%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : LCL843-1 : TPTP v9.3.1. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 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 : Mon Sep 7 11:19:59 AM UTC 2026 % Result : Unsatisfiable 0.27s 0.49s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL843-1 : TPTP v9.3.1. Released v4.1.0. % 0.00/0.03 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.08/0.35 % Computer : n016.cluster.edu % 0.08/0.35 % Model : x86_64 x86_64 % 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.35 % Memory : 8046.5625MB % 0.08/0.35 % OS : Linux 6.8.0-71-generic % 0.08/0.35 % CPULimit : 300 % 0.08/0.35 % WCLimit : 300 % 0.08/0.35 % DateTime : Fri Sep 4 18:55:58 UTC 2026 % 0.08/0.35 % CPUTime : % 0.27/0.46 start to proof:theBenchmark % 0.27/0.48 %------------------------------------------- % 0.27/0.48 % File :CSE---1.7 % 0.27/0.48 % Problem :theBenchmark % 0.27/0.48 % Transform :cnf % 0.27/0.48 % Format :tptp:raw % 0.27/0.48 % Command :java -jar mcs_scs.jar %d %s % 0.27/0.48 % 0.27/0.48 % Result :Theorem 0.006635s % 0.27/0.48 % Output :CNFRefutation 0.006635s % 0.27/0.48 %------------------------------------------- % 0.27/0.48 %------------------------------------------------------------------------------ % 0.27/0.48 % File : LCL843-1 : TPTP v9.3.1. Released v4.1.0. % 0.27/0.48 % Domain : Logic Calculi % 0.27/0.48 % Problem : Strong normalization of typed lambda calculus 254_14 % 0.27/0.48 % Version : Especial. % 0.27/0.48 % English : % 0.27/0.48 % 0.27/0.48 % Refs : [vON99] von Oheimb & Nipkow (1999), Machine-Checking the Java % 0.27/0.48 % : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe % 0.27/0.48 % : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 0.27/0.48 % Source : [Nip10] % 0.27/0.48 % Names : StrongNorm-254_14 [Nip10] % 0.27/0.48 % 0.27/0.48 % Status : Unsatisfiable % 0.27/0.48 % Rating : 0.08 v9.3.0, 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 % 0.27/0.48 % Syntax : Number of clauses : 69 ( 26 unt; 10 nHn; 45 RR) % 0.27/0.48 % Number of literals : 138 ( 36 equ; 72 neg) % 0.27/0.48 % Maximal clause size : 4 ( 2 avg) % 0.27/0.48 % Maximal term depth : 3 ( 1 avg) % 0.27/0.48 % Number of predicates : 11 ( 10 usr; 0 prp; 1-3 aty) % 0.27/0.48 % Number of functors : 12 ( 12 usr; 3 con; 0-3 aty) % 0.27/0.48 % Number of variables : 148 ( 33 sgn) % 0.27/0.48 % SPC : CNF_UNS_RFO_SEQ_NHN % 0.27/0.48 % 0.27/0.48 % Comments : % 0.27/0.48 %------------------------------------------------------------------------------ % 0.27/0.48 cnf(cls_of__nat__less__0__iff_0,axiom, % 0.27/0.48 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.27/0.48 | ~ 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) ) ). % 0.27/0.48 % 0.27/0.48 cnf(cls_of__nat__0_0,axiom, % 0.27/0.48 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 0.27/0.48 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.27/0.48 % 0.27/0.48 cnf(cls_of__nat__eq__iff_0,axiom, % 0.27/0.48 ( ~ class_Nat_Osemiring__char__0(T_a) % 0.27/0.48 | c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a) != c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) % 0.27/0.48 | V_m = V_n ) ). % 0.27/0.48 % 0.27/0.48 cnf(cls_of__nat__less__iff_1,axiom, % 0.27/0.48 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.27/0.48 | 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) % 0.27/0.48 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.27/0.48 % 0.27/0.48 cnf(cls_of__nat__less__iff_0,axiom, % 