TSTP Solution File: SWW513_5 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SWW513_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n017.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 00:26:37 EDT 2023
% Result : Theorem 31.09s 31.32s
% Output : Proof 31.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW513_5 : TPTP v8.1.2. Released v6.0.0.
% 0.14/0.13 % Command : duper %s
% 0.14/0.34 % Computer : n017.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 17:08:11 EDT 2023
% 0.14/0.34 % CPUTime :
% 31.09/31.32 SZS status Theorem for theBenchmark.p
% 31.09/31.32 SZS output start Proof for theBenchmark.p
% 31.09/31.32 Clause #1 (by assumption #[]): Eq
% 31.09/31.32 (∀ (B : Type) (Tsa Ts G1 : fun (hoare_28830079triple B) bool),
% 31.09/31.32 hoare_992312373derivs B G1 Ts →
% 31.09/31.32 pp
% 31.09/31.32 (aa (fun (hoare_28830079triple B) bool) bool
% 31.09/31.32 (aa (fun (hoare_28830079triple B) bool) (fun (fun (hoare_28830079triple B) bool) bool)
% 31.09/31.32 (ord_less_eq (fun (hoare_28830079triple B) bool)) Tsa)
% 31.09/31.32 Ts) →
% 31.09/31.32 hoare_992312373derivs B G1 Tsa)
% 31.09/31.32 True
% 31.09/31.32 Clause #55 (by assumption #[]): Eq
% 31.09/31.32 (∀ (B : Type) (A1 : fun B bool),
% 31.09/31.32 Eq (pow B A1) (collect (fun B bool) (combc (fun B bool) (fun B bool) bool (ord_less_eq (fun B bool)) A1)))
% 31.09/31.32 True
% 31.09/31.32 Clause #74 (by assumption #[]): Eq (∀ (B : Type) (P1 : fun B bool), Eq (collect B P1) P1) True
% 31.09/31.32 Clause #111 (by assumption #[]): Eq
% 31.09/31.32 (∀ (A C B : Type) (R : A) (Q : B) (P : fun A (fun B C)),
% 31.09/31.32 Eq (aa A C (combc A B C P Q) R) (aa B C (aa A (fun B C) P R) Q))
% 31.09/31.32 True
% 31.09/31.32 Clause #114 (by assumption #[]): Eq
% 31.09/31.32 (pp
% 31.09/31.32 (aa (fun (hoare_28830079triple a) bool) bool
% 31.09/31.32 (aa (fun (hoare_28830079triple a) bool) (fun (fun (hoare_28830079triple a) bool) bool)
% 31.09/31.32 (ord_less_eq (fun (hoare_28830079triple a) bool)) tsa)
% 31.09/31.32 ts))
% 31.09/31.32 True
% 31.09/31.32 Clause #116 (by assumption #[]): Eq (hoare_992312373derivs a ga ts) True
% 31.09/31.32 Clause #117 (by assumption #[]): Eq (Not (hoare_992312373derivs a ga tsa)) True
% 31.09/31.32 Clause #123 (by clausification #[117]): Eq (hoare_992312373derivs a ga tsa) False
% 31.09/31.32 Clause #124 (by clausification #[1]): ∀ (a : Type),
% 31.09/31.32 Eq
% 31.09/31.32 (∀ (Tsa Ts G1 : fun (hoare_28830079triple a) bool),
% 31.09/31.32 hoare_992312373derivs a G1 Ts →
% 31.09/31.32 pp
% 31.09/31.32 (aa (fun (hoare_28830079triple a) bool) bool
% 31.09/31.32 (aa (fun (hoare_28830079triple a) bool) (fun (fun (hoare_28830079triple a) bool) bool)
% 31.09/31.32 (ord_less_eq (fun (hoare_28830079triple a) bool)) Tsa)
% 31.09/31.32 Ts) →
% 31.09/31.32 hoare_992312373derivs a G1 Tsa)
% 31.09/31.32 True
