TSTP Solution File: SEU633^2 by Duper---1.0
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% File : Duper---1.0
% Problem : SEU633^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n001.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 16:43:06 EDT 2023
% Result : Theorem 3.80s 4.01s
% Output : Proof 3.87s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU633^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : duper %s
% 0.15/0.38 % Computer : n001.cluster.edu
% 0.15/0.38 % Model : x86_64 x86_64
% 0.15/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38 % Memory : 8042.1875MB
% 0.15/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38 % CPULimit : 300
% 0.15/0.38 % WCLimit : 300
% 0.15/0.38 % DateTime : Wed Aug 23 18:10:25 EDT 2023
% 0.15/0.38 % CPUTime :
% 3.80/4.01 SZS status Theorem for theBenchmark.p
% 3.80/4.01 SZS output start Proof for theBenchmark.p
% 3.80/4.01 Clause #0 (by assumption #[]): Eq
% 3.80/4.01 (Eq setunionE (∀ (A Xx : Iota), in Xx (setunion A) → ∀ (Xphi : Prop), (∀ (B : Iota), in Xx B → in B A → Xphi) → Xphi))
% 3.80/4.01 True
% 3.80/4.01 Clause #1 (by assumption #[]): Eq (Not (setunionE → ∀ (A Xx : Iota), in Xx (setunion A) → Exists fun X => And (in X A) (in Xx X))) True
% 3.80/4.01 Clause #2 (by clausification #[0]): Eq setunionE (∀ (A Xx : Iota), in Xx (setunion A) → ∀ (Xphi : Prop), (∀ (B : Iota), in Xx B → in B A → Xphi) → Xphi)
% 3.80/4.01 Clause #33 (by clausification #[1]): Eq (setunionE → ∀ (A Xx : Iota), in Xx (setunion A) → Exists fun X => And (in X A) (in Xx X)) False
% 3.80/4.01 Clause #34 (by clausification #[33]): Eq setunionE True
% 3.80/4.01 Clause #35 (by clausification #[33]): Eq (∀ (A Xx : Iota), in Xx (setunion A) → Exists fun X => And (in X A) (in Xx X)) False
% 3.80/4.01 Clause #36 (by backward demodulation #[34, 2]): Eq True (∀ (A Xx : Iota), in Xx (setunion A) → ∀ (Xphi : Prop), (∀ (B : Iota), in Xx B → in B A → Xphi) → Xphi)
% 3.80/4.01 Clause #39 (by clausification #[36]): ∀ (a : Iota),
% 3.80/4.01 Eq (∀ (Xx : Iota), in Xx (setunion a) → ∀ (Xphi : Prop), (∀ (B : Iota), in Xx B → in B a → Xphi) → Xphi) True
% 3.80/4.01 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), Eq (in a (setunion a_1) → ∀ (Xphi : Prop), (∀ (B : Iota), in a B → in B a_1 → Xphi) → Xphi) True
% 3.80/4.01 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota),
% 3.80/4.01 Or (Eq (in a (setunion a_1)) False) (Eq (∀ (Xphi : Prop), (∀ (B : Iota), in a B → in B a_1 → Xphi) → Xphi) True)
% 3.80/4.01 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota) (a_2 : Prop),
% 3.80/4.01 Or (Eq (in a (setunion a_1)) False) (Eq ((∀ (B : Iota), in a B → in B a_1 → a_2) → a_2) True)
% 3.80/4.01 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota) (a_2 : Prop),
% 3.80/4.01 Or (Eq (in a (setunion a_1)) False) (Or (Eq (∀ (B : Iota), in a B → in B a_1 → a_2) False) (Eq a_2 True))
