TSTP Solution File: SEU177+1 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU177+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n031.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 16:40:38 EDT 2023
% Result : Theorem 12.86s 13.02s
% Output : Proof 12.86s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU177+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n031.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 15:34:05 EDT 2023
% 0.14/0.35 % CPUTime :
% 12.86/13.02 SZS status Theorem for theBenchmark.p
% 12.86/13.02 SZS output start Proof for theBenchmark.p
% 12.86/13.02 Clause #17 (by assumption #[]): Eq (Not (∀ (A B C : Iota), relation C → in (ordered_pair A B) C → And (in A (relation_dom C)) (in B (relation_rng C))))
% 12.86/13.02 True
% 12.86/13.02 Clause #18 (by assumption #[]): Eq
% 12.86/13.02 (∀ (A : Iota),
% 12.86/13.02 relation A →
% 12.86/13.02 ∀ (B : Iota), Iff (Eq B (relation_dom A)) (∀ (C : Iota), Iff (in C B) (Exists fun D => in (ordered_pair C D) A)))
% 12.86/13.02 True
% 12.86/13.02 Clause #19 (by assumption #[]): Eq
% 12.86/13.02 (∀ (A : Iota),
% 12.86/13.02 relation A →
% 12.86/13.02 ∀ (B : Iota), Iff (Eq B (relation_rng A)) (∀ (C : Iota), Iff (in C B) (Exists fun D => in (ordered_pair D C) A)))
% 12.86/13.02 True
% 12.86/13.02 Clause #80 (by clausification #[17]): Eq (∀ (A B C : Iota), relation C → in (ordered_pair A B) C → And (in A (relation_dom C)) (in B (relation_rng C))) False
% 12.86/13.02 Clause #81 (by clausification #[80]): ∀ (a : Iota),
% 12.86/13.02 Eq
% 12.86/13.02 (Not
% 12.86/13.02 (∀ (B C : Iota),
% 12.86/13.02 relation C → in (ordered_pair (skS.0 4 a) B) C → And (in (skS.0 4 a) (relation_dom C)) (in B (relation_rng C))))
% 12.86/13.02 True
% 12.86/13.02 Clause #82 (by clausification #[81]): ∀ (a : Iota),
% 12.86/13.02 Eq
% 12.86/13.02 (∀ (B C : Iota),
% 12.86/13.02 relation C → in (ordered_pair (skS.0 4 a) B) C → And (in (skS.0 4 a) (relation_dom C)) (in B (relation_rng C)))
% 12.86/13.02 False
% 12.86/13.02 Clause #83 (by clausification #[82]): ∀ (a a_1 : Iota),
% 12.86/13.02 Eq
% 12.86/13.02 (Not
% 12.86/13.02 (∀ (C : Iota),
% 12.86/13.02 relation C →
% 12.86/13.02 in (ordered_pair (skS.0 4 a) (skS.0 5 a a_1)) C →
% 12.86/13.02 And (in (skS.0 4 a) (relation_dom C)) (in (skS.0 5 a a_1) (relation_rng C))))
% 12.86/13.02 True
% 12.86/13.02 Clause #84 (by clausification #[83]): ∀ (a a_1 : Iota),
% 12.86/13.02 Eq
% 12.86/13.02 (∀ (C : Iota),
% 12.86/13.02 relation C →
% 12.86/13.02 in (ordered_pair (skS.0 4 a) (skS.0 5 a a_1)) C →
% 12.86/13.02 And (in (skS.0 4 a) (relation_dom C)) (in (skS.0 5 a a_1) (relation_rng C)))
% 12.86/13.02 False
% 12.86/13.02 Clause #85 (by clausification #[84]): ∀ (a a_1 a_2 : Iota),
% 12.86/13.02 Eq
% 12.86/13.02 (Not
% 12.86/13.02 (relation (skS.0 6 a a_1 a_2) →
