TSTP Solution File: SET014^5 by Duper---1.0
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% File : Duper---1.0
% Problem : SET014^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n021.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 14:45:01 EDT 2023
% Result : Theorem 3.49s 3.78s
% Output : Proof 3.49s
% 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 : SET014^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : duper %s
% 0.15/0.35 % Computer : n021.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat Aug 26 09:59:12 EDT 2023
% 0.15/0.36 % CPUTime :
% 3.49/3.78 SZS status Theorem for theBenchmark.p
% 3.49/3.78 SZS output start Proof for theBenchmark.p
% 3.49/3.78 Clause #0 (by assumption #[]): Eq
% 3.49/3.78 (Not
% 3.49/3.78 (∀ (X Y Z : a → Prop),
% 3.49/3.78 And (∀ (Xx : a), X Xx → Z Xx) (∀ (Xx : a), Y Xx → Z Xx) → ∀ (Xx : a), Or (X Xx) (Y Xx) → Z Xx))
% 3.49/3.78 True
% 3.49/3.78 Clause #1 (by clausification #[0]): Eq (∀ (X Y Z : a → Prop), And (∀ (Xx : a), X Xx → Z Xx) (∀ (Xx : a), Y Xx → Z Xx) → ∀ (Xx : a), Or (X Xx) (Y Xx) → Z Xx)
% 3.49/3.78 False
% 3.49/3.78 Clause #2 (by clausification #[1]): ∀ (a_1 : a → Prop),
% 3.49/3.78 Eq
% 3.49/3.78 (Not
% 3.49/3.78 (∀ (Y Z : a → Prop),
% 3.49/3.78 And (∀ (Xx : a), skS.0 0 a_1 Xx → Z Xx) (∀ (Xx : a), Y Xx → Z Xx) →
% 3.49/3.78 ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (Y Xx) → Z Xx))
% 3.49/3.78 True
% 3.49/3.78 Clause #3 (by clausification #[2]): ∀ (a_1 : a → Prop),
% 3.49/3.78 Eq
% 3.49/3.78 (∀ (Y Z : a → Prop),
% 3.49/3.78 And (∀ (Xx : a), skS.0 0 a_1 Xx → Z Xx) (∀ (Xx : a), Y Xx → Z Xx) → ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (Y Xx) → Z Xx)
% 3.49/3.78 False
% 3.49/3.78 Clause #4 (by clausification #[3]): ∀ (a_1 a_2 : a → Prop),
% 3.49/3.78 Eq
% 3.49/3.78 (Not
% 3.49/3.78 (∀ (Z : a → Prop),
% 3.49/3.78 And (∀ (Xx : a), skS.0 0 a_1 Xx → Z Xx) (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → Z Xx) →
% 3.49/3.78 ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (skS.0 1 a_1 a_2 Xx) → Z Xx))
% 3.49/3.78 True
% 3.49/3.78 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : a → Prop),
% 3.49/3.78 Eq
% 3.49/3.78 (∀ (Z : a → Prop),
% 3.49/3.78 And (∀ (Xx : a), skS.0 0 a_1 Xx → Z Xx) (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → Z Xx) →
% 3.49/3.78 ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (skS.0 1 a_1 a_2 Xx) → Z Xx)
% 3.49/3.78 False
% 3.49/3.78 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 a_3 : a → Prop),
% 3.49/3.78 Eq
% 3.49/3.78 (Not
% 3.49/3.78 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 2 a_1 a_2 a_3 Xx)
% 3.49/3.78 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx) →
% 3.49/3.78 ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (skS.0 1 a_1 a_2 Xx) → skS.0 2 a_1 a_2 a_3 Xx))
% 3.49/3.78 True
% 3.49/3.78 Clause #7 (by clausification #[6]): ∀ (a_1 a_2 a_3 : a → Prop),
% 3.49/3.78 Eq
% 3.49/3.78 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 2 a_1 a_2 a_3 Xx)
% 3.49/3.78 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx) →
% 3.49/3.78 ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (skS.0 1 a_1 a_2 Xx) → skS.0 2 a_1 a_2 a_3 Xx)
% 3.49/3.78 False
% 3.49/3.78 Clause #8 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop),
% 3.49/3.78 Eq
% 3.49/3.78 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 2 a_1 a_2 a_3 Xx)
% 3.49/3.78 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx))
% 3.49/3.78 True
% 3.49/3.78 Clause #9 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop), Eq (∀ (Xx : a), Or (skS.0 0 a_1 Xx) (skS.0 1 a_1 a_2 Xx) → skS.0 2 a_1 a_2 a_3 Xx) False
% 3.49/3.78 Clause #10 (by clausification #[8]): ∀ (a_1 a_2 a_3 : a → Prop), Eq (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx) True
