TSTP Solution File: LCL808-1 by ConnectPP---0.2.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ConnectPP---0.2.2
% Problem : LCL808-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% Computer : n017.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 : Wed Mar 6 09:10:29 EST 2024
% Result : Unsatisfiable 0.75s 0.91s
% Output : Proof 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL808-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Mar 3 13:36:43 EST 2024
% 0.12/0.34 % CPUTime :
% 0.75/0.91 % SZS status Unsatisfiable for theBenchmark
% 0.75/0.91 % SZS output start Proof for theBenchmark
% 0.75/0.91
% 0.75/0.91 % Problem matrix:
% 0.75/0.91 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 0.75/0.91 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 0.75/0.91 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 0.75/0.91 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( c_Nat_Osemiring__1__class_Oof__nat(__eqx_0, __eqx_1) = c_Nat_Osemiring__1__class_Oof__nat(__eqy_0, __eqy_1)) )).
% 0.75/0.91 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( c_HOL_Ozero__class_Ozero(__eqx_0) = c_HOL_Ozero__class_Ozero(__eqy_0)) )).
% 0.75/0.91 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( c_Lambda_OdB_OApp(__eqx_0, __eqx_1) = c_Lambda_OdB_OApp(__eqy_0, __eqy_1)) )).
% 0.75/0.91 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( c_Lambda_OdB_OVar(__eqx_0) = c_Lambda_OdB_OVar(__eqy_0)) )).
% 0.75/0.91 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( c_Lambda_OdB_OAbs(__eqx_0) = c_Lambda_OdB_OAbs(__eqy_0)) )).
% 0.75/0.91 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1(__eqx_0, __eqx_1) = c_Lambda_Osko__Lambda__Xbeta__cases__2__1(__eqy_0, __eqy_1)) )).
% 0.75/0.91 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( c_Lambda_Olift(__eqx_0, __eqx_1) = c_Lambda_Olift(__eqy_0, __eqy_1)) )).
% 0.75/0.91 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( c_Lambda_Osubst(__eqx_0, __eqx_1, __eqx_2) = c_Lambda_Osubst(__eqy_0, __eqy_1, __eqy_2)) )).
% 0.75/0.91 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( c_Type_Oshift(__eqx_0, __eqx_1, __eqx_2, __eqx_3) = c_Type_Oshift(__eqy_0, __eqy_1, __eqy_2, __eqy_3)) )).
% 0.75/0.91 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ~class_Ring__and__Field_Oordered__semidom(__eqx_0) | class_Ring__and__Field_Oordered__semidom(__eqy_0) )).
% 0.75/0.91 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~c_HOL_Oord__class_Oless(__eqx_0, __eqx_1, __eqx_2) | c_HOL_Oord__class_Oless(__eqy_0, __eqy_1, __eqy_2) )).
% 0.75/0.91 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ~class_Ring__and__Field_Osemiring__1(__eqx_0) | class_Ring__and__Field_Osemiring__1(__eqy_0) )).
% 0.75/0.91 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ~class_Nat_Osemiring__char__0(__eqx_0) | class_Nat_Osemiring__char__0(__eqy_0) )).
% 0.75/0.91 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ~class_Orderings_Opreorder(__eqx_0) | class_Orderings_Opreorder(__eqy_0) )).
% 0.75/0.91 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ~class_Orderings_Olinorder(__eqx_0) | class_Orderings_Olinorder(__eqy_0) )).
% 0.75/0.91 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ~class_Orderings_Oorder(__eqx_0) | class_Orderings_Oorder(__eqy_0) )).
% 0.75/0.91 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ~class_Ring__and__Field_Oordered__idom(__eqx_0) | class_Ring__and__Field_Oordered__idom(__eqy_0) )).
% 0.75/0.91 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~c_Lambda_Obeta(__eqx_0, __eqx_1) | c_Lambda_Obeta(__eqy_0, __eqy_1) )).