% 31.09/31.32 Clause #125 (by clausification #[124]): ∀ (a : Type) (a_1 : fun (hoare_28830079triple a) bool),
% 31.09/31.32 Eq
% 31.09/31.32 (∀ (Ts G1 : fun (hoare_28830079triple a) bool),
% 31.09/31.32 hoare_992312373derivs a G1 Ts →
% 31.09/31.32 pp
% 31.09/31.32 (aa (fun (hoare_28830079triple a) bool) bool
% 31.09/31.32 (aa (fun (hoare_28830079triple a) bool) (fun (fun (hoare_28830079triple a) bool) bool)
% 31.09/31.32 (ord_less_eq (fun (hoare_28830079triple a) bool)) a_1)
% 31.09/31.32 Ts) →
% 31.09/31.32 hoare_992312373derivs a G1 a_1)
% 31.09/31.32 True
% 31.09/31.32 Clause #126 (by clausification #[125]): ∀ (a : Type) (a_1 a_2 : fun (hoare_28830079triple a) bool),
% 31.09/31.32 Eq
% 31.09/31.32 (∀ (G1 : fun (hoare_28830079triple a) bool),
% 31.09/31.32 hoare_992312373derivs a G1 a_1 →
% 31.09/31.32 pp
% 31.09/31.32 (aa (fun (hoare_28830079triple a) bool) bool
% 31.09/31.32 (aa (fun (hoare_28830079triple a) bool) (fun (fun (hoare_28830079triple a) bool) bool)
% 31.09/31.32 (ord_less_eq (fun (hoare_28830079triple a) bool)) a_2)
% 31.09/31.32 a_1) →
% 31.09/31.32 hoare_992312373derivs a G1 a_2)
% 31.09/31.32 True
% 31.09/31.32 Clause #127 (by clausification #[126]): ∀ (a : Type) (a_1 a_2 a_3 : fun (hoare_28830079triple a) bool),
% 31.09/31.32 Eq
% 31.09/31.32 (hoare_992312373derivs a a_1 a_2 →
% 31.09/31.32 pp
% 31.09/31.32 (aa (fun (hoare_28830079triple a) bool) bool
% 31.09/31.32 (aa (fun (hoare_28830079triple a) bool) (fun (fun (hoare_28830079triple a) bool) bool)
% 31.09/31.32 (ord_less_eq (fun (hoare_28830079triple a) bool)) a_3)
% 31.09/31.32 a_2) →
% 31.09/31.32 hoare_992312373derivs a a_1 a_3)
% 31.09/31.32 True
% 31.09/31.32 Clause #128 (by clausification #[127]): ∀ (a : Type) (a_1 a_2 a_3 : fun (hoare_28830079triple a) bool),
% 31.09/31.32 Or (Eq (hoare_992312373derivs a a_1 a_2) False)
% 31.09/31.32 (Eq
% 31.09/31.32 (pp
% 31.09/31.32 (aa (fun (hoare_28830079triple a) bool) bool
% 31.09/31.32 (aa (fun (hoare_28830079triple a) bool) (fun (fun (hoare_28830079triple a) bool) bool)
% 31.09/31.32 (ord_less_eq (fun (hoare_28830079triple a) bool)) a_3)
% 31.09/31.32 a_2) →
% 31.09/31.32 hoare_992312373derivs a a_1 a_3)
% 31.09/31.32 True)
% 31.09/31.32 Clause #129 (by clausification #[128]): ∀ (a : Type) (a_1 a_2 a_3 : fun (hoare_28830079triple a) bool),
% 31.09/31.32 Or (Eq (hoare_992312373derivs a a_1 a_2) False)
% 31.09/31.32 (Or
% 31.09/31.32 (Eq
% 31.09/31.32 (pp
% 31.09/31.32 (aa (fun (hoare_28830079triple a) bool) bool
% 31.16/31.34 (aa (fun (hoare_28830079triple a) bool) (fun (fun (hoare_28830079triple a) bool) bool)
% 31.16/31.34 (ord_less_eq (fun (hoare_28830079triple a) bool)) a_3)
% 31.16/31.34 a_2))
% 31.16/31.34 False)
% 31.16/31.34 (Eq (hoare_992312373derivs a a_1 a_3) True))
% 31.16/31.34 Clause #130 (by superposition #[129, 116]): ∀ (a_1 : fun (hoare_28830079triple a) bool),
