TSTP Solution File: NUM414+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : NUM414+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n019.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 10:55:30 EDT 2023
% Result : Theorem 204.14s 204.47s
% Output : Proof 204.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM414+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : duper %s
% 0.11/0.33 % Computer : n019.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Aug 25 10:06:44 EDT 2023
% 0.11/0.34 % CPUTime :
% 204.14/204.47 SZS status Theorem for theBenchmark.p
% 204.14/204.47 SZS output start Proof for theBenchmark.p
% 204.14/204.47 Clause #8 (by assumption #[]): Eq (∀ (A B : Iota), And (ordinal A) (ordinal B) → Or (ordinal_subset A B) (ordinal_subset B A)) True
% 204.14/204.47 Clause #9 (by assumption #[]): Eq (∀ (A B : Iota), Iff (proper_subset A B) (And (subset A B) (Ne A B))) True
% 204.14/204.47 Clause #30 (by assumption #[]): Eq (∀ (A B : Iota), And (ordinal A) (ordinal B) → Iff (ordinal_subset A B) (subset A B)) True
% 204.14/204.47 Clause #37 (by assumption #[]): Eq
% 204.14/204.47 (Not
% 204.14/204.47 (∀ (A : Iota),
% 204.14/204.47 ordinal A →
% 204.14/204.47 ∀ (B : Iota), ordinal B → Not (And (And (Not (proper_subset A B)) (Ne A B)) (Not (proper_subset B A)))))
% 204.14/204.47 True
% 204.14/204.47 Clause #133 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (B : Iota), And (ordinal a) (ordinal B) → Or (ordinal_subset a B) (ordinal_subset B a)) True
% 204.14/204.47 Clause #134 (by clausification #[133]): ∀ (a a_1 : Iota), Eq (And (ordinal a) (ordinal a_1) → Or (ordinal_subset a a_1) (ordinal_subset a_1 a)) True
% 204.14/204.47 Clause #135 (by clausification #[134]): ∀ (a a_1 : Iota),
% 204.14/204.47 Or (Eq (And (ordinal a) (ordinal a_1)) False) (Eq (Or (ordinal_subset a a_1) (ordinal_subset a_1 a)) True)
% 204.14/204.47 Clause #136 (by clausification #[135]): ∀ (a a_1 : Iota),
% 204.14/204.47 Or (Eq (Or (ordinal_subset a a_1) (ordinal_subset a_1 a)) True) (Or (Eq (ordinal a) False) (Eq (ordinal a_1) False))
% 204.14/204.47 Clause #137 (by clausification #[136]): ∀ (a a_1 : Iota),
% 204.14/204.47 Or (Eq (ordinal a) False)
% 204.14/204.47 (Or (Eq (ordinal a_1) False) (Or (Eq (ordinal_subset a a_1) True) (Eq (ordinal_subset a_1 a) True)))
% 204.14/204.47 Clause #144 (by clausification #[9]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (proper_subset a B) (And (subset a B) (Ne a B))) True
% 204.14/204.47 Clause #145 (by clausification #[144]): ∀ (a a_1 : Iota), Eq (Iff (proper_subset a a_1) (And (subset a a_1) (Ne a a_1))) True
% 204.14/204.47 Clause #146 (by clausification #[145]): ∀ (a a_1 : Iota), Or (Eq (proper_subset a a_1) True) (Eq (And (subset a a_1) (Ne a a_1)) False)
