TSTP Solution File: LCL843-1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : LCL843-1 : 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 : n023.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 06:51:20 EDT 2023
% Result : Unsatisfiable 0.54s 0.62s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : LCL843-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.12/0.33 % Computer : n023.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 05:25:42 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.55 start to proof:theBenchmark
% 0.54/0.60 %-------------------------------------------
% 0.54/0.60 % File :CSE---1.6
% 0.54/0.60 % Problem :theBenchmark
% 0.54/0.60 % Transform :cnf
% 0.54/0.60 % Format :tptp:raw
% 0.54/0.60 % Command :java -jar mcs_scs.jar %d %s
% 0.54/0.60
% 0.54/0.60 % Result :Theorem 0.000000s
% 0.54/0.60 % Output :CNFRefutation 0.000000s
% 0.54/0.60 %-------------------------------------------
% 0.54/0.60 %------------------------------------------------------------------------------
% 0.54/0.60 % File : LCL843-1 : TPTP v8.1.2. Released v4.1.0.
% 0.54/0.60 % Domain : Logic Calculi
% 0.54/0.60 % Problem : Strong normalization of typed lambda calculus 254_14
% 0.54/0.60 % Version : Especial.
% 0.54/0.60 % English :
% 0.54/0.60
% 0.54/0.60 % Refs : [vON99] von Oheimb & Nipkow (1999), Machine-Checking the Java
% 0.54/0.60 % : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe
% 0.54/0.60 % : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.54/0.60 % Source : [Nip10]
% 0.54/0.60 % Names : StrongNorm-254_14 [Nip10]
% 0.54/0.60
% 0.54/0.60 % Status : Unsatisfiable
% 0.54/0.60 % Rating : 0.00 v8.1.0, 0.05 v7.4.0, 0.06 v7.3.0, 0.08 v7.0.0, 0.13 v6.4.0, 0.07 v6.3.0, 0.09 v6.2.0, 0.10 v6.1.0, 0.00 v5.5.0, 0.05 v5.3.0, 0.06 v5.2.0, 0.00 v5.1.0, 0.06 v5.0.0, 0.07 v4.1.0
% 0.54/0.60 % Syntax : Number of clauses : 69 ( 26 unt; 10 nHn; 45 RR)
% 0.54/0.60 % Number of literals : 138 ( 36 equ; 72 neg)
% 0.54/0.60 % Maximal clause size : 4 ( 2 avg)
% 0.54/0.60 % Maximal term depth : 3 ( 1 avg)
% 0.54/0.60 % Number of predicates : 11 ( 10 usr; 0 prp; 1-3 aty)
% 0.54/0.60 % Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% 0.54/0.60 % Number of variables : 148 ( 33 sgn)
% 0.54/0.60 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.54/0.60
% 0.54/0.60 % Comments :
% 0.54/0.60 %------------------------------------------------------------------------------
% 0.54/0.60 cnf(cls_of__nat__less__0__iff_0,axiom,
% 0.54/0.60 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.54/0.61 | ~ 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) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_of__nat__0_0,axiom,
% 0.54/0.61 ( ~ class_Ring__and__Field_Osemiring__1(T_a)
% 0.54/0.61 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_of__nat__eq__iff_0,axiom,
% 0.54/0.61 ( ~ class_Nat_Osemiring__char__0(T_a)
% 0.54/0.61 | c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a) != c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)
% 0.54/0.61 | V_m = V_n ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_of__nat__less__iff_1,axiom,
% 0.54/0.61 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.54/0.61 | 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)
% 0.54/0.61 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_of__nat__less__iff_0,axiom,
% 0.54/0.61 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.54/0.61 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.54/0.61 | ~ 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) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_order__less__asym_H_0,axiom,
% 0.54/0.61 ( ~ class_Orderings_Opreorder(T_a)
% 0.54/0.61 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
% 0.54/0.61 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_order__less__asym_0,axiom,
% 0.54/0.61 ( ~ class_Orderings_Opreorder(T_a)
% 0.54/0.61 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
% 0.54/0.61 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_not__less__iff__gr__or__eq_1,axiom,
% 0.54/0.61 ( ~ class_Orderings_Olinorder(T_a)
% 0.54/0.61 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
% 0.54/0.61 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_xt1_I9_J_0,axiom,
% 0.54/0.61 ( ~ class_Orderings_Oorder(T_a)
% 0.54/0.61 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
% 0.54/0.61 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_neq0__conv_1,axiom,
