TSTP Solution File: LCL808-1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : LCL808-1 : 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 : n004.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 06:51:05 EDT 2023
% Result : Unsatisfiable 0.21s 0.64s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL808-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 17:30:38 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.57 start to proof:theBenchmark
% 0.21/0.63 %-------------------------------------------
% 0.21/0.63 % File :CSE---1.6
% 0.21/0.63 % Problem :theBenchmark
% 0.21/0.63 % Transform :cnf
% 0.21/0.63 % Format :tptp:raw
% 0.21/0.63 % Command :java -jar mcs_scs.jar %d %s
% 0.21/0.63
% 0.21/0.63 % Result :Theorem 0.010000s
% 0.21/0.63 % Output :CNFRefutation 0.010000s
% 0.21/0.63 %-------------------------------------------
% 0.21/0.63 %------------------------------------------------------------------------------
% 0.21/0.63 % File : LCL808-1 : TPTP v8.1.2. Released v4.1.0.
% 0.21/0.63 % Domain : Logic Calculi
% 0.21/0.63 % Problem : Strong normalization of typed lambda calculus 168_48
% 0.21/0.63 % Version : Especial.
% 0.21/0.63 % English :
% 0.21/0.63
% 0.21/0.63 % Refs : [vON99] von Oheimb & Nipkow (1999), Machine-Checking the Java
% 0.21/0.63 % : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe
% 0.21/0.63 % : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.21/0.63 % Source : [Nip10]
% 0.21/0.63 % Names : StrongNorm-168_48 [Nip10]
% 0.21/0.63
% 0.21/0.63 % Status : Unsatisfiable
% 0.21/0.63 % Rating : 0.05 v8.1.0, 0.00 v7.5.0, 0.05 v7.4.0, 0.06 v7.3.0, 0.08 v7.1.0, 0.00 v7.0.0, 0.07 v6.4.0, 0.00 v5.5.0, 0.10 v5.3.0, 0.11 v5.2.0, 0.12 v5.1.0, 0.18 v5.0.0, 0.07 v4.1.0
% 0.21/0.63 % Syntax : Number of clauses : 75 ( 31 unt; 10 nHn; 51 RR)
% 0.21/0.63 % Number of literals : 147 ( 36 equ; 75 neg)
% 0.21/0.63 % Maximal clause size : 4 ( 1 avg)
% 0.21/0.63 % Maximal term depth : 3 ( 1 avg)
% 0.21/0.63 % Number of predicates : 12 ( 11 usr; 0 prp; 1-3 aty)
% 0.21/0.63 % Number of functors : 19 ( 19 usr; 10 con; 0-4 aty)
% 0.21/0.63 % Number of variables : 152 ( 34 sgn)
% 0.21/0.63 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.21/0.63
% 0.21/0.63 % Comments :
% 0.21/0.63 %------------------------------------------------------------------------------
% 0.21/0.63 cnf(cls_of__nat__less__0__iff_0,axiom,
% 0.21/0.63 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.21/0.63 | ~ 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) ) ).
% 0.21/0.63
% 0.21/0.63 cnf(cls_of__nat__0_0,axiom,
% 0.21/0.63 ( ~ class_Ring__and__Field_Osemiring__1(T_a)
% 0.21/0.63 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
% 0.21/0.63
% 0.21/0.63 cnf(cls_of__nat__eq__iff_0,axiom,
% 0.21/0.63 ( ~ class_Nat_Osemiring__char__0(T_a)
% 0.21/0.63 | c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a) != c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)
% 0.21/0.63 | V_m = V_n ) ).
% 0.21/0.63
% 0.21/0.63 cnf(cls_of__nat__less__iff_1,axiom,
% 0.21/0.63 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.21/0.63 | 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)
% 0.21/0.63 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
% 0.21/0.63
% 0.21/0.63 cnf(cls_of__nat__less__iff_0,axiom,
% 0.21/0.63 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.21/0.63 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.21/0.63 | ~ 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) ) ).
