TSTP Solution File: SEU523^2 by Duper---1.0
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% File : Duper---1.0
% Problem : SEU523^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n023.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 16:42:30 EDT 2023
% Result : Theorem 3.74s 3.93s
% Output : Proof 3.74s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU523^2 : TPTP v8.1.2. Released v3.7.0.
% 0.12/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n023.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 19:58:57 EDT 2023
% 0.14/0.35 % CPUTime :
% 3.74/3.93 SZS status Theorem for theBenchmark.p
% 3.74/3.93 SZS output start Proof for theBenchmark.p
% 3.74/3.93 Clause #0 (by assumption #[]): Eq (Eq setunionAx (∀ (A Xx : Iota), Iff (in Xx (setunion A)) (Exists fun B => And (in Xx B) (in B A)))) True
% 3.74/3.93 Clause #1 (by assumption #[]): Eq
% 3.74/3.93 (Not
% 3.74/3.93 (setunionAx →
% 3.74/3.93 ∀ (A Xx : Iota), in Xx (setunion A) → ∀ (Xphi : Prop), (∀ (B : Iota), in Xx B → in B A → Xphi) → Xphi))
% 3.74/3.93 True
% 3.74/3.93 Clause #2 (by clausification #[1]): Eq (setunionAx → ∀ (A Xx : Iota), in Xx (setunion A) → ∀ (Xphi : Prop), (∀ (B : Iota), in Xx B → in B A → Xphi) → Xphi)
% 3.74/3.93 False
% 3.74/3.93 Clause #3 (by clausification #[2]): Eq setunionAx True
% 3.74/3.93 Clause #4 (by clausification #[2]): Eq (∀ (A Xx : Iota), in Xx (setunion A) → ∀ (Xphi : Prop), (∀ (B : Iota), in Xx B → in B A → Xphi) → Xphi) False
% 3.74/3.93 Clause #5 (by clausification #[4]): ∀ (a : Iota),
% 3.74/3.93 Eq
% 3.74/3.93 (Not
% 3.74/3.93 (∀ (Xx : Iota),
% 3.74/3.93 in Xx (setunion (skS.0 0 a)) → ∀ (Xphi : Prop), (∀ (B : Iota), in Xx B → in B (skS.0 0 a) → Xphi) → Xphi))
% 3.74/3.93 True
% 3.74/3.93 Clause #6 (by clausification #[5]): ∀ (a : Iota),
% 3.74/3.93 Eq
% 3.74/3.93 (∀ (Xx : Iota),
% 3.74/3.93 in Xx (setunion (skS.0 0 a)) → ∀ (Xphi : Prop), (∀ (B : Iota), in Xx B → in B (skS.0 0 a) → Xphi) → Xphi)
% 3.74/3.93 False
% 3.74/3.93 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota),
% 3.74/3.93 Eq
% 3.74/3.93 (Not
% 3.74/3.93 (in (skS.0 1 a a_1) (setunion (skS.0 0 a)) →
% 3.74/3.93 ∀ (Xphi : Prop), (∀ (B : Iota), in (skS.0 1 a a_1) B → in B (skS.0 0 a) → Xphi) → Xphi))
% 3.74/3.93 True
% 3.74/3.93 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota),
% 3.74/3.93 Eq
% 3.74/3.93 (in (skS.0 1 a a_1) (setunion (skS.0 0 a)) →
% 3.74/3.93 ∀ (Xphi : Prop), (∀ (B : Iota), in (skS.0 1 a a_1) B → in B (skS.0 0 a) → Xphi) → Xphi)
% 3.74/3.93 False
% 3.74/3.93 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Eq (in (skS.0 1 a a_1) (setunion (skS.0 0 a))) True
% 3.74/3.93 Clause #10 (by clausification #[8]): ∀ (a a_1 : Iota), Eq (∀ (Xphi : Prop), (∀ (B : Iota), in (skS.0 1 a a_1) B → in B (skS.0 0 a) → Xphi) → Xphi) False
% 3.74/3.93 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota) (a_2 : Prop),
% 3.74/3.93 Eq (Not ((∀ (B : Iota), in (skS.0 1 a a_1) B → in B (skS.0 0 a) → skS.0 2 a a_1 a_2) → skS.0 2 a a_1 a_2)) True
% 3.74/3.93 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota) (a_2 : Prop),
% 3.74/3.93 Eq ((∀ (B : Iota), in (skS.0 1 a a_1) B → in B (skS.0 0 a) → skS.0 2 a a_1 a_2) → skS.0 2 a a_1 a_2) False
% 3.74/3.93 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota) (a_2 : Prop), Eq (∀ (B : Iota), in (skS.0 1 a a_1) B → in B (skS.0 0 a) → skS.0 2 a a_1 a_2) True
% 3.74/3.93 Clause #14 (by clausification #[12]): ∀ (a a_1 : Iota) (a_2 : Prop), Eq (skS.0 2 a a_1 a_2) False
% 3.74/3.93 Clause #15 (by clausification #[13]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), Eq (in (skS.0 1 a a_1) a_2 → in a_2 (skS.0 0 a) → skS.0 2 a a_1 a_3) True
% 3.74/3.93 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop),