% 3.49/3.78 Clause #11 (by clausification #[8]): ∀ (a_1 a_2 a_3 : a → Prop), Eq (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 2 a_1 a_2 a_3 Xx) True
% 3.49/3.78 Clause #12 (by clausification #[10]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop), Eq (skS.0 1 a_1 a_2 a_3 → skS.0 2 a_1 a_2 a_4 a_3) True
% 3.49/3.78 Clause #13 (by clausification #[12]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop),
% 3.49/3.78 Or (Eq (skS.0 1 a_1 a_2 a_3) False) (Eq (skS.0 2 a_1 a_2 a_4 a_3) True)
% 3.49/3.78 Clause #14 (by clausification #[9]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a),
% 3.49/3.78 Eq
% 3.49/3.78 (Not
% 3.49/3.78 (Or (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) →
% 3.49/3.78 skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)))
% 3.49/3.78 True
% 3.49/3.78 Clause #15 (by clausification #[14]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a),
% 3.49/3.78 Eq
% 3.49/3.78 (Or (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) →
% 3.49/3.78 skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4))
% 3.49/3.78 False
% 3.49/3.78 Clause #16 (by clausification #[15]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a),
% 3.49/3.78 Eq (Or (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4))) True
% 3.49/3.78 Clause #17 (by clausification #[15]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) False
% 3.49/3.78 Clause #18 (by clausification #[16]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a),
% 3.49/3.78 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 3.49/3.79 Clause #19 (by superposition #[18, 13]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 3.49/3.79 Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 3 (fun x => a_1 x) (fun x => a_2 x) a_3 a_4)) True)
% 3.49/3.79 (Or (Eq True False) (Eq (skS.0 2 a_1 a_2 a_5 (skS.0 3 a_1 a_2 a_3 a_4)) True))
% 3.49/3.79 Clause #20 (by clausification #[11]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop), Eq (skS.0 0 a_1 a_2 → skS.0 2 a_1 a_3 a_4 a_2) True
% 3.49/3.79 Clause #21 (by clausification #[20]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop), Or (Eq (skS.0 0 a_1 a_2) False) (Eq (skS.0 2 a_1 a_3 a_4 a_2) True)
% 3.49/3.79 Clause #22 (by betaEtaReduce #[19]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 3.49/3.79 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 3.49/3.79 (Or (Eq True False) (Eq (skS.0 2 a_1 a_2 a_5 (skS.0 3 a_1 a_2 a_3 a_4)) True))
% 3.49/3.79 Clause #23 (by clausification #[22]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 3.49/3.79 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 2 a_1 a_2 a_5 (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 3.49/3.79 Clause #24 (by superposition #[23, 17]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a),
% 3.49/3.79 Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 3 (fun x => a_1 x) (fun x => a_2 x) (fun x => a_3 x) a_4)) True)
% 3.49/3.79 (Eq True False)
% 3.49/3.79 Clause #25 (by betaEtaReduce #[24]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq True False)
% 3.49/3.79 Clause #26 (by clausification #[25]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True
% 3.49/3.79 Clause #29 (by superposition #[26, 21]): ∀ (a_1 a_2 a_3 a_4 a_5 : a → Prop) (a_6 : a),
% 3.49/3.79 Or (Eq True False) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_4 a_5 a_6)) True)
% 3.49/3.79 Clause #30 (by clausification #[29]): ∀ (a_1 a_2 a_3 a_4 a_5 : a → Prop) (a_6 : a), Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_4 a_5 a_6)) True
% 3.49/3.79 Clause #31 (by superposition #[30, 17]): Eq True False
% 3.49/3.79 Clause #32 (by clausification #[31]): False
% 3.49/3.79 SZS output end Proof for theBenchmark.p
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