TSTP Solution File: SEU019+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU019+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n008.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 16:40:03 EDT 2023
% Result : Theorem 9.12s 9.26s
% Output : Proof 9.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU019+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : duper %s
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 23 17:01:18 EDT 2023
% 0.14/0.34 % CPUTime :
% 9.12/9.26 SZS status Theorem for theBenchmark.p
% 9.12/9.26 SZS output start Proof for theBenchmark.p
% 9.12/9.26 Clause #3 (by assumption #[]): Eq
% 9.12/9.26 (∀ (A : Iota),
% 9.12/9.26 And (relation A) (function A) →
% 9.12/9.26 Iff (one_to_one A)
% 9.12/9.26 (∀ (B C : Iota),
% 9.12/9.26 And (And (in B (relation_dom A)) (in C (relation_dom A))) (Eq (apply A B) (apply A C)) → Eq B C))
% 9.12/9.26 True
% 9.12/9.26 Clause #4 (by assumption #[]): Eq (∀ (A : Iota), relation (identity_relation A)) True
% 9.12/9.26 Clause #9 (by assumption #[]): Eq (∀ (A : Iota), And (relation (identity_relation A)) (function (identity_relation A))) True
% 9.12/9.26 Clause #24 (by assumption #[]): Eq
% 9.12/9.26 (∀ (A B : Iota),
% 9.12/9.26 And (relation B) (function B) →
% 9.12/9.26 Iff (Eq B (identity_relation A)) (And (Eq (relation_dom B) A) (∀ (C : Iota), in C A → Eq (apply B C) C)))
% 9.12/9.26 True
% 9.12/9.26 Clause #27 (by assumption #[]): Eq (Not (∀ (A : Iota), one_to_one (identity_relation A))) True
% 9.12/9.26 Clause #32 (by clausification #[4]): ∀ (a : Iota), Eq (relation (identity_relation a)) True
% 9.12/9.26 Clause #47 (by clausification #[27]): Eq (∀ (A : Iota), one_to_one (identity_relation A)) False
% 9.12/9.26 Clause #48 (by clausification #[47]): ∀ (a : Iota), Eq (Not (one_to_one (identity_relation (skS.0 0 a)))) True
% 9.12/9.26 Clause #49 (by clausification #[48]): ∀ (a : Iota), Eq (one_to_one (identity_relation (skS.0 0 a))) False
% 9.12/9.26 Clause #52 (by clausification #[3]): ∀ (a : Iota),
% 9.12/9.26 Eq
% 9.12/9.26 (And (relation a) (function a) →
% 9.12/9.26 Iff (one_to_one a)
% 9.12/9.26 (∀ (B C : Iota),
% 9.12/9.26 And (And (in B (relation_dom a)) (in C (relation_dom a))) (Eq (apply a B) (apply a C)) → Eq B C))
% 9.12/9.26 True
% 9.12/9.26 Clause #53 (by clausification #[52]): ∀ (a : Iota),
% 9.12/9.26 Or (Eq (And (relation a) (function a)) False)
% 9.12/9.26 (Eq
% 9.12/9.26 (Iff (one_to_one a)
% 9.12/9.26 (∀ (B C : Iota),
% 9.12/9.26 And (And (in B (relation_dom a)) (in C (relation_dom a))) (Eq (apply a B) (apply a C)) → Eq B C))
% 9.12/9.26 True)
% 9.12/9.26 Clause #54 (by clausification #[53]): ∀ (a : Iota),
% 9.12/9.26 Or
% 9.12/9.26 (Eq
% 9.12/9.26 (Iff (one_to_one a)
% 9.12/9.26 (∀ (B C : Iota),
% 9.12/9.26 And (And (in B (relation_dom a)) (in C (relation_dom a))) (Eq (apply a B) (apply a C)) → Eq B C))
% 9.12/9.26 True)
% 9.12/9.26 (Or (Eq (relation a) False) (Eq (function a) False))