% 204.14/204.47 Clause #148 (by clausification #[146]): ∀ (a a_1 : Iota), Or (Eq (proper_subset a a_1) True) (Or (Eq (subset a a_1) False) (Eq (Ne a a_1) False))
% 204.14/204.47 Clause #149 (by clausification #[148]): ∀ (a a_1 : Iota), Or (Eq (proper_subset a a_1) True) (Or (Eq (subset a a_1) False) (Eq a a_1))
% 204.14/204.47 Clause #223 (by clausification #[30]): ∀ (a : Iota), Eq (∀ (B : Iota), And (ordinal a) (ordinal B) → Iff (ordinal_subset a B) (subset a B)) True
% 204.14/204.47 Clause #224 (by clausification #[223]): ∀ (a a_1 : Iota), Eq (And (ordinal a) (ordinal a_1) → Iff (ordinal_subset a a_1) (subset a a_1)) True
% 204.14/204.47 Clause #225 (by clausification #[224]): ∀ (a a_1 : Iota), Or (Eq (And (ordinal a) (ordinal a_1)) False) (Eq (Iff (ordinal_subset a a_1) (subset a a_1)) True)
% 204.14/204.47 Clause #226 (by clausification #[225]): ∀ (a a_1 : Iota),
% 204.14/204.47 Or (Eq (Iff (ordinal_subset a a_1) (subset a a_1)) True) (Or (Eq (ordinal a) False) (Eq (ordinal a_1) False))
% 204.14/204.47 Clause #228 (by clausification #[226]): ∀ (a a_1 : Iota),
% 204.14/204.47 Or (Eq (ordinal a) False)
% 204.14/204.47 (Or (Eq (ordinal a_1) False) (Or (Eq (ordinal_subset a a_1) False) (Eq (subset a a_1) True)))
% 204.14/204.47 Clause #263 (by clausification #[37]): Eq
% 204.14/204.47 (∀ (A : Iota),
% 204.14/204.47 ordinal A → ∀ (B : Iota), ordinal B → Not (And (And (Not (proper_subset A B)) (Ne A B)) (Not (proper_subset B A))))
% 204.14/204.47 False
% 204.14/204.47 Clause #264 (by clausification #[263]): ∀ (a : Iota),
% 204.14/204.47 Eq
% 204.14/204.47 (Not
% 204.14/204.47 (ordinal (skS.0 15 a) →
% 204.14/204.47 ∀ (B : Iota),
% 204.14/204.47 ordinal B →
% 204.14/204.47 Not
% 204.14/204.47 (And (And (Not (proper_subset (skS.0 15 a) B)) (Ne (skS.0 15 a) B))
% 204.14/204.47 (Not (proper_subset B (skS.0 15 a))))))
% 204.14/204.47 True
% 204.14/204.47 Clause #265 (by clausification #[264]): ∀ (a : Iota),
% 204.14/204.47 Eq
% 204.14/204.47 (ordinal (skS.0 15 a) →
% 204.14/204.47 ∀ (B : Iota),
% 204.14/204.47 ordinal B →
% 204.14/204.47 Not (And (And (Not (proper_subset (skS.0 15 a) B)) (Ne (skS.0 15 a) B)) (Not (proper_subset B (skS.0 15 a)))))
% 204.14/204.47 False
% 204.14/204.47 Clause #266 (by clausification #[265]): ∀ (a : Iota), Eq (ordinal (skS.0 15 a)) True
% 204.14/204.47 Clause #267 (by clausification #[265]): ∀ (a : Iota),
% 204.14/204.47 Eq
% 204.14/204.47 (∀ (B : Iota),
% 204.14/204.47 ordinal B →
% 204.14/204.47 Not (And (And (Not (proper_subset (skS.0 15 a) B)) (Ne (skS.0 15 a) B)) (Not (proper_subset B (skS.0 15 a)))))
% 204.14/204.47 False
% 204.22/204.50 Clause #271 (by superposition #[266, 137]): ∀ (a a_1 : Iota),
% 204.22/204.50 Or (Eq True False)
% 204.22/204.50 (Or (Eq (ordinal a) False)
