TSTP Solution File: SEV076^5 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEV076^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n006.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 19:24:12 EDT 2023
% Result : Theorem 3.94s 4.14s
% Output : Proof 3.94s
% 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 : SEV076^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 03:45:23 EDT 2023
% 0.14/0.35 % CPUTime :
% 3.94/4.14 SZS status Theorem for theBenchmark.p
% 3.94/4.14 SZS output start Proof for theBenchmark.p
% 3.94/4.14 Clause #0 (by assumption #[]): Eq
% 3.94/4.14 (Not
% 3.94/4.14 (∀ (RRR : a → a → Prop) (U : (a → Prop) → a),
% 3.94/4.14 And (∀ (Xx Xy Xz : a), And (RRR Xx Xy) (RRR Xy Xz) → RRR Xx Xz)
% 3.94/4.14 (∀ (Xs : a → Prop),
% 3.94/4.14 And (∀ (Xz : a), Xs Xz → RRR Xz (U Xs)) (∀ (Xj : a), (∀ (Xk : a), Xs Xk → RRR Xk Xj) → RRR (U Xs) Xj)) →
% 3.94/4.14 ∀ (Xs : a → Prop), Exists fun Xb => ∀ (Xz : a), Xs Xz → RRR Xz Xb))
% 3.94/4.14 True
% 3.94/4.14 Clause #1 (by clausification #[0]): Eq
% 3.94/4.14 (∀ (RRR : a → a → Prop) (U : (a → Prop) → a),
% 3.94/4.14 And (∀ (Xx Xy Xz : a), And (RRR Xx Xy) (RRR Xy Xz) → RRR Xx Xz)
% 3.94/4.14 (∀ (Xs : a → Prop),
% 3.94/4.14 And (∀ (Xz : a), Xs Xz → RRR Xz (U Xs)) (∀ (Xj : a), (∀ (Xk : a), Xs Xk → RRR Xk Xj) → RRR (U Xs) Xj)) →
% 3.94/4.14 ∀ (Xs : a → Prop), Exists fun Xb => ∀ (Xz : a), Xs Xz → RRR Xz Xb)
% 3.94/4.14 False
% 3.94/4.14 Clause #2 (by clausification #[1]): ∀ (a_1 : a → a → Prop),
% 3.94/4.14 Eq
% 3.94/4.14 (Not
% 3.94/4.14 (∀ (U : (a → Prop) → a),
% 3.94/4.14 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)
% 3.94/4.14 (∀ (Xs : a → Prop),
% 3.94/4.14 And (∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz (U Xs))
% 3.94/4.14 (∀ (Xj : a), (∀ (Xk : a), Xs Xk → skS.0 0 a_1 Xk Xj) → skS.0 0 a_1 (U Xs) Xj)) →
% 3.94/4.14 ∀ (Xs : a → Prop), Exists fun Xb => ∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz Xb))
% 3.94/4.14 True
% 3.94/4.14 Clause #3 (by clausification #[2]): ∀ (a_1 : a → a → Prop),
% 3.94/4.14 Eq
% 3.94/4.14 (∀ (U : (a → Prop) → a),
% 3.94/4.14 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)
% 3.94/4.14 (∀ (Xs : a → Prop),
% 3.94/4.14 And (∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz (U Xs))
% 3.94/4.14 (∀ (Xj : a), (∀ (Xk : a), Xs Xk → skS.0 0 a_1 Xk Xj) → skS.0 0 a_1 (U Xs) Xj)) →
% 3.94/4.14 ∀ (Xs : a → Prop), Exists fun Xb => ∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz Xb)
% 3.94/4.14 False
% 3.94/4.14 Clause #4 (by clausification #[3]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a),
% 3.94/4.14 Eq
% 3.94/4.14 (Not
% 3.94/4.14 (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)
% 3.94/4.14 (∀ (Xs : a → Prop),
% 3.94/4.14 And (∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz (skS.0 1 a_1 a_2 Xs))
% 3.94/4.14 (∀ (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)) →
% 3.94/4.14 ∀ (Xs : a → Prop), Exists fun Xb => ∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz Xb))
% 3.94/4.14 True
% 3.94/4.14 Clause #5 (by clausification #[4]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a),
% 3.94/4.14 Eq
% 3.94/4.14 (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)
% 3.94/4.14 (∀ (Xs : a → Prop),
% 3.94/4.14 And (∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz (skS.0 1 a_1 a_2 Xs))
