TSTP Solution File: SYO357^5 by Duper---1.0
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% File : Duper---1.0
% Problem : SYO357^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n019.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 04:22:14 EDT 2023
% Result : Theorem 4.30s 4.46s
% Output : Proof 4.30s
% 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 : SYO357^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : duper %s
% 0.18/0.35 % Computer : n019.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Fri Aug 25 23:19:44 EDT 2023
% 0.18/0.35 % CPUTime :
% 4.30/4.46 SZS status Theorem for theBenchmark.p
% 4.30/4.46 SZS output start Proof for theBenchmark.p
% 4.30/4.46 Clause #0 (by assumption #[]): Eq
% 4.30/4.46 (Not
% 4.30/4.46 ((∀ (P : atype → Prop), And (Or a (Not a)) (P u) → And (Or b (Not b)) (P v)) → ∀ (Xq : atype → Prop), Xq u → Xq v))
% 4.30/4.46 True
% 4.30/4.46 Clause #1 (by clausification #[0]): Eq ((∀ (P : atype → Prop), And (Or a (Not a)) (P u) → And (Or b (Not b)) (P v)) → ∀ (Xq : atype → Prop), Xq u → Xq v)
% 4.30/4.46 False
% 4.30/4.46 Clause #2 (by clausification #[1]): Eq (∀ (P : atype → Prop), And (Or a (Not a)) (P u) → And (Or b (Not b)) (P v)) True
% 4.30/4.46 Clause #3 (by clausification #[1]): Eq (∀ (Xq : atype → Prop), Xq u → Xq v) False
% 4.30/4.46 Clause #4 (by clausification #[2]): ∀ (a_1 : atype → Prop), Eq (And (Or a (Not a)) (a_1 u) → And (Or b (Not b)) (a_1 v)) True
% 4.30/4.46 Clause #5 (by clausification #[4]): ∀ (a_1 : atype → Prop), Or (Eq (And (Or a (Not a)) (a_1 u)) False) (Eq (And (Or b (Not b)) (a_1 v)) True)
% 4.30/4.46 Clause #6 (by clausification #[5]): ∀ (a_1 : atype → Prop), Or (Eq (And (Or b (Not b)) (a_1 v)) True) (Or (Eq (Or a (Not a)) False) (Eq (a_1 u) False))
% 4.30/4.46 Clause #7 (by clausification #[6]): ∀ (a_1 : atype → Prop), Or (Eq (Or a (Not a)) False) (Or (Eq (a_1 u) False) (Eq (a_1 v) True))
% 4.30/4.46 Clause #9 (by clausification #[7]): ∀ (a_1 : atype → Prop), Or (Eq (a_1 u) False) (Or (Eq (a_1 v) True) (Eq (Not a) False))
% 4.30/4.46 Clause #10 (by clausification #[7]): ∀ (a_1 : atype → Prop), Or (Eq (a_1 u) False) (Or (Eq (a_1 v) True) (Eq a False))
% 4.30/4.46 Clause #11 (by clausification #[9]): ∀ (a_1 : atype → Prop), Or (Eq (a_1 u) False) (Or (Eq (a_1 v) True) (Eq a True))
% 4.30/4.46 Clause #13 (by neHoist #[11]): ∀ (a_1 : atype → Sort _abstMVar.0) (a_2 a_3 : (x : atype) → a_1 x),
% 4.30/4.46 Or (Eq ((fun x => Ne (a_2 x) (a_3 x)) v) True) (Or (Eq a True) (Or (Eq True False) (Eq (a_2 u) (a_3 u))))
% 4.30/4.46 Clause #19 (by clausification #[3]): ∀ (a : atype → Prop), Eq (Not (skS.0 0 a u → skS.0 0 a v)) True
% 4.30/4.46 Clause #20 (by clausification #[19]): ∀ (a : atype → Prop), Eq (skS.0 0 a u → skS.0 0 a v) False
% 4.30/4.46 Clause #21 (by clausification #[20]): ∀ (a : atype → Prop), Eq (skS.0 0 a u) True
