TSTP Solution File: LCL798-1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : LCL798-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n024.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 06:51:00 EDT 2023
% Result : Unsatisfiable 0.18s 0.62s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL798-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Aug 25 04:37:24 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.54 start to proof:theBenchmark
% 0.18/0.60 %-------------------------------------------
% 0.18/0.60 % File :CSE---1.6
% 0.18/0.60 % Problem :theBenchmark
% 0.18/0.60 % Transform :cnf
% 0.18/0.60 % Format :tptp:raw
% 0.18/0.60 % Command :java -jar mcs_scs.jar %d %s
% 0.18/0.60
% 0.18/0.60 % Result :Theorem 0.000000s
% 0.18/0.60 % Output :CNFRefutation 0.000000s
% 0.18/0.60 %-------------------------------------------
% 0.18/0.60 %------------------------------------------------------------------------------
% 0.18/0.60 % File : LCL798-1 : TPTP v8.1.2. Released v4.1.0.
% 0.18/0.60 % Domain : Logic Calculi
% 0.18/0.60 % Problem : Strong normalization of typed lambda calculus 148_51
% 0.18/0.60 % Version : Especial.
% 0.18/0.60 % English :
% 0.18/0.60
% 0.18/0.60 % Refs : [vON99] von Oheimb & Nipkow (1999), Machine-Checking the Java
% 0.18/0.60 % : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe
% 0.18/0.60 % : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.18/0.60 % Source : [Nip10]
% 0.18/0.60 % Names : StrongNorm-148_51 [Nip10]
% 0.18/0.60
% 0.18/0.60 % Status : Unsatisfiable
% 0.18/0.60 % Rating : 0.10 v8.1.0, 0.05 v7.5.0, 0.11 v7.4.0, 0.12 v7.3.0, 0.08 v7.1.0, 0.00 v7.0.0, 0.07 v6.4.0, 0.00 v6.2.0, 0.10 v6.1.0, 0.00 v5.5.0, 0.10 v5.3.0, 0.11 v5.2.0, 0.19 v5.1.0, 0.24 v5.0.0, 0.14 v4.1.0
% 0.18/0.60 % Syntax : Number of clauses : 80 ( 34 unt; 10 nHn; 56 RR)
% 0.18/0.60 % Number of literals : 154 ( 43 equ; 79 neg)
% 0.18/0.60 % Maximal clause size : 4 ( 1 avg)
% 0.18/0.60 % Maximal term depth : 3 ( 1 avg)
% 0.18/0.60 % Number of predicates : 12 ( 11 usr; 0 prp; 1-3 aty)
% 0.18/0.60 % Number of functors : 23 ( 23 usr; 13 con; 0-4 aty)
% 0.18/0.60 % Number of variables : 168 ( 42 sgn)
% 0.18/0.60 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.18/0.60
% 0.18/0.60 % Comments :
% 0.18/0.60 %------------------------------------------------------------------------------
% 0.18/0.60 cnf(cls_of__nat__less__0__iff_0,axiom,
% 0.18/0.60 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.18/0.60 | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
% 0.18/0.60
% 0.18/0.60 cnf(cls_of__nat__0_0,axiom,
% 0.18/0.60 ( ~ class_Ring__and__Field_Osemiring__1(T_a)
% 0.18/0.60 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.18/0.60
% 0.18/0.60 cnf(cls_of__nat__eq__iff_0,axiom,
% 0.18/0.60 ( ~ class_Nat_Osemiring__char__0(T_a)
% 0.18/0.60 | c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a) != c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)
% 0.18/0.60 | V_m = V_n ) ).
% 0.18/0.60
% 0.18/0.60 cnf(cls_of__nat__less__iff_1,axiom,
% 0.18/0.60 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.18/0.60 | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)
% 0.18/0.60 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
% 0.18/0.60
% 0.18/0.60 cnf(cls_of__nat__less__iff_0,axiom,
% 0.18/0.60 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.18/0.60 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.18/0.60 | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ).
