TSTP Solution File: SET968+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET968+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n002.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 14:48:11 EDT 2023
% Result : Theorem 16.13s 16.30s
% Output : Proof 16.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET968+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.12 % Command : duper %s
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 15:19:03 EDT 2023
% 0.12/0.34 % CPUTime :
% 16.13/16.30 SZS status Theorem for theBenchmark.p
% 16.13/16.30 SZS output start Proof for theBenchmark.p
% 16.13/16.30 Clause #0 (by assumption #[]): Eq (∀ (A B : Iota), Eq (set_union2 A B) (set_union2 B A)) True
% 16.13/16.30 Clause #6 (by assumption #[]): Eq
% 16.13/16.30 (∀ (A B C : Iota),
% 16.13/16.30 And (Eq (cartesian_product2 (set_union2 A B) C) (set_union2 (cartesian_product2 A C) (cartesian_product2 B C)))
% 16.13/16.30 (Eq (cartesian_product2 C (set_union2 A B)) (set_union2 (cartesian_product2 C A) (cartesian_product2 C B))))
% 16.13/16.30 True
% 16.13/16.30 Clause #7 (by assumption #[]): Eq
% 16.13/16.30 (Not
% 16.13/16.30 (∀ (A B C D : Iota),
% 16.13/16.30 Eq (cartesian_product2 (set_union2 A B) (set_union2 C D))
% 16.13/16.30 (set_union2 (set_union2 (set_union2 (cartesian_product2 A C) (cartesian_product2 A D)) (cartesian_product2 B C))
% 16.13/16.30 (cartesian_product2 B D))))
% 16.13/16.30 True
% 16.13/16.30 Clause #8 (by assumption #[]): Eq (∀ (A B C : Iota), Eq (set_union2 (set_union2 A B) C) (set_union2 A (set_union2 B C))) True
% 16.13/16.30 Clause #22 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (set_union2 a B) (set_union2 B a)) True
% 16.13/16.30 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Eq (Eq (set_union2 a a_1) (set_union2 a_1 a)) True
% 16.13/16.30 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (set_union2 a a_1) (set_union2 a_1 a)
% 16.13/16.30 Clause #30 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (B C : Iota), Eq (set_union2 (set_union2 a B) C) (set_union2 a (set_union2 B C))) True
% 16.13/16.30 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), Eq (set_union2 (set_union2 a a_1) C) (set_union2 a (set_union2 a_1 C))) True
% 16.13/16.30 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Eq (Eq (set_union2 (set_union2 a a_1) a_2) (set_union2 a (set_union2 a_1 a_2))) True
% 16.13/16.30 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Eq (set_union2 (set_union2 a a_1) a_2) (set_union2 a (set_union2 a_1 a_2))
% 16.13/16.30 Clause #41 (by superposition #[33, 24]): ∀ (a a_1 a_2 : Iota), Eq (set_union2 (set_union2 a a_1) a_2) (set_union2 a_1 (set_union2 a a_2))
% 16.13/16.30 Clause #48 (by clausification #[6]): ∀ (a : Iota),
% 16.13/16.30 Eq
% 16.13/16.30 (∀ (B C : Iota),
% 16.13/16.30 And (Eq (cartesian_product2 (set_union2 a B) C) (set_union2 (cartesian_product2 a C) (cartesian_product2 B C)))
% 16.13/16.30 (Eq (cartesian_product2 C (set_union2 a B)) (set_union2 (cartesian_product2 C a) (cartesian_product2 C B))))
% 16.13/16.30 True
% 16.13/16.30 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota),
% 16.13/16.30 Eq
% 16.13/16.30 (∀ (C : Iota),
% 16.13/16.30 And
% 16.13/16.30 (Eq (cartesian_product2 (set_union2 a a_1) C) (set_union2 (cartesian_product2 a C) (cartesian_product2 a_1 C)))
% 16.13/16.30 (Eq (cartesian_product2 C (set_union2 a a_1)) (set_union2 (cartesian_product2 C a) (cartesian_product2 C a_1))))
% 16.13/16.30 True
% 16.13/16.30 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 : Iota),
% 16.13/16.30 Eq
% 16.13/16.30 (And
% 16.13/16.30 (Eq (cartesian_product2 (set_union2 a a_1) a_2)