% 9.12/9.26 Clause #55 (by clausification #[54]): ∀ (a : Iota),
% 9.12/9.26 Or (Eq (relation a) False)
% 9.12/9.26 (Or (Eq (function a) False)
% 9.12/9.26 (Or (Eq (one_to_one a) True)
% 9.12/9.26 (Eq
% 9.12/9.26 (∀ (B C : Iota),
% 9.12/9.26 And (And (in B (relation_dom a)) (in C (relation_dom a))) (Eq (apply a B) (apply a C)) → Eq B C)
% 9.12/9.26 False)))
% 9.12/9.26 Clause #57 (by clausification #[55]): ∀ (a a_1 : Iota),
% 9.12/9.26 Or (Eq (relation a) False)
% 9.12/9.26 (Or (Eq (function a) False)
% 9.12/9.26 (Or (Eq (one_to_one a) True)
% 9.12/9.26 (Eq
% 9.12/9.26 (Not
% 9.12/9.26 (∀ (C : Iota),
% 9.12/9.26 And (And (in (skS.0 1 a a_1) (relation_dom a)) (in C (relation_dom a)))
% 9.12/9.26 (Eq (apply a (skS.0 1 a a_1)) (apply a C)) →
% 9.12/9.26 Eq (skS.0 1 a a_1) C))
% 9.12/9.26 True)))
% 9.12/9.26 Clause #58 (by clausification #[57]): ∀ (a a_1 : Iota),
% 9.12/9.26 Or (Eq (relation a) False)
% 9.12/9.26 (Or (Eq (function a) False)
% 9.12/9.26 (Or (Eq (one_to_one a) True)
% 9.12/9.26 (Eq
% 9.12/9.26 (∀ (C : Iota),
% 9.12/9.26 And (And (in (skS.0 1 a a_1) (relation_dom a)) (in C (relation_dom a)))
% 9.12/9.26 (Eq (apply a (skS.0 1 a a_1)) (apply a C)) →
% 9.12/9.26 Eq (skS.0 1 a a_1) C)
% 9.12/9.26 False)))
% 9.12/9.26 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 : Iota),
% 9.12/9.26 Or (Eq (relation a) False)
% 9.12/9.26 (Or (Eq (function a) False)
% 9.12/9.26 (Or (Eq (one_to_one a) True)
% 9.12/9.26 (Eq
% 9.12/9.26 (Not
% 9.12/9.26 (And (And (in (skS.0 1 a a_1) (relation_dom a)) (in (skS.0 2 a a_1 a_2) (relation_dom a)))
% 9.12/9.26 (Eq (apply a (skS.0 1 a a_1)) (apply a (skS.0 2 a a_1 a_2))) →
% 9.12/9.26 Eq (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 9.12/9.26 True)))
% 9.12/9.26 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 : Iota),
% 9.12/9.26 Or (Eq (relation a) False)
% 9.12/9.26 (Or (Eq (function a) False)
% 9.12/9.26 (Or (Eq (one_to_one a) True)
% 9.12/9.26 (Eq
% 9.12/9.26 (And (And (in (skS.0 1 a a_1) (relation_dom a)) (in (skS.0 2 a a_1 a_2) (relation_dom a)))
% 9.12/9.26 (Eq (apply a (skS.0 1 a a_1)) (apply a (skS.0 2 a a_1 a_2))) →
% 9.12/9.26 Eq (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))
% 9.12/9.28 False)))
% 9.12/9.28 Clause #61 (by clausification #[60]): ∀ (a a_1 a_2 : Iota),
% 9.12/9.28 Or (Eq (relation a) False)
% 9.12/9.28 (Or (Eq (function a) False)
% 9.12/9.28 (Or (Eq (one_to_one a) True)
% 9.12/9.28 (Eq
% 9.12/9.28 (And (And (in (skS.0 1 a a_1) (relation_dom a)) (in (skS.0 2 a a_1 a_2) (relation_dom a)))
% 9.12/9.28 (Eq (apply a (skS.0 1 a a_1)) (apply a (skS.0 2 a a_1 a_2))))
% 9.12/9.28 True)))
% 9.12/9.28 Clause #62 (by clausification #[60]): ∀ (a a_1 a_2 : Iota),
% 9.12/9.28 Or (Eq (relation a) False)
% 9.12/9.28 (Or (Eq (function a) False) (Or (Eq (one_to_one a) True) (Eq (Eq (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) False)))