% 0.18/0.60
% 0.18/0.60 cnf(cls_order__less__asym_H_0,axiom,
% 0.18/0.60 ( ~ class_Orderings_Opreorder(T_a)
% 0.18/0.60 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
% 0.18/0.60 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
% 0.18/0.60
% 0.18/0.60 cnf(cls_order__less__asym_0,axiom,
% 0.18/0.60 ( ~ class_Orderings_Opreorder(T_a)
% 0.18/0.61 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
% 0.18/0.61 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_not__less__iff__gr__or__eq_1,axiom,
% 0.18/0.61 ( ~ class_Orderings_Olinorder(T_a)
% 0.18/0.61 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
% 0.18/0.61 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_xt1_I9_J_0,axiom,
% 0.18/0.61 ( ~ class_Orderings_Oorder(T_a)
% 0.18/0.61 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
% 0.18/0.61 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_neq0__conv_1,axiom,
% 0.18/0.61 ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_gr0I_0,axiom,
% 0.18/0.61 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
% 0.18/0.61 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_of__nat__0__less__iff_0,axiom,
% 0.18/0.61 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.18/0.61 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
% 0.18/0.61 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_of__nat__0__less__iff_1,axiom,
% 0.18/0.61 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.18/0.61 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)
% 0.18/0.61 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_linorder__antisym__conv3_0,axiom,
% 0.18/0.61 ( ~ class_Orderings_Olinorder(T_a)
% 0.18/0.61 | V_x = V_y
% 0.18/0.61 | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
% 0.18/0.61 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_linorder__less__linear_0,axiom,
% 0.18/0.61 ( ~ class_Orderings_Olinorder(T_a)
% 0.18/0.61 | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
% 0.18/0.61 | V_x = V_y
% 0.18/0.61 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_linorder__neqE_0,axiom,
% 0.18/0.61 ( ~ class_Orderings_Olinorder(T_a)
% 0.18/0.61 | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
% 0.18/0.61 | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
% 0.18/0.61 | V_x = V_y ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_linorder__neqE__nat_0,axiom,
% 0.18/0.61 ( c_HOL_Oord__class_Oless(V_y,V_x,tc_nat)
% 0.18/0.61 | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)
% 0.18/0.61 | V_x = V_y ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_nat__neq__iff_0,axiom,
% 0.18/0.61 ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
% 0.18/0.61 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.18/0.61 | V_m = V_n ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_not__less__iff__gr__or__eq_0,axiom,
% 0.18/0.61 ( ~ class_Orderings_Olinorder(T_a)
% 0.18/0.61 | V_x = V_y
% 0.18/0.61 | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
% 0.18/0.61 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_linorder__neqE__ordered__idom_0,axiom,
% 0.18/0.61 ( ~ class_Ring__and__Field_Oordered__idom(T_a)
% 0.18/0.61 | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
% 0.18/0.61 | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
% 0.18/0.61 | V_x = V_y ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_order__less__irrefl_0,axiom,
% 0.18/0.61 ( ~ class_Orderings_Opreorder(T_a)
% 0.18/0.61 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_linorder__neq__iff_1,axiom,
% 0.18/0.61 ( ~ class_Orderings_Olinorder(T_a)
% 0.18/0.61 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_order__less__le_1,axiom,
% 0.18/0.61 ( ~ class_Orderings_Oorder(T_a)
% 0.18/0.61 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_less__not__refl_0,axiom,
% 0.18/0.61 ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_nat__less__le_1,axiom,
% 0.18/0.61 ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_order__less__trans_0,axiom,
% 0.18/0.61 ( ~ class_Orderings_Opreorder(T_a)
% 0.18/0.61 | c_HOL_Oord__class_Oless(V_x,V_z,T_a)
% 0.18/0.61 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
% 0.18/0.61 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_xt1_I10_J_0,axiom,
% 0.18/0.61 ( ~ class_Orderings_Oorder(T_a)
% 0.18/0.61 | c_HOL_Oord__class_Oless(V_z,V_x,T_a)
