%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LCL856-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:50:15 AM UTC 2026
% Result : Unsatisfiable 30.27s 35.51s
% Output : Proof 30.27s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_not__Nil__step1_0,axiom,
~ c_ListOrder_Ostep1(V_r,c_List_Olist_ONil(T_a),V_xs,T_a),
file('theBenchmark.p',cls_not__Nil__step1_0) ).
cnf(cls_not__step1__Nil_0,axiom,
~ c_ListOrder_Ostep1(V_r,V_xs,c_List_Olist_ONil(T_a),T_a),
file('theBenchmark.p',cls_not__step1__Nil_0) ).
cnf(cls_type_Osimps_I2_J_1,axiom,
( V_type2 = V_type2_H
| c_Type_Otype_OFun(V_type1,V_type2) != c_Type_Otype_OFun(V_type1_H,V_type2_H) ),
file('theBenchmark.p',cls_type_Osimps_I2_J_1) ).
cnf(cls_type_Osimps_I2_J_0,axiom,
( V_type1 = V_type1_H
| c_Type_Otype_OFun(V_type1,V_type2) != c_Type_Otype_OFun(V_type1_H,V_type2_H) ),
file('theBenchmark.p',cls_type_Osimps_I2_J_0) ).
cnf(cls_App_0,axiom,
( ~ c_Type_Otyping(V_env,V_s,c_Type_Otype_OFun(V_T,V_U))
| ~ c_Type_Otyping(V_env,V_t,V_T)
| c_Type_Otyping(V_env,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_U) ),
file('theBenchmark.p',cls_App_0) ).
cnf(cls_Abs__eq__apps__conv_1,axiom,
( V_ss = c_List_Olist_ONil(tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(V_r) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('theBenchmark.p',cls_Abs__eq__apps__conv_1) ).
cnf(cls_Abs__eq__apps__conv_2,axiom,
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),
file('theBenchmark.p',cls_Abs__eq__apps__conv_2) ).
cnf(cls_apps__eq__Abs__conv_1,axiom,
( V_ss = c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(V_r) ),
file('theBenchmark.p',cls_apps__eq__Abs__conv_1) ).
cnf(cls_apps__eq__Abs__conv_2,axiom,
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),
file('theBenchmark.p',cls_apps__eq__Abs__conv_2) ).
cnf(cls_apps__preserves__betas_0,axiom,
( ~ c_ListOrder_Ostep1(c_Lambda_Obeta,V_rs,V_ss,tc_Lambda_OdB)
| 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))) ),
file('theBenchmark.p',cls_apps__preserves__betas_0) ).
cnf(cls_lift__type_0,axiom,
( ~ c_Type_Otyping(V_e,V_t,V_T)
| c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_U,tc_Type_Otype),c_Lambda_Olift(V_t,V_i),V_T) ),
file('theBenchmark.p',cls_lift__type_0) ).
cnf(cls_subst__lemma_0,axiom,
( c_Type_Otyping(V_e_H,c_Lambda_Osubst(V_t,V_u,V_i),V_T)
| ~ c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)
| ~ c_Type_Otyping(V_e_H,V_u,V_U) ),
file('theBenchmark.p',cls_subst__lemma_0) ).
cnf(cls_head__Var__reduction_0,axiom,
( ~ 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))
| 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) ),
file('theBenchmark.p',cls_head__Var__reduction_0) ).
cnf(cls_App__eq__foldl__conv_4,axiom,
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),
file('theBenchmark.p',cls_App__eq__foldl__conv_4) ).
cnf(cls_App__eq__foldl__conv_0,axiom,
( hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) = V_t
| 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) ),
file('theBenchmark.p',cls_App__eq__foldl__conv_0) ).
cnf(cls_Abs_0,axiom,
( ~ c_Type_Otyping(c_Type_Oshift(V_env,c_HOL_Ozero__class_Ozero(tc_nat),V_T,tc_Type_Otype),V_t,V_U)
| c_Type_Otyping(V_env,c_Lambda_OdB_OAbs(V_t),c_Type_Otype_OFun(V_T,V_U)) ),
file('theBenchmark.p',cls_Abs_0) ).
cnf(cls_shift__eq_0,axiom,
hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T,
file('theBenchmark.p',cls_shift__eq_0) ).
cnf(cls_foldl__Nil_0,axiom,
c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a,
file('theBenchmark.p',cls_foldl__Nil_0) ).
cnf(cls_listsp_ONil_0,axiom,
c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a),
file('theBenchmark.p',cls_listsp_ONil_0) ).
cnf(cls_App__eq__foldl__conv_2,axiom,
( V_ts = c_List_Olist_ONil(tc_Lambda_OdB)
| V_r = c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(V_r,V_s,V_t,V_ts),tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('theBenchmark.p',cls_App__eq__foldl__conv_2) ).
cnf(cls_Var__eq__apps__conv_1,axiom,
( V_ss = c_List_Olist_ONil(tc_Lambda_OdB)
| c_Lambda_OdB_OVar(V_m) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('theBenchmark.p',cls_Var__eq__apps__conv_1) ).
cnf(cls_Var__eq__apps__conv_2,axiom,
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),
file('theBenchmark.p',cls_Var__eq__apps__conv_2) ).
