TSTP Solution File: LAT382+3 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : LAT382+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n010.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 06:08:19 EDT 2023
% Result : Theorem 19.55s 19.71s
% Output : Proof 19.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LAT382+3 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % Command : duper %s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 06:25:05 EDT 2023
% 0.20/0.35 % CPUTime :
% 19.55/19.71 SZS status Theorem for theBenchmark.p
% 19.55/19.71 SZS output start Proof for theBenchmark.p
% 19.55/19.71 Clause #2 (by assumption #[]): Eq (∀ (W0 : Iota), aSet0 W0 → ∀ (W1 : Iota), aElementOf0 W1 W0 → aElement0 W1) True
% 19.55/19.71 Clause #7 (by assumption #[]): Eq (∀ (W0 W1 : Iota), And (aElement0 W0) (aElement0 W1) → And (sdtlseqdt0 W0 W1) (sdtlseqdt0 W1 W0) → Eq W0 W1) True
% 19.55/19.71 Clause #9 (by assumption #[]): Eq
% 19.55/19.71 (∀ (W0 : Iota),
% 19.55/19.71 aSet0 W0 →
% 19.55/19.71 ∀ (W1 : Iota),
% 19.55/19.71 aSubsetOf0 W1 W0 →
% 19.55/19.71 ∀ (W2 : Iota),
% 19.55/19.71 Iff (aLowerBoundOfIn0 W2 W1 W0)
% 19.55/19.71 (And (aElementOf0 W2 W0) (∀ (W3 : Iota), aElementOf0 W3 W1 → sdtlseqdt0 W2 W3)))
% 19.55/19.71 True
% 19.55/19.71 Clause #11 (by assumption #[]): Eq
% 19.55/19.71 (∀ (W0 : Iota),
% 19.55/19.71 aSet0 W0 →
% 19.55/19.71 ∀ (W1 : Iota),
% 19.55/19.71 aSubsetOf0 W1 W0 →
% 19.55/19.71 ∀ (W2 : Iota),
% 19.55/19.71 Iff (aInfimumOfIn0 W2 W1 W0)
% 19.55/19.71 (And (And (aElementOf0 W2 W0) (aLowerBoundOfIn0 W2 W1 W0))
% 19.55/19.71 (∀ (W3 : Iota), aLowerBoundOfIn0 W3 W1 W0 → sdtlseqdt0 W3 W2)))
% 19.55/19.71 True
% 19.55/19.71 Clause #14 (by assumption #[]): Eq (aSet0 xT) True
% 19.55/19.71 Clause #15 (by assumption #[]): Eq (And (And (aSet0 xS) (∀ (W0 : Iota), aElementOf0 W0 xS → aElementOf0 W0 xT)) (aSubsetOf0 xS xT)) True
% 19.55/19.71 Clause #16 (by assumption #[]): Eq
% 19.55/19.71 (And
% 19.55/19.71 (And
% 19.55/19.71 (And
% 19.55/19.71 (And
% 19.55/19.71 (And
% 19.55/19.71 (And
% 19.55/19.71 (And
% 19.55/19.71 (And
% 19.55/19.71 (And
% 19.55/19.71 (And (And (aElementOf0 xu xT) (aElementOf0 xu xT))
% 19.55/19.71 (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 xu W0))
% 19.55/19.71 (aLowerBoundOfIn0 xu xS xT))
% 19.55/19.71 (∀ (W0 : Iota),
% 19.55/19.71 Or (And (aElementOf0 W0 xT) (∀ (W1 : Iota), aElementOf0 W1 xS → sdtlseqdt0 W0 W1))
% 19.55/19.71 (aLowerBoundOfIn0 W0 xS xT) →
% 19.55/19.71 sdtlseqdt0 W0 xu))
% 19.55/19.71 (aInfimumOfIn0 xu xS xT))
% 19.55/19.71 (aElementOf0 xv xT))
% 19.55/19.71 (aElementOf0 xv xT))
% 19.55/19.71 (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 xv W0))
% 19.55/19.71 (aLowerBoundOfIn0 xv xS xT))
% 19.55/19.71 (∀ (W0 : Iota),
% 19.55/19.71 Or (And (aElementOf0 W0 xT) (∀ (W1 : Iota), aElementOf0 W1 xS → sdtlseqdt0 W0 W1)) (aLowerBoundOfIn0 W0 xS xT) →
% 19.55/19.71 sdtlseqdt0 W0 xv))