% 9.12/9.28 Clause #63 (by clausification #[61]): ∀ (a a_1 a_2 : Iota),
% 9.12/9.28 Or (Eq (relation a) False)
% 9.12/9.28 (Or (Eq (function a) False)
% 9.12/9.28 (Or (Eq (one_to_one a) True) (Eq (Eq (apply a (skS.0 1 a a_1)) (apply a (skS.0 2 a a_1 a_2))) True)))
% 9.12/9.28 Clause #64 (by clausification #[61]): ∀ (a a_1 a_2 : Iota),
% 9.12/9.28 Or (Eq (relation a) False)
% 9.12/9.28 (Or (Eq (function a) False)
% 9.12/9.28 (Or (Eq (one_to_one a) True)
% 9.12/9.28 (Eq (And (in (skS.0 1 a a_1) (relation_dom a)) (in (skS.0 2 a a_1 a_2) (relation_dom a))) True)))
% 9.12/9.28 Clause #65 (by clausification #[63]): ∀ (a a_1 a_2 : Iota),
% 9.12/9.28 Or (Eq (relation a) False)
% 9.12/9.28 (Or (Eq (function a) False)
% 9.12/9.28 (Or (Eq (one_to_one a) True) (Eq (apply a (skS.0 1 a a_1)) (apply a (skS.0 2 a a_1 a_2)))))
% 9.12/9.28 Clause #66 (by superposition #[65, 32]): ∀ (a a_1 a_2 : Iota),
% 9.12/9.28 Or (Eq (function (identity_relation a)) False)
% 9.12/9.28 (Or (Eq (one_to_one (identity_relation a)) True)
% 9.12/9.28 (Or
% 9.12/9.28 (Eq (apply (identity_relation a) (skS.0 1 (identity_relation a) a_1))
% 9.12/9.28 (apply (identity_relation a) (skS.0 2 (identity_relation a) a_1 a_2)))
% 9.12/9.28 (Eq False True)))
% 9.12/9.28 Clause #102 (by clausification #[9]): ∀ (a : Iota), Eq (And (relation (identity_relation a)) (function (identity_relation a))) True
% 9.12/9.28 Clause #103 (by clausification #[102]): ∀ (a : Iota), Eq (function (identity_relation a)) True
% 9.12/9.28 Clause #184 (by clausification #[24]): ∀ (a : Iota),
% 9.12/9.28 Eq
% 9.12/9.28 (∀ (B : Iota),
% 9.12/9.28 And (relation B) (function B) →
% 9.12/9.28 Iff (Eq B (identity_relation a)) (And (Eq (relation_dom B) a) (∀ (C : Iota), in C a → Eq (apply B C) C)))
% 9.12/9.28 True
% 9.12/9.28 Clause #185 (by clausification #[184]): ∀ (a a_1 : Iota),
% 9.12/9.28 Eq
% 9.12/9.28 (And (relation a) (function a) →
% 9.12/9.28 Iff (Eq a (identity_relation a_1)) (And (Eq (relation_dom a) a_1) (∀ (C : Iota), in C a_1 → Eq (apply a C) C)))
% 9.12/9.28 True
% 9.12/9.28 Clause #186 (by clausification #[185]): ∀ (a a_1 : Iota),
% 9.12/9.28 Or (Eq (And (relation a) (function a)) False)
% 9.12/9.28 (Eq (Iff (Eq a (identity_relation a_1)) (And (Eq (relation_dom a) a_1) (∀ (C : Iota), in C a_1 → Eq (apply a C) C)))
% 9.12/9.28 True)
% 9.12/9.28 Clause #187 (by clausification #[186]): ∀ (a a_1 : Iota),
% 9.12/9.28 Or
% 9.12/9.28 (Eq (Iff (Eq a (identity_relation a_1)) (And (Eq (relation_dom a) a_1) (∀ (C : Iota), in C a_1 → Eq (apply a C) C)))
% 9.12/9.28 True)
% 9.12/9.28 (Or (Eq (relation a) False) (Eq (function a) False))
% 9.12/9.28 Clause #189 (by clausification #[187]): ∀ (a a_1 : Iota),
% 9.12/9.28 Or (Eq (relation a) False)
% 9.12/9.28 (Or (Eq (function a) False)
% 9.12/9.28 (Or (Eq (Eq a (identity_relation a_1)) False)
% 9.12/9.28 (Eq (And (Eq (relation_dom a) a_1) (∀ (C : Iota), in C a_1 → Eq (apply a C) C)) True)))