% 0.18/0.61 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a)
% 0.18/0.61 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_gr__implies__not0_0,axiom,
% 0.18/0.61 ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_not__less0_0,axiom,
% 0.18/0.61 ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_dB_Osimps_I5_J_0,axiom,
% 0.18/0.61 c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) != c_Lambda_OdB_OVar(V_nat) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_abs_0,axiom,
% 0.18/0.61 ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_s),c_Lambda_OdB_OAbs(V_t))
% 0.18/0.61 | ~ c_Lambda_Obeta(V_s,V_t) ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_beta__cases_I2_J_0,axiom,
% 0.18/0.61 ( V_s = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(V_r,V_s))
% 0.18/0.61 | ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_r),V_s) ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_app__Var__IT_0,axiom,
% 0.18/0.61 ( c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i)))
% 0.18/0.61 | ~ c_InductTermi_OIT(V_t) ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_not__Cons__self_0,axiom,
% 0.18/0.61 V_xs != c_List_Olist_OCons(V_x,V_xs,T_a) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_not__Cons__self2_0,axiom,
% 0.18/0.61 c_List_Olist_OCons(V_x,V_t,T_a) != V_t ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_lift__preserves__beta_0,axiom,
% 0.18/0.61 ( c_Lambda_Obeta(c_Lambda_Olift(V_r,V_i),c_Lambda_Olift(V_s,V_i))
% 0.18/0.61 | ~ c_Lambda_Obeta(V_r,V_s) ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_lift_Osimps_I1_J_0,axiom,
% 0.18/0.61 ( c_Lambda_Olift(c_Lambda_OdB_OVar(V_i),V_k) = c_Lambda_OdB_OVar(V_i)
% 0.18/0.61 | ~ c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_appL_0,axiom,
% 0.18/0.61 ( c_Lambda_Obeta(c_Lambda_OdB_OApp(V_s,V_u),c_Lambda_OdB_OApp(V_t,V_u))
% 0.18/0.61 | ~ c_Lambda_Obeta(V_s,V_t) ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_appR_0,axiom,
% 0.18/0.61 ( c_Lambda_Obeta(c_Lambda_OdB_OApp(V_u,V_s),c_Lambda_OdB_OApp(V_u,V_t))
% 0.18/0.61 | ~ c_Lambda_Obeta(V_s,V_t) ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_subst__Var_1,axiom,
% 0.18/0.61 ( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)
% 0.18/0.61 | c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x),V_s,V_x) = V_s ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_subst__Var_2,axiom,
% 0.18/0.61 ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_i),V_s,V_k) = c_Lambda_OdB_OVar(V_i)
% 0.18/0.61 | V_i = V_k
% 0.18/0.61 | c_HOL_Oord__class_Oless(V_k,V_i,tc_nat) ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_lift_Osimps_I2_J_0,axiom,
% 0.18/0.61 c_Lambda_Olift(c_Lambda_OdB_OApp(V_s,V_t),V_k) = c_Lambda_OdB_OApp(c_Lambda_Olift(V_s,V_k),c_Lambda_Olift(V_t,V_k)) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_dB_Osimps_I6_J_0,axiom,
% 0.18/0.61 c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_dB_Osimps_I3_J_0,axiom,
% 0.18/0.61 ( c_Lambda_OdB_OAbs(V_dB) != c_Lambda_OdB_OAbs(V_dB_H)
% 0.18/0.61 | V_dB = V_dB_H ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_dB_Osimps_I4_J_0,axiom,
% 0.18/0.61 c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_beta_0,axiom,
% 0.18/0.61 c_Lambda_Obeta(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))) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_dB_Osimps_I2_J_1,axiom,
% 0.18/0.61 ( c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H)
% 0.18/0.61 | V_dB2 = V_dB2_H ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_dB_Osimps_I2_J_0,axiom,
% 0.18/0.61 ( c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H)
% 0.18/0.61 | V_dB1 = V_dB1_H ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_beta__cases_I1_J_0,axiom,
% 0.18/0.61 ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(V_i),V_t) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_beta__cases_I2_J_1,axiom,
% 0.18/0.61 ( c_Lambda_Obeta(V_r,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(V_r,V_s))
% 0.18/0.61 | ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_r),V_s) ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_subst__lt_0,axiom,
% 0.18/0.61 ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_j),V_u,V_i) = c_Lambda_OdB_OVar(V_j)
% 0.18/0.61 | ~ c_HOL_Oord__class_Oless(V_j,V_i,tc_nat) ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_list_Oinject_0,axiom,