% 0.54/0.61 ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_gr0I_0,axiom,
% 0.54/0.61 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
% 0.54/0.61 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_of__nat__0__less__iff_0,axiom,
% 0.54/0.61 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.54/0.61 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
% 0.54/0.61 | ~ 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) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_of__nat__0__less__iff_1,axiom,
% 0.54/0.61 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.54/0.61 | 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)
% 0.54/0.61 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_linorder__antisym__conv3_0,axiom,
% 0.54/0.61 ( ~ class_Orderings_Olinorder(T_a)
% 0.54/0.61 | V_x = V_y
% 0.54/0.61 | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
% 0.54/0.61 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_linorder__less__linear_0,axiom,
% 0.54/0.61 ( ~ class_Orderings_Olinorder(T_a)
% 0.54/0.61 | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
% 0.54/0.61 | V_x = V_y
% 0.54/0.61 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_linorder__neqE_0,axiom,
% 0.54/0.61 ( ~ class_Orderings_Olinorder(T_a)
% 0.54/0.61 | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
% 0.54/0.61 | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
% 0.54/0.61 | V_x = V_y ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_linorder__neqE__nat_0,axiom,
% 0.54/0.61 ( c_HOL_Oord__class_Oless(V_y,V_x,tc_nat)
% 0.54/0.61 | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)
% 0.54/0.61 | V_x = V_y ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_nat__neq__iff_0,axiom,
% 0.54/0.61 ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
% 0.54/0.61 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.54/0.61 | V_m = V_n ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_not__less__iff__gr__or__eq_0,axiom,
% 0.54/0.61 ( ~ class_Orderings_Olinorder(T_a)
% 0.54/0.61 | V_x = V_y
% 0.54/0.61 | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
% 0.54/0.61 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_linorder__neqE__ordered__idom_0,axiom,
% 0.54/0.61 ( ~ class_Ring__and__Field_Oordered__idom(T_a)
% 0.54/0.61 | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
% 0.54/0.61 | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
% 0.54/0.61 | V_x = V_y ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_order__less__irrefl_0,axiom,
% 0.54/0.61 ( ~ class_Orderings_Opreorder(T_a)
% 0.54/0.61 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_linorder__neq__iff_1,axiom,
% 0.54/0.61 ( ~ class_Orderings_Olinorder(T_a)
% 0.54/0.61 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_order__less__le_1,axiom,
% 0.54/0.61 ( ~ class_Orderings_Oorder(T_a)
% 0.54/0.61 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_less__not__refl_0,axiom,
% 0.54/0.61 ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_nat__less__le_1,axiom,
% 0.54/0.61 ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_order__less__trans_0,axiom,
% 0.54/0.61 ( ~ class_Orderings_Opreorder(T_a)
% 0.54/0.61 | c_HOL_Oord__class_Oless(V_x,V_z,T_a)
% 0.54/0.61 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
% 0.54/0.61 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_xt1_I10_J_0,axiom,
% 0.54/0.61 ( ~ class_Orderings_Oorder(T_a)
% 0.54/0.61 | c_HOL_Oord__class_Oless(V_z,V_x,T_a)
% 0.54/0.61 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a)
% 0.54/0.61 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_gr__implies__not0_0,axiom,
% 0.54/0.61 ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_not__less0_0,axiom,
% 0.54/0.61 ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_abs_0,axiom,
% 0.54/0.61 ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_s),c_Lambda_OdB_OAbs(V_t))
% 0.54/0.61 | ~ c_Lambda_Obeta(V_s,V_t) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_beta__cases_I2_J_0,axiom,
% 0.54/0.61 ( V_s = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(V_r,V_s))
% 0.54/0.61 | ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_r),V_s) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_lift__preserves__beta_0,axiom,
% 0.54/0.61 ( c_Lambda_Obeta(c_Lambda_Olift(V_r,V_i),c_Lambda_Olift(V_s,V_i))