cnf(cls_subst__type__IT_0,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| ~ c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_U,tc_Type_Otype),V_t,V_T)
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
| ~ c_Type_Otyping(V_e,V_u,V_U)
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(V_t,V_u,V_i))) ),
file('theBenchmark.p',cls_subst__type__IT_0) ).
cnf(cls_head__Var__reduction_1,axiom,
( ~ 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))
| 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) ),
file('theBenchmark.p',cls_head__Var__reduction_1) ).
cnf(cls_IT_OVar_0,axiom,
( ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB)
| 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))) ),
file('theBenchmark.p',cls_IT_OVar_0) ).
cnf(cls_dB_Osimps_I5_J_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) != c_Lambda_OdB_OVar(V_nat),
file('theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
cnf(cls_rtranclp__idemp_0,axiom,
c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(V_r,T_a),T_a) = c_Transitive__Closure_Ortranclp(V_r,T_a),
file('theBenchmark.p',cls_rtranclp__idemp_0) ).
cnf(cls_Abs__App__neq__Var__apps_0,axiom,
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),
file('theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
cnf(cls_inf2E_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_fun(T_b,tc_bool))),V_x),V_y))
| hBOOL(hAPP(hAPP(V_A,V_x),V_y)) ),
file('theBenchmark.p',cls_inf2E_0) ).
cnf(cls_inf2E_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_fun(T_b,tc_bool))),V_x),V_y))
| hBOOL(hAPP(hAPP(V_B,V_x),V_y)) ),
file('theBenchmark.p',cls_inf2E_1) ).
cnf(cls_app__Var__IT_0,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),c_Lambda_OdB_OVar(V_i)))) ),
file('theBenchmark.p',cls_app__Var__IT_0) ).
cnf(cls_subst__lift_0,axiom,
c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t,
file('theBenchmark.p',cls_subst__lift_0) ).
cnf(cls_tranclp_Or__into__trancl_0,axiom,
( ~ hBOOL(hAPP(hAPP(V_r,V_a),V_b))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(V_r,T_a),V_a),V_b)) ),
file('theBenchmark.p',cls_tranclp_Or__into__trancl_0) ).
cnf(cls_inf__sup__aci_I8_J_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
cnf(cls_sup__left__idem_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_sup__left__idem_0) ).
cnf(cls_inf__sup__aci_I5_J_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,V_x,T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
cnf(cls_sup__commute_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,V_x,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_sup__commute_0) ).
cnf(cls_rtrancl__beta__App_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H))
| 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))) ),
file('theBenchmark.p',cls_rtrancl__beta__App_0) ).
cnf(cls_Lambda_0,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_r))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(V_r))) ),
file('theBenchmark.p',cls_Lambda_0) ).
cnf(cls_apps__eq__tail__conv_0,axiom,
( V_r = V_s
| 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) ),
file('theBenchmark.p',cls_apps__eq__tail__conv_0) ).
cnf(cls_rtrancl__beta__AppL_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H))
| 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))) ),
file('theBenchmark.p',cls_rtrancl__beta__AppL_0) ).
cnf(cls_rtrancl__beta__AppR_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H))
| 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))) ),
file('theBenchmark.p',cls_rtrancl__beta__AppR_0) ).
cnf(cls_Abs__eq__apps__conv_0,axiom,
( c_Lambda_OdB_OAbs(V_r) = V_s
| c_Lambda_OdB_OAbs(V_r) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('theBenchmark.p',cls_Abs__eq__apps__conv_0) ).
cnf(cls_inf__sup__aci_I1_J_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
cnf(cls_inf__commute_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_inf__commute_0) ).
cnf(cls_inf__sup__aci_I6_J_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
cnf(cls_inf__sup__aci_I7_J_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
cnf(cls_sup__left__commute_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_sup__left__commute_0) ).
cnf(cls_sup__assoc_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_sup__assoc_0) ).
cnf(cls_sup__idem_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_x,V_x,T_a) = V_x
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_sup__idem_0) ).
cnf(cls_inf__sup__distrib2_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),V_x,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a),c_Lattices_Olower__semilattice__class_Oinf(V_z,V_x,T_a),T_a)
| ~ class_Lattices_Odistrib__lattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__distrib2_0) ).
cnf(cls_inf__sup__distrib1_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a)
| ~ class_Lattices_Odistrib__lattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__distrib1_0) ).
cnf(cls_rtrancl__beta__Abs_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H))
| 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))) ),
file('theBenchmark.p',cls_rtrancl__beta__Abs_0) ).
cnf(cls_pred__comp_Ointros_0,axiom,
( ~ hBOOL(hAPP(hAPP(V_r,V_a),V_b))
| ~ hBOOL(hAPP(hAPP(V_s,V_b),V_c))
| hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(V_r,V_s,T_a,T_b,T_c),V_a),V_c)) ),
file('theBenchmark.p',cls_pred__comp_Ointros_0) ).
cnf(cls_tranclp__rtranclp__tranclp_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(V_r,T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_c))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(V_r,T_a),V_a),V_c)) ),
file('theBenchmark.p',cls_tranclp__rtranclp__tranclp_0) ).
cnf(cls_rtranclp__tranclp__tranclp_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(V_r,T_a),V_y),V_z))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(V_r,T_a),V_x),V_z)) ),
file('theBenchmark.p',cls_rtranclp__tranclp__tranclp_0) ).
cnf(cls_rtranclp_Ortrancl__refl_0,axiom,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_a)),
file('theBenchmark.p',cls_rtranclp_Ortrancl__refl_0) ).
