TSTP Solution File: SET909+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET909+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n001.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 14:48:00 EDT 2023
% Result : Theorem 6.86s 7.19s
% Output : Proof 6.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET909+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.11 % Command : duper %s
% 0.12/0.31 % Computer : n001.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Sat Aug 26 13:38:15 EDT 2023
% 0.12/0.31 % CPUTime :
% 6.86/7.19 SZS status Theorem for theBenchmark.p
% 6.86/7.19 SZS output start Proof for theBenchmark.p
% 6.86/7.19 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Eq (unordered_pair A B) (unordered_pair B A)) True
% 6.86/7.19 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Eq (set_union2 A B) (set_union2 B A)) True
% 6.86/7.19 Clause #3 (by assumption #[]): Eq (∀ (A : Iota), Iff (Eq A empty_set) (∀ (B : Iota), Not (in B A))) True
% 6.86/7.19 Clause #4 (by assumption #[]): Eq (∀ (A B C : Iota), Iff (Eq C (unordered_pair A B)) (∀ (D : Iota), Iff (in D C) (Or (Eq D A) (Eq D B)))) True
% 6.86/7.19 Clause #5 (by assumption #[]): Eq (∀ (A B C : Iota), Iff (Eq C (set_union2 A B)) (∀ (D : Iota), Iff (in D C) (Or (in D A) (in D B)))) True
% 6.86/7.19 Clause #12 (by assumption #[]): Eq (Not (∀ (A B C : Iota), Ne (set_union2 (unordered_pair A B) C) empty_set)) True
% 6.86/7.19 Clause #26 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (unordered_pair a B) (unordered_pair B a)) True
% 6.86/7.19 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (Eq (unordered_pair a a_1) (unordered_pair a_1 a)) True
% 6.86/7.19 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (unordered_pair a a_1) (unordered_pair a_1 a)
% 6.86/7.19 Clause #38 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (set_union2 a B) (set_union2 B a)) True
% 6.86/7.19 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Eq (Eq (set_union2 a a_1) (set_union2 a_1 a)) True
% 6.86/7.19 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), Eq (set_union2 a a_1) (set_union2 a_1 a)
% 6.86/7.19 Clause #41 (by clausification #[3]): ∀ (a : Iota), Eq (Iff (Eq a empty_set) (∀ (B : Iota), Not (in B a))) True
% 6.86/7.19 Clause #43 (by clausification #[41]): ∀ (a : Iota), Or (Eq (Eq a empty_set) False) (Eq (∀ (B : Iota), Not (in B a)) True)
% 6.86/7.19 Clause #51 (by clausification #[4]): ∀ (a : Iota),
% 6.86/7.19 Eq (∀ (B C : Iota), Iff (Eq C (unordered_pair a B)) (∀ (D : Iota), Iff (in D C) (Or (Eq D a) (Eq D B)))) True
% 6.86/7.19 Clause #52 (by clausification #[51]): ∀ (a a_1 : Iota),
% 6.86/7.19 Eq (∀ (C : Iota), Iff (Eq C (unordered_pair a a_1)) (∀ (D : Iota), Iff (in D C) (Or (Eq D a) (Eq D a_1)))) True
% 6.86/7.19 Clause #53 (by clausification #[52]): ∀ (a a_1 a_2 : Iota),
% 6.86/7.19 Eq (Iff (Eq a (unordered_pair a_1 a_2)) (∀ (D : Iota), Iff (in D a) (Or (Eq D a_1) (Eq D a_2)))) True
% 6.86/7.19 Clause #55 (by clausification #[53]): ∀ (a a_1 a_2 : Iota),
% 6.86/7.19 Or (Eq (Eq a (unordered_pair a_1 a_2)) False) (Eq (∀ (D : Iota), Iff (in D a) (Or (Eq D a_1) (Eq D a_2))) True)
% 6.86/7.19 Clause #64 (by clausification #[43]): ∀ (a : Iota), Or (Eq (∀ (B : Iota), Not (in B a)) True) (Ne a empty_set)
% 6.86/7.19 Clause #65 (by clausification #[64]): ∀ (a a_1 : Iota), Or (Ne a empty_set) (Eq (Not (in a_1 a)) True)
% 6.86/7.19 Clause #66 (by clausification #[65]): ∀ (a a_1 : Iota), Or (Ne a empty_set) (Eq (in a_1 a) False)
% 6.86/7.19 Clause #67 (by destructive equality resolution #[66]): ∀ (a : Iota), Eq (in a empty_set) False
% 6.86/7.19 Clause #69 (by clausification #[12]): Eq (∀ (A B C : Iota), Ne (set_union2 (unordered_pair A B) C) empty_set) False
% 6.86/7.19 Clause #70 (by clausification #[69]): ∀ (a : Iota), Eq (Not (∀ (B C : Iota), Ne (set_union2 (unordered_pair (skS.0 4 a) B) C) empty_set)) True
% 6.86/7.19 Clause #71 (by clausification #[70]): ∀ (a : Iota), Eq (∀ (B C : Iota), Ne (set_union2 (unordered_pair (skS.0 4 a) B) C) empty_set) False
% 6.86/7.19 Clause #72 (by clausification #[71]): ∀ (a a_1 : Iota), Eq (Not (∀ (C : Iota), Ne (set_union2 (unordered_pair (skS.0 4 a) (skS.0 5 a a_1)) C) empty_set)) True
% 6.86/7.19 Clause #73 (by clausification #[72]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), Ne (set_union2 (unordered_pair (skS.0 4 a) (skS.0 5 a a_1)) C) empty_set) False
