TSTP Solution File: SET617+3 by Duper---1.0
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% File : Duper---1.0
% Problem : SET617+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n023.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 14:47:06 EDT 2023
% Result : Theorem 5.50s 5.69s
% Output : Proof 5.50s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET617+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n023.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 : Sat Aug 26 11:41:11 EDT 2023
% 0.14/0.35 % CPUTime :
% 5.50/5.69 SZS status Theorem for theBenchmark.p
% 5.50/5.69 SZS output start Proof for theBenchmark.p
% 5.50/5.69 Clause #0 (by assumption #[]): Eq (∀ (B C : Iota), Eq (symmetric_difference B C) (union (difference B C) (difference C B))) True
% 5.50/5.69 Clause #1 (by assumption #[]): Eq (∀ (B : Iota), Eq (union B empty_set) B) True
% 5.50/5.69 Clause #2 (by assumption #[]): Eq (∀ (B : Iota), Eq (difference B empty_set) B) True
% 5.50/5.69 Clause #3 (by assumption #[]): Eq (∀ (B : Iota), Eq (difference empty_set B) empty_set) True
% 5.50/5.69 Clause #6 (by assumption #[]): Eq (∀ (B C : Iota), Eq (union B C) (union C B)) True
% 5.50/5.69 Clause #12 (by assumption #[]): Eq (Not (∀ (B : Iota), And (Eq (symmetric_difference B empty_set) B) (Eq (symmetric_difference empty_set B) B))) True
% 5.50/5.69 Clause #16 (by clausification #[3]): ∀ (a : Iota), Eq (Eq (difference empty_set a) empty_set) True
% 5.50/5.69 Clause #17 (by clausification #[16]): ∀ (a : Iota), Eq (difference empty_set a) empty_set
% 5.50/5.69 Clause #18 (by clausification #[2]): ∀ (a : Iota), Eq (Eq (difference a empty_set) a) True
% 5.50/5.69 Clause #19 (by clausification #[18]): ∀ (a : Iota), Eq (difference a empty_set) a
% 5.50/5.69 Clause #20 (by clausification #[1]): ∀ (a : Iota), Eq (Eq (union a empty_set) a) True
% 5.50/5.69 Clause #21 (by clausification #[20]): ∀ (a : Iota), Eq (union a empty_set) a
% 5.50/5.69 Clause #22 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (symmetric_difference a C) (union (difference a C) (difference C a))) True
% 5.50/5.69 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Eq (Eq (symmetric_difference a a_1) (union (difference a a_1) (difference a_1 a))) True
% 5.50/5.69 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (symmetric_difference a a_1) (union (difference a a_1) (difference a_1 a))
% 5.50/5.69 Clause #27 (by superposition #[24, 19]): ∀ (a : Iota), Eq (symmetric_difference a empty_set) (union a (difference empty_set a))
% 5.50/5.69 Clause #28 (by superposition #[24, 17]): ∀ (a : Iota), Eq (symmetric_difference empty_set a) (union empty_set (difference a empty_set))
% 5.50/5.69 Clause #29 (by forward demodulation #[28, 19]): ∀ (a : Iota), Eq (symmetric_difference empty_set a) (union empty_set a)
% 5.50/5.69 Clause #31 (by forward demodulation #[27, 17]): ∀ (a : Iota), Eq (symmetric_difference a empty_set) (union a empty_set)
% 5.50/5.69 Clause #32 (by superposition #[31, 21]): ∀ (a : Iota), Eq (symmetric_difference a empty_set) a
% 5.50/5.69 Clause #51 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (union a C) (union C a)) True
% 5.50/5.69 Clause #52 (by clausification #[51]): ∀ (a a_1 : Iota), Eq (Eq (union a a_1) (union a_1 a)) True
% 5.50/5.69 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), Eq (union a a_1) (union a_1 a)
% 5.50/5.69 Clause #55 (by superposition #[53, 21]): ∀ (a : Iota), Eq (union empty_set a) a
% 5.50/5.69 Clause #57 (by superposition #[55, 29]): ∀ (a : Iota), Eq (symmetric_difference empty_set a) a
% 5.50/5.69 Clause #95 (by clausification #[12]): Eq (∀ (B : Iota), And (Eq (symmetric_difference B empty_set) B) (Eq (symmetric_difference empty_set B) B)) False
% 5.50/5.69 Clause #96 (by clausification #[95]): ∀ (a : Iota),
% 5.50/5.69 Eq
% 5.50/5.69 (Not
% 5.50/5.69 (And (Eq (symmetric_difference (skS.0 3 a) empty_set) (skS.0 3 a))
% 5.50/5.69 (Eq (symmetric_difference empty_set (skS.0 3 a)) (skS.0 3 a))))
% 5.50/5.69 True
% 5.50/5.69 Clause #97 (by clausification #[96]): ∀ (a : Iota),
% 5.50/5.69 Eq
% 5.50/5.69 (And (Eq (symmetric_difference (skS.0 3 a) empty_set) (skS.0 3 a))
% 5.50/5.69 (Eq (symmetric_difference empty_set (skS.0 3 a)) (skS.0 3 a)))
% 5.50/5.69 False
% 5.50/5.69 Clause #98 (by clausification #[97]): ∀ (a : Iota),
% 5.50/5.69 Or (Eq (Eq (symmetric_difference (skS.0 3 a) empty_set) (skS.0 3 a)) False)
% 5.50/5.69 (Eq (Eq (symmetric_difference empty_set (skS.0 3 a)) (skS.0 3 a)) False)
% 5.50/5.69 Clause #99 (by clausification #[98]): ∀ (a : Iota),
% 5.50/5.69 Or (Eq (Eq (symmetric_difference empty_set (skS.0 3 a)) (skS.0 3 a)) False)
% 5.50/5.69 (Ne (symmetric_difference (skS.0 3 a) empty_set) (skS.0 3 a))
% 5.50/5.69 Clause #100 (by clausification #[99]): ∀ (a : Iota),
% 5.50/5.69 Or (Ne (symmetric_difference (skS.0 3 a) empty_set) (skS.0 3 a))
% 5.50/5.69 (Ne (symmetric_difference empty_set (skS.0 3 a)) (skS.0 3 a))
% 5.50/5.69 Clause #101 (by forward demodulation #[100, 32]): ∀ (a : Iota), Or (Ne (skS.0 3 a) (skS.0 3 a)) (Ne (symmetric_difference empty_set (skS.0 3 a)) (skS.0 3 a))
% 5.50/5.69 Clause #102 (by eliminate resolved literals #[101]): ∀ (a : Iota), Ne (symmetric_difference empty_set (skS.0 3 a)) (skS.0 3 a)
% 5.50/5.69 Clause #103 (by forward demodulation #[102, 57]): ∀ (a : Iota), Ne (skS.0 3 a) (skS.0 3 a)
% 5.50/5.69 Clause #104 (by eliminate resolved literals #[103]): False
% 5.50/5.69 SZS output end Proof for theBenchmark.p
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