TSTP Solution File: COM012+3 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : COM012+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n031.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 : Wed Aug 30 18:38:07 EDT 2023
% Result : Theorem 4.30s 4.66s
% Output : Proof 4.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : COM012+3 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : duper %s
% 0.14/0.35 % Computer : n031.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 : Tue Aug 29 13:54:26 EDT 2023
% 0.14/0.35 % CPUTime :
% 4.30/4.66 SZS status Theorem for theBenchmark.p
% 4.30/4.66 SZS output start Proof for theBenchmark.p
% 4.30/4.66 Clause #6 (by assumption #[]): Eq
% 4.30/4.66 (∀ (W0 W1 W2 W3 : Iota),
% 4.30/4.66 And (And (And (aElement0 W0) (aRewritingSystem0 W1)) (aElement0 W2)) (aElement0 W3) →
% 4.30/4.66 And (sdtmndtplgtdt0 W0 W1 W2) (sdtmndtplgtdt0 W2 W1 W3) → sdtmndtplgtdt0 W0 W1 W3)
% 4.30/4.66 True
% 4.30/4.66 Clause #7 (by assumption #[]): Eq
% 4.30/4.66 (∀ (W0 W1 W2 : Iota),
% 4.30/4.66 And (And (aElement0 W0) (aRewritingSystem0 W1)) (aElement0 W2) →
% 4.30/4.66 Iff (sdtmndtasgtdt0 W0 W1 W2) (Or (Eq W0 W2) (sdtmndtplgtdt0 W0 W1 W2)))
% 4.30/4.66 True
% 4.30/4.66 Clause #8 (by assumption #[]): Eq (And (And (And (aElement0 xx) (aRewritingSystem0 xR)) (aElement0 xy)) (aElement0 xz)) True
% 4.30/4.66 Clause #9 (by assumption #[]): Eq
% 4.30/4.66 (Not
% 4.30/4.66 (And
% 4.30/4.66 (And
% 4.30/4.66 (And
% 4.30/4.66 (Or (Eq xx xy)
% 4.30/4.66 (And
% 4.30/4.66 (Or (aReductOfIn0 xy xx xR)
% 4.30/4.66 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xx xR)) (sdtmndtplgtdt0 W0 xR xy)))
% 4.30/4.66 (sdtmndtplgtdt0 xx xR xy)))
% 4.30/4.66 (sdtmndtasgtdt0 xx xR xy))
% 4.30/4.66 (Or (Eq xy xz)
% 4.30/4.66 (And
% 4.30/4.66 (Or (aReductOfIn0 xz xy xR)
% 4.30/4.66 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xy xR)) (sdtmndtplgtdt0 W0 xR xz)))
% 4.30/4.66 (sdtmndtplgtdt0 xy xR xz))))
% 4.30/4.66 (sdtmndtasgtdt0 xy xR xz) →
% 4.30/4.66 Or
% 4.30/4.66 (Or
% 4.30/4.66 (Or (Or (Eq xx xz) (aReductOfIn0 xz xx xR))
% 4.30/4.66 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xx xR)) (sdtmndtplgtdt0 W0 xR xz)))
% 4.30/4.66 (sdtmndtplgtdt0 xx xR xz))
% 4.30/4.66 (sdtmndtasgtdt0 xx xR xz)))
% 4.30/4.66 True
% 4.30/4.66 Clause #45 (by clausification #[6]): ∀ (a : Iota),
% 4.30/4.66 Eq
% 4.30/4.66 (∀ (W1 W2 W3 : Iota),
% 4.30/4.66 And (And (And (aElement0 a) (aRewritingSystem0 W1)) (aElement0 W2)) (aElement0 W3) →
% 4.30/4.66 And (sdtmndtplgtdt0 a W1 W2) (sdtmndtplgtdt0 W2 W1 W3) → sdtmndtplgtdt0 a W1 W3)
% 4.30/4.66 True
% 4.30/4.66 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota),
% 4.30/4.66 Eq
% 4.30/4.66 (∀ (W2 W3 : Iota),
% 4.30/4.66 And (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 W2)) (aElement0 W3) →
% 4.30/4.66 And (sdtmndtplgtdt0 a a_1 W2) (sdtmndtplgtdt0 W2 a_1 W3) → sdtmndtplgtdt0 a a_1 W3)
