TSTP Solution File: SET047+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET047+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n025.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 14:45:19 EDT 2023
% Result : Theorem 4.87s 5.12s
% Output : Proof 4.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET047+1 : TPTP v8.1.2. Released v2.0.0.
% 0.11/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 13:34:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 4.87/5.12 SZS status Theorem for theBenchmark.p
% 4.87/5.12 SZS output start Proof for theBenchmark.p
% 4.87/5.12 Clause #0 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (set_equal X Y) (∀ (Z : Iota), Iff (element Z X) (element Z Y))) True
% 4.87/5.12 Clause #1 (by assumption #[]): Eq (Not (∀ (X Y : Iota), Iff (set_equal X Y) (set_equal Y X))) True
% 4.87/5.12 Clause #2 (by clausification #[1]): Eq (∀ (X Y : Iota), Iff (set_equal X Y) (set_equal Y X)) False
% 4.87/5.12 Clause #3 (by clausification #[2]): ∀ (a : Iota), Eq (Not (∀ (Y : Iota), Iff (set_equal (skS.0 0 a) Y) (set_equal Y (skS.0 0 a)))) True
% 4.87/5.12 Clause #4 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (set_equal (skS.0 0 a) Y) (set_equal Y (skS.0 0 a))) False
% 4.87/5.12 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), Eq (Not (Iff (set_equal (skS.0 0 a) (skS.0 1 a a_1)) (set_equal (skS.0 1 a a_1) (skS.0 0 a)))) True
% 4.87/5.12 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), Eq (Iff (set_equal (skS.0 0 a) (skS.0 1 a a_1)) (set_equal (skS.0 1 a a_1) (skS.0 0 a))) False
% 4.87/5.12 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota),
% 4.87/5.12 Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) False) (Eq (set_equal (skS.0 1 a a_1) (skS.0 0 a)) False)
% 4.87/5.12 Clause #8 (by clausification #[6]): ∀ (a a_1 : Iota), Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq (set_equal (skS.0 1 a a_1) (skS.0 0 a)) True)
% 4.87/5.12 Clause #9 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (set_equal a Y) (∀ (Z : Iota), Iff (element Z a) (element Z Y))) True
% 4.87/5.12 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (Iff (set_equal a a_1) (∀ (Z : Iota), Iff (element Z a) (element Z a_1))) True
% 4.87/5.12 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Or (Eq (set_equal a a_1) True) (Eq (∀ (Z : Iota), Iff (element Z a) (element Z a_1)) False)
% 4.87/5.12 Clause #12 (by clausification #[10]): ∀ (a a_1 : Iota), Or (Eq (set_equal a a_1) False) (Eq (∀ (Z : Iota), Iff (element Z a) (element Z a_1)) True)
% 4.87/5.12 Clause #13 (by clausification #[11]): ∀ (a a_1 a_2 : Iota),
% 4.87/5.12 Or (Eq (set_equal a a_1) True) (Eq (Not (Iff (element (skS.0 2 a a_1 a_2) a) (element (skS.0 2 a a_1 a_2) a_1))) True)
% 4.87/5.12 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 : Iota),
% 4.87/5.12 Or (Eq (set_equal a a_1) True) (Eq (Iff (element (skS.0 2 a a_1 a_2) a) (element (skS.0 2 a a_1 a_2) a_1)) False)
% 4.87/5.12 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota),
% 4.87/5.12 Or (Eq (set_equal a a_1) True)
% 4.87/5.12 (Or (Eq (element (skS.0 2 a a_1 a_2) a) False) (Eq (element (skS.0 2 a a_1 a_2) a_1) False))
% 4.87/5.12 Clause #16 (by clausification #[14]): ∀ (a a_1 a_2 : Iota),
% 4.87/5.12 Or (Eq (set_equal a a_1) True)
% 4.87/5.12 (Or (Eq (element (skS.0 2 a a_1 a_2) a) True) (Eq (element (skS.0 2 a a_1 a_2) a_1) True))
