21/0.77 | hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_xa),V_xb))) ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_type_Osplit_1,axiom,
% 0.21/0.77 ( ~ hBOOL(hAPP(V_P,c_Type_Otype_Otype__case(V_f1,V_f2,hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2),t_a)))
% 0.21/0.77 | hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_type1),V_type2))) ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_type_Osimps_I3_J_0,axiom,
% 0.21/0.77 c_Type_Otype_OAtom(V_nat) != hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_typing__elims_I2_J_0,axiom,
% 0.21/0.77 ( 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))
% 0.21/0.77 | ~ c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T) ) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_conjecture_0,negated_conjecture,
% 0.21/0.77 ~ c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)) ).
% 0.21/0.77
% 0.21/0.77 cnf(clsarity_fun__Orderings_Opreorder,axiom,
% 0.21/0.77 ( class_Orderings_Opreorder(tc_fun(T_2,T_1))
% 0.21/0.77 | ~ class_Orderings_Opreorder(T_1) ) ).
% 0.21/0.77
% 0.21/0.77 cnf(clsarity_fun__Orderings_Oorder,axiom,
% 0.21/0.77 ( class_Orderings_Oorder(tc_fun(T_2,T_1))
% 0.21/0.77 | ~ class_Orderings_Oorder(T_1) ) ).
% 0.21/0.77
% 0.21/0.77 cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
% 0.21/0.77 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ).
% 0.21/0.77
% 0.21/0.77 cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,axiom,
% 0.21/0.77 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ).
% 0.21/0.77
% 0.21/0.77 cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom,
% 0.21/0.77 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ).
% 0.21/0.77
% 0.21/0.77 cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
% 0.21/0.77 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ).
% 0.21/0.77
% 0.21/0.77 cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom,
% 0.21/0.77 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ).
% 0.21/0.77
% 0.21/0.77 cnf(clsarity_nat__Ring__and__Field_Ono__zero__divisors,axiom,
% 0.21/0.77 class_Ring__and__Field_Ono__zero__divisors(tc_nat) ).
% 0.21/0.77
% 0.21/0.77 cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom,
% 0.21/0.77 class_Ring__and__Field_Oordered__semidom(tc_nat) ).
% 0.21/0.77
% 0.21/0.77 cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
% 0.21/0.77 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ).
% 0.21/0.77
% 0.21/0.77 cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom,
% 0.21/0.77 class_OrderedGroup_Oab__semigroup__add(tc_nat) ).
% 0.21/0.77
% 0.21/0.77 cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom,
% 0.21/0.77 class_OrderedGroup_Ocomm__monoid__add(tc_nat) ).
% 0.21/0.77
% 0.21/0.77 cnf(clsarity_nat__Ring__and__Field_Ozero__neq__one,axiom,
% 0.21/0.77 class_Ring__and__Field_Ozero__neq__one(tc_nat) ).
% 0.21/0.77
% 0.21/0.77 cnf(clsarity_nat__OrderedGroup_Osemigroup__add,axiom,
% 0.21/0.77 class_OrderedGroup_Osemigroup__add(tc_nat) ).
% 0.21/0.77
% 0.21/0.77 cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom,
% 0.21/0.77 class_Ring__and__Field_Osemiring__1(tc_nat) ).
% 0.21/0.77
% 0.21/0.77 cnf(clsarity_nat__Ring__and__Field_Osemiring__0,axiom,
% 0.21/0.77 class_Ring__and__Field_Osemiring__0(tc_nat) ).
% 0.21/0.77
% 0.21/0.77 cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom,
% 0.21/0.77 class_Ring__and__Field_Omult__zero(tc_nat) ).
% 0.21/0.77
% 0.21/0.77 cnf(clsarity_nat__OrderedGroup_Omonoid__mult,axiom,
% 0.21/0.77 class_OrderedGroup_Omonoid__mult(tc_nat) ).
% 0.21/0.77
% 0.21/0.77 cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom,
% 0.21/0.77 class_OrderedGroup_Omonoid__add(tc_nat) ).
% 0.21/0.77
% 0.21/0.77 cnf(clsarity_nat__Nat_Osemiring__char__0,axiom,
% 0.21/0.77 class_Nat_Osemiring__char__0(tc_nat) ).
% 0.21/0.77
% 0.21/0.77 cnf(clsarity_nat__Orderings_Opreorder,axiom,
% 0.21/0.77 class_Orderings_Opreorder(tc_nat) ).
% 0.21/0.77
% 0.21/0.77 cnf(clsarity_nat__Orderings_Olinorder,axiom,
% 0.21/0.77 class_Orderings_Olinorder(tc_nat) ).
% 0.21/0.77
% 0.21/0.77 cnf(clsarity_nat__Orderings_Oorder,axiom,
% 0.21/0.77 class_Orderings_Oorder(tc_nat) ).
% 0.21/0.77
% 0.21/0.77 cnf(clsarity_nat__Power_Opower,axiom,
% 0.21/0.77 class_Power_Opower(tc_nat) ).
% 0.21/0.77
% 0.21/0.77 cnf(clsarity_bool__Orderings_Opreorder,axiom,
% 0.21/0.77 class_Orderings_Opreorder(tc_bool) ).
% 0.21/0.77
% 0.21/0.77 cnf(clsarity_bool__Orderings_Oorder,axiom,
% 0.21/0.77 class_Orderings_Oorder(tc_bool) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
% 0.21/0.77 hBOOL(hAPP(hAPP(c_fequal(T_a),V_x),V_x)) ).
% 0.21/0.77
% 0.21/0.77 cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom,
% 0.21/0.77 ( V_X = V_Y
% 0.21/0.77 | ~ hBOOL(hAPP(hAPP(c_fequal(T_a),V_X),V_Y)) ) ).
% 0.21/0.77
% 0.21/0.77 %------------------------------------------------------------------------------
% 0.21/0.77 %-------------------------------------------
