TSTP Solution File: REL023+2 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : REL023+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n021.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 13:37:47 EDT 2023
% Result : Theorem 129.37s 129.56s
% Output : Proof 129.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : REL023+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : duper %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 20:29:26 EDT 2023
% 0.13/0.35 % CPUTime :
% 129.37/129.56 SZS status Theorem for theBenchmark.p
% 129.37/129.56 SZS output start Proof for theBenchmark.p
% 129.37/129.56 Clause #0 (by assumption #[]): Eq (∀ (X0 X1 : Iota), Eq (join X0 X1) (join X1 X0)) True
% 129.37/129.56 Clause #1 (by assumption #[]): Eq (∀ (X0 X1 X2 : Iota), Eq (join X0 (join X1 X2)) (join (join X0 X1) X2)) True
% 129.37/129.56 Clause #2 (by assumption #[]): Eq
% 129.37/129.56 (∀ (X0 X1 : Iota),
% 129.37/129.56 Eq X0 (join (complement (join (complement X0) (complement X1))) (complement (join (complement X0) X1))))
% 129.37/129.56 True
% 129.37/129.56 Clause #3 (by assumption #[]): Eq (∀ (X0 X1 : Iota), Eq (meet X0 X1) (complement (join (complement X0) (complement X1)))) True
% 129.37/129.56 Clause #5 (by assumption #[]): Eq (∀ (X0 : Iota), Eq (composition X0 one) X0) True
% 129.37/129.56 Clause #6 (by assumption #[]): Eq (∀ (X0 X1 X2 : Iota), Eq (composition (join X0 X1) X2) (join (composition X0 X2) (composition X1 X2))) True
% 129.37/129.56 Clause #7 (by assumption #[]): Eq (∀ (X0 : Iota), Eq (converse (converse X0)) X0) True
% 129.37/129.56 Clause #9 (by assumption #[]): Eq (∀ (X0 X1 : Iota), Eq (converse (composition X0 X1)) (composition (converse X1) (converse X0))) True
% 129.37/129.56 Clause #11 (by assumption #[]): Eq (∀ (X0 : Iota), Eq top (join X0 (complement X0))) True
% 129.37/129.56 Clause #12 (by assumption #[]): Eq (∀ (X0 : Iota), Eq zero (meet X0 (complement X0))) True
% 129.37/129.56 Clause #15 (by assumption #[]): Eq
% 129.37/129.56 (∀ (X0 X1 X2 : Iota),
% 129.37/129.56 Eq (join (meet (composition X0 X1) X2) (meet (composition (meet X0 (composition X2 (converse X1))) X1) X2))
% 129.37/129.56 (meet (composition (meet X0 (composition X2 (converse X1))) X1) X2))
% 129.37/129.56 True
% 129.37/129.56 Clause #16 (by assumption #[]): Eq
% 129.37/129.56 (Not
% 129.37/129.56 (∀ (X0 X1 X2 : Iota),
% 129.37/129.56 Eq (join (composition (meet X0 (converse X1)) (meet X1 X2)) (composition X0 (meet X1 X2)))
% 129.37/129.56 (composition X0 (meet X1 X2))))
% 129.37/129.56 True
% 129.37/129.56 Clause #17 (by clausification #[7]): ∀ (a : Iota), Eq (Eq (converse (converse a)) a) True
% 129.37/129.56 Clause #18 (by clausification #[17]): ∀ (a : Iota), Eq (converse (converse a)) a
% 129.37/129.56 Clause #19 (by clausification #[5]): ∀ (a : Iota), Eq (Eq (composition a one) a) True
% 129.37/129.56 Clause #20 (by clausification #[19]): ∀ (a : Iota), Eq (composition a one) a
% 129.37/129.56 Clause #21 (by clausification #[12]): ∀ (a : Iota), Eq (Eq zero (meet a (complement a))) True
% 129.37/129.56 Clause #22 (by clausification #[21]): ∀ (a : Iota), Eq zero (meet a (complement a))
% 129.37/129.56 Clause #23 (by clausification #[11]): ∀ (a : Iota), Eq (Eq top (join a (complement a))) True
% 129.37/129.56 Clause #24 (by clausification #[23]): ∀ (a : Iota), Eq top (join a (complement a))