cnf(cls_Nitpick_Ortranclp__def_1,axiom,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_x)),
file('theBenchmark.p',cls_Nitpick_Ortranclp__def_1) ).
cnf(cls_rtranclp__trans_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_y),V_z))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_z)) ),
file('theBenchmark.p',cls_rtranclp__trans_0) ).
cnf(cls_subst__preserves__beta2_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s))
| 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))) ),
file('theBenchmark.p',cls_subst__preserves__beta2_0) ).
cnf(cls_rtranclp__into__tranclp2_0,axiom,
( ~ hBOOL(hAPP(hAPP(V_r,V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_c))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(V_r,T_a),V_a),V_c)) ),
file('theBenchmark.p',cls_rtranclp__into__tranclp2_0) ).
cnf(cls_rtranclp__into__tranclp1_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(V_r,V_b),V_c))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(V_r,T_a),V_a),V_c)) ),
file('theBenchmark.p',cls_rtranclp__into__tranclp1_0) ).
cnf(cls_lift_Osimps_I2_J_0,axiom,
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)),
file('theBenchmark.p',cls_lift_Osimps_I2_J_0) ).
cnf(cls_wfP__trancl_0,axiom,
( ~ c_Wellfounded_OwfP(V_r,T_a)
| c_Wellfounded_OwfP(c_Transitive__Closure_Otranclp(V_r,T_a),T_a) ),
file('theBenchmark.p',cls_wfP__trancl_0) ).
cnf(cls_Nitpick_Ortranclp__def_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(V_r,T_a),V_a),V_b))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_b)) ),
file('theBenchmark.p',cls_Nitpick_Ortranclp__def_2) ).
cnf(cls_subst__preserves__beta_H_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s))
| 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))) ),
file('theBenchmark.p',cls_subst__preserves__beta_H_0) ).
cnf(cls_subst__preserves__beta2_H_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s))
| 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))) ),
file('theBenchmark.p',cls_subst__preserves__beta2_H_0) ).
cnf(cls_Var__IT_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n))),
file('theBenchmark.p',cls_Var__IT_0) ).
cnf(cls_dB_Osimps_I6_J_0,axiom,
c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H),
file('theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
cnf(cls_r__into__rtranclp_0,axiom,
( ~ hBOOL(hAPP(hAPP(V_r,V_x),V_y))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_y)) ),
file('theBenchmark.p',cls_r__into__rtranclp_0) ).
cnf(cls_sup2E_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_fun(T_b,tc_bool))),V_x),V_y))
| hBOOL(hAPP(hAPP(V_A,V_x),V_y))
| hBOOL(hAPP(hAPP(V_B,V_x),V_y)) ),
file('theBenchmark.p',cls_sup2E_0) ).
cnf(cls_sup2CI_0,axiom,
( ~ hBOOL(hAPP(hAPP(V_B,V_x),V_y))
| hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_fun(T_b,tc_bool))),V_x),V_y)) ),
file('theBenchmark.p',cls_sup2CI_0) ).
cnf(cls_sup2CI_1,axiom,
( ~ hBOOL(hAPP(hAPP(V_A,V_x),V_y))
| hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_fun(T_b,tc_bool))),V_x),V_y)) ),
file('theBenchmark.p',cls_sup2CI_1) ).
cnf(cls_Beta_0,axiom,
( ~ 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)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_s))
| 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))) ),
file('theBenchmark.p',cls_Beta_0) ).
cnf(cls_lift__IT_0,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(V_t,V_i))) ),
file('theBenchmark.p',cls_lift__IT_0) ).
cnf(cls_Var__apps__neq__Abs__apps_0,axiom,
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),
file('theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).
cnf(cls_inf__sup__aci_I2_J_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
cnf(cls_inf__sup__aci_I3_J_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
cnf(cls_inf__left__commute_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_inf__left__commute_0) ).
cnf(cls_inf__assoc_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_inf__assoc_0) ).
cnf(cls_dB_Osimps_I3_J_0,axiom,
( V_dB = V_dB_H
| c_Lambda_OdB_OAbs(V_dB) != c_Lambda_OdB_OAbs(V_dB_H) ),
file('theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
cnf(cls_dB_Osimps_I4_J_0,axiom,
c_Lambda_OdB_OVar(V_nat) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H),
file('theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
cnf(cls_Var__eq__apps__conv_0,axiom,
( c_Lambda_OdB_OVar(V_m) = V_s
| c_Lambda_OdB_OVar(V_m) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('theBenchmark.p',cls_Var__eq__apps__conv_0) ).
cnf(cls_apps__preserves__beta_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s))
| 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))) ),
file('theBenchmark.p',cls_apps__preserves__beta_0) ).
cnf(cls_sup__inf__absorb_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = V_x
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_sup__inf__absorb_0) ).
cnf(cls_beta_0,axiom,
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)))),
file('theBenchmark.p',cls_beta_0) ).
cnf(cls_lift__preserves__beta_H_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s))
| 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))) ),
file('theBenchmark.p',cls_lift__preserves__beta_H_0) ).
cnf(cls_var__app__type__eq_0,axiom,
( ~ 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)
| ~ 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)
| V_T = V_U ),
file('theBenchmark.p',cls_var__app__type__eq_0) ).