% 19.55/19.71 (aInfimumOfIn0 xv xS xT))
% 19.55/19.71 True
% 19.55/19.71 Clause #17 (by assumption #[]): Eq (Not (Eq xu xv)) True
% 19.55/19.71 Clause #29 (by clausification #[2]): ∀ (a : Iota), Eq (aSet0 a → ∀ (W1 : Iota), aElementOf0 W1 a → aElement0 W1) True
% 19.55/19.71 Clause #30 (by clausification #[29]): ∀ (a : Iota), Or (Eq (aSet0 a) False) (Eq (∀ (W1 : Iota), aElementOf0 W1 a → aElement0 W1) True)
% 19.55/19.71 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Or (Eq (aSet0 a) False) (Eq (aElementOf0 a_1 a → aElement0 a_1) True)
% 19.55/19.71 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Or (Eq (aSet0 a) False) (Or (Eq (aElementOf0 a_1 a) False) (Eq (aElement0 a_1) True))
% 19.55/19.71 Clause #33 (by superposition #[32, 14]): ∀ (a : Iota), Or (Eq (aElementOf0 a xT) False) (Or (Eq (aElement0 a) True) (Eq False True))
% 19.55/19.71 Clause #34 (by clausification #[17]): Eq (Eq xu xv) False
% 19.55/19.71 Clause #35 (by clausification #[34]): Ne xu xv
% 19.55/19.71 Clause #36 (by clausification #[7]): ∀ (a : Iota),
% 19.55/19.71 Eq (∀ (W1 : Iota), And (aElement0 a) (aElement0 W1) → And (sdtlseqdt0 a W1) (sdtlseqdt0 W1 a) → Eq a W1) True
% 19.55/19.71 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Eq (And (aElement0 a) (aElement0 a_1) → And (sdtlseqdt0 a a_1) (sdtlseqdt0 a_1 a) → Eq a a_1) True
% 19.55/19.71 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota),
% 19.55/19.71 Or (Eq (And (aElement0 a) (aElement0 a_1)) False) (Eq (And (sdtlseqdt0 a a_1) (sdtlseqdt0 a_1 a) → Eq a a_1) True)
% 19.55/19.71 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota),
% 19.55/19.71 Or (Eq (And (sdtlseqdt0 a a_1) (sdtlseqdt0 a_1 a) → Eq a a_1) True)
% 19.55/19.71 (Or (Eq (aElement0 a) False) (Eq (aElement0 a_1) False))
% 19.55/19.71 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota),
% 19.55/19.71 Or (Eq (aElement0 a) False)
% 19.55/19.71 (Or (Eq (aElement0 a_1) False) (Or (Eq (And (sdtlseqdt0 a a_1) (sdtlseqdt0 a_1 a)) False) (Eq (Eq a a_1) True)))
% 19.55/19.71 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota),
% 19.55/19.71 Or (Eq (aElement0 a) False)
% 19.55/19.71 (Or (Eq (aElement0 a_1) False)
% 19.55/19.73 (Or (Eq (Eq a a_1) True) (Or (Eq (sdtlseqdt0 a a_1) False) (Eq (sdtlseqdt0 a_1 a) False))))
% 19.55/19.73 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota),
% 19.55/19.73 Or (Eq (aElement0 a) False)
% 19.55/19.73 (Or (Eq (aElement0 a_1) False) (Or (Eq (sdtlseqdt0 a a_1) False) (Or (Eq (sdtlseqdt0 a_1 a) False) (Eq a a_1))))
% 19.55/19.73 Clause #51 (by clausification #[33]): ∀ (a : Iota), Or (Eq (aElementOf0 a xT) False) (Eq (aElement0 a) True)
% 19.55/19.73 Clause #69 (by clausification #[15]): Eq (aSubsetOf0 xS xT) True
% 19.55/19.73 Clause #106 (by clausification #[9]): ∀ (a : Iota),
% 19.55/19.73 Eq
% 19.55/19.73 (aSet0 a →
% 19.55/19.73 ∀ (W1 : Iota),
% 19.55/19.73 aSubsetOf0 W1 a →
