TSTP Solution File: SYO513^1 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYO513^1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n026.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 04:22:55 EDT 2023
% Result : Theorem 3.86s 4.06s
% Output : Proof 3.86s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SYO513^1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.16 % Command : duper %s
% 0.15/0.38 % Computer : n026.cluster.edu
% 0.15/0.38 % Model : x86_64 x86_64
% 0.15/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38 % Memory : 8042.1875MB
% 0.15/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38 % CPULimit : 300
% 0.15/0.38 % WCLimit : 300
% 0.15/0.38 % DateTime : Sat Aug 26 03:53:18 EDT 2023
% 0.15/0.38 % CPUTime :
% 3.86/4.06 SZS status Theorem for theBenchmark.p
% 3.86/4.06 SZS output start Proof for theBenchmark.p
% 3.86/4.06 Clause #0 (by assumption #[]): Eq (Not (Exists fun C => ∀ (P : Prop → Prop), (Exists fun X => P X) → P (C P))) True
% 3.86/4.06 Clause #1 (by betaEtaReduce #[0]): Eq (Not (Exists fun C => ∀ (P : Prop → Prop), Exists P → P (C P))) True
% 3.86/4.06 Clause #2 (by clausification #[1]): Eq (Exists fun C => ∀ (P : Prop → Prop), Exists P → P (C P)) False
% 3.86/4.06 Clause #3 (by clausification #[2]): ∀ (a : (Prop → Prop) → Prop), Eq (∀ (P : Prop → Prop), Exists P → P (a P)) False
% 3.86/4.06 Clause #4 (by clausification #[3]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop),
% 3.86/4.06 Eq (Not (Exists (skS.0 0 a a_1) → skS.0 0 a a_1 (a (skS.0 0 a a_1)))) True
% 3.86/4.06 Clause #5 (by clausification #[4]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop), Eq (Exists (skS.0 0 a a_1) → skS.0 0 a a_1 (a (skS.0 0 a a_1))) False
% 3.86/4.06 Clause #6 (by clausification #[5]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop), Eq (Exists (skS.0 0 a a_1)) True
% 3.86/4.06 Clause #7 (by clausification #[5]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop), Eq (skS.0 0 a a_1 (a (skS.0 0 a a_1))) False
% 3.86/4.06 Clause #8 (by clausification #[6]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop) (a_2 : Prop), Eq (skS.0 0 a a_1 (skS.0 1 a a_1 a_2)) True
% 3.86/4.06 Clause #9 (by identity loobHoist #[8]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop) (a_2 : Prop),
% 3.86/4.06 Or (Eq (skS.0 0 a a_1 True) True) (Eq (skS.0 1 a a_1 a_2) False)
% 3.86/4.06 Clause #10 (by identity boolHoist #[8]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop) (a_2 : Prop),
% 3.86/4.06 Or (Eq (skS.0 0 a a_1 False) True) (Eq (skS.0 1 a a_1 a_2) True)
% 3.86/4.06 Clause #12 (by identity boolHoist #[9]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop) (a_2 : Prop),
% 3.86/4.06 Or (Eq (skS.0 0 a a_1 True) True) (Or (Eq (skS.0 1 a a_1 False) False) (Eq a_2 True))
% 3.86/4.06 Clause #13 (by identity loobHoist #[7]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop), Or (Eq (skS.0 0 a a_1 True) False) (Eq (a (skS.0 0 a a_1)) False)
% 3.86/4.06 Clause #14 (by identity boolHoist #[7]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop), Or (Eq (skS.0 0 a a_1 False) False) (Eq (a (skS.0 0 a a_1)) True)
% 3.86/4.06 Clause #16 (by identity boolHoist #[10]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop) (a_2 : Prop),
% 3.86/4.06 Or (Eq (skS.0 0 a a_1 False) True) (Or (Eq (skS.0 1 a a_1 False) True) (Eq a_2 True))
% 3.86/4.06 Clause #29 (by equality factoring #[16]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop),
% 3.86/4.06 Or (Eq (skS.0 0 a a_1 False) True) (Or (Ne True True) (Eq (skS.0 1 a a_1 False) True))