cnf(cls_dB_Osimps_I2_J_1,axiom,
( V_dB2 = V_dB2_H
| hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) ),
file('theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
cnf(cls_dB_Osimps_I2_J_0,axiom,
( V_dB1 = V_dB1_H
| hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) ),
file('theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
cnf(cls_inf__sup__absorb_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = V_x
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__absorb_0) ).
cnf(cls_Abs__apps__eq__Abs__apps__conv_1,axiom,
( V_rs = V_ss
| 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) ),
file('theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_1) ).
cnf(cls_Abs__apps__eq__Abs__apps__conv_0,axiom,
( V_r = V_s
| 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) ),
file('theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_0) ).
cnf(cls_apps__eq__Abs__conv_0,axiom,
( V_s = c_Lambda_OdB_OAbs(V_r)
| c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(V_r) ),
file('theBenchmark.p',cls_apps__eq__Abs__conv_0) ).
cnf(cls_rtranclp__reflcl_0,axiom,
c_Transitive__Closure_Ortranclp(c_Lattices_Oupper__semilattice__class_Osup(V_R,c_fequal(T_a),tc_fun(T_a,tc_fun(T_a,tc_bool))),T_a) = c_Transitive__Closure_Ortranclp(V_R,T_a),
file('theBenchmark.p',cls_rtranclp__reflcl_0) ).
cnf(cls_Nitpick_Ortranclp__def_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_b))
| V_a = V_b
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(V_r,T_a),V_a),V_b)) ),
file('theBenchmark.p',cls_Nitpick_Ortranclp__def_0) ).
cnf(cls_rtranclpD_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_R,T_a),V_a),V_b))
| V_a = V_b
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(V_R,T_a),V_a),V_b)) ),
file('theBenchmark.p',cls_rtranclpD_0) ).
cnf(cls_apps__preserves__beta2_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s))
| 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))) ),
file('theBenchmark.p',cls_apps__preserves__beta2_0) ).
cnf(cls_rtranclp__sup__rtranclp_0,axiom,
c_Transitive__Closure_Ortranclp(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortranclp(V_R,T_a),c_Transitive__Closure_Ortranclp(V_S,T_a),tc_fun(T_a,tc_fun(T_a,tc_bool))),T_a) = c_Transitive__Closure_Ortranclp(c_Lattices_Oupper__semilattice__class_Osup(V_R,V_S,tc_fun(T_a,tc_fun(T_a,tc_bool))),T_a),
file('theBenchmark.p',cls_rtranclp__sup__rtranclp_0) ).
cnf(cls_sup__inf__distrib2_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),V_x,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_y,V_x,T_a),c_Lattices_Oupper__semilattice__class_Osup(V_z,V_x,T_a),T_a)
| ~ class_Lattices_Odistrib__lattice(T_a) ),
file('theBenchmark.p',cls_sup__inf__distrib2_0) ).
cnf(cls_sup__inf__distrib1_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a)
| ~ class_Lattices_Odistrib__lattice(T_a) ),
file('theBenchmark.p',cls_sup__inf__distrib1_0) ).
cnf(cls_inf__sup__aci_I4_J_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
cnf(cls_inf__left__idem_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_inf__left__idem_0) ).
cnf(cls_subst__Var__IT_0,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_r))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j))) ),
file('theBenchmark.p',cls_subst__Var__IT_0) ).
cnf(cls_reflcl__tranclp_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otranclp(V_r,T_a),c_fequal(T_a),tc_fun(T_a,tc_fun(T_a,tc_bool))) = c_Transitive__Closure_Ortranclp(V_r,T_a),
file('theBenchmark.p',cls_reflcl__tranclp_0) ).
cnf(cls_inf__idem_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_x,T_a) = V_x
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_inf__idem_0) ).
cnf(cls_subst__eq_0,axiom,
c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k) = V_u,
file('theBenchmark.p',cls_subst__eq_0) ).
cnf(cls_Var__apps__eq__Var__apps__conv_1,axiom,
( V_rs = V_ss
| 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) ),
file('theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).
cnf(cls_Var__apps__eq__Var__apps__conv_0,axiom,
( V_m = V_n
| 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) ),
file('theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).
cnf(cls_dB_Osimps_I9_J_0,axiom,
c_Lambda_OdB_OAbs(V_dB_H) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),
file('theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
cnf(cls_tranclp__trans_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(V_r,T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(V_r,T_a),V_y),V_z))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(V_r,T_a),V_x),V_z)) ),
file('theBenchmark.p',cls_tranclp__trans_0) ).
cnf(cls_dB_Osimps_I1_J_0,axiom,
( V_nat = V_nat_H
| c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OVar(V_nat_H) ),
file('theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
cnf(cls_dB_Osimps_I8_J_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != c_Lambda_OdB_OAbs(V_dB_H),
file('theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
cnf(cls_dB_Osimps_I7_J_0,axiom,
c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat),
file('theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
cnf(cls_subst__App_0,axiom,
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)),
file('theBenchmark.p',cls_subst__App_0) ).
cnf(cls_inf2I_0,axiom,
( ~ hBOOL(hAPP(hAPP(V_A,V_x),V_y))
| ~ hBOOL(hAPP(hAPP(V_B,V_x),V_y))
| hBOOL(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_fun(T_b,tc_bool))),V_x),V_y)) ),
file('theBenchmark.p',cls_inf2I_0) ).
