TSTP Solution File: SET175+3 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET175+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n031.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 14:45:56 EDT 2023
% Result : Theorem 54.87s 55.02s
% Output : Proof 54.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET175+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n031.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 12:23:38 EDT 2023
% 0.14/0.35 % CPUTime :
% 54.87/55.02 SZS status Theorem for theBenchmark.p
% 54.87/55.02 SZS output start Proof for theBenchmark.p
% 54.87/55.02 Clause #0 (by assumption #[]): Eq (∀ (B C D : Iota), Iff (member D (union B C)) (Or (member D B) (member D C))) True
% 54.87/55.02 Clause #1 (by assumption #[]): Eq (∀ (B C D : Iota), Iff (member D (intersection B C)) (And (member D B) (member D C))) True
% 54.87/55.02 Clause #2 (by assumption #[]): Eq (∀ (B C : Iota), Iff (Eq B C) (And (subset B C) (subset C B))) True
% 54.87/55.02 Clause #3 (by assumption #[]): Eq (∀ (B C : Iota), Eq (union B C) (union C B)) True
% 54.87/55.02 Clause #4 (by assumption #[]): Eq (∀ (B C : Iota), Eq (intersection B C) (intersection C B)) True
% 54.87/55.02 Clause #5 (by assumption #[]): Eq (∀ (B C : Iota), Iff (subset B C) (∀ (D : Iota), member D B → member D C)) True
% 54.87/55.02 Clause #8 (by assumption #[]): Eq (Not (∀ (B C : Iota), Eq (union B (intersection B C)) B)) True
% 54.87/55.02 Clause #10 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (union a C) (union C a)) True
% 54.87/55.02 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (Eq (union a a_1) (union a_1 a)) True
% 54.87/55.02 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (union a a_1) (union a_1 a)
% 54.87/55.02 Clause #13 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (intersection a C) (intersection C a)) True
% 54.87/55.02 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Eq (Eq (intersection a a_1) (intersection a_1 a)) True
% 54.87/55.02 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Eq (intersection a a_1) (intersection a_1 a)
% 54.87/55.02 Clause #16 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (subset a C) (∀ (D : Iota), member D a → member D C)) True
% 54.87/55.02 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (D : Iota), member D a → member D a_1)) True
% 54.87/55.02 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Eq (∀ (D : Iota), member D a → member D a_1) False)
% 54.87/55.02 Clause #20 (by clausification #[18]): ∀ (a a_1 a_2 : Iota),
% 54.87/55.02 Or (Eq (subset a a_1) True) (Eq (Not (member (skS.0 0 a a_1 a_2) a → member (skS.0 0 a a_1 a_2) a_1)) True)
% 54.87/55.02 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota),
% 54.87/55.02 Or (Eq (subset a a_1) True) (Eq (member (skS.0 0 a a_1 a_2) a → member (skS.0 0 a a_1 a_2) a_1) False)
% 54.87/55.02 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (member (skS.0 0 a a_1 a_2) a) True)
% 54.87/55.02 Clause #23 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (member (skS.0 0 a a_1 a_2) a_1) False)
% 54.87/55.02 Clause #27 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C D : Iota), Iff (member D (union a C)) (Or (member D a) (member D C))) True
% 54.87/55.02 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (∀ (D : Iota), Iff (member D (union a a_1)) (Or (member D a) (member D a_1))) True