% 19.55/19.73 ∀ (W2 : Iota),
% 19.55/19.73 Iff (aLowerBoundOfIn0 W2 W1 a)
% 19.55/19.73 (And (aElementOf0 W2 a) (∀ (W3 : Iota), aElementOf0 W3 W1 → sdtlseqdt0 W2 W3)))
% 19.55/19.73 True
% 19.55/19.73 Clause #107 (by clausification #[106]): ∀ (a : Iota),
% 19.55/19.73 Or (Eq (aSet0 a) False)
% 19.55/19.73 (Eq
% 19.55/19.73 (∀ (W1 : Iota),
% 19.55/19.73 aSubsetOf0 W1 a →
% 19.55/19.73 ∀ (W2 : Iota),
% 19.55/19.73 Iff (aLowerBoundOfIn0 W2 W1 a)
% 19.55/19.73 (And (aElementOf0 W2 a) (∀ (W3 : Iota), aElementOf0 W3 W1 → sdtlseqdt0 W2 W3)))
% 19.55/19.73 True)
% 19.55/19.73 Clause #108 (by clausification #[107]): ∀ (a a_1 : Iota),
% 19.55/19.73 Or (Eq (aSet0 a) False)
% 19.55/19.73 (Eq
% 19.55/19.73 (aSubsetOf0 a_1 a →
% 19.55/19.73 ∀ (W2 : Iota),
% 19.55/19.73 Iff (aLowerBoundOfIn0 W2 a_1 a)
% 19.55/19.73 (And (aElementOf0 W2 a) (∀ (W3 : Iota), aElementOf0 W3 a_1 → sdtlseqdt0 W2 W3)))
% 19.55/19.73 True)
% 19.55/19.73 Clause #109 (by clausification #[108]): ∀ (a a_1 : Iota),
% 19.55/19.73 Or (Eq (aSet0 a) False)
% 19.55/19.73 (Or (Eq (aSubsetOf0 a_1 a) False)
% 19.55/19.73 (Eq
% 19.55/19.73 (∀ (W2 : Iota),
% 19.55/19.73 Iff (aLowerBoundOfIn0 W2 a_1 a)
% 19.55/19.73 (And (aElementOf0 W2 a) (∀ (W3 : Iota), aElementOf0 W3 a_1 → sdtlseqdt0 W2 W3)))
% 19.55/19.73 True))
% 19.55/19.73 Clause #110 (by clausification #[109]): ∀ (a a_1 a_2 : Iota),
% 19.55/19.73 Or (Eq (aSet0 a) False)
% 19.55/19.73 (Or (Eq (aSubsetOf0 a_1 a) False)
% 19.55/19.73 (Eq
% 19.55/19.73 (Iff (aLowerBoundOfIn0 a_2 a_1 a)
% 19.55/19.73 (And (aElementOf0 a_2 a) (∀ (W3 : Iota), aElementOf0 W3 a_1 → sdtlseqdt0 a_2 W3)))
% 19.55/19.73 True))
% 19.55/19.73 Clause #112 (by clausification #[110]): ∀ (a a_1 a_2 : Iota),
% 19.55/19.73 Or (Eq (aSet0 a) False)
% 19.55/19.73 (Or (Eq (aSubsetOf0 a_1 a) False)
% 19.55/19.73 (Or (Eq (aLowerBoundOfIn0 a_2 a_1 a) False)
% 19.55/19.73 (Eq (And (aElementOf0 a_2 a) (∀ (W3 : Iota), aElementOf0 W3 a_1 → sdtlseqdt0 a_2 W3)) True)))
% 19.55/19.73 Clause #153 (by clausification #[11]): ∀ (a : Iota),
% 19.55/19.73 Eq
% 19.55/19.73 (aSet0 a →
% 19.55/19.73 ∀ (W1 : Iota),
% 19.55/19.73 aSubsetOf0 W1 a →
% 19.55/19.73 ∀ (W2 : Iota),
% 19.55/19.73 Iff (aInfimumOfIn0 W2 W1 a)
% 19.55/19.73 (And (And (aElementOf0 W2 a) (aLowerBoundOfIn0 W2 W1 a))
% 19.55/19.73 (∀ (W3 : Iota), aLowerBoundOfIn0 W3 W1 a → sdtlseqdt0 W3 W2)))
% 19.55/19.73 True
% 19.55/19.73 Clause #154 (by clausification #[153]): ∀ (a : Iota),
% 19.55/19.73 Or (Eq (aSet0 a) False)
% 19.55/19.73 (Eq
% 19.55/19.73 (∀ (W1 : Iota),
% 19.55/19.73 aSubsetOf0 W1 a →
% 19.55/19.73 ∀ (W2 : Iota),
% 19.55/19.73 Iff (aInfimumOfIn0 W2 W1 a)
% 19.55/19.73 (And (And (aElementOf0 W2 a) (aLowerBoundOfIn0 W2 W1 a))
% 19.55/19.73 (∀ (W3 : Iota), aLowerBoundOfIn0 W3 W1 a → sdtlseqdt0 W3 W2)))
% 19.55/19.73 True)
% 19.55/19.73 Clause #155 (by clausification #[154]): ∀ (a a_1 : Iota),
% 19.55/19.73 Or (Eq (aSet0 a) False)
% 19.55/19.73 (Eq
