TSTP Solution File: LCL828-1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : LCL828-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n032.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 06:51:14 EDT 2023
% Result : Unsatisfiable 0.14s 0.53s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : LCL828-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.10 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Fri Aug 25 03:54:42 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.14/0.48 start to proof:theBenchmark
% 0.14/0.52 %-------------------------------------------
% 0.14/0.52 % File :CSE---1.6
% 0.14/0.52 % Problem :theBenchmark
% 0.14/0.52 % Transform :cnf
% 0.14/0.52 % Format :tptp:raw
% 0.14/0.52 % Command :java -jar mcs_scs.jar %d %s
% 0.14/0.52
% 0.14/0.52 % Result :Theorem 0.000000s
% 0.14/0.52 % Output :CNFRefutation 0.000000s
% 0.14/0.52 %-------------------------------------------
% 0.14/0.52 %------------------------------------------------------------------------------
% 0.14/0.52 % File : LCL828-1 : TPTP v8.1.2. Released v4.1.0.
% 0.14/0.52 % Domain : Logic Calculi
% 0.14/0.52 % Problem : Strong normalization of typed lambda calculus 207_44
% 0.14/0.52 % Version : Especial.
% 0.14/0.52 % English :
% 0.14/0.52
% 0.14/0.52 % Refs : [vON99] von Oheimb & Nipkow (1999), Machine-Checking the Java
% 0.14/0.52 % : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe
% 0.14/0.52 % : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.14/0.52 % Source : [Nip10]
% 0.14/0.52 % Names : StrongNorm-207_44 [Nip10]
% 0.14/0.52
% 0.14/0.52 % Status : Unsatisfiable
% 0.14/0.52 % 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
% 0.14/0.52 % Syntax : Number of clauses : 75 ( 31 unt; 10 nHn; 51 RR)
% 0.14/0.52 % Number of literals : 147 ( 36 equ; 76 neg)
% 0.14/0.52 % Maximal clause size : 4 ( 1 avg)
% 0.14/0.52 % Maximal term depth : 3 ( 1 avg)
% 0.14/0.52 % Number of predicates : 12 ( 11 usr; 0 prp; 1-3 aty)
% 0.14/0.52 % Number of functors : 19 ( 19 usr; 10 con; 0-4 aty)
% 0.14/0.52 % Number of variables : 152 ( 34 sgn)
% 0.14/0.52 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.14/0.52
% 0.14/0.52 % Comments :
% 0.14/0.52 %------------------------------------------------------------------------------
% 0.14/0.52 cnf(cls_of__nat__less__0__iff_0,axiom,
% 0.14/0.52 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.14/0.52 | ~ 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) ) ).
% 0.14/0.52
% 0.14/0.52 cnf(cls_of__nat__0_0,axiom,
% 0.14/0.52 ( ~ class_Ring__and__Field_Osemiring__1(T_a)
% 0.14/0.52 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.14/0.52
% 0.14/0.52 cnf(cls_of__nat__eq__iff_0,axiom,
% 0.14/0.52 ( ~ class_Nat_Osemiring__char__0(T_a)
% 0.14/0.52 | c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a) != c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)
% 0.14/0.52 | V_m = V_n ) ).
% 0.14/0.52
% 0.14/0.52 cnf(cls_of__nat__less__iff_1,axiom,
% 0.14/0.52 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.14/0.52 | 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)
% 0.14/0.52 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
% 0.14/0.52
% 0.14/0.52 cnf(cls_of__nat__less__iff_0,axiom,
% 0.14/0.52 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.14/0.52 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.14/0.52 | ~ 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) ) ).
% 0.14/0.52
% 0.14/0.52 cnf(cls_order__less__asym_H_0,axiom,
% 0.14/0.52 ( ~ class_Orderings_Opreorder(T_a)
% 0.14/0.52 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
% 0.14/0.52 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
% 0.14/0.52
% 0.14/0.52 cnf(cls_order__less__asym_0,axiom,
% 0.14/0.52 ( ~ class_Orderings_Opreorder(T_a)
% 0.14/0.52 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
% 0.14/0.52 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
% 0.14/0.52
% 0.14/0.52 cnf(cls_not__less__iff__gr__or__eq_1,axiom,
% 0.14/0.52 ( ~ class_Orderings_Olinorder(T_a)
% 0.14/0.52 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
% 0.14/0.52 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
% 0.14/0.52
% 0.14/0.52 cnf(cls_xt1_I9_J_0,axiom,
% 0.14/0.52 ( ~ class_Orderings_Oorder(T_a)
% 0.14/0.52 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
% 0.14/0.52 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ).