% 0.21/0.63
% 0.21/0.63 cnf(cls_order__less__asym_H_0,axiom,
% 0.21/0.63 ( ~ class_Orderings_Opreorder(T_a)
% 0.21/0.63 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
% 0.21/0.63 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
% 0.21/0.63
% 0.21/0.63 cnf(cls_order__less__asym_0,axiom,
% 0.21/0.63 ( ~ class_Orderings_Opreorder(T_a)
% 0.21/0.63 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
% 0.21/0.63 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
% 0.21/0.63
% 0.21/0.63 cnf(cls_not__less__iff__gr__or__eq_1,axiom,
% 0.21/0.63 ( ~ class_Orderings_Olinorder(T_a)
% 0.21/0.63 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
% 0.21/0.63 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
% 0.21/0.63
% 0.21/0.63 cnf(cls_xt1_I9_J_0,axiom,
% 0.21/0.63 ( ~ class_Orderings_Oorder(T_a)
% 0.21/0.63 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
% 0.21/0.63 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ).
% 0.21/0.63
% 0.21/0.63 cnf(cls_neq0__conv_1,axiom,
% 0.21/0.64 ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_gr0I_0,axiom,
% 0.21/0.64 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
% 0.21/0.64 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_of__nat__0__less__iff_0,axiom,
% 0.21/0.64 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.21/0.64 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
% 0.21/0.64 | ~ 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) ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_of__nat__0__less__iff_1,axiom,
% 0.21/0.64 ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
% 0.21/0.64 | 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)
% 0.21/0.64 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_linorder__antisym__conv3_0,axiom,
% 0.21/0.64 ( ~ class_Orderings_Olinorder(T_a)
% 0.21/0.64 | V_x = V_y
% 0.21/0.64 | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
% 0.21/0.64 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_linorder__less__linear_0,axiom,
% 0.21/0.64 ( ~ class_Orderings_Olinorder(T_a)
% 0.21/0.64 | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
% 0.21/0.64 | V_x = V_y
% 0.21/0.64 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_linorder__neqE_0,axiom,
% 0.21/0.64 ( ~ class_Orderings_Olinorder(T_a)
% 0.21/0.64 | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
% 0.21/0.64 | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
% 0.21/0.64 | V_x = V_y ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_linorder__neqE__nat_0,axiom,
% 0.21/0.64 ( c_HOL_Oord__class_Oless(V_y,V_x,tc_nat)
% 0.21/0.64 | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)
% 0.21/0.64 | V_x = V_y ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_nat__neq__iff_0,axiom,
% 0.21/0.64 ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
% 0.21/0.64 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
% 0.21/0.64 | V_m = V_n ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_not__less__iff__gr__or__eq_0,axiom,
% 0.21/0.64 ( ~ class_Orderings_Olinorder(T_a)
% 0.21/0.64 | V_x = V_y
% 0.21/0.64 | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
% 0.21/0.64 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_linorder__neqE__ordered__idom_0,axiom,
% 0.21/0.64 ( ~ class_Ring__and__Field_Oordered__idom(T_a)
% 0.21/0.64 | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
% 0.21/0.64 | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
% 0.21/0.64 | V_x = V_y ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_order__less__irrefl_0,axiom,
% 0.21/0.64 ( ~ class_Orderings_Opreorder(T_a)
% 0.21/0.64 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_linorder__neq__iff_1,axiom,
% 0.21/0.64 ( ~ class_Orderings_Olinorder(T_a)
% 0.21/0.64 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_order__less__le_1,axiom,
% 0.21/0.64 ( ~ class_Orderings_Oorder(T_a)
% 0.21/0.64 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_less__not__refl_0,axiom,
% 0.21/0.64 ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_nat__less__le_1,axiom,