% 204.22/204.50 (Or (Eq (ordinal_subset (skS.0 15 a_1) a) True) (Eq (ordinal_subset a (skS.0 15 a_1)) True)))
% 204.22/204.50 Clause #289 (by superposition #[228, 266]): ∀ (a a_1 : Iota),
% 204.22/204.50 Or (Eq True False)
% 204.22/204.50 (Or (Eq (ordinal a) False) (Or (Eq (ordinal_subset (skS.0 15 a_1) a) False) (Eq (subset (skS.0 15 a_1) a) True)))
% 204.22/204.50 Clause #480 (by clausification #[267]): ∀ (a a_1 : Iota),
% 204.22/204.50 Eq
% 204.22/204.50 (Not
% 204.22/204.50 (ordinal (skS.0 16 a a_1) →
% 204.22/204.50 Not
% 204.22/204.50 (And (And (Not (proper_subset (skS.0 15 a) (skS.0 16 a a_1))) (Ne (skS.0 15 a) (skS.0 16 a a_1)))
% 204.22/204.50 (Not (proper_subset (skS.0 16 a a_1) (skS.0 15 a))))))
% 204.22/204.50 True
% 204.22/204.50 Clause #481 (by clausification #[480]): ∀ (a a_1 : Iota),
% 204.22/204.50 Eq
% 204.22/204.50 (ordinal (skS.0 16 a a_1) →
% 204.22/204.50 Not
% 204.22/204.50 (And (And (Not (proper_subset (skS.0 15 a) (skS.0 16 a a_1))) (Ne (skS.0 15 a) (skS.0 16 a a_1)))
% 204.22/204.50 (Not (proper_subset (skS.0 16 a a_1) (skS.0 15 a)))))
% 204.22/204.50 False
% 204.22/204.50 Clause #482 (by clausification #[481]): ∀ (a a_1 : Iota), Eq (ordinal (skS.0 16 a a_1)) True
% 204.22/204.50 Clause #483 (by clausification #[481]): ∀ (a a_1 : Iota),
% 204.22/204.50 Eq
% 204.22/204.50 (Not
% 204.22/204.50 (And (And (Not (proper_subset (skS.0 15 a) (skS.0 16 a a_1))) (Ne (skS.0 15 a) (skS.0 16 a a_1)))
% 204.22/204.50 (Not (proper_subset (skS.0 16 a a_1) (skS.0 15 a)))))
% 204.22/204.50 False
% 204.22/204.50 Clause #491 (by superposition #[482, 228]): ∀ (a a_1 a_2 : Iota),
% 204.22/204.50 Or (Eq True False)
% 204.22/204.50 (Or (Eq (ordinal a) False)
% 204.22/204.50 (Or (Eq (ordinal_subset (skS.0 16 a_1 a_2) a) False) (Eq (subset (skS.0 16 a_1 a_2) a) True)))
% 204.22/204.50 Clause #507 (by clausification #[271]): ∀ (a a_1 : Iota),
% 204.22/204.50 Or (Eq (ordinal a) False) (Or (Eq (ordinal_subset (skS.0 15 a_1) a) True) (Eq (ordinal_subset a (skS.0 15 a_1)) True))
% 204.22/204.50 Clause #513 (by superposition #[507, 482]): ∀ (a a_1 a_2 : Iota),
% 204.22/204.50 Or (Eq (ordinal_subset (skS.0 15 a) (skS.0 16 a_1 a_2)) True)
% 204.22/204.50 (Or (Eq (ordinal_subset (skS.0 16 a_1 a_2) (skS.0 15 a)) True) (Eq False True))
% 204.22/204.50 Clause #579 (by clausification #[289]): ∀ (a a_1 : Iota),
% 204.22/204.50 Or (Eq (ordinal a) False) (Or (Eq (ordinal_subset (skS.0 15 a_1) a) False) (Eq (subset (skS.0 15 a_1) a) True))
% 204.22/204.50 Clause #585 (by superposition #[579, 482]): ∀ (a a_1 a_2 : Iota),
% 204.22/204.50 Or (Eq (ordinal_subset (skS.0 15 a) (skS.0 16 a_1 a_2)) False)
% 204.22/204.50 (Or (Eq (subset (skS.0 15 a) (skS.0 16 a_1 a_2)) True) (Eq False True))
% 204.22/204.50 Clause #779 (by clausification #[491]): ∀ (a a_1 a_2 : Iota),
