TSTP Solution File: SEU080+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU080+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n012.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 16:40:10 EDT 2023
% Result : Theorem 44.65s 45.00s
% Output : Proof 44.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU080+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n012.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 : Wed Aug 23 19:59:42 EDT 2023
% 0.14/0.36 % CPUTime :
% 44.65/45.00 SZS status Theorem for theBenchmark.p
% 44.65/45.00 SZS output start Proof for theBenchmark.p
% 44.65/45.00 Clause #4 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq A B) (And (subset A B) (subset B A))) True
% 44.65/45.00 Clause #22 (by assumption #[]): Eq (∀ (A : Iota), Iota → subset A A) True
% 44.65/45.00 Clause #23 (by assumption #[]): Eq
% 44.65/45.00 (∀ (A B C : Iota),
% 44.65/45.00 And (relation C) (function C) →
% 44.65/45.00 And (subset (relation_inverse_image C A) (relation_inverse_image C B)) (subset A (relation_rng C)) → subset A B)
% 44.65/45.00 True
% 44.65/45.00 Clause #24 (by assumption #[]): Eq
% 44.65/45.00 (Not
% 44.65/45.00 (∀ (A B C : Iota),
% 44.65/45.00 And (relation C) (function C) →
% 44.65/45.00 And (And (Eq (relation_inverse_image C A) (relation_inverse_image C B)) (subset A (relation_rng C)))
% 44.65/45.00 (subset B (relation_rng C)) →
% 44.65/45.00 Eq A B))
% 44.65/45.00 True
% 44.65/45.00 Clause #51 (by clausification #[22]): ∀ (a : Iota), Eq (Iota → subset a a) True
% 44.65/45.00 Clause #52 (by clausification #[51]): ∀ (a : Iota), Iota → Eq (subset a a) True
% 44.65/45.00 Clause #82 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq a B) (And (subset a B) (subset B a))) True
% 44.65/45.00 Clause #83 (by clausification #[82]): ∀ (a a_1 : Iota), Eq (Iff (Eq a a_1) (And (subset a a_1) (subset a_1 a))) True
% 44.65/45.00 Clause #84 (by clausification #[83]): ∀ (a a_1 : Iota), Or (Eq (Eq a a_1) True) (Eq (And (subset a a_1) (subset a_1 a)) False)
% 44.65/45.00 Clause #86 (by clausification #[84]): ∀ (a a_1 : Iota), Or (Eq (And (subset a a_1) (subset a_1 a)) False) (Eq a a_1)
% 44.65/45.00 Clause #87 (by clausification #[86]): ∀ (a a_1 : Iota), Or (Eq a a_1) (Or (Eq (subset a a_1) False) (Eq (subset a_1 a) False))
% 44.65/45.00 Clause #136 (by clausification #[23]): ∀ (a : Iota),
% 44.65/45.00 Eq
% 44.65/45.00 (∀ (B C : Iota),
% 44.65/45.00 And (relation C) (function C) →
% 44.65/45.00 And (subset (relation_inverse_image C a) (relation_inverse_image C B)) (subset a (relation_rng C)) → subset a B)
% 44.65/45.00 True
% 44.65/45.00 Clause #137 (by clausification #[136]): ∀ (a a_1 : Iota),