% 0.21/0.64 ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_order__less__trans_0,axiom,
% 0.21/0.64 ( ~ class_Orderings_Opreorder(T_a)
% 0.21/0.64 | c_HOL_Oord__class_Oless(V_x,V_z,T_a)
% 0.21/0.64 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
% 0.21/0.64 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_xt1_I10_J_0,axiom,
% 0.21/0.64 ( ~ class_Orderings_Oorder(T_a)
% 0.21/0.64 | c_HOL_Oord__class_Oless(V_z,V_x,T_a)
% 0.21/0.64 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a)
% 0.21/0.64 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_gr__implies__not0_0,axiom,
% 0.21/0.64 ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_not__less0_0,axiom,
% 0.21/0.64 ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_dB_Osimps_I5_J_0,axiom,
% 0.21/0.64 c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) != c_Lambda_OdB_OVar(V_nat) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_abs_0,axiom,
% 0.21/0.64 ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_s),c_Lambda_OdB_OAbs(V_t))
% 0.21/0.64 | ~ c_Lambda_Obeta(V_s,V_t) ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_beta__cases_I2_J_0,axiom,
% 0.21/0.64 ( V_s = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(V_r,V_s))
% 0.21/0.64 | ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_r),V_s) ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_app__Var__IT_0,axiom,
% 0.21/0.64 ( c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i)))
% 0.21/0.64 | ~ c_InductTermi_OIT(V_t) ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_lift__preserves__beta_0,axiom,
% 0.21/0.64 ( c_Lambda_Obeta(c_Lambda_Olift(V_r,V_i),c_Lambda_Olift(V_s,V_i))
% 0.21/0.64 | ~ c_Lambda_Obeta(V_r,V_s) ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_lift_Osimps_I1_J_0,axiom,
% 0.21/0.64 ( c_Lambda_Olift(c_Lambda_OdB_OVar(V_i),V_k) = c_Lambda_OdB_OVar(V_i)
% 0.21/0.64 | ~ c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_appL_0,axiom,
% 0.21/0.64 ( c_Lambda_Obeta(c_Lambda_OdB_OApp(V_s,V_u),c_Lambda_OdB_OApp(V_t,V_u))
% 0.21/0.64 | ~ c_Lambda_Obeta(V_s,V_t) ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_appR_0,axiom,
% 0.21/0.64 ( c_Lambda_Obeta(c_Lambda_OdB_OApp(V_u,V_s),c_Lambda_OdB_OApp(V_u,V_t))
% 0.21/0.64 | ~ c_Lambda_Obeta(V_s,V_t) ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_subst__Var_1,axiom,
% 0.21/0.64 ( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)
% 0.21/0.64 | c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x),V_s,V_x) = V_s ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_subst__Var_2,axiom,
% 0.21/0.64 ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_i),V_s,V_k) = c_Lambda_OdB_OVar(V_i)
% 0.21/0.64 | V_i = V_k
% 0.21/0.64 | c_HOL_Oord__class_Oless(V_k,V_i,tc_nat) ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_lift_Osimps_I2_J_0,axiom,
% 0.21/0.64 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)) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_dB_Osimps_I6_J_0,axiom,
% 0.21/0.64 c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_dB_Osimps_I3_J_0,axiom,
% 0.21/0.64 ( c_Lambda_OdB_OAbs(V_dB) != c_Lambda_OdB_OAbs(V_dB_H)
% 0.21/0.64 | V_dB = V_dB_H ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_dB_Osimps_I4_J_0,axiom,
% 0.21/0.64 c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_beta_0,axiom,
% 0.21/0.64 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))) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_dB_Osimps_I2_J_1,axiom,
% 0.21/0.64 ( c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H)
% 0.21/0.64 | V_dB2 = V_dB2_H ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_dB_Osimps_I2_J_0,axiom,
% 0.21/0.64 ( c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H)
% 0.21/0.64 | V_dB1 = V_dB1_H ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_beta__cases_I1_J_0,axiom,
% 0.21/0.64 ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(V_i),V_t) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_beta__cases_I2_J_1,axiom,
% 0.21/0.64 ( c_Lambda_Obeta(V_r,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(V_r,V_s))
