%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : LCL828-1 : 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 : n028.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 11:19:56 AM UTC 2026 % Result : Unsatisfiable 0.24s 0.52s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL828-1 : 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 % 0.08/0.34 % Computer : n028.cluster.edu % 0.08/0.34 % Model : x86_64 x86_64 % 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.34 % Memory : 8046.5625MB % 0.08/0.34 % OS : Linux 6.8.0-71-generic % 0.08/0.34 % CPULimit : 300 % 0.08/0.34 % WCLimit : 300 % 0.08/0.34 % DateTime : Sat Sep 5 22:34:45 UTC 2026 % 0.08/0.35 % CPUTime : % 0.24/0.51 start to proof:theBenchmark % 0.24/0.51 %------------------------------------------- % 0.24/0.51 % File :CSE---1.7 % 0.24/0.51 % Problem :theBenchmark % 0.24/0.51 % Transform :cnf % 0.24/0.51 % Format :tptp:raw % 0.24/0.51 % Command :java -jar mcs_scs.jar %d %s % 0.24/0.51 % 0.24/0.51 % Result :Theorem 0.006062s % 0.24/0.51 % Output :CNFRefutation 0.006062s % 0.24/0.51 %------------------------------------------- % 0.24/0.51 %------------------------------------------------------------------------------ % 0.24/0.51 % File : LCL828-1 : TPTP v9.3.1. Released v4.1.0. % 0.24/0.51 % Domain : Logic Calculi % 0.24/0.51 % Problem : Strong normalization of typed lambda calculus 207_44 % 0.24/0.51 % Version : Especial. % 0.24/0.51 % English : % 0.24/0.51 % 0.24/0.51 % Refs : [vON99] von Oheimb & Nipkow (1999), Machine-Checking the Java % 0.24/0.51 % : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe % 0.24/0.51 % : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 0.24/0.51 % Source : [Nip10] % 0.24/0.51 % Names : StrongNorm-207_44 [Nip10] % 0.24/0.51 % 0.24/0.51 % Status : Unsatisfiable % 0.24/0.51 % Rating : 0.17 v9.3.0, 0.09 v9.1.0, 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 % 0.24/0.51 % Syntax : Number of clauses : 75 ( 31 unt; 10 nHn; 51 RR) % 0.24/0.51 % Number of literals : 147 ( 36 equ; 76 neg) % 0.24/0.51 % Maximal clause size : 4 ( 1 avg) % 0.24/0.51 % Maximal term depth : 3 ( 1 avg) % 0.24/0.51 % Number of predicates : 12 ( 11 usr; 0 prp; 1-3 aty) % 0.24/0.51 % Number of functors : 19 ( 19 usr; 10 con; 0-4 aty) % 0.24/0.51 % Number of variables : 152 ( 34 sgn) % 0.24/0.51 % SPC : CNF_UNS_RFO_SEQ_NHN % 0.24/0.51 % 0.24/0.51 % Comments : % 0.24/0.51 %------------------------------------------------------------------------------ % 0.24/0.51 cnf(cls_of__nat__less__0__iff_0,axiom, % 0.24/0.51 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.24/0.51 | ~ 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) ) ). % 0.24/0.51 % 0.24/0.51 cnf(cls_of__nat__0_0,axiom, % 0.24/0.51 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 0.24/0.51 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.24/0.51 % 0.24/0.51 cnf(cls_of__nat__eq__iff_0,axiom, % 0.24/0.51 ( ~ class_Nat_Osemiring__char__0(T_a) % 0.24/0.51 | c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a) != c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) % 0.24/0.51 | V_m = V_n ) ). % 0.24/0.51 % 0.24/0.51 cnf(cls_of__nat__less__iff_1,axiom, % 0.24/0.51 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.24/0.51 | 