% 3.94/4.14 (∀ (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)) →
% 3.94/4.14 ∀ (Xs : a → Prop), Exists fun Xb => ∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz Xb)
% 3.94/4.14 False
% 3.94/4.14 Clause #6 (by clausification #[5]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a),
% 3.94/4.14 Eq
% 3.94/4.14 (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)
% 3.94/4.14 (∀ (Xs : a → Prop),
% 3.94/4.14 And (∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz (skS.0 1 a_1 a_2 Xs))
% 3.94/4.14 (∀ (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)))
% 3.94/4.14 True
% 3.94/4.14 Clause #7 (by clausification #[5]): ∀ (a_1 : a → a → Prop), Eq (∀ (Xs : a → Prop), Exists fun Xb => ∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz Xb) False
% 3.94/4.14 Clause #8 (by clausification #[6]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a),
% 3.94/4.14 Eq
% 3.94/4.14 (∀ (Xs : a → Prop),
% 3.94/4.14 And (∀ (Xz : a), Xs Xz → skS.0 0 a_1 Xz (skS.0 1 a_1 a_2 Xs))
% 3.94/4.14 (∀ (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))
% 3.94/4.14 True
% 3.94/4.14 Clause #10 (by clausification #[8]): ∀ (a_1 : a → Prop) (a_2 : a → a → Prop) (a_3 : (a → Prop) → a),
% 3.94/4.14 Eq
% 3.94/4.14 (And (∀ (Xz : a), a_1 Xz → skS.0 0 a_2 Xz (skS.0 1 a_2 a_3 a_1))
% 3.94/4.17 (∀ (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))
% 3.94/4.17 True
% 3.94/4.17 Clause #11 (by clausification #[10]): ∀ (a_1 : a → Prop) (a_2 : a → a → Prop) (a_3 : (a → Prop) → a),
% 3.94/4.17 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
% 3.94/4.17 Clause #12 (by clausification #[10]): ∀ (a_1 : a → Prop) (a_2 : a → a → Prop) (a_3 : (a → Prop) → a),
% 3.94/4.17 Eq (∀ (Xz : a), a_1 Xz → skS.0 0 a_2 Xz (skS.0 1 a_2 a_3 a_1)) True
% 3.94/4.17 Clause #13 (by clausification #[11]): ∀ (a_1 : a → Prop) (a_2 : a → a → Prop) (a_3 : a) (a_4 : (a → Prop) → a),
% 3.94/4.17 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
% 3.94/4.17 Clause #14 (by clausification #[13]): ∀ (a_1 : a → Prop) (a_2 : a → a → Prop) (a_3 : a) (a_4 : (a → Prop) → a),
% 3.94/4.17 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)
% 3.94/4.17 Clause #15 (by clausification #[14]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a) (a_3 : a → Prop) (a_4 a_5 : a),
% 3.94/4.17 Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 a_3) a_4) True)
% 3.94/4.17 (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)
% 3.94/4.17 Clause #16 (by clausification #[15]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a) (a_3 : a → Prop) (a_4 a_5 : a),
% 3.94/4.17 Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 a_3) a_4) True)
% 3.94/4.17 (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)
% 3.94/4.17 Clause #17 (by clausification #[16]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a) (a_3 : a → Prop) (a_4 a_5 : a),
% 3.94/4.17 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)
% 3.94/4.17 Clause #51 (by clausification #[7]): ∀ (a_1 : a → a → Prop) (a_2 : a → Prop),
% 3.94/4.17 Eq (Not (Exists fun Xb => ∀ (Xz : a), skS.0 3 a_1 a_2 Xz → skS.0 0 a_1 Xz Xb)) True
% 3.94/4.17 Clause #52 (by clausification #[51]): ∀ (a_1 : a → a → Prop) (a_2 : a → Prop), Eq (Exists fun Xb => ∀ (Xz : a), skS.0 3 a_1 a_2 Xz → skS.0 0 a_1 Xz Xb) False