% 54.87/55.02 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Eq (Iff (member a (union a_1 a_2)) (Or (member a a_1) (member a a_2))) True
% 54.87/55.02 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (union a_1 a_2)) True) (Eq (Or (member a a_1) (member a a_2)) False)
% 54.87/55.02 Clause #31 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (union a_1 a_2)) False) (Eq (Or (member a a_1) (member a a_2)) True)
% 54.87/55.02 Clause #32 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (union a_1 a_2)) True) (Eq (member a a_2) False)
% 54.87/55.02 Clause #34 (by superposition #[32, 22]): ∀ (a a_1 a_2 a_3 : Iota),
% 54.87/55.02 Or (Eq (member (skS.0 0 a a_1 a_2) (union a_3 a)) True) (Or (Eq (subset a a_1) True) (Eq False True))
% 54.87/55.02 Clause #37 (by clausification #[8]): Eq (∀ (B C : Iota), Eq (union B (intersection B C)) B) False
% 54.87/55.02 Clause #38 (by clausification #[37]): ∀ (a : Iota), Eq (Not (∀ (C : Iota), Eq (union (skS.0 1 a) (intersection (skS.0 1 a) C)) (skS.0 1 a))) True
% 54.87/55.02 Clause #39 (by clausification #[38]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (union (skS.0 1 a) (intersection (skS.0 1 a) C)) (skS.0 1 a)) False
% 54.87/55.02 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), Eq (Not (Eq (union (skS.0 1 a) (intersection (skS.0 1 a) (skS.0 2 a a_1))) (skS.0 1 a))) True
% 54.87/55.02 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), Eq (Eq (union (skS.0 1 a) (intersection (skS.0 1 a) (skS.0 2 a a_1))) (skS.0 1 a)) False
% 54.87/55.04 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), Ne (union (skS.0 1 a) (intersection (skS.0 1 a) (skS.0 2 a a_1))) (skS.0 1 a)
% 54.87/55.04 Clause #43 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (union a_1 a_2)) False) (Or (Eq (member a a_1) True) (Eq (member a a_2) True))
% 54.87/55.04 Clause #44 (by superposition #[43, 22]): ∀ (a a_1 a_2 a_3 : Iota),
% 54.87/55.04 Or (Eq (member (skS.0 0 (union a a_1) a_2 a_3) a) True)
% 54.87/55.04 (Or (Eq (member (skS.0 0 (union a a_1) a_2 a_3) a_1) True)
% 54.87/55.04 (Or (Eq (subset (union a a_1) a_2) True) (Eq False True)))
% 54.87/55.04 Clause #47 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (C D : Iota), Iff (member D (intersection a C)) (And (member D a) (member D C))) True
% 54.87/55.04 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota), Eq (∀ (D : Iota), Iff (member D (intersection a a_1)) (And (member D a) (member D a_1))) True
% 54.87/55.04 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 : Iota), Eq (Iff (member a (intersection a_1 a_2)) (And (member a a_1) (member a a_2))) True
% 54.87/55.04 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (intersection a_1 a_2)) True) (Eq (And (member a a_1) (member a a_2)) False)
% 54.87/55.04 Clause #51 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (intersection a_1 a_2)) False) (Eq (And (member a a_1) (member a a_2)) True)
% 54.87/55.04 Clause #52 (by clausification #[50]): ∀ (a a_1 a_2 : Iota),
% 54.87/55.04 Or (Eq (member a (intersection a_1 a_2)) True) (Or (Eq (member a a_1) False) (Eq (member a a_2) False))
% 54.87/55.04 Clause #53 (by superposition #[52, 22]): ∀ (a a_1 a_2 a_3 : Iota),
% 54.87/55.04 Or (Eq (member (skS.0 0 a a_1 a_2) (intersection a a_3)) True)
