TSTP Solution File: SET679+3 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET679+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n026.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 14:47:20 EDT 2023
% Result : Theorem 23.20s 23.43s
% Output : Proof 23.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET679+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : duper %s
% 0.14/0.36 % Computer : n026.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 13:15:33 EDT 2023
% 0.14/0.36 % CPUTime :
% 23.20/23.43 SZS status Theorem for theBenchmark.p
% 23.20/23.43 SZS output start Proof for theBenchmark.p
% 23.20/23.43 Clause #1 (by assumption #[]): Eq (∀ (B : Iota), ilf_type B set_type → Not (member B empty_set)) True
% 23.20/23.43 Clause #4 (by assumption #[]): Eq
% 23.20/23.43 (∀ (B : Iota),
% 23.20/23.43 ilf_type B set_type →
% 23.20/23.43 ∀ (C : Iota),
% 23.20/23.43 ilf_type C set_type →
% 23.20/23.43 ∀ (D : Iota),
% 23.20/23.43 ilf_type D set_type → Iff (member (ordered_pair C D) (identity_relation_of B)) (And (member C B) (Eq C D)))
% 23.20/23.43 True
% 23.20/23.43 Clause #7 (by assumption #[]): Eq (∀ (B : Iota), ilf_type B set_type → ∀ (C : Iota), ilf_type C set_type → Iff (not_equal B C) (Ne B C)) True
% 23.20/23.43 Clause #8 (by assumption #[]): Eq (∀ (B : Iota), ilf_type B set_type → Iff (empty B) (∀ (C : Iota), ilf_type C set_type → Not (member C B))) True
% 23.20/23.43 Clause #22 (by assumption #[]): Eq (∀ (B : Iota), ilf_type B set_type) True
% 23.20/23.43 Clause #23 (by assumption #[]): Eq (Not (∀ (B : Iota), And (Not (empty B)) (ilf_type B set_type) → not_equal (identity_relation_of B) empty_set)) True
% 23.20/23.43 Clause #28 (by clausification #[22]): ∀ (a : Iota), Eq (ilf_type a set_type) True
% 23.20/23.43 Clause #40 (by clausification #[1]): ∀ (a : Iota), Eq (ilf_type a set_type → Not (member a empty_set)) True
% 23.20/23.43 Clause #41 (by clausification #[40]): ∀ (a : Iota), Or (Eq (ilf_type a set_type) False) (Eq (Not (member a empty_set)) True)
% 23.20/23.43 Clause #42 (by clausification #[41]): ∀ (a : Iota), Or (Eq (ilf_type a set_type) False) (Eq (member a empty_set) False)
% 23.20/23.43 Clause #43 (by forward demodulation #[42, 28]): ∀ (a : Iota), Or (Eq True False) (Eq (member a empty_set) False)
% 23.20/23.43 Clause #44 (by clausification #[43]): ∀ (a : Iota), Eq (member a empty_set) False
% 23.20/23.43 Clause #49 (by clausification #[23]): Eq (∀ (B : Iota), And (Not (empty B)) (ilf_type B set_type) → not_equal (identity_relation_of B) empty_set) False
% 23.20/23.43 Clause #50 (by clausification #[49]): ∀ (a : Iota),
% 23.20/23.43 Eq
% 23.20/23.43 (Not
% 23.20/23.43 (And (Not (empty (skS.0 1 a))) (ilf_type (skS.0 1 a) set_type) →
% 23.20/23.43 not_equal (identity_relation_of (skS.0 1 a)) empty_set))
% 23.20/23.43 True
% 23.20/23.43 Clause #51 (by clausification #[50]): ∀ (a : Iota),
% 23.20/23.43 Eq
% 23.20/23.43 (And (Not (empty (skS.0 1 a))) (ilf_type (skS.0 1 a) set_type) →
