TSTP Solution File: SET872+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET872+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n002.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 14:47:53 EDT 2023
% Result : Theorem 3.63s 3.82s
% Output : Proof 3.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET872+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n002.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 12:49:03 EDT 2023
% 0.14/0.35 % CPUTime :
% 3.63/3.82 SZS status Theorem for theBenchmark.p
% 3.63/3.82 SZS output start Proof for theBenchmark.p
% 3.63/3.82 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Eq (unordered_pair A B) (unordered_pair B A)) True
% 3.63/3.82 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (singleton A)) (∀ (C : Iota), Iff (in C B) (Eq C A))) True
% 3.63/3.82 Clause #3 (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
% 3.63/3.82 Clause #4 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset A B) (∀ (C : Iota), in C A → in C B)) True
% 3.63/3.82 Clause #8 (by assumption #[]): Eq (Not (∀ (A B : Iota), subset (singleton A) (unordered_pair A B))) True
% 3.63/3.82 Clause #19 (by clausification #[8]): Eq (∀ (A B : Iota), subset (singleton A) (unordered_pair A B)) False
% 3.63/3.82 Clause #20 (by clausification #[19]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), subset (singleton (skS.0 2 a)) (unordered_pair (skS.0 2 a) B))) True
% 3.63/3.82 Clause #21 (by clausification #[20]): ∀ (a : Iota), Eq (∀ (B : Iota), subset (singleton (skS.0 2 a)) (unordered_pair (skS.0 2 a) B)) False
% 3.63/3.82 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (Not (subset (singleton (skS.0 2 a)) (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)))) True
% 3.63/3.82 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Eq (subset (singleton (skS.0 2 a)) (unordered_pair (skS.0 2 a) (skS.0 3 a a_1))) False
% 3.63/3.82 Clause #24 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (unordered_pair a B) (unordered_pair B a)) True
% 3.63/3.82 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Eq (Eq (unordered_pair a a_1) (unordered_pair a_1 a)) True
% 3.63/3.82 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (unordered_pair a a_1) (unordered_pair a_1 a)
% 3.63/3.82 Clause #27 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset a B) (∀ (C : Iota), in C a → in C B)) True
% 3.63/3.82 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (C : Iota), in C a → in C a_1)) True
% 3.63/3.82 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Eq (∀ (C : Iota), in C a → in C a_1) False)
% 3.63/3.82 Clause #31 (by clausification #[29]): ∀ (a a_1 a_2 : Iota),
% 3.63/3.82 Or (Eq (subset a a_1) True) (Eq (Not (in (skS.0 4 a a_1 a_2) a → in (skS.0 4 a a_1 a_2) a_1)) True)
% 3.63/3.82 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 4 a a_1 a_2) a → in (skS.0 4 a a_1 a_2) a_1) False)
% 3.63/3.82 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 4 a a_1 a_2) a) True)
% 3.63/3.82 Clause #34 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 4 a a_1 a_2) a_1) False)
% 3.63/3.82 Clause #43 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (singleton a)) (∀ (C : Iota), Iff (in C B) (Eq C a))) True
% 3.63/3.82 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (singleton a_1)) (∀ (C : Iota), Iff (in C a) (Eq C a_1))) True
% 3.63/3.82 Clause #46 (by clausification #[44]): ∀ (a a_1 : Iota), Or (Eq (Eq a (singleton a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True)
% 3.63/3.82 Clause #53 (by clausification #[46]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) (Ne a (singleton a_1))
% 3.63/3.82 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Eq (Iff (in a_2 a) (Eq a_2 a_1)) True)
% 3.63/3.82 Clause #56 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) False) (Eq (Eq a_2 a_1) True))
% 3.63/3.82 Clause #62 (by clausification #[56]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) False) (Eq a_2 a_1))
% 3.63/3.82 Clause #63 (by destructive equality resolution #[62]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) False) (Eq a a_1)
% 3.63/3.82 Clause #65 (by superposition #[63, 33]): ∀ (a a_1 a_2 : Iota),
% 3.63/3.82 Or (Eq (skS.0 4 (singleton a) a_1 a_2) a) (Or (Eq (subset (singleton a) a_1) True) (Eq False True))
% 3.63/3.82 Clause #67 (by clausification #[65]): ∀ (a a_1 a_2 : Iota), Or (Eq (skS.0 4 (singleton a) a_1 a_2) a) (Eq (subset (singleton a) a_1) True)
% 3.63/3.82 Clause #69 (by superposition #[67, 34]): ∀ (a a_1 : Iota),
% 3.68/3.83 Or (Eq (subset (singleton a) a_1) True) (Or (Eq (subset (singleton a) a_1) True) (Eq (in a a_1) False))
% 3.68/3.83 Clause #71 (by clausification #[3]): ∀ (a : Iota),
% 3.68/3.83 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
% 3.68/3.83 Clause #72 (by clausification #[71]): ∀ (a a_1 : Iota),
% 3.68/3.83 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
% 3.68/3.83 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 : Iota),
% 3.68/3.83 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
% 3.68/3.83 Clause #75 (by clausification #[73]): ∀ (a a_1 a_2 : Iota),
% 3.68/3.83 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)
% 3.68/3.83 Clause #84 (by eliminate duplicate literals #[69]): ∀ (a a_1 : Iota), Or (Eq (subset (singleton a) a_1) True) (Eq (in a a_1) False)
% 3.68/3.83 Clause #109 (by clausification #[75]): ∀ (a a_1 a_2 : Iota),
% 3.68/3.83 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))
% 3.68/3.83 Clause #110 (by clausification #[109]): ∀ (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)
% 3.68/3.83 Clause #111 (by clausification #[110]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.68/3.83 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))
% 3.68/3.83 Clause #113 (by clausification #[111]): ∀ (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))
% 3.68/3.83 Clause #115 (by clausification #[113]): ∀ (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))
% 3.68/3.83 Clause #116 (by destructive equality resolution #[115]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (unordered_pair a_1 a_2)) True) (Ne a a_2)
% 3.68/3.83 Clause #117 (by destructive equality resolution #[116]): ∀ (a a_1 : Iota), Eq (in a (unordered_pair a_1 a)) True
% 3.68/3.83 Clause #120 (by superposition #[117, 26]): ∀ (a a_1 : Iota), Eq (in a (unordered_pair a a_1)) True
% 3.68/3.83 Clause #122 (by superposition #[120, 84]): ∀ (a a_1 : Iota), Or (Eq (subset (singleton a) (unordered_pair a a_1)) True) (Eq True False)
% 3.68/3.83 Clause #130 (by clausification #[122]): ∀ (a a_1 : Iota), Eq (subset (singleton a) (unordered_pair a a_1)) True
% 3.68/3.83 Clause #131 (by superposition #[130, 23]): Eq True False
% 3.68/3.83 Clause #135 (by clausification #[131]): False
% 3.68/3.83 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------