% 54.87/55.04 (Or (Eq (member (skS.0 0 a a_1 a_2) a_3) False) (Or (Eq (subset a a_1) True) (Eq False True)))
% 54.87/55.04 Clause #54 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (intersection a_1 a_2)) False) (Eq (member a a_2) True)
% 54.87/55.04 Clause #56 (by superposition #[54, 22]): ∀ (a a_1 a_2 a_3 : Iota),
% 54.87/55.04 Or (Eq (member (skS.0 0 (intersection a a_1) a_2 a_3) a_1) True)
% 54.87/55.04 (Or (Eq (subset (intersection a a_1) a_2) True) (Eq False True))
% 54.87/55.04 Clause #58 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (Eq a C) (And (subset a C) (subset C a))) True
% 54.87/55.04 Clause #59 (by clausification #[58]): ∀ (a a_1 : Iota), Eq (Iff (Eq a a_1) (And (subset a a_1) (subset a_1 a))) True
% 54.87/55.04 Clause #60 (by clausification #[59]): ∀ (a a_1 : Iota), Or (Eq (Eq a a_1) True) (Eq (And (subset a a_1) (subset a_1 a)) False)
% 54.87/55.04 Clause #62 (by clausification #[60]): ∀ (a a_1 : Iota), Or (Eq (And (subset a a_1) (subset a_1 a)) False) (Eq a a_1)
% 54.87/55.04 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota), Or (Eq a a_1) (Or (Eq (subset a a_1) False) (Eq (subset a_1 a) False))
% 54.87/55.04 Clause #85 (by clausification #[34]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (member (skS.0 0 a a_1 a_2) (union a_3 a)) True) (Eq (subset a a_1) True)
% 54.87/55.04 Clause #86 (by superposition #[85, 23]): ∀ (a a_1 : Iota), Or (Eq (subset a (union a_1 a)) True) (Or (Eq (subset a (union a_1 a)) True) (Eq True False))
% 54.87/55.04 Clause #91 (by clausification #[86]): ∀ (a a_1 : Iota), Or (Eq (subset a (union a_1 a)) True) (Eq (subset a (union a_1 a)) True)
% 54.87/55.04 Clause #92 (by eliminate duplicate literals #[91]): ∀ (a a_1 : Iota), Eq (subset a (union a_1 a)) True
% 54.87/55.04 Clause #95 (by superposition #[92, 12]): ∀ (a a_1 : Iota), Eq (subset a (union a a_1)) True
% 54.87/55.04 Clause #97 (by superposition #[95, 63]): ∀ (a a_1 : Iota), Or (Eq a (union a a_1)) (Or (Eq True False) (Eq (subset (union a a_1) a) False))
% 54.87/55.04 Clause #99 (by clausification #[97]): ∀ (a a_1 : Iota), Or (Eq a (union a a_1)) (Eq (subset (union a a_1) a) False)
% 54.87/55.04 Clause #114 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota),
% 54.87/55.04 Or (Eq (member (skS.0 0 (union a a_1) a_2 a_3) a) True)
% 54.87/55.04 (Or (Eq (member (skS.0 0 (union a a_1) a_2 a_3) a_1) True) (Eq (subset (union a a_1) a_2) True))
% 54.87/55.04 Clause #115 (by superposition #[114, 54]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 54.87/55.04 Or (Eq (member (skS.0 0 (union (intersection a a_1) a_2) a_3 a_4) a_2) True)
% 54.87/55.04 (Or (Eq (subset (union (intersection a a_1) a_2) a_3) True)
% 54.91/55.07 (Or (Eq True False) (Eq (member (skS.0 0 (union (intersection a a_1) a_2) a_3 a_4) a_1) True)))
% 54.91/55.07 Clause #168 (by clausification #[53]): ∀ (a a_1 a_2 a_3 : Iota),
% 54.91/55.07 Or (Eq (member (skS.0 0 a a_1 a_2) (intersection a a_3)) True)
% 54.91/55.07 (Or (Eq (member (skS.0 0 a a_1 a_2) a_3) False) (Eq (subset a a_1) True))
% 54.91/55.07 Clause #173 (by clausification #[56]): ∀ (a a_1 a_2 a_3 : Iota),
% 54.91/55.07 Or (Eq (member (skS.0 0 (intersection a a_1) a_2 a_3) a_1) True) (Eq (subset (intersection a a_1) a_2) True)
% 54.91/55.07 Clause #176 (by superposition #[173, 23]): ∀ (a a_1 : Iota),