% 6.86/7.19 Clause #74 (by clausification #[73]): ∀ (a a_1 a_2 : Iota),
% 6.86/7.19 Eq (Not (Ne (set_union2 (unordered_pair (skS.0 4 a) (skS.0 5 a a_1)) (skS.0 6 a a_1 a_2)) empty_set)) True
% 6.86/7.19 Clause #75 (by clausification #[74]): ∀ (a a_1 a_2 : Iota),
% 6.86/7.19 Eq (Ne (set_union2 (unordered_pair (skS.0 4 a) (skS.0 5 a a_1)) (skS.0 6 a a_1 a_2)) empty_set) False
% 6.86/7.19 Clause #76 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), Eq (set_union2 (unordered_pair (skS.0 4 a) (skS.0 5 a a_1)) (skS.0 6 a a_1 a_2)) empty_set
% 6.86/7.19 Clause #79 (by superposition #[76, 40]): ∀ (a a_1 a_2 : Iota), Eq empty_set (set_union2 (skS.0 6 a a_1 a_2) (unordered_pair (skS.0 4 a) (skS.0 5 a a_1)))
% 6.86/7.22 Clause #85 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (B C : Iota), Iff (Eq C (set_union2 a B)) (∀ (D : Iota), Iff (in D C) (Or (in D a) (in D B)))) True
% 6.86/7.22 Clause #86 (by clausification #[85]): ∀ (a a_1 : Iota),
% 6.86/7.22 Eq (∀ (C : Iota), Iff (Eq C (set_union2 a a_1)) (∀ (D : Iota), Iff (in D C) (Or (in D a) (in D a_1)))) True
% 6.86/7.22 Clause #87 (by clausification #[86]): ∀ (a a_1 a_2 : Iota), Eq (Iff (Eq a (set_union2 a_1 a_2)) (∀ (D : Iota), Iff (in D a) (Or (in D a_1) (in D a_2)))) True
% 6.86/7.22 Clause #89 (by clausification #[87]): ∀ (a a_1 a_2 : Iota),
% 6.86/7.22 Or (Eq (Eq a (set_union2 a_1 a_2)) False) (Eq (∀ (D : Iota), Iff (in D a) (Or (in D a_1) (in D a_2))) True)
% 6.86/7.22 Clause #172 (by clausification #[55]): ∀ (a a_1 a_2 : Iota),
% 6.86/7.22 Or (Eq (∀ (D : Iota), Iff (in D a) (Or (Eq D a_1) (Eq D a_2))) True) (Ne a (unordered_pair a_1 a_2))
% 6.86/7.22 Clause #173 (by clausification #[172]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (unordered_pair a_1 a_2)) (Eq (Iff (in a_3 a) (Or (Eq a_3 a_1) (Eq a_3 a_2))) True)
% 6.86/7.22 Clause #174 (by clausification #[173]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.86/7.22 Or (Ne a (unordered_pair a_1 a_2)) (Or (Eq (in a_3 a) True) (Eq (Or (Eq a_3 a_1) (Eq a_3 a_2)) False))
% 6.86/7.22 Clause #176 (by clausification #[174]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (unordered_pair a_1 a_2)) (Or (Eq (in a_3 a) True) (Eq (Eq a_3 a_2) False))
% 6.86/7.22 Clause #178 (by clausification #[176]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (unordered_pair a_1 a_2)) (Or (Eq (in a_3 a) True) (Ne a_3 a_2))
% 6.86/7.22 Clause #179 (by destructive equality resolution #[178]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (unordered_pair a_1 a_2)) True) (Ne a a_2)
% 6.86/7.22 Clause #180 (by destructive equality resolution #[179]): ∀ (a a_1 : Iota), Eq (in a (unordered_pair a_1 a)) True
% 6.86/7.22 Clause #183 (by superposition #[180, 28]): ∀ (a a_1 : Iota), Eq (in a (unordered_pair a a_1)) True
% 6.86/7.22 Clause #265 (by clausification #[89]): ∀ (a a_1 a_2 : Iota), Or (Eq (∀ (D : Iota), Iff (in D a) (Or (in D a_1) (in D a_2))) True) (Ne a (set_union2 a_1 a_2))
% 6.86/7.22 Clause #266 (by clausification #[265]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (set_union2 a_1 a_2)) (Eq (Iff (in a_3 a) (Or (in a_3 a_1) (in a_3 a_2))) True)
% 6.86/7.22 Clause #267 (by clausification #[266]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.86/7.22 Or (Ne a (set_union2 a_1 a_2)) (Or (Eq (in a_3 a) True) (Eq (Or (in a_3 a_1) (in a_3 a_2)) False))
% 6.86/7.22 Clause #269 (by clausification #[267]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (set_union2 a_1 a_2)) (Or (Eq (in a_3 a) True) (Eq (in a_3 a_2) False))
% 6.86/7.22 Clause #271 (by destructive equality resolution #[269]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (set_union2 a_1 a_2)) True) (Eq (in a a_2) False)
% 6.86/7.22 Clause #274 (by superposition #[271, 183]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (set_union2 a_1 (unordered_pair a a_2))) True) (Eq False True)
% 6.86/7.22 Clause #280 (by clausification #[274]): ∀ (a a_1 a_2 : Iota), Eq (in a (set_union2 a_1 (unordered_pair a a_2))) True
% 6.86/7.22 Clause #308 (by superposition #[79, 280]): ∀ (a : Iota), Eq (in (skS.0 4 a) empty_set) True
% 6.86/7.22 Clause #326 (by superposition #[308, 67]): Eq True False
% 6.86/7.22 Clause #335 (by clausification #[326]): False
% 6.86/7.22 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------