TSTP Solution File: SET923+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET923+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n019.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 14:48:03 EDT 2023
% Result : Theorem 3.61s 3.84s
% Output : Proof 3.61s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET923+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : duper %s
% 0.17/0.34 % Computer : n019.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Sat Aug 26 16:21:43 EDT 2023
% 0.17/0.35 % CPUTime :
% 3.61/3.84 SZS status Theorem for theBenchmark.p
% 3.61/3.84 SZS output start Proof for theBenchmark.p
% 3.61/3.84 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset A (singleton B)) (Or (Eq A empty_set) (Eq A (singleton B)))) True
% 3.61/3.84 Clause #5 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq (set_difference A B) empty_set) (subset A B)) True
% 3.61/3.84 Clause #6 (by assumption #[]): Eq
% 3.61/3.84 (Not
% 3.61/3.84 (∀ (A B : Iota),
% 3.61/3.84 Not (And (And (Eq (set_difference A (singleton B)) empty_set) (Ne A empty_set)) (Ne A (singleton B)))))
% 3.61/3.84 True
% 3.61/3.84 Clause #13 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq (set_difference a B) empty_set) (subset a B)) True
% 3.61/3.84 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Eq (Iff (Eq (set_difference a a_1) empty_set) (subset a a_1)) True
% 3.61/3.84 Clause #16 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (Eq (set_difference a a_1) empty_set) False) (Eq (subset a a_1) True)
% 3.61/3.84 Clause #19 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset a (singleton B)) (Or (Eq a empty_set) (Eq a (singleton B)))) True
% 3.61/3.84 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (Iff (subset a (singleton a_1)) (Or (Eq a empty_set) (Eq a (singleton a_1)))) True
% 3.61/3.84 Clause #22 (by clausification #[20]): ∀ (a a_1 : Iota), Or (Eq (subset a (singleton a_1)) False) (Eq (Or (Eq a empty_set) (Eq a (singleton a_1))) True)
% 3.61/3.84 Clause #32 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Ne (set_difference a a_1) empty_set)
% 3.61/3.84 Clause #36 (by clausification #[6]): Eq
% 3.61/3.84 (∀ (A B : Iota),
% 3.61/3.84 Not (And (And (Eq (set_difference A (singleton B)) empty_set) (Ne A empty_set)) (Ne A (singleton B))))
% 3.61/3.84 False
% 3.61/3.84 Clause #37 (by clausification #[36]): ∀ (a : Iota),
% 3.61/3.84 Eq
% 3.61/3.84 (Not
% 3.61/3.84 (∀ (B : Iota),
% 3.61/3.84 Not
% 3.61/3.84 (And (And (Eq (set_difference (skS.0 2 a) (singleton B)) empty_set) (Ne (skS.0 2 a) empty_set))
% 3.61/3.84 (Ne (skS.0 2 a) (singleton B)))))
% 3.61/3.84 True
% 3.61/3.84 Clause #38 (by clausification #[37]): ∀ (a : Iota),
% 3.61/3.84 Eq
% 3.61/3.84 (∀ (B : Iota),
% 3.61/3.84 Not
% 3.61/3.84 (And (And (Eq (set_difference (skS.0 2 a) (singleton B)) empty_set) (Ne (skS.0 2 a) empty_set))
% 3.61/3.84 (Ne (skS.0 2 a) (singleton B))))
% 3.61/3.84 False
% 3.61/3.84 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota),
% 3.61/3.84 Eq
% 3.61/3.84 (Not
% 3.61/3.84 (Not
% 3.61/3.84 (And (And (Eq (set_difference (skS.0 2 a) (singleton (skS.0 3 a a_1))) empty_set) (Ne (skS.0 2 a) empty_set))
% 3.61/3.84 (Ne (skS.0 2 a) (singleton (skS.0 3 a a_1))))))
% 3.61/3.84 True
% 3.61/3.84 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota),
% 3.61/3.84 Eq
% 3.61/3.84 (Not
% 3.61/3.84 (And (And (Eq (set_difference (skS.0 2 a) (singleton (skS.0 3 a a_1))) empty_set) (Ne (skS.0 2 a) empty_set))
% 3.61/3.84 (Ne (skS.0 2 a) (singleton (skS.0 3 a a_1)))))
% 3.61/3.84 False
% 3.61/3.84 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota),
% 3.61/3.84 Eq
% 3.61/3.84 (And (And (Eq (set_difference (skS.0 2 a) (singleton (skS.0 3 a a_1))) empty_set) (Ne (skS.0 2 a) empty_set))
% 3.61/3.84 (Ne (skS.0 2 a) (singleton (skS.0 3 a a_1))))
% 3.61/3.84 True
% 3.61/3.84 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), Eq (Ne (skS.0 2 a) (singleton (skS.0 3 a a_1))) True
% 3.61/3.84 Clause #43 (by clausification #[41]): ∀ (a a_1 : Iota),
% 3.61/3.84 Eq (And (Eq (set_difference (skS.0 2 a) (singleton (skS.0 3 a a_1))) empty_set) (Ne (skS.0 2 a) empty_set)) True
% 3.61/3.84 Clause #44 (by clausification #[42]): ∀ (a a_1 : Iota), Ne (skS.0 2 a) (singleton (skS.0 3 a a_1))
% 3.61/3.84 Clause #45 (by clausification #[22]): ∀ (a a_1 : Iota),
% 3.61/3.84 Or (Eq (subset a (singleton a_1)) False) (Or (Eq (Eq a empty_set) True) (Eq (Eq a (singleton a_1)) True))
% 3.61/3.84 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), Or (Eq (subset a (singleton a_1)) False) (Or (Eq (Eq a (singleton a_1)) True) (Eq a empty_set))
% 3.61/3.84 Clause #47 (by clausification #[46]): ∀ (a a_1 : Iota), Or (Eq (subset a (singleton a_1)) False) (Or (Eq a empty_set) (Eq a (singleton a_1)))
% 3.61/3.84 Clause #52 (by clausification #[43]): ∀ (a : Iota), Eq (Ne (skS.0 2 a) empty_set) True
% 3.61/3.84 Clause #53 (by clausification #[43]): ∀ (a a_1 : Iota), Eq (Eq (set_difference (skS.0 2 a) (singleton (skS.0 3 a a_1))) empty_set) True
% 3.61/3.84 Clause #54 (by clausification #[52]): ∀ (a : Iota), Ne (skS.0 2 a) empty_set
% 3.61/3.84 Clause #55 (by clausification #[53]): ∀ (a a_1 : Iota), Eq (set_difference (skS.0 2 a) (singleton (skS.0 3 a a_1))) empty_set
% 3.61/3.85 Clause #56 (by superposition #[55, 32]): ∀ (a a_1 : Iota), Or (Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) True) (Ne empty_set empty_set)
% 3.61/3.85 Clause #57 (by eliminate resolved literals #[56]): ∀ (a a_1 : Iota), Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) True
% 3.61/3.85 Clause #58 (by superposition #[57, 47]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))))
% 3.61/3.85 Clause #60 (by clausification #[58]): ∀ (a a_1 : Iota), Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1)))
% 3.61/3.85 Clause #61 (by forward contextual literal cutting #[60, 54]): ∀ (a a_1 : Iota), Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))
% 3.61/3.85 Clause #62 (by forward contextual literal cutting #[61, 44]): False
% 3.61/3.85 SZS output end Proof for theBenchmark.p
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