% 19.55/19.73 (aSubsetOf0 a_1 a →
% 19.55/19.73 ∀ (W2 : Iota),
% 19.55/19.73 Iff (aInfimumOfIn0 W2 a_1 a)
% 19.55/19.73 (And (And (aElementOf0 W2 a) (aLowerBoundOfIn0 W2 a_1 a))
% 19.55/19.73 (∀ (W3 : Iota), aLowerBoundOfIn0 W3 a_1 a → sdtlseqdt0 W3 W2)))
% 19.55/19.73 True)
% 19.55/19.73 Clause #156 (by clausification #[155]): ∀ (a a_1 : Iota),
% 19.55/19.73 Or (Eq (aSet0 a) False)
% 19.55/19.73 (Or (Eq (aSubsetOf0 a_1 a) False)
% 19.55/19.73 (Eq
% 19.55/19.73 (∀ (W2 : Iota),
% 19.55/19.73 Iff (aInfimumOfIn0 W2 a_1 a)
% 19.55/19.73 (And (And (aElementOf0 W2 a) (aLowerBoundOfIn0 W2 a_1 a))
% 19.55/19.73 (∀ (W3 : Iota), aLowerBoundOfIn0 W3 a_1 a → sdtlseqdt0 W3 W2)))
% 19.55/19.73 True))
% 19.55/19.73 Clause #157 (by clausification #[156]): ∀ (a a_1 a_2 : Iota),
% 19.55/19.73 Or (Eq (aSet0 a) False)
% 19.55/19.73 (Or (Eq (aSubsetOf0 a_1 a) False)
% 19.55/19.73 (Eq
% 19.55/19.73 (Iff (aInfimumOfIn0 a_2 a_1 a)
% 19.55/19.73 (And (And (aElementOf0 a_2 a) (aLowerBoundOfIn0 a_2 a_1 a))
% 19.55/19.73 (∀ (W3 : Iota), aLowerBoundOfIn0 W3 a_1 a → sdtlseqdt0 W3 a_2)))
% 19.55/19.73 True))
% 19.59/19.75 Clause #159 (by clausification #[157]): ∀ (a a_1 a_2 : Iota),
% 19.59/19.75 Or (Eq (aSet0 a) False)
% 19.59/19.75 (Or (Eq (aSubsetOf0 a_1 a) False)
% 19.59/19.75 (Or (Eq (aInfimumOfIn0 a_2 a_1 a) False)
% 19.59/19.75 (Eq
% 19.59/19.75 (And (And (aElementOf0 a_2 a) (aLowerBoundOfIn0 a_2 a_1 a))
% 19.59/19.75 (∀ (W3 : Iota), aLowerBoundOfIn0 W3 a_1 a → sdtlseqdt0 W3 a_2))
% 19.59/19.75 True)))
% 19.59/19.75 Clause #208 (by clausification #[16]): Eq (aInfimumOfIn0 xv xS xT) True
% 19.59/19.75 Clause #209 (by clausification #[16]): Eq
% 19.59/19.75 (And
% 19.59/19.75 (And
% 19.59/19.75 (And
% 19.59/19.75 (And
% 19.59/19.75 (And
% 19.59/19.75 (And
% 19.59/19.75 (And
% 19.59/19.75 (And
% 19.59/19.75 (And (And (aElementOf0 xu xT) (aElementOf0 xu xT))
% 19.59/19.75 (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 xu W0))
% 19.59/19.75 (aLowerBoundOfIn0 xu xS xT))
% 19.59/19.75 (∀ (W0 : Iota),
% 19.59/19.75 Or (And (aElementOf0 W0 xT) (∀ (W1 : Iota), aElementOf0 W1 xS → sdtlseqdt0 W0 W1))
% 19.59/19.75 (aLowerBoundOfIn0 W0 xS xT) →
% 19.59/19.75 sdtlseqdt0 W0 xu))
% 19.59/19.75 (aInfimumOfIn0 xu xS xT))
% 19.59/19.75 (aElementOf0 xv xT))
% 19.59/19.75 (aElementOf0 xv xT))
% 19.59/19.75 (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 xv W0))
% 19.59/19.75 (aLowerBoundOfIn0 xv xS xT))
% 19.59/19.75 (∀ (W0 : Iota),
% 19.59/19.75 Or (And (aElementOf0 W0 xT) (∀ (W1 : Iota), aElementOf0 W1 xS → sdtlseqdt0 W0 W1)) (aLowerBoundOfIn0 W0 xS xT) →
% 19.59/19.75 sdtlseqdt0 W0 xv))
% 19.59/19.75 True
% 19.59/19.75 Clause #218 (by clausification #[112]): ∀ (a a_1 a_2 : Iota),
% 19.59/19.75 Or (Eq (aSet0 a) False)
% 19.59/19.75 (Or (Eq (aSubsetOf0 a_1 a) False) (Or (Eq (aLowerBoundOfIn0 a_2 a_1 a) False) (Eq (aElementOf0 a_2 a) True)))
