TSTP Solution File: SEV055^5 by Duper---1.0
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% File : Duper---1.0
% Problem : SEV055^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n011.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 19:24:09 EDT 2023
% Result : Theorem 4.15s 4.30s
% Output : Proof 4.15s
% 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 : SEV055^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : duper %s
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 02:31:22 EDT 2023
% 0.14/0.34 % CPUTime :
% 4.15/4.30 SZS status Theorem for theBenchmark.p
% 4.15/4.30 SZS output start Proof for theBenchmark.p
% 4.15/4.30 Clause #0 (by assumption #[]): Eq
% 4.15/4.30 (Not
% 4.15/4.30 (∀ (R : a → a → Prop) (U : (a → Prop) → a),
% 4.15/4.30 And (∀ (Xx Xy Xz : a), And (R Xx Xy) (R Xy Xz) → R Xx Xz)
% 4.15/4.30 (∀ (Xs : a → Prop),
% 4.15/4.30 And (∀ (Xz : a), Xs Xz → R Xz (U Xs)) (∀ (Xj : a), (∀ (Xk : a), Xs Xk → R Xk Xj) → R (U Xs) Xj)) →
% 4.15/4.30 ∀ (Xf : a → a), (∀ (Xx Xy : a), R Xx Xy → R (Xf Xx) (Xf Xy)) → Exists fun Xw => R Xw (Xf Xw)))
% 4.15/4.30 True
% 4.15/4.30 Clause #1 (by clausification #[0]): Eq
% 4.15/4.30 (∀ (R : a → a → Prop) (U : (a → Prop) → a),
% 4.15/4.30 And (∀ (Xx Xy Xz : a), And (R Xx Xy) (R Xy Xz) → R Xx Xz)
% 4.15/4.30 (∀ (Xs : a → Prop),
% 4.15/4.30 And (∀ (Xz : a), Xs Xz → R Xz (U Xs)) (∀ (Xj : a), (∀ (Xk : a), Xs Xk → R Xk Xj) → R (U Xs) Xj)) →
% 4.15/4.30 ∀ (Xf : a → a), (∀ (Xx Xy : a), R Xx Xy → R (Xf Xx) (Xf Xy)) → Exists fun Xw => R Xw (Xf Xw))
% 4.15/4.30 False
% 4.15/4.30 Clause #2 (by clausification #[1]): ∀ (a_1 : a → a → Prop),
% 4.15/4.30 Eq
% 4.15/4.30 (Not
% 4.15/4.30 (∀ (U : (a → Prop) → a),
% 4.15/4.30 And (∀ (Xx Xy Xz : a), And (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xz) → skS.0 0 a_1 Xx Xz)
% 4.15/4.30 (∀ (Xs : a → Prop),
% 4.15/4.30 And (∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz (U Xs))
% 4.15/4.30 (∀ (Xj : a), (∀ (Xk : a), Xs Xk → skS.0 0 a_1 Xk Xj) → skS.0 0 a_1 (U Xs) Xj)) →
% 4.15/4.30 ∀ (Xf : a → a),
% 4.15/4.30 (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 (Xf Xx) (Xf Xy)) → Exists fun Xw => skS.0 0 a_1 Xw (Xf Xw)))
% 4.15/4.30 True
% 4.15/4.30 Clause #3 (by clausification #[2]): ∀ (a_1 : a → a → Prop),
% 4.15/4.30 Eq
% 4.15/4.30 (∀ (U : (a → Prop) → a),
% 4.15/4.30 And (∀ (Xx Xy Xz : a), And (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xz) → skS.0 0 a_1 Xx Xz)
% 4.15/4.30 (∀ (Xs : a → Prop),
% 4.15/4.30 And (∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz (U Xs))
% 4.15/4.30 (∀ (Xj : a), (∀ (Xk : a), Xs Xk → skS.0 0 a_1 Xk Xj) → skS.0 0 a_1 (U Xs) Xj)) →
% 4.15/4.30 ∀ (Xf : a → a),
% 4.15/4.30 (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 (Xf Xx) (Xf Xy)) → Exists fun Xw => skS.0 0 a_1 Xw (Xf Xw))
% 4.15/4.30 False
% 4.15/4.30 Clause #4 (by clausification #[3]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a),
% 4.15/4.30 Eq
% 4.15/4.30 (Not