% 0.54/0.61 | ~ c_Lambda_Obeta(V_r,V_s) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_lift_Osimps_I1_J_0,axiom,
% 0.54/0.61 ( c_Lambda_Olift(c_Lambda_OdB_OVar(V_i),V_k) = c_Lambda_OdB_OVar(V_i)
% 0.54/0.61 | ~ c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_subst__lift_0,axiom,
% 0.54/0.61 c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_appL_0,axiom,
% 0.54/0.61 ( c_Lambda_Obeta(c_Lambda_OdB_OApp(V_s,V_u),c_Lambda_OdB_OApp(V_t,V_u))
% 0.54/0.61 | ~ c_Lambda_Obeta(V_s,V_t) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_appR_0,axiom,
% 0.54/0.61 ( c_Lambda_Obeta(c_Lambda_OdB_OApp(V_u,V_s),c_Lambda_OdB_OApp(V_u,V_t))
% 0.54/0.61 | ~ c_Lambda_Obeta(V_s,V_t) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_subst__Var_1,axiom,
% 0.54/0.61 ( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)
% 0.54/0.61 | c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x),V_s,V_x) = V_s ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_subst__Var_2,axiom,
% 0.54/0.61 ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_i),V_s,V_k) = c_Lambda_OdB_OVar(V_i)
% 0.54/0.61 | V_i = V_k
% 0.54/0.61 | c_HOL_Oord__class_Oless(V_k,V_i,tc_nat) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_subst__preserves__beta_0,axiom,
% 0.54/0.61 ( c_Lambda_Obeta(c_Lambda_Osubst(V_r,V_t,V_i),c_Lambda_Osubst(V_s,V_t,V_i))
% 0.54/0.61 | ~ c_Lambda_Obeta(V_r,V_s) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_lift_Osimps_I2_J_0,axiom,
% 0.54/0.61 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)) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_dB_Osimps_I3_J_0,axiom,
% 0.54/0.61 ( c_Lambda_OdB_OAbs(V_dB) != c_Lambda_OdB_OAbs(V_dB_H)
% 0.54/0.61 | V_dB = V_dB_H ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_beta_0,axiom,
% 0.54/0.61 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))) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_dB_Osimps_I2_J_1,axiom,
% 0.54/0.61 ( c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H)
% 0.54/0.61 | V_dB2 = V_dB2_H ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_dB_Osimps_I2_J_0,axiom,
% 0.54/0.61 ( c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H)
% 0.54/0.61 | V_dB1 = V_dB1_H ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_beta__cases_I2_J_1,axiom,
% 0.54/0.61 ( c_Lambda_Obeta(V_r,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(V_r,V_s))
% 0.54/0.61 | ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_r),V_s) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_subst__lt_0,axiom,
% 0.54/0.61 ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_j),V_u,V_i) = c_Lambda_OdB_OVar(V_j)
% 0.54/0.61 | ~ c_HOL_Oord__class_Oless(V_j,V_i,tc_nat) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_dB_Osimps_I9_J_0,axiom,
% 0.54/0.61 c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OApp(V_dB1,V_dB2) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_dB_Osimps_I8_J_0,axiom,
% 0.54/0.61 c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OAbs(V_dB_H) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_subst__App_0,axiom,
% 0.54/0.61 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)) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_dB_Osimps_I7_J_0,axiom,
% 0.54/0.61 c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_dB_Osimps_I1_J_0,axiom,
% 0.54/0.61 ( c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OVar(V_nat_H)
% 0.54/0.61 | V_nat = V_nat_H ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_subst__eq_0,axiom,
% 0.54/0.61 c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k) = V_u ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_Var_0,axiom,
% 0.54/0.61 v_env______(v_x______) = v_Ta______ ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_subst__Var__IT_0,axiom,
% 0.54/0.61 ( c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j))
% 0.54/0.61 | ~ c_InductTermi_OIT(V_r) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_beta__cases_I1_J_0,axiom,
% 0.54/0.61 ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(V_i),V_t) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_dB_Osimps_I4_J_0,axiom,
% 0.54/0.61 c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_lift__IT_0,axiom,
% 0.54/0.61 ( c_InductTermi_OIT(c_Lambda_Olift(V_t,V_i))
% 0.54/0.61 | ~ c_InductTermi_OIT(V_t) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(cls_dB_Osimps_I6_J_0,axiom,
% 0.54/0.62 c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H) ).