% 0.21/0.77 % Proof found
% 0.21/0.77 % SZS status Theorem for theBenchmark
% 0.21/0.77 % SZS output start Proof
% 0.21/0.77 %ClaNum:437(EqnAxiom:141)
% 0.21/0.77 %VarNum:1607(SingletonVarNum:697)
% 0.21/0.77 %MaxLitNum:6
% 0.21/0.77 %MaxfuncDepth:5
% 0.21/0.77 %SharedTerms:61
% 0.21/0.77 %goalClause: 235
% 0.21/0.77 %singleGoalClaCount:1
% 0.21/0.77 [142]P1(a1)
% 0.21/0.77 [143]P12(a1)
% 0.21/0.77 [144]P13(a1)
% 0.21/0.77 [145]P27(a1)
% 0.21/0.77 [146]P14(a1)
% 0.21/0.77 [147]P15(a1)
% 0.21/0.77 [148]P31(a1)
% 0.21/0.77 [149]P34(a1)
% 0.21/0.77 [150]P17(a1)
% 0.21/0.77 [151]P2(a1)
% 0.21/0.77 [152]P18(a1)
% 0.21/0.77 [153]P19(a1)
% 0.21/0.77 [154]P21(a1)
% 0.21/0.77 [155]P22(a1)
% 0.21/0.77 [156]P23(a1)
% 0.21/0.77 [157]P23(a2)
% 0.21/0.77 [158]P25(a1)
% 0.21/0.77 [159]P26(a1)
% 0.21/0.77 [160]P26(a2)
% 0.21/0.77 [161]P24(a1)
% 0.21/0.77 [162]P28(a1)
% 0.21/0.77 [163]P29(a1)
% 0.21/0.77 [164]P3(a1)
% 0.21/0.77 [165]P32(a1)
% 0.21/0.77 [173]P4(a49,a47,a50)
% 0.21/0.77 [170]P35(f42(a7,a47))
% 0.21/0.77 [171]P35(f42(a7,a48))
% 0.21/0.77 [192]P4(a49,a48,f42(f42(a38,a50),a51))
% 0.21/0.77 [235]~P4(a49,a48,f42(f42(a38,a50),a51))
% 0.21/0.77 [221]~E(f25(x2211),x2211)
% 0.21/0.77 [225]~E(f25(x2251),f4(a1))
% 0.21/0.77 [166]E(f11(f3(x1661)),f4(a1))
% 0.21/0.77 [167]E(f37(f12(x1671)),f4(a1))
% 0.21/0.77 [168]E(f13(f3(x1681),a41),f4(a1))
% 0.21/0.77 [169]E(f13(f12(x1691),a45),f4(a1))
% 0.21/0.77 [172]P35(f42(a7,f3(x1721)))
% 0.21/0.77 [175]E(f42(f42(f5(a1),x1751),f4(a1)),x1751)
% 0.21/0.77 [181]E(f23(f43(x1811),x1811,x1811),f43(x1811))
% 0.21/0.77 [176]E(f42(f42(f5(a1),f4(a1)),x1761),x1761)
% 0.21/0.77 [184]E(f42(f42(f5(a1),f11(x1841)),f25(f4(a1))),f11(f8(x1841)))
% 0.21/0.77 [193]E(f42(f42(f5(a1),f13(x1931,a41)),f25(f4(a1))),f13(f8(x1931),a41))
% 0.21/0.77 [179]P5(x1791,f14(x1792),x1792)
% 0.21/0.77 [188]P4(x1881,f3(x1882),f42(x1881,x1882))
% 0.21/0.77 [227]~E(f8(x2271),f3(x2272))
% 0.21/0.77 [177]E(f22(f22(x1771,x1772),x1772),f22(x1771,x1772))
% 0.21/0.77 [180]E(f15(f3(x1801),x1802,x1801),x1802)
% 0.21/0.77 [189]E(f42(f42(f5(a1),x1891),x1892),f42(f42(f5(a1),x1892),x1891))
% 0.21/0.77 [190]P35(f42(f42(f43(x1901),x1902),x1902))
% 0.21/0.77 [191]E(f42(f42(f5(a1),f25(x1911)),x1912),f42(f42(f5(a1),x1911),f25(x1912)))
% 0.21/0.77 [205]E(f42(f42(f5(a1),f42(f42(f5(a1),f11(x2051)),f11(x2052))),f25(f4(a1))),f11(f42(f42(a10,x2051),x2052)))
% 0.21/0.77 [206]E(f42(f42(f5(a1),f42(f42(f5(a1),f37(x2061)),f37(x2062))),f25(f4(a1))),f37(f42(f42(a38,x2061),x2062)))
% 0.21/0.77 [209]E(f42(f42(f5(a1),f42(f42(f5(a1),f13(x2091,a41)),f13(x2092,a41))),f25(f4(a1))),f13(f42(f42(a10,x2091),x2092),a41))
% 0.21/0.77 [210]E(f42(f42(f5(a1),f42(f42(f5(a1),f13(x2101,a45)),f13(x2102,a45))),f25(f4(a1))),f13(f42(f42(a38,x2101),x2102),a45))
% 0.21/0.77 [211]P35(f42(f42(a9,f42(f42(a10,f8(x2111)),x2112)),f15(x2111,x2112,f4(a1))))
% 0.21/0.77 [234]~P35(f42(f42(a9,f3(x2341)),x2342))
% 0.21/0.77 [194]E(f25(f42(f42(f5(a1),x1941),x1942)),f42(f42(f5(a1),x1941),f25(x1942)))
% 0.21/0.77 [195]E(f25(f42(f42(f5(a1),x1951),x1952)),f42(f42(f5(a1),f25(x1951)),x1952))
% 0.21/0.77 [236]~P6(x2361,x2362,f14(x2363),x2363)
% 0.21/0.77 [237]~P6(x2371,f14(x2372),x2373,x2372)
% 0.21/0.77 [187]E(f15(f16(x1871,x1872),x1873,x1872),x1871)
% 0.21/0.77 [196]E(f23(f23(x1961,x1962,x1963),x1963,x1962),x1961)
% 0.21/0.77 [228]~E(f3(x2281),f42(f42(a10,x2282),x2283))
% 0.21/0.77 [229]~E(f8(x2291),f42(f42(a10,x2292),x2293))
% 0.21/0.77 [230]~E(f12(x2301),f42(f42(a38,x2302),x2303))
% 0.21/0.77 [231]~E(f42(f42(a10,x2311),x2312),f3(x2313))
% 0.21/0.77 [232]~E(f42(f42(a10,x2321),x2322),f8(x2323))
% 0.21/0.77 [233]~E(f42(f42(a38,x2331),x2332),f12(x2333))
% 0.21/0.77 [198]P35(f42(f42(f22(x1981,x1982),x1983),x1983))
% 0.21/0.77 [199]E(f42(f42(a10,f16(x1991,x1992)),f16(x1993,x1992)),f16(f42(f42(a10,x1991),x1993),x1992))
% 0.21/0.77 [202]E(f42(f42(f5(a1),x2021),f42(f42(f5(a1),x2022),x2023)),f42(f42(f5(a1),x2022),f42(f42(f5(a1),x2021),x2023)))
% 0.21/0.77 [204]E(f42(f42(f5(a1),f42(f42(f5(a1),x2041),x2042)),x2043),f42(f42(f5(a1),x2041),f42(f42(f5(a1),x2042),x2043)))
% 0.21/0.77 [200]E(f39(x2001,x2002,f12(x2003),x2004),f42(x2001,x2003))
% 0.21/0.77 [201]E(f40(x2011,x2012,f12(x2013),x2014),f42(x2011,x2013))
% 0.21/0.77 [208]E(f42(f26(x2081,x2082,x2083,x2084),x2082),x2083)
% 0.21/0.77 [212]E(f18(x2121,x2122,f14(x2123),x2124,x2123),x2122)
% 0.21/0.77 [213]E(f20(x2131,f14(x2132),x2133,x2132,x2134),x2133)
% 0.21/0.77 [239]~E(f18(a10,f8(x2391),x2392,a41,a41),f18(a10,f3(x2393),x2394,a41,a41))
% 0.21/0.77 [207]E(f42(f42(a10,f15(x2071,x2072,x2073)),f15(x2074,x2072,x2073)),f15(f42(f42(a10,x2071),x2074),x2072,x2073))
% 0.21/0.77 [238]~E(f42(f42(a10,f8(x2381)),x2382),f18(a10,f3(x2383),x2384,a41,a41))
% 0.21/0.77 [218]E(f26(f26(x2181,f4(a1),x2182,x2183),f25(x2184),x2185,x2183),f26(f26(x2181,x2184,x2185,x2183),f4(a1),x2182,x2183))
% 0.21/0.77 [203]E(f39(x2031,x2032,f42(f42(a38,x2033),x2034),x2035),f42(f42(x2032,x2033),x2034))
