TSTP Solution File: SEU515^2 by Duper---1.0

View Problem - Process Solution

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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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