TSTP Solution File: SEV056^5 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEV056^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n004.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 11.05s 11.24s
% Output : Proof 11.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV056^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n004.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 03:16:23 EDT 2023
% 0.13/0.35 % CPUTime :
% 11.05/11.24 SZS status Theorem for theBenchmark.p
% 11.05/11.24 SZS output start Proof for theBenchmark.p
% 11.05/11.24 Clause #0 (by assumption #[]): Eq
% 11.05/11.24 (Not
% 11.05/11.24 (∀ (Xr : a → a → Prop),
% 11.05/11.24 Exists fun Xp =>
% 11.05/11.24 And (∀ (Xx Xy : a), Xr Xx Xy → Xp Xx Xy) (∀ (Xx Xy Xz : a), And (Xp Xx Xy) (Xp Xy Xz) → Xp Xx Xz)))
% 11.05/11.24 True
% 11.05/11.24 Clause #1 (by clausification #[0]): Eq
% 11.05/11.24 (∀ (Xr : a → a → Prop),
% 11.05/11.24 Exists fun Xp => And (∀ (Xx Xy : a), Xr Xx Xy → Xp Xx Xy) (∀ (Xx Xy Xz : a), And (Xp Xx Xy) (Xp Xy Xz) → Xp Xx Xz))
% 11.05/11.24 False
% 11.05/11.24 Clause #2 (by clausification #[1]): ∀ (a_1 : a → a → Prop),
% 11.05/11.24 Eq
% 11.05/11.24 (Not
% 11.05/11.24 (Exists fun Xp =>
% 11.05/11.24 And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → Xp Xx Xy) (∀ (Xx Xy Xz : a), And (Xp Xx Xy) (Xp Xy Xz) → Xp Xx Xz)))
% 11.05/11.24 True
% 11.05/11.24 Clause #3 (by clausification #[2]): ∀ (a_1 : a → a → Prop),
% 11.05/11.24 Eq
% 11.05/11.24 (Exists fun Xp =>
% 11.05/11.24 And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → Xp Xx Xy) (∀ (Xx Xy Xz : a), And (Xp Xx Xy) (Xp Xy Xz) → Xp Xx Xz))
% 11.05/11.24 False
% 11.05/11.24 Clause #4 (by clausification #[3]): ∀ (a_1 a_2 : a → a → Prop),
% 11.05/11.24 Eq (And (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → a_2 Xx Xy) (∀ (Xx Xy Xz : a), And (a_2 Xx Xy) (a_2 Xy Xz) → a_2 Xx Xz))
% 11.05/11.24 False
% 11.05/11.24 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : a → a → Prop),
% 11.05/11.24 Or (Eq (∀ (Xx Xy : a), skS.0 0 a_1 Xx Xy → a_2 Xx Xy) False)
% 11.05/11.24 (Eq (∀ (Xx Xy Xz : a), And (a_2 Xx Xy) (a_2 Xy Xz) → a_2 Xx Xz) False)
% 11.05/11.24 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 : a → a → Prop) (a_3 : a),
% 11.05/11.24 Or (Eq (∀ (Xx Xy Xz : a), And (a_1 Xx Xy) (a_1 Xy Xz) → a_1 Xx Xz) False)
% 11.05/11.24 (Eq (Not (∀ (Xy : a), skS.0 0 a_2 (skS.0 1 a_2 a_1 a_3) Xy → a_1 (skS.0 1 a_2 a_1 a_3) Xy)) True)
% 11.05/11.24 Clause #7 (by clausification #[6]): ∀ (a_1 a_2 : a → a → Prop) (a_3 a_4 : a),
% 11.05/11.24 Or (Eq (Not (∀ (Xy : a), skS.0 0 a_1 (skS.0 1 a_1 a_2 a_3) Xy → a_2 (skS.0 1 a_1 a_2 a_3) Xy)) True)
% 11.05/11.24 (Eq (Not (∀ (Xy Xz : a), And (a_2 (skS.0 2 a_2 a_4) Xy) (a_2 Xy Xz) → a_2 (skS.0 2 a_2 a_4) Xz)) True)
% 11.05/11.24 Clause #8 (by clausification #[7]): ∀ (a_1 : a → a → Prop) (a_2 : a) (a_3 : a → a → Prop) (a_4 : a),
% 11.05/11.24 Or (Eq (Not (∀ (Xy Xz : a), And (a_1 (skS.0 2 a_1 a_2) Xy) (a_1 Xy Xz) → a_1 (skS.0 2 a_1 a_2) Xz)) True)
% 11.05/11.24 (Eq (∀ (Xy : a), skS.0 0 a_3 (skS.0 1 a_3 a_1 a_4) Xy → a_1 (skS.0 1 a_3 a_1 a_4) Xy) False)