% 19.59/19.75 Clause #223 (by superposition #[218, 14]): ∀ (a a_1 : Iota),
% 19.59/19.75 Or (Eq (aSubsetOf0 a xT) False)
% 19.59/19.75 (Or (Eq (aLowerBoundOfIn0 a_1 a xT) False) (Or (Eq (aElementOf0 a_1 xT) True) (Eq False True)))
% 19.59/19.75 Clause #228 (by clausification #[223]): ∀ (a a_1 : Iota),
% 19.59/19.75 Or (Eq (aSubsetOf0 a xT) False) (Or (Eq (aLowerBoundOfIn0 a_1 a xT) False) (Eq (aElementOf0 a_1 xT) True))
% 19.59/19.75 Clause #229 (by superposition #[228, 69]): ∀ (a : Iota), Or (Eq (aLowerBoundOfIn0 a xS xT) False) (Or (Eq (aElementOf0 a xT) True) (Eq False True))
% 19.59/19.75 Clause #230 (by clausification #[229]): ∀ (a : Iota), Or (Eq (aLowerBoundOfIn0 a xS xT) False) (Eq (aElementOf0 a xT) True)
% 19.59/19.75 Clause #383 (by clausification #[159]): ∀ (a a_1 a_2 : Iota),
% 19.59/19.75 Or (Eq (aSet0 a) False)
% 19.59/19.75 (Or (Eq (aSubsetOf0 a_1 a) False)
% 19.59/19.75 (Or (Eq (aInfimumOfIn0 a_2 a_1 a) False)
% 19.59/19.75 (Eq (∀ (W3 : Iota), aLowerBoundOfIn0 W3 a_1 a → sdtlseqdt0 W3 a_2) True)))
% 19.59/19.75 Clause #384 (by clausification #[159]): ∀ (a a_1 a_2 : Iota),
% 19.59/19.75 Or (Eq (aSet0 a) False)
% 19.59/19.75 (Or (Eq (aSubsetOf0 a_1 a) False)
% 19.59/19.75 (Or (Eq (aInfimumOfIn0 a_2 a_1 a) False) (Eq (And (aElementOf0 a_2 a) (aLowerBoundOfIn0 a_2 a_1 a)) True)))
% 19.59/19.75 Clause #385 (by clausification #[383]): ∀ (a a_1 a_2 a_3 : Iota),
% 19.59/19.75 Or (Eq (aSet0 a) False)
% 19.59/19.75 (Or (Eq (aSubsetOf0 a_1 a) False)
% 19.59/19.75 (Or (Eq (aInfimumOfIn0 a_2 a_1 a) False) (Eq (aLowerBoundOfIn0 a_3 a_1 a → sdtlseqdt0 a_3 a_2) True)))
% 19.59/19.75 Clause #386 (by clausification #[385]): ∀ (a a_1 a_2 a_3 : Iota),
% 19.59/19.75 Or (Eq (aSet0 a) False)
% 19.59/19.75 (Or (Eq (aSubsetOf0 a_1 a) False)
% 19.59/19.75 (Or (Eq (aInfimumOfIn0 a_2 a_1 a) False)
% 19.59/19.75 (Or (Eq (aLowerBoundOfIn0 a_3 a_1 a) False) (Eq (sdtlseqdt0 a_3 a_2) True))))
% 19.59/19.75 Clause #387 (by superposition #[386, 14]): ∀ (a a_1 a_2 : Iota),
% 19.59/19.75 Or (Eq (aSubsetOf0 a xT) False)
% 19.59/19.75 (Or (Eq (aInfimumOfIn0 a_1 a xT) False)
% 19.59/19.75 (Or (Eq (aLowerBoundOfIn0 a_2 a xT) False) (Or (Eq (sdtlseqdt0 a_2 a_1) True) (Eq False True))))
% 19.59/19.75 Clause #392 (by clausification #[387]): ∀ (a a_1 a_2 : Iota),
% 19.59/19.75 Or (Eq (aSubsetOf0 a xT) False)
% 19.59/19.75 (Or (Eq (aInfimumOfIn0 a_1 a xT) False) (Or (Eq (aLowerBoundOfIn0 a_2 a xT) False) (Eq (sdtlseqdt0 a_2 a_1) True)))
% 19.59/19.75 Clause #393 (by superposition #[392, 69]): ∀ (a a_1 : Iota),
% 19.59/19.75 Or (Eq (aInfimumOfIn0 a xS xT) False)
% 19.59/19.75 (Or (Eq (aLowerBoundOfIn0 a_1 xS xT) False) (Or (Eq (sdtlseqdt0 a_1 a) True) (Eq False True)))
% 19.59/19.75 Clause #396 (by clausification #[393]): ∀ (a a_1 : Iota),
% 19.59/19.75 Or (Eq (aInfimumOfIn0 a xS xT) False) (Or (Eq (aLowerBoundOfIn0 a_1 xS xT) False) (Eq (sdtlseqdt0 a_1 a) True))