% 0.14/0.52
% 0.14/0.52 cnf(cls_neq0__conv_1,axiom,
% 0.14/0.52 ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
% 0.14/0.52
% 0.14/0.52 cnf(cls_gr0I_0,axiom,
% 0.14/0.52 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
% 0.14/0.52 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
% 0.14/0.52
% 0.14/0.52 cnf(cls_of__nat__0__less__iff_0,axiom,
% 0.14/0.52 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.14/0.52 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
% 0.14/0.52 | ~ 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) ) ).
% 0.14/0.52
% 0.14/0.52 cnf(cls_of__nat__0__less__iff_1,axiom,
% 0.14/0.52 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.14/0.52 | 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)
% 0.14/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ).
% 0.14/0.52
% 0.14/0.52 cnf(cls_linorder__antisym__conv3_0,axiom,
% 0.14/0.52 ( ~ class_Orderings_Olinorder(T_a)
% 0.14/0.52 | V_x = V_y
% 0.14/0.52 | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
% 0.14/0.52 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
% 0.14/0.52
% 0.14/0.52 cnf(cls_linorder__less__linear_0,axiom,
% 0.14/0.52 ( ~ class_Orderings_Olinorder(T_a)
% 0.14/0.52 | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
% 0.14/0.52 | V_x = V_y
% 0.14/0.52 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
% 0.14/0.52
% 0.14/0.52 cnf(cls_linorder__neqE_0,axiom,
% 0.14/0.52 ( ~ class_Orderings_Olinorder(T_a)
% 0.14/0.52 | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
% 0.14/0.52 | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
% 0.14/0.52 | V_x = V_y ) ).
% 0.14/0.52
% 0.14/0.52 cnf(cls_linorder__neqE__nat_0,axiom,
% 0.14/0.52 ( c_HOL_Oord__class_Oless(V_y,V_x,tc_nat)
% 0.14/0.52 | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)
% 0.14/0.52 | V_x = V_y ) ).
% 0.14/0.52
% 0.14/0.52 cnf(cls_nat__neq__iff_0,axiom,
% 0.14/0.52 ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
% 0.14/0.52 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.14/0.52 | V_m = V_n ) ).
% 0.14/0.52
% 0.14/0.52 cnf(cls_not__less__iff__gr__or__eq_0,axiom,
% 0.14/0.52 ( ~ class_Orderings_Olinorder(T_a)
% 0.14/0.52 | V_x = V_y
% 0.14/0.52 | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
% 0.14/0.52 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
% 0.14/0.52
% 0.14/0.52 cnf(cls_linorder__neqE__ordered__idom_0,axiom,
% 0.14/0.52 ( ~ class_Ring__and__Field_Oordered__idom(T_a)
% 0.14/0.52 | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
% 0.14/0.52 | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
% 0.14/0.52 | V_x = V_y ) ).
% 0.14/0.52
% 0.14/0.52 cnf(cls_order__less__irrefl_0,axiom,
% 0.14/0.52 ( ~ class_Orderings_Opreorder(T_a)
% 0.14/0.52 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
% 0.14/0.52
% 0.14/0.52 cnf(cls_linorder__neq__iff_1,axiom,
% 0.14/0.52 ( ~ class_Orderings_Olinorder(T_a)
% 0.14/0.52 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
% 0.14/0.52
% 0.14/0.52 cnf(cls_order__less__le_1,axiom,
% 0.14/0.52 ( ~ class_Orderings_Oorder(T_a)
% 0.14/0.52 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
% 0.14/0.52
% 0.14/0.52 cnf(cls_less__not__refl_0,axiom,
% 0.14/0.52 ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ).
% 0.14/0.52
% 0.14/0.52 cnf(cls_nat__less__le_1,axiom,
% 0.14/0.52 ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ).