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) % 0.24/0.51 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.24/0.51 % 0.24/0.51 cnf(cls_of__nat__less__iff_0,axiom, % 0.24/0.51 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.24/0.51 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.24/0.51 | ~ 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) ) ). % 0.24/0.51 % 0.24/0.51 cnf(cls_order__less__asym_H_0,axiom, % 0.24/0.51 ( ~ class_Orderings_Opreorder(T_a) % 0.24/0.51 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.24/0.51 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.24/0.51 % 0.24/0.51 cnf(cls_order__less__asym_0,axiom, % 0.24/0.51 ( ~ class_Orderings_Opreorder(T_a) % 0.24/0.51 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.24/0.51 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.24/0.51 % 0.24/0.51 cnf(cls_not__less__iff__gr__or__eq_1,axiom, % 0.24/0.51 ( ~ class_Orderings_Olinorder(T_a) % 0.24/0.51 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.24/0.51 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.24/0.51 % 0.24/0.51 cnf(cls_xt1_I9_J_0,axiom, % 0.24/0.51 ( ~ class_Orderings_Oorder(T_a) % 0.24/0.51 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.24/0.51 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 0.24/0.51 % 0.24/0.51 cnf(cls_neq0__conv_1,axiom, % 0.24/0.51 ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 0.24/0.51 % 0.24/0.51 cnf(cls_gr0I_0,axiom, % 0.24/0.51 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.24/0.51 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.24/0.51 % 0.24/0.51 cnf(cls_of__nat__0__less__iff_0,axiom, % 0.24/0.51 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.24/0.51 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.24/0.51 | ~ 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) ) ). % 0.24/0.51 % 0.24/0.51 cnf(cls_of__nat__0__less__iff_1,axiom, % 0.24/0.51 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.24/0.51 | 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) % 0.24/0.51 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.24/0.51 % 0.24/0.51 cnf(cls_linorder__antisym__conv3_0,axiom, % 0.24/0.51 ( ~ class_Orderings_Olinorder(T_a) % 0.24/0.51 | V_x = V_y % 0.24/0.51 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.24/0.51 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.24/0.51 % 0.24/0.51 cnf(cls_linorder__less__linear_0,axiom, % 0.24/0.51 ( ~ class_Orderings_Olinorder(T_a) % 0.24/0.51 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.24/0.51 | V_x = V_y % 0.24/0.51 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.24/0.51 % 0.24/0.51 cnf(cls_linorder__neqE_0,axiom, % 0.24/0.51 ( ~ class_Orderings_Olinorder(T_a) % 0.24/0.51 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.24/0.51 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.24/0.51 | V_x = V_y ) ). % 0.24/0.51 % 0.24/0.51 cnf(cls_linorder__neqE__nat_0,axiom, % 0.24/0.51 ( c_HOL_Oord__class_Oless(V_y,V_x,tc_nat) % 0.24/0.51 | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) % 0.24/0.51 | V_x = V_y ) ). % 0.24/0.51 % 0.24/0.51 cnf(cls_nat__neq__iff_0,axiom, % 0.24/0.51 ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) % 0.24/0.51 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.24/0.51 | V_m = V_n ) ). % 0.24/0.51 % 0.24/0.51 cnf(cls_not__less__iff__gr__or__eq_0,axiom, % 0.24/0.51 ( ~ class_Orderings_Olinorder(T_a) % 0.24/0.51 | V_x = V_y % 0.24/0.51 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.24/0.51 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.24/0.51 % 0.24/0.51 cnf(cls_linorder__neqE__ordered__idom_0,axiom, % 0.24/0.51 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.24/0.51 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.24/0.51 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.24/0.51 | V_x = V_y ) ). % 0.24/0.51 % 0.24/0.51 cnf(cls_order__less__irrefl_0,axiom, % 0.24/0.51 ( ~ class_Orderings_Opreorder(T_a) % 0.24/0.52 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_linorder__neq__iff_1,axiom, % 0.24/0.52 ( ~ class_Orderings_Olinorder(T_a) % 0.24/0.52 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_order__less__le_1,axiom, % 0.24/0.52 ( ~ class_Orderings_Oorder(T_a) % 0.24/0.52 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_less__not__refl_0,axiom, % 0.24/0.52 ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_nat__less__le_1,axiom, % 0.24/0.52 ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_order__less__trans_0,axiom, % 0.24/0.52 ( ~ class_Orderings_Opreorder(T_a) % 0.24/0.52 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 0.24/0.52 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 0.24/0.52 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_xt1_I10_J_0,axiom, % 0.24/0.52 ( ~ class_Orderings_Oorder(T_a) % 0.24/0.52 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 0.24/0.52 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 0.24/0.52 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_gr__implies__not0_0,axiom, % 0.24/0.52 ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_not__less0_0,axiom, % 0.24/0.52 ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_dB_Osimps_I5_J_0,axiom, % 0.24/0.52 c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) != c_Lambda_OdB_OVar(V_nat) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_abs_0,axiom, % 0.24/0.52 ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_s),c_Lambda_OdB_OAbs(V_t)) % 0.24/0.52 | ~ c_Lambda_Obeta(V_s,V_t) ) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_beta__cases_I2_J_0,axiom, % 0.24/0.52 ( V_s = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(V_r,V_s)) % 0.24/0.52 | ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_r),V_s) ) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_app__Var__IT_0,axiom, % 0.24/0.52 ( c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i))) % 0.24/0.52 | ~ c_InductTermi_OIT(V_t) ) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_lift__preserves__beta_0,axiom, % 0.24/0.52 ( c_Lambda_Obeta(c_Lambda_Olift(V_r,V_i),c_Lambda_Olift(V_s,V_i)) % 0.24/0.52 | ~ c_Lambda_Obeta(V_r,V_s) ) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_lift_Osimps_I1_J_0,axiom, % 0.24/0.52 ( c_Lambda_Olift(c_Lambda_OdB_OVar(V_i),V_k) = c_Lambda_OdB_OVar(V_i) % 0.24/0.52 | ~ c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_appL_0,axiom, % 0.24/0.52 ( c_Lambda_Obeta(c_Lambda_OdB_OApp(V_s,V_u),c_Lambda_OdB_OApp(V_t,V_u)) % 0.24/0.52 | ~ c_Lambda_Obeta(V_s,V_t) ) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_appR_0,axiom, % 0.24/0.52 ( c_Lambda_Obeta(c_Lambda_OdB_OApp(V_u,V_s),c_Lambda_OdB_OApp(V_u,V_t)) % 0.24/0.52 | ~ c_Lambda_Obeta(V_s,V_t) ) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_subst__Var_1,axiom, % 0.24/0.52 ( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) % 0.24/0.52 | c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x),V_s,V_x) = V_s ) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_subst__Var_2,axiom, % 0.24/0.52 ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_i),V_s,V_k) = c_Lambda_OdB_OVar(V_i) % 0.24/0.52 | V_i = V_k % 0.24/0.52 | c_HOL_Oord__class_Oless(V_k,V_i,tc_nat) ) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_lift_Osimps_I2_J_0,axiom, % 0.24/0.52 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)) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_dB_Osimps_I6_J_0,axiom, % 0.24/0.52 c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_dB_Osimps_I3_J_0,axiom, % 0.24/0.52 ( c_Lambda_OdB_OAbs(V_dB) != c_Lambda_OdB_OAbs(V_dB_H) % 0.24/0.52 | V_dB = V_dB_H ) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_dB_Osimps_I4_J_0,axiom, % 0.24/0.52 c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_beta_0,axiom, % 0.24/0.52 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))) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_dB_Osimps_I2_J_1,axiom, % 0.24/0.52 ( c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) % 0.24/0.52 | V_dB2 = V_dB2_H ) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_dB_Osimps_I2_J_0,axiom, % 0.24/0.52 ( c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) % 0.24/0.52 | V_dB1 = V_dB1_H ) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_beta__cases_I1_J_0,axiom, % 0.24/0.52 ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(V_i),V_t) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_beta__cases_I2_J_1,axiom, % 0.24/0.52 ( c_Lambda_Obeta(V_r,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(V_r,V_s)) % 0.24/0.52 | ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_r),V_s) ) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_subst__lt_0,axiom, % 0.24/0.52 ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_j),V_u,V_i) = c_Lambda_OdB_OVar(V_j) % 0.24/0.52 | ~ c_HOL_Oord__class_Oless(V_j,V_i,tc_nat) ) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_dB_Osimps_I9_J_0,axiom, % 0.24/0.52 c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OApp(V_dB1,V_dB2) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_dB_Osimps_I1_J_0,axiom, % 0.24/0.52 ( c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OVar(V_nat_H) % 0.24/0.52 | V_nat = V_nat_H ) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_dB_Osimps_I8_J_0,axiom, % 0.24/0.52 c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OAbs(V_dB_H) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_dB_Osimps_I7_J_0,axiom, % 0.24/0.52 c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_subst__App_0,axiom, % 0.24/0.52 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)) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_subst__eq_0,axiom, % 0.24/0.52 c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k) = V_u ). % 0.24/0.52 % 0.24/0.52 cnf(cls_subst__Var__IT_0,axiom, % 