% 19.59/19.77 Clause #397 (by superposition #[396, 208]): ∀ (a : Iota), Or (Eq (aLowerBoundOfIn0 a xS xT) False) (Or (Eq (sdtlseqdt0 a xv) True) (Eq False True))
% 19.59/19.77 Clause #400 (by clausification #[397]): ∀ (a : Iota), Or (Eq (aLowerBoundOfIn0 a xS xT) False) (Eq (sdtlseqdt0 a xv) True)
% 19.59/19.77 Clause #401 (by clausification #[384]): ∀ (a a_1 a_2 : Iota),
% 19.59/19.77 Or (Eq (aSet0 a) False)
% 19.59/19.77 (Or (Eq (aSubsetOf0 a_1 a) False) (Or (Eq (aInfimumOfIn0 a_2 a_1 a) False) (Eq (aLowerBoundOfIn0 a_2 a_1 a) True)))
% 19.59/19.77 Clause #402 (by clausification #[384]): ∀ (a a_1 a_2 : Iota),
% 19.59/19.77 Or (Eq (aSet0 a) False)
% 19.59/19.77 (Or (Eq (aSubsetOf0 a_1 a) False) (Or (Eq (aInfimumOfIn0 a_2 a_1 a) False) (Eq (aElementOf0 a_2 a) True)))
% 19.59/19.77 Clause #403 (by superposition #[401, 14]): ∀ (a a_1 : Iota),
% 19.59/19.77 Or (Eq (aSubsetOf0 a xT) False)
% 19.59/19.77 (Or (Eq (aInfimumOfIn0 a_1 a xT) False) (Or (Eq (aLowerBoundOfIn0 a_1 a xT) True) (Eq False True)))
% 19.59/19.77 Clause #408 (by clausification #[403]): ∀ (a a_1 : Iota),
% 19.59/19.77 Or (Eq (aSubsetOf0 a xT) False) (Or (Eq (aInfimumOfIn0 a_1 a xT) False) (Eq (aLowerBoundOfIn0 a_1 a xT) True))
% 19.59/19.77 Clause #409 (by superposition #[408, 69]): ∀ (a : Iota), Or (Eq (aInfimumOfIn0 a xS xT) False) (Or (Eq (aLowerBoundOfIn0 a xS xT) True) (Eq False True))
% 19.59/19.77 Clause #415 (by clausification #[409]): ∀ (a : Iota), Or (Eq (aInfimumOfIn0 a xS xT) False) (Eq (aLowerBoundOfIn0 a xS xT) True)
% 19.59/19.77 Clause #416 (by superposition #[415, 208]): Or (Eq (aLowerBoundOfIn0 xv xS xT) True) (Eq False True)
% 19.59/19.77 Clause #417 (by clausification #[416]): Eq (aLowerBoundOfIn0 xv xS xT) True
% 19.59/19.77 Clause #418 (by superposition #[417, 230]): Or (Eq True False) (Eq (aElementOf0 xv xT) True)
% 19.59/19.77 Clause #422 (by clausification #[418]): Eq (aElementOf0 xv xT) True
% 19.59/19.77 Clause #423 (by superposition #[422, 51]): Or (Eq True False) (Eq (aElement0 xv) True)
% 19.59/19.77 Clause #428 (by clausification #[423]): Eq (aElement0 xv) True
% 19.59/19.77 Clause #429 (by superposition #[428, 42]): ∀ (a : Iota),
% 19.59/19.77 Or (Eq True False)
% 19.59/19.77 (Or (Eq (aElement0 a) False) (Or (Eq (sdtlseqdt0 xv a) False) (Or (Eq (sdtlseqdt0 a xv) False) (Eq xv a))))
% 19.59/19.77 Clause #437 (by clausification #[429]): ∀ (a : Iota), Or (Eq (aElement0 a) False) (Or (Eq (sdtlseqdt0 xv a) False) (Or (Eq (sdtlseqdt0 a xv) False) (Eq xv a)))
% 19.59/19.77 Clause #443 (by superposition #[402, 14]): ∀ (a a_1 : Iota),
% 19.59/19.77 Or (Eq (aSubsetOf0 a xT) False)
% 19.59/19.77 (Or (Eq (aInfimumOfIn0 a_1 a xT) False) (Or (Eq (aElementOf0 a_1 xT) True) (Eq False True)))
% 19.59/19.77 Clause #450 (by clausification #[443]): ∀ (a a_1 : Iota),
% 19.59/19.77 Or (Eq (aSubsetOf0 a xT) False) (Or (Eq (aInfimumOfIn0 a_1 a xT) False) (Eq (aElementOf0 a_1 xT) True))
