TSTP Solution File: SWW568_5 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SWW568_5 : TPTP v8.1.2. Released v6.0.0.
% 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 00:26:45 EDT 2023
% Result : Theorem 45.64s 46.01s
% Output : Proof 45.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW568_5 : TPTP v8.1.2. Released v6.0.0.
% 0.12/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 19:59:49 EDT 2023
% 0.14/0.35 % CPUTime :
% 45.64/46.01 SZS status Theorem for theBenchmark.p
% 45.64/46.01 SZS output start Proof for theBenchmark.p
% 45.64/46.01 Clause #0 (by assumption #[]): Eq (wTrt p h_a e e_a u) True
% 45.64/46.01 Clause #4 (by assumption #[]): Eq
% 45.64/46.01 (∀ (M : Type) (T1 : ty)
% 45.64/46.01 (P2 :
% 45.64/46.01 list
% 45.64/46.01 (product_prod (list char)
% 45.64/46.01 (product_prod (list char)
% 45.64/46.01 (product_prod (list (product_prod (list char) ty))
% 45.64/46.01 (list (product_prod (list char) (product_prod (list ty) (product_prod ty M)))))))),
% 45.64/46.01 widen M P2 T1 T1)
% 45.64/46.01 True
% 45.64/46.01 Clause #9 (by assumption #[]): Eq
% 45.64/46.01 (∀ (Ta : ty) (Da Fa : list char) (Eb : exp (list char)) (Ea : fun (list char) (option ty))
% 45.64/46.01 (Hb : fun nat (option (product_prod (list char) (fun (product_prod (list char) (list char)) (option val)))))
% 45.64/46.01 (Pa :
% 45.64/46.01 list
% 45.64/46.01 (product_prod (list char)
% 45.64/46.01 (product_prod (list char)
% 45.64/46.01 (product_prod (list (product_prod (list char) ty))
% 45.64/46.01 (list
% 45.64/46.01 (product_prod (list char)
% 45.64/46.01 (product_prod (list ty) (product_prod ty (product_prod (list (list char)) (exp (list char))))))))))),
% 45.64/46.01 wTrt Pa Hb Ea Eb nt → wTrt Pa Hb Ea (fAcc (list char) Eb Fa Da) Ta)
% 45.64/46.01 True
% 45.64/46.01 Clause #12 (by assumption #[]): Eq (Eq u nt) True
% 45.64/46.01 Clause #98 (by assumption #[]): Eq
% 45.64/46.01 (Not
% 45.64/46.01 (Exists fun T =>
% 45.64/46.01 And (wTrt p h_a e (fAcc (list char) e_a f d) T)
% 45.64/46.01 (widen (product_prod (list (list char)) (exp (list char))) p T t)))
% 45.64/46.01 True
% 45.64/46.01 Clause #101 (by clausification #[12]): Eq u nt
% 45.64/46.01 Clause #102 (by forward demodulation #[0, 101]): Eq (wTrt p h_a e e_a nt) True
% 45.64/46.01 Clause #107 (by clausification #[4]): ∀ (a : Type),
% 45.64/46.01 Eq
% 45.64/46.01 (∀ (T1 : ty)
% 45.64/46.01 (P2 :
% 45.64/46.01 list
% 45.64/46.01 (product_prod (list char)
% 45.64/46.01 (product_prod (list char)
% 45.64/46.01 (product_prod (list (product_prod (list char) ty))
% 45.64/46.01 (list (product_prod (list char) (product_prod (list ty) (product_prod ty a)))))))),
% 45.64/46.01 widen a P2 T1 T1)
% 45.64/46.01 True
% 45.64/46.01 Clause #108 (by clausification #[107]): ∀ (a : Type) (a_1 : ty),
% 45.64/46.01 Eq
% 45.64/46.01 (∀
% 45.64/46.01 (P2 :
% 45.64/46.01 list
% 45.64/46.01 (product_prod (list char)
% 45.64/46.01 (product_prod (list char)
% 45.64/46.01 (product_prod (list (product_prod (list char) ty))
% 45.64/46.01 (list (product_prod (list char) (product_prod (list ty) (product_prod ty a)))))))),
% 45.64/46.01 widen a P2 a_1 a_1)
% 45.64/46.01 True
% 45.64/46.01 Clause #109 (by clausification #[108]): ∀ (a : Type)
% 45.64/46.01 (a_1 :
% 45.64/46.01 list
% 45.64/46.01 (product_prod (list char)
% 45.64/46.01 (product_prod (list char)
% 45.64/46.01 (product_prod (list (product_prod (list char) ty))
% 45.64/46.01 (list (product_prod (list char) (product_prod (list ty) (product_prod ty a))))))))
% 45.64/46.01 (a_2 : ty), Eq (widen a a_1 a_2 a_2) True
% 45.64/46.01 Clause #242 (by clausification #[9]): ∀ (a : ty),
% 45.64/46.01 Eq
% 45.64/46.01 (∀ (Da Fa : list char) (Eb : exp (list char)) (Ea : fun (list char) (option ty))