% 129.37/129.56 Clause #25 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (X1 : Iota), Eq (join a X1) (join X1 a)) True
% 129.37/129.56 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (Eq (join a a_1) (join a_1 a)) True
% 129.37/129.56 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (join a a_1) (join a_1 a)
% 129.37/129.56 Clause #28 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (X1 X2 : Iota), Eq (join a (join X1 X2)) (join (join a X1) X2)) True
% 129.37/129.56 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (∀ (X2 : Iota), Eq (join a (join a_1 X2)) (join (join a a_1) X2)) True
% 129.37/129.56 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Eq (Eq (join a (join a_1 a_2)) (join (join a a_1) a_2)) True
% 129.37/129.56 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), Eq (join a (join a_1 a_2)) (join (join a a_1) a_2)
% 129.37/129.56 Clause #32 (by superposition #[31, 24]): ∀ (a a_1 : Iota), Eq top (join a (join a_1 (complement (join a a_1))))
% 129.37/129.56 Clause #35 (by superposition #[31, 31]): ∀ (a a_1 a_2 a_3 : Iota), Eq (join (join a a_1) (join a_2 a_3)) (join (join a (join a_1 a_2)) a_3)
% 129.37/129.56 Clause #36 (by superposition #[31, 24]): ∀ (a a_1 : Iota), Eq (join a (join (complement a) a_1)) (join top a_1)
% 129.37/129.56 Clause #37 (by superposition #[31, 27]): ∀ (a a_1 a_2 : Iota), Eq (join a (join a_1 a_2)) (join (join a_1 a) a_2)
% 129.37/129.56 Clause #41 (by superposition #[36, 24]): ∀ (a : Iota), Eq (join a top) (join top (complement (complement a)))
% 129.37/129.56 Clause #42 (by superposition #[36, 27]): ∀ (a a_1 : Iota), Eq (join a (join a_1 (complement a))) (join top a_1)
% 129.37/129.56 Clause #47 (by superposition #[42, 41]): ∀ (a : Iota), Eq (join (complement a) (join a top)) (join top top)
% 129.37/129.56 Clause #53 (by superposition #[47, 27]): ∀ (a : Iota), Eq (join (complement a) (join top a)) (join top top)
% 129.37/129.58 Clause #54 (by clausification #[2]): ∀ (a : Iota),
% 129.37/129.58 Eq
% 129.37/129.58 (∀ (X1 : Iota),
% 129.37/129.58 Eq a (join (complement (join (complement a) (complement X1))) (complement (join (complement a) X1))))
% 129.37/129.58 True
% 129.37/129.58 Clause #55 (by clausification #[54]): ∀ (a a_1 : Iota),
% 129.37/129.58 Eq (Eq a (join (complement (join (complement a) (complement a_1))) (complement (join (complement a) a_1)))) True
% 129.37/129.58 Clause #56 (by clausification #[55]): ∀ (a a_1 : Iota), Eq a (join (complement (join (complement a) (complement a_1))) (complement (join (complement a) a_1)))
% 129.37/129.58 Clause #58 (by superposition #[56, 42]): ∀ (a a_1 : Iota), Eq (join (join (complement a) a_1) a) (join top (complement (join (complement a) (complement a_1))))
% 129.37/129.58 Clause #61 (by superposition #[56, 27]): ∀ (a a_1 : Iota), Eq a (join (complement (join (complement a) a_1)) (complement (join (complement a) (complement a_1))))
% 129.37/129.58 Clause #64 (by superposition #[56, 47]): ∀ (a : Iota), Eq a (join (complement (join (complement a) (complement (join a top)))) (complement (join top top)))
% 129.37/129.58 Clause #68 (by superposition #[56, 27]): ∀ (a a_1 : Iota), Eq a (join (complement (join (complement a) (complement a_1))) (complement (join a_1 (complement a))))