cnf(cls_converse__rtranclp__into__rtranclp_0,axiom,
( ~ hBOOL(hAPP(hAPP(V_r,V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_c))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_c)) ),
file('theBenchmark.p',cls_converse__rtranclp__into__rtranclp_0) ).
cnf(cls_rtranclp_Ortrancl__into__rtrancl_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(V_r,V_b),V_c))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_c)) ),
file('theBenchmark.p',cls_rtranclp_Ortrancl__into__rtrancl_0) ).
cnf(cls_tranclp_Otrancl__into__trancl_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(V_r,T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(V_r,V_b),V_c))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(V_r,T_a),V_a),V_c)) ),
file('theBenchmark.p',cls_tranclp_Otrancl__into__trancl_0) ).
cnf(cls_tranclp__into__tranclp2_0,axiom,
( ~ hBOOL(hAPP(hAPP(V_r,V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(V_r,T_a),V_b),V_c))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(V_r,T_a),V_a),V_c)) ),
file('theBenchmark.p',cls_tranclp__into__tranclp2_0) ).
cnf(cls_accp__downward_0,axiom,
( ~ c_Wellfounded_Oaccp(V_r,V_b,T_a)
| ~ hBOOL(hAPP(hAPP(V_r,V_a),V_b))
| c_Wellfounded_Oaccp(V_r,V_a,T_a) ),
file('theBenchmark.p',cls_accp__downward_0) ).
cnf(cls_accp_Ocases_0,axiom,
( ~ c_Wellfounded_Oaccp(V_r,V_a,T_a)
| ~ hBOOL(hAPP(hAPP(V_r,V_y),V_a))
| c_Wellfounded_Oaccp(V_r,V_y,T_a) ),
file('theBenchmark.p',cls_accp_Ocases_0) ).
cnf(cls_accp__induct_2,axiom,
( ~ c_Wellfounded_Oaccp(V_r,V_a,T_a)
| ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1(V_P,V_r,T_a)))
| hBOOL(hAPP(V_P,V_a)) ),
file('theBenchmark.p',cls_accp__induct_2) ).
cnf(cls_accp__induct_1,axiom,
( ~ c_Wellfounded_Oaccp(V_r,V_a,T_a)
| ~ hBOOL(hAPP(hAPP(V_r,V_y),c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1(V_P,V_r,T_a)))
| hBOOL(hAPP(V_P,V_y))
| hBOOL(hAPP(V_P,V_a)) ),
file('theBenchmark.p',cls_accp__induct_1) ).
cnf(cls_not__accp__down_0,axiom,
( c_Wellfounded_Oaccp(V_R,V_x,T_a)
| hBOOL(hAPP(hAPP(V_R,c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1(V_R,V_x,T_a)),V_x)) ),
file('theBenchmark.p',cls_not__accp__down_0) ).
cnf(cls_subject__reduction_0,axiom,
( ~ c_Type_Otyping(V_e,V_t,V_T)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H))
| c_Type_Otyping(V_e,V_t_H,V_T) ),
file('theBenchmark.p',cls_subject__reduction_0) ).
cnf(cls_accp__wfPD_0,axiom,
( ~ c_Wellfounded_OwfP(V_r,T_a)
| c_Wellfounded_Oaccp(V_r,V_x,T_a) ),
file('theBenchmark.p',cls_accp__wfPD_0) ).
cnf(cls_conversep__conversep_0,axiom,
c_Predicate_Oconversep(c_Predicate_Oconversep(V_r,T_a,T_b),T_b,T_a) = V_r,
file('theBenchmark.p',cls_conversep__conversep_0) ).
cnf(cls_beta__cases_I1_J_0,axiom,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)),
file('theBenchmark.p',cls_beta__cases_I1_J_0) ).
cnf(cls_accp_OaccI_0,axiom,
( hBOOL(hAPP(hAPP(V_r,c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1(V_r,V_x,T_a)),V_x))
| c_Wellfounded_Oaccp(V_r,V_x,T_a) ),
file('theBenchmark.p',cls_accp_OaccI_0) ).
cnf(cls_conversep__eq_0,axiom,
c_Predicate_Oconversep(c_fequal(T_a),T_a,T_a) = c_fequal(T_a),
file('theBenchmark.p',cls_conversep__eq_0) ).
cnf(cls_tranclp__converseD_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(c_Predicate_Oconversep(V_r,T_a,T_a),T_a),V_x),V_y))
| hBOOL(hAPP(hAPP(c_Predicate_Oconversep(c_Transitive__Closure_Otranclp(V_r,T_a),T_a,T_a),V_x),V_y)) ),
file('theBenchmark.p',cls_tranclp__converseD_0) ).
cnf(cls_tranclp__converseI_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(c_Transitive__Closure_Otranclp(V_r,T_a),T_a,T_a),V_x),V_y))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Otranclp(c_Predicate_Oconversep(V_r,T_a,T_a),T_a),V_x),V_y)) ),
file('theBenchmark.p',cls_tranclp__converseI_0) ).
cnf(cls_typing__elims_I1_J_0,axiom,
( ~ c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T)
| hAPP(V_e,V_i) = V_T ),
file('theBenchmark.p',cls_typing__elims_I1_J_0) ).