% 4.30/4.66 True
% 4.30/4.66 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 : Iota),
% 4.30/4.66 Eq
% 4.30/4.66 (∀ (W3 : Iota),
% 4.30/4.66 And (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2)) (aElement0 W3) →
% 4.30/4.66 And (sdtmndtplgtdt0 a a_1 a_2) (sdtmndtplgtdt0 a_2 a_1 W3) → sdtmndtplgtdt0 a a_1 W3)
% 4.30/4.66 True
% 4.30/4.66 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.30/4.66 Eq
% 4.30/4.66 (And (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2)) (aElement0 a_3) →
% 4.30/4.66 And (sdtmndtplgtdt0 a a_1 a_2) (sdtmndtplgtdt0 a_2 a_1 a_3) → sdtmndtplgtdt0 a a_1 a_3)
% 4.30/4.66 True
% 4.30/4.66 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.30/4.66 Or (Eq (And (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2)) (aElement0 a_3)) False)
% 4.30/4.66 (Eq (And (sdtmndtplgtdt0 a a_1 a_2) (sdtmndtplgtdt0 a_2 a_1 a_3) → sdtmndtplgtdt0 a a_1 a_3) True)
% 4.30/4.66 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.30/4.66 Or (Eq (And (sdtmndtplgtdt0 a a_1 a_2) (sdtmndtplgtdt0 a_2 a_1 a_3) → sdtmndtplgtdt0 a a_1 a_3) True)
% 4.30/4.66 (Or (Eq (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2)) False) (Eq (aElement0 a_3) False))
% 4.30/4.66 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.30/4.66 Or (Eq (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2)) False)
% 4.30/4.66 (Or (Eq (aElement0 a_3) False)
% 4.30/4.66 (Or (Eq (And (sdtmndtplgtdt0 a a_1 a_2) (sdtmndtplgtdt0 a_2 a_1 a_3)) False)
% 4.30/4.66 (Eq (sdtmndtplgtdt0 a a_1 a_3) True)))
% 4.30/4.66 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.30/4.66 Or (Eq (aElement0 a) False)
% 4.30/4.66 (Or (Eq (And (sdtmndtplgtdt0 a_1 a_2 a_3) (sdtmndtplgtdt0 a_3 a_2 a)) False)
% 4.30/4.66 (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a) True)
% 4.30/4.66 (Or (Eq (And (aElement0 a_1) (aRewritingSystem0 a_2)) False) (Eq (aElement0 a_3) False))))
% 4.30/4.66 Clause #53 (by clausification #[52]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.30/4.66 Or (Eq (aElement0 a) False)
% 4.30/4.66 (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a) True)
% 4.30/4.66 (Or (Eq (And (aElement0 a_1) (aRewritingSystem0 a_2)) False)
% 4.45/4.68 (Or (Eq (aElement0 a_3) False)
% 4.45/4.68 (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a_3) False) (Eq (sdtmndtplgtdt0 a_3 a_2 a) False)))))
% 4.45/4.68 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.45/4.68 Or (Eq (aElement0 a) False)
% 4.45/4.68 (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a) True)
% 4.45/4.68 (Or (Eq (aElement0 a_3) False)
% 4.45/4.68 (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a_3) False)
% 4.45/4.68 (Or (Eq (sdtmndtplgtdt0 a_3 a_2 a) False)
% 4.45/4.68 (Or (Eq (aElement0 a_1) False) (Eq (aRewritingSystem0 a_2) False))))))
% 4.45/4.68 Clause #55 (by clausification #[8]): Eq (aElement0 xz) True