% 0.54/0.62
% 0.54/0.62 cnf(cls_Var__IT_0,axiom,
% 0.54/0.62 c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n)) ).
% 0.54/0.62
% 0.54/0.62 cnf(cls_Lambda_0,axiom,
% 0.54/0.62 ( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
% 0.54/0.62 | ~ c_InductTermi_OIT(V_r) ) ).
% 0.54/0.62
% 0.54/0.62 cnf(cls_app__Var__IT_0,axiom,
% 0.54/0.62 ( c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i)))
% 0.54/0.62 | ~ c_InductTermi_OIT(V_t) ) ).
% 0.54/0.62
% 0.54/0.62 cnf(cls_dB_Osimps_I5_J_0,axiom,
% 0.54/0.62 c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) != c_Lambda_OdB_OVar(V_nat) ).
% 0.54/0.62
% 0.54/0.62 cnf(cls_conjecture_0,negated_conjecture,
% 0.54/0.62 ~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_x______)) ).
% 0.54/0.62
% 0.54/0.62 cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom,
% 0.54/0.62 class_Ring__and__Field_Oordered__semidom(tc_nat) ).
% 0.54/0.62
% 0.54/0.62 cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom,
% 0.54/0.62 class_Ring__and__Field_Osemiring__1(tc_nat) ).
% 0.54/0.62
% 0.54/0.62 cnf(clsarity_nat__Nat_Osemiring__char__0,axiom,
% 0.54/0.62 class_Nat_Osemiring__char__0(tc_nat) ).
% 0.54/0.62
% 0.54/0.62 cnf(clsarity_nat__Orderings_Opreorder,axiom,
% 0.54/0.62 class_Orderings_Opreorder(tc_nat) ).
% 0.54/0.62
% 0.54/0.62 cnf(clsarity_nat__Orderings_Olinorder,axiom,
% 0.54/0.62 class_Orderings_Olinorder(tc_nat) ).
% 0.54/0.62
% 0.54/0.62 cnf(clsarity_nat__Orderings_Oorder,axiom,
% 0.54/0.62 class_Orderings_Oorder(tc_nat) ).
% 0.54/0.62
% 0.54/0.62 %------------------------------------------------------------------------------
% 0.54/0.62 %-------------------------------------------
% 0.54/0.62 % Proof found
% 0.54/0.62 % SZS status Theorem for theBenchmark
% 0.54/0.62 % SZS output start Proof
% 0.54/0.62 %ClaNum:100(EqnAxiom:31)
% 0.54/0.62 %VarNum:263(SingletonVarNum:128)
% 0.54/0.62 %MaxLitNum:4
% 0.54/0.62 %MaxfuncDepth:2
% 0.54/0.62 %SharedTerms:15
% 0.54/0.62 %goalClause: 45
% 0.54/0.62 %singleGoalClaCount:1
% 0.54/0.62 [33]P1(a4)
% 0.54/0.62 [34]P10(a4)
% 0.54/0.62 [35]P2(a4)
% 0.54/0.62 [36]P6(a4)
% 0.54/0.62 [37]P7(a4)
% 0.54/0.62 [38]P8(a4)
% 0.54/0.62 [32]E(f2(a1),a3)
% 0.54/0.62 [45]~P3(f5(a1))
% 0.54/0.62 [54]~P4(x541,x541,a4)
% 0.54/0.62 [39]P3(f5(x391))
% 0.54/0.62 [56]~P4(x561,f8(a4),a4)
% 0.54/0.62 [47]~E(f5(x471),f7(x472))
% 0.54/0.62 [52]~P5(f5(x521),x522)
% 0.54/0.62 [40]E(f9(f5(x401),x402,x401),x402)