% 31.16/31.34 Or
% 31.16/31.34 (Eq
% 31.16/31.34 (pp
% 31.16/31.34 (aa (fun (hoare_28830079triple a) bool) bool
% 31.16/31.34 (aa (fun (hoare_28830079triple a) bool) (fun (fun (hoare_28830079triple a) bool) bool)
% 31.16/31.34 (ord_less_eq (fun (hoare_28830079triple a) bool)) a_1)
% 31.16/31.34 ts))
% 31.16/31.34 False)
% 31.16/31.34 (Or (Eq (hoare_992312373derivs a ga a_1) True) (Eq False True))
% 31.16/31.34 Clause #213 (by clausification #[74]): ∀ (a : Type), Eq (∀ (P1 : fun a bool), Eq (collect a P1) P1) True
% 31.16/31.34 Clause #214 (by clausification #[213]): ∀ (a : Type) (a_1 : fun a bool), Eq (Eq (collect a a_1) a_1) True
% 31.16/31.34 Clause #215 (by clausification #[214]): ∀ (a : Type) (a_1 : fun a bool), Eq (collect a a_1) a_1
% 31.16/31.34 Clause #3941 (by clausification #[55]): ∀ (a : Type),
% 31.16/31.34 Eq
% 31.16/31.34 (∀ (A1 : fun a bool),
% 31.16/31.34 Eq (pow a A1) (collect (fun a bool) (combc (fun a bool) (fun a bool) bool (ord_less_eq (fun a bool)) A1)))
% 31.16/31.34 True
% 31.16/31.34 Clause #3942 (by clausification #[3941]): ∀ (a : Type) (a_1 : fun a bool),
% 31.16/31.34 Eq (Eq (pow a a_1) (collect (fun a bool) (combc (fun a bool) (fun a bool) bool (ord_less_eq (fun a bool)) a_1))) True
% 31.16/31.34 Clause #3943 (by clausification #[3942]): ∀ (a : Type) (a_1 : fun a bool),
% 31.16/31.34 Eq (pow a a_1) (collect (fun a bool) (combc (fun a bool) (fun a bool) bool (ord_less_eq (fun a bool)) a_1))
% 31.16/31.34 Clause #3944 (by superposition #[3943, 215]): ∀ (a : Type) (a_1 : fun a bool), Eq (pow a a_1) (combc (fun a bool) (fun a bool) bool (ord_less_eq (fun a bool)) a_1)
% 31.16/31.34 Clause #9802 (by clausification #[111]): ∀ (a : Type),
% 31.16/31.34 Eq
% 31.16/31.34 (∀ (C B : Type) (R : a) (Q : B) (P : fun a (fun B C)),
% 31.16/31.34 Eq (aa a C (combc a B C P Q) R) (aa B C (aa a (fun B C) P R) Q))
% 31.16/31.34 True
% 31.16/31.34 Clause #9803 (by clausification #[9802]): ∀ (a a_1 : Type),
% 31.16/31.34 Eq
% 31.16/31.34 (∀ (B : Type) (R : a) (Q : B) (P : fun a (fun B a_1)),
% 31.16/31.34 Eq (aa a a_1 (combc a B a_1 P Q) R) (aa B a_1 (aa a (fun B a_1) P R) Q))
% 31.16/31.34 True
% 31.16/31.34 Clause #9804 (by clausification #[9803]): ∀ (a a_1 a_2 : Type),
% 31.16/31.34 Eq
% 31.16/31.34 (∀ (R : a) (Q : a_1) (P : fun a (fun a_1 a_2)),
% 31.16/31.34 Eq (aa a a_2 (combc a a_1 a_2 P Q) R) (aa a_1 a_2 (aa a (fun a_1 a_2) P R) Q))
% 31.16/31.34 True
% 31.16/31.34 Clause #9805 (by clausification #[9804]): ∀ (a a_1 a_2 : Type) (a_3 : a_1),
% 31.16/31.34 Eq
% 31.16/31.34 (∀ (Q : a) (P : fun a_1 (fun a a_2)),
% 31.16/31.34 Eq (aa a_1 a_2 (combc a_1 a a_2 P Q) a_3) (aa a a_2 (aa a_1 (fun a a_2) P a_3) Q))
% 31.16/31.34 True
% 31.16/31.34 Clause #9806 (by clausification #[9805]): ∀ (a a_1 a_2 : Type) (a_3 : a_1) (a_4 : a),
% 31.16/31.34 Eq