% 44.65/45.00 Eq
% 44.65/45.00 (∀ (C : Iota),
% 44.65/45.00 And (relation C) (function C) →
% 44.65/45.00 And (subset (relation_inverse_image C a) (relation_inverse_image C a_1)) (subset a (relation_rng C)) →
% 44.65/45.00 subset a a_1)
% 44.65/45.00 True
% 44.65/45.00 Clause #138 (by clausification #[137]): ∀ (a a_1 a_2 : Iota),
% 44.65/45.00 Eq
% 44.65/45.00 (And (relation a) (function a) →
% 44.65/45.00 And (subset (relation_inverse_image a a_1) (relation_inverse_image a a_2)) (subset a_1 (relation_rng a)) →
% 44.65/45.00 subset a_1 a_2)
% 44.65/45.00 True
% 44.65/45.00 Clause #139 (by clausification #[138]): ∀ (a a_1 a_2 : Iota),
% 44.65/45.00 Or (Eq (And (relation a) (function a)) False)
% 44.65/45.00 (Eq
% 44.65/45.00 (And (subset (relation_inverse_image a a_1) (relation_inverse_image a a_2)) (subset a_1 (relation_rng a)) →
% 44.65/45.00 subset a_1 a_2)
% 44.65/45.00 True)
% 44.65/45.00 Clause #140 (by clausification #[139]): ∀ (a a_1 a_2 : Iota),
% 44.65/45.00 Or
% 44.65/45.00 (Eq
% 44.65/45.00 (And (subset (relation_inverse_image a a_1) (relation_inverse_image a a_2)) (subset a_1 (relation_rng a)) →
% 44.65/45.00 subset a_1 a_2)
% 44.65/45.00 True)
% 44.65/45.00 (Or (Eq (relation a) False) (Eq (function a) False))
% 44.65/45.00 Clause #141 (by clausification #[140]): ∀ (a a_1 a_2 : Iota),
% 44.65/45.00 Or (Eq (relation a) False)
% 44.65/45.00 (Or (Eq (function a) False)
% 44.65/45.00 (Or
% 44.65/45.00 (Eq (And (subset (relation_inverse_image a a_1) (relation_inverse_image a a_2)) (subset a_1 (relation_rng a)))
% 44.65/45.00 False)
% 44.65/45.00 (Eq (subset a_1 a_2) True)))
% 44.65/45.00 Clause #142 (by clausification #[141]): ∀ (a a_1 a_2 : Iota),
% 44.65/45.00 Or (Eq (relation a) False)
% 44.65/45.00 (Or (Eq (function a) False)
% 44.65/45.00 (Or (Eq (subset a_1 a_2) True)
% 44.65/45.00 (Or (Eq (subset (relation_inverse_image a a_1) (relation_inverse_image a a_2)) False)
% 44.65/45.00 (Eq (subset a_1 (relation_rng a)) False))))
% 44.65/45.00 Clause #200 (by clausification #[24]): Eq
% 44.65/45.00 (∀ (A B C : Iota),
% 44.65/45.00 And (relation C) (function C) →
% 44.65/45.00 And (And (Eq (relation_inverse_image C A) (relation_inverse_image C B)) (subset A (relation_rng C)))
% 44.65/45.00 (subset B (relation_rng C)) →
% 44.65/45.00 Eq A B)
% 44.65/45.00 False
% 44.65/45.00 Clause #201 (by clausification #[200]): ∀ (a : Iota),
% 44.65/45.00 Eq
% 44.65/45.00 (Not
% 44.65/45.00 (∀ (B C : Iota),
% 44.65/45.00 And (relation C) (function C) →
% 44.65/45.00 And
% 44.65/45.00 (And (Eq (relation_inverse_image C (skS.0 11 a)) (relation_inverse_image C B))