% 54.91/55.07 Or (Eq (subset (intersection a a_1) a_1) True) (Or (Eq (subset (intersection a a_1) a_1) True) (Eq True False))
% 54.91/55.07 Clause #177 (by superposition #[173, 168]): ∀ (a a_1 a_2 a_3 : Iota),
% 54.91/55.07 Or (Eq (subset (intersection a a_1) a_2) True)
% 54.91/55.07 (Or (Eq (member (skS.0 0 (intersection a a_1) a_2 a_3) (intersection (intersection a a_1) a_1)) True)
% 54.91/55.07 (Or (Eq True False) (Eq (subset (intersection a a_1) a_2) True)))
% 54.91/55.07 Clause #186 (by clausification #[176]): ∀ (a a_1 : Iota), Or (Eq (subset (intersection a a_1) a_1) True) (Eq (subset (intersection a a_1) a_1) True)
% 54.91/55.07 Clause #187 (by eliminate duplicate literals #[186]): ∀ (a a_1 : Iota), Eq (subset (intersection a a_1) a_1) True
% 54.91/55.07 Clause #189 (by superposition #[187, 63]): ∀ (a a_1 : Iota), Or (Eq (intersection a a_1) a_1) (Or (Eq True False) (Eq (subset a_1 (intersection a a_1)) False))
% 54.91/55.07 Clause #193 (by clausification #[189]): ∀ (a a_1 : Iota), Or (Eq (intersection a a_1) a_1) (Eq (subset a_1 (intersection a a_1)) False)
% 54.91/55.07 Clause #670 (by clausification #[115]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 54.91/55.07 Or (Eq (member (skS.0 0 (union (intersection a a_1) a_2) a_3 a_4) a_2) True)
% 54.91/55.07 (Or (Eq (subset (union (intersection a a_1) a_2) a_3) True)
% 54.91/55.07 (Eq (member (skS.0 0 (union (intersection a a_1) a_2) a_3 a_4) a_1) True))
% 54.91/55.07 Clause #719 (by superposition #[670, 15]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 54.91/55.07 Or (Eq (member (skS.0 0 (union (intersection a a_1) a_2) a_3 a_4) a_2) True)
% 54.91/55.07 (Or (Eq (subset (union (intersection a a_1) a_2) a_3) True)
% 54.91/55.07 (Eq (member (skS.0 0 (union (intersection a a_1) a_2) a_3 a_4) a) True))
% 54.91/55.07 Clause #816 (by superposition #[719, 12]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 54.91/55.07 Or (Eq (member (skS.0 0 (union a (intersection a_1 a_2)) a_3 a_4) a) True)
% 54.91/55.07 (Or (Eq (subset (union a (intersection a_1 a_2)) a_3) True)
% 54.91/55.07 (Eq (member (skS.0 0 (union a (intersection a_1 a_2)) a_3 a_4) a_1) True))
% 54.91/55.07 Clause #1325 (by equality factoring #[816]): ∀ (a a_1 a_2 a_3 : Iota),
% 54.91/55.07 Or (Eq (subset (union a (intersection a a_1)) a_2) True)
% 54.91/55.07 (Or (Ne True True) (Eq (member (skS.0 0 (union a (intersection a a_1)) a_2 a_3) a) True))
% 54.91/55.07 Clause #2834 (by clausification #[177]): ∀ (a a_1 a_2 a_3 : Iota),
% 54.91/55.07 Or (Eq (subset (intersection a a_1) a_2) True)
% 54.91/55.07 (Or (Eq (member (skS.0 0 (intersection a a_1) a_2 a_3) (intersection (intersection a a_1) a_1)) True)
% 54.91/55.07 (Eq (subset (intersection a a_1) a_2) True))
% 54.91/55.07 Clause #2835 (by eliminate duplicate literals #[2834]): ∀ (a a_1 a_2 a_3 : Iota),
% 54.91/55.07 Or (Eq (subset (intersection a a_1) a_2) True)
% 54.91/55.07 (Eq (member (skS.0 0 (intersection a a_1) a_2 a_3) (intersection (intersection a a_1) a_1)) True)
% 54.91/55.07 Clause #2836 (by forward demodulation #[2835, 15]): ∀ (a a_1 a_2 a_3 : Iota),
% 54.91/55.07 Or (Eq (subset (intersection a a_1) a_2) True)
% 54.91/55.07 (Eq (member (skS.0 0 (intersection a a_1) a_2 a_3) (intersection a_1 (intersection a a_1))) True)
% 54.91/55.07 Clause #2868 (by superposition #[2836, 15]): ∀ (a a_1 a_2 a_3 : Iota),