% 4.87/5.12 Clause #17 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Or (Eq (set_equal a a_1) False) (Eq (Iff (element a_2 a) (element a_2 a_1)) True)
% 4.87/5.12 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), Or (Eq (set_equal a a_1) False) (Or (Eq (element a_2 a) True) (Eq (element a_2 a_1) False))
% 4.87/5.12 Clause #19 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), Or (Eq (set_equal a a_1) False) (Or (Eq (element a_2 a) False) (Eq (element a_2 a_1) True))
% 4.87/5.12 Clause #22 (by superposition #[8, 18]): ∀ (a a_1 a_2 : Iota),
% 4.87/5.12 Or (Eq (element a (skS.0 1 a_1 a_2)) True)
% 4.87/5.12 (Or (Eq (element a (skS.0 0 a_1)) False) (Or (Eq (set_equal (skS.0 0 a_1) (skS.0 1 a_1 a_2)) True) (Eq False True)))
% 4.87/5.12 Clause #23 (by superposition #[8, 19]): ∀ (a a_1 a_2 : Iota),
% 4.87/5.12 Or (Eq (element a (skS.0 1 a_1 a_2)) False)
% 4.87/5.12 (Or (Eq (element a (skS.0 0 a_1)) True) (Or (Eq (set_equal (skS.0 0 a_1) (skS.0 1 a_1 a_2)) True) (Eq False True)))
% 4.87/5.12 Clause #38 (by clausification #[23]): ∀ (a a_1 a_2 : Iota),
% 4.87/5.12 Or (Eq (element a (skS.0 1 a_1 a_2)) False)
% 4.87/5.12 (Or (Eq (element a (skS.0 0 a_1)) True) (Eq (set_equal (skS.0 0 a_1) (skS.0 1 a_1 a_2)) True))
% 4.87/5.12 Clause #41 (by clausification #[22]): ∀ (a a_1 a_2 : Iota),
% 4.87/5.12 Or (Eq (element a (skS.0 1 a_1 a_2)) True)
% 4.87/5.12 (Or (Eq (element a (skS.0 0 a_1)) False) (Eq (set_equal (skS.0 0 a_1) (skS.0 1 a_1 a_2)) True))
% 4.87/5.12 Clause #42 (by superposition #[41, 16]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.87/5.12 Or (Eq (element (skS.0 2 (skS.0 0 a) a_1 a_2) (skS.0 1 a a_3)) True)
% 4.87/5.15 (Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_3)) True)
% 4.87/5.15 (Or (Eq (set_equal (skS.0 0 a) a_1) True)
% 4.87/5.15 (Or (Eq False True) (Eq (element (skS.0 2 (skS.0 0 a) a_1 a_2) a_1) True))))
% 4.87/5.15 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.87/5.15 Or (Eq (element (skS.0 2 (skS.0 0 a) a_1 a_2) (skS.0 1 a a_3)) True)
% 4.87/5.15 (Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_3)) True)
% 4.87/5.15 (Or (Eq (set_equal (skS.0 0 a) a_1) True) (Eq (element (skS.0 2 (skS.0 0 a) a_1 a_2) a_1) True)))
% 4.87/5.15 Clause #48 (by equality factoring #[44]): ∀ (a a_1 a_2 : Iota),
% 4.87/5.15 Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.87/5.15 (Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.87/5.15 (Or (Ne True True) (Eq (element (skS.0 2 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 1 a a_1)) True)))
% 4.87/5.15 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 : Iota),
% 4.87/5.15 Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.87/5.15 (Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.87/5.15 (Or (Eq (element (skS.0 2 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 1 a a_1)) True)
% 4.87/5.15 (Or (Eq True False) (Eq True False))))
% 4.87/5.15 Clause #51 (by clausification #[49]): ∀ (a a_1 a_2 : Iota),
% 4.87/5.15 Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.87/5.15 (Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.87/5.15 (Or (Eq (element (skS.0 2 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 1 a a_1)) True) (Eq True False)))
% 4.87/5.15 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 : Iota),
% 4.87/5.15 Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.87/5.15 (Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.87/5.15 (Eq (element (skS.0 2 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 1 a a_1)) True))