% 0.21/0.77 [219]E(f42(f42(f42(f42(x2191,x2192),x2193),f40(x2194,x2191,x2192,x2195)),f40(x2194,x2191,x2193,x2195)),f40(x2194,x2191,f42(f42(a38,x2192),x2193),x2195))
% 0.21/0.77 [246]~P34(x2461)+~E(f6(x2461),f4(x2461))
% 0.21/0.77 [264]~P27(x2641)+P7(f4(x2641),f6(x2641),x2641)
% 0.21/0.77 [293]~P27(x2931)+~P7(f6(x2931),f4(x2931),x2931)
% 0.21/0.77 [318]P8(f23(a9,a41,a41),x3181,a41)+~P35(f42(a7,x3181))
% 0.21/0.77 [325]~P8(f23(a9,a41,a41),x3251,a41)+P35(f42(a7,x3251))
% 0.21/0.77 [247]~P31(x2471)+E(f21(f4(a1),x2471),f4(x2471))
% 0.21/0.77 [269]~P16(x2691)+E(f42(f42(f5(x2691),f4(x2691)),f4(x2691)),f4(x2691))
% 0.21/0.77 [271]~P35(f42(a7,x2711))+P35(f42(a7,f8(x2711)))
% 0.21/0.77 [251]~P23(x2512)+P7(x2511,x2511,x2512)
% 0.21/0.77 [252]~P26(x2522)+P7(x2521,x2521,x2522)
% 0.21/0.77 [240]E(x2401,x2402)+~E(f3(x2401),f3(x2402))
% 0.21/0.77 [242]E(x2421,x2422)+~E(f25(x2421),f25(x2422))
% 0.21/0.77 [243]E(x2431,x2432)+~E(f8(x2431),f8(x2432))
% 0.21/0.77 [244]E(x2441,x2442)+~E(f12(x2441),f12(x2442))
% 0.21/0.77 [248]~P23(x2482)+P23(f46(x2481,x2482))
% 0.21/0.77 [249]~P26(x2492)+P26(f46(x2491,x2492))
% 0.21/0.77 [277]~P27(x2771)+P7(f4(x2771),f21(x2772,x2771),x2771)
% 0.21/0.77 [253]~P13(x2531)+E(f42(f42(f5(x2531),x2532),f4(x2531)),x2532)
% 0.21/0.77 [254]~P14(x2541)+E(f42(f42(f5(x2541),x2542),f4(x2541)),x2542)
% 0.21/0.77 [255]~P15(x2551)+E(f42(f42(f5(x2551),x2552),f4(x2551)),x2552)
% 0.21/0.77 [256]~P13(x2562)+E(f24(x2561,f4(a1),x2562),f6(x2562))
% 0.21/0.77 [257]~P25(x2572)+E(f24(x2571,f4(a1),x2572),f6(x2572))
% 0.21/0.77 [258]~P17(x2581)+E(f24(f6(x2581),x2582,x2581),f6(x2581))
% 0.21/0.77 [283]P35(f42(x2831,x2832))+~P35(f42(x2831,f27(x2831)))
% 0.21/0.77 [295]~P31(x2951)+E(f42(f42(f5(x2951),f6(x2951)),f21(x2952,x2951)),f21(f25(x2952),x2951))
% 0.21/0.77 [300]~P35(f42(a7,x3001))+P35(f42(a7,f16(x3001,x3002)))
% 0.21/0.77 [319]~P35(f42(f42(a9,x3191),x3192))+P35(f42(f42(a9,f8(x3191)),f8(x3192)))
% 0.21/0.77 [411]~P15(x4111)+E(f20(f5(x4111),x4112,f4(x4111),x4111,x4111),f18(f5(x4111),f4(x4111),x4112,x4111,x4111))
% 0.21/0.77 [260]~P13(x2601)+E(f42(f42(f5(x2601),f4(x2601)),x2602),x2602)
% 0.21/0.77 [261]~P14(x2611)+E(f42(f42(f5(x2611),f4(x2611)),x2612),x2612)
% 0.21/0.77 [262]~P15(x2621)+E(f42(f42(f5(x2621),f4(x2621)),x2622),x2622)
% 0.21/0.77 [266]E(x2661,f4(a1))+~E(f42(f42(f5(a1),x2662),x2661),x2662)
% 0.21/0.77 [267]E(x2671,f4(a1))+~E(f42(f42(f5(a1),x2672),x2671),f4(a1))
% 0.21/0.77 [268]E(x2681,f4(a1))+~E(f42(f42(f5(a1),x2681),x2682),f4(a1))
% 0.21/0.77 [317]E(f8(f17(x3171,x3172)),x3172)+~P35(f42(f42(a9,f8(x3171)),x3172))
% 0.21/0.77 [322]~P35(f42(a7,x3221))+P35(f42(a7,f42(f42(a10,x3221),f3(x3222))))
% 0.21/0.77 [332]P35(f42(f42(a9,x3321),f17(x3321,x3322)))+~P35(f42(f42(a9,f8(x3321)),x3322))
% 0.21/0.77 [363]P35(f42(f42(f22(a9,a41),f8(x3631)),f8(x3632)))+~P35(f42(f42(f22(a9,a41),x3631),x3632))
% 0.21/0.77 [423]~P5(a7,x4232,a41)+P35(f42(a7,f18(a10,f3(x4231),x4232,a41,a41)))
% 0.21/0.77 [289]~P4(x2891,f3(x2892),x2893)+E(f42(x2891,x2892),x2893)
% 0.21/0.77 [400]~E(f3(x4002),f18(a10,x4003,x4001,a41,a41))+E(x4001,f14(a41))
% 0.21/0.77 [401]~E(f8(x4012),f18(a10,x4013,x4011,a41,a41))+E(x4011,f14(a41))
% 0.21/0.77 [402]~E(f18(a10,x4022,x4021,a41,a41),f8(x4023))+E(x4021,f14(a41))
% 0.21/0.77 [403]E(x4031,f8(x4032))+~E(f18(a10,x4031,x4033,a41,a41),f8(x4032))
% 0.21/0.77 [404]E(f3(x4041),x4042)+~E(f3(x4041),f18(a10,x4042,x4043,a41,a41))
% 0.21/0.77 [405]E(f8(x4051),x4052)+~E(f8(x4051),f18(a10,x4052,x4053,a41,a41))
% 0.21/0.77 [414]E(x4141,x4142)+~E(f18(a10,x4141,x4143,a41,a41),f18(a10,x4142,x4143,a41,a41))
% 0.21/0.77 [342]~P35(f42(f42(a9,x3421),x3423))+P35(f42(f42(a9,f16(x3421,x3422)),f16(x3423,x3422)))
% 0.21/0.77 [364]~P4(x3642,f8(x3643),x3641)+E(f42(f42(a38,f32(x3641,x3642,x3643)),f34(x3641,x3642,x3643)),x3641)
% 0.21/0.77 [379]~P4(x3791,f8(x3792),x3793)+P4(f26(x3791,f4(a1),f28(x3791,x3792),a45),x3792,f29(x3791,x3792))
% 0.21/0.77 [389]~P4(x3891,f8(x3893),x3892)+P4(f26(x3891,f4(a1),f32(x3892,x3891,x3893),a45),x3893,f34(x3892,x3891,x3893))
% 0.21/0.77 [406]E(f42(f42(a10,x4061),x4062),x4063)+~E(f42(f42(a10,x4061),x4062),f18(a10,x4063,f14(a41),a41,a41))
% 0.21/0.77 [410]~P2(x4101)+E(f20(f5(x4101),x4102,x4103,x4101,x4101),f18(f5(x4101),x4103,x4102,x4101,x4101))
% 0.21/0.77 [431]~P35(f42(f42(a9,x4311),x4313))+P35(f42(f42(a9,f18(a10,x4311,x4312,a41,a41)),f18(a10,x4313,x4312,a41,a41)))
% 0.21/0.77 [433]~P6(a9,x4332,x4333,a41)+P35(f42(f42(a9,f18(a10,x4331,x4332,a41,a41)),f18(a10,x4331,x4333,a41,a41)))
% 0.21/0.77 [291]~P13(x2911)+E(f42(f42(f5(x2911),x2912),x2913),f42(f42(f5(x2911),x2913),x2912))
% 0.21/0.77 [292]~P14(x2921)+E(f42(f42(f5(x2921),x2922),x2923),f42(f42(f5(x2921),x2923),x2922))
% 0.21/0.77 [306]E(x3061,x3062)+~E(f42(f42(f5(a1),x3063),x3061),f42(f42(f5(a1),x3063),x3062))
% 0.21/0.77 [307]E(x3071,x3072)+~E(f42(f42(f5(a1),x3071),x3073),f42(f42(f5(a1),x3072),x3073))