% 129.37/129.58 Clause #84 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (X1 : Iota), Eq (meet a X1) (complement (join (complement a) (complement X1)))) True
% 129.37/129.58 Clause #85 (by clausification #[84]): ∀ (a a_1 : Iota), Eq (Eq (meet a a_1) (complement (join (complement a) (complement a_1)))) True
% 129.37/129.58 Clause #86 (by clausification #[85]): ∀ (a a_1 : Iota), Eq (meet a a_1) (complement (join (complement a) (complement a_1)))
% 129.37/129.58 Clause #97 (by superposition #[86, 24]): ∀ (a : Iota), Eq (meet a (complement a)) (complement top)
% 129.37/129.58 Clause #98 (by superposition #[86, 27]): ∀ (a a_1 : Iota), Eq (meet a a_1) (complement (join (complement a_1) (complement a)))
% 129.37/129.58 Clause #99 (by superposition #[97, 22]): Eq zero (complement top)
% 129.37/129.58 Clause #104 (by superposition #[99, 24]): Eq top (join top zero)
% 129.37/129.58 Clause #105 (by superposition #[99, 36]): ∀ (a : Iota), Eq (join top (join zero a)) (join top a)
% 129.37/129.58 Clause #109 (by superposition #[99, 86]): ∀ (a : Iota), Eq (meet a top) (complement (join (complement a) zero))
% 129.37/129.58 Clause #110 (by superposition #[99, 86]): ∀ (a : Iota), Eq (meet top a) (complement (join zero (complement a)))
% 129.37/129.58 Clause #112 (by superposition #[104, 27]): Eq (join zero top) top
% 129.37/129.58 Clause #125 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (X1 X2 : Iota), Eq (composition (join a X1) X2) (join (composition a X2) (composition X1 X2))) True
% 129.37/129.58 Clause #126 (by clausification #[125]): ∀ (a a_1 : Iota),
% 129.37/129.58 Eq (∀ (X2 : Iota), Eq (composition (join a a_1) X2) (join (composition a X2) (composition a_1 X2))) True
% 129.37/129.58 Clause #127 (by clausification #[126]): ∀ (a a_1 a_2 : Iota), Eq (Eq (composition (join a a_1) a_2) (join (composition a a_2) (composition a_1 a_2))) True
% 129.37/129.58 Clause #128 (by clausification #[127]): ∀ (a a_1 a_2 : Iota), Eq (composition (join a a_1) a_2) (join (composition a a_2) (composition a_1 a_2))
% 129.37/129.58 Clause #145 (by superposition #[110, 41]): ∀ (a : Iota), Eq (join (join zero (complement a)) top) (join top (complement (meet top a)))
% 129.37/129.58 Clause #180 (by clausification #[9]): ∀ (a : Iota), Eq (∀ (X1 : Iota), Eq (converse (composition a X1)) (composition (converse X1) (converse a))) True
% 129.37/129.58 Clause #181 (by clausification #[180]): ∀ (a a_1 : Iota), Eq (Eq (converse (composition a a_1)) (composition (converse a_1) (converse a))) True
% 129.37/129.58 Clause #182 (by clausification #[181]): ∀ (a a_1 : Iota), Eq (converse (composition a a_1)) (composition (converse a_1) (converse a))
% 129.37/129.58 Clause #186 (by superposition #[182, 18]): ∀ (a a_1 : Iota), Eq (converse (composition (converse a) a_1)) (composition (converse a_1) a)
% 129.37/129.58 Clause #188 (by forward demodulation #[109, 27]): ∀ (a : Iota), Eq (meet a top) (complement (join zero (complement a)))
% 129.37/129.58 Clause #201 (by superposition #[188, 24]): Eq (meet zero top) (complement top)
% 129.37/129.58 Clause #205 (by forward demodulation #[201, 99]): Eq (meet zero top) zero
% 129.37/129.58 Clause #263 (by superposition #[98, 86]): ∀ (a a_1 : Iota), Eq (meet a a_1) (meet a_1 a)
% 129.37/129.58 Clause #330 (by clausification #[15]): ∀ (a : Iota),
% 129.41/129.60 Eq
% 129.41/129.60 (∀ (X1 X2 : Iota),