% 54.91/55.07 Or (Eq (subset (intersection a a_1) a_2) True)
% 54.91/55.07 (Eq (member (skS.0 0 (intersection a a_1) a_2 a_3) (intersection a (intersection a a_1))) True)
% 54.91/55.07 Clause #3417 (by superposition #[2868, 23]): ∀ (a a_1 : Iota),
% 54.91/55.07 Or (Eq (subset (intersection a a_1) (intersection a (intersection a a_1))) True)
% 54.91/55.07 (Or (Eq (subset (intersection a a_1) (intersection a (intersection a a_1))) True) (Eq True False))
% 54.91/55.07 Clause #6045 (by clausification #[3417]): ∀ (a a_1 : Iota),
% 54.91/55.07 Or (Eq (subset (intersection a a_1) (intersection a (intersection a a_1))) True)
% 54.91/55.07 (Eq (subset (intersection a a_1) (intersection a (intersection a a_1))) True)
% 54.99/55.18 Clause #6046 (by eliminate duplicate literals #[6045]): ∀ (a a_1 : Iota), Eq (subset (intersection a a_1) (intersection a (intersection a a_1))) True
% 54.99/55.18 Clause #6047 (by superposition #[6046, 193]): ∀ (a a_1 : Iota), Or (Eq (intersection a (intersection a a_1)) (intersection a a_1)) (Eq True False)
% 54.99/55.18 Clause #6123 (by clausification #[6047]): ∀ (a a_1 : Iota), Eq (intersection a (intersection a a_1)) (intersection a a_1)
% 54.99/55.18 Clause #6167 (by superposition #[6123, 15]): ∀ (a a_1 : Iota), Eq (intersection a (intersection a_1 a)) (intersection a_1 a)
% 54.99/55.18 Clause #10409 (by clausification #[1325]): ∀ (a a_1 a_2 a_3 : Iota),
% 54.99/55.18 Or (Eq (subset (union a (intersection a a_1)) a_2) True)
% 54.99/55.18 (Or (Eq (member (skS.0 0 (union a (intersection a a_1)) a_2 a_3) a) True) (Or (Eq True False) (Eq True False)))
% 54.99/55.18 Clause #10411 (by clausification #[10409]): ∀ (a a_1 a_2 a_3 : Iota),
% 54.99/55.18 Or (Eq (subset (union a (intersection a a_1)) a_2) True)
% 54.99/55.18 (Or (Eq (member (skS.0 0 (union a (intersection a a_1)) a_2 a_3) a) True) (Eq True False))
% 54.99/55.18 Clause #10412 (by clausification #[10411]): ∀ (a a_1 a_2 a_3 : Iota),
% 54.99/55.18 Or (Eq (subset (union a (intersection a a_1)) a_2) True)
% 54.99/55.18 (Eq (member (skS.0 0 (union a (intersection a a_1)) a_2 a_3) a) True)
% 54.99/55.18 Clause #10431 (by superposition #[10412, 23]): ∀ (a a_1 : Iota),
% 54.99/55.18 Or (Eq (subset (union a (intersection a a_1)) a) True)
% 54.99/55.18 (Or (Eq (subset (union a (intersection a a_1)) a) True) (Eq True False))
% 54.99/55.18 Clause #10489 (by clausification #[10431]): ∀ (a a_1 : Iota),
% 54.99/55.18 Or (Eq (subset (union a (intersection a a_1)) a) True) (Eq (subset (union a (intersection a a_1)) a) True)
% 54.99/55.18 Clause #10490 (by eliminate duplicate literals #[10489]): ∀ (a a_1 : Iota), Eq (subset (union a (intersection a a_1)) a) True
% 54.99/55.18 Clause #10509 (by superposition #[10490, 6167]): ∀ (a a_1 : Iota), Eq (subset (union a (intersection a_1 a)) a) True
% 54.99/55.18 Clause #10517 (by superposition #[10509, 99]): ∀ (a a_1 : Iota), Or (Eq a (union a (intersection a_1 a))) (Eq True False)
% 54.99/55.18 Clause #10537 (by clausification #[10517]): ∀ (a a_1 : Iota), Eq a (union a (intersection a_1 a))
% 54.99/55.18 Clause #10618 (by superposition #[10537, 15]): ∀ (a a_1 : Iota), Eq a (union a (intersection a a_1))
% 54.99/55.18 Clause #10629 (by backward contextual literal cutting #[10618, 42]): False
% 54.99/55.18 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------