% 0.18/0.61 ( c_List_Olist_OCons(V_a,V_list,T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a)
% 0.18/0.61 | V_a = V_a_H ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_list_Oinject_1,axiom,
% 0.18/0.61 ( c_List_Olist_OCons(V_a,V_list,T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a)
% 0.18/0.61 | V_list = V_list_H ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_dB_Osimps_I9_J_0,axiom,
% 0.18/0.61 c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OApp(V_dB1,V_dB2) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_dB_Osimps_I1_J_0,axiom,
% 0.18/0.61 ( c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OVar(V_nat_H)
% 0.18/0.61 | V_nat = V_nat_H ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_dB_Osimps_I8_J_0,axiom,
% 0.18/0.61 c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OAbs(V_dB_H) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_dB_Osimps_I7_J_0,axiom,
% 0.18/0.61 c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_subst__App_0,axiom,
% 0.18/0.61 c_Lambda_Osubst(c_Lambda_OdB_OApp(V_t,V_u),V_s,V_k) = c_Lambda_OdB_OApp(c_Lambda_Osubst(V_t,V_s,V_k),c_Lambda_Osubst(V_u,V_s,V_k)) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_subst__eq_0,axiom,
% 0.18/0.61 c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k) = V_u ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_subst__Var__IT_0,axiom,
% 0.18/0.61 ( c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j))
% 0.18/0.61 | ~ c_InductTermi_OIT(V_r) ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_lift__IT_0,axiom,
% 0.18/0.61 ( c_InductTermi_OIT(c_Lambda_Olift(V_t,V_i))
% 0.18/0.61 | ~ c_InductTermi_OIT(V_t) ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_True_0,axiom,
% 0.18/0.61 v_n____ = v_i____ ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_Var__IT_0,axiom,
% 0.18/0.61 c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n)) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_subst__preserves__beta_0,axiom,
% 0.18/0.61 ( c_Lambda_Obeta(c_Lambda_Osubst(V_r,V_t,V_i),c_Lambda_Osubst(V_s,V_t,V_i))
% 0.18/0.61 | ~ c_Lambda_Obeta(V_r,V_s) ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_Var_I3_J_0,axiom,
% 0.18/0.61 c_InductTermi_OIT(v_ua______) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_Lambda_0,axiom,
% 0.18/0.61 ( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
% 0.18/0.61 | ~ c_InductTermi_OIT(V_r) ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_uIT_0,axiom,
% 0.18/0.61 c_InductTermi_OIT(v_u____) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_subst__lift_0,axiom,
% 0.18/0.61 c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_Cons_0,axiom,
% 0.18/0.61 v_rs____ = c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_CHAINED_0,axiom,
% 0.18/0.61 ( c_InductTermi_OIT(c_Lambda_Osubst(v_a____,V_u,V_i))
% 0.18/0.61 | ~ c_Type_Otyping(V_e,V_u,v_T____)
% 0.18/0.61 | ~ c_InductTermi_OIT(V_u)
% 0.18/0.61 | ~ c_Type_Otyping(c_Type_Oshift(V_e,V_i,v_T____,tc_Type_Otype),v_a____,V_T_H) ) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_CHAINED_0_01,axiom,
% 0.18/0.61 c_Type_Otyping(v_e____,v_u____,v_T____) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_CHAINED_0_02,axiom,
% 0.18/0.61 c_InductTermi_OIT(v_u____) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_CHAINED_0_03,axiom,
% 0.18/0.61 c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____) ).
% 0.18/0.61
% 0.18/0.61 cnf(cls_conjecture_0,negated_conjecture,
% 0.18/0.61 ~ c_InductTermi_OIT(c_Lambda_Osubst(v_a____,v_u____,v_i____)) ).
% 0.18/0.61
% 0.18/0.61 cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom,
% 0.18/0.61 class_Ring__and__Field_Oordered__semidom(tc_nat) ).
% 0.18/0.61
% 0.18/0.62 cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom,
% 0.18/0.62 class_Ring__and__Field_Osemiring__1(tc_nat) ).
% 0.18/0.62
% 0.18/0.62 cnf(clsarity_nat__Nat_Osemiring__char__0,axiom,
% 0.18/0.62 class_Nat_Osemiring__char__0(tc_nat) ).
% 0.18/0.62
% 0.18/0.62 cnf(clsarity_nat__Orderings_Opreorder,axiom,
% 0.18/0.62 class_Orderings_Opreorder(tc_nat) ).
% 0.18/0.62
% 0.18/0.62 cnf(clsarity_nat__Orderings_Olinorder,axiom,
% 0.18/0.62 class_Orderings_Olinorder(tc_nat) ).
% 0.18/0.62
% 0.18/0.62 cnf(clsarity_nat__Orderings_Oorder,axiom,
% 0.18/0.62 class_Orderings_Oorder(tc_nat) ).