% 12.86/13.02 in (ordered_pair (skS.0 4 a) (skS.0 5 a a_1)) (skS.0 6 a a_1 a_2) →
% 12.86/13.02 And (in (skS.0 4 a) (relation_dom (skS.0 6 a a_1 a_2)))
% 12.86/13.02 (in (skS.0 5 a a_1) (relation_rng (skS.0 6 a a_1 a_2)))))
% 12.86/13.02 True
% 12.86/13.02 Clause #86 (by clausification #[85]): ∀ (a a_1 a_2 : Iota),
% 12.86/13.02 Eq
% 12.86/13.02 (relation (skS.0 6 a a_1 a_2) →
% 12.86/13.02 in (ordered_pair (skS.0 4 a) (skS.0 5 a a_1)) (skS.0 6 a a_1 a_2) →
% 12.86/13.02 And (in (skS.0 4 a) (relation_dom (skS.0 6 a a_1 a_2))) (in (skS.0 5 a a_1) (relation_rng (skS.0 6 a a_1 a_2))))
% 12.86/13.02 False
% 12.86/13.02 Clause #87 (by clausification #[86]): ∀ (a a_1 a_2 : Iota), Eq (relation (skS.0 6 a a_1 a_2)) True
% 12.86/13.02 Clause #88 (by clausification #[86]): ∀ (a a_1 a_2 : Iota),
% 12.86/13.02 Eq
% 12.86/13.02 (in (ordered_pair (skS.0 4 a) (skS.0 5 a a_1)) (skS.0 6 a a_1 a_2) →
% 12.86/13.02 And (in (skS.0 4 a) (relation_dom (skS.0 6 a a_1 a_2))) (in (skS.0 5 a a_1) (relation_rng (skS.0 6 a a_1 a_2))))
% 12.86/13.02 False
% 12.86/13.02 Clause #98 (by clausification #[18]): ∀ (a : Iota),
% 12.86/13.02 Eq
% 12.86/13.02 (relation a →
% 12.86/13.02 ∀ (B : Iota), Iff (Eq B (relation_dom a)) (∀ (C : Iota), Iff (in C B) (Exists fun D => in (ordered_pair C D) a)))
% 12.86/13.02 True
% 12.86/13.02 Clause #99 (by clausification #[98]): ∀ (a : Iota),
% 12.86/13.02 Or (Eq (relation a) False)
% 12.86/13.02 (Eq
% 12.86/13.02 (∀ (B : Iota), Iff (Eq B (relation_dom a)) (∀ (C : Iota), Iff (in C B) (Exists fun D => in (ordered_pair C D) a)))
% 12.86/13.02 True)
% 12.86/13.02 Clause #100 (by clausification #[99]): ∀ (a a_1 : Iota),
% 12.86/13.02 Or (Eq (relation a) False)
% 12.86/13.02 (Eq (Iff (Eq a_1 (relation_dom a)) (∀ (C : Iota), Iff (in C a_1) (Exists fun D => in (ordered_pair C D) a))) True)
% 12.86/13.02 Clause #102 (by clausification #[100]): ∀ (a a_1 : Iota),
% 12.86/13.02 Or (Eq (relation a) False)
% 12.86/13.02 (Or (Eq (Eq a_1 (relation_dom a)) False)
% 12.86/13.02 (Eq (∀ (C : Iota), Iff (in C a_1) (Exists fun D => in (ordered_pair C D) a)) True))
% 12.86/13.02 Clause #125 (by clausification #[19]): ∀ (a : Iota),
% 12.86/13.02 Eq
% 12.86/13.02 (relation a →
% 12.86/13.02 ∀ (B : Iota), Iff (Eq B (relation_rng a)) (∀ (C : Iota), Iff (in C B) (Exists fun D => in (ordered_pair D C) a)))
% 12.86/13.02 True
% 12.86/13.02 Clause #126 (by clausification #[125]): ∀ (a : Iota),
% 12.86/13.02 Or (Eq (relation a) False)
% 12.86/13.02 (Eq
% 12.86/13.02 (∀ (B : Iota), Iff (Eq B (relation_rng a)) (∀ (C : Iota), Iff (in C B) (Exists fun D => in (ordered_pair D C) a)))
% 12.86/13.05 True)
% 12.86/13.05 Clause #127 (by clausification #[126]): ∀ (a a_1 : Iota),
% 12.86/13.05 Or (Eq (relation a) False)