% 3.86/4.06 Clause #39 (by clausification #[29]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop),
% 3.86/4.06 Or (Eq (skS.0 0 a a_1 False) True) (Or (Eq (skS.0 1 a a_1 False) True) (Or (Eq True False) (Eq True False)))
% 3.86/4.06 Clause #41 (by clausification #[39]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop),
% 3.86/4.06 Or (Eq (skS.0 0 a a_1 False) True) (Or (Eq (skS.0 1 a a_1 False) True) (Eq True False))
% 3.86/4.06 Clause #42 (by clausification #[41]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop), Or (Eq (skS.0 0 a a_1 False) True) (Eq (skS.0 1 a a_1 False) True)
% 3.86/4.06 Clause #43 (by superposition #[42, 12]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop) (a_2 : Prop),
% 3.86/4.06 Or (Eq (skS.0 0 (fun x => a x) (fun x => a_1 x) False) True)
% 3.86/4.06 (Or (Eq (skS.0 0 a a_1 True) True) (Or (Eq True False) (Eq a_2 True)))
% 3.86/4.06 Clause #48 (by betaEtaReduce #[43]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop) (a_2 : Prop),
% 3.86/4.06 Or (Eq (skS.0 0 a a_1 False) True) (Or (Eq (skS.0 0 a a_1 True) True) (Or (Eq True False) (Eq a_2 True)))
% 3.86/4.06 Clause #49 (by clausification #[48]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop) (a_2 : Prop),
% 3.86/4.06 Or (Eq (skS.0 0 a a_1 False) True) (Or (Eq (skS.0 0 a a_1 True) True) (Eq a_2 True))
% 3.86/4.06 Clause #55 (by equality factoring #[49]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop),
% 3.86/4.06 Or (Eq (skS.0 0 a a_1 True) True) (Or (Ne True True) (Eq (skS.0 0 a a_1 False) True))
% 3.86/4.06 Clause #66 (by clausification #[55]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop),
% 3.86/4.06 Or (Eq (skS.0 0 a a_1 True) True) (Or (Eq (skS.0 0 a a_1 False) True) (Or (Eq True False) (Eq True False)))
% 3.86/4.07 Clause #68 (by clausification #[66]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop),
% 3.86/4.07 Or (Eq (skS.0 0 a a_1 True) True) (Or (Eq (skS.0 0 a a_1 False) True) (Eq True False))
% 3.86/4.07 Clause #69 (by clausification #[68]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop), Or (Eq (skS.0 0 a a_1 True) True) (Eq (skS.0 0 a a_1 False) True)
% 3.86/4.07 Clause #70 (by superposition #[69, 14]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop),
% 3.86/4.07 Or (Eq (skS.0 0 (fun x => a x) (fun x => a_1 x) True) True) (Or (Eq True False) (Eq (a (skS.0 0 a a_1)) True))
% 3.86/4.07 Clause #77 (by betaEtaReduce #[70]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop),
% 3.86/4.07 Or (Eq (skS.0 0 a a_1 True) True) (Or (Eq True False) (Eq (a (skS.0 0 a a_1)) True))
% 3.86/4.07 Clause #78 (by clausification #[77]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop), Or (Eq (skS.0 0 a a_1 True) True) (Eq (a (skS.0 0 a a_1)) True)
% 3.86/4.07 Clause #82 (by equality factoring #[78]): ∀ (a : Prop → Prop), Or (Ne True True) (Eq (skS.0 0 (fun x => x True) a True) True)
% 3.86/4.07 Clause #118 (by clausification #[82]): ∀ (a : Prop → Prop), Or (Eq (skS.0 0 (fun x => x True) a True) True) (Or (Eq True False) (Eq True False))
% 3.86/4.07 Clause #120 (by clausification #[118]): ∀ (a : Prop → Prop), Or (Eq (skS.0 0 (fun x => x True) a True) True) (Eq True False)
% 3.86/4.07 Clause #121 (by clausification #[120]): ∀ (a : Prop → Prop), Eq (skS.0 0 (fun x => x True) a True) True
% 3.86/4.07 Clause #122 (by superposition #[121, 13]): Or (Eq True False) (Eq True False)
% 3.86/4.07 Clause #132 (by clausification #[122]): Eq True False
% 3.86/4.07 Clause #133 (by clausification #[132]): False
% 3.86/4.07 SZS output end Proof for theBenchmark.p
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