% 44.65/45.00 (subset (skS.0 11 a) (relation_rng C)))
% 44.65/45.00 (subset B (relation_rng C)) →
% 44.65/45.02 Eq (skS.0 11 a) B))
% 44.65/45.02 True
% 44.65/45.02 Clause #202 (by clausification #[201]): ∀ (a : Iota),
% 44.65/45.02 Eq
% 44.65/45.02 (∀ (B C : Iota),
% 44.65/45.02 And (relation C) (function C) →
% 44.65/45.02 And
% 44.65/45.02 (And (Eq (relation_inverse_image C (skS.0 11 a)) (relation_inverse_image C B))
% 44.65/45.02 (subset (skS.0 11 a) (relation_rng C)))
% 44.65/45.02 (subset B (relation_rng C)) →
% 44.65/45.02 Eq (skS.0 11 a) B)
% 44.65/45.02 False
% 44.65/45.02 Clause #203 (by clausification #[202]): ∀ (a a_1 : Iota),
% 44.65/45.02 Eq
% 44.65/45.02 (Not
% 44.65/45.02 (∀ (C : Iota),
% 44.65/45.02 And (relation C) (function C) →
% 44.65/45.02 And
% 44.65/45.02 (And (Eq (relation_inverse_image C (skS.0 11 a)) (relation_inverse_image C (skS.0 12 a a_1)))
% 44.65/45.02 (subset (skS.0 11 a) (relation_rng C)))
% 44.65/45.02 (subset (skS.0 12 a a_1) (relation_rng C)) →
% 44.65/45.02 Eq (skS.0 11 a) (skS.0 12 a a_1)))
% 44.65/45.02 True
% 44.65/45.02 Clause #204 (by clausification #[203]): ∀ (a a_1 : Iota),
% 44.65/45.02 Eq
% 44.65/45.02 (∀ (C : Iota),
% 44.65/45.02 And (relation C) (function C) →
% 44.65/45.02 And
% 44.65/45.02 (And (Eq (relation_inverse_image C (skS.0 11 a)) (relation_inverse_image C (skS.0 12 a a_1)))
% 44.65/45.02 (subset (skS.0 11 a) (relation_rng C)))
% 44.65/45.02 (subset (skS.0 12 a a_1) (relation_rng C)) →
% 44.65/45.02 Eq (skS.0 11 a) (skS.0 12 a a_1))
% 44.65/45.02 False
% 44.65/45.02 Clause #205 (by clausification #[204]): ∀ (a a_1 a_2 : Iota),
% 44.65/45.02 Eq
% 44.65/45.02 (Not
% 44.65/45.02 (And (relation (skS.0 13 a a_1 a_2)) (function (skS.0 13 a a_1 a_2)) →
% 44.65/45.02 And
% 44.65/45.02 (And
% 44.65/45.02 (Eq (relation_inverse_image (skS.0 13 a a_1 a_2) (skS.0 11 a))
% 44.65/45.02 (relation_inverse_image (skS.0 13 a a_1 a_2) (skS.0 12 a a_1)))
% 44.65/45.02 (subset (skS.0 11 a) (relation_rng (skS.0 13 a a_1 a_2))))
% 44.65/45.02 (subset (skS.0 12 a a_1) (relation_rng (skS.0 13 a a_1 a_2))) →
% 44.65/45.02 Eq (skS.0 11 a) (skS.0 12 a a_1)))
% 44.65/45.02 True
% 44.65/45.02 Clause #206 (by clausification #[205]): ∀ (a a_1 a_2 : Iota),
% 44.65/45.02 Eq
% 44.65/45.02 (And (relation (skS.0 13 a a_1 a_2)) (function (skS.0 13 a a_1 a_2)) →
% 44.65/45.02 And
% 44.65/45.02 (And
% 44.65/45.02 (Eq (relation_inverse_image (skS.0 13 a a_1 a_2) (skS.0 11 a))
% 44.65/45.02 (relation_inverse_image (skS.0 13 a a_1 a_2) (skS.0 12 a a_1)))
% 44.65/45.02 (subset (skS.0 11 a) (relation_rng (skS.0 13 a a_1 a_2))))
% 44.65/45.02 (subset (skS.0 12 a a_1) (relation_rng (skS.0 13 a a_1 a_2))) →