% 0.21/0.77 [308]E(x3081,x3082)+~P35(f42(f42(f43(x3083),x3081),x3082))
% 0.21/0.77 [335]~P35(f42(a7,x3351))+P35(f42(a7,f15(x3351,f3(x3352),x3353)))
% 0.21/0.77 [370]P35(f42(f42(f22(a9,a41),f16(x3701,x3702)),f16(x3703,x3702)))+~P35(f42(f42(f22(a9,a41),x3701),x3703))
% 0.21/0.78 [374]~P35(f42(f42(a9,x3741),x3743))+P35(f42(f42(a9,f42(f42(a10,x3741),x3742)),f42(f42(a10,x3743),x3742)))
% 0.21/0.78 [375]~P35(f42(f42(a9,x3752),x3753))+P35(f42(f42(a9,f42(f42(a10,x3751),x3752)),f42(f42(a10,x3751),x3753)))
% 0.21/0.78 [384]~P35(f42(f42(f22(a9,a41),x3841),x3843))+P35(f42(f42(f22(a9,a41),f42(f42(a10,x3841),x3842)),f42(f42(a10,x3843),x3842)))
% 0.21/0.78 [385]~P35(f42(f42(f22(a9,a41),x3852),x3853))+P35(f42(f42(f22(a9,a41),f42(f42(a10,x3851),x3852)),f42(f42(a10,x3851),x3853)))
% 0.21/0.78 [412]~P15(x4121)+E(f42(f42(f5(x4121),x4122),f20(f5(x4121),x4123,f4(x4121),x4121,x4121)),f18(f5(x4121),x4122,x4123,x4121,x4121))
% 0.21/0.78 [413]~P15(x4131)+E(f42(f42(f5(x4131),x4132),f18(f5(x4131),f4(x4131),x4133,x4131,x4131)),f18(f5(x4131),x4132,x4133,x4131,x4131))
% 0.21/0.78 [432]P35(f42(f42(f22(a9,a41),f18(a10,x4321,x4322,a41,a41)),f18(a10,x4323,x4322,a41,a41)))+~P35(f42(f42(f22(a9,a41),x4321),x4323))
% 0.21/0.78 [323]~P31(x3231)+E(f42(f42(f5(x3231),f21(x3232,x3231)),f21(x3233,x3231)),f21(f42(f42(f5(a1),x3232),x3233),x3231))
% 0.21/0.78 [434]P6(a9,x4341,f19(x4342,x4341,x4343),a41)+~P35(f42(f42(a9,f18(a10,f3(x4342),x4341,a41,a41)),x4343))
% 0.21/0.78 [436]E(f18(a10,f3(x4361),f19(x4361,x4362,x4363),a41,a41),x4363)+~P35(f42(f42(a9,f18(a10,f3(x4361),x4362,a41,a41)),x4363))
% 0.21/0.78 [420]P9(x4201,x4202,f30(x4203,x4201,x4204,x4202))+~P4(x4201,f18(a10,x4204,x4202,a41,a41),x4203)
% 0.21/0.78 [421]P9(x4211,x4212,f31(x4213,x4211,x4214,x4212))+~P4(x4211,f18(a10,x4214,x4212,a41,a41),x4213)
% 0.21/0.78 [296]E(x2961,x2962)+~E(f42(f42(a10,x2963),x2961),f42(f42(a10,x2964),x2962))
% 0.21/0.78 [297]E(x2971,x2972)+~E(f42(f42(a38,x2973),x2971),f42(f42(a38,x2974),x2972))
% 0.21/0.78 [298]E(x2981,x2982)+~E(f42(f42(a10,x2981),x2983),f42(f42(a10,x2982),x2984))
% 0.21/0.78 [299]E(x2991,x2992)+~E(f42(f42(a38,x2991),x2993),f42(f42(a38,x2992),x2994))
% 0.21/0.78 [381]P4(x3811,x3812,f33(x3813,x3811,x3814,x3812))+~P4(x3811,f42(f42(a10,x3814),x3812),x3813)
% 0.21/0.78 [383]~P35(f42(f42(a9,x3831),x3834))+P35(f42(f42(a9,f15(x3831,x3832,x3833)),f15(x3834,x3832,x3833)))
% 0.21/0.78 [388]P35(f42(f42(f22(a9,a41),f15(x3881,x3882,x3883)),f15(x3881,x3884,x3883)))+~P35(f42(f42(a9,x3882),x3884))
% 0.21/0.78 [390]P4(x3901,f8(x3902),f42(f42(a38,x3903),x3904))+~P4(f26(x3901,f4(a1),x3903,a45),x3902,x3904)
% 0.21/0.78 [416]E(x4161,x4162)+~E(f18(a10,f3(x4163),x4161,a41,a41),f18(a10,f3(x4164),x4162,a41,a41))
% 0.21/0.78 [417]E(x4171,x4172)+~E(f18(a10,f8(x4173),x4171,a41,a41),f18(a10,f8(x4174),x4172,a41,a41))
% 0.21/0.78 [418]E(x4181,x4182)+~E(f18(a10,f3(x4181),x4183,a41,a41),f18(a10,f3(x4182),x4184,a41,a41))
% 0.21/0.78 [419]E(x4191,x4192)+~E(f18(a10,f8(x4191),x4193,a41,a41),f18(a10,f8(x4192),x4194,a41,a41))
% 0.21/0.78 [422]P9(x4221,x4222,f35(x4223,x4221,x4224,x4222))+~P4(x4221,f18(a10,f3(x4224),x4222,a41,a41),x4223)
% 0.21/0.78 [425]~P4(x4251,f18(a10,x4252,x4254,a41,a41),x4253)+P4(x4251,x4252,f20(a38,f30(x4253,x4251,x4252,x4254),x4253,a45,a45))
% 0.21/0.78 [426]~P4(x4261,f18(a10,x4262,x4264,a41,a41),x4263)+P4(x4261,x4262,f20(a38,f31(x4263,x4261,x4262,x4264),x4263,a45,a45))
% 0.21/0.78 [427]~P4(x4271,f18(a10,f3(x4272),x4274,a41,a41),x4273)+P4(x4271,f3(x4272),f20(a38,f35(x4273,x4271,x4272,x4274),x4273,a45,a45))
% 0.21/0.78 [336]~P35(f42(f42(x3361,x3363),x3364))+P35(f42(f42(f22(x3361,x3362),x3363),x3364))
% 0.21/0.78 [391]P35(f42(f42(f22(a9,a41),f15(x3911,x3912,x3913)),f15(x3914,x3912,x3913)))+~P35(f42(f42(f22(a9,a41),x3911),x3914))
% 0.21/0.78 [392]P35(f42(f42(f22(a9,a41),f15(x3921,x3922,x3923)),f15(x3921,x3924,x3923)))+~P35(f42(f42(f22(a9,a41),x3922),x3924))
% 0.21/0.78 [398]P35(f42(x3981,f42(x3982,x3983)))+~P35(f42(x3981,f39(x3982,x3984,f12(x3983),a44)))
% 0.21/0.78 [409]~P4(x4091,f42(f42(a10,x4092),x4094),x4093)+P4(x4091,x4092,f42(f42(a38,f33(x4093,x4091,x4092,x4094)),x4093))
% 0.21/0.78 [337]~P13(x3371)+E(f42(f42(f5(x3371),x3372),f42(f42(f5(x3371),x3373),x3374)),f42(f42(f5(x3371),x3373),f42(f42(f5(x3371),x3372),x3374)))
% 0.21/0.78 [338]~P14(x3381)+E(f42(f42(f5(x3381),x3382),f42(f42(f5(x3381),x3383),x3384)),f42(f42(f5(x3381),x3383),f42(f42(f5(x3381),x3382),x3384)))
% 0.21/0.78 [339]~P11(x3391)+E(f42(f42(f5(x3391),x3392),f42(f42(f5(x3391),x3393),x3394)),f42(f42(f5(x3391),x3393),f42(f42(f5(x3391),x3392),x3394)))
% 0.21/0.78 [396]~P35(f42(f42(f22(x3961,x3962),x3964),x3963))+P35(f42(f42(f22(f23(x3961,x3962,x3962),x3962),x3963),x3964))
% 0.21/0.78 [399]P35(f42(f42(f22(x3991,x3992),x3993),x3994))+~P35(f42(f42(f22(f23(x3991,x3992,x3992),x3992),x3994),x3993))
% 0.21/0.78 [415]~P22(x4151)+E(f18(f5(x4151),f42(f42(f5(x4151),x4152),x4153),x4154,x4151,x4151),f42(f42(f5(x4151),x4152),f18(f5(x4151),x4153,x4154,x4151,x4151)))