cnf(cls_not__accp__down_1,axiom,
( c_Wellfounded_Oaccp(V_R,V_x,T_a)
| ~ c_Wellfounded_Oaccp(V_R,c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1(V_R,V_x,T_a),T_a) ),
file('theBenchmark.p',cls_not__accp__down_1) ).
cnf(cls_tranclp__converse_0,axiom,
c_Transitive__Closure_Otranclp(c_Predicate_Oconversep(V_r,T_a,T_a),T_a) = c_Predicate_Oconversep(c_Transitive__Closure_Otranclp(V_r,T_a),T_a,T_a),
file('theBenchmark.p',cls_tranclp__converse_0) ).
cnf(cls_termi__implies__IT_0,axiom,
( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_r,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,V_r)) ),
file('theBenchmark.p',cls_termi__implies__IT_0) ).
cnf(cls_IT__implies__termi_0,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) ),
file('theBenchmark.p',cls_IT__implies__termi_0) ).
cnf(cls_accp__downwards__aux_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_a))
| ~ c_Wellfounded_Oaccp(V_r,V_a,T_a)
| c_Wellfounded_Oaccp(V_r,V_b,T_a) ),
file('theBenchmark.p',cls_accp__downwards__aux_0) ).
cnf(cls_accp__downwards_0,axiom,
( ~ c_Wellfounded_Oaccp(V_r,V_a,T_a)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_a))
| c_Wellfounded_Oaccp(V_r,V_b,T_a) ),
file('theBenchmark.p',cls_accp__downwards_0) ).
cnf(cls_subst__preserves__beta_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(V_r,V_t,V_i)),c_Lambda_Osubst(V_s,V_t,V_i))) ),
file('theBenchmark.p',cls_subst__preserves__beta_0) ).
cnf(cls_accp_Oinducts_2,axiom,
( ~ c_Wellfounded_Oaccp(V_r,V_x,t_a)
| ~ hBOOL(hAPP(V_P,v_sko__Wellfounded__Xaccp__Xinducts__1(V_P,V_r)))
| hBOOL(hAPP(V_P,V_x)) ),
file('theBenchmark.p',cls_accp_Oinducts_2) ).
cnf(cls_accp_Oinducts_1,axiom,
( ~ c_Wellfounded_Oaccp(V_r,V_x,t_a)
| ~ hBOOL(hAPP(hAPP(V_r,V_y),v_sko__Wellfounded__Xaccp__Xinducts__1(V_P,V_r)))
| hBOOL(hAPP(V_P,V_y))
| hBOOL(hAPP(V_P,V_x)) ),
file('theBenchmark.p',cls_accp_Oinducts_1) ).
cnf(cls_double__induction__lemma_0,axiom,
( 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)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_s,tc_Lambda_OdB)
| ~ 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) ),
file('theBenchmark.p',cls_double__induction__lemma_0) ).
cnf(cls_accp_Oinduct_2,axiom,
( ~ c_Wellfounded_Oaccp(V_r,V_x,t_a)
| ~ hBOOL(hAPP(V_P,v_sko__Wellfounded__Xaccp__Xinduct__1(V_P,V_r)))
| hBOOL(hAPP(V_P,V_x)) ),
file('theBenchmark.p',cls_accp_Oinduct_2) ).
cnf(cls_accp_Oinduct_1,axiom,
( ~ c_Wellfounded_Oaccp(V_r,V_x,t_a)
| ~ hBOOL(hAPP(hAPP(V_r,V_y),v_sko__Wellfounded__Xaccp__Xinduct__1(V_P,V_r)))
| hBOOL(hAPP(V_P,V_y))
| hBOOL(hAPP(V_P,V_x)) ),
file('theBenchmark.p',cls_accp_Oinduct_1) ).
cnf(cls_conversep_Ointros_0,axiom,
( ~ hBOOL(hAPP(hAPP(V_r,V_a),V_b))
| hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_b),V_a)) ),
file('theBenchmark.p',cls_conversep_Ointros_0) ).
cnf(cls_conversep_Ocases_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_a1),V_a2))
| hBOOL(hAPP(hAPP(V_r,V_a2),V_a1)) ),
file('theBenchmark.p',cls_conversep_Ocases_0) ).
cnf(cls_conversep__iff_1,axiom,
( ~ hBOOL(hAPP(hAPP(V_r,V_b),V_a))
| hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_a),V_b)) ),
file('theBenchmark.p',cls_conversep__iff_1) ).
cnf(cls_conversepD_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_a),V_b))
| hBOOL(hAPP(hAPP(V_r,V_b),V_a)) ),
file('theBenchmark.p',cls_conversepD_0) ).
cnf(cls_accp_Oinducts_0,axiom,
( ~ c_Wellfounded_Oaccp(V_r,V_x,t_a)
| ~ hBOOL(hAPP(hAPP(V_r,V_ya),v_sko__Wellfounded__Xaccp__Xinducts__1(V_P,V_r)))
| c_Wellfounded_Oaccp(V_r,V_ya,t_a)
| hBOOL(hAPP(V_P,V_x)) ),
file('theBenchmark.p',cls_accp_Oinducts_0) ).
cnf(cls_accp_Oinduct_0,axiom,
( ~ c_Wellfounded_Oaccp(V_r,V_x,t_a)
| ~ hBOOL(hAPP(hAPP(V_r,V_ya),v_sko__Wellfounded__Xaccp__Xinduct__1(V_P,V_r)))
| c_Wellfounded_Oaccp(V_r,V_ya,t_a)
| hBOOL(hAPP(V_P,V_x)) ),
file('theBenchmark.p',cls_accp_Oinduct_0) ).