% 12.86/13.05 (Eq (Iff (Eq a_1 (relation_rng a)) (∀ (C : Iota), Iff (in C a_1) (Exists fun D => in (ordered_pair D C) a))) True)
% 12.86/13.05 Clause #129 (by clausification #[127]): ∀ (a a_1 : Iota),
% 12.86/13.05 Or (Eq (relation a) False)
% 12.86/13.05 (Or (Eq (Eq a_1 (relation_rng a)) False)
% 12.86/13.05 (Eq (∀ (C : Iota), Iff (in C a_1) (Exists fun D => in (ordered_pair D C) a)) True))
% 12.86/13.05 Clause #173 (by clausification #[88]): ∀ (a a_1 a_2 : Iota), Eq (in (ordered_pair (skS.0 4 a) (skS.0 5 a a_1)) (skS.0 6 a a_1 a_2)) True
% 12.86/13.05 Clause #174 (by clausification #[88]): ∀ (a a_1 a_2 : Iota),
% 12.86/13.05 Eq (And (in (skS.0 4 a) (relation_dom (skS.0 6 a a_1 a_2))) (in (skS.0 5 a a_1) (relation_rng (skS.0 6 a a_1 a_2))))
% 12.86/13.05 False
% 12.86/13.05 Clause #202 (by clausification #[102]): ∀ (a a_1 : Iota),
% 12.86/13.05 Or (Eq (relation a) False)
% 12.86/13.05 (Or (Eq (∀ (C : Iota), Iff (in C a_1) (Exists fun D => in (ordered_pair C D) a)) True) (Ne a_1 (relation_dom a)))
% 12.86/13.05 Clause #203 (by clausification #[202]): ∀ (a a_1 a_2 : Iota),
% 12.86/13.05 Or (Eq (relation a) False)
% 12.86/13.05 (Or (Ne a_1 (relation_dom a)) (Eq (Iff (in a_2 a_1) (Exists fun D => in (ordered_pair a_2 D) a)) True))
% 12.86/13.05 Clause #204 (by clausification #[203]): ∀ (a a_1 a_2 : Iota),
% 12.86/13.05 Or (Eq (relation a) False)
% 12.86/13.05 (Or (Ne a_1 (relation_dom a)) (Or (Eq (in a_2 a_1) True) (Eq (Exists fun D => in (ordered_pair a_2 D) a) False)))
% 12.86/13.05 Clause #206 (by clausification #[204]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.86/13.05 Or (Eq (relation a) False)
% 12.86/13.05 (Or (Ne a_1 (relation_dom a)) (Or (Eq (in a_2 a_1) True) (Eq (in (ordered_pair a_2 a_3) a) False)))
% 12.86/13.05 Clause #207 (by destructive equality resolution #[206]): ∀ (a a_1 a_2 : Iota),
% 12.86/13.05 Or (Eq (relation a) False) (Or (Eq (in a_1 (relation_dom a)) True) (Eq (in (ordered_pair a_1 a_2) a) False))
% 12.86/13.05 Clause #209 (by superposition #[207, 87]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.86/13.05 Or (Eq (in a (relation_dom (skS.0 6 a_1 a_2 a_3))) True)
% 12.86/13.05 (Or (Eq (in (ordered_pair a a_4) (skS.0 6 a_1 a_2 a_3)) False) (Eq False True))
% 12.86/13.05 Clause #340 (by clausification #[129]): ∀ (a a_1 : Iota),
% 12.86/13.05 Or (Eq (relation a) False)
% 12.86/13.05 (Or (Eq (∀ (C : Iota), Iff (in C a_1) (Exists fun D => in (ordered_pair D C) a)) True) (Ne a_1 (relation_rng a)))
% 12.86/13.05 Clause #341 (by clausification #[340]): ∀ (a a_1 a_2 : Iota),
% 12.86/13.05 Or (Eq (relation a) False)
% 12.86/13.05 (Or (Ne a_1 (relation_rng a)) (Eq (Iff (in a_2 a_1) (Exists fun D => in (ordered_pair D a_2) a)) True))
% 12.86/13.05 Clause #342 (by clausification #[341]): ∀ (a a_1 a_2 : Iota),
% 12.86/13.05 Or (Eq (relation a) False)