% 9.12/9.28 Clause #260 (by clausification #[62]): ∀ (a a_1 a_2 : Iota),
% 9.12/9.28 Or (Eq (relation a) False)
% 9.12/9.28 (Or (Eq (function a) False) (Or (Eq (one_to_one a) True) (Ne (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))))
% 9.12/9.28 Clause #261 (by superposition #[260, 32]): ∀ (a a_1 a_2 : Iota),
% 9.12/9.28 Or (Eq (function (identity_relation a)) False)
% 9.12/9.28 (Or (Eq (one_to_one (identity_relation a)) True)
% 9.12/9.28 (Or (Ne (skS.0 1 (identity_relation a) a_1) (skS.0 2 (identity_relation a) a_1 a_2)) (Eq False True)))
% 9.12/9.28 Clause #271 (by clausification #[64]): ∀ (a a_1 a_2 : Iota),
% 9.12/9.28 Or (Eq (relation a) False)
% 9.12/9.28 (Or (Eq (function a) False) (Or (Eq (one_to_one a) True) (Eq (in (skS.0 2 a a_1 a_2) (relation_dom a)) True)))
% 9.12/9.28 Clause #272 (by clausification #[64]): ∀ (a a_1 : Iota),
% 9.12/9.28 Or (Eq (relation a) False)
% 9.12/9.28 (Or (Eq (function a) False) (Or (Eq (one_to_one a) True) (Eq (in (skS.0 1 a a_1) (relation_dom a)) True)))
% 9.12/9.28 Clause #273 (by superposition #[271, 32]): ∀ (a a_1 a_2 : Iota),
% 9.12/9.30 Or (Eq (function (identity_relation a)) False)
% 9.12/9.30 (Or (Eq (one_to_one (identity_relation a)) True)
% 9.12/9.30 (Or (Eq (in (skS.0 2 (identity_relation a) a_1 a_2) (relation_dom (identity_relation a))) True) (Eq False True)))
% 9.12/9.30 Clause #291 (by clausification #[66]): ∀ (a a_1 a_2 : Iota),
% 9.12/9.30 Or (Eq (function (identity_relation a)) False)
% 9.12/9.30 (Or (Eq (one_to_one (identity_relation a)) True)
% 9.12/9.30 (Eq (apply (identity_relation a) (skS.0 1 (identity_relation a) a_1))
% 9.12/9.30 (apply (identity_relation a) (skS.0 2 (identity_relation a) a_1 a_2))))
% 9.12/9.30 Clause #292 (by forward demodulation #[291, 103]): ∀ (a a_1 a_2 : Iota),
% 9.12/9.30 Or (Eq True False)
% 9.12/9.30 (Or (Eq (one_to_one (identity_relation a)) True)
% 9.12/9.30 (Eq (apply (identity_relation a) (skS.0 1 (identity_relation a) a_1))
% 9.12/9.30 (apply (identity_relation a) (skS.0 2 (identity_relation a) a_1 a_2))))
% 9.12/9.30 Clause #293 (by clausification #[292]): ∀ (a a_1 a_2 : Iota),
% 9.12/9.30 Or (Eq (one_to_one (identity_relation a)) True)
% 9.12/9.30 (Eq (apply (identity_relation a) (skS.0 1 (identity_relation a) a_1))
% 9.12/9.30 (apply (identity_relation a) (skS.0 2 (identity_relation a) a_1 a_2)))
% 9.12/9.30 Clause #362 (by superposition #[272, 32]): ∀ (a a_1 : Iota),
% 9.12/9.30 Or (Eq (function (identity_relation a)) False)
% 9.12/9.30 (Or (Eq (one_to_one (identity_relation a)) True)
% 9.12/9.30 (Or (Eq (in (skS.0 1 (identity_relation a) a_1) (relation_dom (identity_relation a))) True) (Eq False True)))
% 9.12/9.30 Clause #406 (by clausification #[189]): ∀ (a a_1 : Iota),
% 9.12/9.30 Or (Eq (relation a) False)
% 9.12/9.30 (Or (Eq (function a) False)
% 9.12/9.30 (Or (Eq (And (Eq (relation_dom a) a_1) (∀ (C : Iota), in C a_1 → Eq (apply a C) C)) True)