% 4.45/4.68 Clause #56 (by clausification #[8]): Eq (And (And (aElement0 xx) (aRewritingSystem0 xR)) (aElement0 xy)) True
% 4.45/4.68 Clause #59 (by superposition #[55, 54]): ∀ (a a_1 a_2 : Iota),
% 4.45/4.68 Or (Eq True False)
% 4.45/4.68 (Or (Eq (sdtmndtplgtdt0 a a_1 xz) True)
% 4.45/4.68 (Or (Eq (aElement0 a_2) False)
% 4.45/4.68 (Or (Eq (sdtmndtplgtdt0 a a_1 a_2) False)
% 4.45/4.68 (Or (Eq (sdtmndtplgtdt0 a_2 a_1 xz) False)
% 4.45/4.68 (Or (Eq (aElement0 a) False) (Eq (aRewritingSystem0 a_1) False))))))
% 4.45/4.68 Clause #60 (by clausification #[56]): Eq (aElement0 xy) True
% 4.45/4.68 Clause #61 (by clausification #[56]): Eq (And (aElement0 xx) (aRewritingSystem0 xR)) True
% 4.45/4.68 Clause #65 (by clausification #[61]): Eq (aRewritingSystem0 xR) True
% 4.45/4.68 Clause #66 (by clausification #[61]): Eq (aElement0 xx) True
% 4.45/4.68 Clause #70 (by clausification #[7]): ∀ (a : Iota),
% 4.45/4.68 Eq
% 4.45/4.68 (∀ (W1 W2 : Iota),
% 4.45/4.68 And (And (aElement0 a) (aRewritingSystem0 W1)) (aElement0 W2) →
% 4.45/4.68 Iff (sdtmndtasgtdt0 a W1 W2) (Or (Eq a W2) (sdtmndtplgtdt0 a W1 W2)))
% 4.45/4.68 True
% 4.45/4.68 Clause #71 (by clausification #[70]): ∀ (a a_1 : Iota),
% 4.45/4.68 Eq
% 4.45/4.68 (∀ (W2 : Iota),
% 4.45/4.68 And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 W2) →
% 4.45/4.68 Iff (sdtmndtasgtdt0 a a_1 W2) (Or (Eq a W2) (sdtmndtplgtdt0 a a_1 W2)))
% 4.45/4.68 True
% 4.45/4.68 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 : Iota),
% 4.45/4.68 Eq
% 4.45/4.68 (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2) →
% 4.45/4.68 Iff (sdtmndtasgtdt0 a a_1 a_2) (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2)))
% 4.45/4.68 True
% 4.45/4.68 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 : Iota),
% 4.45/4.68 Or (Eq (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2)) False)
% 4.45/4.68 (Eq (Iff (sdtmndtasgtdt0 a a_1 a_2) (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2))) True)
% 4.45/4.68 Clause #74 (by clausification #[73]): ∀ (a a_1 a_2 : Iota),
% 4.45/4.68 Or (Eq (Iff (sdtmndtasgtdt0 a a_1 a_2) (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2))) True)
% 4.45/4.68 (Or (Eq (And (aElement0 a) (aRewritingSystem0 a_1)) False) (Eq (aElement0 a_2) False))
% 4.45/4.68 Clause #76 (by clausification #[74]): ∀ (a a_1 a_2 : Iota),
% 4.45/4.68 Or (Eq (And (aElement0 a) (aRewritingSystem0 a_1)) False)
% 4.45/4.68 (Or (Eq (aElement0 a_2) False)
% 4.45/4.68 (Or (Eq (sdtmndtasgtdt0 a a_1 a_2) False) (Eq (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2)) True)))
% 4.45/4.68 Clause #91 (by clausification #[9]): Eq
% 4.45/4.68 (And
% 4.45/4.68 (And
% 4.45/4.68 (And
% 4.45/4.68 (Or (Eq xx xy)
% 4.45/4.68 (And
% 4.45/4.68 (Or (aReductOfIn0 xy xx xR)
% 4.45/4.68 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xx xR)) (sdtmndtplgtdt0 W0 xR xy)))
% 4.45/4.68 (sdtmndtplgtdt0 xx xR xy)))
% 4.45/4.68 (sdtmndtasgtdt0 xx xR xy))