% 44.65/45.02 Eq (skS.0 11 a) (skS.0 12 a a_1))
% 44.65/45.02 False
% 44.65/45.02 Clause #207 (by clausification #[206]): ∀ (a a_1 a_2 : Iota), Eq (And (relation (skS.0 13 a a_1 a_2)) (function (skS.0 13 a a_1 a_2))) True
% 44.65/45.02 Clause #208 (by clausification #[206]): ∀ (a a_1 a_2 : Iota),
% 44.65/45.02 Eq
% 44.65/45.02 (And
% 44.65/45.02 (And
% 44.65/45.02 (Eq (relation_inverse_image (skS.0 13 a a_1 a_2) (skS.0 11 a))
% 44.65/45.02 (relation_inverse_image (skS.0 13 a a_1 a_2) (skS.0 12 a a_1)))
% 44.65/45.02 (subset (skS.0 11 a) (relation_rng (skS.0 13 a a_1 a_2))))
% 44.65/45.02 (subset (skS.0 12 a a_1) (relation_rng (skS.0 13 a a_1 a_2))) →
% 44.65/45.02 Eq (skS.0 11 a) (skS.0 12 a a_1))
% 44.65/45.02 False
% 44.65/45.02 Clause #209 (by clausification #[207]): ∀ (a a_1 a_2 : Iota), Eq (function (skS.0 13 a a_1 a_2)) True
% 44.65/45.02 Clause #210 (by clausification #[207]): ∀ (a a_1 a_2 : Iota), Eq (relation (skS.0 13 a a_1 a_2)) True
% 44.65/45.02 Clause #234 (by superposition #[210, 142]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 44.65/45.02 Or (Eq True False)
% 44.65/45.02 (Or (Eq (function (skS.0 13 a a_1 a_2)) False)
% 44.65/45.02 (Or (Eq (subset a_3 a_4) True)
% 44.65/45.02 (Or
% 44.65/45.02 (Eq
% 44.65/45.02 (subset (relation_inverse_image (skS.0 13 a a_1 a_2) a_3) (relation_inverse_image (skS.0 13 a a_1 a_2) a_4))
% 44.65/45.02 False)
% 44.65/45.02 (Eq (subset a_3 (relation_rng (skS.0 13 a a_1 a_2))) False))))
% 44.65/45.02 Clause #347 (by clausification #[208]): ∀ (a a_1 a_2 : Iota),
% 44.65/45.02 Eq
% 44.65/45.02 (And
% 44.65/45.02 (And
% 44.65/45.02 (Eq (relation_inverse_image (skS.0 13 a a_1 a_2) (skS.0 11 a))
% 44.65/45.02 (relation_inverse_image (skS.0 13 a a_1 a_2) (skS.0 12 a a_1)))
% 44.65/45.02 (subset (skS.0 11 a) (relation_rng (skS.0 13 a a_1 a_2))))
% 44.65/45.02 (subset (skS.0 12 a a_1) (relation_rng (skS.0 13 a a_1 a_2))))
% 44.65/45.02 True
% 44.65/45.02 Clause #348 (by clausification #[208]): ∀ (a a_1 : Iota), Eq (Eq (skS.0 11 a) (skS.0 12 a a_1)) False
% 44.65/45.02 Clause #349 (by clausification #[347]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 12 a a_1) (relation_rng (skS.0 13 a a_1 a_2))) True
% 44.77/45.04 Clause #350 (by clausification #[347]): ∀ (a a_1 a_2 : Iota),
% 44.77/45.04 Eq
% 44.77/45.04 (And
% 44.77/45.04 (Eq (relation_inverse_image (skS.0 13 a a_1 a_2) (skS.0 11 a))
% 44.77/45.04 (relation_inverse_image (skS.0 13 a a_1 a_2) (skS.0 12 a a_1)))
% 44.77/45.04 (subset (skS.0 11 a) (relation_rng (skS.0 13 a a_1 a_2))))
% 44.77/45.04 True
% 44.77/45.04 Clause #353 (by clausification #[348]): ∀ (a a_1 : Iota), Ne (skS.0 11 a) (skS.0 12 a a_1)