% 0.21/0.64 | ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_r),V_s) ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_subst__lt_0,axiom,
% 0.21/0.64 ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_j),V_u,V_i) = c_Lambda_OdB_OVar(V_j)
% 0.21/0.64 | ~ c_HOL_Oord__class_Oless(V_j,V_i,tc_nat) ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_dB_Osimps_I9_J_0,axiom,
% 0.21/0.64 c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OApp(V_dB1,V_dB2) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_dB_Osimps_I1_J_0,axiom,
% 0.21/0.64 ( c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OVar(V_nat_H)
% 0.21/0.64 | V_nat = V_nat_H ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_dB_Osimps_I8_J_0,axiom,
% 0.21/0.64 c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OAbs(V_dB_H) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_dB_Osimps_I7_J_0,axiom,
% 0.21/0.64 c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_subst__App_0,axiom,
% 0.21/0.64 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)) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_subst__eq_0,axiom,
% 0.21/0.64 c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k) = V_u ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_subst__Var__IT_0,axiom,
% 0.21/0.64 ( c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j))
% 0.21/0.64 | ~ c_InductTermi_OIT(V_r) ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_lift__IT_0,axiom,
% 0.21/0.64 ( c_InductTermi_OIT(c_Lambda_Olift(V_t,V_i))
% 0.21/0.64 | ~ c_InductTermi_OIT(V_t) ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_True_0,axiom,
% 0.21/0.64 v_n____ = v_i____ ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_Var__IT_0,axiom,
% 0.21/0.64 c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n)) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_subst__preserves__beta_0,axiom,
% 0.21/0.64 ( c_Lambda_Obeta(c_Lambda_Osubst(V_r,V_t,V_i),c_Lambda_Osubst(V_s,V_t,V_i))
% 0.21/0.64 | ~ c_Lambda_Obeta(V_r,V_s) ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_Var_I3_J_0,axiom,
% 0.21/0.64 c_InductTermi_OIT(v_ua______) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_Lambda_0,axiom,
% 0.21/0.64 ( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
% 0.21/0.64 | ~ c_InductTermi_OIT(V_r) ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_uIT_0,axiom,
% 0.21/0.64 c_InductTermi_OIT(v_u____) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_subst__lift_0,axiom,
% 0.21/0.64 c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_CHAINED_0,axiom,
% 0.21/0.64 c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_b____,v_Ua____) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_CHAINED_0_01,axiom,
% 0.21/0.64 ( c_InductTermi_OIT(c_Lambda_Osubst(v_b____,V_ua,V_ia))
% 0.21/0.64 | ~ c_Type_Otyping(V_ea,V_ua,v_T____)
% 0.21/0.64 | ~ c_InductTermi_OIT(V_ua)
% 0.21/0.64 | ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_b____,V_T_H) ) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_CHAINED_0_02,axiom,
% 0.21/0.64 c_InductTermi_OIT(v_u____) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_CHAINED_0_03,axiom,
% 0.21/0.64 c_Type_Otyping(v_e____,v_u____,v_T____) ).
% 0.21/0.64
% 0.21/0.64 cnf(cls_conjecture_0,negated_conjecture,
% 0.21/0.64 ~ c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____)) ).
% 0.21/0.64
% 0.21/0.64 cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom,
% 0.21/0.64 class_Ring__and__Field_Oordered__semidom(tc_nat) ).
% 0.21/0.64
% 0.21/0.64 cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom,
% 0.21/0.64 class_Ring__and__Field_Osemiring__1(tc_nat) ).
% 0.21/0.64
% 0.21/0.64 cnf(clsarity_nat__Nat_Osemiring__char__0,axiom,
% 0.21/0.64 class_Nat_Osemiring__char__0(tc_nat) ).
% 0.21/0.64
% 0.21/0.64 cnf(clsarity_nat__Orderings_Opreorder,axiom,
% 0.21/0.64 class_Orderings_Opreorder(tc_nat) ).
% 0.21/0.64
% 0.21/0.64 cnf(clsarity_nat__Orderings_Olinorder,axiom,
% 0.21/0.64 class_Orderings_Olinorder(tc_nat) ).
% 0.21/0.64
% 0.21/0.64 cnf(clsarity_nat__Orderings_Oorder,axiom,
% 0.21/0.64 class_Orderings_Oorder(tc_nat) ).
