TSTP Solution File: SEU739^2 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU739^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n022.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 : Thu Aug 31 16:43:39 EDT 2023
% Result : Theorem 3.85s 4.01s
% Output : Proof 3.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU739^2 : TPTP v8.1.2. Released v3.7.0.
% 0.11/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 01:14:26 EDT 2023
% 0.13/0.34 % CPUTime :
% 3.85/4.01 SZS status Theorem for theBenchmark.p
% 3.85/4.01 SZS output start Proof for theBenchmark.p
% 3.85/4.01 Clause #0 (by assumption #[]): Eq (Eq binunionIR (∀ (A B Xx : Iota), in Xx B → in Xx (binunion A B))) True
% 3.85/4.01 Clause #1 (by assumption #[]): Eq
% 3.85/4.01 (Not
% 3.85/4.01 (binunionIR →
% 3.85/4.01 ∀ (A X : Iota),
% 3.85/4.01 in X (powerset A) →
% 3.85/4.01 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx (binunion X Y)) → Not (in Xx Y)))
% 3.85/4.01 True
% 3.85/4.01 Clause #2 (by clausification #[0]): Eq binunionIR (∀ (A B Xx : Iota), in Xx B → in Xx (binunion A B))
% 3.85/4.01 Clause #18 (by clausification #[1]): Eq
% 3.85/4.01 (binunionIR →
% 3.85/4.01 ∀ (A X : Iota),
% 3.85/4.01 in X (powerset A) →
% 3.85/4.01 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx (binunion X Y)) → Not (in Xx Y))
% 3.85/4.01 False
% 3.85/4.01 Clause #19 (by clausification #[18]): Eq binunionIR True
% 3.85/4.01 Clause #20 (by clausification #[18]): Eq
% 3.85/4.01 (∀ (A X : Iota),
% 3.85/4.01 in X (powerset A) →
% 3.85/4.01 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx (binunion X Y)) → Not (in Xx Y))
% 3.85/4.01 False
% 3.85/4.01 Clause #21 (by backward demodulation #[19, 2]): Eq True (∀ (A B Xx : Iota), in Xx B → in Xx (binunion A B))
% 3.85/4.01 Clause #25 (by clausification #[21]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx B → in Xx (binunion a B)) True
% 3.85/4.01 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx a → in Xx (binunion a_1 a)) True
% 3.85/4.01 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Eq (in a a_1 → in a (binunion a_2 a_1)) True
% 3.85/4.01 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Eq (in a (binunion a_2 a_1)) True)
% 3.85/4.01 Clause #29 (by clausification #[20]): ∀ (a : Iota),
% 3.85/4.01 Eq
% 3.85/4.01 (Not
% 3.85/4.01 (∀ (X : Iota),
% 3.85/4.01 in X (powerset (skS.0 3 a)) →
% 3.85/4.01 ∀ (Y : Iota),
% 3.85/4.01 in Y (powerset (skS.0 3 a)) →
% 3.85/4.01 ∀ (Xx : Iota), in Xx (skS.0 3 a) → Not (in Xx (binunion X Y)) → Not (in Xx Y)))
% 3.85/4.01 True
% 3.85/4.01 Clause #30 (by clausification #[29]): ∀ (a : Iota),
% 3.85/4.01 Eq
% 3.85/4.01 (∀ (X : Iota),
% 3.85/4.01 in X (powerset (skS.0 3 a)) →
% 3.85/4.01 ∀ (Y : Iota),
% 3.85/4.01 in Y (powerset (skS.0 3 a)) → ∀ (Xx : Iota), in Xx (skS.0 3 a) → Not (in Xx (binunion X Y)) → Not (in Xx Y))
% 3.85/4.01 False
% 3.85/4.01 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota),
% 3.85/4.01 Eq
% 3.85/4.01 (Not
% 3.85/4.01 (in (skS.0 4 a a_1) (powerset (skS.0 3 a)) →
% 3.85/4.01 ∀ (Y : Iota),
% 3.85/4.01 in Y (powerset (skS.0 3 a)) →
% 3.85/4.01 ∀ (Xx : Iota), in Xx (skS.0 3 a) → Not (in Xx (binunion (skS.0 4 a a_1) Y)) → Not (in Xx Y)))
% 3.85/4.01 True
% 3.85/4.01 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota),
% 3.85/4.01 Eq
% 3.85/4.01 (in (skS.0 4 a a_1) (powerset (skS.0 3 a)) →
% 3.85/4.01 ∀ (Y : Iota),
% 3.85/4.01 in Y (powerset (skS.0 3 a)) →
% 3.85/4.01 ∀ (Xx : Iota), in Xx (skS.0 3 a) → Not (in Xx (binunion (skS.0 4 a a_1) Y)) → Not (in Xx Y))