% 129.41/129.60 Eq (join (meet (composition a X1) X2) (meet (composition (meet a (composition X2 (converse X1))) X1) X2))
% 129.41/129.60 (meet (composition (meet a (composition X2 (converse X1))) X1) X2))
% 129.41/129.60 True
% 129.41/129.60 Clause #331 (by clausification #[330]): ∀ (a a_1 : Iota),
% 129.41/129.60 Eq
% 129.41/129.60 (∀ (X2 : Iota),
% 129.41/129.60 Eq (join (meet (composition a a_1) X2) (meet (composition (meet a (composition X2 (converse a_1))) a_1) X2))
% 129.41/129.60 (meet (composition (meet a (composition X2 (converse a_1))) a_1) X2))
% 129.41/129.60 True
% 129.41/129.60 Clause #332 (by clausification #[331]): ∀ (a a_1 a_2 : Iota),
% 129.41/129.60 Eq
% 129.41/129.60 (Eq (join (meet (composition a a_1) a_2) (meet (composition (meet a (composition a_2 (converse a_1))) a_1) a_2))
% 129.41/129.60 (meet (composition (meet a (composition a_2 (converse a_1))) a_1) a_2))
% 129.41/129.60 True
% 129.41/129.60 Clause #333 (by clausification #[332]): ∀ (a a_1 a_2 : Iota),
% 129.41/129.60 Eq (join (meet (composition a a_1) a_2) (meet (composition (meet a (composition a_2 (converse a_1))) a_1) a_2))
% 129.41/129.60 (meet (composition (meet a (composition a_2 (converse a_1))) a_1) a_2)
% 129.41/129.60 Clause #334 (by forward demodulation #[333, 263]): ∀ (a a_1 a_2 : Iota),
% 129.41/129.60 Eq (join (meet (composition a a_1) a_2) (meet a_2 (composition (meet a (composition a_2 (converse a_1))) a_1)))
% 129.41/129.60 (meet (composition (meet a (composition a_2 (converse a_1))) a_1) a_2)
% 129.41/129.60 Clause #335 (by forward demodulation #[334, 263]): ∀ (a a_1 a_2 : Iota),
% 129.41/129.60 Eq (join (meet (composition a a_1) a_2) (meet a_2 (composition (meet a (composition a_2 (converse a_1))) a_1)))
% 129.41/129.60 (meet a_2 (composition (meet a (composition a_2 (converse a_1))) a_1))
% 129.41/129.60 Clause #337 (by superposition #[335, 20]): ∀ (a a_1 : Iota),
% 129.41/129.60 Eq (join (meet (composition a one) a_1) (meet a_1 (meet a (composition a_1 (converse one)))))
% 129.41/129.60 (meet a_1 (meet a (composition a_1 (converse one))))
% 129.41/129.60 Clause #396 (by superposition #[32, 27]): ∀ (a a_1 : Iota), Eq top (join a (join a_1 (complement (join a_1 a))))
% 129.41/129.60 Clause #397 (by clausification #[16]): Eq
% 129.41/129.60 (∀ (X0 X1 X2 : Iota),
% 129.41/129.60 Eq (join (composition (meet X0 (converse X1)) (meet X1 X2)) (composition X0 (meet X1 X2)))
% 129.41/129.60 (composition X0 (meet X1 X2)))
% 129.41/129.60 False
% 129.41/129.60 Clause #398 (by clausification #[397]): ∀ (a : Iota),
% 129.41/129.60 Eq
% 129.41/129.60 (Not
% 129.41/129.60 (∀ (X1 X2 : Iota),
% 129.41/129.60 Eq (join (composition (meet (skS.0 0 a) (converse X1)) (meet X1 X2)) (composition (skS.0 0 a) (meet X1 X2)))
% 129.41/129.60 (composition (skS.0 0 a) (meet X1 X2))))
% 129.41/129.60 True
% 129.41/129.60 Clause #399 (by clausification #[398]): ∀ (a : Iota),
% 129.41/129.60 Eq
% 129.41/129.60 (∀ (X1 X2 : Iota),
% 129.41/129.60 Eq (join (composition (meet (skS.0 0 a) (converse X1)) (meet X1 X2)) (composition (skS.0 0 a) (meet X1 X2)))
% 129.41/129.60 (composition (skS.0 0 a) (meet X1 X2)))
% 129.41/129.60 False
% 129.41/129.60 Clause #400 (by clausification #[399]): ∀ (a a_1 : Iota),
% 129.41/129.60 Eq
% 129.41/129.60 (Not
% 129.41/129.60 (∀ (X2 : Iota),