% 9.12/9.30 (Ne a (identity_relation a_1))))
% 9.12/9.30 Clause #407 (by clausification #[406]): ∀ (a a_1 : Iota),
% 9.12/9.30 Or (Eq (relation a) False)
% 9.12/9.30 (Or (Eq (function a) False)
% 9.12/9.30 (Or (Ne a (identity_relation a_1)) (Eq (∀ (C : Iota), in C a_1 → Eq (apply a C) C) True)))
% 9.12/9.30 Clause #408 (by clausification #[406]): ∀ (a a_1 : Iota),
% 9.12/9.30 Or (Eq (relation a) False)
% 9.12/9.30 (Or (Eq (function a) False) (Or (Ne a (identity_relation a_1)) (Eq (Eq (relation_dom a) a_1) True)))
% 9.12/9.30 Clause #409 (by clausification #[407]): ∀ (a a_1 a_2 : Iota),
% 9.12/9.30 Or (Eq (relation a) False)
% 9.12/9.30 (Or (Eq (function a) False) (Or (Ne a (identity_relation a_1)) (Eq (in a_2 a_1 → Eq (apply a a_2) a_2) True)))
% 9.12/9.30 Clause #410 (by clausification #[409]): ∀ (a a_1 a_2 : Iota),
% 9.12/9.30 Or (Eq (relation a) False)
% 9.12/9.30 (Or (Eq (function a) False)
% 9.12/9.30 (Or (Ne a (identity_relation a_1)) (Or (Eq (in a_2 a_1) False) (Eq (Eq (apply a a_2) a_2) True))))
% 9.12/9.30 Clause #411 (by clausification #[410]): ∀ (a a_1 a_2 : Iota),
% 9.12/9.30 Or (Eq (relation a) False)
% 9.12/9.30 (Or (Eq (function a) False) (Or (Ne a (identity_relation a_1)) (Or (Eq (in a_2 a_1) False) (Eq (apply a a_2) a_2))))
% 9.12/9.30 Clause #412 (by destructive equality resolution #[411]): ∀ (a a_1 : Iota),
% 9.12/9.30 Or (Eq (relation (identity_relation a)) False)
% 9.12/9.30 (Or (Eq (function (identity_relation a)) False)
% 9.12/9.30 (Or (Eq (in a_1 a) False) (Eq (apply (identity_relation a) a_1) a_1)))
% 9.12/9.30 Clause #413 (by forward demodulation #[412, 32]): ∀ (a a_1 : Iota),
% 9.12/9.30 Or (Eq True False)
% 9.12/9.30 (Or (Eq (function (identity_relation a)) False)
% 9.12/9.30 (Or (Eq (in a_1 a) False) (Eq (apply (identity_relation a) a_1) a_1)))
% 9.12/9.30 Clause #414 (by clausification #[413]): ∀ (a a_1 : Iota),
% 9.12/9.30 Or (Eq (function (identity_relation a)) False) (Or (Eq (in a_1 a) False) (Eq (apply (identity_relation a) a_1) a_1))
% 9.12/9.30 Clause #415 (by superposition #[414, 103]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Or (Eq (apply (identity_relation a_1) a) a) (Eq False True))
% 9.12/9.30 Clause #416 (by clausification #[415]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (apply (identity_relation a_1) a) a)
% 9.12/9.30 Clause #423 (by clausification #[408]): ∀ (a a_1 : Iota),
% 9.12/9.30 Or (Eq (relation a) False) (Or (Eq (function a) False) (Or (Ne a (identity_relation a_1)) (Eq (relation_dom a) a_1)))
% 9.12/9.30 Clause #424 (by destructive equality resolution #[423]): ∀ (a : Iota),
% 9.12/9.30 Or (Eq (relation (identity_relation a)) False)
% 9.12/9.30 (Or (Eq (function (identity_relation a)) False) (Eq (relation_dom (identity_relation a)) a))
% 9.12/9.30 Clause #425 (by forward demodulation #[424, 32]): ∀ (a : Iota),
% 9.12/9.32 Or (Eq True False) (Or (Eq (function (identity_relation a)) False) (Eq (relation_dom (identity_relation a)) a))