% 0.54/0.62 [43]P5(f6(f7(x431),x432),f9(x431,x432,f8(a4)))
% 0.54/0.62 [48]~E(f7(x481),f6(x482,x483))
% 0.54/0.62 [49]~E(f5(x491),f6(x492,x493))
% 0.54/0.62 [50]~E(f6(x501,x502),f7(x503))
% 0.54/0.62 [51]~E(f6(x511,x512),f5(x513))
% 0.54/0.62 [41]E(f9(f10(x411,x412),x413,x412),x411)
% 0.54/0.62 [42]E(f6(f10(x421,x422),f10(x423,x422)),f10(f6(x421,x423),x422))
% 0.54/0.62 [44]E(f6(f9(x441,x442,x443),f9(x444,x442,x443)),f9(f6(x441,x444),x442,x443))
% 0.54/0.62 [60]~P3(x601)+P3(f7(x601))
% 0.54/0.62 [68]E(x681,f8(a4))+P4(f8(a4),x681,a4)
% 0.54/0.62 [61]~P10(x611)+E(f12(f8(a4),x611),f8(x611))
% 0.54/0.62 [74]~P4(x742,x742,x741)+~P6(x741)
% 0.54/0.62 [75]~P4(x752,x752,x751)+~P7(x751)
% 0.54/0.62 [76]~P4(x762,x762,x761)+~P8(x761)
% 0.54/0.62 [58]E(x581,x582)+~E(f7(x581),f7(x582))
% 0.54/0.62 [59]E(x591,x592)+~E(f5(x591),f5(x592))
% 0.54/0.62 [62]~P3(x621)+P3(f10(x621,x622))
% 0.54/0.62 [65]~P5(x651,x652)+P5(f7(x651),f7(x652))
% 0.54/0.62 [70]~P5(f7(x701),x702)+P5(x701,f11(x701,x702))
% 0.54/0.62 [88]~P1(x881)+~P4(f12(x882,x881),f8(x881),x881)
% 0.54/0.62 [66]~P3(x661)+P3(f6(x661,f5(x662)))
% 0.54/0.62 [69]~P5(f7(x691),x692)+E(f7(f11(x691,x692)),x692)
% 0.54/0.62 [77]~P4(x771,x772,a4)+E(f10(f5(x771),x772),f5(x771))
% 0.54/0.62 [71]~P5(x711,x713)+P5(f10(x711,x712),f10(x713,x712))
% 0.54/0.62 [72]~P5(x721,x723)+P5(f6(x721,x722),f6(x723,x722))
% 0.54/0.62 [73]~P5(x732,x733)+P5(f6(x731,x732),f6(x731,x733))
% 0.54/0.62 [87]~P3(x871)+P3(f9(x871,f5(x872),x873))
% 0.54/0.62 [89]~P4(x891,x893,a4)+E(f9(f5(x891),x892,x893),f5(x891))
% 0.54/0.62 [63]E(x631,x632)+~E(f6(x633,x631),f6(x634,x632))
% 0.54/0.62 [64]E(x641,x642)+~E(f6(x641,x643),f6(x642,x644))
% 0.54/0.62 [100]~P5(x1001,x1004)+P5(f9(x1001,x1002,x1003),f9(x1004,x1002,x1003))
% 0.54/0.62 [79]E(x791,x792)+P4(x792,x791,a4)+P4(x791,x792,a4)
% 0.54/0.62 [94]~P1(x941)+P4(f8(x941),f12(x942,x941),x941)+~P4(f8(a4),x942,a4)
% 0.54/0.62 [96]~P1(x962)+~P4(f8(x962),f12(x961,x962),x962)+P4(f8(a4),x961,a4)
% 0.54/0.62 [91]~P4(x913,x912,x911)+~P6(x911)+~P4(x912,x913,x911)
% 0.54/0.62 [92]~P4(x923,x922,x921)+~P7(x921)+~P4(x922,x923,x921)
% 0.54/0.62 [93]~P4(x933,x932,x931)+~P8(x931)+~P4(x932,x933,x931)
% 0.54/0.62 [67]~P2(x673)+E(x671,x672)+~E(f12(x671,x673),f12(x672,x673))
% 0.54/0.62 [95]~P1(x952)+~P4(x951,x953,a4)+P4(f12(x951,x952),f12(x953,x952),x952)
% 0.54/0.62 [97]~P1(x973)+~P4(f12(x971,x973),f12(x972,x973),x973)+P4(x971,x972,a4)
% 0.54/0.62 [86]E(x861,x862)+P4(x862,x861,a4)+E(f9(f5(x861),x863,x862),f5(x861))