% 4.15/4.30 (And (∀ (Xx Xy Xz : a), And (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xz) → skS.0 0 a_1 Xx Xz)
% 4.15/4.30 (∀ (Xs : a → Prop),
% 4.15/4.30 And (∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz (skS.0 1 a_1 a_2 Xs))
% 4.15/4.30 (∀ (Xj : a), (∀ (Xk : a), Xs Xk → skS.0 0 a_1 Xk Xj) → skS.0 0 a_1 (skS.0 1 a_1 a_2 Xs) Xj)) →
% 4.15/4.30 ∀ (Xf : a → a),
% 4.15/4.30 (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 (Xf Xx) (Xf Xy)) → Exists fun Xw => skS.0 0 a_1 Xw (Xf Xw)))
% 4.15/4.30 True
% 4.15/4.30 Clause #5 (by clausification #[4]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a),
% 4.15/4.30 Eq
% 4.15/4.30 (And (∀ (Xx Xy Xz : a), And (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xz) → skS.0 0 a_1 Xx Xz)
% 4.15/4.30 (∀ (Xs : a → Prop),
% 4.15/4.30 And (∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz (skS.0 1 a_1 a_2 Xs))
% 4.15/4.30 (∀ (Xj : a), (∀ (Xk : a), Xs Xk → skS.0 0 a_1 Xk Xj) → skS.0 0 a_1 (skS.0 1 a_1 a_2 Xs) Xj)) →
% 4.15/4.30 ∀ (Xf : a → a),
% 4.15/4.30 (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 (Xf Xx) (Xf Xy)) → Exists fun Xw => skS.0 0 a_1 Xw (Xf Xw))
% 4.15/4.30 False
% 4.15/4.30 Clause #6 (by clausification #[5]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a),
% 4.15/4.30 Eq
% 4.15/4.30 (And (∀ (Xx Xy Xz : a), And (skS.0 0 a_1 Xx Xy) (skS.0 0 a_1 Xy Xz) → skS.0 0 a_1 Xx Xz)
% 4.15/4.30 (∀ (Xs : a → Prop),
% 4.15/4.30 And (∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz (skS.0 1 a_1 a_2 Xs))
% 4.15/4.30 (∀ (Xj : a), (∀ (Xk : a), Xs Xk → skS.0 0 a_1 Xk Xj) → skS.0 0 a_1 (skS.0 1 a_1 a_2 Xs) Xj)))
% 4.15/4.30 True
% 4.15/4.30 Clause #7 (by clausification #[5]): ∀ (a_1 : a → a → Prop),
% 4.15/4.30 Eq
% 4.15/4.30 (∀ (Xf : a → a),
% 4.15/4.30 (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 (Xf Xx) (Xf Xy)) → Exists fun Xw => skS.0 0 a_1 Xw (Xf Xw))
% 4.15/4.30 False
% 4.15/4.30 Clause #8 (by clausification #[6]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a),
% 4.15/4.30 Eq
% 4.15/4.30 (∀ (Xs : a → Prop),
% 4.15/4.30 And (∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz (skS.0 1 a_1 a_2 Xs))
% 4.15/4.32 (∀ (Xj : a), (∀ (Xk : a), Xs Xk → skS.0 0 a_1 Xk Xj) → skS.0 0 a_1 (skS.0 1 a_1 a_2 Xs) Xj))
% 4.15/4.32 True
% 4.15/4.32 Clause #10 (by clausification #[8]): ∀ (a_1 : a → Prop) (a_2 : a → a → Prop) (a_3 : (a → Prop) → a),
% 4.15/4.32 Eq
% 4.15/4.32 (And (∀ (Xz : a), a_1 Xz → skS.0 0 a_2 Xz (skS.0 1 a_2 a_3 a_1))
% 4.15/4.32 (∀ (Xj : a), (∀ (Xk : a), a_1 Xk → skS.0 0 a_2 Xk Xj) → skS.0 0 a_2 (skS.0 1 a_2 a_3 a_1) Xj))
% 4.15/4.32 True
% 4.15/4.32 Clause #11 (by clausification #[10]): ∀ (a_1 : a → Prop) (a_2 : a → a → Prop) (a_3 : (a → Prop) → a),
% 4.15/4.32 Eq (∀ (Xj : a), (∀ (Xk : a), a_1 Xk → skS.0 0 a_2 Xk Xj) → skS.0 0 a_2 (skS.0 1 a_2 a_3 a_1) Xj) True
% 4.15/4.32 Clause #13 (by clausification #[11]): ∀ (a_1 : a → Prop) (a_2 : a → a → Prop) (a_3 : a) (a_4 : (a → Prop) → a),
