TSTP Solution File: SEU275+1 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU275+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n029.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 16:41:11 EDT 2023
% Result : Theorem 3.48s 3.74s
% Output : Proof 3.48s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU275+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : duper %s
% 0.16/0.34 % Computer : n029.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Wed Aug 23 14:25:53 EDT 2023
% 0.20/0.35 % CPUTime :
% 3.48/3.74 SZS status Theorem for theBenchmark.p
% 3.48/3.74 SZS output start Proof for theBenchmark.p
% 3.48/3.74 Clause #2 (by assumption #[]): Eq
% 3.48/3.74 (∀ (A : Iota),
% 3.48/3.74 relation A →
% 3.48/3.74 Iff (well_ordering A)
% 3.48/3.74 (And (And (And (And (reflexive A) (transitive A)) (antisymmetric A)) (connected A)) (well_founded_relation A)))
% 3.48/3.74 True
% 3.48/3.74 Clause #3 (by assumption #[]): Eq (∀ (A : Iota), relation (inclusion_relation A)) True
% 3.48/3.74 Clause #5 (by assumption #[]): Eq (∀ (A : Iota), reflexive (inclusion_relation A)) True
% 3.48/3.74 Clause #6 (by assumption #[]): Eq (∀ (A : Iota), transitive (inclusion_relation A)) True
% 3.48/3.74 Clause #7 (by assumption #[]): Eq (∀ (A : Iota), ordinal A → connected (inclusion_relation A)) True
% 3.48/3.74 Clause #8 (by assumption #[]): Eq (∀ (A : Iota), antisymmetric (inclusion_relation A)) True
% 3.48/3.74 Clause #9 (by assumption #[]): Eq (∀ (A : Iota), ordinal A → well_founded_relation (inclusion_relation A)) True
% 3.48/3.74 Clause #10 (by assumption #[]): Eq (Not (∀ (A : Iota), ordinal A → well_ordering (inclusion_relation A))) True
% 3.48/3.74 Clause #11 (by clausification #[8]): ∀ (a : Iota), Eq (antisymmetric (inclusion_relation a)) True
% 3.48/3.74 Clause #12 (by clausification #[6]): ∀ (a : Iota), Eq (transitive (inclusion_relation a)) True
% 3.48/3.74 Clause #13 (by clausification #[3]): ∀ (a : Iota), Eq (relation (inclusion_relation a)) True
% 3.48/3.74 Clause #14 (by clausification #[5]): ∀ (a : Iota), Eq (reflexive (inclusion_relation a)) True
% 3.48/3.74 Clause #22 (by clausification #[7]): ∀ (a : Iota), Eq (ordinal a → connected (inclusion_relation a)) True
% 3.48/3.74 Clause #23 (by clausification #[22]): ∀ (a : Iota), Or (Eq (ordinal a) False) (Eq (connected (inclusion_relation a)) True)
% 3.48/3.74 Clause #24 (by clausification #[9]): ∀ (a : Iota), Eq (ordinal a → well_founded_relation (inclusion_relation a)) True
% 3.48/3.74 Clause #25 (by clausification #[24]): ∀ (a : Iota), Or (Eq (ordinal a) False) (Eq (well_founded_relation (inclusion_relation a)) True)
% 3.48/3.74 Clause #26 (by clausification #[10]): Eq (∀ (A : Iota), ordinal A → well_ordering (inclusion_relation A)) False
% 3.48/3.74 Clause #27 (by clausification #[26]): ∀ (a : Iota), Eq (Not (ordinal (skS.0 0 a) → well_ordering (inclusion_relation (skS.0 0 a)))) True
% 3.48/3.74 Clause #28 (by clausification #[27]): ∀ (a : Iota), Eq (ordinal (skS.0 0 a) → well_ordering (inclusion_relation (skS.0 0 a))) False
% 3.48/3.74 Clause #29 (by clausification #[28]): ∀ (a : Iota), Eq (ordinal (skS.0 0 a)) True
% 3.48/3.74 Clause #30 (by clausification #[28]): ∀ (a : Iota), Eq (well_ordering (inclusion_relation (skS.0 0 a))) False