cnf(cls_converse__join_0,axiom,
c_Predicate_Oconversep(c_Lattices_Oupper__semilattice__class_Osup(V_r,V_s,tc_fun(T_b,tc_fun(T_a,tc_bool))),T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Predicate_Oconversep(V_r,T_b,T_a),c_Predicate_Oconversep(V_s,T_b,T_a),tc_fun(T_a,tc_fun(T_b,tc_bool))),
file('theBenchmark.p',cls_converse__join_0) ).
cnf(cls_rtranclp__converseD_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(V_r,T_a,T_a),T_a),V_x),V_y))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_y),V_x)) ),
file('theBenchmark.p',cls_rtranclp__converseD_0) ).
cnf(cls_rtranclp__converseI_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_y),V_x))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(V_r,T_a,T_a),T_a),V_x),V_y)) ),
file('theBenchmark.p',cls_rtranclp__converseI_0) ).
cnf(cls_accp__induct_0,axiom,
( ~ c_Wellfounded_Oaccp(V_r,V_a,T_a)
| c_Wellfounded_Oaccp(V_r,c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1(V_P,V_r,T_a),T_a)
| hBOOL(hAPP(V_P,V_a)) ),
file('theBenchmark.p',cls_accp__induct_0) ).
cnf(cls_typing_OVar_0,axiom,
c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)),
file('theBenchmark.p',cls_typing_OVar_0) ).
cnf(cls_converse__meet_0,axiom,
c_Predicate_Oconversep(c_Lattices_Olower__semilattice__class_Oinf(V_r,V_s,tc_fun(T_b,tc_fun(T_a,tc_bool))),T_b,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Predicate_Oconversep(V_r,T_b,T_a),c_Predicate_Oconversep(V_s,T_b,T_a),tc_fun(T_a,tc_fun(T_b,tc_bool))),
file('theBenchmark.p',cls_converse__meet_0) ).
cnf(cls_accp_OaccI_1,axiom,
( ~ c_Wellfounded_Oaccp(V_r,c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1(V_r,V_x,T_a),T_a)
| c_Wellfounded_Oaccp(V_r,V_x,T_a) ),
file('theBenchmark.p',cls_accp_OaccI_1) ).
cnf(cls_accpI_1,axiom,
( ~ c_Wellfounded_Oaccp(V_r,c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1(V_r,V_x,T_a),T_a)
| c_Wellfounded_Oaccp(V_r,V_x,T_a) ),
file('theBenchmark.p',cls_accpI_1) ).
cnf(cls_accpI_0,axiom,
( hBOOL(hAPP(hAPP(V_r,c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1(V_r,V_x,T_a)),V_x))
| c_Wellfounded_Oaccp(V_r,V_x,T_a) ),
file('theBenchmark.p',cls_accpI_0) ).
cnf(cls_appR_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t))
| 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))) ),
file('theBenchmark.p',cls_appR_0) ).
cnf(cls_appL_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t))
| 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))) ),
file('theBenchmark.p',cls_appL_0) ).
cnf(cls_accp__induct__rule_0,axiom,
( ~ c_Wellfounded_Oaccp(V_r,V_a,T_a)
| c_Wellfounded_Oaccp(V_r,c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1(V_P,V_r,T_a),T_a)
| hBOOL(hAPP(V_P,V_a)) ),
file('theBenchmark.p',cls_accp__induct__rule_0) ).
cnf(cls_subject__reduction_H_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H))
| ~ c_Type_Otyping(V_e,V_t,V_T)
| c_Type_Otyping(V_e,V_t_H,V_T) ),
file('theBenchmark.p',cls_subject__reduction_H_0) ).
cnf(cls_lift__preserves__beta_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(V_r,V_i)),c_Lambda_Olift(V_s,V_i))) ),
file('theBenchmark.p',cls_lift__preserves__beta_0) ).
cnf(cls_accp__induct__rule_2,axiom,
( ~ c_Wellfounded_Oaccp(V_r,V_a,T_a)
| ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1(V_P,V_r,T_a)))
| hBOOL(hAPP(V_P,V_a)) ),
file('theBenchmark.p',cls_accp__induct__rule_2) ).
cnf(cls_accp__induct__rule_1,axiom,
( ~ c_Wellfounded_Oaccp(V_r,V_a,T_a)
| ~ hBOOL(hAPP(hAPP(V_r,V_y),c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1(V_P,V_r,T_a)))
| hBOOL(hAPP(V_P,V_y))
| hBOOL(hAPP(V_P,V_a)) ),
file('theBenchmark.p',cls_accp__induct__rule_1) ).
cnf(cls_converse__pred__comp_0,axiom,
c_Predicate_Oconversep(c_Predicate_Opred__comp(V_r,V_s,T_b,T_c,T_a),T_b,T_a) = c_Predicate_Opred__comp(c_Predicate_Oconversep(V_s,T_c,T_a),c_Predicate_Oconversep(V_r,T_b,T_c),T_a,T_c,T_b),
file('theBenchmark.p',cls_converse__pred__comp_0) ).
cnf(cls_type__implies__IT_0,axiom,
( ~ c_Type_Otyping(V_e,V_t,V_T)
| hBOOL(hAPP(c_InductTermi_OIT,V_t)) ),
file('theBenchmark.p',cls_type__implies__IT_0) ).