% 19.59/19.77 Clause #451 (by superposition #[450, 69]): ∀ (a : Iota), Or (Eq (aInfimumOfIn0 a xS xT) False) (Or (Eq (aElementOf0 a xT) True) (Eq False True))
% 19.59/19.77 Clause #454 (by clausification #[451]): ∀ (a : Iota), Or (Eq (aInfimumOfIn0 a xS xT) False) (Eq (aElementOf0 a xT) True)
% 19.59/19.77 Clause #635 (by clausification #[209]): Eq
% 19.59/19.77 (And
% 19.59/19.77 (And
% 19.59/19.77 (And
% 19.59/19.77 (And
% 19.59/19.77 (And
% 19.59/19.77 (And
% 19.59/19.77 (And
% 19.59/19.77 (And (And (aElementOf0 xu xT) (aElementOf0 xu xT))
% 19.59/19.77 (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 xu W0))
% 19.59/19.77 (aLowerBoundOfIn0 xu xS xT))
% 19.59/19.77 (∀ (W0 : Iota),
% 19.59/19.77 Or (And (aElementOf0 W0 xT) (∀ (W1 : Iota), aElementOf0 W1 xS → sdtlseqdt0 W0 W1))
% 19.59/19.77 (aLowerBoundOfIn0 W0 xS xT) →
% 19.59/19.77 sdtlseqdt0 W0 xu))
% 19.59/19.77 (aInfimumOfIn0 xu xS xT))
% 19.59/19.77 (aElementOf0 xv xT))
% 19.59/19.77 (aElementOf0 xv xT))
% 19.59/19.77 (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 xv W0))
% 19.59/19.77 (aLowerBoundOfIn0 xv xS xT))
% 19.59/19.77 True
% 19.59/19.77 Clause #3358 (by clausification #[635]): Eq
% 19.59/19.77 (And
% 19.59/19.77 (And
% 19.59/19.77 (And
% 19.59/19.77 (And
% 19.59/19.77 (And
% 19.59/19.77 (And
% 19.59/19.77 (And (And (aElementOf0 xu xT) (aElementOf0 xu xT)) (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 xu W0))
% 19.59/19.77 (aLowerBoundOfIn0 xu xS xT))
% 19.59/19.77 (∀ (W0 : Iota),
% 19.59/19.77 Or (And (aElementOf0 W0 xT) (∀ (W1 : Iota), aElementOf0 W1 xS → sdtlseqdt0 W0 W1))
% 19.59/19.77 (aLowerBoundOfIn0 W0 xS xT) →
% 19.59/19.77 sdtlseqdt0 W0 xu))
% 19.59/19.77 (aInfimumOfIn0 xu xS xT))
% 19.59/19.80 (aElementOf0 xv xT))
% 19.59/19.80 (aElementOf0 xv xT))
% 19.59/19.80 (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 xv W0))
% 19.59/19.80 True
% 19.59/19.80 Clause #3360 (by clausification #[3358]): Eq
% 19.59/19.80 (And
% 19.59/19.80 (And
% 19.59/19.80 (And
% 19.59/19.80 (And
% 19.59/19.80 (And (And (And (aElementOf0 xu xT) (aElementOf0 xu xT)) (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 xu W0))
% 19.59/19.80 (aLowerBoundOfIn0 xu xS xT))
% 19.59/19.80 (∀ (W0 : Iota),
% 19.59/19.80 Or (And (aElementOf0 W0 xT) (∀ (W1 : Iota), aElementOf0 W1 xS → sdtlseqdt0 W0 W1))
% 19.59/19.80 (aLowerBoundOfIn0 W0 xS xT) →
% 19.59/19.80 sdtlseqdt0 W0 xu))
% 19.59/19.80 (aInfimumOfIn0 xu xS xT))
% 19.59/19.80 (aElementOf0 xv xT))
% 19.59/19.80 (aElementOf0 xv xT))
% 19.59/19.80 True
% 19.59/19.80 Clause #3362 (by clausification #[3360]): Eq
% 19.59/19.80 (And
% 19.59/19.80 (And
% 19.59/19.80 (And
% 19.59/19.80 (And (And (And (aElementOf0 xu xT) (aElementOf0 xu xT)) (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 xu W0))
% 19.59/19.80 (aLowerBoundOfIn0 xu xS xT))
% 19.59/19.80 (∀ (W0 : Iota),
% 19.59/19.80 Or (And (aElementOf0 W0 xT) (∀ (W1 : Iota), aElementOf0 W1 xS → sdtlseqdt0 W0 W1))