% 11.05/11.24 Clause #9 (by clausification #[8]): ∀ (a_1 a_2 : a → a → Prop) (a_3 a_4 : a),
% 11.05/11.24 Or (Eq (∀ (Xy : a), skS.0 0 a_1 (skS.0 1 a_1 a_2 a_3) Xy → a_2 (skS.0 1 a_1 a_2 a_3) Xy) False)
% 11.05/11.24 (Eq (∀ (Xy Xz : a), And (a_2 (skS.0 2 a_2 a_4) Xy) (a_2 Xy Xz) → a_2 (skS.0 2 a_2 a_4) Xz) False)
% 11.05/11.24 Clause #10 (by clausification #[9]): ∀ (a_1 : a → a → Prop) (a_2 : a) (a_3 : a → a → Prop) (a_4 a_5 : a),
% 11.05/11.24 Or (Eq (∀ (Xy Xz : a), And (a_1 (skS.0 2 a_1 a_2) Xy) (a_1 Xy Xz) → a_1 (skS.0 2 a_1 a_2) Xz) False)
% 11.05/11.24 (Eq
% 11.05/11.24 (Not
% 11.05/11.24 (skS.0 0 a_3 (skS.0 1 a_3 a_1 a_4) (skS.0 3 a_3 a_1 a_4 a_5) →
% 11.05/11.24 a_1 (skS.0 1 a_3 a_1 a_4) (skS.0 3 a_3 a_1 a_4 a_5)))
% 11.05/11.24 True)
% 11.05/11.24 Clause #11 (by clausification #[10]): ∀ (a_1 a_2 : a → a → Prop) (a_3 a_4 a_5 a_6 : a),
% 11.05/11.24 Or
% 11.05/11.24 (Eq
% 11.05/11.24 (Not
% 11.05/11.24 (skS.0 0 a_1 (skS.0 1 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4) →
% 11.05/11.24 a_2 (skS.0 1 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4)))
% 11.05/11.24 True)
% 11.05/11.24 (Eq
% 11.05/11.24 (Not
% 11.05/11.24 (∀ (Xz : a),
% 11.05/11.24 And (a_2 (skS.0 2 a_2 a_5) (skS.0 4 a_2 a_5 a_6)) (a_2 (skS.0 4 a_2 a_5 a_6) Xz) → a_2 (skS.0 2 a_2 a_5) Xz))
% 11.05/11.24 True)
% 11.05/11.24 Clause #12 (by clausification #[11]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → a → Prop) (a_5 a_6 : a),
% 11.05/11.24 Or
% 11.05/11.24 (Eq
% 11.05/11.24 (Not
% 11.05/11.24 (∀ (Xz : a),
% 11.05/11.24 And (a_1 (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3)) (a_1 (skS.0 4 a_1 a_2 a_3) Xz) → a_1 (skS.0 2 a_1 a_2) Xz))
% 11.05/11.24 True)
% 11.05/11.24 (Eq
% 11.05/11.24 (skS.0 0 a_4 (skS.0 1 a_4 a_1 a_5) (skS.0 3 a_4 a_1 a_5 a_6) →
% 11.05/11.24 a_1 (skS.0 1 a_4 a_1 a_5) (skS.0 3 a_4 a_1 a_5 a_6))
% 11.05/11.24 False)
% 11.05/11.24 Clause #13 (by clausification #[12]): ∀ (a_1 a_2 : a → a → Prop) (a_3 a_4 a_5 a_6 : a),
% 11.05/11.24 Or
% 11.05/11.24 (Eq
% 11.05/11.24 (skS.0 0 a_1 (skS.0 1 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4) →
% 11.05/11.24 a_2 (skS.0 1 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4))
% 11.05/11.27 False)
% 11.05/11.27 (Eq
% 11.05/11.27 (∀ (Xz : a),
% 11.05/11.27 And (a_2 (skS.0 2 a_2 a_5) (skS.0 4 a_2 a_5 a_6)) (a_2 (skS.0 4 a_2 a_5 a_6) Xz) → a_2 (skS.0 2 a_2 a_5) Xz)
% 11.05/11.27 False)
% 11.05/11.27 Clause #14 (by clausification #[13]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → a → Prop) (a_5 a_6 : a),
% 11.05/11.27 Or
% 11.05/11.27 (Eq
% 11.05/11.27 (∀ (Xz : a),
% 11.05/11.27 And (a_1 (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3)) (a_1 (skS.0 4 a_1 a_2 a_3) Xz) → a_1 (skS.0 2 a_1 a_2) Xz)
% 11.05/11.27 False)
% 11.05/11.27 (Eq (skS.0 0 a_4 (skS.0 1 a_4 a_1 a_5) (skS.0 3 a_4 a_1 a_5 a_6)) True)
% 11.05/11.27 Clause #15 (by clausification #[13]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → a → Prop) (a_5 a_6 : a),
% 11.05/11.27 Or
% 11.05/11.27 (Eq
% 11.05/11.27 (∀ (Xz : a),