% 3.94/4.17 Clause #53 (by clausification #[52]): ∀ (a_1 : a → a → Prop) (a_2 : a → Prop) (a_3 : a), Eq (∀ (Xz : a), skS.0 3 a_1 a_2 Xz → skS.0 0 a_1 Xz a_3) False
% 3.94/4.17 Clause #54 (by clausification #[53]): ∀ (a_1 : a → a → Prop) (a_2 : a → Prop) (a_3 a_4 : a),
% 3.94/4.17 Eq (Not (skS.0 3 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4) → skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4) a_3)) True
% 3.94/4.17 Clause #55 (by clausification #[54]): ∀ (a_1 : a → a → Prop) (a_2 : a → Prop) (a_3 a_4 : a),
% 3.94/4.17 Eq (skS.0 3 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4) → skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4) a_3) False
% 3.94/4.17 Clause #57 (by clausification #[55]): ∀ (a_1 : a → a → Prop) (a_2 : a → Prop) (a_3 a_4 : a), Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4) a_3) False
% 3.94/4.17 Clause #67 (by fluidSup #[57, 17]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a) (a_3 : Prop) (a_4 : a),
% 3.94/4.17 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)
% 3.94/4.17 Clause #68 (by clausification #[12]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → a → Prop) (a_4 : (a → Prop) → a),
% 3.94/4.17 Eq (a_1 a_2 → skS.0 0 a_3 a_2 (skS.0 1 a_3 a_4 a_1)) True
% 3.94/4.17 Clause #69 (by clausification #[68]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → a → Prop) (a_4 : (a → Prop) → a),
% 3.94/4.17 Or (Eq (a_1 a_2) False) (Eq (skS.0 0 a_3 a_2 (skS.0 1 a_3 a_4 a_1)) True)
% 3.94/4.17 Clause #83 (by betaEtaReduce #[67]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a) (a_3 : Prop) (a_4 : a),
% 3.94/4.17 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)
% 3.94/4.17 Clause #118 (by fluidBoolHoist #[83]): ∀ (a_1 : Prop) (a_2 : a → a → Prop) (a_3 : (a → Prop) → a) (a_4 : a),
% 3.94/4.17 Or (Eq a_1 True) (Or (Eq (skS.0 0 a_2 (skS.0 1 a_2 a_3 fun x => False) a_4) True) (Eq a_1 True))
% 3.94/4.17 Clause #121 (by eliminate duplicate literals #[118]): ∀ (a_1 : Prop) (a_2 : a → a → Prop) (a_3 : (a → Prop) → a) (a_4 : a),
% 3.94/4.17 Or (Eq a_1 True) (Eq (skS.0 0 a_2 (skS.0 1 a_2 a_3 fun x => False) a_4) True)
% 3.94/4.17 Clause #122 (by superposition #[121, 57]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a) (a_3 : a),
% 3.94/4.17 Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 fun x => False) a_3) True) (Eq True False)
% 3.94/4.17 Clause #153 (by clausification #[122]): ∀ (a_1 : a → a → Prop) (a_2 : (a → Prop) → a) (a_3 : a), Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2 fun x => False) a_3) True
% 3.94/4.17 Clause #162 (by fluidSup #[153, 69]): ∀ (a_1 : Prop) (a_2 : a → a → Prop) (a_3 : a) (a_4 : (a → Prop) → a),
% 3.94/4.17 Or (Eq ((fun _ => a_1) True) False) (Eq (skS.0 0 a_2 a_3 (skS.0 1 a_2 a_4 fun x => a_1)) True)
% 3.94/4.17 Clause #168 (by betaEtaReduce #[162]): ∀ (a_1 : Prop) (a_2 : a → a → Prop) (a_3 : a) (a_4 : (a → Prop) → a),
% 3.94/4.17 Or (Eq a_1 False) (Eq (skS.0 0 a_2 a_3 (skS.0 1 a_2 a_4 fun x => a_1)) True)
% 3.94/4.17 Clause #173 (by falseElim #[168]): ∀ (a_1 : a → a → Prop) (a_2 : a) (a_3 : (a → Prop) → a), Eq (skS.0 0 a_1 a_2 (skS.0 1 a_1 a_3 fun x => True)) True
% 3.94/4.17 Clause #180 (by superposition #[173, 57]): Eq True False
% 3.94/4.17 Clause #194 (by clausification #[180]): False
% 3.94/4.17 SZS output end Proof for theBenchmark.p
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