% 3.80/4.01 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota) (a_2 : Prop) (a_3 : Iota),
% 3.80/4.01 Or (Eq (in a (setunion a_1)) False)
% 3.80/4.01 (Or (Eq a_2 True) (Eq (Not (in a (skS.0 4 a a_1 a_2 a_3) → in (skS.0 4 a a_1 a_2 a_3) a_1 → a_2)) True))
% 3.80/4.01 Clause #45 (by clausification #[44]): ∀ (a a_1 : Iota) (a_2 : Prop) (a_3 : Iota),
% 3.80/4.01 Or (Eq (in a (setunion a_1)) False)
% 3.80/4.01 (Or (Eq a_2 True) (Eq (in a (skS.0 4 a a_1 a_2 a_3) → in (skS.0 4 a a_1 a_2 a_3) a_1 → a_2) False))
% 3.80/4.01 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota) (a_2 : Prop) (a_3 : Iota),
% 3.80/4.01 Or (Eq (in a (setunion a_1)) False) (Or (Eq a_2 True) (Eq (in a (skS.0 4 a a_1 a_2 a_3)) True))
% 3.80/4.01 Clause #47 (by clausification #[45]): ∀ (a a_1 : Iota) (a_2 : Prop) (a_3 : Iota),
% 3.80/4.01 Or (Eq (in a (setunion a_1)) False) (Or (Eq a_2 True) (Eq (in (skS.0 4 a a_1 a_2 a_3) a_1 → a_2) False))
% 3.80/4.01 Clause #49 (by identity boolHoist #[46]): ∀ (a a_1 : Iota) (a_2 : Prop) (a_3 : Iota),
% 3.80/4.01 Or (Eq (in a (setunion a_1)) False) (Or (Eq a_2 True) (Or (Eq (in a (skS.0 4 a a_1 False a_3)) True) (Eq a_2 True)))
% 3.80/4.01 Clause #50 (by clausification #[47]): ∀ (a a_1 : Iota) (a_2 : Prop) (a_3 : Iota),
% 3.80/4.01 Or (Eq (in a (setunion a_1)) False) (Or (Eq a_2 True) (Eq (in (skS.0 4 a a_1 a_2 a_3) a_1) True))
% 3.80/4.01 Clause #53 (by identity boolHoist #[50]): ∀ (a a_1 : Iota) (a_2 : Prop) (a_3 : Iota),
% 3.80/4.01 Or (Eq (in a (setunion a_1)) False) (Or (Eq a_2 True) (Or (Eq (in (skS.0 4 a a_1 False a_3) a_1) True) (Eq a_2 True)))
% 3.80/4.01 Clause #64 (by clausification #[35]): ∀ (a : Iota),
% 3.80/4.01 Eq (Not (∀ (Xx : Iota), in Xx (setunion (skS.0 5 a)) → Exists fun X => And (in X (skS.0 5 a)) (in Xx X))) True
% 3.80/4.01 Clause #65 (by clausification #[64]): ∀ (a : Iota), Eq (∀ (Xx : Iota), in Xx (setunion (skS.0 5 a)) → Exists fun X => And (in X (skS.0 5 a)) (in Xx X)) False
% 3.80/4.01 Clause #66 (by clausification #[65]): ∀ (a a_1 : Iota),
% 3.80/4.01 Eq (Not (in (skS.0 6 a a_1) (setunion (skS.0 5 a)) → Exists fun X => And (in X (skS.0 5 a)) (in (skS.0 6 a a_1) X)))
% 3.80/4.01 True
% 3.80/4.01 Clause #67 (by clausification #[66]): ∀ (a a_1 : Iota),
% 3.80/4.01 Eq (in (skS.0 6 a a_1) (setunion (skS.0 5 a)) → Exists fun X => And (in X (skS.0 5 a)) (in (skS.0 6 a a_1) X)) False
% 3.87/4.03 Clause #68 (by clausification #[67]): ∀ (a a_1 : Iota), Eq (in (skS.0 6 a a_1) (setunion (skS.0 5 a))) True
% 3.87/4.03 Clause #69 (by clausification #[67]): ∀ (a a_1 : Iota), Eq (Exists fun X => And (in X (skS.0 5 a)) (in (skS.0 6 a a_1) X)) False
% 3.87/4.03 Clause #71 (by clausification #[69]): ∀ (a a_1 a_2 : Iota), Eq (And (in a (skS.0 5 a_1)) (in (skS.0 6 a_1 a_2) a)) False