0.27/0.48 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.27/0.48 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.27/0.48 | ~ 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) ) ). % 0.27/0.48 % 0.27/0.48 cnf(cls_order__less__asym_H_0,axiom, % 0.27/0.48 ( ~ class_Orderings_Opreorder(T_a) % 0.27/0.48 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.27/0.48 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.27/0.48 % 0.27/0.48 cnf(cls_order__less__asym_0,axiom, % 0.27/0.48 ( ~ class_Orderings_Opreorder(T_a) % 0.27/0.48 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.27/0.48 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.27/0.48 % 0.27/0.48 cnf(cls_not__less__iff__gr__or__eq_1,axiom, % 0.27/0.48 ( ~ class_Orderings_Olinorder(T_a) % 0.27/0.48 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.27/0.48 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.27/0.48 % 0.27/0.48 cnf(cls_xt1_I9_J_0,axiom, % 0.27/0.48 ( ~ class_Orderings_Oorder(T_a) % 0.27/0.48 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.27/0.48 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 0.27/0.48 % 0.27/0.48 cnf(cls_neq0__conv_1,axiom, % 0.27/0.48 ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 0.27/0.48 % 0.27/0.48 cnf(cls_gr0I_0,axiom, % 0.27/0.48 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.27/0.48 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.27/0.48 % 0.27/0.48 cnf(cls_of__nat__0__less__iff_0,axiom, % 0.27/0.48 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.27/0.48 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.27/0.48 | ~ 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) ) ). % 0.27/0.48 % 0.27/0.48 cnf(cls_of__nat__0__less__iff_1,axiom, % 0.27/0.48 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.27/0.48 | 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) % 0.27/0.48 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.27/0.48 % 0.27/0.48 cnf(cls_linorder__antisym__conv3_0,axiom, % 0.27/0.48 ( ~ class_Orderings_Olinorder(T_a) % 0.27/0.48 | V_x = V_y % 0.27/0.48 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.27/0.48 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.27/0.48 % 0.27/0.48 cnf(cls_linorder__less__linear_0,axiom, % 0.27/0.48 ( ~ class_Orderings_Olinorder(T_a) % 0.27/0.48 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.27/0.48 | V_x = V_y % 0.27/0.48 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.27/0.48 % 0.27/0.48 cnf(cls_linorder__neqE_0,axiom, % 0.27/0.48 ( ~ class_Orderings_Olinorder(T_a) % 0.27/0.48 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.27/0.48 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.27/0.48 | V_x = V_y ) ). % 0.27/0.48 % 0.27/0.48 cnf(cls_linorder__neqE__nat_0,axiom, % 0.27/0.48 ( c_HOL_Oord__class_Oless(V_y,V_x,tc_nat) % 0.27/0.48 | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) % 0.27/0.48 | V_x = V_y ) ). % 0.27/0.48 % 0.27/0.48 cnf(cls_nat__neq__iff_0,axiom, % 0.27/0.48 ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) % 0.27/0.48 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.27/0.48 | V_m = V_n ) ). % 0.27/0.48 % 0.27/0.48 cnf(cls_not__less__iff__gr__or__eq_0,axiom, % 0.27/0.48 ( ~ class_Orderings_Olinorder(T_a) % 0.27/0.49 | V_x = V_y % 0.27/0.49 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.27/0.49 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_linorder__neqE__ordered__idom_0,axiom, % 0.27/0.49 