% 129.41/129.60 Eq
% 129.41/129.60 (join (composition (meet (skS.0 0 a) (converse (skS.0 1 a a_1))) (meet (skS.0 1 a a_1) X2))
% 129.41/129.60 (composition (skS.0 0 a) (meet (skS.0 1 a a_1) X2)))
% 129.41/129.60 (composition (skS.0 0 a) (meet (skS.0 1 a a_1) X2))))
% 129.41/129.60 True
% 129.41/129.60 Clause #401 (by clausification #[400]): ∀ (a a_1 : Iota),
% 129.41/129.60 Eq
% 129.41/129.60 (∀ (X2 : Iota),
% 129.41/129.60 Eq
% 129.41/129.60 (join (composition (meet (skS.0 0 a) (converse (skS.0 1 a a_1))) (meet (skS.0 1 a a_1) X2))
% 129.41/129.60 (composition (skS.0 0 a) (meet (skS.0 1 a a_1) X2)))
% 129.41/129.60 (composition (skS.0 0 a) (meet (skS.0 1 a a_1) X2)))
% 129.41/129.60 False
% 129.41/129.60 Clause #402 (by clausification #[401]): ∀ (a a_1 a_2 : Iota),
% 129.41/129.60 Eq
% 129.41/129.60 (Not
% 129.41/129.60 (Eq
% 129.41/129.60 (join (composition (meet (skS.0 0 a) (converse (skS.0 1 a a_1))) (meet (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 129.41/129.60 (composition (skS.0 0 a) (meet (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))))
% 129.41/129.60 (composition (skS.0 0 a) (meet (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))))
% 129.41/129.60 True
% 129.41/129.60 Clause #403 (by clausification #[402]): ∀ (a a_1 a_2 : Iota),
% 129.41/129.60 Eq
% 129.41/129.60 (Eq
% 129.41/129.60 (join (composition (meet (skS.0 0 a) (converse (skS.0 1 a a_1))) (meet (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 129.41/129.60 (composition (skS.0 0 a) (meet (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))))
% 129.41/129.60 (composition (skS.0 0 a) (meet (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))))
% 129.41/129.60 False
% 129.41/129.60 Clause #404 (by clausification #[403]): ∀ (a a_1 a_2 : Iota),
% 129.41/129.62 Ne
% 129.41/129.62 (join (composition (meet (skS.0 0 a) (converse (skS.0 1 a a_1))) (meet (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 129.41/129.62 (composition (skS.0 0 a) (meet (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))))
% 129.41/129.62 (composition (skS.0 0 a) (meet (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 129.41/129.62 Clause #405 (by forward demodulation #[404, 128]): ∀ (a a_1 a_2 : Iota),
% 129.41/129.62 Ne
% 129.41/129.62 (composition (join (meet (skS.0 0 a) (converse (skS.0 1 a a_1))) (skS.0 0 a))
% 129.41/129.62 (meet (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 129.41/129.62 (composition (skS.0 0 a) (meet (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 129.41/129.62 Clause #406 (by forward demodulation #[405, 27]): ∀ (a a_1 a_2 : Iota),
% 129.41/129.62 Ne
% 129.41/129.62 (composition (join (skS.0 0 a) (meet (skS.0 0 a) (converse (skS.0 1 a a_1))))
% 129.41/129.62 (meet (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 129.41/129.62 (composition (skS.0 0 a) (meet (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 129.41/129.62 Clause #581 (by forward demodulation #[35, 31]): ∀ (a a_1 a_2 a_3 : Iota), Eq (join a (join a_1 (join a_2 a_3))) (join (join a (join a_1 a_2)) a_3)
% 129.41/129.62 Clause #596 (by superposition #[581, 53]): ∀ (a a_1 : Iota), Eq (join (complement a) (join top (join a a_1))) (join (join top top) a_1)
% 129.41/129.62 Clause #688 (by superposition #[37, 24]): ∀ (a a_1 : Iota), Eq (join (complement a) (join a a_1)) (join top a_1)