% 3.87/4.03 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 5 a_1)) False) (Eq (in (skS.0 6 a_1 a_2) a) False)
% 3.87/4.03 Clause #73 (by eliminate duplicate literals #[53]): ∀ (a a_1 : Iota) (a_2 : Prop) (a_3 : Iota),
% 3.87/4.03 Or (Eq (in a (setunion a_1)) False) (Or (Eq a_2 True) (Eq (in (skS.0 4 a a_1 False a_3) a_1) True))
% 3.87/4.03 Clause #74 (by superposition #[73, 68]): ∀ (a : Prop) (a_1 a_2 a_3 : Iota),
% 3.87/4.03 Or (Eq a True) (Or (Eq (in (skS.0 4 (skS.0 6 a_1 a_2) (skS.0 5 a_1) False a_3) (skS.0 5 a_1)) True) (Eq False True))
% 3.87/4.03 Clause #78 (by eliminate duplicate literals #[49]): ∀ (a a_1 : Iota) (a_2 : Prop) (a_3 : Iota),
% 3.87/4.03 Or (Eq (in a (setunion a_1)) False) (Or (Eq a_2 True) (Eq (in a (skS.0 4 a a_1 False a_3)) True))
% 3.87/4.03 Clause #79 (by superposition #[78, 68]): ∀ (a : Prop) (a_1 a_2 a_3 : Iota),
% 3.87/4.03 Or (Eq a True)
% 3.87/4.03 (Or (Eq (in (skS.0 6 a_1 a_2) (skS.0 4 (skS.0 6 a_1 a_2) (skS.0 5 a_1) False a_3)) True) (Eq False True))
% 3.87/4.03 Clause #83 (by clausification #[74]): ∀ (a : Prop) (a_1 a_2 a_3 : Iota),
% 3.87/4.03 Or (Eq a True) (Eq (in (skS.0 4 (skS.0 6 a_1 a_2) (skS.0 5 a_1) False a_3) (skS.0 5 a_1)) True)
% 3.87/4.03 Clause #91 (by equality factoring #[83]): ∀ (a a_1 a_2 : Iota), Or (Ne True True) (Eq (in (skS.0 4 (skS.0 6 a a_1) (skS.0 5 a) False a_2) (skS.0 5 a)) True)
% 3.87/4.03 Clause #100 (by clausification #[91]): ∀ (a a_1 a_2 : Iota),
% 3.87/4.03 Or (Eq (in (skS.0 4 (skS.0 6 a a_1) (skS.0 5 a) False a_2) (skS.0 5 a)) True) (Or (Eq True False) (Eq True False))
% 3.87/4.03 Clause #102 (by clausification #[100]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 4 (skS.0 6 a a_1) (skS.0 5 a) False a_2) (skS.0 5 a)) True) (Eq True False)
% 3.87/4.03 Clause #103 (by clausification #[102]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 4 (skS.0 6 a a_1) (skS.0 5 a) False a_2) (skS.0 5 a)) True
% 3.87/4.03 Clause #104 (by superposition #[103, 72]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.87/4.03 Or (Eq True False) (Eq (in (skS.0 6 a a_1) (skS.0 4 (skS.0 6 a a_2) (skS.0 5 a) False a_3)) False)
% 3.87/4.03 Clause #105 (by clausification #[104]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 6 a a_1) (skS.0 4 (skS.0 6 a a_2) (skS.0 5 a) False a_3)) False
% 3.87/4.03 Clause #120 (by clausification #[79]): ∀ (a : Prop) (a_1 a_2 a_3 : Iota),
% 3.87/4.03 Or (Eq a True) (Eq (in (skS.0 6 a_1 a_2) (skS.0 4 (skS.0 6 a_1 a_2) (skS.0 5 a_1) False a_3)) True)
% 3.87/4.03 Clause #127 (by superposition #[120, 105]): ∀ (a : Prop), Or (Eq a True) (Eq True False)
% 3.87/4.03 Clause #130 (by clausification #[127]): ∀ (a : Prop), Eq a True
% 3.87/4.03 Clause #133 (by falseElim #[130]): False
% 3.87/4.03 SZS output end Proof for theBenchmark.p
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