% 0.18/0.62
% 0.18/0.62 %------------------------------------------------------------------------------
% 0.18/0.62 %-------------------------------------------
% 0.18/0.62 % Proof found
% 0.18/0.62 % SZS status Theorem for theBenchmark
% 0.18/0.62 % SZS output start Proof
% 0.18/0.62 %ClaNum:120(EqnAxiom:40)
% 0.18/0.62 %VarNum:291(SingletonVarNum:145)
% 0.18/0.62 %MaxLitNum:4
% 0.18/0.62 %MaxfuncDepth:2
% 0.18/0.62 %SharedTerms:31
% 0.18/0.62 %goalClause: 74
% 0.18/0.62 %singleGoalClaCount:1
% 0.18/0.62 [41]E(a1,a20)
% 0.18/0.62 [42]P1(a2)
% 0.18/0.62 [43]P11(a2)
% 0.18/0.62 [44]P2(a2)
% 0.18/0.62 [45]P7(a2)
% 0.18/0.62 [46]P8(a2)
% 0.18/0.62 [47]P9(a2)
% 0.18/0.62 [48]P3(a21)
% 0.18/0.62 [50]P3(a22)
% 0.18/0.62 [53]P5(a19,a22,a16)
% 0.18/0.62 [52]E(f8(a15,a18,a7),a23)
% 0.18/0.62 [59]P5(f12(a19,a1,a16,a14),a15,a17)
% 0.18/0.62 [74]~P3(f9(a15,a22,a1))
% 0.18/0.62 [68]~P4(x681,x681,a2)
% 0.18/0.62 [51]P3(f3(x511))
% 0.18/0.62 [72]~P4(x721,f6(a2),a2)
% 0.18/0.62 [61]~E(f5(x611),f3(x612))
% 0.18/0.62 [66]~P6(f3(x661),x662)
% 0.18/0.62 [54]E(f9(f3(x541),x542,x541),x542)
% 0.18/0.62 [57]P6(f4(f5(x571),x572),f9(x571,x572,f6(a2)))
% 0.18/0.62 [62]~E(f3(x621),f4(x622,x623))
% 0.18/0.62 [63]~E(f5(x631),f4(x632,x633))
% 0.18/0.62 [64]~E(f4(x641,x642),f3(x643))
% 0.18/0.62 [65]~E(f4(x651,x652),f5(x653))
% 0.18/0.62 [70]~E(f8(x701,x702,x703),x702)
% 0.18/0.62 [55]E(f9(f10(x551,x552),x553,x552),x551)
% 0.18/0.62 [56]E(f4(f10(x561,x562),f10(x563,x562)),f10(f4(x561,x563),x562))
% 0.18/0.62 [58]E(f4(f9(x581,x582,x583),f9(x584,x582,x583)),f9(f4(x581,x584),x582,x583))
% 0.18/0.62 [77]~P3(x771)+P3(f5(x771))
% 0.18/0.62 [85]E(x851,f6(a2))+P4(f6(a2),x851,a2)
% 0.18/0.62 [78]~P11(x781)+E(f13(f6(a2),x781),f6(x781))
% 0.18/0.62 [91]~P4(x912,x912,x911)+~P7(x911)
% 0.18/0.62 [92]~P4(x922,x922,x921)+~P8(x921)
% 0.18/0.62 [93]~P4(x932,x932,x931)+~P9(x931)
% 0.18/0.62 [75]E(x751,x752)+~E(f3(x751),f3(x752))
% 0.18/0.62 [76]E(x761,x762)+~E(f5(x761),f5(x762))
% 0.18/0.62 [79]~P3(x791)+P3(f10(x791,x792))
% 0.18/0.62 [82]~P6(x821,x822)+P6(f5(x821),f5(x822))
% 0.18/0.62 [87]~P6(f5(x871),x872)+P6(x871,f11(x871,x872))
% 0.18/0.62 [105]~P1(x1051)+~P4(f13(x1052,x1051),f6(x1051),x1051)
% 0.18/0.62 [83]~P3(x831)+P3(f4(x831,f3(x832)))
% 0.18/0.62 [86]~P6(f5(x861),x862)+E(f5(f11(x861,x862)),x862)
% 0.18/0.62 [94]~P4(x941,x942,a2)+E(f10(f3(x941),x942),f3(x941))
% 0.18/0.62 [88]~P6(x881,x883)+P6(f4(x881,x882),f4(x883,x882))
