%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : LCL844-1 : TPTP v9.3.1. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n019.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 0.25s 0.54s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL844-1 : TPTP v9.3.1. Released v4.1.0. % 0.00/0.03 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.09/0.35 % Computer : n019.cluster.edu % 0.09/0.35 % Model : x86_64 x86_64 % 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.35 % Memory : 8046.5625MB % 0.09/0.35 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Sat Sep 5 08:37:23 UTC 2026 % 0.09/0.35 % CPUTime : % 0.25/0.52 start to proof:theBenchmark % 0.25/0.52 %------------------------------------------- % 0.25/0.52 % File :CSE---1.7 % 0.25/0.52 % Problem :theBenchmark % 0.25/0.52 % Transform :cnf % 0.25/0.52 % Format :tptp:raw % 0.25/0.52 % Command :java -jar mcs_scs.jar %d %s % 0.25/0.52 % 0.25/0.52 % Result :Theorem 0.006937s % 0.25/0.52 % Output :CNFRefutation 0.006937s % 0.25/0.52 %------------------------------------------- % 0.25/0.52 %------------------------------------------------------------------------------ % 0.25/0.52 % File : LCL844-1 : TPTP v9.3.1. Released v4.1.0. % 0.25/0.52 % Domain : Logic Calculi % 0.25/0.52 % Problem : Strong normalization of typed lambda calculus 257_14 % 0.25/0.52 % Version : Especial. % 0.25/0.52 % English : % 0.25/0.52 % 0.25/0.52 % Refs : [vON99] von Oheimb & Nipkow (1999), Machine-Checking the Java % 0.25/0.52 % : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe % 0.25/0.52 % : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 0.25/0.52 % Source : [Nip10] % 0.25/0.52 % Names : StrongNorm-257_14 [Nip10] % 0.25/0.52 % 0.25/0.52 % Status : Unsatisfiable % 0.25/0.52 % Rating : 0.08 v9.3.0, 0.00 v7.0.0, 0.07 v6.4.0, 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 % 0.25/0.52 % Syntax : Number of clauses : 69 ( 26 unt; 10 nHn; 45 RR) % 0.25/0.52 % Number of literals : 138 ( 35 equ; 72 neg) % 0.25/0.52 % Maximal clause size : 4 ( 2 avg) % 0.25/0.52 % Maximal term depth : 3 ( 1 avg) % 0.25/0.52 % Number of predicates : 11 ( 10 usr; 0 prp; 1-3 aty) % 0.25/0.52 % Number of functors : 10 ( 10 usr; 2 con; 0-3 aty) % 0.25/0.52 % Number of variables : 148 ( 33 sgn) % 0.25/0.52 % SPC : CNF_UNS_RFO_SEQ_NHN % 0.25/0.52 % 0.25/0.52 % Comments : % 0.25/0.52 %------------------------------------------------------------------------------ % 0.25/0.52 cnf(cls_of__nat__less__0__iff_0,axiom, % 0.25/0.52 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.25/0.52 | ~ 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) ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_of__nat__0_0,axiom, % 0.25/0.53 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 0.25/0.53 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_of__nat__eq__iff_0,axiom, % 0.25/0.53 ( ~ class_Nat_Osemiring__char__0(T_a) % 0.25/0.53 | c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a) != c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) % 0.25/0.53 | V_m = V_n ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_of__nat__less__iff_1,axiom, % 0.25/0.53 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.25/0.53 | 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) % 0.25/0.53 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_of__nat__less__iff_0,axiom, % 0.25/0.53 