TSTP Solution File: SET622+3 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET622+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n005.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 14:47:07 EDT 2023
% Result : Theorem 4.78s 4.98s
% Output : Proof 4.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET622+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.14 % Command : duper %s
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 09:52:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 4.78/4.98 SZS status Theorem for theBenchmark.p
% 4.78/4.98 SZS output start Proof for theBenchmark.p
% 4.78/4.98 Clause #0 (by assumption #[]): Eq (∀ (B C D : Iota), Eq (intersection (intersection B C) D) (intersection B (intersection C D))) True
% 4.78/4.98 Clause #1 (by assumption #[]): Eq (∀ (B C D : Iota), Eq (difference B (difference C D)) (union (difference B C) (intersection B D))) True
% 4.78/4.98 Clause #2 (by assumption #[]): Eq (∀ (B C : Iota), Eq (symmetric_difference B C) (difference (union B C) (intersection B C))) True
% 4.78/4.98 Clause #8 (by assumption #[]): Eq (∀ (B C : Iota), Eq (union B C) (union C B)) True
% 4.78/4.98 Clause #14 (by assumption #[]): Eq
% 4.78/4.98 (Not
% 4.78/4.98 (∀ (B C D : Iota),
% 4.78/4.98 Eq (difference B (symmetric_difference C D))
% 4.78/4.98 (union (difference B (union C D)) (intersection (intersection B C) D))))
% 4.78/4.98 True
% 4.78/4.98 Clause #22 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (union a C) (union C a)) True
% 4.78/4.98 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Eq (Eq (union a a_1) (union a_1 a)) True
% 4.78/4.98 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (union a a_1) (union a_1 a)
% 4.78/4.98 Clause #33 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C D : Iota), Eq (intersection (intersection a C) D) (intersection a (intersection C D))) True
% 4.78/4.98 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Eq (∀ (D : Iota), Eq (intersection (intersection a a_1) D) (intersection a (intersection a_1 D))) True
% 4.78/4.98 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), Eq (Eq (intersection (intersection a a_1) a_2) (intersection a (intersection a_1 a_2))) True
% 4.78/4.98 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), Eq (intersection (intersection a a_1) a_2) (intersection a (intersection a_1 a_2))
% 4.78/4.98 Clause #84 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (C D : Iota), Eq (difference a (difference C D)) (union (difference a C) (intersection a D))) True
% 4.78/4.98 Clause #85 (by clausification #[84]): ∀ (a a_1 : Iota),
% 4.78/4.98 Eq (∀ (D : Iota), Eq (difference a (difference a_1 D)) (union (difference a a_1) (intersection a D))) True
% 4.78/4.98 Clause #86 (by clausification #[85]): ∀ (a a_1 a_2 : Iota), Eq (Eq (difference a (difference a_1 a_2)) (union (difference a a_1) (intersection a a_2))) True
% 4.78/4.98 Clause #87 (by clausification #[86]): ∀ (a a_1 a_2 : Iota), Eq (difference a (difference a_1 a_2)) (union (difference a a_1) (intersection a a_2))
% 4.78/4.98 Clause #89 (by superposition #[87, 24]): ∀ (a a_1 a_2 : Iota), Eq (union (intersection a a_1) (difference a a_2)) (difference a (difference a_2 a_1))
% 4.78/4.98 Clause #125 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (symmetric_difference a C) (difference (union a C) (intersection a C))) True
% 4.78/4.98 Clause #126 (by clausification #[125]): ∀ (a a_1 : Iota), Eq (Eq (symmetric_difference a a_1) (difference (union a a_1) (intersection a a_1))) True
% 4.78/4.98 Clause #127 (by clausification #[126]): ∀ (a a_1 : Iota), Eq (symmetric_difference a a_1) (difference (union a a_1) (intersection a a_1))
% 4.78/4.98 Clause #718 (by clausification #[14]): Eq
% 4.78/4.98 (∀ (B C D : Iota),
% 4.78/4.98 Eq (difference B (symmetric_difference C D)) (union (difference B (union C D)) (intersection (intersection B C) D)))
% 4.78/4.98 False
% 4.78/4.98 Clause #719 (by clausification #[718]): ∀ (a : Iota),
% 4.78/4.98 Eq
% 4.78/4.98 (Not
% 4.78/4.98 (∀ (C D : Iota),
% 4.78/4.98 Eq (difference (skS.0 2 a) (symmetric_difference C D))