% 204.22/204.50 Or (Eq (ordinal a) False)
% 204.22/204.50 (Or (Eq (ordinal_subset (skS.0 16 a_1 a_2) a) False) (Eq (subset (skS.0 16 a_1 a_2) a) True))
% 204.22/204.50 Clause #784 (by superposition #[779, 266]): ∀ (a a_1 a_2 : Iota),
% 204.22/204.50 Or (Eq (ordinal_subset (skS.0 16 a a_1) (skS.0 15 a_2)) False)
% 204.22/204.50 (Or (Eq (subset (skS.0 16 a a_1) (skS.0 15 a_2)) True) (Eq False True))
% 204.22/204.50 Clause #943 (by clausification #[483]): ∀ (a a_1 : Iota),
% 204.22/204.50 Eq
% 204.22/204.50 (And (And (Not (proper_subset (skS.0 15 a) (skS.0 16 a a_1))) (Ne (skS.0 15 a) (skS.0 16 a a_1)))
% 204.22/204.50 (Not (proper_subset (skS.0 16 a a_1) (skS.0 15 a))))
% 204.22/204.50 True
% 204.22/204.50 Clause #944 (by clausification #[943]): ∀ (a a_1 : Iota), Eq (Not (proper_subset (skS.0 16 a a_1) (skS.0 15 a))) True
% 204.22/204.50 Clause #945 (by clausification #[943]): ∀ (a a_1 : Iota), Eq (And (Not (proper_subset (skS.0 15 a) (skS.0 16 a a_1))) (Ne (skS.0 15 a) (skS.0 16 a a_1))) True
% 204.22/204.50 Clause #946 (by clausification #[944]): ∀ (a a_1 : Iota), Eq (proper_subset (skS.0 16 a a_1) (skS.0 15 a)) False
% 204.22/204.50 Clause #1018 (by clausification #[513]): ∀ (a a_1 a_2 : Iota),
% 204.22/204.50 Or (Eq (ordinal_subset (skS.0 15 a) (skS.0 16 a_1 a_2)) True)
% 204.22/204.50 (Eq (ordinal_subset (skS.0 16 a_1 a_2) (skS.0 15 a)) True)
% 204.22/204.50 Clause #1168 (by clausification #[585]): ∀ (a a_1 a_2 : Iota),
% 204.22/204.50 Or (Eq (ordinal_subset (skS.0 15 a) (skS.0 16 a_1 a_2)) False) (Eq (subset (skS.0 15 a) (skS.0 16 a_1 a_2)) True)
% 204.22/204.50 Clause #1169 (by superposition #[1168, 1018]): ∀ (a a_1 a_2 : Iota),
% 204.22/204.50 Or (Eq (subset (skS.0 15 a) (skS.0 16 a_1 a_2)) True)
% 204.22/204.50 (Or (Eq False True) (Eq (ordinal_subset (skS.0 16 a_1 a_2) (skS.0 15 a)) True))
% 204.22/204.50 Clause #1307 (by clausification #[784]): ∀ (a a_1 a_2 : Iota),
% 204.22/204.50 Or (Eq (ordinal_subset (skS.0 16 a a_1) (skS.0 15 a_2)) False) (Eq (subset (skS.0 16 a a_1) (skS.0 15 a_2)) True)
% 204.31/204.59 Clause #1535 (by clausification #[1169]): ∀ (a a_1 a_2 : Iota),
% 204.31/204.59 Or (Eq (subset (skS.0 15 a) (skS.0 16 a_1 a_2)) True) (Eq (ordinal_subset (skS.0 16 a_1 a_2) (skS.0 15 a)) True)
% 204.31/204.59 Clause #1536 (by superposition #[1535, 1307]): ∀ (a a_1 a_2 : Iota),
% 204.31/204.59 Or (Eq (subset (skS.0 15 a) (skS.0 16 a_1 a_2)) True)
% 204.31/204.59 (Or (Eq True False) (Eq (subset (skS.0 16 a_1 a_2) (skS.0 15 a)) True))
% 204.31/204.59 Clause #1537 (by clausification #[1536]): ∀ (a a_1 a_2 : Iota),
% 204.31/204.59 Or (Eq (subset (skS.0 15 a) (skS.0 16 a_1 a_2)) True) (Eq (subset (skS.0 16 a_1 a_2) (skS.0 15 a)) True)
% 204.31/204.59 Clause #1539 (by superposition #[1537, 149]): ∀ (a a_1 a_2 : Iota),