% 4.87/5.15 Clause #53 (by eliminate duplicate literals #[52]): ∀ (a a_1 a_2 : Iota),
% 4.87/5.15 Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.87/5.15 (Eq (element (skS.0 2 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 1 a a_1)) True)
% 4.87/5.15 Clause #54 (by superposition #[53, 38]): ∀ (a a_1 a_2 : Iota),
% 4.87/5.15 Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.87/5.15 (Or (Eq True False)
% 4.87/5.15 (Or (Eq (element (skS.0 2 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 0 a)) True)
% 4.87/5.15 (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True)))
% 4.87/5.15 Clause #65 (by clausification #[54]): ∀ (a a_1 a_2 : Iota),
% 4.87/5.15 Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.87/5.15 (Or (Eq (element (skS.0 2 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 0 a)) True)
% 4.87/5.15 (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True))
% 4.87/5.15 Clause #66 (by eliminate duplicate literals #[65]): ∀ (a a_1 a_2 : Iota),
% 4.87/5.15 Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.87/5.15 (Eq (element (skS.0 2 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 0 a)) True)
% 4.87/5.15 Clause #68 (by superposition #[66, 15]): ∀ (a a_1 a_2 : Iota),
% 4.87/5.15 Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.87/5.15 (Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.87/5.15 (Or (Eq True False) (Eq (element (skS.0 2 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 1 a a_1)) False)))
% 4.87/5.15 Clause #71 (by clausification #[68]): ∀ (a a_1 a_2 : Iota),
% 4.87/5.15 Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.87/5.15 (Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.87/5.15 (Eq (element (skS.0 2 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 1 a a_1)) False))
% 4.87/5.15 Clause #72 (by eliminate duplicate literals #[71]): ∀ (a a_1 a_2 : Iota),
% 4.87/5.15 Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.87/5.15 (Eq (element (skS.0 2 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 1 a a_1)) False)
% 4.87/5.15 Clause #73 (by superposition #[72, 53]): ∀ (a a_1 : Iota),
% 4.87/5.15 Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.87/5.15 (Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq False True))
% 4.87/5.15 Clause #83 (by clausification #[73]): ∀ (a a_1 : Iota), Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True)
% 4.87/5.15 Clause #84 (by eliminate duplicate literals #[83]): ∀ (a a_1 : Iota), Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True
% 4.87/5.15 Clause #85 (by backward demodulation #[84, 7]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (set_equal (skS.0 1 a a_1) (skS.0 0 a)) False)
% 4.87/5.15 Clause #94 (by superposition #[84, 18]): ∀ (a a_1 a_2 : Iota),
% 4.87/5.15 Or (Eq True False) (Or (Eq (element a (skS.0 0 a_1)) True) (Eq (element a (skS.0 1 a_1 a_2)) False))
% 4.87/5.17 Clause #95 (by superposition #[84, 19]): ∀ (a a_1 a_2 : Iota),
% 4.87/5.17 Or (Eq True False) (Or (Eq (element a (skS.0 0 a_1)) False) (Eq (element a (skS.0 1 a_1 a_2)) True))
% 4.87/5.17 Clause #96 (by clausification #[85]): ∀ (a a_1 : Iota), Eq (set_equal (skS.0 1 a a_1) (skS.0 0 a)) False
% 4.87/5.17 Clause #97 (by clausification #[95]): ∀ (a a_1 a_2 : Iota), Or (Eq (element a (skS.0 0 a_1)) False) (Eq (element a (skS.0 1 a_1 a_2)) True)