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.25/0.53 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.25/0.53 | ~ 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) ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_order__less__asym_H_0,axiom, % 0.25/0.53 ( ~ class_Orderings_Opreorder(T_a) % 0.25/0.53 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.25/0.53 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_order__less__asym_0,axiom, % 0.25/0.53 ( ~ class_Orderings_Opreorder(T_a) % 0.25/0.53 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.25/0.53 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_not__less__iff__gr__or__eq_1,axiom, % 0.25/0.53 ( ~ class_Orderings_Olinorder(T_a) % 0.25/0.53 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.25/0.53 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_xt1_I9_J_0,axiom, % 0.25/0.53 ( ~ class_Orderings_Oorder(T_a) % 0.25/0.53 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.25/0.53 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_subst__App_0,axiom, % 0.25/0.53 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)) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_subst__eq_0,axiom, % 0.25/0.53 c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k) = V_u ). % 0.25/0.53 % 0.25/0.53 cnf(cls_subst__lt_0,axiom, % 0.25/0.53 ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_j),V_u,V_i) = c_Lambda_OdB_OVar(V_j) % 0.25/0.53 | ~ c_HOL_Oord__class_Oless(V_j,V_i,tc_nat) ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_neq0__conv_1,axiom, % 0.25/0.53 ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_gr0I_0,axiom, % 0.25/0.53 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.25/0.53 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_of__nat__0__less__iff_0,axiom, % 0.25/0.53 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.25/0.53 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.25/0.53 | ~ 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) ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_of__nat__0__less__iff_1,axiom, % 0.25/0.53 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.25/0.53 | 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) % 0.25/0.53 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_linorder__antisym__conv3_0,axiom, % 0.25/0.53 ( ~ class_Orderings_Olinorder(T_a) % 0.25/0.53 | V_x = V_y % 0.25/0.53 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.25/0.53 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_linorder__less__linear_0,axiom, % 0.25/0.53 ( ~ class_Orderings_Olinorder(T_a) % 0.25/0.53 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.25/0.53 | V_x = V_y % 0.25/0.53 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_linorder__neqE_0,axiom, % 0.25/0.53 ( ~ class_Orderings_Olinorder(T_a) % 0.25/0.53 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.25/0.53 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.25/0.53 | V_x = V_y ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_linorder__neqE__nat_0,axiom, % 0.25/0.53 ( c_HOL_Oord__class_Oless(V_y,V_x,tc_nat) % 0.25/0.53 | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) % 0.25/0.53 | V_x = V_y ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_nat__neq__iff_0,axiom, % 0.25/0.53 ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) % 0.25/0.53 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.25/0.53 | V_m = V_n ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_not__less__iff__gr__or__eq_0,axiom, % 0.25/0.53 ( ~ class_Orderings_Olinorder(T_a) % 0.25/0.53 | V_x = V_y % 0.25/0.53 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.25/0.53 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_linorder__neqE__ordered__idom_0,axiom, % 0.25/0.53 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.25/0.53 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.25/0.53 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.25/0.53 | V_x = V_y ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_order__less__irrefl_0,axiom, % 0.25/0.53 ( ~ class_Orderings_Opreorder(T_a) % 0.25/0.53 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_linorder__neq__iff_1,axiom, % 0.25/0.53 ( ~ class_Orderings_Olinorder(T_a) % 0.25/0.53 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_order__less__le_1,axiom, % 0.25/0.53 ( ~ class_Orderings_Oorder(T_a) % 0.25/0.53 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_less__not__refl_0,axiom, % 0.25/0.53 ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_nat__less__le_1,axiom, % 0.25/0.53 ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_subst__preserves__beta_0,axiom, % 0.25/0.53 ( c_Lambda_Obeta(c_Lambda_Osubst(V_r,V_t,V_i),c_Lambda_Osubst(V_s,V_t,V_i)) % 0.25/0.53 | ~ c_Lambda_Obeta(V_r,V_s) ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_subst__Var_2,axiom, % 0.25/0.53 ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_i),V_s,V_k) = c_Lambda_OdB_OVar(V_i) % 0.25/0.53 | V_i = V_k % 0.25/0.53 | c_HOL_Oord__class_Oless(V_k,V_i,tc_nat) ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_order__less__trans_0,axiom, % 0.25/0.53 ( ~ class_Orderings_Opreorder(T_a) % 0.25/0.53 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 0.25/0.53 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 0.25/0.53 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_xt1_I10_J_0,axiom, % 0.25/0.53 ( ~ class_Orderings_Oorder(T_a) % 0.25/0.53 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 0.25/0.53 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 0.25/0.53 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_gr__implies__not0_0,axiom, % 0.25/0.53 ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_not__less0_0,axiom, % 0.25/0.53 ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_subst__Var_1,axiom, % 0.25/0.53 ( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) % 0.25/0.53 | c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x),V_s,V_x) = V_s ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_subst__lift_0,axiom, % 0.25/0.53 c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t ). % 0.25/0.53 % 0.25/0.53 cnf(cls_dB_Osimps_I5_J_0,axiom, % 0.25/0.53 c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) != c_Lambda_OdB_OVar(V_nat) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_beta__cases_I2_J_0,axiom, % 0.25/0.53 ( V_s = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(V_r,V_s)) % 0.25/0.53 | ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_r),V_s) ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_app__Var__IT_0,axiom, % 0.25/0.53 ( c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i))) % 0.25/0.53 | ~ c_InductTermi_OIT(V_t) ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_lift__preserves__beta_0,axiom, % 0.25/0.53 ( c_Lambda_Obeta(c_Lambda_Olift(V_r,V_i),c_Lambda_Olift(V_s,V_i)) % 0.25/0.53 | ~ c_Lambda_Obeta(V_r,V_s) ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_lift_Osimps_I1_J_0,axiom, % 0.25/0.53 ( c_Lambda_Olift(c_Lambda_OdB_OVar(V_i),V_k) = c_Lambda_OdB_OVar(V_i) % 0.25/0.53 | ~ c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ) ). % 0.25/0.53 % 0.25/0.53 cnf(cls_appL_0,axiom, % 0.25/0.53 ( c_Lambda_Obeta(c_Lambda_OdB_OApp(V_s,V_u),c_Lambda_OdB_OApp(V_t,V_u)) % 0.25/0.54 | ~ c_Lambda_Obeta(V_s,V_t) ) ). % 0.25/0.54 % 0.25/0.54 cnf(cls_appR_0,axiom, % 0.25/0.54 ( c_Lambda_Obeta(c_Lambda_OdB_OApp(V_u,V_s),c_Lambda_OdB_OApp(V_u,V_t)) % 0.25/0.54 | ~ c_Lambda_Obeta(V_s,V_t) ) ). % 0.25/0.54 % 0.25/0.54 cnf(cls_lift_Osimps_I2_J_0,axiom, % 0.25/0.54 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)) ). % 0.25/0.54 % 0.25/0.54 cnf(cls_dB_Osimps_I4_J_0,axiom, % 0.25/0.54 c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) ). % 0.25/0.54 % 0.25/0.54 cnf(cls_beta_0,axiom, % 0.25/0.54 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))) ). % 0.25/0.54 % 0.25/0.54 cnf(cls_dB_Osimps_I2_J_1,axiom, % 0.25/0.54 ( c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) % 0.25/0.54 | V_dB2 = V_dB2_H ) ). % 0.25/0.54 % 0.25/0.54 cnf(cls_dB_Osimps_I2_J_0,axiom, % 0.25/0.54 ( c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) % 0.25/0.54 | V_dB1 = V_dB1_H ) ). % 0.25/0.54 % 0.25/0.54 cnf(cls_beta__cases_I1_J_0,axiom, % 0.25/0.54 ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(V_i),V_t) ). % 0.25/0.54 % 0.25/0.54 cnf(cls_beta__cases_I2_J_1,axiom, % 0.25/0.54 ( c_Lambda_Obeta(V_r,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(V_r,V_s)) % 0.25/0.54 | ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_r),V_s) ) ). % 0.25/0.54 % 0.25/0.54 cnf(cls_subst__Var__IT_0,axiom, % 0.25/0.54 ( c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j)) % 0.25/0.54 | ~ c_InductTermi_OIT(V_r) ) ). % 0.25/0.54 % 0.25/0.54 cnf(cls_dB_Osimps_I1_J_0,axiom, % 0.25/0.54 ( c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OVar(V_nat_H) % 0.25/0.54 | V_nat = V_nat_H ) ). % 0.25/0.54 % 0.25/0.54 cnf(cls_dB_Osimps_I7_J_0,axiom, % 0.25/0.54 c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat) ). % 0.25/0.54 % 0.25/0.54 cnf(cls_dB_Osimps_I8_J_0,axiom, % 0.25/0.54 c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OAbs(V_dB_H) ). % 0.25/0.54 % 0.25/0.54 cnf(cls_dB_Osimps_I9_J_0,axiom, % 0.25/0.54 c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OApp(V_dB1,V_dB2) ). % 0.25/0.54 % 0.25/0.54 cnf(cls_Abs_I2_J_0,axiom, % 0.25/0.54 c_InductTermi_OIT(v_ta______) ). % 0.25/0.54 % 0.25/0.54 cnf(cls_dB_Osimps_I3_J_0,axiom, % 0.25/0.54 ( c_Lambda_OdB_OAbs(V_dB) != c_Lambda_OdB_OAbs(V_dB_H) % 0.25/0.54 | V_dB = V_dB_H ) ). % 0.25/0.54 % 0.25/0.54 cnf(cls_lift__IT_0,axiom, % 0.25/0.54 ( c_InductTermi_OIT(c_Lambda_Olift(V_t,V_i)) % 0.25/0.54 | ~ c_InductTermi_OIT(V_t) ) ). % 0.25/0.54 % 0.25/0.54 cnf(cls_dB_Osimps_I6_J_0,axiom, % 0.25/0.54 c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H) ). % 0.25/0.54 % 0.25/0.54 cnf(cls_Var__IT_0,axiom, % 0.25/0.54 c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n)) ). % 0.25/0.54 % 0.25/0.54 cnf(cls_Lambda_0,axiom, % 0.25/0.54 ( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r)) % 0.25/0.54 | ~ c_InductTermi_OIT(V_r) ) ). % 0.25/0.54 % 0.25/0.54 cnf(cls_abs_0,axiom, % 