% 19.59/19.80 (aLowerBoundOfIn0 W0 xS xT) →
% 19.59/19.80 sdtlseqdt0 W0 xu))
% 19.59/19.80 (aInfimumOfIn0 xu xS xT))
% 19.59/19.80 (aElementOf0 xv xT))
% 19.59/19.80 True
% 19.59/19.80 Clause #3363 (by clausification #[3362]): Eq
% 19.59/19.80 (And
% 19.59/19.80 (And
% 19.59/19.80 (And (And (And (aElementOf0 xu xT) (aElementOf0 xu xT)) (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 xu W0))
% 19.59/19.80 (aLowerBoundOfIn0 xu xS xT))
% 19.59/19.80 (∀ (W0 : Iota),
% 19.59/19.80 Or (And (aElementOf0 W0 xT) (∀ (W1 : Iota), aElementOf0 W1 xS → sdtlseqdt0 W0 W1)) (aLowerBoundOfIn0 W0 xS xT) →
% 19.59/19.80 sdtlseqdt0 W0 xu))
% 19.59/19.80 (aInfimumOfIn0 xu xS xT))
% 19.59/19.80 True
% 19.59/19.80 Clause #3364 (by clausification #[3363]): Eq (aInfimumOfIn0 xu xS xT) True
% 19.59/19.80 Clause #3366 (by superposition #[3364, 396]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (aLowerBoundOfIn0 a xS xT) False) (Eq (sdtlseqdt0 a xu) True))
% 19.59/19.80 Clause #3367 (by superposition #[3364, 415]): Or (Eq True False) (Eq (aLowerBoundOfIn0 xu xS xT) True)
% 19.59/19.80 Clause #3368 (by superposition #[3364, 454]): Or (Eq True False) (Eq (aElementOf0 xu xT) True)
% 19.59/19.80 Clause #3370 (by clausification #[3368]): Eq (aElementOf0 xu xT) True
% 19.59/19.80 Clause #3371 (by superposition #[3370, 51]): Or (Eq True False) (Eq (aElement0 xu) True)
% 19.59/19.80 Clause #3390 (by clausification #[3371]): Eq (aElement0 xu) True
% 19.59/19.80 Clause #3398 (by superposition #[3390, 437]): Or (Eq True False) (Or (Eq (sdtlseqdt0 xv xu) False) (Or (Eq (sdtlseqdt0 xu xv) False) (Eq xv xu)))
% 19.59/19.80 Clause #3431 (by clausification #[3367]): Eq (aLowerBoundOfIn0 xu xS xT) True
% 19.59/19.80 Clause #3433 (by superposition #[3431, 400]): Or (Eq True False) (Eq (sdtlseqdt0 xu xv) True)
% 19.59/19.80 Clause #3434 (by clausification #[3433]): Eq (sdtlseqdt0 xu xv) True
% 19.59/19.80 Clause #3461 (by clausification #[3366]): ∀ (a : Iota), Or (Eq (aLowerBoundOfIn0 a xS xT) False) (Eq (sdtlseqdt0 a xu) True)
% 19.59/19.80 Clause #3462 (by superposition #[3461, 417]): Or (Eq (sdtlseqdt0 xv xu) True) (Eq False True)
% 19.59/19.80 Clause #3464 (by clausification #[3462]): Eq (sdtlseqdt0 xv xu) True
% 19.59/19.80 Clause #3465 (by clausification #[3398]): Or (Eq (sdtlseqdt0 xv xu) False) (Or (Eq (sdtlseqdt0 xu xv) False) (Eq xv xu))
% 19.59/19.80 Clause #3466 (by forward demodulation #[3465, 3434]): Or (Eq (sdtlseqdt0 xv xu) False) (Or (Eq True False) (Eq xv xu))
% 19.59/19.80 Clause #3467 (by clausification #[3466]): Or (Eq (sdtlseqdt0 xv xu) False) (Eq xv xu)
% 19.59/19.80 Clause #3468 (by forward contextual literal cutting #[3467, 35]): Eq (sdtlseqdt0 xv xu) False
% 19.59/19.80 Clause #3469 (by superposition #[3468, 3464]): Eq False True
% 19.59/19.80 Clause #3471 (by clausification #[3469]): False
% 19.59/19.80 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------