% 23.20/23.43 not_equal (identity_relation_of (skS.0 1 a)) empty_set)
% 23.20/23.43 False
% 23.20/23.43 Clause #52 (by clausification #[51]): ∀ (a : Iota), Eq (And (Not (empty (skS.0 1 a))) (ilf_type (skS.0 1 a) set_type)) True
% 23.20/23.43 Clause #53 (by clausification #[51]): ∀ (a : Iota), Eq (not_equal (identity_relation_of (skS.0 1 a)) empty_set) False
% 23.20/23.43 Clause #55 (by clausification #[52]): ∀ (a : Iota), Eq (Not (empty (skS.0 1 a))) True
% 23.20/23.43 Clause #56 (by clausification #[55]): ∀ (a : Iota), Eq (empty (skS.0 1 a)) False
% 23.20/23.43 Clause #59 (by clausification #[4]): ∀ (a : Iota),
% 23.20/23.43 Eq
% 23.20/23.43 (ilf_type a set_type →
% 23.20/23.43 ∀ (C : Iota),
% 23.20/23.43 ilf_type C set_type →
% 23.20/23.43 ∀ (D : Iota),
% 23.20/23.43 ilf_type D set_type → Iff (member (ordered_pair C D) (identity_relation_of a)) (And (member C a) (Eq C D)))
% 23.20/23.43 True
% 23.20/23.43 Clause #60 (by clausification #[59]): ∀ (a : Iota),
% 23.20/23.43 Or (Eq (ilf_type a set_type) False)
% 23.20/23.43 (Eq
% 23.20/23.43 (∀ (C : Iota),
% 23.20/23.43 ilf_type C set_type →
% 23.20/23.43 ∀ (D : Iota),
% 23.20/23.43 ilf_type D set_type → Iff (member (ordered_pair C D) (identity_relation_of a)) (And (member C a) (Eq C D)))
% 23.20/23.43 True)
% 23.20/23.43 Clause #61 (by clausification #[60]): ∀ (a a_1 : Iota),
% 23.20/23.43 Or (Eq (ilf_type a set_type) False)
% 23.20/23.43 (Eq
% 23.20/23.43 (ilf_type a_1 set_type →
% 23.20/23.43 ∀ (D : Iota),
% 23.20/23.43 ilf_type D set_type →
% 23.20/23.43 Iff (member (ordered_pair a_1 D) (identity_relation_of a)) (And (member a_1 a) (Eq a_1 D)))
% 23.20/23.43 True)
% 23.20/23.43 Clause #62 (by clausification #[61]): ∀ (a a_1 : Iota),
% 23.20/23.43 Or (Eq (ilf_type a set_type) False)
% 23.20/23.43 (Or (Eq (ilf_type a_1 set_type) False)
% 23.20/23.43 (Eq
% 23.20/23.43 (∀ (D : Iota),
% 23.20/23.43 ilf_type D set_type →
% 23.20/23.43 Iff (member (ordered_pair a_1 D) (identity_relation_of a)) (And (member a_1 a) (Eq a_1 D)))
% 23.20/23.43 True))
% 23.20/23.43 Clause #63 (by clausification #[62]): ∀ (a a_1 a_2 : Iota),
% 23.20/23.43 Or (Eq (ilf_type a set_type) False)
% 23.20/23.43 (Or (Eq (ilf_type a_1 set_type) False)
% 23.20/23.43 (Eq
% 23.20/23.43 (ilf_type a_2 set_type →
% 23.20/23.43 Iff (member (ordered_pair a_1 a_2) (identity_relation_of a)) (And (member a_1 a) (Eq a_1 a_2)))
% 23.28/23.45 True))
% 23.28/23.45 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 : Iota),
% 23.28/23.45 Or (Eq (ilf_type a set_type) False)
% 23.28/23.45 (Or (Eq (ilf_type a_1 set_type) False)
% 23.28/23.45 (Or (Eq (ilf_type a_2 set_type) False)
% 23.28/23.45 (Eq (Iff (member (ordered_pair a_1 a_2) (identity_relation_of a)) (And (member a_1 a) (Eq a_1 a_2))) True)))
% 23.28/23.45 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota),
% 23.28/23.45 Or (Eq (ilf_type a set_type) False)
% 23.28/23.45 (Or (Eq (ilf_type a_1 set_type) False)