% 16.13/16.30 (set_union2 (cartesian_product2 a a_2) (cartesian_product2 a_1 a_2)))
% 16.13/16.30 (Eq (cartesian_product2 a_2 (set_union2 a a_1))
% 16.13/16.30 (set_union2 (cartesian_product2 a_2 a) (cartesian_product2 a_2 a_1))))
% 16.13/16.30 True
% 16.13/16.30 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota),
% 16.13/16.30 Eq (Eq (cartesian_product2 a (set_union2 a_1 a_2)) (set_union2 (cartesian_product2 a a_1) (cartesian_product2 a a_2)))
% 16.13/16.30 True
% 16.13/16.30 Clause #52 (by clausification #[50]): ∀ (a a_1 a_2 : Iota),
% 16.13/16.30 Eq
% 16.13/16.30 (Eq (cartesian_product2 (set_union2 a a_1) a_2)
% 16.13/16.30 (set_union2 (cartesian_product2 a a_2) (cartesian_product2 a_1 a_2)))
% 16.13/16.30 True
% 16.13/16.30 Clause #53 (by clausification #[51]): ∀ (a a_1 a_2 : Iota),
% 16.13/16.30 Eq (cartesian_product2 a (set_union2 a_1 a_2)) (set_union2 (cartesian_product2 a a_1) (cartesian_product2 a a_2))
% 16.13/16.30 Clause #59 (by superposition #[53, 33]): ∀ (a a_1 a_2 a_3 : Iota),
% 16.13/16.30 Eq (set_union2 (cartesian_product2 a (set_union2 a_1 a_2)) a_3)
% 16.13/16.30 (set_union2 (cartesian_product2 a a_1) (set_union2 (cartesian_product2 a a_2) a_3))
% 16.13/16.30 Clause #68 (by superposition #[41, 33]): ∀ (a a_1 a_2 : Iota), Eq (set_union2 a (set_union2 a_1 a_2)) (set_union2 a_1 (set_union2 a a_2))
% 16.13/16.30 Clause #70 (by superposition #[41, 24]): ∀ (a a_1 a_2 : Iota), Eq (set_union2 a (set_union2 a_1 a_2)) (set_union2 a_2 (set_union2 a_1 a))
% 16.13/16.30 Clause #116 (by clausification #[7]): Eq
% 16.13/16.30 (∀ (A B C D : Iota),
% 16.15/16.34 Eq (cartesian_product2 (set_union2 A B) (set_union2 C D))
% 16.15/16.34 (set_union2 (set_union2 (set_union2 (cartesian_product2 A C) (cartesian_product2 A D)) (cartesian_product2 B C))
% 16.15/16.34 (cartesian_product2 B D)))
% 16.15/16.34 False
% 16.15/16.34 Clause #117 (by clausification #[116]): ∀ (a : Iota),
% 16.15/16.34 Eq
% 16.15/16.34 (Not
% 16.15/16.34 (∀ (B C D : Iota),
% 16.15/16.34 Eq (cartesian_product2 (set_union2 (skS.0 2 a) B) (set_union2 C D))
% 16.15/16.34 (set_union2
% 16.15/16.34 (set_union2 (set_union2 (cartesian_product2 (skS.0 2 a) C) (cartesian_product2 (skS.0 2 a) D))
% 16.15/16.34 (cartesian_product2 B C))
% 16.15/16.34 (cartesian_product2 B D))))
% 16.15/16.34 True
% 16.15/16.34 Clause #118 (by clausification #[117]): ∀ (a : Iota),
% 16.15/16.34 Eq
% 16.15/16.34 (∀ (B C D : Iota),
% 16.15/16.34 Eq (cartesian_product2 (set_union2 (skS.0 2 a) B) (set_union2 C D))
% 16.15/16.34 (set_union2
% 16.15/16.34 (set_union2 (set_union2 (cartesian_product2 (skS.0 2 a) C) (cartesian_product2 (skS.0 2 a) D))
% 16.15/16.34 (cartesian_product2 B C))
% 16.15/16.34 (cartesian_product2 B D)))
% 16.15/16.34 False
% 16.15/16.34 Clause #119 (by clausification #[118]): ∀ (a a_1 : Iota),
% 16.15/16.34 Eq
% 16.15/16.34 (Not
% 16.15/16.34 (∀ (C D : Iota),
% 16.15/16.34 Eq (cartesian_product2 (set_union2 (skS.0 2 a) (skS.0 3 a a_1)) (set_union2 C D))
% 16.15/16.34 (set_union2
% 16.15/16.34 (set_union2 (set_union2 (cartesian_product2 (skS.0 2 a) C) (cartesian_product2 (skS.0 2 a) D))
% 16.15/16.34 (cartesian_product2 (skS.0 3 a a_1) C))
% 16.15/16.34 (cartesian_product2 (skS.0 3 a a_1) D))))
% 16.15/16.34 True
% 16.15/16.34 Clause #120 (by clausification #[119]): ∀ (a a_1 : Iota),
% 16.15/16.34 Eq
% 16.15/16.34 (∀ (C D : Iota),
% 16.15/16.34 Eq (cartesian_product2 (set_union2 (skS.0 2 a) (skS.0 3 a a_1)) (set_union2 C D))
% 16.15/16.34 (set_union2
% 16.15/16.34 (set_union2 (set_union2 (cartesian_product2 (skS.0 2 a) C) (cartesian_product2 (skS.0 2 a) D))
% 16.15/16.34 (cartesian_product2 (skS.0 3 a a_1) C))
% 16.15/16.34 (cartesian_product2 (skS.0 3 a a_1) D)))