% 4.15/4.32 Eq ((∀ (Xk : a), a_1 Xk → skS.0 0 a_2 Xk a_3) → skS.0 0 a_2 (skS.0 1 a_2 a_4 a_1) a_3) True
% 4.15/4.32 Clause #14 (by clausification #[13]): ∀ (a_1 : a → Prop) (a_2 : a → a → Prop) (a_3 : a) (a_4 : (a → Prop) → a),
% 4.15/4.32 Or (Eq (∀ (Xk : a), a_1 Xk → skS.0 0 a_2 Xk a_3) False) (Eq (skS.0 0 a_2 (skS.0 1 a_2 a_4 a_1) a_3) True)
% 4.15/4.32 Clause #15 (by clausification #[14]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a) (a_3 : a → Prop) (a_4 a_5 : a),
% 4.15/4.32 Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 a_3) a_4) True)
% 4.15/4.32 (Eq (Not (a_3 (skS.0 2 a_3 a_1 a_4 a_5) → skS.0 0 a_1 (skS.0 2 a_3 a_1 a_4 a_5) a_4)) True)
% 4.15/4.32 Clause #16 (by clausification #[15]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a) (a_3 : a → Prop) (a_4 a_5 : a),
% 4.15/4.32 Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 a_3) a_4) True)
% 4.15/4.32 (Eq (a_3 (skS.0 2 a_3 a_1 a_4 a_5) → skS.0 0 a_1 (skS.0 2 a_3 a_1 a_4 a_5) a_4) False)
% 4.15/4.32 Clause #17 (by clausification #[16]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a) (a_3 : a → Prop) (a_4 a_5 : a),
% 4.15/4.32 Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 a_3) a_4) True) (Eq (a_3 (skS.0 2 a_3 a_1 a_4 a_5)) True)
% 4.15/4.32 Clause #51 (by clausification #[7]): ∀ (a_1 : a → a → Prop) (a_2 : a → a),
% 4.15/4.32 Eq
% 4.15/4.32 (Not
% 4.15/4.32 ((∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 (skS.0 3 a_1 a_2 Xx) (skS.0 3 a_1 a_2 Xy)) →
% 4.15/4.32 Exists fun Xw => skS.0 0 a_1 Xw (skS.0 3 a_1 a_2 Xw)))
% 4.15/4.32 True
% 4.15/4.32 Clause #52 (by clausification #[51]): ∀ (a_1 : a → a → Prop) (a_2 : a → a),
% 4.15/4.32 Eq
% 4.15/4.32 ((∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → skS.0 0 a_1 (skS.0 3 a_1 a_2 Xx) (skS.0 3 a_1 a_2 Xy)) →
% 4.15/4.32 Exists fun Xw => skS.0 0 a_1 Xw (skS.0 3 a_1 a_2 Xw))
% 4.15/4.32 False
% 4.15/4.32 Clause #54 (by clausification #[52]): ∀ (a_1 : a → a → Prop) (a_2 : a → a), Eq (Exists fun Xw => skS.0 0 a_1 Xw (skS.0 3 a_1 a_2 Xw)) False
% 4.15/4.32 Clause #73 (by clausification #[54]): ∀ (a_1 : a → a → Prop) (a_2 : a) (a_3 : a → a), Eq (skS.0 0 a_1 a_2 (skS.0 3 a_1 a_3 a_2)) False
% 4.15/4.32 Clause #75 (by fluidSup #[73, 17]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a) (a_3 : Prop) (a_4 : a),
% 4.15/4.32 Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 fun x => a_3) a_4) True) (Eq ((fun _ => a_3) False) True)
% 4.15/4.32 Clause #84 (by betaEtaReduce #[75]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a) (a_3 : Prop) (a_4 : a),
% 4.15/4.32 Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 fun x => a_3) a_4) True) (Eq a_3 True)
% 4.15/4.32 Clause #85 (by superposition #[84, 73]): ∀ (a : Prop), Or (Eq a True) (Eq True False)
% 4.15/4.32 Clause #124 (by clausification #[85]): ∀ (a : Prop), Eq a True
% 4.15/4.32 Clause #126 (by falseElim #[124]): False
% 4.15/4.32 SZS output end Proof for theBenchmark.p
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