TSTP Solution File: SYO031^1 by Duper---1.0
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% File : Duper---1.0
% Problem : SYO031^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n029.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 : Fri Sep 1 04:21:11 EDT 2023
% Result : Theorem 4.79s 4.97s
% Output : Proof 4.79s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : SYO031^1 : TPTP v8.1.2. Released v3.7.0.
% 0.15/0.15 % Command : duper %s
% 0.16/0.36 % Computer : n029.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sat Aug 26 07:10:55 EDT 2023
% 0.16/0.37 % CPUTime :
% 4.79/4.97 SZS status Theorem for theBenchmark.p
% 4.79/4.97 SZS output start Proof for theBenchmark.p
% 4.79/4.97 Clause #0 (by assumption #[]): Eq (Not (Not (∀ (F : Prop → Prop), Exists fun X => Eq (F X) X))) True
% 4.79/4.97 Clause #1 (by clausification #[0]): Eq (Not (∀ (F : Prop → Prop), Exists fun X => Eq (F X) X)) False
% 4.79/4.97 Clause #2 (by clausification #[1]): Eq (∀ (F : Prop → Prop), Exists fun X => Eq (F X) X) True
% 4.79/4.97 Clause #3 (by clausification #[2]): ∀ (a : Prop → Prop), Eq (Exists fun X => Eq (a X) X) True
% 4.79/4.97 Clause #4 (by clausification #[3]): ∀ (a : Prop → Prop) (a_1 : Prop), Eq (Eq (a (skS.0 0 a a_1)) (skS.0 0 a a_1)) True
% 4.79/4.97 Clause #5 (by clausification #[4]): ∀ (a : Prop → Prop) (a_1 : Prop), Eq (a (skS.0 0 a a_1)) (skS.0 0 a a_1)
% 4.79/4.97 Clause #6 (by identity loobHoist #[5]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (a True) (skS.0 0 a a_1)) (Eq (skS.0 0 a a_1) False)
% 4.79/4.97 Clause #7 (by identity boolHoist #[5]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (a False) (skS.0 0 a a_1)) (Eq (skS.0 0 a a_1) True)
% 4.79/4.97 Clause #8 (by identity loobHoist #[6]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (skS.0 0 a a_1) False) (Or (Eq (a True) (skS.0 0 a True)) (Eq a_1 False))
% 4.79/4.97 Clause #10 (by identity loobHoist #[8]): ∀ (a : Prop → Prop) (a_1 : Prop),
% 4.79/4.97 Or (Eq (a True) (skS.0 0 a True)) (Or (Eq a_1 False) (Or (Eq (skS.0 0 a True) False) (Eq a_1 False)))
% 4.79/4.97 Clause #12 (by eliminate duplicate literals #[10]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (a True) (skS.0 0 a True)) (Or (Eq a_1 False) (Eq (skS.0 0 a True) False))
% 4.79/4.97 Clause #13 (by falseElim #[12]): ∀ (a : Prop → Prop), Or (Eq (a True) (skS.0 0 a True)) (Eq (skS.0 0 a True) False)
% 4.79/4.97 Clause #14 (by identity loobHoist #[7]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (skS.0 0 a a_1) True) (Or (Eq (a False) (skS.0 0 a True)) (Eq a_1 False))
% 4.79/4.97 Clause #16 (by identity loobHoist #[14]): ∀ (a : Prop → Prop) (a_1 : Prop),
% 4.79/4.97 Or (Eq (a False) (skS.0 0 a True)) (Or (Eq a_1 False) (Or (Eq (skS.0 0 a True) True) (Eq a_1 False)))
% 4.79/4.97 Clause #18 (by eliminate duplicate literals #[16]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (a False) (skS.0 0 a True)) (Or (Eq a_1 False) (Eq (skS.0 0 a True) True))
% 4.79/4.97 Clause #19 (by falseElim #[18]): ∀ (a : Prop → Prop), Or (Eq (a False) (skS.0 0 a True)) (Eq (skS.0 0 a True) True)
% 4.79/4.97 Clause #22 (by equality factoring #[19]): ∀ (a : Prop → Prop), Or (Ne (a False) True) (Eq (skS.0 0 a True) True)
% 4.79/4.97 Clause #26 (by clausification #[22]): ∀ (a : Prop → Prop), Or (Eq (skS.0 0 a True) True) (Or (Eq (a False) False) (Eq True False))
% 4.79/4.97 Clause #28 (by clausification #[26]): ∀ (a : Prop → Prop), Or (Eq (skS.0 0 a True) True) (Eq (a False) False)
% 4.79/4.97 Clause #30 (by neHoist #[28]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x),
% 4.79/4.97 Or (Eq (skS.0 0 (fun x => Ne (a_1 x) (a_2 x)) True) True) (Or (Eq True False) (Eq (a_1 False) (a_2 False)))
% 4.79/4.97 Clause #277 (by clausification #[30]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x),
% 4.79/4.97 Or (Eq (skS.0 0 (fun x => Ne (a_1 x) (a_2 x)) True) True) (Eq (a_1 False) (a_2 False))
% 4.79/4.97 Clause #278 (by superposition #[277, 13]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x),
% 4.79/4.97 Or (Eq (a_1 False) (a_2 False)) (Or (Eq (Ne (a_1 True) (a_2 True)) True) (Eq True False))
% 4.79/4.97 Clause #367 (by clausification #[278]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x),
% 4.79/4.97 Or (Eq (a_1 False) (a_2 False)) (Or (Eq True False) (Ne (a_1 True) (a_2 True)))
% 4.79/4.97 Clause #368 (by clausification #[367]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), Or (Eq (a_1 False) (a_2 False)) (Ne (a_1 True) (a_2 True))
% 4.79/4.97 Clause #369 (by equality resolution #[368]): Eq ((fun x => x) False) ((fun x => True) False)
% 4.79/4.97 Clause #390 (by betaEtaReduce #[369]): Eq False True
% 4.79/4.97 Clause #391 (by clausification #[390]): False
% 4.79/4.97 SZS output end Proof for theBenchmark.p
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