% 16.15/16.34 False
% 16.15/16.34 Clause #121 (by clausification #[120]): ∀ (a a_1 a_2 : Iota),
% 16.15/16.34 Eq
% 16.15/16.34 (Not
% 16.15/16.34 (∀ (D : Iota),
% 16.15/16.34 Eq (cartesian_product2 (set_union2 (skS.0 2 a) (skS.0 3 a a_1)) (set_union2 (skS.0 4 a a_1 a_2) D))
% 16.15/16.34 (set_union2
% 16.15/16.34 (set_union2
% 16.15/16.34 (set_union2 (cartesian_product2 (skS.0 2 a) (skS.0 4 a a_1 a_2)) (cartesian_product2 (skS.0 2 a) D))
% 16.15/16.34 (cartesian_product2 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 16.15/16.34 (cartesian_product2 (skS.0 3 a a_1) D))))
% 16.15/16.34 True
% 16.15/16.34 Clause #122 (by clausification #[121]): ∀ (a a_1 a_2 : Iota),
% 16.15/16.34 Eq
% 16.15/16.34 (∀ (D : Iota),
% 16.15/16.34 Eq (cartesian_product2 (set_union2 (skS.0 2 a) (skS.0 3 a a_1)) (set_union2 (skS.0 4 a a_1 a_2) D))
% 16.15/16.34 (set_union2
% 16.15/16.34 (set_union2
% 16.15/16.34 (set_union2 (cartesian_product2 (skS.0 2 a) (skS.0 4 a a_1 a_2)) (cartesian_product2 (skS.0 2 a) D))
% 16.15/16.34 (cartesian_product2 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 16.15/16.34 (cartesian_product2 (skS.0 3 a a_1) D)))
% 16.15/16.34 False
% 16.15/16.34 Clause #123 (by clausification #[122]): ∀ (a a_1 a_2 a_3 : Iota),
% 16.15/16.34 Eq
% 16.15/16.34 (Not
% 16.15/16.34 (Eq
% 16.15/16.34 (cartesian_product2 (set_union2 (skS.0 2 a) (skS.0 3 a a_1))
% 16.15/16.34 (set_union2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)))
% 16.15/16.34 (set_union2
% 16.15/16.34 (set_union2
% 16.15/16.34 (set_union2 (cartesian_product2 (skS.0 2 a) (skS.0 4 a a_1 a_2))
% 16.15/16.34 (cartesian_product2 (skS.0 2 a) (skS.0 5 a a_1 a_2 a_3)))
% 16.15/16.34 (cartesian_product2 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 16.15/16.34 (cartesian_product2 (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3)))))
% 16.15/16.34 True
% 16.15/16.34 Clause #124 (by clausification #[123]): ∀ (a a_1 a_2 a_3 : Iota),
% 16.15/16.34 Eq
% 16.15/16.34 (Eq
% 16.15/16.34 (cartesian_product2 (set_union2 (skS.0 2 a) (skS.0 3 a a_1))
% 16.15/16.34 (set_union2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)))
% 16.15/16.34 (set_union2
% 16.15/16.34 (set_union2
% 16.15/16.34 (set_union2 (cartesian_product2 (skS.0 2 a) (skS.0 4 a a_1 a_2))
% 16.15/16.34 (cartesian_product2 (skS.0 2 a) (skS.0 5 a a_1 a_2 a_3)))
% 16.15/16.34 (cartesian_product2 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 16.15/16.34 (cartesian_product2 (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3))))
% 16.15/16.34 False
% 16.15/16.34 Clause #125 (by clausification #[124]): ∀ (a a_1 a_2 a_3 : Iota),
% 16.15/16.34 Ne
% 16.15/16.34 (cartesian_product2 (set_union2 (skS.0 2 a) (skS.0 3 a a_1))
% 16.15/16.34 (set_union2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)))
% 16.23/16.46 (set_union2
% 16.23/16.46 (set_union2
% 16.23/16.46 (set_union2 (cartesian_product2 (skS.0 2 a) (skS.0 4 a a_1 a_2))
% 16.23/16.46 (cartesian_product2 (skS.0 2 a) (skS.0 5 a a_1 a_2 a_3)))
% 16.23/16.46 (cartesian_product2 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 16.23/16.46 (cartesian_product2 (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3)))
% 16.23/16.46 Clause #126 (by forward demodulation #[125, 33]): ∀ (a a_1 a_2 a_3 : Iota),
% 16.23/16.46 Ne
% 16.23/16.46 (cartesian_product2 (set_union2 (skS.0 2 a) (skS.0 3 a a_1))
% 16.23/16.46 (set_union2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)))
% 16.23/16.46 (set_union2
% 16.23/16.46 (set_union2 (cartesian_product2 (skS.0 2 a) (skS.0 4 a a_1 a_2))
% 16.23/16.46 (cartesian_product2 (skS.0 2 a) (skS.0 5 a a_1 a_2 a_3)))