% 4.30/4.46 Clause #22 (by clausification #[20]): ∀ (a : atype → Prop), Eq (skS.0 0 a v) False
% 4.30/4.46 Clause #28 (by neHoist #[10]): ∀ (a_1 : atype → Sort _abstMVar.0) (a_2 a_3 : (x : atype) → a_1 x),
% 4.30/4.46 Or (Eq ((fun x => Ne (a_2 x) (a_3 x)) v) True) (Or (Eq a False) (Or (Eq True False) (Eq (a_2 u) (a_3 u))))
% 4.30/4.46 Clause #65 (by betaEtaReduce #[13]): ∀ (a_1 : atype → Sort _abstMVar.0) (a_2 a_3 : (x : atype) → a_1 x),
% 4.30/4.46 Or (Eq (Ne (a_2 v) (a_3 v)) True) (Or (Eq a True) (Or (Eq True False) (Eq (a_2 u) (a_3 u))))
% 4.30/4.46 Clause #66 (by clausification #[65]): ∀ (a_1 : atype → Sort _abstMVar.0) (a_2 a_3 : (x : atype) → a_1 x),
% 4.30/4.46 Or (Eq a True) (Or (Eq True False) (Or (Eq (a_2 u) (a_3 u)) (Ne (a_2 v) (a_3 v))))
% 4.30/4.46 Clause #67 (by clausification #[66]): ∀ (a_1 : atype → Sort _abstMVar.0) (a_2 a_3 : (x : atype) → a_1 x),
% 4.30/4.46 Or (Eq a True) (Or (Eq (a_2 u) (a_3 u)) (Ne (a_2 v) (a_3 v)))
% 4.30/4.46 Clause #68 (by equality resolution #[67]): Or (Eq a True) (Eq ((fun x => x) u) ((fun x => v) u))
% 4.30/4.46 Clause #78 (by betaEtaReduce #[68]): Or (Eq a True) (Eq u v)
% 4.30/4.46 Clause #324 (by betaEtaReduce #[28]): ∀ (a_1 : atype → Sort _abstMVar.0) (a_2 a_3 : (x : atype) → a_1 x),
% 4.30/4.46 Or (Eq (Ne (a_2 v) (a_3 v)) True) (Or (Eq a False) (Or (Eq True False) (Eq (a_2 u) (a_3 u))))
% 4.30/4.46 Clause #325 (by clausification #[324]): ∀ (a_1 : atype → Sort _abstMVar.0) (a_2 a_3 : (x : atype) → a_1 x),
% 4.30/4.46 Or (Eq a False) (Or (Eq True False) (Or (Eq (a_2 u) (a_3 u)) (Ne (a_2 v) (a_3 v))))
% 4.30/4.46 Clause #326 (by clausification #[325]): ∀ (a_1 : atype → Sort _abstMVar.0) (a_2 a_3 : (x : atype) → a_1 x),
% 4.30/4.46 Or (Eq a False) (Or (Eq (a_2 u) (a_3 u)) (Ne (a_2 v) (a_3 v)))
% 4.30/4.46 Clause #327 (by superposition #[326, 78]): ∀ (a : atype → Sort _abstMVar.0) (a_1 a_2 : (x : atype) → a x),
% 4.30/4.46 Or (Eq (a_1 u) (a_2 u)) (Or (Ne (a_1 v) (a_2 v)) (Or (Eq False True) (Eq u v)))
% 4.30/4.46 Clause #348 (by clausification #[327]): ∀ (a : atype → Sort _abstMVar.0) (a_1 a_2 : (x : atype) → a x),
% 4.30/4.46 Or (Eq (a_1 u) (a_2 u)) (Or (Ne (a_1 v) (a_2 v)) (Eq u v))
% 4.30/4.46 Clause #349 (by equality resolution #[348]): Or (Eq ((fun x => x) u) ((fun x => v) u)) (Eq u v)
% 4.30/4.47 Clause #365 (by betaEtaReduce #[349]): Or (Eq u v) (Eq u v)
% 4.30/4.47 Clause #366 (by eliminate duplicate literals #[365]): Eq u v
% 4.30/4.47 Clause #369 (by backward demodulation #[366, 22]): ∀ (a : atype → Prop), Eq (skS.0 0 a u) False
% 4.30/4.47 Clause #393 (by superposition #[369, 21]): Eq False True
% 4.30/4.47 Clause #399 (by clausification #[393]): False
% 4.30/4.47 SZS output end Proof for theBenchmark.p
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