% 3.74/3.93 Or (Eq (in (skS.0 1 a a_1) a_2) False) (Eq (in a_2 (skS.0 0 a) → skS.0 2 a a_1 a_3) True)
% 3.74/3.93 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop),
% 3.74/3.93 Or (Eq (in (skS.0 1 a a_1) a_2) False) (Or (Eq (in a_2 (skS.0 0 a)) False) (Eq (skS.0 2 a a_1 a_3) True))
% 3.74/3.93 Clause #18 (by identity loobHoist #[17]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop),
% 3.74/3.93 Or (Eq (in (skS.0 1 a a_1) a_2) False)
% 3.74/3.93 (Or (Eq (in a_2 (skS.0 0 a)) False) (Or (Eq (skS.0 2 a a_1 True) True) (Eq a_3 False)))
% 3.74/3.93 Clause #21 (by identity loobHoist #[14]): ∀ (a a_1 : Iota) (a_2 : Prop), Or (Eq (skS.0 2 a a_1 True) False) (Eq a_2 False)
% 3.74/3.93 Clause #23 (by clausification #[0]): Eq setunionAx (∀ (A Xx : Iota), Iff (in Xx (setunion A)) (Exists fun B => And (in Xx B) (in B A)))
% 3.74/3.93 Clause #24 (by forward demodulation #[23, 3]): Eq True (∀ (A Xx : Iota), Iff (in Xx (setunion A)) (Exists fun B => And (in Xx B) (in B A)))
% 3.74/3.93 Clause #25 (by clausification #[24]): ∀ (a : Iota), Eq (∀ (Xx : Iota), Iff (in Xx (setunion a)) (Exists fun B => And (in Xx B) (in B a))) True
% 3.74/3.93 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (Iff (in a (setunion a_1)) (Exists fun B => And (in a B) (in B a_1))) True
% 3.74/3.93 Clause #28 (by clausification #[26]): ∀ (a a_1 : Iota), Or (Eq (in a (setunion a_1)) False) (Eq (Exists fun B => And (in a B) (in B a_1)) True)
% 3.74/3.94 Clause #32 (by clausification #[28]): ∀ (a a_1 a_2 : Iota),
% 3.74/3.94 Or (Eq (in a (setunion a_1)) False) (Eq (And (in a (skS.0 3 a a_1 a_2)) (in (skS.0 3 a a_1 a_2) a_1)) True)
% 3.74/3.94 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setunion a_1)) False) (Eq (in (skS.0 3 a a_1 a_2) a_1) True)
% 3.74/3.94 Clause #34 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setunion a_1)) False) (Eq (in a (skS.0 3 a a_1 a_2)) True)
% 3.74/3.94 Clause #35 (by superposition #[33, 9]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 3 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) True) (Eq False True)
% 3.74/3.94 Clause #36 (by superposition #[34, 9]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 1 a a_1) (skS.0 3 (skS.0 1 a a_1) (skS.0 0 a) a_2)) True) (Eq False True)
% 3.74/3.94 Clause #39 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 3 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) True
% 3.74/3.94 Clause #43 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 1 a a_1) (skS.0 3 (skS.0 1 a a_1) (skS.0 0 a) a_2)) True
% 3.74/3.94 Clause #44 (by superposition #[43, 18]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop),
% 3.74/3.94 Or (Eq True False)
% 3.74/3.94 (Or (Eq (in (skS.0 3 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) False)
% 3.74/3.94 (Or (Eq (skS.0 2 a a_1 True) True) (Eq a_3 False)))
% 3.74/3.94 Clause #50 (by clausification #[44]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop),
% 3.74/3.94 Or (Eq (in (skS.0 3 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) False)
% 3.74/3.94 (Or (Eq (skS.0 2 a a_1 True) True) (Eq a_3 False))
% 3.74/3.94 Clause #51 (by superposition #[50, 39]): ∀ (a a_1 : Iota) (a_2 : Prop), Or (Eq (skS.0 2 a a_1 True) True) (Or (Eq a_2 False) (Eq False True))
% 3.74/3.94 Clause #52 (by clausification #[51]): ∀ (a a_1 : Iota) (a_2 : Prop), Or (Eq (skS.0 2 a a_1 True) True) (Eq a_2 False)
% 3.74/3.94 Clause #54 (by falseElim #[52]): ∀ (a a_1 : Iota), Eq (skS.0 2 a a_1 True) True
% 3.74/3.94 Clause #55 (by superposition #[54, 21]): ∀ (a : Prop), Or (Eq True False) (Eq a False)
% 3.74/3.94 Clause #56 (by clausification #[55]): ∀ (a : Prop), Eq a False
% 3.74/3.94 Clause #58 (by falseElim #[56]): False
% 3.74/3.94 SZS output end Proof for theBenchmark.p
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