% 0.21/0.64
% 0.21/0.64 %------------------------------------------------------------------------------
% 0.21/0.64 %-------------------------------------------
% 0.21/0.64 % Proof found
% 0.21/0.64 % SZS status Theorem for theBenchmark
% 0.21/0.64 % SZS output start Proof
% 0.21/0.64 %ClaNum:112(EqnAxiom:37)
% 0.21/0.64 %VarNum:271(SingletonVarNum:132)
% 0.21/0.64 %MaxLitNum:4
% 0.21/0.65 %MaxfuncDepth:2
% 0.21/0.65 %SharedTerms:26
% 0.21/0.65 %goalClause: 68
% 0.21/0.65 %singleGoalClaCount:1
% 0.21/0.65 [38]E(a1,a17)
% 0.21/0.65 [39]P1(a2)
% 0.21/0.65 [40]P11(a2)
% 0.21/0.65 [41]P2(a2)
% 0.21/0.65 [42]P7(a2)
% 0.21/0.65 [43]P8(a2)
% 0.21/0.65 [44]P9(a2)
% 0.21/0.65 [45]P3(a18)
% 0.21/0.65 [47]P3(a19)
% 0.21/0.65 [49]P5(a13,a19,a14)
% 0.21/0.65 [55]P5(f11(a13,a1,a14,a10),a15,a16)
% 0.21/0.65 [68]~P3(f7(a15,a19,a1))
% 0.21/0.65 [64]~P4(x641,x641,a2)
% 0.21/0.65 [48]P3(f3(x481))
% 0.21/0.65 [66]~P4(x661,f6(a2),a2)
% 0.21/0.65 [57]~E(f5(x571),f3(x572))
% 0.21/0.65 [62]~P6(f3(x621),x622)
% 0.21/0.65 [50]E(f7(f3(x501),x502,x501),x502)
% 0.21/0.65 [53]P6(f4(f5(x531),x532),f7(x531,x532,f6(a2)))
% 0.21/0.65 [58]~E(f3(x581),f4(x582,x583))
% 0.21/0.65 [59]~E(f5(x591),f4(x592,x593))
% 0.21/0.65 [60]~E(f4(x601,x602),f3(x603))
% 0.21/0.65 [61]~E(f4(x611,x612),f5(x613))
% 0.21/0.65 [51]E(f7(f8(x511,x512),x513,x512),x511)
% 0.21/0.65 [52]E(f4(f8(x521,x522),f8(x523,x522)),f8(f4(x521,x523),x522))
% 0.21/0.65 [54]E(f4(f7(x541,x542,x543),f7(x544,x542,x543)),f7(f4(x541,x544),x542,x543))
% 0.21/0.65 [71]~P3(x711)+P3(f5(x711))
% 0.21/0.65 [79]E(x791,f6(a2))+P4(f6(a2),x791,a2)
% 0.21/0.65 [72]~P11(x721)+E(f12(f6(a2),x721),f6(x721))
% 0.21/0.65 [85]~P4(x852,x852,x851)+~P7(x851)
% 0.21/0.65 [86]~P4(x862,x862,x861)+~P8(x861)
% 0.21/0.65 [87]~P4(x872,x872,x871)+~P9(x871)
% 0.21/0.65 [69]E(x691,x692)+~E(f3(x691),f3(x692))
% 0.21/0.65 [70]E(x701,x702)+~E(f5(x701),f5(x702))
% 0.21/0.65 [73]~P3(x731)+P3(f8(x731,x732))
% 0.21/0.65 [76]~P6(x761,x762)+P6(f5(x761),f5(x762))
% 0.21/0.65 [81]~P6(f5(x811),x812)+P6(x811,f9(x811,x812))
% 0.21/0.65 [99]~P1(x991)+~P4(f12(x992,x991),f6(x991),x991)
% 0.21/0.65 [77]~P3(x771)+P3(f4(x771,f3(x772)))
% 0.21/0.65 [80]~P6(f5(x801),x802)+E(f5(f9(x801,x802)),x802)
% 0.21/0.65 [88]~P4(x881,x882,a2)+E(f8(f3(x881),x882),f3(x881))