% 0.14/0.52
% 0.14/0.52 cnf(cls_order__less__trans_0,axiom,
% 0.14/0.52 ( ~ class_Orderings_Opreorder(T_a)
% 0.14/0.52 | c_HOL_Oord__class_Oless(V_x,V_z,T_a)
% 0.14/0.52 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
% 0.14/0.52 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
% 0.14/0.52
% 0.14/0.52 cnf(cls_xt1_I10_J_0,axiom,
% 0.14/0.52 ( ~ class_Orderings_Oorder(T_a)
% 0.14/0.52 | c_HOL_Oord__class_Oless(V_z,V_x,T_a)
% 0.14/0.52 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a)
% 0.14/0.52 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
% 0.14/0.52
% 0.14/0.52 cnf(cls_gr__implies__not0_0,axiom,
% 0.14/0.52 ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
% 0.14/0.52
% 0.14/0.52 cnf(cls_not__less0_0,axiom,
% 0.14/0.52 ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
% 0.14/0.52
% 0.14/0.52 cnf(cls_dB_Osimps_I5_J_0,axiom,
% 0.14/0.52 c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) != c_Lambda_OdB_OVar(V_nat) ).
% 0.14/0.52
% 0.14/0.52 cnf(cls_abs_0,axiom,
% 0.14/0.52 ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_s),c_Lambda_OdB_OAbs(V_t))
% 0.14/0.52 | ~ c_Lambda_Obeta(V_s,V_t) ) ).
% 0.14/0.52
% 0.14/0.52 cnf(cls_beta__cases_I2_J_0,axiom,
% 0.14/0.52 ( V_s = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(V_r,V_s))
% 0.14/0.53 | ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_r),V_s) ) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_app__Var__IT_0,axiom,
% 0.14/0.53 ( c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i)))
% 0.14/0.53 | ~ c_InductTermi_OIT(V_t) ) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_lift__preserves__beta_0,axiom,
% 0.14/0.53 ( c_Lambda_Obeta(c_Lambda_Olift(V_r,V_i),c_Lambda_Olift(V_s,V_i))
% 0.14/0.53 | ~ c_Lambda_Obeta(V_r,V_s) ) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_lift_Osimps_I1_J_0,axiom,
% 0.14/0.53 ( c_Lambda_Olift(c_Lambda_OdB_OVar(V_i),V_k) = c_Lambda_OdB_OVar(V_i)
% 0.14/0.53 | ~ c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_appL_0,axiom,
% 0.14/0.53 ( c_Lambda_Obeta(c_Lambda_OdB_OApp(V_s,V_u),c_Lambda_OdB_OApp(V_t,V_u))
% 0.14/0.53 | ~ c_Lambda_Obeta(V_s,V_t) ) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_appR_0,axiom,
% 0.14/0.53 ( c_Lambda_Obeta(c_Lambda_OdB_OApp(V_u,V_s),c_Lambda_OdB_OApp(V_u,V_t))
% 0.14/0.53 | ~ c_Lambda_Obeta(V_s,V_t) ) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_subst__Var_1,axiom,
% 0.14/0.53 ( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)
% 0.14/0.53 | c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x),V_s,V_x) = V_s ) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_subst__Var_2,axiom,
% 0.14/0.53 ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_i),V_s,V_k) = c_Lambda_OdB_OVar(V_i)
% 0.14/0.53 | V_i = V_k
% 0.14/0.53 | c_HOL_Oord__class_Oless(V_k,V_i,tc_nat) ) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_lift_Osimps_I2_J_0,axiom,
% 0.14/0.53 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)) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_dB_Osimps_I6_J_0,axiom,
% 0.14/0.53 c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_dB_Osimps_I3_J_0,axiom,
% 0.14/0.53 ( c_Lambda_OdB_OAbs(V_dB) != c_Lambda_OdB_OAbs(V_dB_H)
% 0.14/0.53 | V_dB = V_dB_H ) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_dB_Osimps_I4_J_0,axiom,
% 0.14/0.53 c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_beta_0,axiom,
% 0.14/0.53 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))) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_dB_Osimps_I2_J_1,axiom,
% 0.14/0.53 ( c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H)
% 0.14/0.53 | V_dB2 = V_dB2_H ) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_dB_Osimps_I2_J_0,axiom,
% 0.14/0.53 ( c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H)
% 0.14/0.53 | V_dB1 = V_dB1_H ) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_beta__cases_I1_J_0,axiom,
% 0.14/0.53 ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(V_i),V_t) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_beta__cases_I2_J_1,axiom,