% 0.21/0.78 [357]~P13(x3571)+E(f42(f42(f5(x3571),f42(f42(f5(x3571),x3572),x3573)),x3574),f42(f42(f5(x3571),x3572),f42(f42(f5(x3571),x3573),x3574)))
% 0.21/0.78 [358]~P14(x3581)+E(f42(f42(f5(x3581),f42(f42(f5(x3581),x3582),x3583)),x3584),f42(f42(f5(x3581),x3582),f42(f42(f5(x3581),x3583),x3584)))
% 0.21/0.78 [359]~P2(x3591)+E(f42(f42(f5(x3591),f42(f42(f5(x3591),x3592),x3593)),x3594),f42(f42(f5(x3591),x3592),f42(f42(f5(x3591),x3593),x3594)))
% 0.21/0.78 [369]~P13(x3691)+E(f42(f42(f5(x3691),f42(f42(f5(x3691),x3692),x3693)),x3694),f42(f42(f5(x3691),f42(f42(f5(x3691),x3692),x3694)),x3693))
% 0.21/0.78 [378]~P4(x3781,x3784,x3785)+P4(f26(x3781,x3782,x3783,a45),f16(x3784,x3782),x3785)
% 0.21/0.78 [377]~P35(f42(f42(x3771,x3775),x3774))+P35(f42(f42(f23(x3771,x3772,x3773),x3774),x3775))
% 0.21/0.78 [387]P35(f42(f42(x3871,x3872),x3873))+~P35(f42(f42(f23(x3871,x3874,x3875),x3873),x3872))
% 0.21/0.78 [380]~P13(x3801)+E(f42(f42(f5(x3801),f42(f42(f5(x3801),x3802),x3803)),f42(f42(f5(x3801),x3804),x3805)),f42(f42(f5(x3801),f42(f42(f5(x3801),x3802),x3804)),f42(f42(f5(x3801),x3803),x3805)))
% 0.21/0.78 [408]P35(f42(x4081,f42(f42(x4082,x4083),x4084)))+~P35(f42(x4081,f39(x4085,x4082,f42(f42(a38,x4083),x4084),a44)))
% 0.21/0.78 [316]~P18(x3161)+~P7(f4(x3161),f4(x3161),x3161)+E(f42(f42(f5(x3161),f4(x3161)),f4(x3161)),f4(x3161))
% 0.21/0.78 [263]~P30(x2631)+~P10(x2631)+E(f42(f42(f5(x2631),x2632),f4(x2631)),x2632)
% 0.21/0.78 [273]~P25(x2731)+~P32(x2731)+E(f24(f4(x2731),f25(x2732),x2731),f4(x2731))
% 0.21/0.78 [275]E(x2751,f4(a1))+E(x2752,f4(a1))+~E(f42(f42(f5(a1),x2752),x2751),f25(f4(a1)))
% 0.21/0.78 [280]E(x2801,f4(a1))+E(x2801,f25(f4(a1)))+~E(f42(f42(f5(a1),x2802),x2801),f25(f4(a1)))
% 0.21/0.78 [281]E(x2811,f4(a1))+E(x2811,f25(f4(a1)))+~E(f42(f42(f5(a1),x2811),x2812),f25(f4(a1)))
% 0.21/0.78 [285]E(x2851,f25(f4(a1)))+E(x2852,f25(f4(a1)))+~E(f42(f42(f5(a1),x2852),x2851),f25(f4(a1)))
% 0.21/0.78 [286]~P16(x2862)+E(x2861,f4(x2862))+~E(f42(f42(f5(x2862),x2861),x2861),f4(x2862))
% 0.21/0.78 [326]~P16(x3261)+~P7(f4(x3261),x3262,x3261)+P7(f4(x3261),f42(f42(f5(x3261),x3262),x3262),x3261)
% 0.21/0.78 [327]~P16(x3271)+~P7(x3272,f4(x3271),x3271)+P7(f42(f42(f5(x3271),x3272),x3272),f4(x3271),x3271)
% 0.21/0.78 [340]~P16(x3402)+P7(x3401,f4(x3402),x3402)+~P7(f42(f42(f5(x3402),x3401),x3401),f4(x3402),x3402)
% 0.21/0.78 [341]~P16(x3411)+P7(f4(x3411),x3412,x3411)+~P7(f4(x3411),f42(f42(f5(x3411),x3412),x3412),x3411)
% 0.21/0.78 [294]P7(x2942,x2941,x2943)+~P24(x2943)+P7(x2941,x2942,x2943)
% 0.21/0.78 [250]~P3(x2503)+E(x2501,x2502)+~E(f21(x2501,x2503),f21(x2502,x2503))
% 0.21/0.78 [288]~P33(x2882)+~E(f24(x2881,x2883,x2882),f4(x2882))+E(x2881,f4(x2882))
% 0.21/0.78 [330]~P27(x3301)+~P7(f4(x3301),x3302,x3301)+P7(f4(x3301),f24(x3302,x3303,x3301),x3301)
% 0.21/0.78 [331]~P27(x3311)+~P7(f6(x3311),x3312,x3311)+P7(f6(x3311),f24(x3312,x3313,x3311),x3311)
% 0.21/0.78 [428]~P8(f23(a9,a41,a41),x4282,a41)+~P8(f23(a9,a41,a41),f18(a10,f15(x4281,x4282,f4(a1)),x4283,a41,a41),a41)+P8(f23(a9,a41,a41),f18(a10,f42(f42(a10,f8(x4281)),x4282),x4283,a41,a41),a41)
% 0.21/0.78 [430]~P35(f42(a7,x4302))+~P35(f42(a7,f18(a10,f15(x4301,x4302,f4(a1)),x4303,a41,a41)))+P35(f42(a7,f18(a10,f42(f42(a10,f8(x4301)),x4302),x4303,a41,a41)))
% 0.21/0.78 [301]P35(f42(x3011,x3012))+P35(f42(x3011,x3013))+~E(f27(x3011),f42(f42(a38,x3014),x3013))
% 0.21/0.78 [302]P35(f42(x3021,x3022))+P35(f42(x3021,x3023))+~E(f27(x3021),f42(f42(a38,x3023),x3024))
% 0.21/0.78 [324]P4(x3241,x3242,x3243)+~P4(x3241,x3244,x3243)+~P35(f42(f42(a9,x3244),x3242))
% 0.21/0.78 [329]P8(x3291,x3292,x3293)+~P8(x3291,x3294,x3293)+~P35(f42(f42(x3291,x3292),x3294))
% 0.21/0.78 [309]~P1(x3093)+E(x3091,x3092)+~E(f42(f42(f5(x3093),x3094),x3091),f42(f42(f5(x3093),x3094),x3092))
% 0.21/0.78 [310]~P12(x3103)+E(x3101,x3102)+~E(f42(f42(f5(x3103),x3104),x3101),f42(f42(f5(x3103),x3104),x3102))
% 0.21/0.78 [311]~P12(x3113)+E(x3111,x3112)+~E(f42(f42(f5(x3113),x3111),x3114),f42(f42(f5(x3113),x3112),x3114))
% 0.21/0.78 [343]~P19(x3431)+~P7(x3432,x3434,x3431)+P7(f42(f42(f5(x3431),x3432),x3433),f42(f42(f5(x3431),x3434),x3433),x3431)
% 0.21/0.78 [344]~P21(x3441)+~P7(x3442,x3444,x3441)+P7(f42(f42(f5(x3441),x3442),x3443),f42(f42(f5(x3441),x3444),x3443),x3441)
% 0.21/0.78 [345]~P19(x3451)+~P7(x3453,x3454,x3451)+P7(f42(f42(f5(x3451),x3452),x3453),f42(f42(f5(x3451),x3452),x3454),x3451)
% 0.21/0.78 [346]~P21(x3461)+~P7(x3463,x3464,x3461)+P7(f42(f42(f5(x3461),x3462),x3463),f42(f42(f5(x3461),x3462),x3464),x3461)
% 0.21/0.78 [353]P4(x3531,x3532,x3533)+~P4(x3531,x3534,x3533)+~P35(f42(f42(f22(a9,a41),x3534),x3532))
% 0.21/0.78 [361]P8(x3611,x3612,x3613)+~P8(x3611,x3614,x3613)+~P35(f42(f42(f22(x3611,x3613),x3612),x3614))
% 0.21/0.78 [366]~P21(x3663)+P7(x3661,x3662,x3663)+~P7(f42(f42(f5(x3663),x3664),x3661),f42(f42(f5(x3663),x3664),x3662),x3663)
% 0.21/0.78 [367]~P21(x3673)+P7(x3671,x3672,x3673)+~P7(f42(f42(f5(x3673),x3671),x3674),f42(f42(f5(x3673),x3672),x3674),x3673)
