TSTP Solution File: SEU515^2 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU515^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n014.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 16:42:27 EDT 2023
% Result : Theorem 4.17s 4.35s
% Output : Proof 4.17s
% 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 : SEU515^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 19:03:04 EDT 2023
% 0.13/0.35 % CPUTime :
% 4.17/4.35 SZS status Theorem for theBenchmark.p
% 4.17/4.35 SZS output start Proof for theBenchmark.p
% 4.17/4.35 Clause #0 (by assumption #[]): Eq (Eq setadjoinAx (∀ (Xx A Xy : Iota), Iff (in Xy (setadjoin Xx A)) (Or (Eq Xy Xx) (in Xy A)))) True
% 4.17/4.35 Clause #1 (by assumption #[]): Eq
% 4.17/4.35 (Not
% 4.17/4.35 (setadjoinAx →
% 4.17/4.35 ∀ (Xx A Xy : Iota), in Xy (setadjoin Xx A) → ∀ (Xphi : Prop), (Eq Xy Xx → Xphi) → (in Xy A → Xphi) → Xphi))
% 4.17/4.35 True
% 4.17/4.35 Clause #2 (by clausification #[1]): Eq
% 4.17/4.35 (setadjoinAx →
% 4.17/4.35 ∀ (Xx A Xy : Iota), in Xy (setadjoin Xx A) → ∀ (Xphi : Prop), (Eq Xy Xx → Xphi) → (in Xy A → Xphi) → Xphi)
% 4.17/4.35 False
% 4.17/4.35 Clause #3 (by clausification #[2]): Eq setadjoinAx True
% 4.17/4.35 Clause #4 (by clausification #[2]): Eq (∀ (Xx A Xy : Iota), in Xy (setadjoin Xx A) → ∀ (Xphi : Prop), (Eq Xy Xx → Xphi) → (in Xy A → Xphi) → Xphi) False
% 4.17/4.35 Clause #5 (by clausification #[4]): ∀ (a : Iota),
% 4.17/4.35 Eq
% 4.17/4.35 (Not
% 4.17/4.35 (∀ (A Xy : Iota),
% 4.17/4.35 in Xy (setadjoin (skS.0 0 a) A) → ∀ (Xphi : Prop), (Eq Xy (skS.0 0 a) → Xphi) → (in Xy A → Xphi) → Xphi))
% 4.17/4.35 True
% 4.17/4.35 Clause #6 (by clausification #[5]): ∀ (a : Iota),
% 4.17/4.35 Eq
% 4.17/4.35 (∀ (A Xy : Iota),
% 4.17/4.35 in Xy (setadjoin (skS.0 0 a) A) → ∀ (Xphi : Prop), (Eq Xy (skS.0 0 a) → Xphi) → (in Xy A → Xphi) → Xphi)
% 4.17/4.35 False
% 4.17/4.35 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota),
% 4.17/4.35 Eq
% 4.17/4.35 (Not
% 4.17/4.35 (∀ (Xy : Iota),
% 4.17/4.35 in Xy (setadjoin (skS.0 0 a) (skS.0 1 a a_1)) →
% 4.17/4.35 ∀ (Xphi : Prop), (Eq Xy (skS.0 0 a) → Xphi) → (in Xy (skS.0 1 a a_1) → Xphi) → Xphi))
% 4.17/4.35 True
% 4.17/4.35 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota),
% 4.17/4.35 Eq
% 4.17/4.35 (∀ (Xy : Iota),
% 4.17/4.35 in Xy (setadjoin (skS.0 0 a) (skS.0 1 a a_1)) →
% 4.17/4.35 ∀ (Xphi : Prop), (Eq Xy (skS.0 0 a) → Xphi) → (in Xy (skS.0 1 a a_1) → Xphi) → Xphi)
% 4.17/4.35 False
% 4.17/4.35 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota),
% 4.17/4.35 Eq
% 4.17/4.35 (Not
% 4.17/4.35 (in (skS.0 2 a a_1 a_2) (setadjoin (skS.0 0 a) (skS.0 1 a a_1)) →
% 4.17/4.35 ∀ (Xphi : Prop),
% 4.17/4.35 (Eq (skS.0 2 a a_1 a_2) (skS.0 0 a) → Xphi) → (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1) → Xphi) → Xphi))
% 4.17/4.35 True
% 4.17/4.35 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota),
% 4.17/4.35 Eq
% 4.17/4.35 (in (skS.0 2 a a_1 a_2) (setadjoin (skS.0 0 a) (skS.0 1 a a_1)) →
% 4.17/4.35 ∀ (Xphi : Prop),
% 4.17/4.35 (Eq (skS.0 2 a a_1 a_2) (skS.0 0 a) → Xphi) → (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1) → Xphi) → Xphi)
% 4.17/4.35 False
% 4.17/4.35 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (setadjoin (skS.0 0 a) (skS.0 1 a a_1))) True
% 4.17/4.35 Clause #12 (by clausification #[10]): ∀ (a a_1 a_2 : Iota),
% 4.17/4.35 Eq
% 4.17/4.35 (∀ (Xphi : Prop),
% 4.17/4.35 (Eq (skS.0 2 a a_1 a_2) (skS.0 0 a) → Xphi) → (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1) → Xphi) → Xphi)
% 4.17/4.35 False
% 4.17/4.35 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop),
% 4.17/4.35 Eq
% 4.17/4.35 (Not
% 4.17/4.35 ((Eq (skS.0 2 a a_1 a_2) (skS.0 0 a) → skS.0 3 a a_1 a_2 a_3) →
% 4.17/4.35 (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1) → skS.0 3 a a_1 a_2 a_3) → skS.0 3 a a_1 a_2 a_3))
% 4.17/4.35 True
% 4.17/4.35 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop),
% 4.17/4.35 Eq
% 4.17/4.35 ((Eq (skS.0 2 a a_1 a_2) (skS.0 0 a) → skS.0 3 a a_1 a_2 a_3) →
% 4.17/4.35 (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1) → skS.0 3 a a_1 a_2 a_3) → skS.0 3 a a_1 a_2 a_3)
% 4.17/4.35 False
% 4.17/4.35 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), Eq (Eq (skS.0 2 a a_1 a_2) (skS.0 0 a) → skS.0 3 a a_1 a_2 a_3) True