% 23.28/23.45 (Or (Eq (ilf_type a_2 set_type) False)
% 23.28/23.45 (Or (Eq (member (ordered_pair a_1 a_2) (identity_relation_of a)) True)
% 23.28/23.45 (Eq (And (member a_1 a) (Eq a_1 a_2)) False))))
% 23.28/23.45 Clause #67 (by clausification #[65]): ∀ (a a_1 a_2 : Iota),
% 23.28/23.45 Or (Eq (ilf_type a set_type) False)
% 23.28/23.45 (Or (Eq (ilf_type a_1 set_type) False)
% 23.28/23.45 (Or (Eq (ilf_type a_2 set_type) False)
% 23.28/23.45 (Or (Eq (member (ordered_pair a_1 a_2) (identity_relation_of a)) True)
% 23.28/23.45 (Or (Eq (member a_1 a) False) (Eq (Eq a_1 a_2) False)))))
% 23.28/23.45 Clause #68 (by clausification #[67]): ∀ (a a_1 a_2 : Iota),
% 23.28/23.45 Or (Eq (ilf_type a set_type) False)
% 23.28/23.45 (Or (Eq (ilf_type a_1 set_type) False)
% 23.28/23.45 (Or (Eq (ilf_type a_2 set_type) False)
% 23.28/23.45 (Or (Eq (member (ordered_pair a_1 a_2) (identity_relation_of a)) True)
% 23.28/23.45 (Or (Eq (member a_1 a) False) (Ne a_1 a_2)))))
% 23.28/23.45 Clause #69 (by destructive equality resolution #[68]): ∀ (a a_1 : Iota),
% 23.28/23.45 Or (Eq (ilf_type a set_type) False)
% 23.28/23.45 (Or (Eq (ilf_type a_1 set_type) False)
% 23.28/23.45 (Or (Eq (ilf_type a_1 set_type) False)
% 23.28/23.45 (Or (Eq (member (ordered_pair a_1 a_1) (identity_relation_of a)) True) (Eq (member a_1 a) False))))
% 23.28/23.45 Clause #70 (by eliminate duplicate literals #[69]): ∀ (a a_1 : Iota),
% 23.28/23.45 Or (Eq (ilf_type a set_type) False)
% 23.28/23.45 (Or (Eq (ilf_type a_1 set_type) False)
% 23.28/23.45 (Or (Eq (member (ordered_pair a_1 a_1) (identity_relation_of a)) True) (Eq (member a_1 a) False)))
% 23.28/23.45 Clause #71 (by forward demodulation #[70, 28]): ∀ (a a_1 : Iota),
% 23.28/23.45 Or (Eq True False)
% 23.28/23.45 (Or (Eq (ilf_type a set_type) False)
% 23.28/23.45 (Or (Eq (member (ordered_pair a a) (identity_relation_of a_1)) True) (Eq (member a a_1) False)))
% 23.28/23.45 Clause #72 (by clausification #[71]): ∀ (a a_1 : Iota),
% 23.28/23.45 Or (Eq (ilf_type a set_type) False)
% 23.28/23.45 (Or (Eq (member (ordered_pair a a) (identity_relation_of a_1)) True) (Eq (member a a_1) False))
% 23.28/23.45 Clause #73 (by forward demodulation #[72, 28]): ∀ (a a_1 : Iota),
% 23.28/23.45 Or (Eq True False) (Or (Eq (member (ordered_pair a a) (identity_relation_of a_1)) True) (Eq (member a a_1) False))
% 23.28/23.45 Clause #74 (by clausification #[73]): ∀ (a a_1 : Iota), Or (Eq (member (ordered_pair a a) (identity_relation_of a_1)) True) (Eq (member a a_1) False)
% 23.28/23.45 Clause #131 (by clausification #[8]): ∀ (a : Iota), Eq (ilf_type a set_type → Iff (empty a) (∀ (C : Iota), ilf_type C set_type → Not (member C a))) True
% 23.28/23.45 Clause #132 (by clausification #[131]): ∀ (a : Iota),
% 23.28/23.45 Or (Eq (ilf_type a set_type) False) (Eq (Iff (empty a) (∀ (C : Iota), ilf_type C set_type → Not (member C a))) True)
% 23.28/23.45 Clause #133 (by clausification #[132]): ∀ (a : Iota),