% 0.21/0.78 [393]~P35(f42(f42(f22(a9,a41),x3931),x3933))+~P35(f42(f42(f22(a9,a41),x3932),x3934))+P35(f42(f42(f22(a9,a41),f42(f42(a10,x3931),x3932)),f42(f42(a10,x3933),x3934)))
% 0.21/0.78 [424]~P9(x4241,x4243,x4245)+~P4(x4241,x4242,f20(a38,x4245,x4244,a45,a45))+P4(x4241,f18(a10,x4242,x4243,a41,a41),x4244)
% 0.21/0.78 [354]~P4(x3541,x3543,x3545)+~P4(x3541,x3542,f42(f42(a38,x3545),x3544))+P4(x3541,f42(f42(a10,x3542),x3543),x3544)
% 0.21/0.78 [429]E(x4291,x4292)+~P4(x4293,f18(a10,f3(x4294),x4295,a41,a41),x4291)+~P4(x4293,f18(a10,f3(x4294),x4295,a41,a41),x4292)
% 0.21/0.78 [371]~P35(f42(f42(x3711,x3715),x3714))+~P35(f42(f42(f22(x3711,x3712),x3713),x3715))+P35(f42(f42(f22(x3711,x3712),x3713),x3714))
% 0.21/0.78 [372]~P35(f42(f42(x3721,x3723),x3725))+~P35(f42(f42(f22(x3721,x3722),x3725),x3724))+P35(f42(f42(f22(x3721,x3722),x3723),x3724))
% 0.21/0.78 [382]~P35(f42(f42(f22(x3821,x3822),x3823),x3825))+P35(f42(f42(f22(x3821,x3822),x3823),x3824))+~P35(f42(f42(f22(x3821,x3822),x3825),x3824))
% 0.21/0.78 [351]~P11(x3511)+E(f42(f42(f5(x3511),x3512),x3513),x3514)+~E(f42(f42(f5(x3511),x3512),f42(f42(f5(x3511),x3515),x3513)),f42(f42(f5(x3511),x3515),x3514))
% 0.21/0.78 [394]~P4(x3941,x3943,x3946)+P4(x3941,f15(x3942,x3943,x3944),x3945)+~P4(f26(x3941,x3944,x3946,a45),x3942,x3945)
% 0.21/0.78 [272]~P25(x2722)+~P32(x2722)+E(x2721,f4(a1))+E(f24(f4(x2722),x2721,x2722),f4(x2722))
% 0.21/0.78 [315]~P7(x3152,x3151,x3153)+~P7(x3151,x3152,x3153)+E(x3151,x3152)+~P23(x3153)
% 0.21/0.78 [287]~P30(x2872)+~P10(x2872)+E(x2871,f4(x2872))+~E(f42(f42(f5(x2872),x2873),x2871),x2873)
% 0.21/0.78 [349]~P18(x3491)+~P7(f4(x3491),x3493,x3491)+~P7(f4(x3491),x3492,x3491)+P7(f4(x3491),f42(f42(f5(x3491),x3492),x3493),x3491)
% 0.21/0.78 [350]~P18(x3501)+~P7(x3503,f4(x3501),x3501)+~P7(x3502,f4(x3501),x3501)+P7(f42(f42(f5(x3501),x3502),x3503),f4(x3501),x3501)
% 0.21/0.78 [320]~P23(x3203)+~P7(x3201,x3204,x3203)+P7(x3201,x3202,x3203)+~P7(x3204,x3202,x3203)
% 0.21/0.78 [321]~P26(x3213)+~P7(x3211,x3214,x3213)+P7(x3211,x3212,x3213)+~P7(x3214,x3212,x3213)
% 0.21/0.78 [365]~P27(x3653)+~P7(x3651,x3654,x3653)+~P7(f4(x3653),x3651,x3653)+P7(f24(x3651,x3652,x3653),f24(x3654,x3652,x3653),x3653)
% 0.21/0.78 [373]~P27(x3733)+P7(x3731,x3732,x3733)+~P7(f4(x3733),x3732,x3733)+~P7(f24(x3731,f25(x3734),x3733),f24(x3732,f25(x3734),x3733),x3733)
% 0.21/0.78 [312]~P30(x3123)+~P10(x3123)+E(x3121,x3122)+~E(f42(f42(f5(x3123),x3124),x3121),f42(f42(f5(x3123),x3124),x3122))
% 0.21/0.78 [362]~P19(x3621)+~P7(x3623,x3625,x3621)+~P7(x3622,x3624,x3621)+P7(f42(f42(f5(x3621),x3622),x3623),f42(f42(f5(x3621),x3624),x3625),x3621)
% 0.21/0.78 [368]~P20(x3682)+~P7(x3685,x3684,x3682)+~P7(x3681,f42(f42(f5(x3682),x3683),x3685),x3682)+P7(x3681,f42(f42(f5(x3682),x3683),x3684),x3682)
% 0.21/0.78 [435]~P9(x4351,x4355,x4356)+P9(x4351,x4352,f36(x4353,x4354,x4351,x4352))+~P4(x4351,f18(a10,f3(x4357),x4355,a41,a41),x4354)+~P4(x4351,f18(a10,f18(a10,f3(x4357),x4355,a41,a41),x4352,a41,a41),x4353)
% 0.21/0.78 [437]~P9(x4373,x4375,x4376)+~P4(x4373,f18(a10,f3(x4377),x4375,a41,a41),x4372)+~P4(x4373,f18(a10,f18(a10,f3(x4377),x4375,a41,a41),x4374,a41,a41),x4371)+E(f20(a38,f36(x4371,x4372,x4373,x4374),x4371,a45,a45),x4372)
% 0.21/0.78 [303]~P34(x3032)+~P25(x3032)+~P28(x3032)+~P29(x3032)+~E(f24(x3031,f4(a1),x3032),f4(x3032))
% 0.21/0.78 [333]~P18(x3332)+~P7(f4(x3332),x3331,x3332)+~P7(f4(x3332),x3333,x3332)+E(x3331,f4(x3332))+~E(f42(f42(f5(x3332),x3333),x3331),f4(x3332))
% 0.21/0.78 [334]~P18(x3342)+~P7(f4(x3342),x3343,x3342)+~P7(f4(x3342),x3341,x3342)+E(x3341,f4(x3342))+~E(f42(f42(f5(x3342),x3341),x3343),f4(x3342))
% 0.21/0.78 [352]~P27(x3524)+E(x3521,x3522)+~P7(f4(x3524),x3522,x3524)+~P7(f4(x3524),x3521,x3524)+~E(f24(x3521,f25(x3523),x3524),f24(x3522,f25(x3523),x3524))
% 0.21/0.78 [347]~P14(x3472)+~P21(x3472)+~P7(x3471,x3474,x3472)+~P7(f4(x3472),x3473,x3472)+P7(x3471,f42(f42(f5(x3472),x3473),x3474),x3472)
% 0.21/0.78 [348]~P14(x3482)+~P21(x3482)+~P7(x3481,x3483,x3482)+~P7(f4(x3482),x3484,x3482)+P7(x3481,f42(f42(f5(x3482),x3483),x3484),x3482)
% 0.21/0.78 [395]~P4(x3954,x3952,x3955)+~P4(f26(x3954,x3953,x3955,a45),x3951,x3956)+~P35(f42(a7,x3952))+~P35(f42(a7,x3951))+P35(f42(a7,f15(x3951,x3952,x3953)))
% 0.21/0.78 [282]~P34(x2822)+~P25(x2822)+~P28(x2822)+~P29(x2822)+E(x2821,f4(a1))+E(f24(f4(x2822),x2821,x2822),f4(x2822))
% 0.21/0.78 [304]~P34(x3042)+~P25(x3042)+~P28(x3042)+~P29(x3042)+~E(f24(x3041,x3043,x3042),f4(x3042))+E(x3041,f4(x3042))
% 0.21/0.78 %EqnAxiom
% 0.21/0.78 [1]E(x11,x11)
% 0.21/0.78 [2]E(x22,x21)+~E(x21,x22)
% 0.21/0.78 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.21/0.78 [4]~E(x41,x42)+E(f3(x41),f3(x42))
% 0.21/0.78 [5]~E(x51,x52)+E(f11(x51),f11(x52))
% 0.21/0.78 [6]~E(x61,x62)+E(f4(x61),f4(x62))
% 0.21/0.78 [7]~E(x71,x72)+E(f12(x71),f12(x72))
% 0.21/0.78 [8]~E(x81,x82)+E(f37(x81),f37(x82))
% 0.21/0.78 [9]~E(x91,x92)+E(f42(x91,x93),f42(x92,x93))
