TSTP Solution File: SET200^5 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET200^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n028.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 14:46:01 EDT 2023
% Result : Theorem 3.70s 3.89s
% Output : Proof 3.70s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET200^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : duper %s
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 12:19:22 EDT 2023
% 0.12/0.34 % CPUTime :
% 3.70/3.89 SZS status Theorem for theBenchmark.p
% 3.70/3.89 SZS output start Proof for theBenchmark.p
% 3.70/3.89 Clause #0 (by assumption #[]): Eq
% 3.70/3.89 (Not
% 3.70/3.89 (∀ (X Y Z V : a → Prop),
% 3.70/3.89 And (∀ (Xx : a), X Xx → Y Xx) (∀ (Xx : a), Z Xx → V Xx) → ∀ (Xx : a), Or (X Xx) (Z Xx) → Or (Y Xx) (V Xx)))
% 3.70/3.89 True
% 3.70/3.89 Clause #1 (by clausification #[0]): Eq
% 3.70/3.89 (∀ (X Y Z V : a → Prop),
% 3.70/3.89 And (∀ (Xx : a), X Xx → Y Xx) (∀ (Xx : a), Z Xx → V Xx) → ∀ (Xx : a), Or (X Xx) (Z Xx) → Or (Y Xx) (V Xx))
% 3.70/3.89 False
% 3.70/3.89 Clause #2 (by clausification #[1]): ∀ (a_1 : a → Prop),
% 3.70/3.89 Eq
% 3.70/3.89 (Not
% 3.70/3.89 (∀ (Y Z V : a → Prop),
% 3.70/3.89 And (∀ (Xx : a), skS.0 0 a_1 Xx → Y Xx) (∀ (Xx : a), Z Xx → V Xx) →
% 3.70/3.89 ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (Z Xx) → Or (Y Xx) (V Xx)))
% 3.70/3.89 True
% 3.70/3.89 Clause #3 (by clausification #[2]): ∀ (a_1 : a → Prop),
% 3.70/3.89 Eq
% 3.70/3.89 (∀ (Y Z V : a → Prop),
% 3.70/3.89 And (∀ (Xx : a), skS.0 0 a_1 Xx → Y Xx) (∀ (Xx : a), Z Xx → V Xx) →
% 3.70/3.89 ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (Z Xx) → Or (Y Xx) (V Xx))
% 3.70/3.89 False
% 3.70/3.89 Clause #4 (by clausification #[3]): ∀ (a_1 a_2 : a → Prop),
% 3.70/3.89 Eq
% 3.70/3.89 (Not
% 3.70/3.89 (∀ (Z V : a → Prop),
% 3.70/3.89 And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) (∀ (Xx : a), Z Xx → V Xx) →
% 3.70/3.89 ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (Z Xx) → Or (skS.0 1 a_1 a_2 Xx) (V Xx)))
% 3.70/3.89 True
% 3.70/3.89 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : a → Prop),
% 3.70/3.89 Eq
% 3.70/3.89 (∀ (Z V : a → Prop),
% 3.70/3.89 And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) (∀ (Xx : a), Z Xx → V Xx) →
% 3.70/3.89 ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (Z Xx) → Or (skS.0 1 a_1 a_2 Xx) (V Xx))
% 3.70/3.89 False
% 3.70/3.89 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 a_3 : a → Prop),
% 3.70/3.89 Eq
% 3.70/3.89 (Not
% 3.70/3.89 (∀ (V : a → Prop),
% 3.70/3.89 And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) (∀ (Xx : a), skS.0 2 a_1 a_2 a_3 Xx → V Xx) →
% 3.70/3.89 ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx) → Or (skS.0 1 a_1 a_2 Xx) (V Xx)))
% 3.70/3.89 True
% 3.70/3.89 Clause #7 (by clausification #[6]): ∀ (a_1 a_2 a_3 : a → Prop),
% 3.70/3.89 Eq
% 3.70/3.89 (∀ (V : a → Prop),
% 3.70/3.89 And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) (∀ (Xx : a), skS.0 2 a_1 a_2 a_3 Xx → V Xx) →
% 3.70/3.89 ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx) → Or (skS.0 1 a_1 a_2 Xx) (V Xx))
% 3.70/3.89 False
% 3.70/3.89 Clause #8 (by clausification #[7]): ∀ (a_1 a_2 a_3 a_4 : a → Prop),
% 3.70/3.89 Eq
% 3.70/3.89 (Not
% 3.70/3.89 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx)
% 3.70/3.89 (∀ (Xx : a), skS.0 2 a_1 a_2 a_3 Xx → skS.0 3 a_1 a_2 a_3 a_4 Xx) →
% 3.70/3.89 ∀ (Xx : a),
% 3.70/3.89 Or (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx) → Or (skS.0 1 a_1 a_2 Xx) (skS.0 3 a_1 a_2 a_3 a_4 Xx)))
% 3.70/3.89 True
% 3.70/3.89 Clause #9 (by clausification #[8]): ∀ (a_1 a_2 a_3 a_4 : a → Prop),
% 3.70/3.89 Eq
% 3.70/3.89 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx)
% 3.70/3.89 (∀ (Xx : a), skS.0 2 a_1 a_2 a_3 Xx → skS.0 3 a_1 a_2 a_3 a_4 Xx) →
% 3.70/3.89 ∀ (Xx : a), Or (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx) → Or (skS.0 1 a_1 a_2 Xx) (skS.0 3 a_1 a_2 a_3 a_4 Xx))
% 3.70/3.89 False
% 3.70/3.89 Clause #10 (by clausification #[9]): ∀ (a_1 a_2 a_3 a_4 : a → Prop),
% 3.70/3.89 Eq
% 3.70/3.89 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx)
% 3.70/3.89 (∀ (Xx : a), skS.0 2 a_1 a_2 a_3 Xx → skS.0 3 a_1 a_2 a_3 a_4 Xx))
% 3.70/3.89 True
% 3.70/3.89 Clause #11 (by clausification #[9]): ∀ (a_1 a_2 a_3 a_4 : a → Prop),
% 3.70/3.89 Eq (∀ (Xx : a), Or (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx) → Or (skS.0 1 a_1 a_2 Xx) (skS.0 3 a_1 a_2 a_3 a_4 Xx))
% 3.70/3.89 False