% 45.64/46.01 (Hb : fun nat (option (product_prod (list char) (fun (product_prod (list char) (list char)) (option val)))))
% 45.64/46.01 (Pa :
% 45.64/46.01 list
% 45.64/46.01 (product_prod (list char)
% 45.64/46.01 (product_prod (list char)
% 45.64/46.01 (product_prod (list (product_prod (list char) ty))
% 45.64/46.01 (list
% 45.64/46.01 (product_prod (list char)
% 45.64/46.01 (product_prod (list ty)
% 45.64/46.01 (product_prod ty (product_prod (list (list char)) (exp (list char))))))))))),
% 45.64/46.01 wTrt Pa Hb Ea Eb nt → wTrt Pa Hb Ea (fAcc (list char) Eb Fa Da) a)
% 45.64/46.01 True
% 45.64/46.01 Clause #243 (by clausification #[242]): ∀ (a : list char) (a_1 : ty),
% 45.64/46.01 Eq
% 45.64/46.01 (∀ (Fa : list char) (Eb : exp (list char)) (Ea : fun (list char) (option ty))
% 45.64/46.01 (Hb : fun nat (option (product_prod (list char) (fun (product_prod (list char) (list char)) (option val)))))
% 45.64/46.01 (Pa :
% 45.64/46.01 list
% 45.64/46.01 (product_prod (list char)
% 45.64/46.01 (product_prod (list char)
% 45.64/46.01 (product_prod (list (product_prod (list char) ty))
% 45.64/46.01 (list
% 45.64/46.01 (product_prod (list char)
% 45.64/46.01 (product_prod (list ty)
% 45.64/46.01 (product_prod ty (product_prod (list (list char)) (exp (list char))))))))))),
% 45.64/46.01 wTrt Pa Hb Ea Eb nt → wTrt Pa Hb Ea (fAcc (list char) Eb Fa a) a_1)
% 45.64/46.01 True
% 45.64/46.01 Clause #244 (by clausification #[243]): ∀ (a a_1 : list char) (a_2 : ty),
% 45.81/46.02 Eq
% 45.81/46.02 (∀ (Eb : exp (list char)) (Ea : fun (list char) (option ty))
% 45.81/46.02 (Hb : fun nat (option (product_prod (list char) (fun (product_prod (list char) (list char)) (option val)))))
% 45.81/46.02 (Pa :
% 45.81/46.02 list
% 45.81/46.02 (product_prod (list char)
% 45.81/46.02 (product_prod (list char)
% 45.81/46.02 (product_prod (list (product_prod (list char) ty))
% 45.81/46.02 (list
% 45.81/46.02 (product_prod (list char)
% 45.81/46.02 (product_prod (list ty)
% 45.81/46.02 (product_prod ty (product_prod (list (list char)) (exp (list char))))))))))),
% 45.81/46.02 wTrt Pa Hb Ea Eb nt → wTrt Pa Hb Ea (fAcc (list char) Eb a a_1) a_2)
% 45.81/46.02 True
% 45.81/46.02 Clause #245 (by clausification #[244]): ∀ (a : exp (list char)) (a_1 a_2 : list char) (a_3 : ty),
% 45.81/46.02 Eq
% 45.81/46.02 (∀ (Ea : fun (list char) (option ty))
% 45.81/46.02 (Hb : fun nat (option (product_prod (list char) (fun (product_prod (list char) (list char)) (option val)))))
% 45.81/46.02 (Pa :
% 45.81/46.02 list
% 45.81/46.02 (product_prod (list char)
% 45.81/46.02 (product_prod (list char)
% 45.81/46.02 (product_prod (list (product_prod (list char) ty))
% 45.81/46.02 (list
% 45.81/46.02 (product_prod (list char)
% 45.81/46.02 (product_prod (list ty)
% 45.81/46.02 (product_prod ty (product_prod (list (list char)) (exp (list char))))))))))),
% 45.81/46.02 wTrt Pa Hb Ea a nt → wTrt Pa Hb Ea (fAcc (list char) a a_1 a_2) a_3)
% 45.81/46.02 True
% 45.81/46.02 Clause #246 (by clausification #[245]): ∀ (a : fun (list char) (option ty)) (a_1 : exp (list char)) (a_2 a_3 : list char) (a_4 : ty),
% 45.81/46.02 Eq
% 45.81/46.02 (∀ (Hb : fun nat (option (product_prod (list char) (fun (product_prod (list char) (list char)) (option val)))))
% 45.81/46.02 (Pa :
% 45.81/46.02 list
% 45.81/46.02 (product_prod (list char)
% 45.81/46.02 (product_prod (list char)
% 45.81/46.02 (product_prod (list (product_prod (list char) ty))
% 45.81/46.02 (list
% 45.81/46.02 (product_prod (list char)
% 45.81/46.02 (product_prod (list ty)
% 45.81/46.02 (product_prod ty (product_prod (list (list char)) (exp (list char))))))))))),
% 45.81/46.02 wTrt Pa Hb a a_1 nt → wTrt Pa Hb a (fAcc (list char) a_1 a_2 a_3) a_4)
% 45.81/46.02 True