cnf(cls_abs_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(V_s)),c_Lambda_OdB_OAbs(V_t))) ),
file('theBenchmark.p',cls_abs_0) ).
cnf(cls_conjecture_0,negated_conjecture,
c_Type_Otyping(v_e,v_t,v_T),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_1,negated_conjecture,
~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),v_t,tc_Lambda_OdB),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(clsarity_fun__Lattices_Oupper__semilattice,axiom,
( ~ class_Lattices_Olattice(T_1)
| class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
cnf(clsarity_fun__Lattices_Olower__semilattice,axiom,
( ~ class_Lattices_Olattice(T_1)
| class_Lattices_Olower__semilattice(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
cnf(clsarity_fun__Lattices_Odistrib__lattice,axiom,
( ~ class_Lattices_Odistrib__lattice(T_1)
| class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
cnf(clsarity_fun__Lattices_Olattice,axiom,
( ~ class_Lattices_Olattice(T_1)
| class_Lattices_Olattice(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
cnf(clsarity_nat__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
file('theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
cnf(clsarity_nat__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_nat),
file('theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
cnf(clsarity_nat__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_nat),
file('theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).
cnf(clsarity_nat__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_nat),
file('theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
cnf(clsarity_bool__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
cnf(clsarity_bool__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
cnf(clsarity_bool__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
file('theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
cnf(clsarity_bool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_bool),
file('theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
hBOOL(hAPP(hAPP(c_fequal(T_a),V_x),V_x)),
file('theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_fequal(T_a),V_X),V_Y))
| V_X = V_Y ),
file('theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( c_List_Olist_ONil(Eq_x_0) = c_List_Olist_ONil(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( c_Type_Otype_OFun(Eq_x_0,Eq_x_1) = c_Type_Otype_OFun(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( hAPP(Eq_x_0,Eq_x_1) = hAPP(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( c_Lambda_OdB_OAbs(Eq_x_0) = c_Lambda_OdB_OAbs(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( c_List_Ofoldl(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_List_Ofoldl(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( c_Type_Oshift(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Type_Oshift(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( c_Lambda_Olift(Eq_x_0,Eq_x_1) = c_Lambda_Olift(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( c_Lambda_Osubst(Eq_x_0,Eq_x_1,Eq_x_2) = c_Lambda_Osubst(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( c_Lambda_OdB_OVar(Eq_x_0) = c_Lambda_OdB_OVar(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( c_HOL_Ozero__class_Ozero(Eq_x_0) = c_HOL_Ozero__class_Ozero(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( c_Transitive__Closure_Ortranclp(Eq_x_0,Eq_x_1) = c_Transitive__Closure_Ortranclp(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( tc_fun(Eq_x_0,Eq_x_1) = tc_fun(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(Eq_x_0,Eq_x_1,Eq_x_2) = c_Lattices_Olower__semilattice__class_Oinf(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( c_Transitive__Closure_Otranclp(Eq_x_0,Eq_x_1) = c_Transitive__Closure_Otranclp(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(Eq_x_0,Eq_x_1,Eq_x_2) = c_Lattices_Oupper__semilattice__class_Osup(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( c_Predicate_Opred__comp(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Predicate_Opred__comp(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( c_fequal(Eq_x_0) = c_fequal(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_24,axiom,
( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,axiom,
( c_Predicate_Oconversep(Eq_x_0,Eq_x_1,Eq_x_2) = c_Predicate_Oconversep(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,axiom,
( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_27,axiom,
( v_sko__Wellfounded__Xaccp__Xinducts__1(Eq_x_0,Eq_x_1) = v_sko__Wellfounded__Xaccp__Xinducts__1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_28,axiom,
( v_sko__Wellfounded__Xaccp__Xinduct__1(Eq_x_0,Eq_x_1) = v_sko__Wellfounded__Xaccp__Xinduct__1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_29,axiom,
( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_30,axiom,
( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_31,axiom,
( c_ListOrder_Ostep1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ c_ListOrder_Ostep1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_32,axiom,
( c_Type_Otyping(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_Type_Otyping(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,axiom,
( hBOOL(Eq_y_0)
| ~ hBOOL(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_34,axiom,
( c_List_Olistsp(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_List_Olistsp(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_35,axiom,
( class_Lattices_Olattice(Eq_y_0)
| ~ class_Lattices_Olattice(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_36,axiom,
( class_Lattices_Oupper__semilattice(Eq_y_0)
| ~ class_Lattices_Oupper__semilattice(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_37,axiom,
( class_Lattices_Olower__semilattice(Eq_y_0)
| ~ class_Lattices_Olower__semilattice(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_38,axiom,
( class_Lattices_Odistrib__lattice(Eq_y_0)
| ~ class_Lattices_Odistrib__lattice(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_39,axiom,
( c_Wellfounded_OwfP(Eq_y_0,Eq_y_1)
| ~ c_Wellfounded_OwfP(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_40,axiom,
( c_Wellfounded_Oaccp(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_Wellfounded_Oaccp(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL856-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n016.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Sat Sep 19 16:01:12 UTC 2026
% 0.11/5.38 % CPUTime :
% 30.27/35.51 % SZS status Unsatisfiable for theBenchmark
% 30.27/35.51 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------