% 3.70/3.89 Clause #12 (by clausification #[10]): ∀ (a_1 a_2 a_3 a_4 : a → Prop), Eq (∀ (Xx : a), skS.0 2 a_1 a_2 a_3 Xx → skS.0 3 a_1 a_2 a_3 a_4 Xx) True
% 3.70/3.89 Clause #13 (by clausification #[10]): ∀ (a_1 a_2 : a → Prop), Eq (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) True
% 3.70/3.89 Clause #14 (by clausification #[12]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), Eq (skS.0 2 a_1 a_2 a_3 a_4 → skS.0 3 a_1 a_2 a_3 a_5 a_4) True
% 3.70/3.89 Clause #15 (by clausification #[14]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 3.70/3.89 Or (Eq (skS.0 2 a_1 a_2 a_3 a_4) False) (Eq (skS.0 3 a_1 a_2 a_3 a_5 a_4) True)
% 3.70/3.89 Clause #16 (by clausification #[13]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop), Eq (skS.0 0 a_1 a_2 → skS.0 1 a_1 a_3 a_2) True
% 3.70/3.91 Clause #17 (by clausification #[16]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop), Or (Eq (skS.0 0 a_1 a_2) False) (Eq (skS.0 1 a_1 a_3 a_2) True)
% 3.70/3.91 Clause #18 (by clausification #[11]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a),
% 3.70/3.91 Eq
% 3.70/3.91 (Not
% 3.70/3.91 (Or (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) →
% 3.70/3.91 Or (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 4 a_1 a_2 a_3 a_4 a_5))))
% 3.70/3.91 True
% 3.70/3.91 Clause #19 (by clausification #[18]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a),
% 3.70/3.91 Eq
% 3.70/3.91 (Or (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) →
% 3.70/3.91 Or (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 4 a_1 a_2 a_3 a_4 a_5)))
% 3.70/3.91 False
% 3.70/3.91 Clause #20 (by clausification #[19]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a),
% 3.70/3.91 Eq (Or (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5))) True
% 3.70/3.91 Clause #21 (by clausification #[19]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a),
% 3.70/3.91 Eq (Or (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 4 a_1 a_2 a_3 a_4 a_5))) False
% 3.70/3.91 Clause #22 (by clausification #[20]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a),
% 3.70/3.91 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) True) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) True)
% 3.70/3.91 Clause #23 (by superposition #[22, 15]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 : a → Prop),
% 3.70/3.91 Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 4 (fun x => a_1 x) (fun x => a_2 x) (fun x => a_3 x) a_4 a_5)) True)
% 3.70/3.91 (Or (Eq True False) (Eq (skS.0 3 a_1 a_2 a_3 a_6 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) True))
% 3.70/3.91 Clause #24 (by clausification #[21]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) False
% 3.70/3.91 Clause #25 (by clausification #[21]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) False
% 3.70/3.91 Clause #26 (by betaEtaReduce #[23]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 : a → Prop),
% 3.70/3.91 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) True)
% 3.70/3.91 (Or (Eq True False) (Eq (skS.0 3 a_1 a_2 a_3 a_6 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) True))
% 3.70/3.91 Clause #27 (by clausification #[26]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 : a → Prop),
% 3.70/3.91 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) True)
% 3.70/3.91 (Eq (skS.0 3 a_1 a_2 a_3 a_6 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) True)
% 3.70/3.91 Clause #28 (by superposition #[27, 24]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a),
% 3.70/3.91 Or
% 3.70/3.91 (Eq (skS.0 0 (fun x => a_1 x) (skS.0 4 (fun x => a_1 x) (fun x => a_2 x) (fun x => a_3 x) (fun x => a_4 x) a_5))
% 3.70/3.91 True)
% 3.70/3.91 (Eq True False)
% 3.70/3.91 Clause #29 (by betaEtaReduce #[28]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) True) (Eq True False)
% 3.70/3.91 Clause #30 (by clausification #[29]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) True
% 3.70/3.91 Clause #33 (by superposition #[30, 17]): ∀ (a_1 a_2 a_3 a_4 a_5 : a → Prop) (a_6 : a),
% 3.70/3.91 Or (Eq True False) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5 a_6)) True)
% 3.70/3.91 Clause #34 (by clausification #[33]): ∀ (a_1 a_2 a_3 a_4 a_5 : a → Prop) (a_6 : a), Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5 a_6)) True
% 3.70/3.91 Clause #35 (by superposition #[34, 25]): Eq True False
% 3.70/3.91 Clause #36 (by clausification #[35]): False
% 3.70/3.91 SZS output end Proof for theBenchmark.p
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