TSTP Solution File: SYO227^5 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYO227^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n021.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 04:21:54 EDT 2023
% Result : Theorem 130.70s 131.10s
% Output : Proof 131.92s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO227^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : duper %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % 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 : Sat Aug 26 00:45:41 EDT 2023
% 0.13/0.35 % CPUTime :
% 130.70/131.10 SZS status Theorem for theBenchmark.p
% 130.70/131.10 SZS output start Proof for theBenchmark.p
% 130.70/131.10 Clause #0 (by assumption #[]): Eq
% 130.70/131.10 (Not
% 130.70/131.10 ((∀ (Xx Xy : Iota), c_less_ Xx Xy → Ne Xx Xy) →
% 130.70/131.10 And (c_less_ a b) (c_less_ b c) → Exists fun A => And (And (Not (A a)) (A b)) (Not (A c))))
% 130.70/131.10 True
% 130.70/131.10 Clause #1 (by clausification #[0]): Eq
% 130.70/131.10 ((∀ (Xx Xy : Iota), c_less_ Xx Xy → Ne Xx Xy) →
% 130.70/131.10 And (c_less_ a b) (c_less_ b c) → Exists fun A => And (And (Not (A a)) (A b)) (Not (A c)))
% 130.70/131.10 False
% 130.70/131.10 Clause #2 (by clausification #[1]): Eq (∀ (Xx Xy : Iota), c_less_ Xx Xy → Ne Xx Xy) True
% 130.70/131.10 Clause #3 (by clausification #[1]): Eq (And (c_less_ a b) (c_less_ b c) → Exists fun A => And (And (Not (A a)) (A b)) (Not (A c))) False
% 130.70/131.10 Clause #4 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (Xy : Iota), c_less_ a Xy → Ne a Xy) True
% 130.70/131.10 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), Eq (c_less_ a a_1 → Ne a a_1) True
% 130.70/131.10 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), Or (Eq (c_less_ a a_1) False) (Eq (Ne a a_1) True)
% 130.70/131.10 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Or (Eq (c_less_ a a_1) False) (Ne a a_1)
% 130.70/131.10 Clause #8 (by destructive equality resolution #[7]): ∀ (a : Iota), Eq (c_less_ a a) False
% 130.70/131.10 Clause #9 (by clausification #[3]): Eq (And (c_less_ a b) (c_less_ b c)) True
% 130.70/131.10 Clause #10 (by clausification #[3]): Eq (Exists fun A => And (And (Not (A a)) (A b)) (Not (A c))) False
% 130.70/131.10 Clause #11 (by clausification #[9]): Eq (c_less_ b c) True
% 130.70/131.10 Clause #12 (by clausification #[9]): Eq (c_less_ a b) True
% 130.70/131.10 Clause #13 (by clausification #[10]): ∀ (a_1 : Iota → Prop), Eq (And (And (Not (a_1 a)) (a_1 b)) (Not (a_1 c))) False
% 130.70/131.10 Clause #14 (by clausification #[13]): ∀ (a_1 : Iota → Prop), Or (Eq (And (Not (a_1 a)) (a_1 b)) False) (Eq (Not (a_1 c)) False)
