TSTP Solution File: COM047_5 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : COM047_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n020.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 : Wed Aug 30 18:38:14 EDT 2023
% Result : Theorem 44.83s 45.01s
% Output : Proof 44.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COM047_5 : TPTP v8.1.2. Released v6.0.0.
% 0.07/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n020.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 : Tue Aug 29 13:08:28 EDT 2023
% 0.14/0.35 % CPUTime :
% 44.83/45.01 SZS status Theorem for theBenchmark.p
% 44.83/45.01 SZS output start Proof for theBenchmark.p
% 44.83/45.01 Clause #0 (by assumption #[]): Eq (Eq a (c_PresArith_Oatom_OLe int1 list1)) True
% 44.83/45.01 Clause #3 (by assumption #[]): Eq
% 44.83/45.01 (pp
% 44.83/45.01 (atom_case bool
% 44.83/45.01 (aa (fun (list int) bool) (fun int (fun (list int) bool)) (combk (fun (list int) bool) int)
% 44.83/45.01 (aa bool (fun (list int) bool) (combk bool (list int)) fFalse))
% 44.83/45.01 (aa (fun int (fun (list int) bool)) (fun int (fun int (fun (list int) bool)))
% 44.83/45.01 (combk (fun int (fun (list int) bool)) int)
% 44.83/45.01 (aa (fun (list int) bool) (fun int (fun (list int) bool)) (combk (fun (list int) bool) int)
% 44.83/45.01 (aa bool (fun (list int) bool) (combk bool (list int)) fTrue)))
% 44.83/45.01 (aa (fun int (fun (list int) bool)) (fun int (fun int (fun (list int) bool)))
% 44.83/45.01 (combk (fun int (fun (list int) bool)) int)
% 44.83/45.01 (aa (fun (list int) bool) (fun int (fun (list int) bool)) (combk (fun (list int) bool) int)
% 44.83/45.01 (aa bool (fun (list int) bool) (combk bool (list int)) fTrue)))
% 44.83/45.01 a))
% 44.83/45.01 True
% 44.83/45.01 Clause #16 (by assumption #[]): Eq
% 44.83/45.01 (∀ (A : Type) (Lista : list int) (Inta : int) (F3 F2 : fun int (fun int (fun (list int) A)))
% 44.83/45.01 (F1 : fun int (fun (list int) A)),
% 44.83/45.01 Eq (atom_case A F1 F2 F3 (c_PresArith_Oatom_OLe Inta Lista))
% 44.83/45.01 (aa (list int) A (aa int (fun (list int) A) F1 Inta) Lista))
% 44.83/45.01 True
% 44.83/45.01 Clause #107 (by assumption #[]): Eq (Not (pp fFalse)) True
% 44.83/45.01 Clause #108 (by assumption #[]): Eq (pp fTrue) True
% 44.83/45.01 Clause #112 (by assumption #[]): Eq (∀ (B A : Type) (Q : B) (P : A), Eq (aa B A (aa A (fun B A) (combk A B) P) Q) P) True
% 44.83/45.01 Clause #114 (by assumption #[]): Eq (∀ (P : bool), Or (Eq P fTrue) (Eq P fFalse)) True
% 44.83/45.01 Clause #121 (by clausification #[0]): Eq a (c_PresArith_Oatom_OLe int1 list1)
% 44.83/45.01 Clause #123 (by clausification #[107]): Eq (pp fFalse) False
% 44.83/45.01 Clause #193 (by clausification #[114]): ∀ (a : bool), Eq (Or (Eq a fTrue) (Eq a fFalse)) True
% 44.83/45.01 Clause #194 (by clausification #[193]): ∀ (a : bool), Or (Eq (Eq a fTrue) True) (Eq (Eq a fFalse) True)
% 44.83/45.01 Clause #195 (by clausification #[194]): ∀ (a : bool), Or (Eq (Eq a fFalse) True) (Eq a fTrue)
% 44.83/45.01 Clause #196 (by clausification #[195]): ∀ (a : bool), Or (Eq a fTrue) (Eq a fFalse)
% 44.83/45.01 Clause #197 (by superposition #[196, 108]): ∀ (a : bool), Or (Eq a fFalse) (Eq (pp a) True)
% 44.83/45.01 Clause #223 (by superposition #[197, 196]): ∀ (a a_1 : bool), Or (Eq (pp a) True) (Or (Eq a_1 fTrue) (Eq a_1 a))
% 44.83/45.01 Clause #403 (by clausification #[16]): ∀ (a : Type),