% 0.18/0.62 [89]~P6(x892,x893)+P6(f4(x891,x892),f4(x891,x893))
% 0.18/0.62 [90]~P6(x901,x903)+P6(f10(x901,x902),f10(x903,x902))
% 0.18/0.62 [104]~P3(x1041)+P3(f9(x1041,f3(x1042),x1043))
% 0.18/0.62 [106]~P4(x1061,x1063,a2)+E(f9(f3(x1061),x1062,x1063),f3(x1061))
% 0.18/0.62 [80]E(x801,x802)+~E(f4(x803,x801),f4(x804,x802))
% 0.18/0.62 [81]E(x811,x812)+~E(f4(x811,x813),f4(x812,x814))
% 0.18/0.62 [119]~P6(x1191,x1194)+P6(f9(x1191,x1192,x1193),f9(x1194,x1192,x1193))
% 0.18/0.62 [107]E(x1071,x1072)+~E(f8(x1073,x1071,x1074),f8(x1075,x1072,x1074))
% 0.18/0.62 [108]E(x1081,x1082)+~E(f8(x1081,x1083,x1084),f8(x1082,x1085,x1084))
% 0.18/0.62 [96]E(x961,x962)+P4(x962,x961,a2)+P4(x961,x962,a2)
% 0.18/0.62 [113]~P1(x1131)+P4(f6(x1131),f13(x1132,x1131),x1131)+~P4(f6(a2),x1132,a2)
% 0.18/0.62 [115]~P1(x1152)+~P4(f6(x1152),f13(x1151,x1152),x1152)+P4(f6(a2),x1151,a2)
% 0.18/0.62 [110]~P4(x1103,x1102,x1101)+~P7(x1101)+~P4(x1102,x1103,x1101)
% 0.18/0.62 [111]~P4(x1113,x1112,x1111)+~P8(x1111)+~P4(x1112,x1113,x1111)
% 0.18/0.62 [112]~P4(x1123,x1122,x1121)+~P9(x1121)+~P4(x1122,x1123,x1121)
% 0.18/0.62 [84]~P2(x843)+E(x841,x842)+~E(f13(x841,x843),f13(x842,x843))
% 0.18/0.62 [114]~P1(x1142)+~P4(x1141,x1143,a2)+P4(f13(x1141,x1142),f13(x1143,x1142),x1142)
% 0.18/0.62 [116]~P1(x1163)+~P4(f13(x1161,x1163),f13(x1162,x1163),x1163)+P4(x1161,x1162,a2)
% 0.18/0.62 [103]E(x1031,x1032)+P4(x1032,x1031,a2)+E(f9(f3(x1031),x1033,x1032),f3(x1031))
% 0.18/0.62 [101]P4(x1011,x1012,x1013)+~P8(x1013)+E(x1011,x1012)+P4(x1012,x1011,x1013)
% 0.18/0.62 [102]P4(x1021,x1022,x1023)+~P10(x1023)+E(x1021,x1022)+P4(x1022,x1021,x1023)
% 0.18/0.62 [117]~P7(x1173)+~P4(x1171,x1174,x1173)+P4(x1171,x1172,x1173)+~P4(x1174,x1172,x1173)
% 0.18/0.62 [118]~P9(x1183)+~P4(x1181,x1184,x1183)+P4(x1181,x1182,x1183)+~P4(x1184,x1182,x1183)
% 0.18/0.62 [120]~P3(x1201)+~P5(x1203,x1201,a16)+~P5(f12(x1203,x1202,a16,a14),a15,x1204)+P3(f9(a15,x1201,x1202))
% 0.18/0.62 %EqnAxiom
% 0.18/0.62 [1]E(x11,x11)
% 0.18/0.62 [2]E(x22,x21)+~E(x21,x22)
% 0.18/0.62 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.18/0.62 [4]~E(x41,x42)+E(f3(x41),f3(x42))
% 0.18/0.62 [5]~E(x51,x52)+E(f8(x51,x53,x54),f8(x52,x53,x54))
% 0.18/0.62 [6]~E(x61,x62)+E(f8(x63,x61,x64),f8(x63,x62,x64))
% 0.18/0.62 [7]~E(x71,x72)+E(f8(x73,x74,x71),f8(x73,x74,x72))
% 0.18/0.62 [8]~E(x81,x82)+E(f12(x81,x83,x84,x85),f12(x82,x83,x84,x85))
% 0.18/0.62 [9]~E(x91,x92)+E(f12(x93,x91,x94,x95),f12(x93,x92,x94,x95))