% 130.70/131.10 Clause #15 (by clausification #[14]): ∀ (a_1 : Iota → Prop), Or (Eq (Not (a_1 c)) False) (Or (Eq (Not (a_1 a)) False) (Eq (a_1 b) False))
% 130.70/131.10 Clause #16 (by clausification #[15]): ∀ (a_1 : Iota → Prop), Or (Eq (Not (a_1 a)) False) (Or (Eq (a_1 b) False) (Eq (a_1 c) True))
% 130.70/131.10 Clause #17 (by clausification #[16]): ∀ (a_1 : Iota → Prop), Or (Eq (a_1 b) False) (Or (Eq (a_1 c) True) (Eq (a_1 a) True))
% 130.70/131.10 Clause #21 (by neHoist #[17]): ∀ (a_1 : Iota → Sort _abstMVar.0) (a_2 a_3 : (x : Iota) → a_1 x),
% 130.70/131.10 Or (Eq ((fun x => Ne (a_2 x) (a_3 x)) c) True)
% 130.70/131.10 (Or (Eq ((fun x => Ne (a_2 x) (a_3 x)) a) True) (Or (Eq True False) (Eq (a_2 b) (a_3 b))))
% 130.70/131.10 Clause #73 (by betaEtaReduce #[21]): ∀ (a_1 : Iota → Sort _abstMVar.0) (a_2 a_3 : (x : Iota) → a_1 x),
% 130.70/131.10 Or (Eq (Ne (a_2 c) (a_3 c)) True) (Or (Eq (Ne (a_2 a) (a_3 a)) True) (Or (Eq True False) (Eq (a_2 b) (a_3 b))))
% 130.70/131.10 Clause #74 (by clausification #[73]): ∀ (a_1 : Iota → Sort _abstMVar.0) (a_2 a_3 : (x : Iota) → a_1 x),
% 130.70/131.10 Or (Eq (Ne (a_2 a) (a_3 a)) True) (Or (Eq True False) (Or (Eq (a_2 b) (a_3 b)) (Ne (a_2 c) (a_3 c))))
% 130.70/131.10 Clause #75 (by clausification #[74]): ∀ (a_1 : Iota → Sort _abstMVar.0) (a_2 a_3 : (x : Iota) → a_1 x),
% 130.70/131.10 Or (Eq True False) (Or (Eq (a_2 b) (a_3 b)) (Or (Ne (a_2 c) (a_3 c)) (Ne (a_2 a) (a_3 a))))
% 130.70/131.10 Clause #76 (by clausification #[75]): ∀ (a_1 : Iota → Sort _abstMVar.0) (a_2 a_3 : (x : Iota) → a_1 x),
% 130.70/131.10 Or (Eq (a_2 b) (a_3 b)) (Or (Ne (a_2 c) (a_3 c)) (Ne (a_2 a) (a_3 a)))
% 130.70/131.10 Clause #92 (by fluidSup #[76, 12]): ∀ (a_1 : Sort _abstMVar.0) (a_2 : (x : Iota) → (fun x => a_1) x) (a_3 : a_1),
% 130.70/131.10 Or (Eq (a_2 b) ((fun x => a_3) b)) (Or (Ne (a_2 c) ((fun _ => a_3) True)) (Ne (a_2 a) ((fun x => a_3) a)))
% 130.70/131.10 Clause #175 (by betaEtaReduce #[92]): ∀ (a_1 : Sort _abstMVar.0) (a_2 : (x : Iota) → (fun x => a_1) x) (a_3 : a_1),
% 130.70/131.10 Or (Eq (a_2 b) a_3) (Or (Ne (a_2 c) a_3) (Ne (a_2 a) a_3))
% 130.70/131.10 Clause #176 (by equality resolution #[175]): ∀ (a_1 : Sort _abstMVar.0) (a_2 : (x : Iota) → (fun x => a_1) x), Or (Eq (a_2 b) (a_2 c)) (Ne (a_2 a) (a_2 c))
% 130.70/131.10 Clause #186 (by fluidBoolHoist #[176]): ∀ (a_1 : (x : Iota) → (fun x => Prop) x), Or (Eq (a_1 b) (a_1 c)) (Or (Ne False (a_1 c)) (Eq (a_1 a) True))
% 130.70/131.10 Clause #236 (by clausification #[186]): ∀ (a_1 : (x : Iota) → (fun x => Prop) x),
% 130.70/131.10 Or (Eq (a_1 b) (a_1 c)) (Or (Eq (a_1 a) True) (Or (Eq False True) (Eq (a_1 c) True)))