% 11.05/11.27 And (a_1 (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3)) (a_1 (skS.0 4 a_1 a_2 a_3) Xz) → a_1 (skS.0 2 a_1 a_2) Xz)
% 11.05/11.27 False)
% 11.05/11.27 (Eq (a_1 (skS.0 1 a_4 a_1 a_5) (skS.0 3 a_4 a_1 a_5 a_6)) False)
% 11.05/11.27 Clause #16 (by clausification #[14]): ∀ (a_1 a_2 : a → a → Prop) (a_3 a_4 a_5 a_6 a_7 : a),
% 11.05/11.27 Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 11.05/11.27 (Eq
% 11.05/11.27 (Not
% 11.05/11.27 (And (a_2 (skS.0 2 a_2 a_5) (skS.0 4 a_2 a_5 a_6)) (a_2 (skS.0 4 a_2 a_5 a_6) (skS.0 5 a_2 a_5 a_6 a_7)) →
% 11.05/11.27 a_2 (skS.0 2 a_2 a_5) (skS.0 5 a_2 a_5 a_6 a_7)))
% 11.05/11.27 True)
% 11.05/11.27 Clause #17 (by clausification #[16]): ∀ (a_1 a_2 : a → a → Prop) (a_3 a_4 a_5 a_6 a_7 : a),
% 11.05/11.27 Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 11.05/11.27 (Eq
% 11.05/11.27 (And (a_2 (skS.0 2 a_2 a_5) (skS.0 4 a_2 a_5 a_6)) (a_2 (skS.0 4 a_2 a_5 a_6) (skS.0 5 a_2 a_5 a_6 a_7)) →
% 11.05/11.27 a_2 (skS.0 2 a_2 a_5) (skS.0 5 a_2 a_5 a_6 a_7))
% 11.05/11.27 False)
% 11.05/11.27 Clause #18 (by clausification #[17]): ∀ (a_1 a_2 : a → a → Prop) (a_3 a_4 a_5 a_6 a_7 : a),
% 11.05/11.27 Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 11.05/11.27 (Eq (And (a_2 (skS.0 2 a_2 a_5) (skS.0 4 a_2 a_5 a_6)) (a_2 (skS.0 4 a_2 a_5 a_6) (skS.0 5 a_2 a_5 a_6 a_7))) True)
% 11.05/11.27 Clause #19 (by clausification #[17]): ∀ (a_1 a_2 : a → a → Prop) (a_3 a_4 a_5 a_6 a_7 : a),
% 11.05/11.27 Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 11.05/11.27 (Eq (a_2 (skS.0 2 a_2 a_5) (skS.0 5 a_2 a_5 a_6 a_7)) False)
% 11.05/11.27 Clause #21 (by clausification #[18]): ∀ (a_1 a_2 : a → a → Prop) (a_3 a_4 a_5 a_6 : a),
% 11.05/11.27 Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 11.05/11.27 (Eq (a_2 (skS.0 2 a_2 a_5) (skS.0 4 a_2 a_5 a_6)) True)
% 11.05/11.27 Clause #47 (by clausification #[15]): ∀ (a_1 a_2 : a → a → Prop) (a_3 a_4 a_5 a_6 a_7 : a),
% 11.05/11.27 Or (Eq (a_1 (skS.0 1 a_2 a_1 a_3) (skS.0 3 a_2 a_1 a_3 a_4)) False)
% 11.05/11.27 (Eq
% 11.05/11.27 (Not
% 11.05/11.27 (And (a_1 (skS.0 2 a_1 a_5) (skS.0 4 a_1 a_5 a_6)) (a_1 (skS.0 4 a_1 a_5 a_6) (skS.0 6 a_1 a_5 a_6 a_7)) →
% 11.05/11.27 a_1 (skS.0 2 a_1 a_5) (skS.0 6 a_1 a_5 a_6 a_7)))
% 11.05/11.27 True)
% 11.05/11.27 Clause #48 (by clausification #[47]): ∀ (a_1 a_2 : a → a → Prop) (a_3 a_4 a_5 a_6 a_7 : a),
% 11.05/11.27 Or (Eq (a_1 (skS.0 1 a_2 a_1 a_3) (skS.0 3 a_2 a_1 a_3 a_4)) False)
% 11.05/11.27 (Eq
% 11.05/11.27 (And (a_1 (skS.0 2 a_1 a_5) (skS.0 4 a_1 a_5 a_6)) (a_1 (skS.0 4 a_1 a_5 a_6) (skS.0 6 a_1 a_5 a_6 a_7)) →
% 11.05/11.27 a_1 (skS.0 2 a_1 a_5) (skS.0 6 a_1 a_5 a_6 a_7))
% 11.05/11.27 False)
% 11.05/11.27 Clause #50 (by clausification #[48]): ∀ (a_1 a_2 : a → a → Prop) (a_3 a_4 a_5 a_6 a_7 : a),
% 11.05/11.27 Or (Eq (a_1 (skS.0 1 a_2 a_1 a_3) (skS.0 3 a_2 a_1 a_3 a_4)) False)
% 11.05/11.27 (Eq (a_1 (skS.0 2 a_1 a_5) (skS.0 6 a_1 a_5 a_6 a_7)) False)
% 11.05/11.27 Clause #203 (by fluidSup #[21, 19]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → a → Prop) (a_5 : Prop) (a_6 a_7 : a),