% 0.14/0.53 ( c_Lambda_Obeta(V_r,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(V_r,V_s))
% 0.14/0.53 | ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_r),V_s) ) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_subst__lt_0,axiom,
% 0.14/0.53 ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_j),V_u,V_i) = c_Lambda_OdB_OVar(V_j)
% 0.14/0.53 | ~ c_HOL_Oord__class_Oless(V_j,V_i,tc_nat) ) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_dB_Osimps_I9_J_0,axiom,
% 0.14/0.53 c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OApp(V_dB1,V_dB2) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_dB_Osimps_I1_J_0,axiom,
% 0.14/0.53 ( c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OVar(V_nat_H)
% 0.14/0.53 | V_nat = V_nat_H ) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_dB_Osimps_I8_J_0,axiom,
% 0.14/0.53 c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OAbs(V_dB_H) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_dB_Osimps_I7_J_0,axiom,
% 0.14/0.53 c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_subst__App_0,axiom,
% 0.14/0.53 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)) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_subst__eq_0,axiom,
% 0.14/0.53 c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k) = V_u ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_subst__Var__IT_0,axiom,
% 0.14/0.53 ( c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j))
% 0.14/0.53 | ~ c_InductTermi_OIT(V_r) ) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_lift__IT_0,axiom,
% 0.14/0.53 ( c_InductTermi_OIT(c_Lambda_Olift(V_t,V_i))
% 0.14/0.53 | ~ c_InductTermi_OIT(V_t) ) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_Var__IT_0,axiom,
% 0.14/0.53 c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n)) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_False_0,axiom,
% 0.14/0.53 v_n____ != v_i____ ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_subst__preserves__beta_0,axiom,
% 0.14/0.53 ( c_Lambda_Obeta(c_Lambda_Osubst(V_r,V_t,V_i),c_Lambda_Osubst(V_s,V_t,V_i))
% 0.14/0.53 | ~ c_Lambda_Obeta(V_r,V_s) ) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_Var_I3_J_0,axiom,
% 0.14/0.53 c_InductTermi_OIT(v_ua______) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_Lambda_0,axiom,
% 0.14/0.53 ( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
% 0.14/0.53 | ~ c_InductTermi_OIT(V_r) ) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_uIT_0,axiom,
% 0.14/0.53 c_InductTermi_OIT(v_u____) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_subst__lift_0,axiom,
% 0.14/0.53 c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_CHAINED_0,axiom,
% 0.14/0.53 c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_Ua____) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_CHAINED_0_01,axiom,
% 0.14/0.53 ( c_InductTermi_OIT(c_Lambda_Osubst(v_a____,V_ua,V_ia))
% 0.14/0.53 | ~ c_Type_Otyping(V_ea,V_ua,v_T____)
% 0.14/0.53 | ~ c_InductTermi_OIT(V_ua)
% 0.14/0.53 | ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_a____,V_T_H) ) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_CHAINED_0_02,axiom,
% 0.14/0.53 c_InductTermi_OIT(v_u____) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_CHAINED_0_03,axiom,
% 0.14/0.53 c_Type_Otyping(v_e____,v_u____,v_T____) ).
% 0.14/0.53
% 0.14/0.53 cnf(cls_conjecture_0,negated_conjecture,
% 0.14/0.53 ~ c_InductTermi_OIT(c_Lambda_Osubst(v_a____,v_u____,v_i____)) ).
% 0.14/0.53
% 0.14/0.53 cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom,
% 0.14/0.53 class_Ring__and__Field_Oordered__semidom(tc_nat) ).
% 0.14/0.53
% 0.14/0.53 cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom,
% 0.14/0.53 class_Ring__and__Field_Osemiring__1(tc_nat) ).
% 0.14/0.53
% 0.14/0.53 cnf(clsarity_nat__Nat_Osemiring__char__0,axiom,
% 0.14/0.53 class_Nat_Osemiring__char__0(tc_nat) ).
% 0.14/0.53
% 0.14/0.53 cnf(clsarity_nat__Orderings_Opreorder,axiom,
% 0.14/0.53 class_Orderings_Opreorder(tc_nat) ).