% 204.31/204.59 Or (Eq (subset (skS.0 16 a a_1) (skS.0 15 a_2)) True)
% 204.31/204.59 (Or (Eq (proper_subset (skS.0 15 a_2) (skS.0 16 a a_1)) True)
% 204.31/204.59 (Or (Eq True False) (Eq (skS.0 15 a_2) (skS.0 16 a a_1))))
% 204.31/204.59 Clause #1559 (by clausification #[945]): ∀ (a a_1 : Iota), Eq (Ne (skS.0 15 a) (skS.0 16 a a_1)) True
% 204.31/204.59 Clause #1560 (by clausification #[945]): ∀ (a a_1 : Iota), Eq (Not (proper_subset (skS.0 15 a) (skS.0 16 a a_1))) True
% 204.31/204.59 Clause #1561 (by clausification #[1559]): ∀ (a a_1 : Iota), Ne (skS.0 15 a) (skS.0 16 a a_1)
% 204.31/204.59 Clause #1562 (by clausification #[1560]): ∀ (a a_1 : Iota), Eq (proper_subset (skS.0 15 a) (skS.0 16 a a_1)) False
% 204.31/204.59 Clause #2469 (by clausification #[1539]): ∀ (a a_1 a_2 : Iota),
% 204.31/204.59 Or (Eq (subset (skS.0 16 a a_1) (skS.0 15 a_2)) True)
% 204.31/204.59 (Or (Eq (proper_subset (skS.0 15 a_2) (skS.0 16 a a_1)) True) (Eq (skS.0 15 a_2) (skS.0 16 a a_1)))
% 204.31/204.59 Clause #2471 (by superposition #[2469, 149]): ∀ (a a_1 a_2 : Iota),
% 204.31/204.59 Or (Eq (proper_subset (skS.0 15 a) (skS.0 16 a_1 a_2)) True)
% 204.31/204.59 (Or (Eq (skS.0 15 a) (skS.0 16 a_1 a_2))
% 204.31/204.59 (Or (Eq (proper_subset (skS.0 16 a_1 a_2) (skS.0 15 a)) True)
% 204.31/204.59 (Or (Eq True False) (Eq (skS.0 16 a_1 a_2) (skS.0 15 a)))))
% 204.31/204.59 Clause #7138 (by clausification #[2471]): ∀ (a a_1 a_2 : Iota),
% 204.31/204.59 Or (Eq (proper_subset (skS.0 15 a) (skS.0 16 a_1 a_2)) True)
% 204.31/204.59 (Or (Eq (skS.0 15 a) (skS.0 16 a_1 a_2))
% 204.31/204.59 (Or (Eq (proper_subset (skS.0 16 a_1 a_2) (skS.0 15 a)) True) (Eq (skS.0 16 a_1 a_2) (skS.0 15 a))))
% 204.31/204.59 Clause #7139 (by eliminate duplicate literals #[7138]): ∀ (a a_1 a_2 : Iota),
% 204.31/204.59 Or (Eq (proper_subset (skS.0 15 a) (skS.0 16 a_1 a_2)) True)
% 204.31/204.59 (Or (Eq (skS.0 15 a) (skS.0 16 a_1 a_2)) (Eq (proper_subset (skS.0 16 a_1 a_2) (skS.0 15 a)) True))
% 204.31/204.59 Clause #7142 (by superposition #[7139, 946]): ∀ (a a_1 : Iota),
% 204.31/204.59 Or (Eq (proper_subset (skS.0 15 a) (skS.0 16 a a_1)) True) (Or (Eq (skS.0 15 a) (skS.0 16 a a_1)) (Eq True False))
% 204.31/204.59 Clause #7144 (by clausification #[7142]): ∀ (a a_1 : Iota), Or (Eq (proper_subset (skS.0 15 a) (skS.0 16 a a_1)) True) (Eq (skS.0 15 a) (skS.0 16 a a_1))
% 204.31/204.59 Clause #7145 (by forward contextual literal cutting #[7144, 1561]): ∀ (a a_1 : Iota), Eq (proper_subset (skS.0 15 a) (skS.0 16 a a_1)) True
% 204.31/204.59 Clause #7146 (by superposition #[7145, 1562]): Eq True False
% 204.31/204.59 Clause #7149 (by clausification #[7146]): False
% 204.31/204.59 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------