TSTP Solution File: LCL800_5 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : LCL800_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% 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 07:11:19 EDT 2023
% Result : Theorem 22.19s 22.36s
% Output : Proof 22.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : LCL800_5 : TPTP v8.1.2. Released v6.0.0.
% 0.00/0.09 % Command : duper %s
% 0.11/0.28 % Computer : n032.cluster.edu
% 0.11/0.28 % Model : x86_64 x86_64
% 0.11/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.28 % Memory : 8042.1875MB
% 0.11/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.28 % CPULimit : 300
% 0.11/0.28 % WCLimit : 300
% 0.11/0.28 % DateTime : Thu Aug 24 21:25:12 EDT 2023
% 0.11/0.28 % CPUTime :
% 22.19/22.36 SZS status Theorem for theBenchmark.p
% 22.19/22.36 SZS output start Proof for theBenchmark.p
% 22.19/22.36 Clause #4 (by assumption #[]): Eq (it (subst (app (lift u (zero_zero nat)) (var (zero_zero nat))) (subst a u i) (zero_zero nat))) True
% 22.19/22.36 Clause #6 (by assumption #[]): Eq (∀ (K : nat) (S U T : dB), Eq (subst (app T U) S K) (app (subst T S K) (subst U S K))) True
% 22.19/22.36 Clause #13 (by assumption #[]): Eq (∀ (S : dB) (K : nat) (T : dB), Eq (subst (lift T K) S K) T) True
% 22.19/22.36 Clause #14 (by assumption #[]): Eq (∀ (U : dB) (K : nat), Eq (subst (var K) U K) U) True
% 22.19/22.36 Clause #59 (by assumption #[]): Eq (∀ (M : nat), Ne (zero_zero nat) (suc M)) True
% 22.19/22.36 Clause #60 (by assumption #[]): Eq (∀ (N : nat), Ne N (zero_zero nat) → Exists fun M2 => Eq N (suc M2)) True
% 22.19/22.36 Clause #101 (by assumption #[]): Eq (Not (it (app u (subst a u i)))) True
% 22.19/22.36 Clause #110 (by clausification #[59]): ∀ (a : nat), Eq (Ne (zero_zero nat) (suc a)) True
% 22.19/22.36 Clause #111 (by clausification #[110]): ∀ (a : nat), Ne (zero_zero nat) (suc a)
% 22.19/22.36 Clause #132 (by clausification #[6]): ∀ (a : nat), Eq (∀ (S U T : dB), Eq (subst (app T U) S a) (app (subst T S a) (subst U S a))) True
% 22.19/22.36 Clause #133 (by clausification #[132]): ∀ (a : dB) (a_1 : nat), Eq (∀ (U T : dB), Eq (subst (app T U) a a_1) (app (subst T a a_1) (subst U a a_1))) True
% 22.19/22.36 Clause #134 (by clausification #[133]): ∀ (a a_1 : dB) (a_2 : nat), Eq (∀ (T : dB), Eq (subst (app T a) a_1 a_2) (app (subst T a_1 a_2) (subst a a_1 a_2))) True
% 22.19/22.36 Clause #135 (by clausification #[134]): ∀ (a a_1 a_2 : dB) (a_3 : nat), Eq (Eq (subst (app a a_1) a_2 a_3) (app (subst a a_2 a_3) (subst a_1 a_2 a_3))) True
% 22.19/22.36 Clause #136 (by clausification #[135]): ∀ (a a_1 a_2 : dB) (a_3 : nat), Eq (subst (app a a_1) a_2 a_3) (app (subst a a_2 a_3) (subst a_1 a_2 a_3))
% 22.19/22.36 Clause #233 (by clausification #[101]): Eq (it (app u (subst a u i))) False
% 22.19/22.36 Clause #248 (by clausification #[13]): ∀ (a : dB), Eq (∀ (K : nat) (T : dB), Eq (subst (lift T K) a K) T) True
% 22.19/22.36 Clause #249 (by clausification #[248]): ∀ (a : nat) (a_1 : dB), Eq (∀ (T : dB), Eq (subst (lift T a) a_1 a) T) True
% 22.19/22.36 Clause #250 (by clausification #[249]): ∀ (a : dB) (a_1 : nat) (a_2 : dB), Eq (Eq (subst (lift a a_1) a_2 a_1) a) True
% 22.19/22.36 Clause #251 (by clausification #[250]): ∀ (a : dB) (a_1 : nat) (a_2 : dB), Eq (subst (lift a a_1) a_2 a_1) a
% 22.19/22.36 Clause #253 (by superposition #[251, 136]): ∀ (a : dB) (a_1 : nat) (a_2 a_3 : dB), Eq (subst (app (lift a a_1) a_2) a_3 a_1) (app a (subst a_2 a_3 a_1))
% 22.19/22.36 Clause #272 (by clausification #[14]): ∀ (a : dB), Eq (∀ (K : nat), Eq (subst (var K) a K) a) True
% 22.19/22.36 Clause #273 (by clausification #[272]): ∀ (a : nat) (a_1 : dB), Eq (Eq (subst (var a) a_1 a) a_1) True
% 22.19/22.36 Clause #274 (by clausification #[273]): ∀ (a : nat) (a_1 : dB), Eq (subst (var a) a_1 a) a_1
% 22.19/22.36 Clause #421 (by clausification #[60]): ∀ (a : nat), Eq (Ne a (zero_zero nat) → Exists fun M2 => Eq a (suc M2)) True
% 22.19/22.36 Clause #422 (by clausification #[421]): ∀ (a : nat), Or (Eq (Ne a (zero_zero nat)) False) (Eq (Exists fun M2 => Eq a (suc M2)) True)
% 22.19/22.36 Clause #423 (by clausification #[422]): ∀ (a : nat), Or (Eq (Exists fun M2 => Eq a (suc M2)) True) (Eq a (zero_zero nat))
% 22.19/22.36 Clause #424 (by clausification #[423]): ∀ (a a_1 : nat), Or (Eq a (zero_zero nat)) (Eq (Eq a (suc (skS.0 2 a a_1))) True)
% 22.19/22.36 Clause #425 (by clausification #[424]): ∀ (a a_1 : nat), Or (Eq a (zero_zero nat)) (Eq a (suc (skS.0 2 a a_1)))
% 22.19/22.36 Clause #426 (by superposition #[425, 4]): ∀ (a_1 a_2 : nat),
% 22.19/22.36 Or (Eq a_1 (suc (skS.0 2 a_1 a_2))) (Eq (it (subst (app (lift u a_1) (var a_1)) (subst a u i) a_1)) True)
% 22.19/22.36 Clause #4966 (by forward demodulation #[426, 253]): ∀ (a_1 a_2 : nat), Or (Eq a_1 (suc (skS.0 2 a_1 a_2))) (Eq (it (app u (subst (var a_1) (subst a u i) a_1))) True)
% 22.19/22.36 Clause #4967 (by forward demodulation #[4966, 274]): ∀ (a_1 a_2 : nat), Or (Eq a_1 (suc (skS.0 2 a_1 a_2))) (Eq (it (app u (subst a u i))) True)
% 22.19/22.36 Clause #4969 (by superposition #[4967, 111]): ∀ (a_1 : nat), Or (Eq (it (app u (subst a u i))) True) (Ne (zero_zero nat) a_1)
% 22.19/22.36 Clause #8952 (by destructive equality resolution #[4969]): Eq (it (app u (subst a u i))) True
% 22.19/22.36 Clause #8953 (by superposition #[8952, 233]): Eq True False
% 22.24/22.41 Clause #8963 (by clausification #[8953]): False
% 22.24/22.41 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------