% 0.14/0.53
% 0.14/0.53 cnf(clsarity_nat__Orderings_Olinorder,axiom,
% 0.14/0.53 class_Orderings_Olinorder(tc_nat) ).
% 0.14/0.53
% 0.14/0.53 cnf(clsarity_nat__Orderings_Oorder,axiom,
% 0.14/0.53 class_Orderings_Oorder(tc_nat) ).
% 0.14/0.53
% 0.14/0.53 %------------------------------------------------------------------------------
% 0.14/0.53 %-------------------------------------------
% 0.14/0.53 % Proof found
% 0.14/0.53 % SZS status Theorem for theBenchmark
% 0.14/0.53 % SZS output start Proof
% 0.14/0.53 %ClaNum:112(EqnAxiom:37)
% 0.14/0.53 %VarNum:271(SingletonVarNum:132)
% 0.14/0.53 %MaxLitNum:4
% 0.14/0.53 %MaxfuncDepth:2
% 0.14/0.53 %SharedTerms:26
% 0.14/0.53 %goalClause: 68
% 0.14/0.53 %singleGoalClaCount:1
% 0.14/0.53 [38]P1(a1)
% 0.14/0.53 [39]P11(a1)
% 0.14/0.53 [40]P2(a1)
% 0.14/0.53 [41]P7(a1)
% 0.14/0.53 [42]P8(a1)
% 0.14/0.53 [43]P9(a1)
% 0.14/0.53 [44]P3(a12)
% 0.14/0.53 [46]P3(a13)
% 0.14/0.53 [48]P5(a14,a13,a15)
% 0.14/0.53 [55]~E(a19,a18)
% 0.14/0.53 [54]P5(f10(a14,a18,a15,a9),a16,a17)
% 0.14/0.53 [68]~P3(f6(a16,a13,a18))
% 0.14/0.53 [64]~P4(x641,x641,a1)
% 0.14/0.53 [47]P3(f2(x471))
% 0.14/0.53 [66]~P4(x661,f5(a1),a1)
% 0.14/0.53 [57]~E(f4(x571),f2(x572))
% 0.14/0.53 [62]~P6(f2(x621),x622)
% 0.14/0.53 [49]E(f6(f2(x491),x492,x491),x492)
% 0.14/0.53 [52]P6(f3(f4(x521),x522),f6(x521,x522,f5(a1)))
% 0.14/0.53 [58]~E(f2(x581),f3(x582,x583))
% 0.14/0.53 [59]~E(f4(x591),f3(x592,x593))
% 0.14/0.53 [60]~E(f3(x601,x602),f2(x603))
% 0.14/0.53 [61]~E(f3(x611,x612),f4(x613))
% 0.14/0.53 [50]E(f6(f7(x501,x502),x503,x502),x501)
% 0.14/0.53 [51]E(f3(f7(x511,x512),f7(x513,x512)),f7(f3(x511,x513),x512))
% 0.14/0.53 [53]E(f3(f6(x531,x532,x533),f6(x534,x532,x533)),f6(f3(x531,x534),x532,x533))
% 0.14/0.53 [71]~P3(x711)+P3(f4(x711))
% 0.14/0.53 [79]E(x791,f5(a1))+P4(f5(a1),x791,a1)
% 0.14/0.53 [72]~P11(x721)+E(f11(f5(a1),x721),f5(x721))
% 0.14/0.53 [85]~P4(x852,x852,x851)+~P7(x851)
% 0.14/0.53 [86]~P4(x862,x862,x861)+~P8(x861)
% 0.14/0.53 [87]~P4(x872,x872,x871)+~P9(x871)
% 0.14/0.53 [69]E(x691,x692)+~E(f2(x691),f2(x692))
% 0.14/0.53 [70]E(x701,x702)+~E(f4(x701),f4(x702))
% 0.14/0.53 [73]~P3(x731)+P3(f7(x731,x732))
% 0.14/0.53 [76]~P6(x761,x762)+P6(f4(x761),f4(x762))
% 0.14/0.53 [81]~P6(f4(x811),x812)+P6(x811,f8(x811,x812))
% 0.14/0.53 [99]~P1(x991)+~P4(f11(x992,x991),f5(x991),x991)