% 44.83/45.01 Eq
% 44.83/45.01 (∀ (Lista : list int) (Inta : int) (F3 F2 : fun int (fun int (fun (list int) a))) (F1 : fun int (fun (list int) a)),
% 44.83/45.01 Eq (atom_case a F1 F2 F3 (c_PresArith_Oatom_OLe Inta Lista))
% 44.83/45.01 (aa (list int) a (aa int (fun (list int) a) F1 Inta) Lista))
% 44.83/45.01 True
% 44.83/45.01 Clause #404 (by clausification #[403]): ∀ (a : Type) (a_1 : list int),
% 44.83/45.01 Eq
% 44.83/45.01 (∀ (Inta : int) (F3 F2 : fun int (fun int (fun (list int) a))) (F1 : fun int (fun (list int) a)),
% 44.83/45.01 Eq (atom_case a F1 F2 F3 (c_PresArith_Oatom_OLe Inta a_1))
% 44.83/45.01 (aa (list int) a (aa int (fun (list int) a) F1 Inta) a_1))
% 44.83/45.01 True
% 44.83/45.01 Clause #405 (by clausification #[404]): ∀ (a : Type) (a_1 : int) (a_2 : list int),
% 44.83/45.01 Eq
% 44.83/45.01 (∀ (F3 F2 : fun int (fun int (fun (list int) a))) (F1 : fun int (fun (list int) a)),
% 44.83/45.01 Eq (atom_case a F1 F2 F3 (c_PresArith_Oatom_OLe a_1 a_2))
% 44.83/45.01 (aa (list int) a (aa int (fun (list int) a) F1 a_1) a_2))
% 44.83/45.01 True
% 44.83/45.01 Clause #406 (by clausification #[405]): ∀ (a : Type) (a_1 : fun int (fun int (fun (list int) a))) (a_2 : int) (a_3 : list int),
% 44.83/45.01 Eq
% 44.83/45.01 (∀ (F2 : fun int (fun int (fun (list int) a))) (F1 : fun int (fun (list int) a)),
% 44.83/45.01 Eq (atom_case a F1 F2 a_1 (c_PresArith_Oatom_OLe a_2 a_3))
% 44.83/45.01 (aa (list int) a (aa int (fun (list int) a) F1 a_2) a_3))
% 44.83/45.01 True
% 44.83/45.01 Clause #407 (by clausification #[406]): ∀ (a : Type) (a_1 a_2 : fun int (fun int (fun (list int) a))) (a_3 : int) (a_4 : list int),
% 44.83/45.01 Eq
% 44.83/45.01 (∀ (F1 : fun int (fun (list int) a)),
% 44.83/45.01 Eq (atom_case a F1 a_1 a_2 (c_PresArith_Oatom_OLe a_3 a_4))
% 44.83/45.01 (aa (list int) a (aa int (fun (list int) a) F1 a_3) a_4))
% 44.83/45.01 True
% 44.83/45.01 Clause #408 (by clausification #[407]): ∀ (a : Type) (a_1 : fun int (fun (list int) a)) (a_2 a_3 : fun int (fun int (fun (list int) a))) (a_4 : int)
% 44.86/45.03 (a_5 : list int),
% 44.86/45.03 Eq
% 44.86/45.03 (Eq (atom_case a a_1 a_2 a_3 (c_PresArith_Oatom_OLe a_4 a_5))
% 44.86/45.03 (aa (list int) a (aa int (fun (list int) a) a_1 a_4) a_5))
% 44.86/45.03 True
% 44.86/45.03 Clause #409 (by clausification #[408]): ∀ (a : Type) (a_1 : fun int (fun (list int) a)) (a_2 a_3 : fun int (fun int (fun (list int) a))) (a_4 : int)
% 44.86/45.03 (a_5 : list int),
% 44.86/45.03 Eq (atom_case a a_1 a_2 a_3 (c_PresArith_Oatom_OLe a_4 a_5)) (aa (list int) a (aa int (fun (list int) a) a_1 a_4) a_5)
% 44.86/45.03 Clause #415 (by superposition #[409, 121]): ∀ (a_1 : Type) (a_2 : fun int (fun (list int) a_1)) (a_3 a_4 : fun int (fun int (fun (list int) a_1))),
% 44.86/45.03 Eq (atom_case a_1 a_2 a_3 a_4 a) (aa (list int) a_1 (aa int (fun (list int) a_1) a_2 int1) list1)
% 44.86/45.03 Clause #430 (by superposition #[223, 3]): ∀ (a_1 a_2 : bool),
% 44.86/45.03 Or (Eq (pp a_1) True)
% 44.86/45.03 (Or (Eq a_2 a_1)
% 44.86/45.03 (Eq
% 44.86/45.03 (pp
% 44.86/45.03 (atom_case bool
% 44.86/45.03 (aa (fun (list int) bool) (fun int (fun (list int) bool)) (combk (fun (list int) bool) int)
% 44.86/45.03 (aa bool (fun (list int) bool) (combk bool (list int)) fFalse))
% 44.86/45.03 (aa (fun int (fun (list int) bool)) (fun int (fun int (fun (list int) bool)))
% 44.86/45.03 (combk (fun int (fun (list int) bool)) int)