% 23.28/23.45 Or (Eq (ilf_type a set_type) False)
% 23.28/23.45 (Or (Eq (empty a) True) (Eq (∀ (C : Iota), ilf_type C set_type → Not (member C a)) False))
% 23.28/23.45 Clause #135 (by clausification #[133]): ∀ (a a_1 : Iota),
% 23.28/23.45 Or (Eq (ilf_type a set_type) False)
% 23.28/23.45 (Or (Eq (empty a) True) (Eq (Not (ilf_type (skS.0 5 a a_1) set_type → Not (member (skS.0 5 a a_1) a))) True))
% 23.28/23.45 Clause #136 (by clausification #[135]): ∀ (a a_1 : Iota),
% 23.28/23.45 Or (Eq (ilf_type a set_type) False)
% 23.28/23.45 (Or (Eq (empty a) True) (Eq (ilf_type (skS.0 5 a a_1) set_type → Not (member (skS.0 5 a a_1) a)) False))
% 23.28/23.45 Clause #138 (by clausification #[136]): ∀ (a a_1 : Iota),
% 23.28/23.45 Or (Eq (ilf_type a set_type) False) (Or (Eq (empty a) True) (Eq (Not (member (skS.0 5 a a_1) a)) False))
% 23.28/23.45 Clause #147 (by clausification #[7]): ∀ (a : Iota), Eq (ilf_type a set_type → ∀ (C : Iota), ilf_type C set_type → Iff (not_equal a C) (Ne a C)) True
% 23.28/23.45 Clause #148 (by clausification #[147]): ∀ (a : Iota),
% 23.28/23.45 Or (Eq (ilf_type a set_type) False) (Eq (∀ (C : Iota), ilf_type C set_type → Iff (not_equal a C) (Ne a C)) True)
% 23.28/23.47 Clause #149 (by clausification #[148]): ∀ (a a_1 : Iota),
% 23.28/23.47 Or (Eq (ilf_type a set_type) False) (Eq (ilf_type a_1 set_type → Iff (not_equal a a_1) (Ne a a_1)) True)
% 23.28/23.47 Clause #150 (by clausification #[149]): ∀ (a a_1 : Iota),
% 23.28/23.47 Or (Eq (ilf_type a set_type) False)
% 23.28/23.47 (Or (Eq (ilf_type a_1 set_type) False) (Eq (Iff (not_equal a a_1) (Ne a a_1)) True))
% 23.28/23.47 Clause #151 (by clausification #[150]): ∀ (a a_1 : Iota),
% 23.28/23.47 Or (Eq (ilf_type a set_type) False)
% 23.28/23.47 (Or (Eq (ilf_type a_1 set_type) False) (Or (Eq (not_equal a a_1) True) (Eq (Ne a a_1) False)))
% 23.28/23.47 Clause #152 (by clausification #[150]): ∀ (a a_1 : Iota),
% 23.28/23.47 Or (Eq (ilf_type a set_type) False)
% 23.28/23.47 (Or (Eq (ilf_type a_1 set_type) False) (Or (Eq (not_equal a a_1) False) (Eq (Ne a a_1) True)))
% 23.28/23.47 Clause #153 (by clausification #[151]): ∀ (a a_1 : Iota),
% 23.28/23.47 Or (Eq (ilf_type a set_type) False)
% 23.28/23.47 (Or (Eq (ilf_type a_1 set_type) False) (Or (Eq (not_equal a a_1) True) (Eq a a_1)))
% 23.28/23.47 Clause #154 (by forward demodulation #[153, 28]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (ilf_type a set_type) False) (Or (Eq (not_equal a_1 a) True) (Eq a_1 a)))
% 23.28/23.47 Clause #155 (by clausification #[154]): ∀ (a a_1 : Iota), Or (Eq (ilf_type a set_type) False) (Or (Eq (not_equal a_1 a) True) (Eq a_1 a))
% 23.28/23.47 Clause #156 (by forward demodulation #[155, 28]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (not_equal a a_1) True) (Eq a a_1))
% 23.28/23.47 Clause #157 (by clausification #[156]): ∀ (a a_1 : Iota), Or (Eq (not_equal a a_1) True) (Eq a a_1)
