TSTP Solution File: SEV394^5 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEV394^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n010.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 19:24:53 EDT 2023
% Result : Theorem 3.76s 3.97s
% Output : Proof 3.76s
% 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 : SEV394^5 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.15 % Command : duper %s
% 0.15/0.36 % Computer : n010.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 24 02:50:21 EDT 2023
% 0.15/0.36 % CPUTime :
% 3.76/3.97 SZS status Theorem for theBenchmark.p
% 3.76/3.97 SZS output start Proof for theBenchmark.p
% 3.76/3.97 Clause #0 (by assumption #[]): Eq
% 3.76/3.97 (Not
% 3.76/3.97 (∀ (Xw Xy Xz : a → Prop),
% 3.76/3.97 And (∀ (Xx : a), And (Xw Xx) (Not (Xz Xx)) → Xy Xx) (Eq (fun Xx => And (Xz Xx) (Not (Xy Xx))) fun Xx => False) →
% 3.76/3.97 ∀ (Xx : a), Xw Xx → Xy Xx))
% 3.76/3.97 True
% 3.76/3.97 Clause #1 (by clausification #[0]): Eq
% 3.76/3.97 (∀ (Xw Xy Xz : a → Prop),
% 3.76/3.97 And (∀ (Xx : a), And (Xw Xx) (Not (Xz Xx)) → Xy Xx) (Eq (fun Xx => And (Xz Xx) (Not (Xy Xx))) fun Xx => False) →
% 3.76/3.97 ∀ (Xx : a), Xw Xx → Xy Xx)
% 3.76/3.97 False
% 3.76/3.97 Clause #2 (by clausification #[1]): ∀ (a_1 : a → Prop),
% 3.76/3.97 Eq
% 3.76/3.97 (Not
% 3.76/3.97 (∀ (Xy Xz : a → Prop),
% 3.76/3.97 And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (Xz Xx)) → Xy Xx)
% 3.76/3.97 (Eq (fun Xx => And (Xz Xx) (Not (Xy Xx))) fun Xx => False) →
% 3.76/3.97 ∀ (Xx : a), skS.0 0 a_1 Xx → Xy Xx))
% 3.76/3.97 True
% 3.76/3.97 Clause #3 (by clausification #[2]): ∀ (a_1 : a → Prop),
% 3.76/3.97 Eq
% 3.76/3.97 (∀ (Xy Xz : a → Prop),
% 3.76/3.97 And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (Xz Xx)) → Xy Xx)
% 3.76/3.97 (Eq (fun Xx => And (Xz Xx) (Not (Xy Xx))) fun Xx => False) →
% 3.76/3.97 ∀ (Xx : a), skS.0 0 a_1 Xx → Xy Xx)
% 3.76/3.97 False
% 3.76/3.97 Clause #4 (by clausification #[3]): ∀ (a_1 a_2 : a → Prop),
% 3.76/3.97 Eq
% 3.76/3.97 (Not
% 3.76/3.97 (∀ (Xz : a → Prop),
% 3.76/3.97 And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (Xz Xx)) → skS.0 1 a_1 a_2 Xx)
% 3.76/3.97 (Eq (fun Xx => And (Xz Xx) (Not (skS.0 1 a_1 a_2 Xx))) fun Xx => False) →
% 3.76/3.97 ∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx))
% 3.76/3.97 True
% 3.76/3.97 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : a → Prop),
% 3.76/3.97 Eq
% 3.76/3.97 (∀ (Xz : a → Prop),
% 3.76/3.97 And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (Xz Xx)) → skS.0 1 a_1 a_2 Xx)
% 3.76/3.97 (Eq (fun Xx => And (Xz Xx) (Not (skS.0 1 a_1 a_2 Xx))) fun Xx => False) →
% 3.76/3.97 ∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx)
% 3.76/3.97 False
% 3.76/3.97 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 a_3 : a → Prop),
% 3.76/3.97 Eq
% 3.76/3.97 (Not
% 3.76/3.97 (And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 2 a_1 a_2 a_3 Xx)) → skS.0 1 a_1 a_2 Xx)
% 3.76/3.97 (Eq (fun Xx => And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 1 a_1 a_2 Xx))) fun Xx => False) →
% 3.76/3.97 ∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx))
% 3.76/3.97 True
% 3.76/3.97 Clause #7 (by clausification #[6]): ∀ (a_1 a_2 a_3 : a → Prop),
% 3.76/3.97 Eq
% 3.76/3.97 (And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 2 a_1 a_2 a_3 Xx)) → skS.0 1 a_1 a_2 Xx)
% 3.76/3.97 (Eq (fun Xx => And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 1 a_1 a_2 Xx))) fun Xx => False) →
% 3.76/3.97 ∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx)
% 3.76/3.97 False
% 3.76/3.97 Clause #8 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop),
% 3.76/3.97 Eq
% 3.76/3.97 (And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 2 a_1 a_2 a_3 Xx)) → skS.0 1 a_1 a_2 Xx)
% 3.76/3.97 (Eq (fun Xx => And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 1 a_1 a_2 Xx))) fun Xx => False))
% 3.76/3.97 True
% 3.76/3.97 Clause #9 (by clausification #[7]): ∀ (a_1 a_2 : a → Prop), Eq (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) False
% 3.76/3.97 Clause #10 (by clausification #[8]): ∀ (a_1 a_2 a_3 : a → Prop),
% 3.76/3.97 Eq (Eq (fun Xx => And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 1 a_1 a_2 Xx))) fun Xx => False) True
% 3.76/3.97 Clause #11 (by clausification #[8]): ∀ (a_1 a_2 a_3 : a → Prop),