% 129.41/129.62 Clause #880 (by superposition #[396, 24]): ∀ (a : Iota), Eq top (join (complement a) (join a (complement top)))
% 129.41/129.62 Clause #888 (by forward demodulation #[880, 99]): ∀ (a : Iota), Eq top (join (complement a) (join a zero))
% 129.41/129.62 Clause #901 (by superposition #[888, 27]): ∀ (a : Iota), Eq top (join (complement a) (join zero a))
% 129.41/129.62 Clause #1637 (by forward demodulation #[58, 31]): ∀ (a a_1 : Iota), Eq (join (complement a) (join a_1 a)) (join top (complement (join (complement a) (complement a_1))))
% 129.41/129.62 Clause #1638 (by forward demodulation #[1637, 86]): ∀ (a a_1 : Iota), Eq (join (complement a) (join a_1 a)) (join top (meet a a_1))
% 129.41/129.62 Clause #1639 (by superposition #[1638, 53]): ∀ (a : Iota), Eq (join top (meet a top)) (join top top)
% 129.41/129.62 Clause #1641 (by superposition #[1638, 901]): ∀ (a : Iota), Eq top (join top (meet a zero))
% 129.41/129.62 Clause #1747 (by superposition #[1641, 263]): ∀ (a : Iota), Eq top (join top (meet zero a))
% 129.41/129.62 Clause #1825 (by superposition #[1639, 1747]): Eq top (join top top)
% 129.41/129.62 Clause #1828 (by backward demodulation #[1825, 53]): ∀ (a : Iota), Eq (join (complement a) (join top a)) top
% 129.41/129.62 Clause #1835 (by backward demodulation #[1825, 1639]): ∀ (a : Iota), Eq (join top (meet a top)) top
% 129.41/129.62 Clause #1924 (by superposition #[1835, 263]): ∀ (a : Iota), Eq (join top (meet top a)) top
% 129.41/129.62 Clause #1935 (by forward demodulation #[61, 86]): ∀ (a a_1 : Iota), Eq a (join (complement (join (complement a) a_1)) (meet a a_1))
% 129.41/129.62 Clause #1992 (by superposition #[1828, 36]): ∀ (a : Iota), Eq (join a top) (join top (join top a))
% 129.41/129.62 Clause #2021 (by superposition #[1828, 1924]): ∀ (a : Iota), Eq (join (complement (meet top a)) top) top
% 129.41/129.62 Clause #2185 (by forward demodulation #[64, 1825]): ∀ (a : Iota), Eq a (join (complement (join (complement a) (complement (join a top)))) (complement top))
% 129.41/129.62 Clause #2186 (by forward demodulation #[2185, 99]): ∀ (a : Iota), Eq a (join (complement (join (complement a) (complement (join a top)))) zero)
% 129.41/129.62 Clause #2187 (by forward demodulation #[2186, 86]): ∀ (a : Iota), Eq a (join (meet a (join a top)) zero)
% 129.41/129.62 Clause #2202 (by superposition #[2187, 112]): Eq zero (join (meet zero top) zero)
% 129.41/129.62 Clause #2236 (by forward demodulation #[2202, 205]): Eq zero (join zero zero)
% 129.41/129.62 Clause #2243 (by superposition #[2236, 31]): ∀ (a : Iota), Eq (join zero (join zero a)) (join zero a)
% 129.41/129.62 Clause #2485 (by forward demodulation #[68, 86]): ∀ (a a_1 : Iota), Eq a (join (meet a a_1) (complement (join a_1 (complement a))))
% 129.41/129.62 Clause #2513 (by superposition #[2485, 24]): ∀ (a : Iota), Eq a (join (meet a a) (complement top))
% 129.41/129.62 Clause #2537 (by forward demodulation #[2513, 99]): ∀ (a : Iota), Eq a (join (meet a a) zero)
% 129.41/129.62 Clause #2542 (by superposition #[2537, 27]): ∀ (a : Iota), Eq (join zero (meet a a)) a
% 129.41/129.62 Clause #2814 (by superposition #[2021, 27]): ∀ (a : Iota), Eq (join top (complement (meet top a))) top
% 129.47/129.64 Clause #2824 (by forward demodulation #[596, 31]): ∀ (a a_1 : Iota), Eq (join (complement a) (join top (join a a_1))) (join top (join top a_1))