% 4.78/4.98 (union (difference (skS.0 2 a) (union C D)) (intersection (intersection (skS.0 2 a) C) D))))
% 4.78/4.98 True
% 4.78/4.98 Clause #720 (by clausification #[719]): ∀ (a : Iota),
% 4.78/4.98 Eq
% 4.78/4.98 (∀ (C D : Iota),
% 4.78/4.98 Eq (difference (skS.0 2 a) (symmetric_difference C D))
% 4.78/4.98 (union (difference (skS.0 2 a) (union C D)) (intersection (intersection (skS.0 2 a) C) D)))
% 4.78/4.98 False
% 4.78/4.98 Clause #721 (by clausification #[720]): ∀ (a a_1 : Iota),
% 4.78/4.98 Eq
% 4.78/4.98 (Not
% 4.78/4.98 (∀ (D : Iota),
% 4.78/4.98 Eq (difference (skS.0 2 a) (symmetric_difference (skS.0 3 a a_1) D))
% 4.78/4.98 (union (difference (skS.0 2 a) (union (skS.0 3 a a_1) D))
% 4.78/4.98 (intersection (intersection (skS.0 2 a) (skS.0 3 a a_1)) D))))
% 4.78/4.98 True
% 4.78/4.98 Clause #722 (by clausification #[721]): ∀ (a a_1 : Iota),
% 4.78/4.98 Eq
% 4.78/4.98 (∀ (D : Iota),
% 4.78/4.98 Eq (difference (skS.0 2 a) (symmetric_difference (skS.0 3 a a_1) D))
% 4.78/4.99 (union (difference (skS.0 2 a) (union (skS.0 3 a a_1) D))
% 4.78/4.99 (intersection (intersection (skS.0 2 a) (skS.0 3 a a_1)) D)))
% 4.78/4.99 False
% 4.78/4.99 Clause #723 (by clausification #[722]): ∀ (a a_1 a_2 : Iota),
% 4.78/4.99 Eq
% 4.78/4.99 (Not
% 4.78/4.99 (Eq (difference (skS.0 2 a) (symmetric_difference (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 4.78/4.99 (union (difference (skS.0 2 a) (union (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 4.78/4.99 (intersection (intersection (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)))))
% 4.78/4.99 True
% 4.78/4.99 Clause #724 (by clausification #[723]): ∀ (a a_1 a_2 : Iota),
% 4.78/4.99 Eq
% 4.78/4.99 (Eq (difference (skS.0 2 a) (symmetric_difference (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 4.78/4.99 (union (difference (skS.0 2 a) (union (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 4.78/4.99 (intersection (intersection (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2))))
% 4.78/4.99 False
% 4.78/4.99 Clause #725 (by clausification #[724]): ∀ (a a_1 a_2 : Iota),
% 4.78/4.99 Ne (difference (skS.0 2 a) (symmetric_difference (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 4.78/4.99 (union (difference (skS.0 2 a) (union (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 4.78/4.99 (intersection (intersection (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)))
% 4.78/4.99 Clause #726 (by forward demodulation #[725, 24]): ∀ (a a_1 a_2 : Iota),
% 4.78/4.99 Ne (difference (skS.0 2 a) (symmetric_difference (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 4.78/4.99 (union (intersection (intersection (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2))
% 4.78/4.99 (difference (skS.0 2 a) (union (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))))
% 4.78/4.99 Clause #727 (by forward demodulation #[726, 36]): ∀ (a a_1 a_2 : Iota),
% 4.78/4.99 Ne (difference (skS.0 2 a) (symmetric_difference (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 4.78/4.99 (union (intersection (skS.0 2 a) (intersection (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 4.78/4.99 (difference (skS.0 2 a) (union (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))))
% 4.78/4.99 Clause #728 (by forward demodulation #[727, 89]): ∀ (a a_1 a_2 : Iota),
% 4.78/4.99 Ne (difference (skS.0 2 a) (symmetric_difference (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 4.78/4.99 (difference (skS.0 2 a)
% 4.78/4.99 (difference (union (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) (intersection (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))))
% 4.78/4.99 Clause #729 (by forward demodulation #[728, 127]): ∀ (a a_1 a_2 : Iota),
% 4.78/4.99 Ne (difference (skS.0 2 a) (symmetric_difference (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 4.78/4.99 (difference (skS.0 2 a) (symmetric_difference (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))
% 4.78/4.99 Clause #730 (by eliminate resolved literals #[729]): False
% 4.78/4.99 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------