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.27/0.49 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.27/0.49 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.27/0.49 | V_x = V_y ) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_order__less__irrefl_0,axiom, % 0.27/0.49 ( ~ class_Orderings_Opreorder(T_a) % 0.27/0.49 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_linorder__neq__iff_1,axiom, % 0.27/0.49 ( ~ class_Orderings_Olinorder(T_a) % 0.27/0.49 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_order__less__le_1,axiom, % 0.27/0.49 ( ~ class_Orderings_Oorder(T_a) % 0.27/0.49 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_less__not__refl_0,axiom, % 0.27/0.49 ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_nat__less__le_1,axiom, % 0.27/0.49 ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_order__less__trans_0,axiom, % 0.27/0.49 ( ~ class_Orderings_Opreorder(T_a) % 0.27/0.49 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 0.27/0.49 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 0.27/0.49 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_xt1_I10_J_0,axiom, % 0.27/0.49 ( ~ class_Orderings_Oorder(T_a) % 0.27/0.49 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 0.27/0.49 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 0.27/0.49 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_gr__implies__not0_0,axiom, % 0.27/0.49 ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_not__less0_0,axiom, % 0.27/0.49 ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_abs_0,axiom, % 0.27/0.49 ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_s),c_Lambda_OdB_OAbs(V_t)) % 0.27/0.49 | ~ c_Lambda_Obeta(V_s,V_t) ) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_beta__cases_I2_J_0,axiom, % 0.27/0.49 ( V_s = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(V_r,V_s)) % 0.27/0.49 | ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_r),V_s) ) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_lift__preserves__beta_0,axiom, % 0.27/0.49 ( c_Lambda_Obeta(c_Lambda_Olift(V_r,V_i),c_Lambda_Olift(V_s,V_i)) % 0.27/0.49 | ~ c_Lambda_Obeta(V_r,V_s) ) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_lift_Osimps_I1_J_0,axiom, % 0.27/0.49 ( c_Lambda_Olift(c_Lambda_OdB_OVar(V_i),V_k) = c_Lambda_OdB_OVar(V_i) % 0.27/0.49 | ~ c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_subst__lift_0,axiom, % 0.27/0.49 c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t ). % 0.27/0.49 % 0.27/0.49 cnf(cls_appL_0,axiom, % 0.27/0.49 ( c_Lambda_Obeta(c_Lambda_OdB_OApp(V_s,V_u),c_Lambda_OdB_OApp(V_t,V_u)) % 0.27/0.49 | ~ c_Lambda_Obeta(V_s,V_t) ) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_appR_0,axiom, % 0.27/0.49 ( c_Lambda_Obeta(c_Lambda_OdB_OApp(V_u,V_s),c_Lambda_OdB_OApp(V_u,V_t)) % 0.27/0.49 | ~ c_Lambda_Obeta(V_s,V_t) ) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_subst__Var_1,axiom, % 0.27/0.49 ( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) % 0.27/0.49 | c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x),V_s,V_x) = V_s ) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_subst__Var_2,axiom, % 0.27/0.49 ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_i),V_s,V_k) = c_Lambda_OdB_OVar(V_i) % 0.27/0.49 | V_i = V_k % 0.27/0.49 | c_HOL_Oord__class_Oless(V_k,V_i,tc_nat) ) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_subst__preserves__beta_0,axiom, % 0.27/0.49 ( c_Lambda_Obeta(c_Lambda_Osubst(V_r,V_t,V_i),c_Lambda_Osubst(V_s,V_t,V_i)) % 