% 0.14/0.53 [77]~P3(x771)+P3(f3(x771,f2(x772)))
% 0.14/0.53 [80]~P6(f4(x801),x802)+E(f4(f8(x801,x802)),x802)
% 0.14/0.53 [88]~P4(x881,x882,a1)+E(f7(f2(x881),x882),f2(x881))
% 0.14/0.53 [82]~P6(x821,x823)+P6(f3(x821,x822),f3(x823,x822))
% 0.14/0.53 [83]~P6(x832,x833)+P6(f3(x831,x832),f3(x831,x833))
% 0.14/0.53 [84]~P6(x841,x843)+P6(f7(x841,x842),f7(x843,x842))
% 0.14/0.53 [98]~P3(x981)+P3(f6(x981,f2(x982),x983))
% 0.14/0.53 [100]~P4(x1001,x1003,a1)+E(f6(f2(x1001),x1002,x1003),f2(x1001))
% 0.14/0.53 [74]E(x741,x742)+~E(f3(x743,x741),f3(x744,x742))
% 0.14/0.53 [75]E(x751,x752)+~E(f3(x751,x753),f3(x752,x754))
% 0.14/0.53 [111]~P6(x1111,x1114)+P6(f6(x1111,x1112,x1113),f6(x1114,x1112,x1113))
% 0.14/0.53 [90]E(x901,x902)+P4(x902,x901,a1)+P4(x901,x902,a1)
% 0.14/0.53 [105]~P1(x1051)+P4(f5(x1051),f11(x1052,x1051),x1051)+~P4(f5(a1),x1052,a1)
% 0.14/0.53 [107]~P1(x1072)+~P4(f5(x1072),f11(x1071,x1072),x1072)+P4(f5(a1),x1071,a1)
% 0.14/0.53 [102]~P4(x1023,x1022,x1021)+~P7(x1021)+~P4(x1022,x1023,x1021)
% 0.14/0.53 [103]~P4(x1033,x1032,x1031)+~P8(x1031)+~P4(x1032,x1033,x1031)
% 0.14/0.53 [104]~P4(x1043,x1042,x1041)+~P9(x1041)+~P4(x1042,x1043,x1041)
% 0.14/0.53 [78]~P2(x783)+E(x781,x782)+~E(f11(x781,x783),f11(x782,x783))
% 0.14/0.53 [106]~P1(x1062)+~P4(x1061,x1063,a1)+P4(f11(x1061,x1062),f11(x1063,x1062),x1062)
% 0.14/0.53 [108]~P1(x1083)+~P4(f11(x1081,x1083),f11(x1082,x1083),x1083)+P4(x1081,x1082,a1)
% 0.14/0.53 [97]E(x971,x972)+P4(x972,x971,a1)+E(f6(f2(x971),x973,x972),f2(x971))
% 0.14/0.53 [95]P4(x951,x952,x953)+~P8(x953)+E(x951,x952)+P4(x952,x951,x953)
% 0.14/0.53 [96]P4(x961,x962,x963)+~P10(x963)+E(x961,x962)+P4(x962,x961,x963)
% 0.14/0.53 [109]~P7(x1093)+~P4(x1091,x1094,x1093)+P4(x1091,x1092,x1093)+~P4(x1094,x1092,x1093)
% 0.14/0.53 [110]~P9(x1103)+~P4(x1101,x1104,x1103)+P4(x1101,x1102,x1103)+~P4(x1104,x1102,x1103)
% 0.14/0.53 [112]~P3(x1121)+~P5(x1123,x1121,a15)+~P5(f10(x1123,x1122,a15,a9),a16,x1124)+P3(f6(a16,x1121,x1122))
% 0.14/0.53 %EqnAxiom
% 0.14/0.53 [1]E(x11,x11)
% 0.14/0.53 [2]E(x22,x21)+~E(x21,x22)
% 0.14/0.53 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.14/0.53 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 0.14/0.53 [5]~E(x51,x52)+E(f10(x51,x53,x54,x55),f10(x52,x53,x54,x55))
% 0.14/0.53 [6]~E(x61,x62)+E(f10(x63,x61,x64,x65),f10(x63,x62,x64,x65))
% 0.14/0.53 [7]~E(x71,x72)+E(f10(x73,x74,x71,x75),f10(x73,x74,x72,x75))