% 0.21/0.78 [10]~E(x101,x102)+E(f42(x103,x101),f42(x103,x102))
% 0.21/0.78 [11]~E(x111,x112)+E(f18(x111,x113,x114,x115,x116),f18(x112,x113,x114,x115,x116))
% 0.21/0.78 [12]~E(x121,x122)+E(f18(x123,x121,x124,x125,x126),f18(x123,x122,x124,x125,x126))
% 0.21/0.78 [13]~E(x131,x132)+E(f18(x133,x134,x131,x135,x136),f18(x133,x134,x132,x135,x136))
% 0.21/0.78 [14]~E(x141,x142)+E(f18(x143,x144,x145,x141,x146),f18(x143,x144,x145,x142,x146))
% 0.21/0.78 [15]~E(x151,x152)+E(f18(x153,x154,x155,x156,x151),f18(x153,x154,x155,x156,x152))
% 0.21/0.78 [16]~E(x161,x162)+E(f13(x161,x163),f13(x162,x163))
% 0.21/0.78 [17]~E(x171,x172)+E(f13(x173,x171),f13(x173,x172))
% 0.21/0.78 [18]~E(x181,x182)+E(f5(x181),f5(x182))
% 0.21/0.78 [19]~E(x191,x192)+E(f22(x191,x193),f22(x192,x193))
% 0.21/0.78 [20]~E(x201,x202)+E(f22(x203,x201),f22(x203,x202))
% 0.21/0.78 [21]~E(x211,x212)+E(f25(x211),f25(x212))
% 0.21/0.78 [22]~E(x221,x222)+E(f15(x221,x223,x224),f15(x222,x223,x224))
% 0.21/0.78 [23]~E(x231,x232)+E(f15(x233,x231,x234),f15(x233,x232,x234))
% 0.21/0.78 [24]~E(x241,x242)+E(f15(x243,x244,x241),f15(x243,x244,x242))
% 0.21/0.78 [25]~E(x251,x252)+E(f30(x251,x253,x254,x255),f30(x252,x253,x254,x255))
% 0.21/0.78 [26]~E(x261,x262)+E(f30(x263,x261,x264,x265),f30(x263,x262,x264,x265))
% 0.21/0.78 [27]~E(x271,x272)+E(f30(x273,x274,x271,x275),f30(x273,x274,x272,x275))
% 0.21/0.78 [28]~E(x281,x282)+E(f30(x283,x284,x285,x281),f30(x283,x284,x285,x282))
% 0.21/0.78 [29]~E(x291,x292)+E(f23(x291,x293,x294),f23(x292,x293,x294))
% 0.21/0.78 [30]~E(x301,x302)+E(f23(x303,x301,x304),f23(x303,x302,x304))
% 0.21/0.78 [31]~E(x311,x312)+E(f23(x313,x314,x311),f23(x313,x314,x312))
% 0.21/0.78 [32]~E(x321,x322)+E(f8(x321),f8(x322))
% 0.21/0.78 [33]~E(x331,x332)+E(f26(x331,x333,x334,x335),f26(x332,x333,x334,x335))
% 0.21/0.78 [34]~E(x341,x342)+E(f26(x343,x341,x344,x345),f26(x343,x342,x344,x345))
% 0.21/0.78 [35]~E(x351,x352)+E(f26(x353,x354,x351,x355),f26(x353,x354,x352,x355))
% 0.21/0.78 [36]~E(x361,x362)+E(f26(x363,x364,x365,x361),f26(x363,x364,x365,x362))
% 0.21/0.78 [37]~E(x371,x372)+E(f21(x371,x373),f21(x372,x373))
% 0.21/0.78 [38]~E(x381,x382)+E(f21(x383,x381),f21(x383,x382))
% 0.21/0.78 [39]~E(x391,x392)+E(f6(x391),f6(x392))
% 0.21/0.78 [40]~E(x401,x402)+E(f24(x401,x403,x404),f24(x402,x403,x404))
% 0.21/0.78 [41]~E(x411,x412)+E(f24(x413,x411,x414),f24(x413,x412,x414))
% 0.21/0.78 [42]~E(x421,x422)+E(f24(x423,x424,x421),f24(x423,x424,x422))
% 0.21/0.78 [43]~E(x431,x432)+E(f39(x431,x433,x434,x435),f39(x432,x433,x434,x435))
% 0.21/0.78 [44]~E(x441,x442)+E(f39(x443,x441,x444,x445),f39(x443,x442,x444,x445))
% 0.21/0.78 [45]~E(x451,x452)+E(f39(x453,x454,x451,x455),f39(x453,x454,x452,x455))
% 0.21/0.78 [46]~E(x461,x462)+E(f39(x463,x464,x465,x461),f39(x463,x464,x465,x462))
% 0.21/0.78 [47]~E(x471,x472)+E(f16(x471,x473),f16(x472,x473))
% 0.21/0.78 [48]~E(x481,x482)+E(f16(x483,x481),f16(x483,x482))
% 0.21/0.78 [49]~E(x491,x492)+E(f43(x491),f43(x492))
% 0.21/0.78 [50]~E(x501,x502)+E(f20(x501,x503,x504,x505,x506),f20(x502,x503,x504,x505,x506))
% 0.21/0.78 [51]~E(x511,x512)+E(f20(x513,x511,x514,x515,x516),f20(x513,x512,x514,x515,x516))
% 0.21/0.78 [52]~E(x521,x522)+E(f20(x523,x524,x521,x525,x526),f20(x523,x524,x522,x525,x526))
% 0.21/0.78 [53]~E(x531,x532)+E(f20(x533,x534,x535,x531,x536),f20(x533,x534,x535,x532,x536))
% 0.21/0.78 [54]~E(x541,x542)+E(f20(x543,x544,x545,x546,x541),f20(x543,x544,x545,x546,x542))
% 0.21/0.78 [55]~E(x551,x552)+E(f14(x551),f14(x552))
% 0.21/0.78 [56]~E(x561,x562)+E(f19(x561,x563,x564),f19(x562,x563,x564))
% 0.21/0.78 [57]~E(x571,x572)+E(f19(x573,x571,x574),f19(x573,x572,x574))
% 0.21/0.78 [58]~E(x581,x582)+E(f19(x583,x584,x581),f19(x583,x584,x582))
% 0.21/0.78 [59]~E(x591,x592)+E(f36(x591,x593,x594,x595),f36(x592,x593,x594,x595))
% 0.21/0.78 [60]~E(x601,x602)+E(f36(x603,x601,x604,x605),f36(x603,x602,x604,x605))
% 0.21/0.78 [61]~E(x611,x612)+E(f36(x613,x614,x611,x615),f36(x613,x614,x612,x615))
% 0.21/0.78 [62]~E(x621,x622)+E(f36(x623,x624,x625,x621),f36(x623,x624,x625,x622))
% 0.21/0.78 [63]~E(x631,x632)+E(f40(x631,x633,x634,x635),f40(x632,x633,x634,x635))
% 0.21/0.78 [64]~E(x641,x642)+E(f40(x643,x641,x644,x645),f40(x643,x642,x644,x645))
% 0.21/0.78 [65]~E(x651,x652)+E(f40(x653,x654,x651,x655),f40(x653,x654,x652,x655))
% 0.21/0.78 [66]~E(x661,x662)+E(f40(x663,x664,x665,x661),f40(x663,x664,x665,x662))
% 0.21/0.78 [67]~E(x671,x672)+E(f28(x671,x673),f28(x672,x673))
% 0.21/0.78 [68]~E(x681,x682)+E(f28(x683,x681),f28(x683,x682))
% 0.21/0.78 [69]~E(x691,x692)+E(f34(x691,x693,x694),f34(x692,x693,x694))
% 0.21/0.78 [70]~E(x701,x702)+E(f34(x703,x701,x704),f34(x703,x702,x704))
% 0.21/0.78 [71]~E(x711,x712)+E(f34(x713,x714,x711),f34(x713,x714,x712))
% 0.21/0.78 [72]~E(x721,x722)+E(f35(x721,x723,x724,x725),f35(x722,x723,x724,x725))
% 0.21/0.78 [73]~E(x731,x732)+E(f35(x733,x731,x734,x735),f35(x733,x732,x734,x735))
% 0.21/0.78 [74]~E(x741,x742)+E(f35(x743,x744,x741,x745),f35(x743,x744,x742,x745))