0.27/0.49 | ~ c_Lambda_Obeta(V_r,V_s) ) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_lift_Osimps_I2_J_0,axiom, % 0.27/0.49 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)) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_dB_Osimps_I3_J_0,axiom, % 0.27/0.49 ( c_Lambda_OdB_OAbs(V_dB) != c_Lambda_OdB_OAbs(V_dB_H) % 0.27/0.49 | V_dB = V_dB_H ) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_beta_0,axiom, % 0.27/0.49 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))) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_dB_Osimps_I2_J_1,axiom, % 0.27/0.49 ( c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) % 0.27/0.49 | V_dB2 = V_dB2_H ) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_dB_Osimps_I2_J_0,axiom, % 0.27/0.49 ( c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) % 0.27/0.49 | V_dB1 = V_dB1_H ) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_beta__cases_I2_J_1,axiom, % 0.27/0.49 ( c_Lambda_Obeta(V_r,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(V_r,V_s)) % 0.27/0.49 | ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_r),V_s) ) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_subst__lt_0,axiom, % 0.27/0.49 ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_j),V_u,V_i) = c_Lambda_OdB_OVar(V_j) % 0.27/0.49 | ~ c_HOL_Oord__class_Oless(V_j,V_i,tc_nat) ) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_dB_Osimps_I9_J_0,axiom, % 0.27/0.49 c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OApp(V_dB1,V_dB2) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_dB_Osimps_I8_J_0,axiom, % 0.27/0.49 c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OAbs(V_dB_H) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_subst__App_0,axiom, % 0.27/0.49 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)) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_dB_Osimps_I7_J_0,axiom, % 0.27/0.49 c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_dB_Osimps_I1_J_0,axiom, % 0.27/0.49 ( c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OVar(V_nat_H) % 0.27/0.49 | V_nat = V_nat_H ) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_subst__eq_0,axiom, % 0.27/0.49 c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k) = V_u ). % 0.27/0.49 % 0.27/0.49 cnf(cls_Var_0,axiom, % 0.27/0.49 v_env______(v_x______) = v_Ta______ ). % 0.27/0.49 % 0.27/0.49 cnf(cls_subst__Var__IT_0,axiom, % 0.27/0.49 ( c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j)) % 0.27/0.49 | ~ c_InductTermi_OIT(V_r) ) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_beta__cases_I1_J_0,axiom, % 0.27/0.49 ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(V_i),V_t) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_dB_Osimps_I4_J_0,axiom, % 0.27/0.49 c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_lift__IT_0,axiom, % 0.27/0.49 ( c_InductTermi_OIT(c_Lambda_Olift(V_t,V_i)) % 0.27/0.49 | ~ c_InductTermi_OIT(V_t) ) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_dB_Osimps_I6_J_0,axiom, % 0.27/0.49 c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_Var__IT_0,axiom, % 0.27/0.49 c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n)) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_Lambda_0,axiom, % 0.27/0.49 ( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r)) % 0.27/0.49 | ~ c_InductTermi_OIT(V_r) ) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_app__Var__IT_0,axiom, % 0.27/0.49 ( c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i))) % 