% 0.14/0.53 [8]~E(x81,x82)+E(f10(x83,x84,x85,x81),f10(x83,x84,x85,x82))
% 0.14/0.53 [9]~E(x91,x92)+E(f6(x91,x93,x94),f6(x92,x93,x94))
% 0.14/0.53 [10]~E(x101,x102)+E(f6(x103,x101,x104),f6(x103,x102,x104))
% 0.14/0.53 [11]~E(x111,x112)+E(f6(x113,x114,x111),f6(x113,x114,x112))
% 0.14/0.53 [12]~E(x121,x122)+E(f7(x121,x123),f7(x122,x123))
% 0.14/0.53 [13]~E(x131,x132)+E(f7(x133,x131),f7(x133,x132))
% 0.14/0.53 [14]~E(x141,x142)+E(f11(x141,x143),f11(x142,x143))
% 0.14/0.53 [15]~E(x151,x152)+E(f11(x153,x151),f11(x153,x152))
% 0.14/0.53 [16]~E(x161,x162)+E(f3(x161,x163),f3(x162,x163))
% 0.14/0.53 [17]~E(x171,x172)+E(f3(x173,x171),f3(x173,x172))
% 0.14/0.53 [18]~E(x181,x182)+E(f4(x181),f4(x182))
% 0.14/0.53 [19]~E(x191,x192)+E(f5(x191),f5(x192))
% 0.14/0.53 [20]~E(x201,x202)+E(f8(x201,x203),f8(x202,x203))
% 0.14/0.53 [21]~E(x211,x212)+E(f8(x213,x211),f8(x213,x212))
% 0.14/0.53 [22]~P1(x221)+P1(x222)+~E(x221,x222)
% 0.14/0.53 [23]~P11(x231)+P11(x232)+~E(x231,x232)
% 0.14/0.53 [24]~P2(x241)+P2(x242)+~E(x241,x242)
% 0.14/0.53 [25]~P7(x251)+P7(x252)+~E(x251,x252)
% 0.14/0.53 [26]~P8(x261)+P8(x262)+~E(x261,x262)
% 0.14/0.53 [27]~P9(x271)+P9(x272)+~E(x271,x272)
% 0.14/0.53 [28]~P3(x281)+P3(x282)+~E(x281,x282)
% 0.14/0.53 [29]P4(x292,x293,x294)+~E(x291,x292)+~P4(x291,x293,x294)
% 0.14/0.53 [30]P4(x303,x302,x304)+~E(x301,x302)+~P4(x303,x301,x304)
% 0.14/0.53 [31]P4(x313,x314,x312)+~E(x311,x312)+~P4(x313,x314,x311)
% 0.14/0.53 [32]P5(x322,x323,x324)+~E(x321,x322)+~P5(x321,x323,x324)
% 0.14/0.53 [33]P5(x333,x332,x334)+~E(x331,x332)+~P5(x333,x331,x334)
% 0.14/0.53 [34]P5(x343,x344,x342)+~E(x341,x342)+~P5(x343,x344,x341)
% 0.14/0.53 [35]~P10(x351)+P10(x352)+~E(x351,x352)
% 0.14/0.53 [36]P6(x362,x363)+~E(x361,x362)+~P6(x361,x363)
% 0.14/0.53 [37]P6(x373,x372)+~E(x371,x372)+~P6(x373,x371)
% 0.14/0.53
% 0.14/0.53 %-------------------------------------------
% 0.14/0.53 cnf(122,plain,
% 0.14/0.53 (E(f6(f7(x1221,x1222),x1223,x1222),x1221)),
% 0.14/0.53 inference(rename_variables,[],[50])).
% 0.14/0.53 cnf(130,plain,
% 0.14/0.53 ($false),
% 0.14/0.53 inference(scs_inference,[],[68,64,38,46,48,55,66,54,62,57,49,50,122,2,81,80,34,28,3,107,108,112]),
% 0.14/0.53 ['proof']).
% 0.14/0.53 % SZS output end Proof
% 0.14/0.53 % Total time :0.000000s
%------------------------------------------------------------------------------