% 44.77/45.04 Clause #410 (by clausification #[234]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 44.77/45.04 Or (Eq (function (skS.0 13 a a_1 a_2)) False)
% 44.77/45.04 (Or (Eq (subset a_3 a_4) True)
% 44.77/45.04 (Or
% 44.77/45.04 (Eq (subset (relation_inverse_image (skS.0 13 a a_1 a_2) a_3) (relation_inverse_image (skS.0 13 a a_1 a_2) a_4))
% 44.77/45.04 False)
% 44.77/45.04 (Eq (subset a_3 (relation_rng (skS.0 13 a a_1 a_2))) False)))
% 44.77/45.04 Clause #411 (by forward demodulation #[410, 209]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 44.77/45.04 Or (Eq True False)
% 44.77/45.04 (Or (Eq (subset a a_1) True)
% 44.77/45.04 (Or
% 44.77/45.04 (Eq
% 44.77/45.04 (subset (relation_inverse_image (skS.0 13 a_2 a_3 a_4) a) (relation_inverse_image (skS.0 13 a_2 a_3 a_4) a_1))
% 44.77/45.04 False)
% 44.77/45.04 (Eq (subset a (relation_rng (skS.0 13 a_2 a_3 a_4))) False)))
% 44.77/45.04 Clause #412 (by clausification #[411]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 44.77/45.04 Or (Eq (subset a a_1) True)
% 44.77/45.04 (Or
% 44.77/45.04 (Eq (subset (relation_inverse_image (skS.0 13 a_2 a_3 a_4) a) (relation_inverse_image (skS.0 13 a_2 a_3 a_4) a_1))
% 44.77/45.04 False)
% 44.77/45.04 (Eq (subset a (relation_rng (skS.0 13 a_2 a_3 a_4))) False))
% 44.77/45.04 Clause #468 (by clausification #[350]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 11 a) (relation_rng (skS.0 13 a a_1 a_2))) True
% 44.77/45.04 Clause #469 (by clausification #[350]): ∀ (a a_1 a_2 : Iota),
% 44.77/45.04 Eq
% 44.77/45.04 (Eq (relation_inverse_image (skS.0 13 a a_1 a_2) (skS.0 11 a))
% 44.77/45.04 (relation_inverse_image (skS.0 13 a a_1 a_2) (skS.0 12 a a_1)))
% 44.77/45.04 True
% 44.77/45.04 Clause #771 (by clausification #[469]): ∀ (a a_1 a_2 : Iota),
% 44.77/45.04 Eq (relation_inverse_image (skS.0 13 a a_1 a_2) (skS.0 11 a))
% 44.77/45.04 (relation_inverse_image (skS.0 13 a a_1 a_2) (skS.0 12 a a_1))
% 44.77/45.05 Clause #772 (by superposition #[771, 412]): ∀ (a a_1 a_2 a_3 : Iota),
% 44.77/45.05 Or (Eq (subset a (skS.0 12 a_1 a_2)) True)
% 44.77/45.05 (Or
% 44.77/45.05 (Eq
% 44.77/45.05 (subset (relation_inverse_image (skS.0 13 a_1 a_2 a_3) a)
% 44.77/45.05 (relation_inverse_image (skS.0 13 a_1 a_2 a_3) (skS.0 11 a_1)))
% 44.77/45.05 False)
% 44.77/45.05 (Eq (subset a (relation_rng (skS.0 13 a_1 a_2 a_3))) False))
% 44.77/45.05 Clause #773 (by superposition #[771, 412]): ∀ (a a_1 a_2 a_3 : Iota),
% 44.77/45.05 Or (Eq (subset (skS.0 12 a a_1) a_2) True)
% 44.77/45.05 (Or
% 44.77/45.05 (Eq
% 44.77/45.05 (subset (relation_inverse_image (skS.0 13 a a_1 a_3) (skS.0 11 a))