% 45.81/46.02 Clause #247 (by clausification #[246]): ∀ (a : fun nat (option (product_prod (list char) (fun (product_prod (list char) (list char)) (option val)))))
% 45.81/46.02 (a_1 : fun (list char) (option ty)) (a_2 : exp (list char)) (a_3 a_4 : list char) (a_5 : ty),
% 45.81/46.02 Eq
% 45.81/46.02 (∀
% 45.81/46.02 (Pa :
% 45.81/46.02 list
% 45.81/46.02 (product_prod (list char)
% 45.81/46.02 (product_prod (list char)
% 45.81/46.02 (product_prod (list (product_prod (list char) ty))
% 45.81/46.02 (list
% 45.81/46.02 (product_prod (list char)
% 45.81/46.02 (product_prod (list ty)
% 45.81/46.02 (product_prod ty (product_prod (list (list char)) (exp (list char))))))))))),
% 45.81/46.02 wTrt Pa a a_1 a_2 nt → wTrt Pa a a_1 (fAcc (list char) a_2 a_3 a_4) a_5)
% 45.81/46.02 True
% 45.81/46.02 Clause #248 (by clausification #[247]): ∀
% 45.81/46.02 (a :
% 45.81/46.02 list
% 45.81/46.02 (product_prod (list char)
% 45.81/46.02 (product_prod (list char)
% 45.81/46.02 (product_prod (list (product_prod (list char) ty))
% 45.81/46.02 (list
% 45.81/46.02 (product_prod (list char)
% 45.81/46.02 (product_prod (list ty) (product_prod ty (product_prod (list (list char)) (exp (list char)))))))))))
% 45.81/46.02 (a_1 : fun nat (option (product_prod (list char) (fun (product_prod (list char) (list char)) (option val)))))
% 45.81/46.02 (a_2 : fun (list char) (option ty)) (a_3 : exp (list char)) (a_4 a_5 : list char) (a_6 : ty),
% 45.81/46.02 Eq (wTrt a a_1 a_2 a_3 nt → wTrt a a_1 a_2 (fAcc (list char) a_3 a_4 a_5) a_6) True
% 45.81/46.02 Clause #249 (by clausification #[248]): ∀
% 45.81/46.02 (a :
% 45.81/46.02 list
% 45.81/46.02 (product_prod (list char)
% 45.81/46.02 (product_prod (list char)
% 45.81/46.02 (product_prod (list (product_prod (list char) ty))
% 45.81/46.02 (list
% 45.81/46.02 (product_prod (list char)
% 45.81/46.02 (product_prod (list ty) (product_prod ty (product_prod (list (list char)) (exp (list char)))))))))))
% 45.81/46.02 (a_1 : fun nat (option (product_prod (list char) (fun (product_prod (list char) (list char)) (option val)))))
% 45.81/46.02 (a_2 : fun (list char) (option ty)) (a_3 : exp (list char)) (a_4 a_5 : list char) (a_6 : ty),
% 45.81/46.02 Or (Eq (wTrt a a_1 a_2 a_3 nt) False) (Eq (wTrt a a_1 a_2 (fAcc (list char) a_3 a_4 a_5) a_6) True)
% 45.88/46.04 Clause #250 (by superposition #[249, 102]): ∀ (a a_1 : list char) (a_2 : ty), Or (Eq (wTrt p h_a e (fAcc (list char) e_a a a_1) a_2) True) (Eq False True)
% 45.88/46.04 Clause #251 (by clausification #[250]): ∀ (a a_1 : list char) (a_2 : ty), Eq (wTrt p h_a e (fAcc (list char) e_a a a_1) a_2) True
% 45.88/46.04 Clause #1651 (by clausification #[98]): Eq
% 45.88/46.04 (Exists fun T =>
% 45.88/46.04 And (wTrt p h_a e (fAcc (list char) e_a f d) T) (widen (product_prod (list (list char)) (exp (list char))) p T t))
% 45.88/46.04 False
% 45.88/46.04 Clause #1652 (by clausification #[1651]): ∀ (a : ty),
% 45.88/46.04 Eq (And (wTrt p h_a e (fAcc (list char) e_a f d) a) (widen (product_prod (list (list char)) (exp (list char))) p a t))
% 45.88/46.04 False
% 45.88/46.04 Clause #1653 (by clausification #[1652]): ∀ (a : ty),
% 45.88/46.04 Or (Eq (wTrt p h_a e (fAcc (list char) e_a f d) a) False)
% 45.88/46.04 (Eq (widen (product_prod (list (list char)) (exp (list char))) p a t) False)
% 45.88/46.04 Clause #1654 (by superposition #[1653, 251]): ∀ (a : ty), Or (Eq (widen (product_prod (list (list char)) (exp (list char))) p a t) False) (Eq False True)
% 45.88/46.04 Clause #1655 (by clausification #[1654]): ∀ (a : ty), Eq (widen (product_prod (list (list char)) (exp (list char))) p a t) False
% 45.88/46.04 Clause #1657 (by superposition #[1655, 109]): Eq False True
% 45.88/46.04 Clause #1658 (by clausification #[1657]): False
% 45.88/46.04 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------