0.27/0.49 | ~ c_InductTermi_OIT(V_t) ) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_dB_Osimps_I5_J_0,axiom, % 0.27/0.49 c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) != c_Lambda_OdB_OVar(V_nat) ). % 0.27/0.49 % 0.27/0.49 cnf(cls_conjecture_0,negated_conjecture, % 0.27/0.49 ~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_x______)) ). % 0.27/0.49 % 0.27/0.49 cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom, % 0.27/0.49 class_Ring__and__Field_Oordered__semidom(tc_nat) ). % 0.27/0.49 % 0.27/0.49 cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom, % 0.27/0.49 class_Ring__and__Field_Osemiring__1(tc_nat) ). % 0.27/0.49 % 0.27/0.49 cnf(clsarity_nat__Nat_Osemiring__char__0,axiom, % 0.27/0.49 class_Nat_Osemiring__char__0(tc_nat) ). % 0.27/0.49 % 0.27/0.49 cnf(clsarity_nat__Orderings_Opreorder,axiom, % 0.27/0.49 class_Orderings_Opreorder(tc_nat) ). % 0.27/0.49 % 0.27/0.49 cnf(clsarity_nat__Orderings_Olinorder,axiom, % 0.27/0.49 class_Orderings_Olinorder(tc_nat) ). % 0.27/0.49 % 0.27/0.49 cnf(clsarity_nat__Orderings_Oorder,axiom, % 0.27/0.49 class_Orderings_Oorder(tc_nat) ). % 0.27/0.49 % 0.27/0.49 %------------------------------------------------------------------------------ % 0.27/0.49 %------------------------------------------- % 0.27/0.49 % Proof found % 0.27/0.49 % SZS status Theorem for theBenchmark % 0.27/0.49 % SZS output start Proof % 0.27/0.49 %ClaNum:100(EqnAxiom:31) % 0.27/0.49 %VarNum:263(SingletonVarNum:128) % 0.27/0.49 %MaxLitNum:4 % 0.27/0.49 %MaxfuncDepth:2 % 0.27/0.49 %SharedTerms:15 % 0.27/0.49 %goalClause: 45 % 0.27/0.49 %singleGoalClaCount:1 % 0.27/0.49 [33]P1(a4) % 0.27/0.49 [34]P10(a4) % 0.27/0.49 [35]P2(a4) % 0.27/0.49 [36]P6(a4) % 0.27/0.49 [37]P7(a4) % 0.27/0.49 [38]P8(a4) % 0.27/0.49 [32]E(f2(a1),a3) % 0.27/0.49 [45]~P3(f5(a1)) % 0.27/0.49 [54]~P4(x541,x541,a4) % 0.27/0.49 [39]P3(f5(x391)) % 0.27/0.49 [56]~P4(x561,f8(a4),a4) % 0.27/0.49 [47]~E(f5(x471),f7(x472)) % 0.27/0.49 [52]~P5(f5(x521),x522) % 0.27/0.49 [40]E(f9(f5(x401),x402,x401),x402) % 0.27/0.49 [43]P5(f6(f7(x431),x432),f9(x431,x432,f8(a4))) % 0.27/0.49 [48]~E(f7(x481),f6(x482,x483)) % 0.27/0.49 [49]~E(f5(x491),f6(x492,x493)) % 0.27/0.49 [50]~E(f6(x501,x502),f7(x503)) % 0.27/0.49 [51]~E(f6(x511,x512),f5(x513)) % 0.27/0.49 [41]E(f9(f10(x411,x412),x413,x412),x411) % 0.27/0.49 [42]E(f6(f10(x421,x422),f10(x423,x422)),f10(f6(x421,x423),x422)) % 0.27/0.49 [44]E(f6(f9(x441,x442,x443),f9(x444,x442,x443)),f9(f6(x441,x444),x442,x443)) % 0.27/0.49 [60]~P3(x601)+P3(f7(x601)) % 0.27/0.49 [68]E(x681,f8(a4))+P4(f8(a4),x681,a4) % 0.27/0.49 [61]~P10(x611)+E(f12(f8(a4),x611),f8(x611)) % 0.27/0.49 [74]~P4(x742,x742,x741)+~P6(x741) % 0.27/0.49 [75]~P4(x752,x752,x751)+~P7(x751) % 0.27/0.49 [76]~P4(x762,x762,x761)+~P8(x761) % 0.27/0.49 [58]E(x581,x582)+~E(f7(x581),f7(x582)) % 0.27/0.49 [59]E(x591,x592)+~E(f5(x591),f5(x592)) % 0.27/0.49 [62]~P3(x621)+P3(f10(x621,x622)) % 0.27/0.49 [65]~P5(x651,x652)+P5(f7(x651),f7(x652)) % 0.27/0.49 [70]~P5(f7(x701),x702)+P5(x701,f11(x701,x702)) % 0.27/0.49 [88]~P1(x881)+~P4(f12(x882,x881),f8(x881),x881) % 0.27/0.49 [66]~P3(x661)+P3(f6(x661,f5(x662))) % 0.27/0.49 [69]~P5(f7(x691),x692)+E(f7(f11(x691,x692)),x692) % 0.27/0.49 [77]~P4(x771,x772,a4)+E(f10(f5(x771),x772),f5(x771)) % 0.27/0.49 [71]~P5(x711,x713)+P5(f10(x711,x712),f10(x713,x712)) % 0.27/0.49 [72]~P5(x721,x723)+P5(f6(x721,x722),f6(x723,x722)) % 0.27/0.49 [73]~P5(x732,x733)+P5(f6(x731,x732),f6(x731,x733)) % 0.27/0.49 [87]~P3(x871)+P3(f9(x871,f5(x872),x873)) % 0.27/0.49 [89]~P4(x891,x893,a4)+E(f9(f5(x891),x892,x893),f5(x891)) % 0.27/0.49 [63]E(x631,x632)+~E(f6(x633,x631),f6(x634,x632)) % 0.27/0.49 [64]E(x641,x642)+~E(f6(x641,x643),f6(x642,x644)) % 0.27/0.49 [100]~P5(x1001,x1004)+P5(f9(x1001,x1002,x1003),f9(x1004,x1002,x1003)) % 0.27/0.49 [79]E(x791,x792)+P4(x792,x791,a4)+P4(x791,x792,a4) % 0.27/0.49 [94]~P1(x941)+P4(f8(x941),f12(x942,x941),x941)+~P4(f8(a4),x942,a4) % 0.27/0.49 [96]~P1(x962)+~P4(f8(x962),f12(x961,x962),x962)+P4(f8(a4),x961,a4) % 0.27/0.49 [91]~P4(x913,x912,x911)+~P6(x911)+~P4(x912,x913,x911) % 0.27/0.49 [92]~P4(x923,x922,x921)+~P7(x921)+~P4(x922,x923,x921) % 0.27/0.49 [93]~P4(x933,x932,x931)+~P8(x931)+~P4(x932,x933,x931) % 0.27/0.49 [67]~P2(x673)+E(x671,x672)+~E(f12(x671,x673),f12(x672,x673)) % 0.27/0.49 [95]~P1(x952)+~P4(x951,x953,a4)+P4(f12(x951,x952),f12(x953,x952),x952) % 0.27/0.49 [97]~P1(x973)+~P4(f12(x971,x973),f12(x972,x973),x973)+P4(x971,x972,a4) % 0.27/0.49 [86]E(x861,x862)+P4(x862,x861,a4)+E(f9(f5(x861),x863,x862),f5(x861)) % 0.27/0.49 [84]P4(x841,x842,x843)+~P7(x843)+E(x841,x842)+P4(x842,x841,x843) % 0.27/0.49 [85]P4(x851,x852,x853)+~P9(x853)+E(x851,x852)+P4(x852,x851,x853) % 0.27/0.49 [98]~P6(x983)+~P4(x981,x984,x983)+P4(x981,x982,x983)+~P4(x984,x982,x983) % 0.27/0.49 [99]~P8(x993)+~P4(x991,x994,x993)+P4(x991,x992,x993)+~P4(x994,x992,x993) % 0.27/0.49 %EqnAxiom % 0.27/0.49 [1]E(x11,x11) % 0.27/0.49 [2]E(x22,x21)+~E(x21,x22) % 0.27/0.49 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.27/0.49 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 0.27/0.49 [5]~E(x51,x52)+E(f5(x51),f5(x52)) % 0.27/0.49 [6]~E(x61,x62)+E(f9(x61,x63,x64),f9(x62,x63,x64)) % 0.27/0.49 [7]~E(x71,x72)+E(f9(x73,x71,x74),f9(x73,x72,x74)) % 0.27/0.49 [8]~E(x81,x82)+E(f9(x83,x84,x81),f9(x83,x84,x82)) % 0.27/0.49 [9]~E(x91,x92)+E(f12(x91,x93),f12(x92,x93)) % 0.27/0.49 [10]~E(x101,x102)+E(f12(x103,x101),f12(x103,x102)) % 0.27/0.49 [11]~E(x111,x112)+E(f10(x111,x113),f10(x112,x113)) % 0.27/0.49 [12]~E(x121,x122)+E(f10(x123,x121),f10(x123,x122)) % 0.27/0.49 [13]~E(x131,x132)+E(f8(x131),f8(x132)) % 0.27/0.49 [14]~E(x141,x142)+E(f7(x141),f7(x142)) % 0.27/0.49 [15]~E(x151,x152)+E(f6(x151,x153),f6(x152,x153)) % 0.27/0.49 [16]~E(x161,x162)+E(f6(x163,x161),f6(x163,x162)) % 0.27/0.49 [17]~E(x171,x172)+E(f11(x171,x173),f11(x172,x173)) % 0.27/0.49 [18]~E(x181,x182)+E(f11(x183,x181),f11(x183,x182)) % 0.27/0.49 [19]~P1(x191)+P1(x192)+~E(x191,x192) % 0.27/0.49 [20]~P10(x201)+P10(x202)+~E(x201,x202) % 0.27/0.49 [21]~P2(x211)+P2(x212)+~E(x211,x212) % 0.27/0.49 [22]~P6(x221)+P6(x222)+~E(x221,x222) % 0.27/0.49 [23]~P7(x231)+P7(x232)+~E(x231,x232) % 0.27/0.49 [24]~P8(x241)+P8(x242)+~E(x241,x242) % 0.27/0.49 [25]~P3(x251)+P3(x252)+~E(x251,x252) % 0.27/0.49 [26]P5(x262,x263)+~E(x261,x262)+~P5(x261,x263) % 0.27/0.49 [27]P5(x273,x272)+~E(x271,x272)+~P5(x273,x271) % 0.27/0.49 [28]P4(x282,x283,x284)+~E(x281,x282)+~P4(x281,x283,x284) % 0.27/0.49 [29]P4(x293,x292,x294)+~E(x291,x292)+~P4(x293,x291,x294) % 0.27/0.49 [30]P4(x303,x304,x302)+~E(x301,x302)+~P4(x303,x304,x301) % 0.27/0.49 [31]~P9(x311)+P9(x312)+~E(x311,x312) % 0.27/0.49 % 0.27/0.49 %------------------------------------------- % 0.27/0.49 cnf(106,plain, % 0.27/0.49 ($false), % 0.27/0.49 inference(scs_inference,[],[45,39]), % 0.27/0.49 ['proof']). % 0.27/0.49 % SZS output end Proof % 0.27/0.49 % Total time :0.006635s %------------------------------------------------------------------------------