% 0.75/0.91 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ~c_InductTermi_OIT(__eqx_0) | c_InductTermi_OIT(__eqy_0) )).
% 0.75/0.91 cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~c_Type_Otyping(__eqx_0, __eqx_1, __eqx_2) | c_Type_Otyping(__eqy_0, __eqy_1, __eqy_2) )).
% 0.75/0.91 cnf(matrix-23, plain, ( ~class_Ring__and__Field_Oordered__semidom(T_a) | ~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) )).
% 0.75/0.91 cnf(matrix-24, plain, ( ~class_Ring__and__Field_Osemiring__1(T_a) | ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat), T_a) = c_HOL_Ozero__class_Ozero(T_a)) )).
% 0.75/0.91 cnf(matrix-25, plain, ( ~class_Nat_Osemiring__char__0(T_a) | ( c_Nat_Osemiring__1__class_Oof__nat(V_m, T_a) != c_Nat_Osemiring__1__class_Oof__nat(V_n, T_a)) | ( V_m = V_n) )).
% 0.75/0.91 cnf(matrix-26, plain, ( ~class_Ring__and__Field_Oordered__semidom(T_a) | 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) | ~c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) )).
% 0.75/0.91 cnf(matrix-27, plain, ( ~class_Ring__and__Field_Oordered__semidom(T_a) | c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) | ~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) )).
% 0.75/0.91 cnf(matrix-28, plain, ( ~class_Orderings_Opreorder(T_a) | ~c_HOL_Oord__class_Oless(V_b, V_a, T_a) | ~c_HOL_Oord__class_Oless(V_a, V_b, T_a) )).
% 0.75/0.91 cnf(matrix-29, plain, ( ~class_Orderings_Opreorder(T_a) | ~c_HOL_Oord__class_Oless(V_y, V_x, T_a) | ~c_HOL_Oord__class_Oless(V_x, V_y, T_a) )).
% 0.75/0.91 cnf(matrix-30, plain, ( ~class_Orderings_Olinorder(T_a) | ~c_HOL_Oord__class_Oless(V_x, V_y, T_a) | ~c_HOL_Oord__class_Oless(V_y, V_x, T_a) )).
% 0.75/0.91 cnf(matrix-31, plain, ( ~class_Orderings_Oorder(T_a) | ~c_HOL_Oord__class_Oless(V_a, V_b, T_a) | ~c_HOL_Oord__class_Oless(V_b, V_a, T_a) )).
% 0.75/0.91 cnf(matrix-32, plain, ( ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_HOL_Ozero__class_Ozero(tc_nat), tc_nat) )).
% 0.75/0.91 cnf(matrix-33, plain, ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_n, tc_nat) | ( V_n = c_HOL_Ozero__class_Ozero(tc_nat)) )).
% 0.75/0.91 cnf(matrix-34, plain, ( ~class_Ring__and__Field_Oordered__semidom(T_a) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_n, tc_nat) | ~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) )).
% 0.75/0.91 cnf(matrix-35, plain, ( ~class_Ring__and__Field_Oordered__semidom(T_a) | 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) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_n, tc_nat) )).
% 0.75/0.91 cnf(matrix-36, plain, ( ~class_Orderings_Olinorder(T_a) | ( V_x = V_y) | c_HOL_Oord__class_Oless(V_x, V_y, T_a) | c_HOL_Oord__class_Oless(V_y, V_x, T_a) )).
% 0.75/0.91 cnf(matrix-37, plain, ( ~class_Orderings_Olinorder(T_a) | c_HOL_Oord__class_Oless(V_y, V_x, T_a) | ( V_x = V_y) | c_HOL_Oord__class_Oless(V_x, V_y, T_a) )).
% 0.75/0.91 cnf(matrix-38, plain, ( ~class_Orderings_Olinorder(T_a) | c_HOL_Oord__class_Oless(V_y, V_x, T_a) | c_HOL_Oord__class_Oless(V_x, V_y, T_a) | ( V_x = V_y) )).