% 23.28/23.47 Clause #158 (by superposition #[157, 53]): ∀ (a : Iota), Or (Eq (identity_relation_of (skS.0 1 a)) empty_set) (Eq True False)
% 23.28/23.47 Clause #161 (by superposition #[157, 44]): ∀ (a a_1 : Iota), Or (Eq (not_equal empty_set a) True) (Eq (member a_1 a) False)
% 23.28/23.47 Clause #358 (by clausification #[158]): ∀ (a : Iota), Eq (identity_relation_of (skS.0 1 a)) empty_set
% 23.28/23.47 Clause #447 (by clausification #[138]): ∀ (a a_1 : Iota), Or (Eq (ilf_type a set_type) False) (Or (Eq (empty a) True) (Eq (member (skS.0 5 a a_1) a) True))
% 23.28/23.47 Clause #448 (by forward demodulation #[447, 28]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (empty a) True) (Eq (member (skS.0 5 a a_1) a) True))
% 23.28/23.47 Clause #449 (by clausification #[448]): ∀ (a a_1 : Iota), Or (Eq (empty a) True) (Eq (member (skS.0 5 a a_1) a) True)
% 23.28/23.47 Clause #451 (by superposition #[449, 74]): ∀ (a a_1 : Iota),
% 23.28/23.47 Or (Eq (empty a) True)
% 23.28/23.47 (Or (Eq (member (ordered_pair (skS.0 5 a a_1) (skS.0 5 a a_1)) (identity_relation_of a)) True) (Eq True False))
% 23.28/23.47 Clause #469 (by clausification #[152]): ∀ (a a_1 : Iota),
% 23.28/23.47 Or (Eq (ilf_type a set_type) False)
% 23.28/23.47 (Or (Eq (ilf_type a_1 set_type) False) (Or (Eq (not_equal a a_1) False) (Ne a a_1)))
% 23.28/23.47 Clause #470 (by destructive equality resolution #[469]): ∀ (a : Iota), Or (Eq (ilf_type a set_type) False) (Or (Eq (ilf_type a set_type) False) (Eq (not_equal a a) False))
% 23.28/23.47 Clause #471 (by eliminate duplicate literals #[470]): ∀ (a : Iota), Or (Eq (ilf_type a set_type) False) (Eq (not_equal a a) False)
% 23.28/23.47 Clause #472 (by forward demodulation #[471, 28]): ∀ (a : Iota), Or (Eq True False) (Eq (not_equal a a) False)
% 23.28/23.47 Clause #473 (by clausification #[472]): ∀ (a : Iota), Eq (not_equal a a) False
% 23.28/23.47 Clause #6757 (by clausification #[451]): ∀ (a a_1 : Iota),
% 23.28/23.47 Or (Eq (empty a) True) (Eq (member (ordered_pair (skS.0 5 a a_1) (skS.0 5 a a_1)) (identity_relation_of a)) True)
% 23.28/23.47 Clause #6767 (by superposition #[6757, 161]): ∀ (a : Iota), Or (Eq (empty a) True) (Or (Eq (not_equal empty_set (identity_relation_of a)) True) (Eq True False))
% 23.28/23.47 Clause #6800 (by clausification #[6767]): ∀ (a : Iota), Or (Eq (empty a) True) (Eq (not_equal empty_set (identity_relation_of a)) True)
% 23.28/23.47 Clause #6803 (by superposition #[6800, 358]): ∀ (a : Iota), Or (Eq (empty (skS.0 1 a)) True) (Eq (not_equal empty_set empty_set) True)
% 23.28/23.47 Clause #6951 (by forward demodulation #[6803, 473]): ∀ (a : Iota), Or (Eq (empty (skS.0 1 a)) True) (Eq False True)
% 23.28/23.47 Clause #6952 (by clausification #[6951]): ∀ (a : Iota), Eq (empty (skS.0 1 a)) True
% 23.28/23.47 Clause #6953 (by superposition #[6952, 56]): Eq True False
% 23.28/23.52 Clause #6969 (by clausification #[6953]): False
% 23.28/23.52 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------