% 129.47/129.64 Clause #2825 (by forward demodulation #[2824, 1992]): ∀ (a a_1 : Iota), Eq (join (complement a) (join top (join a a_1))) (join a_1 top)
% 129.47/129.64 Clause #2847 (by superposition #[2825, 105]): ∀ (a : Iota), Eq (join (complement zero) (join top a)) (join a top)
% 129.47/129.64 Clause #3323 (by superposition #[2847, 2825]): ∀ (a : Iota), Eq (join (join zero a) top) (join a top)
% 129.47/129.64 Clause #5014 (by forward demodulation #[145, 2814]): ∀ (a : Iota), Eq (join (join zero (complement a)) top) top
% 129.47/129.64 Clause #5015 (by superposition #[5014, 3323]): ∀ (a : Iota), Eq top (join (complement a) top)
% 129.47/129.64 Clause #5059 (by superposition #[5015, 27]): ∀ (a : Iota), Eq (join top (complement a)) top
% 129.47/129.64 Clause #5082 (by superposition #[5059, 32]): ∀ (a : Iota), Eq top (join a top)
% 129.47/129.64 Clause #5103 (by backward demodulation #[5082, 2187]): ∀ (a : Iota), Eq a (join (meet a top) zero)
% 129.47/129.64 Clause #5118 (by superposition #[5082, 27]): ∀ (a : Iota), Eq (join top a) top
% 129.47/129.64 Clause #5137 (by backward demodulation #[5118, 688]): ∀ (a a_1 : Iota), Eq (join (complement a) (join a a_1)) top
% 129.47/129.64 Clause #5216 (by superposition #[5103, 263]): ∀ (a : Iota), Eq a (join (meet top a) zero)
% 129.47/129.64 Clause #5617 (by superposition #[5137, 1935]): ∀ (a a_1 : Iota), Eq a (join (complement top) (meet a (join a a_1)))
% 129.47/129.64 Clause #6035 (by superposition #[186, 20]): ∀ (a : Iota), Eq (converse (converse a)) (composition (converse one) a)
% 129.47/129.64 Clause #6037 (by forward demodulation #[6035, 18]): ∀ (a : Iota), Eq a (composition (converse one) a)
% 129.47/129.64 Clause #6041 (by superposition #[6037, 20]): Eq one (converse one)
% 129.47/129.64 Clause #6075 (by superposition #[6041, 18]): Eq (converse one) one
% 129.47/129.64 Clause #7768 (by superposition #[2243, 2542]): ∀ (a : Iota), Eq (join zero a) a
% 129.47/129.64 Clause #7819 (by backward demodulation #[7768, 188]): ∀ (a : Iota), Eq (meet a top) (complement (complement a))
% 129.47/129.64 Clause #7854 (by superposition #[7768, 27]): ∀ (a : Iota), Eq (join a zero) a
% 129.47/129.64 Clause #7860 (by superposition #[7854, 2537]): ∀ (a : Iota), Eq a (meet a a)
% 129.47/129.64 Clause #7861 (by superposition #[7854, 5103]): ∀ (a : Iota), Eq a (meet a top)
% 129.47/129.64 Clause #7862 (by superposition #[7854, 5216]): ∀ (a : Iota), Eq a (meet top a)
% 129.47/129.64 Clause #8372 (by forward demodulation #[7819, 7861]): ∀ (a : Iota), Eq a (complement (complement a))
% 129.47/129.64 Clause #8374 (by superposition #[8372, 86]): ∀ (a a_1 : Iota), Eq (meet a (complement a_1)) (complement (join (complement a) a_1))
% 129.47/129.64 Clause #8408 (by superposition #[8372, 86]): ∀ (a a_1 : Iota), Eq (join (complement a) (complement a_1)) (complement (meet a a_1))
% 129.47/129.64 Clause #13262 (by forward demodulation #[337, 6075]): ∀ (a a_1 : Iota),
% 129.47/129.64 Eq (join (meet (composition a one) a_1) (meet a_1 (meet a (composition a_1 one))))
% 129.47/129.64 (meet a_1 (meet a (composition a_1 (converse one))))
% 129.47/129.64 Clause #13263 (by forward demodulation #[13262, 20]): ∀ (a a_1 : Iota),