% 3.85/4.01 False
% 3.85/4.01 Clause #34 (by clausification #[32]): ∀ (a a_1 : Iota),
% 3.85/4.01 Eq
% 3.85/4.01 (∀ (Y : Iota),
% 3.85/4.01 in Y (powerset (skS.0 3 a)) →
% 3.85/4.01 ∀ (Xx : Iota), in Xx (skS.0 3 a) → Not (in Xx (binunion (skS.0 4 a a_1) Y)) → Not (in Xx Y))
% 3.85/4.01 False
% 3.85/4.01 Clause #36 (by clausification #[34]): ∀ (a a_1 a_2 : Iota),
% 3.85/4.01 Eq
% 3.85/4.01 (Not
% 3.85/4.01 (in (skS.0 5 a a_1 a_2) (powerset (skS.0 3 a)) →
% 3.85/4.01 ∀ (Xx : Iota),
% 3.85/4.01 in Xx (skS.0 3 a) →
% 3.85/4.01 Not (in Xx (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))) → Not (in Xx (skS.0 5 a a_1 a_2))))
% 3.85/4.01 True
% 3.85/4.01 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota),
% 3.85/4.01 Eq
% 3.85/4.01 (in (skS.0 5 a a_1 a_2) (powerset (skS.0 3 a)) →
% 3.85/4.01 ∀ (Xx : Iota),
% 3.85/4.01 in Xx (skS.0 3 a) →
% 3.85/4.01 Not (in Xx (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))) → Not (in Xx (skS.0 5 a a_1 a_2)))
% 3.85/4.01 False
% 3.85/4.01 Clause #39 (by clausification #[37]): ∀ (a a_1 a_2 : Iota),
% 3.85/4.01 Eq
% 3.85/4.01 (∀ (Xx : Iota),
% 3.85/4.01 in Xx (skS.0 3 a) → Not (in Xx (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))) → Not (in Xx (skS.0 5 a a_1 a_2)))
% 3.85/4.01 False
% 3.85/4.01 Clause #41 (by clausification #[39]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.85/4.01 Eq
% 3.85/4.01 (Not
% 3.85/4.01 (in (skS.0 6 a a_1 a_2 a_3) (skS.0 3 a) →
% 3.85/4.01 Not (in (skS.0 6 a a_1 a_2 a_3) (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))) →
% 3.85/4.02 Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2))))
% 3.85/4.02 True
% 3.85/4.02 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.85/4.02 Eq
% 3.85/4.02 (in (skS.0 6 a a_1 a_2 a_3) (skS.0 3 a) →
% 3.85/4.02 Not (in (skS.0 6 a a_1 a_2 a_3) (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))) →
% 3.85/4.02 Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2)))
% 3.85/4.02 False
% 3.85/4.02 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.85/4.02 Eq
% 3.85/4.02 (Not (in (skS.0 6 a a_1 a_2 a_3) (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))) →
% 3.85/4.02 Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2)))
% 3.85/4.02 False
% 3.85/4.02 Clause #56 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota), Eq (Not (in (skS.0 6 a a_1 a_2 a_3) (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)))) True
% 3.85/4.02 Clause #57 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota), Eq (Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2))) False
% 3.85/4.02 Clause #58 (by clausification #[56]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 6 a a_1 a_2 a_3) (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))) False
% 3.85/4.02 Clause #59 (by clausification #[57]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2)) True
% 3.85/4.02 Clause #60 (by superposition #[59, 28]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.85/4.02 Or (Eq True False) (Eq (in (skS.0 6 a a_1 a_2 a_3) (binunion a_4 (skS.0 5 a a_1 a_2))) True)
% 3.85/4.02 Clause #69 (by clausification #[60]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (in (skS.0 6 a a_1 a_2 a_3) (binunion a_4 (skS.0 5 a a_1 a_2))) True
% 3.85/4.02 Clause #70 (by superposition #[69, 58]): Eq True False
% 3.85/4.02 Clause #72 (by clausification #[70]): False
% 3.85/4.02 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------