% 0.75/0.91 cnf(matrix-39, plain, ( c_HOL_Oord__class_Oless(V_y, V_x, tc_nat) | c_HOL_Oord__class_Oless(V_x, V_y, tc_nat) | ( V_x = V_y) )).
% 0.75/0.91 cnf(matrix-40, plain, ( c_HOL_Oord__class_Oless(V_n, V_m, tc_nat) | c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) | ( V_m = V_n) )).
% 0.75/0.91 cnf(matrix-41, plain, ( ~class_Orderings_Olinorder(T_a) | ( V_x = V_y) | c_HOL_Oord__class_Oless(V_y, V_x, T_a) | c_HOL_Oord__class_Oless(V_x, V_y, T_a) )).
% 0.75/0.91 cnf(matrix-42, plain, ( ~class_Ring__and__Field_Oordered__idom(T_a) | c_HOL_Oord__class_Oless(V_y, V_x, T_a) | c_HOL_Oord__class_Oless(V_x, V_y, T_a) | ( V_x = V_y) )).
% 0.75/0.91 cnf(matrix-43, plain, ( ~class_Orderings_Opreorder(T_a) | ~c_HOL_Oord__class_Oless(V_x, V_x, T_a) )).
% 0.75/0.91 cnf(matrix-44, plain, ( ~class_Orderings_Olinorder(T_a) | ~c_HOL_Oord__class_Oless(V_x, V_x, T_a) )).
% 0.75/0.91 cnf(matrix-45, plain, ( ~class_Orderings_Oorder(T_a) | ~c_HOL_Oord__class_Oless(V_x, V_x, T_a) )).
% 0.75/0.91 cnf(matrix-46, plain, ( ~c_HOL_Oord__class_Oless(V_n, V_n, tc_nat) )).
% 0.75/0.91 cnf(matrix-47, plain, ( ~c_HOL_Oord__class_Oless(V_x, V_x, tc_nat) )).
% 0.75/0.91 cnf(matrix-48, plain, ( ~class_Orderings_Opreorder(T_a) | c_HOL_Oord__class_Oless(V_x, V_z, T_a) | ~c_HOL_Oord__class_Oless(V_y, V_z, T_a) | ~c_HOL_Oord__class_Oless(V_x, V_y, T_a) )).
% 0.75/0.91 cnf(matrix-49, plain, ( ~class_Orderings_Oorder(T_a) | c_HOL_Oord__class_Oless(V_z, V_x, T_a) | ~c_HOL_Oord__class_Oless(V_z, V_y, T_a) | ~c_HOL_Oord__class_Oless(V_y, V_x, T_a) )).
% 0.75/0.91 cnf(matrix-50, plain, ( ~c_HOL_Oord__class_Oless(V_m, c_HOL_Ozero__class_Ozero(tc_nat), tc_nat) )).
% 0.75/0.91 cnf(matrix-51, plain, ( ~c_HOL_Oord__class_Oless(V_n, c_HOL_Ozero__class_Ozero(tc_nat), tc_nat) )).
% 0.75/0.91 cnf(matrix-52, plain, ( ( c_Lambda_OdB_OApp(V_dB1_H, V_dB2_H) != c_Lambda_OdB_OVar(V_nat)) )).
% 0.75/0.91 cnf(matrix-53, plain, ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_s), c_Lambda_OdB_OAbs(V_t)) | ~c_Lambda_Obeta(V_s, V_t) )).
% 0.75/0.91 cnf(matrix-54, plain, ( ( V_s = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(V_r, V_s))) | ~c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_r), V_s) )).
% 0.75/0.91 cnf(matrix-55, plain, ( c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t, c_Lambda_OdB_OVar(V_i))) | ~c_InductTermi_OIT(V_t) )).
% 0.75/0.91 cnf(matrix-56, plain, ( c_Lambda_Obeta(c_Lambda_Olift(V_r, V_i), c_Lambda_Olift(V_s, V_i)) | ~c_Lambda_Obeta(V_r, V_s) )).