% 9.12/9.32 Clause #426 (by clausification #[425]): ∀ (a : Iota), Or (Eq (function (identity_relation a)) False) (Eq (relation_dom (identity_relation a)) a)
% 9.12/9.32 Clause #427 (by superposition #[426, 103]): ∀ (a : Iota), Or (Eq (relation_dom (identity_relation a)) a) (Eq False True)
% 9.12/9.32 Clause #428 (by clausification #[427]): ∀ (a : Iota), Eq (relation_dom (identity_relation a)) a
% 9.12/9.32 Clause #475 (by clausification #[362]): ∀ (a a_1 : Iota),
% 9.12/9.32 Or (Eq (function (identity_relation a)) False)
% 9.12/9.32 (Or (Eq (one_to_one (identity_relation a)) True)
% 9.12/9.32 (Eq (in (skS.0 1 (identity_relation a) a_1) (relation_dom (identity_relation a))) True))
% 9.12/9.32 Clause #476 (by forward demodulation #[475, 103]): ∀ (a a_1 : Iota),
% 9.12/9.32 Or (Eq True False)
% 9.12/9.32 (Or (Eq (one_to_one (identity_relation a)) True)
% 9.12/9.32 (Eq (in (skS.0 1 (identity_relation a) a_1) (relation_dom (identity_relation a))) True))
% 9.12/9.32 Clause #477 (by clausification #[476]): ∀ (a a_1 : Iota),
% 9.12/9.32 Or (Eq (one_to_one (identity_relation a)) True)
% 9.12/9.32 (Eq (in (skS.0 1 (identity_relation a) a_1) (relation_dom (identity_relation a))) True)
% 9.12/9.32 Clause #478 (by forward demodulation #[477, 428]): ∀ (a a_1 : Iota), Or (Eq (one_to_one (identity_relation a)) True) (Eq (in (skS.0 1 (identity_relation a) a_1) a) True)
% 9.12/9.32 Clause #484 (by superposition #[478, 416]): ∀ (a a_1 : Iota),
% 9.12/9.32 Or (Eq (one_to_one (identity_relation a)) True)
% 9.12/9.32 (Or (Eq True False)
% 9.12/9.32 (Eq (apply (identity_relation a) (skS.0 1 (identity_relation a) a_1)) (skS.0 1 (identity_relation a) a_1)))
% 9.12/9.32 Clause #635 (by clausification #[261]): ∀ (a a_1 a_2 : Iota),
% 9.12/9.32 Or (Eq (function (identity_relation a)) False)
% 9.12/9.32 (Or (Eq (one_to_one (identity_relation a)) True)
% 9.12/9.32 (Ne (skS.0 1 (identity_relation a) a_1) (skS.0 2 (identity_relation a) a_1 a_2)))
% 9.12/9.32 Clause #636 (by forward demodulation #[635, 103]): ∀ (a a_1 a_2 : Iota),
% 9.12/9.32 Or (Eq True False)
% 9.12/9.32 (Or (Eq (one_to_one (identity_relation a)) True)
% 9.12/9.32 (Ne (skS.0 1 (identity_relation a) a_1) (skS.0 2 (identity_relation a) a_1 a_2)))
% 9.12/9.32 Clause #637 (by clausification #[636]): ∀ (a a_1 a_2 : Iota),
% 9.12/9.32 Or (Eq (one_to_one (identity_relation a)) True)
% 9.12/9.32 (Ne (skS.0 1 (identity_relation a) a_1) (skS.0 2 (identity_relation a) a_1 a_2))
% 9.12/9.32 Clause #726 (by clausification #[273]): ∀ (a a_1 a_2 : Iota),
% 9.12/9.32 Or (Eq (function (identity_relation a)) False)
% 9.12/9.32 (Or (Eq (one_to_one (identity_relation a)) True)
% 9.12/9.32 (Eq (in (skS.0 2 (identity_relation a) a_1 a_2) (relation_dom (identity_relation a))) True))
% 9.12/9.32 Clause #727 (by forward demodulation #[726, 103]): ∀ (a a_1 a_2 : Iota),
% 9.12/9.32 Or (Eq True False)