% 44.77/45.05 (relation_inverse_image (skS.0 13 a a_1 a_3) a_2))
% 44.77/45.05 False)
% 44.77/45.05 (Eq (subset (skS.0 12 a a_1) (relation_rng (skS.0 13 a a_1 a_3))) False))
% 44.77/45.05 Clause #5615 (by superposition #[772, 52]): ∀ (a a_1 a_2 : Iota),
% 44.77/45.05 Or (Eq (subset (skS.0 11 a) (skS.0 12 a a_1)) True)
% 44.77/45.05 (Or (Eq (subset (skS.0 11 a) (relation_rng (skS.0 13 a a_1 a_2))) False) (Eq False True))
% 44.77/45.05 Clause #5617 (by clausification #[5615]): ∀ (a a_1 a_2 : Iota),
% 44.77/45.05 Or (Eq (subset (skS.0 11 a) (skS.0 12 a a_1)) True)
% 44.77/45.05 (Eq (subset (skS.0 11 a) (relation_rng (skS.0 13 a a_1 a_2))) False)
% 44.77/45.05 Clause #5618 (by superposition #[5617, 468]): ∀ (a a_1 : Iota), Or (Eq (subset (skS.0 11 a) (skS.0 12 a a_1)) True) (Eq False True)
% 44.77/45.05 Clause #5619 (by clausification #[5618]): ∀ (a a_1 : Iota), Eq (subset (skS.0 11 a) (skS.0 12 a a_1)) True
% 44.77/45.05 Clause #5629 (by forward demodulation #[773, 349]): ∀ (a a_1 a_2 a_3 : Iota),
% 44.77/45.05 Or (Eq (subset (skS.0 12 a a_1) a_2) True)
% 44.77/45.05 (Or
% 44.77/45.05 (Eq
% 44.77/45.05 (subset (relation_inverse_image (skS.0 13 a a_1 a_3) (skS.0 11 a))
% 44.77/45.05 (relation_inverse_image (skS.0 13 a a_1 a_3) a_2))
% 44.77/45.05 False)
% 44.77/45.05 (Eq True False))
% 44.77/45.05 Clause #5630 (by clausification #[5629]): ∀ (a a_1 a_2 a_3 : Iota),
% 44.77/45.05 Or (Eq (subset (skS.0 12 a a_1) a_2) True)
% 44.77/45.05 (Eq
% 44.77/45.05 (subset (relation_inverse_image (skS.0 13 a a_1 a_3) (skS.0 11 a))
% 44.77/45.05 (relation_inverse_image (skS.0 13 a a_1 a_3) a_2))
% 44.77/45.05 False)
% 44.77/45.05 Clause #5631 (by superposition #[5630, 52]): ∀ (a a_1 : Iota), Or (Eq (subset (skS.0 12 a a_1) (skS.0 11 a)) True) (Eq False True)
% 44.77/45.09 Clause #5633 (by clausification #[5631]): ∀ (a a_1 : Iota), Eq (subset (skS.0 12 a a_1) (skS.0 11 a)) True
% 44.77/45.09 Clause #5634 (by superposition #[5633, 87]): ∀ (a a_1 : Iota),
% 44.77/45.09 Or (Eq (skS.0 12 a a_1) (skS.0 11 a)) (Or (Eq True False) (Eq (subset (skS.0 11 a) (skS.0 12 a a_1)) False))
% 44.77/45.09 Clause #5706 (by clausification #[5634]): ∀ (a a_1 : Iota), Or (Eq (skS.0 12 a a_1) (skS.0 11 a)) (Eq (subset (skS.0 11 a) (skS.0 12 a a_1)) False)
% 44.77/45.09 Clause #5707 (by forward contextual literal cutting #[5706, 353]): ∀ (a a_1 : Iota), Eq (subset (skS.0 11 a) (skS.0 12 a a_1)) False
% 44.77/45.09 Clause #5708 (by superposition #[5707, 5619]): Eq False True
% 44.77/45.09 Clause #5709 (by clausification #[5708]): False
% 44.77/45.09 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------