% 11.05/11.27 Or (Eq (a_1 (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3)) True)
% 11.05/11.27 (Or (Eq (skS.0 0 a_4 (skS.0 1 a_4 (fun x x => a_5) a_6) (skS.0 3 a_4 (fun x x => a_5) a_6 a_7)) True)
% 11.05/11.27 (Eq ((fun _ => a_5) True) False))
% 11.05/11.27 Clause #315 (by betaEtaReduce #[203]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → a → Prop) (a_5 : Prop) (a_6 a_7 : a),
% 11.05/11.27 Or (Eq (a_1 (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3)) True)
% 11.05/11.27 (Or (Eq (skS.0 0 a_4 (skS.0 1 a_4 (fun x x => a_5) a_6) (skS.0 3 a_4 (fun x x => a_5) a_6 a_7)) True)
% 11.05/11.27 (Eq a_5 False))
% 11.05/11.27 Clause #318 (by falseElim #[315]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → a → Prop) (a_5 a_6 : a),
% 11.13/11.32 Or (Eq (a_1 (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3)) True)
% 11.13/11.32 (Eq (skS.0 0 a_4 (skS.0 1 a_4 (fun x x => True) a_5) (skS.0 3 a_4 (fun x x => True) a_5 a_6)) True)
% 11.13/11.32 Clause #426 (by fluidSup #[318, 50]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : Prop) (a_5 a_6 a_7 : a),
% 11.13/11.32 Or (Eq (a_1 (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3)) True)
% 11.13/11.32 (Or (Eq ((fun _ => a_4) True) False)
% 11.13/11.32 (Eq ((fun x x => a_4) (skS.0 2 (fun x x => a_4) a_5) (skS.0 6 (fun x x => a_4) a_5 a_6 a_7)) False))
% 11.13/11.32 Clause #942 (by betaEtaReduce #[426]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : Prop),
% 11.13/11.32 Or (Eq (a_1 (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3)) True) (Or (Eq a_4 False) (Eq a_4 False))
% 11.13/11.32 Clause #943 (by eliminate duplicate literals #[942]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : Prop),
% 11.13/11.32 Or (Eq (a_1 (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3)) True) (Eq a_4 False)
% 11.13/11.32 Clause #948 (by falseElim #[943]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Eq (a_1 (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3)) True
% 11.13/11.32 Clause #1073 (by fluidSup #[948, 21]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → a → Prop) (a_5 : a) (a_6 : Prop → a),
% 11.13/11.32 Or (Eq (a_1 (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3)) True)
% 11.13/11.32 (Eq (a_4 (skS.0 2 a_4 a_5) (skS.0 4 a_4 a_5 (a_6 True))) True)
% 11.13/11.32 Clause #1339 (by equality factoring #[1073]): ∀ (a_1 : Prop) (a_2 a_3 : a),
% 11.13/11.32 Or (Ne True True) (Eq ((fun x x => a_1) (skS.0 2 (fun x x => a_1) a_2) (skS.0 4 (fun x x => a_1) a_2 a_3)) True)
% 11.13/11.32 Clause #1650 (by betaEtaReduce #[1339]): ∀ (a : Prop), Or (Ne True True) (Eq a True)
% 11.13/11.32 Clause #1651 (by clausification #[1650]): ∀ (a : Prop), Or (Eq a True) (Or (Eq True False) (Eq True False))
% 11.13/11.32 Clause #1653 (by clausification #[1651]): ∀ (a : Prop), Or (Eq a True) (Eq True False)
% 11.13/11.32 Clause #1654 (by clausification #[1653]): ∀ (a : Prop), Eq a True
% 11.13/11.32 Clause #1655 (by falseElim #[1654]): False
% 11.13/11.32 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------