% 3.48/3.74 Clause #32 (by superposition #[29, 23]): ∀ (a : Iota), Or (Eq True False) (Eq (connected (inclusion_relation (skS.0 0 a))) True)
% 3.48/3.74 Clause #34 (by superposition #[29, 25]): ∀ (a : Iota), Or (Eq True False) (Eq (well_founded_relation (inclusion_relation (skS.0 0 a))) True)
% 3.48/3.74 Clause #35 (by clausification #[2]): ∀ (a : Iota),
% 3.48/3.74 Eq
% 3.48/3.74 (relation a →
% 3.48/3.74 Iff (well_ordering a)
% 3.48/3.74 (And (And (And (And (reflexive a) (transitive a)) (antisymmetric a)) (connected a)) (well_founded_relation a)))
% 3.48/3.74 True
% 3.48/3.74 Clause #36 (by clausification #[35]): ∀ (a : Iota),
% 3.48/3.74 Or (Eq (relation a) False)
% 3.48/3.74 (Eq
% 3.48/3.74 (Iff (well_ordering a)
% 3.48/3.74 (And (And (And (And (reflexive a) (transitive a)) (antisymmetric a)) (connected a)) (well_founded_relation a)))
% 3.48/3.74 True)
% 3.48/3.74 Clause #37 (by clausification #[36]): ∀ (a : Iota),
% 3.48/3.74 Or (Eq (relation a) False)
% 3.48/3.74 (Or (Eq (well_ordering a) True)
% 3.48/3.74 (Eq (And (And (And (And (reflexive a) (transitive a)) (antisymmetric a)) (connected a)) (well_founded_relation a))
% 3.48/3.74 False))
% 3.48/3.74 Clause #39 (by clausification #[37]): ∀ (a : Iota),
% 3.48/3.74 Or (Eq (relation a) False)
% 3.48/3.74 (Or (Eq (well_ordering a) True)
% 3.48/3.74 (Or (Eq (And (And (And (reflexive a) (transitive a)) (antisymmetric a)) (connected a)) False)
% 3.48/3.74 (Eq (well_founded_relation a) False)))
% 3.48/3.74 Clause #40 (by clausification #[39]): ∀ (a : Iota),
% 3.48/3.74 Or (Eq (relation a) False)
% 3.48/3.74 (Or (Eq (well_ordering a) True)
% 3.48/3.74 (Or (Eq (well_founded_relation a) False)
% 3.48/3.74 (Or (Eq (And (And (reflexive a) (transitive a)) (antisymmetric a)) False) (Eq (connected a) False))))
% 3.48/3.74 Clause #41 (by clausification #[40]): ∀ (a : Iota),
% 3.48/3.74 Or (Eq (relation a) False)
% 3.48/3.76 (Or (Eq (well_ordering a) True)
% 3.48/3.76 (Or (Eq (well_founded_relation a) False)
% 3.48/3.76 (Or (Eq (connected a) False) (Or (Eq (And (reflexive a) (transitive a)) False) (Eq (antisymmetric a) False)))))
% 3.48/3.76 Clause #42 (by clausification #[41]): ∀ (a : Iota),
% 3.48/3.76 Or (Eq (relation a) False)
% 3.48/3.76 (Or (Eq (well_ordering a) True)
% 3.48/3.76 (Or (Eq (well_founded_relation a) False)
% 3.48/3.76 (Or (Eq (connected a) False)
% 3.48/3.76 (Or (Eq (antisymmetric a) False) (Or (Eq (reflexive a) False) (Eq (transitive a) False))))))
% 3.48/3.76 Clause #43 (by superposition #[42, 13]): ∀ (a : Iota),
% 3.48/3.76 Or (Eq (well_ordering (inclusion_relation a)) True)
% 3.48/3.76 (Or (Eq (well_founded_relation (inclusion_relation a)) False)
% 3.48/3.76 (Or (Eq (connected (inclusion_relation a)) False)
% 3.48/3.76 (Or (Eq (antisymmetric (inclusion_relation a)) False)
% 3.48/3.76 (Or (Eq (reflexive (inclusion_relation a)) False)
% 3.48/3.76 (Or (Eq (transitive (inclusion_relation a)) False) (Eq False True))))))
% 3.48/3.76 Clause #47 (by clausification #[32]): ∀ (a : Iota), Eq (connected (inclusion_relation (skS.0 0 a))) True
% 3.48/3.76 Clause #48 (by clausification #[34]): ∀ (a : Iota), Eq (well_founded_relation (inclusion_relation (skS.0 0 a))) True
% 3.48/3.76 Clause #65 (by clausification #[43]): ∀ (a : Iota),
% 3.48/3.76 Or (Eq (well_ordering (inclusion_relation a)) True)