0.25/0.54 ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_s),c_Lambda_OdB_OAbs(V_t)) % 0.25/0.54 | ~ c_Lambda_Obeta(V_s,V_t) ) ). % 0.25/0.54 % 0.25/0.54 cnf(cls_conjecture_0,negated_conjecture, % 0.25/0.54 ~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(v_ta______)) ). % 0.25/0.54 % 0.25/0.54 cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom, % 0.25/0.54 class_Ring__and__Field_Oordered__semidom(tc_nat) ). % 0.25/0.54 % 0.25/0.54 cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom, % 0.25/0.54 class_Ring__and__Field_Osemiring__1(tc_nat) ). % 0.25/0.54 % 0.25/0.54 cnf(clsarity_nat__Nat_Osemiring__char__0,axiom, % 0.25/0.54 class_Nat_Osemiring__char__0(tc_nat) ). % 0.25/0.54 % 0.25/0.54 cnf(clsarity_nat__Orderings_Opreorder,axiom, % 0.25/0.54 class_Orderings_Opreorder(tc_nat) ). % 0.25/0.54 % 0.25/0.54 cnf(clsarity_nat__Orderings_Olinorder,axiom, % 0.25/0.54 class_Orderings_Olinorder(tc_nat) ). % 0.25/0.54 % 0.25/0.54 cnf(clsarity_nat__Orderings_Oorder,axiom, % 0.25/0.54 class_Orderings_Oorder(tc_nat) ). % 0.25/0.54 % 0.25/0.54 %------------------------------------------------------------------------------ % 0.25/0.54 %------------------------------------------- % 0.25/0.54 % Proof found % 0.25/0.54 % SZS status Theorem for theBenchmark % 0.25/0.54 % SZS output start Proof % 0.25/0.54 %ClaNum:99(EqnAxiom:30) % 0.25/0.54 %VarNum:263(SingletonVarNum:128) % 0.25/0.54 %MaxLitNum:4 % 0.25/0.54 %MaxfuncDepth:2 % 0.25/0.54 %SharedTerms:13 % 0.25/0.54 %goalClause: 44 % 0.25/0.54 %singleGoalClaCount:1 % 0.25/0.54 [31]P1(a1) % 0.25/0.54 [32]P10(a1) % 0.25/0.54 [33]P2(a1) % 0.25/0.54 [34]P6(a1) % 0.25/0.54 [35]P7(a1) % 0.25/0.54 [36]P8(a1) % 0.25/0.54 [37]P3(a10) % 0.25/0.54 [44]~P3(f4(a10)) % 0.25/0.54 [53]~P4(x531,x531,a1) % 0.25/0.54 [38]P3(f2(x381)) % 0.25/0.54 [55]~P4(x551,f5(a1),a1) % 0.25/0.54 [46]~E(f4(x461),f2(x462)) % 0.25/0.54 [51]~P5(f2(x511),x512) % 0.25/0.54 [39]E(f6(f2(x391),x392,x391),x392) % 0.25/0.54 [42]P5(f3(f4(x421),x422),f6(x421,x422,f5(a1))) % 0.25/0.54 [47]~E(f2(x471),f3(x472,x473)) % 0.25/0.54 [48]~E(f4(x481),f3(x482,x483)) % 0.25/0.54 [49]~E(f3(x491,x492),f2(x493)) % 0.25/0.54 [50]~E(f3(x501,x502),f4(x503)) % 0.25/0.54 [40]E(f6(f7(x401,x402),x403,x402),x401) % 0.25/0.54 [41]E(f3(f7(x411,x412),f7(x413,x412)),f7(f3(x411,x413),x412)) % 0.25/0.54 [43]E(f3(f6(x431,x432,x433),f6(x434,x432,x433)),f6(f3(x431,x434),x432,x433)) % 0.25/0.54 [59]~P3(x591)+P3(f4(x591)) % 0.25/0.54 [67]E(x671,f5(a1))+P4(f5(a1),x671,a1) % 0.25/0.54 [60]~P10(x601)+E(f9(f5(a1),x601),f5(x601)) % 0.25/0.54 [73]~P4(x732,x732,x731)+~P6(x731) % 0.25/0.54 [74]~P4(x742,x742,x741)+~P7(x741) % 0.25/0.54 [75]~P4(x752,x752,x751)+~P8(x751) % 0.25/0.54 [57]E(x571,x572)+~E(f2(x571),f2(x572)) % 0.25/0.54 [58]E(x581,x582)+~E(f4(x581),f4(x582)) % 0.25/0.54 [61]~P3(x611)+P3(f7(x611,x612)) % 0.25/0.54 [64]~P5(x641,x642)+P5(f4(x641),f4(x642)) % 0.25/0.54 [69]~P5(f4(x691),x692)+P5(x691,f8(x691,x692)) % 0.25/0.54 [87]~P1(x871)+~P4(f9(x872,x871),f5(x871),x871) % 0.25/0.54 [65]~P3(x651)+P3(f3(x651,f2(x652))) % 0.25/0.54 [68]~P5(f4(x681),x682)+E(f4(f8(x681,x682)),x682) % 0.25/0.54 [76]~P4(x761,x762,a1)+E(f7(f2(x761),x762),f2(x761)) % 0.25/0.54 [70]~P5(x701,x703)+P5(f3(x701,x702),f3(x703,x702)) % 0.25/0.54 [71]~P5(x712,x713)+P5(f3(x711,x712),f3(x711,x713)) % 0.25/0.54 [72]~P5(x721,x723)+P5(f7(x721,x722),f7(x723,x722)) % 0.25/0.54 [86]~P3(x861)+P3(f6(x861,f2(x862),x863)) % 0.25/0.54 [88]~P4(x881,x883,a1)+E(f6(f2(x881),x882,x883),f2(x881)) % 0.25/0.54 [62]E(x621,x622)+~E(f3(x623,x621),f3(x624,x622)) % 0.25/0.54 [63]E(x631,x632)+~E(f3(x631,x633),f3(x632,x634)) % 0.25/0.54 [99]~P5(x991,x994)+P5(f6(x991,x992,x993),f6(x994,x992,x993)) % 0.25/0.54 [78]E(x781,x782)+P4(x782,x781,a1)+P4(x781,x782,a1) % 0.25/0.54 [93]~P1(x931)+P4(f5(x931),f9(x932,x931),x931)+~P4(f5(a1),x932,a1) % 0.25/0.54 [95]~P1(x952)+~P4(f5(x952),f9(x951,x952),x952)+P4(f5(a1),x951,a1) % 0.25/0.54 [90]~P4(x903,x902,x901)+~P6(x901)+~P4(x902,x903,x901) % 0.25/0.54 [91]~P4(x913,x912,x911)+~P7(x911)+~P4(x912,x913,x911) % 0.25/0.54 [92]~P4(x923,x922,x921)+~P8(x921)+~P4(x922,x923,x921) % 0.25/0.54 [66]~P2(x663)+E(x661,x662)+~E(f9(x661,x663),f9(x662,x663)) % 0.25/0.54 [94]~P1(x942)+~P4(x941,x943,a1)+P4(f9(x941,x942),f9(x943,x942),x942) % 0.25/0.54 [96]~P1(x963)+~P4(f9(x961,x963),f9(x962,x963),x963)+P4(x961,x962,a1) % 0.25/0.54 [85]E(x851,x852)+P4(x852,x851,a1)+E(f6(f2(x851),x853,x852),f2(x851)) % 0.25/0.54 [83]P4(x831,x832,x833)+~P7(x833)+E(x831,x832)+P4(x832,x831,x833) % 0.25/0.54 [84]P4(x841,x842,x843)+~P9(x843)+E(x841,x842)+P4(x842,x841,x843) % 0.25/0.54 [97]~P6(x973)+~P4(x971,x974,x973)+P4(x971,x972,x973)+~P4(x974,x972,x973) % 0.25/0.54 [98]~P8(x983)+~P4(x981,x984,x983)+P4(x981,x982,x983)+~P4(x984,x982,x983) % 0.25/0.54 %EqnAxiom % 0.25/0.54 [1]E(x11,x11) % 0.25/0.54 [2]E(x22,x21)+~E(x21,x22) % 0.25/0.54 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.25/0.54 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 0.25/0.54 [5]~E(x51,x52)+E(f6(x51,x53,x54),f6(x52,x53,x54)) % 0.25/0.54 [6]~E(x61,x62)+E(f6(x63,x61,x64),f6(x63,x62,x64)) % 0.25/0.54 [7]~E(x71,x72)+E(f6(x73,x74,x71),f6(x73,x74,x72)) % 0.25/0.54 [8]~E(x81,x82)+E(f9(x81,x83),f9(x82,x83)) % 0.25/0.54 [9]~E(x91,x92)+E(f9(x93,x91),f9(x93,x92)) % 0.25/0.54 [10]~E(x101,x102)+E(f7(x101,x103),f7(x102,x103)) % 0.25/0.54 [11]~E(x111,x112)+E(f7(x113,x111),f7(x113,x112)) % 0.25/0.54 [12]~E(x121,x122)+E(f5(x121),f5(x122)) % 0.25/0.54 [13]~E(x131,x132)+E(f8(x131,x133),f8(x132,x133)) % 0.25/0.54 [14]~E(x141,x142)+E(f8(x143,x141),f8(x143,x142)) % 0.25/0.54 [15]~E(x151,x152)+E(f4(x151),f4(x152)) % 0.25/0.54 [16]~E(x161,x162)+E(f3(x161,x163),f3(x162,x163)) % 0.25/0.54 [17]~E(x171,x172)+E(f3(x173,x171),f3(x173,x172)) % 0.25/0.54 [18]~P1(x181)+P1(x182)+~E(x181,x182) % 0.25/0.54 [19]~P10(x191)+P10(x192)+~E(x191,x192) % 0.25/0.54 [20]~P2(x201)+P2(x202)+~E(x201,x202) % 0.25/0.54 [21]~P6(x211)+P6(x212)+~E(x211,x212) % 0.25/0.54 [22]~P7(x221)+P7(x222)+~E(x221,x222) % 0.25/0.54 [23]~P8(x231)+P8(x232)+~E(x231,x232) % 0.25/0.54 [24]~P3(x241)+P3(x242)+~E(x241,x242) % 0.25/0.54 [25]P5(x252,x253)+~E(x251,x252)+~P5(x251,x253) % 0.25/0.54 [26]P5(x263,x262)+~E(x261,x262)+~P5(x263,x261) % 0.25/0.54 [27]P4(x272,x273,x274)+~E(x271,x272)+~P4(x271,x273,x274) % 0.25/0.54 [28]P4(x283,x282,x284)+~E(x281,x282)+~P4(x283,x281,x284) % 0.25/0.54 [29]P4(x293,x294,x292)+~E(x291,x292)+~P4(x293,x294,x291) % 0.25/0.54 [30]~P9(x301)+P9(x302)+~E(x301,x302) % 0.25/0.54 % 0.25/0.54 %------------------------------------------- % 0.25/0.54 cnf(105,plain, % 0.25/0.54 ($false), % 0.25/0.54 inference(scs_inference,[],[37,44,59]), % 0.25/0.54 ['proof']). % 0.25/0.54 % SZS output end Proof % 0.25/0.54 % Total time :0.006937s %------------------------------------------------------------------------------