0.24/0.52 ( c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j)) % 0.24/0.52 | ~ c_InductTermi_OIT(V_r) ) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_lift__IT_0,axiom, % 0.24/0.52 ( c_InductTermi_OIT(c_Lambda_Olift(V_t,V_i)) % 0.24/0.52 | ~ c_InductTermi_OIT(V_t) ) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_Var__IT_0,axiom, % 0.24/0.52 c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n)) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_False_0,axiom, % 0.24/0.52 v_n____ != v_i____ ). % 0.24/0.52 % 0.24/0.52 cnf(cls_subst__preserves__beta_0,axiom, % 0.24/0.52 ( c_Lambda_Obeta(c_Lambda_Osubst(V_r,V_t,V_i),c_Lambda_Osubst(V_s,V_t,V_i)) % 0.24/0.52 | ~ c_Lambda_Obeta(V_r,V_s) ) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_Var_I3_J_0,axiom, % 0.24/0.52 c_InductTermi_OIT(v_ua______) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_Lambda_0,axiom, % 0.24/0.52 ( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r)) % 0.24/0.52 | ~ c_InductTermi_OIT(V_r) ) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_uIT_0,axiom, % 0.24/0.52 c_InductTermi_OIT(v_u____) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_subst__lift_0,axiom, % 0.24/0.52 c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t ). % 0.24/0.52 % 0.24/0.52 cnf(cls_CHAINED_0,axiom, % 0.24/0.52 c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_Ua____) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_CHAINED_0_01,axiom, % 0.24/0.52 ( c_InductTermi_OIT(c_Lambda_Osubst(v_a____,V_ua,V_ia)) % 0.24/0.52 | ~ c_Type_Otyping(V_ea,V_ua,v_T____) % 0.24/0.52 | ~ c_InductTermi_OIT(V_ua) % 0.24/0.52 | ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_a____,V_T_H) ) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_CHAINED_0_02,axiom, % 0.24/0.52 c_InductTermi_OIT(v_u____) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_CHAINED_0_03,axiom, % 0.24/0.52 c_Type_Otyping(v_e____,v_u____,v_T____) ). % 0.24/0.52 % 0.24/0.52 cnf(cls_conjecture_0,negated_conjecture, % 0.24/0.52 ~ c_InductTermi_OIT(c_Lambda_Osubst(v_a____,v_u____,v_i____)) ). % 0.24/0.52 % 0.24/0.52 cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom, % 0.24/0.52 class_Ring__and__Field_Oordered__semidom(tc_nat) ). % 0.24/0.52 % 0.24/0.52 cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom, % 0.24/0.52 class_Ring__and__Field_Osemiring__1(tc_nat) ). % 0.24/0.52 % 0.24/0.52 cnf(clsarity_nat__Nat_Osemiring__char__0,axiom, % 0.24/0.52 class_Nat_Osemiring__char__0(tc_nat) ). % 0.24/0.52 % 0.24/0.52 cnf(clsarity_nat__Orderings_Opreorder,axiom, % 0.24/0.52 class_Orderings_Opreorder(tc_nat) ). % 0.24/0.52 % 0.24/0.52 cnf(clsarity_nat__Orderings_Olinorder,axiom, % 0.24/0.52 class_Orderings_Olinorder(tc_nat) ). % 0.24/0.52 % 0.24/0.52 cnf(clsarity_nat__Orderings_Oorder,axiom, % 0.24/0.52 class_Orderings_Oorder(tc_nat) ). % 0.24/0.52 % 0.24/0.52 %------------------------------------------------------------------------------ % 0.24/0.52 %------------------------------------------- % 0.24/0.52 % Proof found % 0.24/0.52 % SZS status Theorem for theBenchmark % 0.24/0.52 % SZS output start Proof % 0.24/0.52 %ClaNum:112(EqnAxiom:37) % 0.24/0.52 %VarNum:271(SingletonVarNum:132) % 0.24/0.52 %MaxLitNum:4 % 0.24/0.52 %MaxfuncDepth:2 % 0.24/0.52 %SharedTerms:26 % 0.24/0.52 %goalClause: 68 % 0.24/0.52 %singleGoalClaCount:1 % 0.24/0.52 [38]P1(a1) % 0.24/0.52 [39]P11(a1) % 0.24/0.52 [40]P2(a1) % 0.24/0.52 [41]P7(a1) % 0.24/0.52 [42]P8(a1) % 0.24/0.52 [43]P9(a1) % 0.24/0.52 [44]P3(a12) % 0.24/0.52 [46]P3(a13) % 0.24/0.52 [48]P5(a14,a13,a15) % 0.24/0.52 [55]~E(a19,a18) % 0.24/0.52 [54]P5(f10(a14,a18,a15,a9),a16,a17) % 0.24/0.52 [68]~P3(f6(a16,a13,a18)) % 0.24/0.52 [64]~P4(x641,x641,a1) % 0.24/0.52 [47]P3(f2(x471)) % 0.24/0.52 [66]~P4(x661,f5(a1),a1) % 0.24/0.52 [57]~E(f4(x571),f2(x572)) % 0.24/0.52 [62]~P6(f2(x621),x622) % 0.24/0.52 [49]E(f6(f2(x491),x492,x491),x492) % 0.24/0.52 [52]P6(f3(f4(x521),x522),f6(x521,x522,f5(a1))) % 0.24/0.52 [58]~E(f2(x581),f3(x582,x583)) % 0.24/0.52 [59]~E(f4(x591),f3(x592,x593)) % 0.24/0.52 [60]~E(f3(x601,x602),f2(x603)) % 0.24/0.52 [61]~E(f3(x611,x612),f4(x613)) % 0.24/0.52 [50]E(f6(f7(x501,x502),x503,x502),x501) % 0.24/0.52 [51]E(f3(f7(x511,x512),f7(x513,x512)),f7(f3(x511,x513),x512)) % 0.24/0.52 [53]E(f3(f6(x531,x532,x533),f6(x534,x532,x533)),f6(f3(x531,x534),x532,x533)) % 0.24/0.52 [71]~P3(x711)+P3(f4(x711)) % 0.24/0.52 [79]E(x791,f5(a1))+P4(f5(a1),x791,a1) % 0.24/0.52 [72]~P11(x721)+E(f11(f5(a1),x721),f5(x721)) % 0.24/0.52 [85]~P4(x852,x852,x851)+~P7(x851) % 0.24/0.52 [86]~P4(x862,x862,x861)+~P8(x861) % 0.24/0.52 [87]~P4(x872,x872,x871)+~P9(x871) % 0.24/0.52 [69]E(x691,x692)+~E(f2(x691),f2(x692)) % 0.24/0.52 [70]E(x701,x702)+~E(f4(x701),f4(x702)) % 0.24/0.52 [73]~P3(x731)+P3(f7(x731,x732)) % 0.24/0.52 [76]~P6(x761,x762)+P6(f4(x761),f4(x762)) % 0.24/0.53 [81]~P6(f4(x811),x812)+P6(x811,f8(x811,x812)) % 0.24/0.53 [99]~P1(x991)+~P4(f11(x992,x991),f5(x991),x991) % 0.24/0.53 [77]~P3(x771)+P3(f3(x771,f2(x772))) % 0.24/0.53 [80]~P6(f4(x801),x802)+E(f4(f8(x801,x802)),x802) % 0.24/0.53 [88]~P4(x881,x882,a1)+E(f7(f2(x881),x882),f2(x881)) % 0.24/0.53 [82]~P6(x821,x823)+P6(f3(x821,x822),f3(x823,x822)) % 0.24/0.53 [83]~P6(x832,x833)+P6(f3(x831,x832),f3(x831,x833)) % 0.24/0.53 [84]~P6(x841,x843)+P6(f7(x841,x842),f7(x843,x842)) % 0.24/0.53 [98]~P3(x981)+P3(f6(x981,f2(x982),x983)) % 0.24/0.53 [100]~P4(x1001,x1003,a1)+E(f6(f2(x1001),x1002,x1003),f2(x1001)) % 0.24/0.53 [74]E(x741,x742)+~E(f3(x743,x741),f3(x744,x742)) % 0.24/0.53 [75]E(x751,x752)+~E(f3(x751,x753),f3(x752,x754)) % 0.24/0.53 [111]~P6(x1111,x1114)+P6(f6(x1111,x1112,x1113),f6(x1114,x1112,x1113)) % 0.24/0.53 [90]E(x901,x902)+P4(x902,x901,a1)+P4(x901,x902,a1) % 0.24/0.53 [105]~P1(x1051)+P4(f5(x1051),f11(x1052,x1051),x1051)+~P4(f5(a1),x1052,a1) % 0.24/0.53 [107]~P1(x1072)+~P4(f5(x1072),f11(x1071,x1072),x1072)+P4(f5(a1),x1071,a1) % 0.24/0.53 [102]~P4(x1023,x1022,x1021)+~P7(x1021)+~P4(x1022,x1023,x1021) % 0.24/0.53 [103]~P4(x1033,x1032,x1031)+~P8(x1031)+~P4(x1032,x1033,x1031) % 0.24/0.53 [104]~P4(x1043,x1042,x1041)+~P9(x1041)+~P4(x1042,x1043,x1041) % 0.24/0.53 [78]~P2(x783)+E(x781,x782)+~E(f11(x781,x783),f11(x782,x783)) % 0.24/0.53 [106]~P1(x1062)+~P4(x1061,x1063,a1)+P4(f11(x1061,x1062),f11(x1063,x1062),x1062) % 0.24/0.53 [108]~P1(x1083)+~P4(f11(x1081,x1083),f11(x1082,x1083),x1083)+P4(x1081,x1082,a1) % 0.24/0.53 [97]E(x971,x972)+P4(x972,x971,a1)+E(f6(f2(x971),x973,x972),f2(x971)) % 0.24/0.53 [95]P4(x951,x952,x953)+~P8(x953)+E(x951,x952)+P4(x952,x951,x953) % 