% 131.92/132.11 Clause #270 (by clausification #[236]): ∀ (a_1 : (x : Iota) → (fun x => Prop) x), Or (Eq (a_1 b) (a_1 c)) (Or (Eq (a_1 a) True) (Eq (a_1 c) True))
% 131.92/132.11 Clause #291 (by eqHoist #[270]): ∀ (a_1 : Iota → Sort _abstMVar.0) (a_2 a_3 : (x : Iota) → a_1 x),
% 131.92/132.11 Or (Eq ((fun x => Eq (a_2 x) (a_3 x)) a) True)
% 131.92/132.11 (Or (Eq ((fun x => Eq (a_2 x) (a_3 x)) c) True)
% 131.92/132.11 (Or (Eq ((fun x => Eq (a_2 x) (a_3 x)) b) False) (Eq (a_2 c) (a_3 c))))
% 131.92/132.11 Clause #17336 (by betaEtaReduce #[291]): ∀ (a_1 : Iota → Sort _abstMVar.0) (a_2 a_3 : (x : Iota) → a_1 x),
% 131.92/132.11 Or (Eq (Eq (a_2 a) (a_3 a)) True)
% 131.92/132.11 (Or (Eq (Eq (a_2 c) (a_3 c)) True) (Or (Eq (Eq (a_2 b) (a_3 b)) False) (Eq (a_2 c) (a_3 c))))
% 131.92/132.11 Clause #17337 (by clausification #[17336]): ∀ (a_1 : Iota → Sort _abstMVar.0) (a_2 a_3 : (x : Iota) → a_1 x),
% 131.92/132.11 Or (Eq (Eq (a_2 c) (a_3 c)) True) (Or (Eq (Eq (a_2 b) (a_3 b)) False) (Or (Eq (a_2 c) (a_3 c)) (Eq (a_2 a) (a_3 a))))
% 131.92/132.11 Clause #17338 (by clausification #[17337]): ∀ (a_1 : Iota → Sort _abstMVar.0) (a_2 a_3 : (x : Iota) → a_1 x),
% 131.92/132.11 Or (Eq (Eq (a_2 b) (a_3 b)) False) (Or (Eq (a_2 c) (a_3 c)) (Or (Eq (a_2 a) (a_3 a)) (Eq (a_2 c) (a_3 c))))
% 131.92/132.11 Clause #17339 (by clausification #[17338]): ∀ (a_1 : Iota → Sort _abstMVar.0) (a_2 a_3 : (x : Iota) → a_1 x),
% 131.92/132.11 Or (Eq (a_2 c) (a_3 c)) (Or (Eq (a_2 a) (a_3 a)) (Or (Eq (a_2 c) (a_3 c)) (Ne (a_2 b) (a_3 b))))
% 131.92/132.11 Clause #17340 (by eliminate duplicate literals #[17339]): ∀ (a_1 : Iota → Sort _abstMVar.0) (a_2 a_3 : (x : Iota) → a_1 x),
% 131.92/132.11 Or (Eq (a_2 c) (a_3 c)) (Or (Eq (a_2 a) (a_3 a)) (Ne (a_2 b) (a_3 b)))
% 131.92/132.11 Clause #17341 (by equality resolution #[17340]): Or (Eq ((fun x => x) c) ((fun x => b) c)) (Eq ((fun x => x) a) ((fun x => b) a))
% 131.92/132.11 Clause #17446 (by betaEtaReduce #[17341]): Or (Eq c b) (Eq a b)
% 131.92/132.11 Clause #17447 (by superposition #[17446, 11]): Or (Eq a b) (Eq (c_less_ b b) True)
% 131.92/132.11 Clause #19427 (by superposition #[17447, 8]): Or (Eq a b) (Eq True False)
% 131.92/132.11 Clause #19625 (by clausification #[19427]): Eq a b
% 131.92/132.11 Clause #19626 (by backward demodulation #[19625, 12]): Eq (c_less_ b b) True
% 131.92/132.11 Clause #19896 (by superposition #[19626, 8]): Eq True False
% 131.92/132.11 Clause #19913 (by clausification #[19896]): False
% 131.92/132.11 SZS output end Proof for theBenchmark.p
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