% 0.75/0.91 cnf(matrix-57, plain, ( ( c_Lambda_Olift(c_Lambda_OdB_OVar(V_i), V_k) = c_Lambda_OdB_OVar(V_i)) | ~c_HOL_Oord__class_Oless(V_i, V_k, tc_nat) )).
% 0.75/0.91 cnf(matrix-58, plain, ( c_Lambda_Obeta(c_Lambda_OdB_OApp(V_s, V_u), c_Lambda_OdB_OApp(V_t, V_u)) | ~c_Lambda_Obeta(V_s, V_t) )).
% 0.75/0.91 cnf(matrix-59, plain, ( c_Lambda_Obeta(c_Lambda_OdB_OApp(V_u, V_s), c_Lambda_OdB_OApp(V_u, V_t)) | ~c_Lambda_Obeta(V_s, V_t) )).
% 0.75/0.91 cnf(matrix-60, plain, ( c_HOL_Oord__class_Oless(V_x, V_x, tc_nat) | ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x), V_s, V_x) = V_s) )).
% 0.75/0.91 cnf(matrix-61, plain, ( ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_i), V_s, V_k) = c_Lambda_OdB_OVar(V_i)) | ( V_i = V_k) | c_HOL_Oord__class_Oless(V_k, V_i, tc_nat) )).
% 0.75/0.91 cnf(matrix-62, plain, ( ( 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))) )).
% 0.75/0.91 cnf(matrix-63, plain, ( ( c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H)) )).
% 0.75/0.91 cnf(matrix-64, plain, ( ( c_Lambda_OdB_OAbs(V_dB) != c_Lambda_OdB_OAbs(V_dB_H)) | ( V_dB = V_dB_H) )).
% 0.75/0.91 cnf(matrix-65, plain, ( ( c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OApp(V_dB1_H, V_dB2_H)) )).
% 0.75/0.91 cnf(matrix-66, plain, ( 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))) )).
% 0.75/0.91 cnf(matrix-67, plain, ( ( c_Lambda_OdB_OApp(V_dB1, V_dB2) != c_Lambda_OdB_OApp(V_dB1_H, V_dB2_H)) | ( V_dB2 = V_dB2_H) )).
% 0.75/0.91 cnf(matrix-68, plain, ( ( c_Lambda_OdB_OApp(V_dB1, V_dB2) != c_Lambda_OdB_OApp(V_dB1_H, V_dB2_H)) | ( V_dB1 = V_dB1_H) )).
% 0.75/0.91 cnf(matrix-69, plain, ( ~c_Lambda_Obeta(c_Lambda_OdB_OVar(V_i), V_t) )).
% 0.75/0.91 cnf(matrix-70, plain, ( c_Lambda_Obeta(V_r, c_Lambda_Osko__Lambda__Xbeta__cases__2__1(V_r, V_s)) | ~c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_r), V_s) )).
% 0.75/0.91 cnf(matrix-71, plain, ( ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_j), V_u, V_i) = c_Lambda_OdB_OVar(V_j)) | ~c_HOL_Oord__class_Oless(V_j, V_i, tc_nat) )).
% 0.75/0.91 cnf(matrix-72, plain, ( ( c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OApp(V_dB1, V_dB2)) )).
% 0.75/0.91 cnf(matrix-73, plain, ( ( c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OVar(V_nat_H)) | ( V_nat = V_nat_H) )).
% 0.75/0.91 cnf(matrix-74, plain, ( ( c_Lambda_OdB_OApp(V_dB1, V_dB2) != c_Lambda_OdB_OAbs(V_dB_H)) )).
% 0.75/0.91 cnf(matrix-75, plain, ( ( c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat)) )).
% 0.75/0.91 cnf(matrix-76, plain, ( ( 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))) )).
% 0.75/0.91 cnf(matrix-77, plain, ( ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k), V_u, V_k) = V_u) )).