% 4.87/5.17 Clause #99 (by superposition #[97, 16]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.87/5.17 Or (Eq (element (skS.0 2 a (skS.0 0 a_1) a_2) (skS.0 1 a_1 a_3)) True)
% 4.87/5.17 (Or (Eq (set_equal a (skS.0 0 a_1)) True) (Or (Eq (element (skS.0 2 a (skS.0 0 a_1) a_2) a) True) (Eq False True)))
% 4.87/5.17 Clause #100 (by clausification #[94]): ∀ (a a_1 a_2 : Iota), Or (Eq (element a (skS.0 0 a_1)) True) (Eq (element a (skS.0 1 a_1 a_2)) False)
% 4.87/5.17 Clause #108 (by clausification #[99]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.87/5.17 Or (Eq (element (skS.0 2 a (skS.0 0 a_1) a_2) (skS.0 1 a_1 a_3)) True)
% 4.87/5.17 (Or (Eq (set_equal a (skS.0 0 a_1)) True) (Eq (element (skS.0 2 a (skS.0 0 a_1) a_2) a) True))
% 4.87/5.17 Clause #113 (by equality factoring #[108]): ∀ (a a_1 a_2 : Iota),
% 4.87/5.17 Or (Eq (set_equal (skS.0 1 a a_1) (skS.0 0 a)) True)
% 4.87/5.17 (Or (Ne True True) (Eq (element (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 1 a a_1)) True))
% 4.87/5.17 Clause #114 (by clausification #[113]): ∀ (a a_1 a_2 : Iota),
% 4.87/5.17 Or (Eq (set_equal (skS.0 1 a a_1) (skS.0 0 a)) True)
% 4.87/5.17 (Or (Eq (element (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 1 a a_1)) True)
% 4.87/5.17 (Or (Eq True False) (Eq True False)))
% 4.87/5.17 Clause #116 (by clausification #[114]): ∀ (a a_1 a_2 : Iota),
% 4.87/5.17 Or (Eq (set_equal (skS.0 1 a a_1) (skS.0 0 a)) True)
% 4.87/5.17 (Or (Eq (element (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 1 a a_1)) True) (Eq True False))
% 4.87/5.17 Clause #117 (by clausification #[116]): ∀ (a a_1 a_2 : Iota),
% 4.87/5.17 Or (Eq (set_equal (skS.0 1 a a_1) (skS.0 0 a)) True)
% 4.87/5.17 (Eq (element (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 1 a a_1)) True)
% 4.87/5.17 Clause #118 (by forward demodulation #[117, 96]): ∀ (a a_1 a_2 : Iota), Or (Eq False True) (Eq (element (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 1 a a_1)) True)
% 4.87/5.17 Clause #119 (by clausification #[118]): ∀ (a a_1 a_2 : Iota), Eq (element (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 1 a a_1)) True
% 4.87/5.17 Clause #120 (by superposition #[119, 100]): ∀ (a a_1 a_2 : Iota), Or (Eq (element (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) True) (Eq True False)
% 4.87/5.17 Clause #121 (by superposition #[119, 15]): ∀ (a a_1 a_2 : Iota),
% 4.87/5.17 Or (Eq (set_equal (skS.0 1 a a_1) (skS.0 0 a)) True)
% 4.87/5.17 (Or (Eq True False) (Eq (element (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) False))
% 4.87/5.17 Clause #122 (by clausification #[120]): ∀ (a a_1 a_2 : Iota), Eq (element (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) True
% 4.87/5.17 Clause #125 (by clausification #[121]): ∀ (a a_1 a_2 : Iota),
% 4.87/5.17 Or (Eq (set_equal (skS.0 1 a a_1) (skS.0 0 a)) True)
% 4.87/5.17 (Eq (element (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) False)
% 4.87/5.17 Clause #126 (by forward demodulation #[125, 96]): ∀ (a a_1 a_2 : Iota), Or (Eq False True) (Eq (element (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) False)
% 4.87/5.17 Clause #127 (by clausification #[126]): ∀ (a a_1 a_2 : Iota), Eq (element (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) False
% 4.87/5.17 Clause #128 (by superposition #[127, 122]): Eq False True
% 4.87/5.17 Clause #131 (by clausification #[128]): False
% 4.87/5.17 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------