% 0.21/0.65 [82]~P6(x821,x823)+P6(f4(x821,x822),f4(x823,x822))
% 0.21/0.65 [83]~P6(x832,x833)+P6(f4(x831,x832),f4(x831,x833))
% 0.21/0.65 [84]~P6(x841,x843)+P6(f8(x841,x842),f8(x843,x842))
% 0.21/0.65 [98]~P3(x981)+P3(f7(x981,f3(x982),x983))
% 0.21/0.65 [100]~P4(x1001,x1003,a2)+E(f7(f3(x1001),x1002,x1003),f3(x1001))
% 0.21/0.65 [74]E(x741,x742)+~E(f4(x743,x741),f4(x744,x742))
% 0.21/0.65 [75]E(x751,x752)+~E(f4(x751,x753),f4(x752,x754))
% 0.21/0.65 [111]~P6(x1111,x1114)+P6(f7(x1111,x1112,x1113),f7(x1114,x1112,x1113))
% 0.21/0.65 [90]E(x901,x902)+P4(x902,x901,a2)+P4(x901,x902,a2)
% 0.21/0.65 [105]~P1(x1051)+P4(f6(x1051),f12(x1052,x1051),x1051)+~P4(f6(a2),x1052,a2)
% 0.21/0.65 [107]~P1(x1072)+~P4(f6(x1072),f12(x1071,x1072),x1072)+P4(f6(a2),x1071,a2)
% 0.21/0.65 [102]~P4(x1023,x1022,x1021)+~P7(x1021)+~P4(x1022,x1023,x1021)
% 0.21/0.65 [103]~P4(x1033,x1032,x1031)+~P8(x1031)+~P4(x1032,x1033,x1031)
% 0.21/0.65 [104]~P4(x1043,x1042,x1041)+~P9(x1041)+~P4(x1042,x1043,x1041)
% 0.21/0.65 [78]~P2(x783)+E(x781,x782)+~E(f12(x781,x783),f12(x782,x783))
% 0.21/0.65 [106]~P1(x1062)+~P4(x1061,x1063,a2)+P4(f12(x1061,x1062),f12(x1063,x1062),x1062)
% 0.21/0.65 [108]~P1(x1083)+~P4(f12(x1081,x1083),f12(x1082,x1083),x1083)+P4(x1081,x1082,a2)
% 0.21/0.65 [97]E(x971,x972)+P4(x972,x971,a2)+E(f7(f3(x971),x973,x972),f3(x971))
% 0.21/0.65 [95]P4(x951,x952,x953)+~P8(x953)+E(x951,x952)+P4(x952,x951,x953)
% 0.21/0.65 [96]P4(x961,x962,x963)+~P10(x963)+E(x961,x962)+P4(x962,x961,x963)
% 0.21/0.65 [109]~P7(x1093)+~P4(x1091,x1094,x1093)+P4(x1091,x1092,x1093)+~P4(x1094,x1092,x1093)
% 0.21/0.65 [110]~P9(x1103)+~P4(x1101,x1104,x1103)+P4(x1101,x1102,x1103)+~P4(x1104,x1102,x1103)
% 0.21/0.65 [112]~P3(x1121)+~P5(x1123,x1121,a14)+~P5(f11(x1123,x1122,a14,a10),a15,x1124)+P3(f7(a15,x1121,x1122))
% 0.21/0.65 %EqnAxiom
% 0.21/0.65 [1]E(x11,x11)
% 0.21/0.65 [2]E(x22,x21)+~E(x21,x22)
% 0.21/0.65 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.21/0.65 [4]~E(x41,x42)+E(f3(x41),f3(x42))
% 0.21/0.65 [5]~E(x51,x52)+E(f11(x51,x53,x54,x55),f11(x52,x53,x54,x55))
% 0.21/0.65 [6]~E(x61,x62)+E(f11(x63,x61,x64,x65),f11(x63,x62,x64,x65))
% 0.21/0.65 [7]~E(x71,x72)+E(f11(x73,x74,x71,x75),f11(x73,x74,x72,x75))
% 0.21/0.65 [8]~E(x81,x82)+E(f11(x83,x84,x85,x81),f11(x83,x84,x85,x82))