% 3.48/3.76 (Or (Eq (well_founded_relation (inclusion_relation a)) False)
% 3.48/3.76 (Or (Eq (connected (inclusion_relation a)) False)
% 3.48/3.76 (Or (Eq (antisymmetric (inclusion_relation a)) False)
% 3.48/3.76 (Or (Eq (reflexive (inclusion_relation a)) False) (Eq (transitive (inclusion_relation a)) False)))))
% 3.48/3.76 Clause #66 (by forward demodulation #[65, 11]): ∀ (a : Iota),
% 3.48/3.76 Or (Eq (well_ordering (inclusion_relation a)) True)
% 3.48/3.76 (Or (Eq (well_founded_relation (inclusion_relation a)) False)
% 3.48/3.76 (Or (Eq (connected (inclusion_relation a)) False)
% 3.48/3.76 (Or (Eq True False)
% 3.48/3.76 (Or (Eq (reflexive (inclusion_relation a)) False) (Eq (transitive (inclusion_relation a)) False)))))
% 3.48/3.76 Clause #67 (by clausification #[66]): ∀ (a : Iota),
% 3.48/3.76 Or (Eq (well_ordering (inclusion_relation a)) True)
% 3.48/3.76 (Or (Eq (well_founded_relation (inclusion_relation a)) False)
% 3.48/3.76 (Or (Eq (connected (inclusion_relation a)) False)
% 3.48/3.76 (Or (Eq (reflexive (inclusion_relation a)) False) (Eq (transitive (inclusion_relation a)) False))))
% 3.48/3.76 Clause #68 (by forward demodulation #[67, 14]): ∀ (a : Iota),
% 3.48/3.76 Or (Eq (well_ordering (inclusion_relation a)) True)
% 3.48/3.76 (Or (Eq (well_founded_relation (inclusion_relation a)) False)
% 3.48/3.76 (Or (Eq (connected (inclusion_relation a)) False)
% 3.48/3.76 (Or (Eq True False) (Eq (transitive (inclusion_relation a)) False))))
% 3.48/3.76 Clause #69 (by clausification #[68]): ∀ (a : Iota),
% 3.48/3.76 Or (Eq (well_ordering (inclusion_relation a)) True)
% 3.48/3.76 (Or (Eq (well_founded_relation (inclusion_relation a)) False)
% 3.48/3.76 (Or (Eq (connected (inclusion_relation a)) False) (Eq (transitive (inclusion_relation a)) False)))
% 3.48/3.76 Clause #70 (by forward demodulation #[69, 12]): ∀ (a : Iota),
% 3.48/3.76 Or (Eq (well_ordering (inclusion_relation a)) True)
% 3.48/3.76 (Or (Eq (well_founded_relation (inclusion_relation a)) False)
% 3.48/3.76 (Or (Eq (connected (inclusion_relation a)) False) (Eq True False)))
% 3.48/3.76 Clause #71 (by clausification #[70]): ∀ (a : Iota),
% 3.48/3.76 Or (Eq (well_ordering (inclusion_relation a)) True)
% 3.48/3.76 (Or (Eq (well_founded_relation (inclusion_relation a)) False) (Eq (connected (inclusion_relation a)) False))
% 3.48/3.76 Clause #72 (by superposition #[71, 48]): ∀ (a : Iota),
% 3.48/3.76 Or (Eq (well_ordering (inclusion_relation (skS.0 0 a))) True)
% 3.48/3.76 (Or (Eq (connected (inclusion_relation (skS.0 0 a))) False) (Eq False True))
% 3.48/3.76 Clause #82 (by clausification #[72]): ∀ (a : Iota),
% 3.48/3.76 Or (Eq (well_ordering (inclusion_relation (skS.0 0 a))) True) (Eq (connected (inclusion_relation (skS.0 0 a))) False)
% 3.48/3.76 Clause #83 (by forward demodulation #[82, 30]): ∀ (a : Iota), Or (Eq False True) (Eq (connected (inclusion_relation (skS.0 0 a))) False)
% 3.48/3.76 Clause #84 (by clausification #[83]): ∀ (a : Iota), Eq (connected (inclusion_relation (skS.0 0 a))) False
% 3.48/3.76 Clause #85 (by superposition #[84, 47]): Eq False True
% 3.48/3.76 Clause #86 (by clausification #[85]): False
% 3.48/3.76 SZS output end Proof for theBenchmark.p
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