% 0.21/0.78 [75]~E(x751,x752)+E(f35(x753,x754,x755,x751),f35(x753,x754,x755,x752))
% 0.21/0.78 [76]~E(x761,x762)+E(f46(x761,x763),f46(x762,x763))
% 0.21/0.78 [77]~E(x771,x772)+E(f46(x773,x771),f46(x773,x772))
% 0.21/0.78 [78]~E(x781,x782)+E(f31(x781,x783,x784,x785),f31(x782,x783,x784,x785))
% 0.21/0.78 [79]~E(x791,x792)+E(f31(x793,x791,x794,x795),f31(x793,x792,x794,x795))
% 0.21/0.78 [80]~E(x801,x802)+E(f31(x803,x804,x801,x805),f31(x803,x804,x802,x805))
% 0.21/0.78 [81]~E(x811,x812)+E(f31(x813,x814,x815,x811),f31(x813,x814,x815,x812))
% 0.21/0.78 [82]~E(x821,x822)+E(f32(x821,x823,x824),f32(x822,x823,x824))
% 0.21/0.78 [83]~E(x831,x832)+E(f32(x833,x831,x834),f32(x833,x832,x834))
% 0.21/0.78 [84]~E(x841,x842)+E(f32(x843,x844,x841),f32(x843,x844,x842))
% 0.21/0.78 [85]~E(x851,x852)+E(f33(x851,x853,x854,x855),f33(x852,x853,x854,x855))
% 0.21/0.78 [86]~E(x861,x862)+E(f33(x863,x861,x864,x865),f33(x863,x862,x864,x865))
% 0.21/0.78 [87]~E(x871,x872)+E(f33(x873,x874,x871,x875),f33(x873,x874,x872,x875))
% 0.21/0.78 [88]~E(x881,x882)+E(f33(x883,x884,x885,x881),f33(x883,x884,x885,x882))
% 0.21/0.78 [89]~E(x891,x892)+E(f27(x891),f27(x892))
% 0.21/0.78 [90]~E(x901,x902)+E(f17(x901,x903),f17(x902,x903))
% 0.21/0.78 [91]~E(x911,x912)+E(f17(x913,x911),f17(x913,x912))
% 0.21/0.78 [92]~E(x921,x922)+E(f29(x921,x923),f29(x922,x923))
% 0.21/0.78 [93]~E(x931,x932)+E(f29(x933,x931),f29(x933,x932))
% 0.21/0.78 [94]~P1(x941)+P1(x942)+~E(x941,x942)
% 0.21/0.78 [95]~P12(x951)+P12(x952)+~E(x951,x952)
% 0.21/0.78 [96]~P13(x961)+P13(x962)+~E(x961,x962)
% 0.21/0.78 [97]~P27(x971)+P27(x972)+~E(x971,x972)
% 0.21/0.78 [98]~P14(x981)+P14(x982)+~E(x981,x982)
% 0.21/0.78 [99]~P15(x991)+P15(x992)+~E(x991,x992)
% 0.21/0.78 [100]~P31(x1001)+P31(x1002)+~E(x1001,x1002)
% 0.21/0.78 [101]~P34(x1011)+P34(x1012)+~E(x1011,x1012)
% 0.21/0.78 [102]~P17(x1021)+P17(x1022)+~E(x1021,x1022)
% 0.21/0.78 [103]~P2(x1031)+P2(x1032)+~E(x1031,x1032)
% 0.21/0.78 [104]~P18(x1041)+P18(x1042)+~E(x1041,x1042)
% 0.21/0.78 [105]~P19(x1051)+P19(x1052)+~E(x1051,x1052)
% 0.21/0.78 [106]~P21(x1061)+P21(x1062)+~E(x1061,x1062)
% 0.21/0.78 [107]~P22(x1071)+P22(x1072)+~E(x1071,x1072)
% 0.21/0.78 [108]~P23(x1081)+P23(x1082)+~E(x1081,x1082)
% 0.21/0.78 [109]~P35(x1091)+P35(x1092)+~E(x1091,x1092)
% 0.21/0.78 [110]~P25(x1101)+P25(x1102)+~E(x1101,x1102)
% 0.21/0.78 [111]~P26(x1111)+P26(x1112)+~E(x1111,x1112)
% 0.21/0.78 [112]P7(x1122,x1123,x1124)+~E(x1121,x1122)+~P7(x1121,x1123,x1124)
% 0.21/0.78 [113]P7(x1133,x1132,x1134)+~E(x1131,x1132)+~P7(x1133,x1131,x1134)
% 0.21/0.78 [114]P7(x1143,x1144,x1142)+~E(x1141,x1142)+~P7(x1143,x1144,x1141)
% 0.21/0.78 [115]~P24(x1151)+P24(x1152)+~E(x1151,x1152)
% 0.21/0.78 [116]~P28(x1161)+P28(x1162)+~E(x1161,x1162)
% 0.21/0.78 [117]~P29(x1171)+P29(x1172)+~E(x1171,x1172)
% 0.21/0.78 [118]~P3(x1181)+P3(x1182)+~E(x1181,x1182)
% 0.21/0.78 [119]~P32(x1191)+P32(x1192)+~E(x1191,x1192)
% 0.21/0.78 [120]P4(x1202,x1203,x1204)+~E(x1201,x1202)+~P4(x1201,x1203,x1204)
% 0.21/0.78 [121]P4(x1213,x1212,x1214)+~E(x1211,x1212)+~P4(x1213,x1211,x1214)
% 0.21/0.78 [122]P4(x1223,x1224,x1222)+~E(x1221,x1222)+~P4(x1223,x1224,x1221)
% 0.21/0.78 [123]~P10(x1231)+P10(x1232)+~E(x1231,x1232)
% 0.21/0.78 [124]P8(x1242,x1243,x1244)+~E(x1241,x1242)+~P8(x1241,x1243,x1244)
% 0.21/0.78 [125]P8(x1253,x1252,x1254)+~E(x1251,x1252)+~P8(x1253,x1251,x1254)
% 0.21/0.78 [126]P8(x1263,x1264,x1262)+~E(x1261,x1262)+~P8(x1263,x1264,x1261)
% 0.21/0.78 [127]~P11(x1271)+P11(x1272)+~E(x1271,x1272)
% 0.21/0.78 [128]P5(x1282,x1283,x1284)+~E(x1281,x1282)+~P5(x1281,x1283,x1284)
% 0.21/0.78 [129]P5(x1293,x1292,x1294)+~E(x1291,x1292)+~P5(x1293,x1291,x1294)
% 0.21/0.78 [130]P5(x1303,x1304,x1302)+~E(x1301,x1302)+~P5(x1303,x1304,x1301)
% 0.21/0.78 [131]~P16(x1311)+P16(x1312)+~E(x1311,x1312)
% 0.21/0.78 [132]~P30(x1321)+P30(x1322)+~E(x1321,x1322)
% 0.21/0.78 [133]P9(x1332,x1333,x1334)+~E(x1331,x1332)+~P9(x1331,x1333,x1334)
% 0.21/0.78 [134]P9(x1343,x1342,x1344)+~E(x1341,x1342)+~P9(x1343,x1341,x1344)
% 0.21/0.78 [135]P9(x1353,x1354,x1352)+~E(x1351,x1352)+~P9(x1353,x1354,x1351)
% 0.21/0.78 [136]P6(x1362,x1363,x1364,x1365)+~E(x1361,x1362)+~P6(x1361,x1363,x1364,x1365)
% 0.21/0.78 [137]P6(x1373,x1372,x1374,x1375)+~E(x1371,x1372)+~P6(x1373,x1371,x1374,x1375)
% 0.21/0.78 [138]P6(x1383,x1384,x1382,x1385)+~E(x1381,x1382)+~P6(x1383,x1384,x1381,x1385)
% 0.21/0.78 [139]P6(x1393,x1394,x1395,x1392)+~E(x1391,x1392)+~P6(x1393,x1394,x1395,x1391)
% 0.21/0.78 [140]~P33(x1401)+P33(x1402)+~E(x1401,x1402)
% 0.21/0.78 [141]~P20(x1411)+P20(x1412)+~E(x1411,x1412)
% 0.21/0.78
% 0.21/0.78 %-------------------------------------------
% 0.21/0.78 cnf(438,plain,
% 0.21/0.78 ($false),
% 0.21/0.78 inference(scs_inference,[],[235,192]),
% 0.21/0.78 ['proof']).
% 0.21/0.78 % SZS output end Proof
% 0.21/0.78 % Total time :0.030000s
%------------------------------------------------------------------------------