% 44.86/45.03 (aa (fun (list int) bool) (fun int (fun (list int) bool)) (combk (fun (list int) bool) int)
% 44.86/45.03 (aa bool (fun (list int) bool) (combk bool (list int)) a_2)))
% 44.86/45.03 (aa (fun int (fun (list int) bool)) (fun int (fun int (fun (list int) bool)))
% 44.86/45.03 (combk (fun int (fun (list int) bool)) int)
% 44.86/45.03 (aa (fun (list int) bool) (fun int (fun (list int) bool)) (combk (fun (list int) bool) int)
% 44.86/45.03 (aa bool (fun (list int) bool) (combk bool (list int)) a_2)))
% 44.86/45.03 a))
% 44.86/45.03 True))
% 44.86/45.03 Clause #2705 (by clausification #[112]): ∀ (a : Type), Eq (∀ (A : Type) (Q : a) (P : A), Eq (aa a A (aa A (fun a A) (combk A a) P) Q) P) True
% 44.86/45.03 Clause #2706 (by clausification #[2705]): ∀ (a a_1 : Type), Eq (∀ (Q : a) (P : a_1), Eq (aa a a_1 (aa a_1 (fun a a_1) (combk a_1 a) P) Q) P) True
% 44.86/45.03 Clause #2707 (by clausification #[2706]): ∀ (a a_1 : Type) (a_2 : a_1), Eq (∀ (P : a), Eq (aa a_1 a (aa a (fun a_1 a) (combk a a_1) P) a_2) P) True
% 44.86/45.03 Clause #2708 (by clausification #[2707]): ∀ (a a_1 : Type) (a_2 : a) (a_3 : a_1), Eq (Eq (aa a_1 a (aa a (fun a_1 a) (combk a a_1) a_2) a_3) a_2) True
% 44.86/45.03 Clause #2709 (by clausification #[2708]): ∀ (a a_1 : Type) (a_2 : a) (a_3 : a_1), Eq (aa a_1 a (aa a (fun a_1 a) (combk a a_1) a_2) a_3) a_2
% 44.86/45.03 Clause #10700 (by forward demodulation #[430, 415]): ∀ (a a_1 : bool),
% 44.86/45.03 Or (Eq (pp a) True)
% 44.86/45.03 (Or (Eq a_1 a)
% 44.86/45.03 (Eq
% 44.86/45.03 (pp
% 44.86/45.03 (aa (list int) bool
% 44.86/45.03 (aa int (fun (list int) bool)
% 44.86/45.03 (aa (fun (list int) bool) (fun int (fun (list int) bool)) (combk (fun (list int) bool) int)
% 44.86/45.03 (aa bool (fun (list int) bool) (combk bool (list int)) fFalse))
% 44.86/45.03 int1)
% 44.86/45.03 list1))
% 44.86/45.03 True))
% 44.86/45.03 Clause #10701 (by forward demodulation #[10700, 2709]): ∀ (a a_1 : bool),
% 44.86/45.03 Or (Eq (pp a) True)
% 44.86/45.03 (Or (Eq a_1 a)
% 44.86/45.03 (Eq (pp (aa (list int) bool (aa bool (fun (list int) bool) (combk bool (list int)) fFalse) list1)) True))
% 44.86/45.03 Clause #10702 (by forward demodulation #[10701, 2709]): ∀ (a a_1 : bool), Or (Eq (pp a) True) (Or (Eq a_1 a) (Eq (pp fFalse) True))
% 44.86/45.03 Clause #10981 (by equality factoring #[10702]): ∀ (a : bool), Or (Eq a fFalse) (Or (Ne True True) (Eq (pp fFalse) True))
% 44.86/45.03 Clause #10982 (by clausification #[10981]): ∀ (a : bool), Or (Eq a fFalse) (Or (Eq (pp fFalse) True) (Or (Eq True False) (Eq True False)))
% 44.86/45.03 Clause #10984 (by clausification #[10982]): ∀ (a : bool), Or (Eq a fFalse) (Or (Eq (pp fFalse) True) (Eq True False))
% 44.86/45.03 Clause #10985 (by clausification #[10984]): ∀ (a : bool), Or (Eq a fFalse) (Eq (pp fFalse) True)
% 44.86/45.03 Clause #11063 (by superposition #[10985, 123]): ∀ (a : bool), Or (Eq a fFalse) (Eq True False)
% 44.86/45.03 Clause #11143 (by clausification #[11063]): ∀ (a : bool), Eq a fFalse
% 44.86/45.03 Clause #11201 (by superposition #[11143, 11143]): ∀ (a a_1 : bool), Eq a a_1
% 44.86/45.11 Clause #11202 (by superposition #[11201, 108]): ∀ (a : bool), Eq (pp a) True
% 44.86/45.11 Clause #11247 (by superposition #[11202, 123]): Eq True False
% 44.86/45.11 Clause #11250 (by clausification #[11247]): False
% 44.86/45.11 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------