0.24/0.53 [96]P4(x961,x962,x963)+~P10(x963)+E(x961,x962)+P4(x962,x961,x963) % 0.24/0.53 [109]~P7(x1093)+~P4(x1091,x1094,x1093)+P4(x1091,x1092,x1093)+~P4(x1094,x1092,x1093) % 0.24/0.53 [110]~P9(x1103)+~P4(x1101,x1104,x1103)+P4(x1101,x1102,x1103)+~P4(x1104,x1102,x1103) % 0.24/0.53 [112]~P3(x1121)+~P5(x1123,x1121,a15)+~P5(f10(x1123,x1122,a15,a9),a16,x1124)+P3(f6(a16,x1121,x1122)) % 0.24/0.53 %EqnAxiom % 0.24/0.53 [1]E(x11,x11) % 0.24/0.53 [2]E(x22,x21)+~E(x21,x22) % 0.24/0.53 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.24/0.53 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 0.24/0.53 [5]~E(x51,x52)+E(f10(x51,x53,x54,x55),f10(x52,x53,x54,x55)) % 0.24/0.53 [6]~E(x61,x62)+E(f10(x63,x61,x64,x65),f10(x63,x62,x64,x65)) % 0.24/0.53 [7]~E(x71,x72)+E(f10(x73,x74,x71,x75),f10(x73,x74,x72,x75)) % 0.24/0.53 [8]~E(x81,x82)+E(f10(x83,x84,x85,x81),f10(x83,x84,x85,x82)) % 0.24/0.53 [9]~E(x91,x92)+E(f6(x91,x93,x94),f6(x92,x93,x94)) % 0.24/0.53 [10]~E(x101,x102)+E(f6(x103,x101,x104),f6(x103,x102,x104)) % 0.24/0.53 [11]~E(x111,x112)+E(f6(x113,x114,x111),f6(x113,x114,x112)) % 0.24/0.53 [12]~E(x121,x122)+E(f7(x121,x123),f7(x122,x123)) % 0.24/0.53 [13]~E(x131,x132)+E(f7(x133,x131),f7(x133,x132)) % 0.24/0.53 [14]~E(x141,x142)+E(f11(x141,x143),f11(x142,x143)) % 0.24/0.53 [15]~E(x151,x152)+E(f11(x153,x151),f11(x153,x152)) % 0.24/0.53 [16]~E(x161,x162)+E(f3(x161,x163),f3(x162,x163)) % 0.24/0.53 [17]~E(x171,x172)+E(f3(x173,x171),f3(x173,x172)) % 0.24/0.53 [18]~E(x181,x182)+E(f4(x181),f4(x182)) % 0.24/0.53 [19]~E(x191,x192)+E(f5(x191),f5(x192)) % 0.24/0.53 [20]~E(x201,x202)+E(f8(x201,x203),f8(x202,x203)) % 0.24/0.53 [21]~E(x211,x212)+E(f8(x213,x211),f8(x213,x212)) % 0.24/0.53 [22]~P1(x221)+P1(x222)+~E(x221,x222) % 0.24/0.53 [23]~P11(x231)+P11(x232)+~E(x231,x232) % 0.24/0.53 [24]~P2(x241)+P2(x242)+~E(x241,x242) % 0.24/0.53 [25]~P7(x251)+P7(x252)+~E(x251,x252) % 0.24/0.53 [26]~P8(x261)+P8(x262)+~E(x261,x262) % 0.24/0.53 [27]~P9(x271)+P9(x272)+~E(x271,x272) % 0.24/0.53 [28]~P3(x281)+P3(x282)+~E(x281,x282) % 0.24/0.53 [29]P4(x292,x293,x294)+~E(x291,x292)+~P4(x291,x293,x294) % 0.24/0.53 [30]P4(x303,x302,x304)+~E(x301,x302)+~P4(x303,x301,x304) % 0.24/0.53 [31]P4(x313,x314,x312)+~E(x311,x312)+~P4(x313,x314,x311) % 0.24/0.53 [32]P5(x322,x323,x324)+~E(x321,x322)+~P5(x321,x323,x324) % 0.24/0.53 [33]P5(x333,x332,x334)+~E(x331,x332)+~P5(x333,x331,x334) % 0.24/0.53 [34]P5(x343,x344,x342)+~E(x341,x342)+~P5(x343,x344,x341) % 0.24/0.53 [35]~P10(x351)+P10(x352)+~E(x351,x352) % 0.24/0.53 [36]P6(x362,x363)+~E(x361,x362)+~P6(x361,x363) % 0.24/0.53 [37]P6(x373,x372)+~E(x371,x372)+~P6(x373,x371) % 0.24/0.53 % 0.24/0.53 %------------------------------------------- % 0.24/0.53 cnf(119,plain, % 0.24/0.53 (~E(f4(x1191),f2(x1192))), % 0.24/0.53 inference(rename_variables,[],[57])). % 0.24/0.53 cnf(126,plain, % 0.24/0.53 (E(f6(f2(x1261),x1262,x1261),x1262)), % 0.24/0.53 inference(rename_variables,[],[49])). % 0.24/0.53 cnf(134,plain, % 0.24/0.53 ($false), % 0.24/0.53 inference(scs_inference,[],[68,46,48,53,49,126,54,64,57,119,62,66,38,80,2,81,28,3,107,108,112]), % 0.24/0.53 ['proof']). % 0.24/0.53 % SZS output end Proof % 0.24/0.53 % Total time :0.006062s %------------------------------------------------------------------------------