% 12.86/13.05 (Or (Ne a_1 (relation_rng a)) (Or (Eq (in a_2 a_1) True) (Eq (Exists fun D => in (ordered_pair D a_2) a) False)))
% 12.86/13.05 Clause #344 (by clausification #[342]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.86/13.05 Or (Eq (relation a) False)
% 12.86/13.05 (Or (Ne a_1 (relation_rng a)) (Or (Eq (in a_2 a_1) True) (Eq (in (ordered_pair a_3 a_2) a) False)))
% 12.86/13.05 Clause #345 (by destructive equality resolution #[344]): ∀ (a a_1 a_2 : Iota),
% 12.86/13.05 Or (Eq (relation a) False) (Or (Eq (in a_1 (relation_rng a)) True) (Eq (in (ordered_pair a_2 a_1) a) False))
% 12.86/13.05 Clause #347 (by superposition #[345, 87]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.86/13.05 Or (Eq (in a (relation_rng (skS.0 6 a_1 a_2 a_3))) True)
% 12.86/13.05 (Or (Eq (in (ordered_pair a_4 a) (skS.0 6 a_1 a_2 a_3)) False) (Eq False True))
% 12.86/13.05 Clause #1293 (by clausification #[174]): ∀ (a a_1 a_2 : Iota),
% 12.86/13.05 Or (Eq (in (skS.0 4 a) (relation_dom (skS.0 6 a a_1 a_2))) False)
% 12.86/13.05 (Eq (in (skS.0 5 a a_1) (relation_rng (skS.0 6 a a_1 a_2))) False)
% 12.86/13.05 Clause #1964 (by clausification #[209]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.86/13.05 Or (Eq (in a (relation_dom (skS.0 6 a_1 a_2 a_3))) True) (Eq (in (ordered_pair a a_4) (skS.0 6 a_1 a_2 a_3)) False)
% 12.86/13.05 Clause #1965 (by superposition #[1964, 173]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 4 a) (relation_dom (skS.0 6 a a_1 a_2))) True) (Eq False True)
% 12.86/13.05 Clause #1966 (by clausification #[1965]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 4 a) (relation_dom (skS.0 6 a a_1 a_2))) True
% 12.86/13.05 Clause #1967 (by backward demodulation #[1966, 1293]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (in (skS.0 5 a a_1) (relation_rng (skS.0 6 a a_1 a_2))) False)
% 12.86/13.07 Clause #2071 (by clausification #[1967]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 5 a a_1) (relation_rng (skS.0 6 a a_1 a_2))) False
% 12.86/13.07 Clause #2116 (by clausification #[347]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.86/13.07 Or (Eq (in a (relation_rng (skS.0 6 a_1 a_2 a_3))) True) (Eq (in (ordered_pair a_4 a) (skS.0 6 a_1 a_2 a_3)) False)
% 12.86/13.07 Clause #2117 (by superposition #[2116, 173]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 5 a a_1) (relation_rng (skS.0 6 a a_1 a_2))) True) (Eq False True)
% 12.86/13.07 Clause #2118 (by clausification #[2117]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 5 a a_1) (relation_rng (skS.0 6 a a_1 a_2))) True
% 12.86/13.07 Clause #2119 (by superposition #[2118, 2071]): Eq True False
% 12.86/13.07 Clause #2225 (by clausification #[2119]): False
% 12.86/13.07 SZS output end Proof for theBenchmark.p
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