% 31.16/31.34 (∀ (P : fun a (fun a_1 a_2)), Eq (aa a a_2 (combc a a_1 a_2 P a_3) a_4) (aa a_1 a_2 (aa a (fun a_1 a_2) P a_4) a_3))
% 31.16/31.34 True
% 31.16/31.34 Clause #9807 (by clausification #[9806]): ∀ (a a_1 a_2 : Type) (a_3 : fun a_1 (fun a_2 a)) (a_4 : a_2) (a_5 : a_1),
% 31.16/31.34 Eq (Eq (aa a_1 a (combc a_1 a_2 a a_3 a_4) a_5) (aa a_2 a (aa a_1 (fun a_2 a) a_3 a_5) a_4)) True
% 31.16/31.34 Clause #9808 (by clausification #[9807]): ∀ (a a_1 a_2 : Type) (a_3 : fun a_1 (fun a_2 a)) (a_4 : a_2) (a_5 : a_1),
% 31.16/31.34 Eq (aa a_1 a (combc a_1 a_2 a a_3 a_4) a_5) (aa a_2 a (aa a_1 (fun a_2 a) a_3 a_5) a_4)
% 31.16/31.34 Clause #9948 (by forward demodulation #[114, 9808]): Eq
% 31.16/31.34 (pp
% 31.16/31.34 (aa (fun (hoare_28830079triple a) bool) bool
% 31.16/31.34 (combc (fun (hoare_28830079triple a) bool) (fun (hoare_28830079triple a) bool) bool
% 31.16/31.34 (ord_less_eq (fun (hoare_28830079triple a) bool)) ts)
% 31.16/31.34 tsa))
% 31.16/31.34 True
% 31.16/31.34 Clause #9949 (by forward demodulation #[9948, 3944]): Eq (pp (aa (fun (hoare_28830079triple a) bool) bool (pow (hoare_28830079triple a) ts) tsa)) True
% 31.16/31.34 Clause #10170 (by clausification #[130]): ∀ (a_1 : fun (hoare_28830079triple a) bool),
% 31.16/31.34 Or
% 31.16/31.34 (Eq
% 31.16/31.34 (pp
% 31.16/31.34 (aa (fun (hoare_28830079triple a) bool) bool
% 31.16/31.34 (aa (fun (hoare_28830079triple a) bool) (fun (fun (hoare_28830079triple a) bool) bool)
% 31.16/31.34 (ord_less_eq (fun (hoare_28830079triple a) bool)) a_1)
% 31.16/31.34 ts))
% 31.16/31.34 False)
% 31.19/31.39 (Eq (hoare_992312373derivs a ga a_1) True)
% 31.19/31.39 Clause #10171 (by forward demodulation #[10170, 9808]): ∀ (a_1 : fun (hoare_28830079triple a) bool),
% 31.19/31.39 Or
% 31.19/31.39 (Eq
% 31.19/31.39 (pp
% 31.19/31.39 (aa (fun (hoare_28830079triple a) bool) bool
% 31.19/31.39 (combc (fun (hoare_28830079triple a) bool) (fun (hoare_28830079triple a) bool) bool
% 31.19/31.39 (ord_less_eq (fun (hoare_28830079triple a) bool)) ts)
% 31.19/31.39 a_1))
% 31.19/31.39 False)
% 31.19/31.39 (Eq (hoare_992312373derivs a ga a_1) True)
% 31.19/31.39 Clause #10172 (by forward demodulation #[10171, 3944]): ∀ (a_1 : fun (hoare_28830079triple a) bool),
% 31.19/31.39 Or (Eq (pp (aa (fun (hoare_28830079triple a) bool) bool (pow (hoare_28830079triple a) ts) a_1)) False)
% 31.19/31.39 (Eq (hoare_992312373derivs a ga a_1) True)
% 31.19/31.39 Clause #10175 (by superposition #[10172, 9949]): Or (Eq (hoare_992312373derivs a ga tsa) True) (Eq False True)
% 31.19/31.39 Clause #10177 (by clausification #[10175]): Eq (hoare_992312373derivs a ga tsa) True
% 31.19/31.39 Clause #10178 (by superposition #[10177, 123]): Eq True False
% 31.19/31.39 Clause #10181 (by clausification #[10178]): False
% 31.19/31.39 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------