% 3.76/3.97 Eq (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 2 a_1 a_2 a_3 Xx)) → skS.0 1 a_1 a_2 Xx) True
% 3.76/3.97 Clause #12 (by clausification #[10]): ∀ (a_1 a_2 a_3 : a → Prop), Eq (fun Xx => And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 1 a_1 a_2 Xx))) fun Xx => False
% 3.76/3.97 Clause #13 (by argument congruence #[12]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a),
% 3.76/3.97 Eq ((fun Xx => And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 1 a_1 a_2 Xx))) a_4) ((fun Xx => False) a_4)
% 3.76/3.97 Clause #14 (by clausification #[9]): ∀ (a_1 a_2 : a → Prop) (a_3 : a),
% 3.76/3.97 Eq (Not (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3) → skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3))) True
% 3.76/3.97 Clause #15 (by clausification #[14]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3) → skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3)) False
% 3.76/3.97 Clause #16 (by clausification #[15]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3)) True
% 3.76/3.98 Clause #17 (by clausification #[15]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3)) False
% 3.76/3.98 Clause #18 (by clausification #[11]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop),
% 3.76/3.98 Eq (And (skS.0 0 a_1 a_2) (Not (skS.0 2 a_1 a_3 a_4 a_2)) → skS.0 1 a_1 a_3 a_2) True
% 3.76/3.98 Clause #19 (by clausification #[18]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop),
% 3.76/3.98 Or (Eq (And (skS.0 0 a_1 a_2) (Not (skS.0 2 a_1 a_3 a_4 a_2))) False) (Eq (skS.0 1 a_1 a_3 a_2) True)
% 3.76/3.98 Clause #20 (by clausification #[19]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop),
% 3.76/3.98 Or (Eq (skS.0 1 a_1 a_2 a_3) True) (Or (Eq (skS.0 0 a_1 a_3) False) (Eq (Not (skS.0 2 a_1 a_2 a_4 a_3)) False))
% 3.76/3.98 Clause #21 (by clausification #[20]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop),
% 3.76/3.98 Or (Eq (skS.0 1 a_1 a_2 a_3) True) (Or (Eq (skS.0 0 a_1 a_3) False) (Eq (skS.0 2 a_1 a_2 a_4 a_3) True))
% 3.76/3.98 Clause #22 (by superposition #[21, 16]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 3.76/3.98 Or (Eq (skS.0 1 (fun x => a_1 x) a_2 (skS.0 3 a_1 a_3 a_4)) True)
% 3.76/3.98 (Or (Eq (skS.0 2 (fun x => a_1 x) a_2 a_5 (skS.0 3 a_1 a_3 a_4)) True) (Eq False True))
% 3.76/3.98 Clause #23 (by betaEtaReduce #[13]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (And (skS.0 2 a_1 a_2 a_3 a_4) (Not (skS.0 1 a_1 a_2 a_4))) False
% 3.76/3.98 Clause #24 (by clausification #[23]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Eq (skS.0 2 a_1 a_2 a_3 a_4) False) (Eq (Not (skS.0 1 a_1 a_2 a_4)) False)
% 3.76/3.98 Clause #25 (by clausification #[24]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Eq (skS.0 2 a_1 a_2 a_3 a_4) False) (Eq (skS.0 1 a_1 a_2 a_4) True)
% 3.76/3.98 Clause #26 (by betaEtaReduce #[22]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 3.76/3.98 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True)
% 3.76/3.98 (Or (Eq (skS.0 2 a_1 a_2 a_5 (skS.0 3 a_1 a_3 a_4)) True) (Eq False True))
% 3.76/3.98 Clause #27 (by clausification #[26]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 3.76/3.98 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) (Eq (skS.0 2 a_1 a_2 a_5 (skS.0 3 a_1 a_3 a_4)) True)
% 3.76/3.98 Clause #28 (by superposition #[27, 25]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a),
% 3.76/3.98 Or (Eq (skS.0 1 (fun x => a_1 x) (fun x => a_2 x) (skS.0 3 (fun x => a_1 x) a_3 a_4)) True)
% 3.76/3.98 (Or (Eq True False) (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True))
% 3.76/3.98 Clause #29 (by betaEtaReduce #[28]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a),
% 3.76/3.98 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True)
% 3.76/3.98 (Or (Eq True False) (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True))
% 3.76/3.98 Clause #30 (by clausification #[29]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a),
% 3.76/3.98 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True)
% 3.76/3.98 Clause #31 (by eliminate duplicate literals #[30]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True
% 3.76/3.98 Clause #33 (by superposition #[31, 17]): Eq True False
% 3.76/3.98 Clause #34 (by clausification #[33]): False
% 3.76/3.98 SZS output end Proof for theBenchmark.p
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