% 4.17/4.35 Clause #16 (by clausification #[14]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop),
% 4.17/4.35 Eq ((in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1) → skS.0 3 a a_1 a_2 a_3) → skS.0 3 a a_1 a_2 a_3) False
% 4.17/4.35 Clause #17 (by clausification #[15]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), Or (Eq (Eq (skS.0 2 a a_1 a_2) (skS.0 0 a)) False) (Eq (skS.0 3 a a_1 a_2 a_3) True)
% 4.17/4.35 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), Or (Eq (skS.0 3 a a_1 a_2 a_3) True) (Ne (skS.0 2 a a_1 a_2) (skS.0 0 a))
% 4.17/4.35 Clause #20 (by identity boolHoist #[18]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop),
% 4.17/4.35 Or (Ne (skS.0 2 a a_1 a_2) (skS.0 0 a)) (Or (Eq (skS.0 3 a a_1 a_2 False) True) (Eq a_3 True))
% 4.17/4.35 Clause #21 (by clausification #[16]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1) → skS.0 3 a a_1 a_2 a_3) True
% 4.17/4.37 Clause #22 (by clausification #[16]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), Eq (skS.0 3 a a_1 a_2 a_3) False
% 4.17/4.37 Clause #23 (by clausification #[21]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop),
% 4.17/4.37 Or (Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) False) (Eq (skS.0 3 a a_1 a_2 a_3) True)
% 4.17/4.37 Clause #25 (by identity boolHoist #[23]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop),
% 4.17/4.37 Or (Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) False) (Or (Eq (skS.0 3 a a_1 a_2 False) True) (Eq a_3 True))
% 4.17/4.37 Clause #27 (by identity boolHoist #[22]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), Or (Eq (skS.0 3 a a_1 a_2 False) False) (Eq a_3 True)
% 4.17/4.37 Clause #28 (by clausification #[0]): Eq setadjoinAx (∀ (Xx A Xy : Iota), Iff (in Xy (setadjoin Xx A)) (Or (Eq Xy Xx) (in Xy A)))
% 4.17/4.37 Clause #29 (by forward demodulation #[28, 3]): Eq True (∀ (Xx A Xy : Iota), Iff (in Xy (setadjoin Xx A)) (Or (Eq Xy Xx) (in Xy A)))
% 4.17/4.37 Clause #30 (by clausification #[29]): ∀ (a : Iota), Eq (∀ (A Xy : Iota), Iff (in Xy (setadjoin a A)) (Or (Eq Xy a) (in Xy A))) True
% 4.17/4.37 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (∀ (Xy : Iota), Iff (in Xy (setadjoin a a_1)) (Or (Eq Xy a) (in Xy a_1))) True
% 4.17/4.37 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Eq (Iff (in a (setadjoin a_1 a_2)) (Or (Eq a a_1) (in a a_2))) True
% 4.17/4.37 Clause #34 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setadjoin a_1 a_2)) False) (Eq (Or (Eq a a_1) (in a a_2)) True)
% 4.17/4.37 Clause #47 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setadjoin a_1 a_2)) False) (Or (Eq (Eq a a_1) True) (Eq (in a a_2) True))
% 4.17/4.37 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setadjoin a_1 a_2)) False) (Or (Eq (in a a_2) True) (Eq a a_1))
% 4.17/4.37 Clause #49 (by superposition #[48, 11]): ∀ (a a_1 a_2 : Iota),
% 4.17/4.37 Or (Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True) (Or (Eq (skS.0 2 a a_1 a_2) (skS.0 0 a)) (Eq False True))
% 4.17/4.37 Clause #81 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True) (Eq (skS.0 2 a a_1 a_2) (skS.0 0 a))
% 4.17/4.37 Clause #83 (by superposition #[81, 25]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop),
% 4.17/4.37 Or (Eq (skS.0 2 a a_1 a_2) (skS.0 0 a)) (Or (Eq True False) (Or (Eq (skS.0 3 a a_1 a_2 False) True) (Eq a_3 True)))
% 4.17/4.37 Clause #102 (by clausification #[83]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop),
% 4.17/4.37 Or (Eq (skS.0 2 a a_1 a_2) (skS.0 0 a)) (Or (Eq (skS.0 3 a a_1 a_2 False) True) (Eq a_3 True))
% 4.17/4.37 Clause #103 (by forward contextual literal cutting #[102, 20]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), Or (Eq (skS.0 3 a a_1 a_2 False) True) (Eq a_3 True)
% 4.17/4.37 Clause #104 (by superposition #[103, 27]): ∀ (a a_1 : Prop), Or (Eq a True) (Or (Eq True False) (Eq a_1 True))
% 4.17/4.37 Clause #112 (by clausification #[104]): ∀ (a a_1 : Prop), Or (Eq a True) (Eq a_1 True)
% 4.17/4.37 Clause #121 (by falseElim #[112]): ∀ (a : Prop), Eq a True
% 4.17/4.37 Clause #126 (by falseElim #[121]): False
% 4.17/4.37 SZS output end Proof for theBenchmark.p
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