% 16.23/16.46 (set_union2 (cartesian_product2 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))
% 16.23/16.46 (cartesian_product2 (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3))))
% 16.23/16.46 Clause #127 (by forward demodulation #[126, 70]): ∀ (a a_1 a_2 a_3 : Iota),
% 16.23/16.46 Ne
% 16.23/16.46 (cartesian_product2 (set_union2 (skS.0 2 a) (skS.0 3 a a_1))
% 16.23/16.46 (set_union2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)))
% 16.23/16.46 (set_union2 (cartesian_product2 (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3))
% 16.23/16.46 (set_union2 (cartesian_product2 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))
% 16.23/16.46 (set_union2 (cartesian_product2 (skS.0 2 a) (skS.0 4 a a_1 a_2))
% 16.23/16.46 (cartesian_product2 (skS.0 2 a) (skS.0 5 a a_1 a_2 a_3)))))
% 16.23/16.46 Clause #128 (by forward demodulation #[127, 53]): ∀ (a a_1 a_2 a_3 : Iota),
% 16.23/16.46 Ne
% 16.23/16.46 (cartesian_product2 (set_union2 (skS.0 2 a) (skS.0 3 a a_1))
% 16.23/16.46 (set_union2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)))
% 16.23/16.46 (set_union2 (cartesian_product2 (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3))
% 16.23/16.46 (set_union2 (cartesian_product2 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))
% 16.23/16.46 (cartesian_product2 (skS.0 2 a) (set_union2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)))))
% 16.23/16.46 Clause #375 (by superposition #[68, 128]): ∀ (a a_1 a_2 a_3 : Iota),
% 16.23/16.46 Ne
% 16.23/16.46 (cartesian_product2 (set_union2 (skS.0 2 a) (skS.0 3 a a_1))
% 16.23/16.46 (set_union2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)))
% 16.23/16.46 (set_union2 (cartesian_product2 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))
% 16.23/16.46 (set_union2 (cartesian_product2 (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3))
% 16.23/16.46 (cartesian_product2 (skS.0 2 a) (set_union2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)))))
% 16.23/16.46 Clause #617 (by clausification #[52]): ∀ (a a_1 a_2 : Iota),
% 16.23/16.46 Eq (cartesian_product2 (set_union2 a a_1) a_2) (set_union2 (cartesian_product2 a a_2) (cartesian_product2 a_1 a_2))
% 16.23/16.46 Clause #8295 (by forward demodulation #[375, 59]): ∀ (a a_1 a_2 a_3 : Iota),
% 16.23/16.46 Ne
% 16.23/16.46 (cartesian_product2 (set_union2 (skS.0 2 a) (skS.0 3 a a_1))
% 16.23/16.46 (set_union2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)))
% 16.23/16.46 (set_union2 (cartesian_product2 (skS.0 3 a a_1) (set_union2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)))
% 16.23/16.46 (cartesian_product2 (skS.0 2 a) (set_union2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3))))
% 16.23/16.46 Clause #8296 (by forward demodulation #[8295, 617]): ∀ (a a_1 a_2 a_3 : Iota),
% 16.23/16.46 Ne
% 16.23/16.46 (cartesian_product2 (set_union2 (skS.0 2 a) (skS.0 3 a a_1))
% 16.23/16.46 (set_union2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)))
% 16.23/16.46 (cartesian_product2 (set_union2 (skS.0 3 a a_1) (skS.0 2 a))
% 16.23/16.46 (set_union2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)))
% 16.23/16.46 Clause #8297 (by forward demodulation #[8296, 24]): ∀ (a a_1 a_2 a_3 : Iota),
% 16.23/16.46 Ne
% 16.23/16.46 (cartesian_product2 (set_union2 (skS.0 2 a) (skS.0 3 a a_1))
% 16.23/16.46 (set_union2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)))
% 16.23/16.46 (cartesian_product2 (set_union2 (skS.0 2 a) (skS.0 3 a a_1))
% 16.23/16.46 (set_union2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)))
% 16.23/16.46 Clause #8298 (by eliminate resolved literals #[8297]): False
% 16.23/16.46 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------