% 9.12/9.32 (Or (Eq (one_to_one (identity_relation a)) True)
% 9.12/9.32 (Eq (in (skS.0 2 (identity_relation a) a_1 a_2) (relation_dom (identity_relation a))) True))
% 9.12/9.32 Clause #728 (by clausification #[727]): ∀ (a a_1 a_2 : Iota),
% 9.12/9.32 Or (Eq (one_to_one (identity_relation a)) True)
% 9.12/9.32 (Eq (in (skS.0 2 (identity_relation a) a_1 a_2) (relation_dom (identity_relation a))) True)
% 9.12/9.32 Clause #729 (by forward demodulation #[728, 428]): ∀ (a a_1 a_2 : Iota),
% 9.12/9.32 Or (Eq (one_to_one (identity_relation a)) True) (Eq (in (skS.0 2 (identity_relation a) a_1 a_2) a) True)
% 9.12/9.32 Clause #734 (by superposition #[729, 416]): ∀ (a a_1 a_2 : Iota),
% 9.12/9.32 Or (Eq (one_to_one (identity_relation a)) True)
% 9.12/9.32 (Or (Eq True False)
% 9.12/9.32 (Eq (apply (identity_relation a) (skS.0 2 (identity_relation a) a_1 a_2))
% 9.12/9.32 (skS.0 2 (identity_relation a) a_1 a_2)))
% 9.12/9.32 Clause #940 (by clausification #[484]): ∀ (a a_1 : Iota),
% 9.12/9.32 Or (Eq (one_to_one (identity_relation a)) True)
% 9.12/9.32 (Eq (apply (identity_relation a) (skS.0 1 (identity_relation a) a_1)) (skS.0 1 (identity_relation a) a_1))
% 9.12/9.32 Clause #1007 (by clausification #[734]): ∀ (a a_1 a_2 : Iota),
% 9.12/9.32 Or (Eq (one_to_one (identity_relation a)) True)
% 9.12/9.32 (Eq (apply (identity_relation a) (skS.0 2 (identity_relation a) a_1 a_2)) (skS.0 2 (identity_relation a) a_1 a_2))
% 9.12/9.32 Clause #1008 (by superposition #[1007, 293]): ∀ (a a_1 a_2 : Iota),
% 9.12/9.32 Or (Eq (one_to_one (identity_relation a)) True)
% 9.12/9.33 (Or (Eq (one_to_one (identity_relation a)) True)
% 9.12/9.33 (Eq (apply (identity_relation a) (skS.0 1 (identity_relation a) a_1)) (skS.0 2 (identity_relation a) a_1 a_2)))
% 9.12/9.33 Clause #1011 (by eliminate duplicate literals #[1008]): ∀ (a a_1 a_2 : Iota),
% 9.12/9.33 Or (Eq (one_to_one (identity_relation a)) True)
% 9.12/9.33 (Eq (apply (identity_relation a) (skS.0 1 (identity_relation a) a_1)) (skS.0 2 (identity_relation a) a_1 a_2))
% 9.12/9.33 Clause #1012 (by superposition #[1011, 940]): ∀ (a a_1 a_2 : Iota),
% 9.12/9.33 Or (Eq (one_to_one (identity_relation a)) True)
% 9.12/9.33 (Or (Eq (one_to_one (identity_relation a)) True)
% 9.12/9.33 (Eq (skS.0 2 (identity_relation a) a_1 a_2) (skS.0 1 (identity_relation a) a_1)))
% 9.12/9.33 Clause #1089 (by eliminate duplicate literals #[1012]): ∀ (a a_1 a_2 : Iota),
% 9.12/9.33 Or (Eq (one_to_one (identity_relation a)) True)
% 9.12/9.33 (Eq (skS.0 2 (identity_relation a) a_1 a_2) (skS.0 1 (identity_relation a) a_1))
% 9.12/9.33 Clause #1090 (by forward contextual literal cutting #[1089, 637]): ∀ (a : Iota), Eq (one_to_one (identity_relation a)) True
% 9.12/9.33 Clause #1114 (by superposition #[1090, 49]): Eq True False
% 9.12/9.33 Clause #1117 (by clausification #[1114]): False
% 9.12/9.33 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------