% 0.54/0.62 [84]P4(x841,x842,x843)+~P7(x843)+E(x841,x842)+P4(x842,x841,x843)
% 0.54/0.62 [85]P4(x851,x852,x853)+~P9(x853)+E(x851,x852)+P4(x852,x851,x853)
% 0.54/0.62 [98]~P6(x983)+~P4(x981,x984,x983)+P4(x981,x982,x983)+~P4(x984,x982,x983)
% 0.54/0.62 [99]~P8(x993)+~P4(x991,x994,x993)+P4(x991,x992,x993)+~P4(x994,x992,x993)
% 0.54/0.62 %EqnAxiom
% 0.54/0.62 [1]E(x11,x11)
% 0.54/0.62 [2]E(x22,x21)+~E(x21,x22)
% 0.54/0.62 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.54/0.62 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 0.54/0.62 [5]~E(x51,x52)+E(f5(x51),f5(x52))
% 0.54/0.62 [6]~E(x61,x62)+E(f9(x61,x63,x64),f9(x62,x63,x64))
% 0.54/0.62 [7]~E(x71,x72)+E(f9(x73,x71,x74),f9(x73,x72,x74))
% 0.54/0.62 [8]~E(x81,x82)+E(f9(x83,x84,x81),f9(x83,x84,x82))
% 0.54/0.62 [9]~E(x91,x92)+E(f12(x91,x93),f12(x92,x93))
% 0.54/0.62 [10]~E(x101,x102)+E(f12(x103,x101),f12(x103,x102))
% 0.54/0.62 [11]~E(x111,x112)+E(f10(x111,x113),f10(x112,x113))
% 0.54/0.62 [12]~E(x121,x122)+E(f10(x123,x121),f10(x123,x122))
% 0.54/0.62 [13]~E(x131,x132)+E(f8(x131),f8(x132))
% 0.54/0.62 [14]~E(x141,x142)+E(f7(x141),f7(x142))
% 0.54/0.62 [15]~E(x151,x152)+E(f6(x151,x153),f6(x152,x153))
% 0.54/0.62 [16]~E(x161,x162)+E(f6(x163,x161),f6(x163,x162))
% 0.54/0.62 [17]~E(x171,x172)+E(f11(x171,x173),f11(x172,x173))
% 0.54/0.62 [18]~E(x181,x182)+E(f11(x183,x181),f11(x183,x182))
% 0.54/0.62 [19]~P1(x191)+P1(x192)+~E(x191,x192)
% 0.54/0.62 [20]~P10(x201)+P10(x202)+~E(x201,x202)
% 0.54/0.62 [21]~P2(x211)+P2(x212)+~E(x211,x212)
% 0.54/0.62 [22]~P6(x221)+P6(x222)+~E(x221,x222)
% 0.54/0.62 [23]~P7(x231)+P7(x232)+~E(x231,x232)
% 0.54/0.62 [24]~P8(x241)+P8(x242)+~E(x241,x242)
% 0.54/0.62 [25]~P3(x251)+P3(x252)+~E(x251,x252)
% 0.54/0.62 [26]P5(x262,x263)+~E(x261,x262)+~P5(x261,x263)
% 0.54/0.62 [27]P5(x273,x272)+~E(x271,x272)+~P5(x273,x271)
% 0.54/0.62 [28]P4(x282,x283,x284)+~E(x281,x282)+~P4(x281,x283,x284)
% 0.54/0.62 [29]P4(x293,x292,x294)+~E(x291,x292)+~P4(x293,x291,x294)
% 0.54/0.62 [30]P4(x303,x304,x302)+~E(x301,x302)+~P4(x303,x304,x301)
% 0.54/0.62 [31]~P9(x311)+P9(x312)+~E(x311,x312)
% 0.54/0.62
% 0.54/0.62 %-------------------------------------------
% 0.54/0.62 cnf(101,plain,
% 0.54/0.62 ($false),
% 0.54/0.62 inference(scs_inference,[],[45,39]),
% 0.54/0.62 ['proof']).
% 0.54/0.62 % SZS output end Proof
% 0.54/0.62 % Total time :0.000000s
%------------------------------------------------------------------------------