% 0.18/0.62 [10]~E(x101,x102)+E(f12(x103,x104,x101,x105),f12(x103,x104,x102,x105))
% 0.18/0.62 [11]~E(x111,x112)+E(f12(x113,x114,x115,x111),f12(x113,x114,x115,x112))
% 0.18/0.62 [12]~E(x121,x122)+E(f9(x121,x123,x124),f9(x122,x123,x124))
% 0.18/0.62 [13]~E(x131,x132)+E(f9(x133,x131,x134),f9(x133,x132,x134))
% 0.18/0.62 [14]~E(x141,x142)+E(f9(x143,x144,x141),f9(x143,x144,x142))
% 0.18/0.62 [15]~E(x151,x152)+E(f10(x151,x153),f10(x152,x153))
% 0.18/0.62 [16]~E(x161,x162)+E(f10(x163,x161),f10(x163,x162))
% 0.18/0.62 [17]~E(x171,x172)+E(f13(x171,x173),f13(x172,x173))
% 0.18/0.62 [18]~E(x181,x182)+E(f13(x183,x181),f13(x183,x182))
% 0.18/0.62 [19]~E(x191,x192)+E(f4(x191,x193),f4(x192,x193))
% 0.18/0.62 [20]~E(x201,x202)+E(f4(x203,x201),f4(x203,x202))
% 0.18/0.62 [21]~E(x211,x212)+E(f11(x211,x213),f11(x212,x213))
% 0.18/0.62 [22]~E(x221,x222)+E(f11(x223,x221),f11(x223,x222))
% 0.18/0.62 [23]~E(x231,x232)+E(f6(x231),f6(x232))
% 0.18/0.62 [24]~E(x241,x242)+E(f5(x241),f5(x242))
% 0.18/0.62 [25]~P1(x251)+P1(x252)+~E(x251,x252)
% 0.18/0.62 [26]~P11(x261)+P11(x262)+~E(x261,x262)
% 0.18/0.62 [27]~P2(x271)+P2(x272)+~E(x271,x272)
% 0.18/0.62 [28]~P7(x281)+P7(x282)+~E(x281,x282)
% 0.18/0.62 [29]~P8(x291)+P8(x292)+~E(x291,x292)
% 0.18/0.62 [30]~P9(x301)+P9(x302)+~E(x301,x302)
% 0.18/0.62 [31]~P3(x311)+P3(x312)+~E(x311,x312)
% 0.18/0.62 [32]P4(x322,x323,x324)+~E(x321,x322)+~P4(x321,x323,x324)
% 0.18/0.62 [33]P4(x333,x332,x334)+~E(x331,x332)+~P4(x333,x331,x334)
% 0.18/0.62 [34]P4(x343,x344,x342)+~E(x341,x342)+~P4(x343,x344,x341)
% 0.18/0.62 [35]P5(x352,x353,x354)+~E(x351,x352)+~P5(x351,x353,x354)
% 0.18/0.62 [36]P5(x363,x362,x364)+~E(x361,x362)+~P5(x363,x361,x364)
% 0.18/0.62 [37]P5(x373,x374,x372)+~E(x371,x372)+~P5(x373,x374,x371)
% 0.18/0.62 [38]~P10(x381)+P10(x382)+~E(x381,x382)
% 0.18/0.62 [39]P6(x392,x393)+~E(x391,x392)+~P6(x391,x393)
% 0.18/0.62 [40]P6(x403,x402)+~E(x401,x402)+~P6(x403,x401)
% 0.18/0.62
% 0.18/0.62 %-------------------------------------------
% 0.18/0.62 cnf(131,plain,
% 0.18/0.62 (~E(f8(x1311,x1312,x1313),x1312)),
% 0.18/0.62 inference(rename_variables,[],[70])).
% 0.18/0.62 cnf(139,plain,
% 0.18/0.62 ($false),
% 0.18/0.62 inference(scs_inference,[],[74,68,41,42,46,50,53,72,59,70,131,66,61,54,2,87,86,31,3,115,116,101,120]),
% 0.18/0.62 ['proof']).
% 0.18/0.62 % SZS output end Proof
% 0.18/0.62 % Total time :0.000000s
%------------------------------------------------------------------------------