% 129.47/129.64 Eq (join (meet (composition a one) a_1) (meet a_1 (meet a a_1))) (meet a_1 (meet a (composition a_1 (converse one))))
% 129.47/129.64 Clause #13264 (by forward demodulation #[13263, 20]): ∀ (a a_1 : Iota), Eq (join (meet a a_1) (meet a_1 (meet a a_1))) (meet a_1 (meet a (composition a_1 (converse one))))
% 129.47/129.64 Clause #13265 (by forward demodulation #[13264, 6075]): ∀ (a a_1 : Iota), Eq (join (meet a a_1) (meet a_1 (meet a a_1))) (meet a_1 (meet a (composition a_1 one)))
% 129.47/129.64 Clause #13266 (by forward demodulation #[13265, 20]): ∀ (a a_1 : Iota), Eq (join (meet a a_1) (meet a_1 (meet a a_1))) (meet a_1 (meet a a_1))
% 129.47/129.64 Clause #13300 (by superposition #[13266, 7862]): ∀ (a : Iota), Eq (join a (meet a a)) (meet a a)
% 129.47/129.64 Clause #13302 (by forward demodulation #[13300, 7860]): ∀ (a : Iota), Eq (join a a) (meet a a)
% 129.47/129.64 Clause #13303 (by forward demodulation #[13302, 7860]): ∀ (a : Iota), Eq (join a a) a
% 129.47/129.64 Clause #13329 (by superposition #[13303, 31]): ∀ (a a_1 : Iota), Eq (join a (join a a_1)) (join a a_1)
% 129.47/129.64 Clause #13448 (by superposition #[13329, 27]): ∀ (a a_1 : Iota), Eq (join a (join a_1 a)) (join a_1 a)
% 129.47/129.64 Clause #14109 (by backward demodulation #[8408, 98]): ∀ (a a_1 : Iota), Eq (meet a a_1) (complement (complement (meet a_1 a)))
% 129.68/129.86 Clause #14138 (by superposition #[8408, 27]): ∀ (a a_1 : Iota), Eq (complement (meet a a_1)) (join (complement a_1) (complement a))
% 129.68/129.86 Clause #15269 (by superposition #[8374, 8372]): ∀ (a a_1 : Iota), Eq (meet (complement a) (complement a_1)) (complement (join a a_1))
% 129.68/129.86 Clause #15287 (by superposition #[15269, 263]): ∀ (a a_1 : Iota), Eq (complement (join a a_1)) (meet (complement a_1) (complement a))
% 129.68/129.86 Clause #19928 (by forward demodulation #[5617, 99]): ∀ (a a_1 : Iota), Eq a (join zero (meet a (join a a_1)))
% 129.68/129.86 Clause #19929 (by superposition #[19928, 7768]): ∀ (a a_1 : Iota), Eq a (meet a (join a a_1))
% 129.68/129.86 Clause #20168 (by superposition #[19929, 13448]): ∀ (a a_1 : Iota), Eq a (meet a (join a_1 a))
% 129.68/129.86 Clause #20218 (by superposition #[20168, 14109]): ∀ (a a_1 : Iota), Eq (meet (join a a_1) a_1) (complement (complement a_1))
% 129.68/129.86 Clause #20301 (by forward demodulation #[20218, 8372]): ∀ (a a_1 : Iota), Eq (meet (join a a_1) a_1) a_1
% 129.68/129.86 Clause #20410 (by superposition #[20301, 14138]): ∀ (a a_1 : Iota), Eq (meet (complement (meet a a_1)) (complement a)) (complement a)
% 129.68/129.86 Clause #36508 (by superposition #[20410, 15287]): ∀ (a a_1 : Iota), Eq (complement (join a (meet a a_1))) (complement a)
% 129.68/129.86 Clause #36719 (by superposition #[36508, 263]): ∀ (a a_1 : Iota), Eq (complement (join a (meet a_1 a))) (complement a)
% 129.68/129.86 Clause #36753 (by superposition #[36719, 8372]): ∀ (a a_1 : Iota), Eq (join a (meet a_1 a)) (complement (complement a))
% 129.68/129.86 Clause #36834 (by forward demodulation #[36753, 8372]): ∀ (a a_1 : Iota), Eq (join a (meet a_1 a)) a
% 129.68/129.86 Clause #36926 (by superposition #[36834, 263]): ∀ (a a_1 : Iota), Eq (join a (meet a a_1)) a
% 129.68/129.86 Clause #36928 (by backward positive simplify reflect #[36926, 406]): False
% 129.68/129.86 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------