% 0.75/0.91 cnf(matrix-78, plain, ( c_InductTermi_OIT(c_Lambda_Osubst(V_r, c_Lambda_OdB_OVar(V_i), V_j)) | ~c_InductTermi_OIT(V_r) )).
% 0.75/0.91 cnf(matrix-79, plain, ( c_InductTermi_OIT(c_Lambda_Olift(V_t, V_i)) | ~c_InductTermi_OIT(V_t) )).
% 0.75/0.91 cnf(matrix-80, plain, ( ( v_n____ = v_i____) )).
% 0.75/0.91 cnf(matrix-81, plain, ( c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n)) )).
% 0.75/0.91 cnf(matrix-82, plain, ( c_Lambda_Obeta(c_Lambda_Osubst(V_r, V_t, V_i), c_Lambda_Osubst(V_s, V_t, V_i)) | ~c_Lambda_Obeta(V_r, V_s) )).
% 0.75/0.91 cnf(matrix-83, plain, ( c_InductTermi_OIT(v_ua______) )).
% 0.75/0.91 cnf(matrix-84, plain, ( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r)) | ~c_InductTermi_OIT(V_r) )).
% 0.75/0.91 cnf(matrix-85, plain, ( c_InductTermi_OIT(v_u____) )).
% 0.75/0.91 cnf(matrix-86, plain, ( ( c_Lambda_Osubst(c_Lambda_Olift(V_t, V_k), V_s, V_k) = V_t) )).
% 0.75/0.91 cnf(matrix-87, plain, ( c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_b____, v_Ua____) )).
% 0.75/0.91 cnf(matrix-88, plain, ( c_InductTermi_OIT(c_Lambda_Osubst(v_b____, V_ua, V_ia)) | ~c_Type_Otyping(V_ea, V_ua, v_T____) | ~c_InductTermi_OIT(V_ua) | ~c_Type_Otyping(c_Type_Oshift(V_ea, V_ia, v_T____, tc_Type_Otype), v_b____, V_T_H) )).
% 0.75/0.91 cnf(matrix-89, plain, ( c_InductTermi_OIT(v_u____) )).
% 0.75/0.91 cnf(matrix-90, plain, ( c_Type_Otyping(v_e____, v_u____, v_T____) )).
% 0.75/0.91 cnf(matrix-91, plain, ( ~c_InductTermi_OIT(c_Lambda_Osubst(v_b____, v_u____, v_i____)) )).
% 0.75/0.91 cnf(matrix-92, plain, ( class_Ring__and__Field_Oordered__semidom(tc_nat) )).
% 0.75/0.91 cnf(matrix-93, plain, ( class_Ring__and__Field_Osemiring__1(tc_nat) )).
% 0.75/0.91 cnf(matrix-94, plain, ( class_Nat_Osemiring__char__0(tc_nat) )).
% 0.75/0.91 cnf(matrix-95, plain, ( class_Orderings_Opreorder(tc_nat) )).
% 0.75/0.91 cnf(matrix-96, plain, ( class_Orderings_Olinorder(tc_nat) )).
% 0.75/0.91 cnf(matrix-97, plain, ( class_Orderings_Oorder(tc_nat) )).
% 0.75/0.91
% 0.75/0.91 % Proof stack:
% 0.75/0.91 cnf(proof-stack, plain,
% 0.75/0.91 proof_stack(
% 0.75/0.91 start(91),
% 0.75/0.91 left_branch(0, 88, 0, 2),
% 0.75/0.91 left_branch(0, 87, 0, 3),
% 0.75/0.91 right_branch(3),
% 0.75/0.91 left_branch(0, 89, 0, 4),
% 0.75/0.91 right_branch(4),
% 0.75/0.91 left_branch(0, 90, 0, 5),
% 0.75/0.91 right_branch(5),
% 0.75/0.91 right_branch(2)
% 0.75/0.91 )).
% 0.75/0.91 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------