% 0.21/0.65 [9]~E(x91,x92)+E(f7(x91,x93,x94),f7(x92,x93,x94))
% 0.21/0.65 [10]~E(x101,x102)+E(f7(x103,x101,x104),f7(x103,x102,x104))
% 0.21/0.65 [11]~E(x111,x112)+E(f7(x113,x114,x111),f7(x113,x114,x112))
% 0.21/0.65 [12]~E(x121,x122)+E(f8(x121,x123),f8(x122,x123))
% 0.21/0.65 [13]~E(x131,x132)+E(f8(x133,x131),f8(x133,x132))
% 0.21/0.65 [14]~E(x141,x142)+E(f12(x141,x143),f12(x142,x143))
% 0.21/0.65 [15]~E(x151,x152)+E(f12(x153,x151),f12(x153,x152))
% 0.21/0.65 [16]~E(x161,x162)+E(f4(x161,x163),f4(x162,x163))
% 0.21/0.65 [17]~E(x171,x172)+E(f4(x173,x171),f4(x173,x172))
% 0.21/0.65 [18]~E(x181,x182)+E(f5(x181),f5(x182))
% 0.21/0.65 [19]~E(x191,x192)+E(f6(x191),f6(x192))
% 0.21/0.65 [20]~E(x201,x202)+E(f9(x201,x203),f9(x202,x203))
% 0.21/0.65 [21]~E(x211,x212)+E(f9(x213,x211),f9(x213,x212))
% 0.21/0.65 [22]~P1(x221)+P1(x222)+~E(x221,x222)
% 0.21/0.65 [23]~P11(x231)+P11(x232)+~E(x231,x232)
% 0.21/0.65 [24]~P2(x241)+P2(x242)+~E(x241,x242)
% 0.21/0.65 [25]~P7(x251)+P7(x252)+~E(x251,x252)
% 0.21/0.65 [26]~P8(x261)+P8(x262)+~E(x261,x262)
% 0.21/0.65 [27]~P9(x271)+P9(x272)+~E(x271,x272)
% 0.21/0.65 [28]~P3(x281)+P3(x282)+~E(x281,x282)
% 0.21/0.65 [29]P4(x292,x293,x294)+~E(x291,x292)+~P4(x291,x293,x294)
% 0.21/0.65 [30]P4(x303,x302,x304)+~E(x301,x302)+~P4(x303,x301,x304)
% 0.21/0.65 [31]P4(x313,x314,x312)+~E(x311,x312)+~P4(x313,x314,x311)
% 0.21/0.65 [32]P5(x322,x323,x324)+~E(x321,x322)+~P5(x321,x323,x324)
% 0.21/0.65 [33]P5(x333,x332,x334)+~E(x331,x332)+~P5(x333,x331,x334)
% 0.21/0.65 [34]P5(x343,x344,x342)+~E(x341,x342)+~P5(x343,x344,x341)
% 0.21/0.65 [35]~P10(x351)+P10(x352)+~E(x351,x352)
% 0.21/0.65 [36]P6(x362,x363)+~E(x361,x362)+~P6(x361,x363)
% 0.21/0.65 [37]P6(x373,x372)+~E(x371,x372)+~P6(x373,x371)
% 0.21/0.65
% 0.21/0.65 %-------------------------------------------
% 0.21/0.65 cnf(121,plain,
% 0.21/0.65 (E(f7(f3(x1211),x1212,x1211),x1212)),
% 0.21/0.65 inference(rename_variables,[],[50])).
% 0.21/0.65 cnf(129,plain,
% 0.21/0.65 ($false),
% 0.21/0.65 inference(scs_inference,[],[68,64,38,39,47,49,66,55,62,57,50,121,2,81,80,28,3,107,108,112]),
% 0.21/0.65 ['proof']).
% 0.21/0.65 % SZS output end Proof
% 0.21/0.65 % Total time :0.010000s
%------------------------------------------------------------------------------