% 4.45/4.68 (Or (Eq xy xz)
% 4.45/4.68 (And
% 4.45/4.68 (Or (aReductOfIn0 xz xy xR)
% 4.45/4.68 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xy xR)) (sdtmndtplgtdt0 W0 xR xz)))
% 4.45/4.68 (sdtmndtplgtdt0 xy xR xz))))
% 4.45/4.68 (sdtmndtasgtdt0 xy xR xz) →
% 4.45/4.68 Or
% 4.45/4.68 (Or
% 4.45/4.68 (Or (Or (Eq xx xz) (aReductOfIn0 xz xx xR))
% 4.45/4.68 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xx xR)) (sdtmndtplgtdt0 W0 xR xz)))
% 4.45/4.68 (sdtmndtplgtdt0 xx xR xz))
% 4.45/4.68 (sdtmndtasgtdt0 xx xR xz))
% 4.45/4.68 False
% 4.45/4.68 Clause #92 (by clausification #[91]): Eq
% 4.45/4.68 (And
% 4.45/4.68 (And
% 4.45/4.68 (And
% 4.45/4.68 (Or (Eq xx xy)
% 4.45/4.68 (And
% 4.45/4.68 (Or (aReductOfIn0 xy xx xR)
% 4.45/4.68 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xx xR)) (sdtmndtplgtdt0 W0 xR xy)))
% 4.45/4.68 (sdtmndtplgtdt0 xx xR xy)))
% 4.45/4.68 (sdtmndtasgtdt0 xx xR xy))
% 4.45/4.68 (Or (Eq xy xz)
% 4.45/4.68 (And
% 4.45/4.68 (Or (aReductOfIn0 xz xy xR)
% 4.45/4.68 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xy xR)) (sdtmndtplgtdt0 W0 xR xz)))
% 4.45/4.70 (sdtmndtplgtdt0 xy xR xz))))
% 4.45/4.70 (sdtmndtasgtdt0 xy xR xz))
% 4.45/4.70 True
% 4.45/4.70 Clause #93 (by clausification #[91]): Eq
% 4.45/4.70 (Or
% 4.45/4.70 (Or
% 4.45/4.70 (Or (Or (Eq xx xz) (aReductOfIn0 xz xx xR))
% 4.45/4.70 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xx xR)) (sdtmndtplgtdt0 W0 xR xz)))
% 4.45/4.70 (sdtmndtplgtdt0 xx xR xz))
% 4.45/4.70 (sdtmndtasgtdt0 xx xR xz))
% 4.45/4.70 False
% 4.45/4.70 Clause #94 (by clausification #[92]): Eq (sdtmndtasgtdt0 xy xR xz) True
% 4.45/4.70 Clause #95 (by clausification #[92]): Eq
% 4.45/4.70 (And
% 4.45/4.70 (And
% 4.45/4.70 (Or (Eq xx xy)
% 4.45/4.70 (And
% 4.45/4.70 (Or (aReductOfIn0 xy xx xR)
% 4.45/4.70 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xx xR)) (sdtmndtplgtdt0 W0 xR xy)))
% 4.45/4.70 (sdtmndtplgtdt0 xx xR xy)))
% 4.45/4.70 (sdtmndtasgtdt0 xx xR xy))
% 4.45/4.70 (Or (Eq xy xz)
% 4.45/4.70 (And
% 4.45/4.70 (Or (aReductOfIn0 xz xy xR)
% 4.45/4.70 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xy xR)) (sdtmndtplgtdt0 W0 xR xz)))
% 4.45/4.70 (sdtmndtplgtdt0 xy xR xz))))
% 4.45/4.70 True
% 4.45/4.70 Clause #148 (by clausification #[59]): ∀ (a a_1 a_2 : Iota),
% 4.45/4.70 Or (Eq (sdtmndtplgtdt0 a a_1 xz) True)
% 4.45/4.70 (Or (Eq (aElement0 a_2) False)
% 4.45/4.70 (Or (Eq (sdtmndtplgtdt0 a a_1 a_2) False)
% 4.45/4.70 (Or (Eq (sdtmndtplgtdt0 a_2 a_1 xz) False) (Or (Eq (aElement0 a) False) (Eq (aRewritingSystem0 a_1) False)))))
% 4.45/4.70 Clause #150 (by superposition #[148, 60]): ∀ (a a_1 : Iota),
% 4.45/4.70 Or (Eq (sdtmndtplgtdt0 a a_1 xz) True)
% 4.45/4.70 (Or (Eq (sdtmndtplgtdt0 a a_1 xy) False)
% 4.45/4.70 (Or (Eq (sdtmndtplgtdt0 xy a_1 xz) False)
% 4.45/4.70 (Or (Eq (aElement0 a) False) (Or (Eq (aRewritingSystem0 a_1) False) (Eq False True)))))
% 4.45/4.70 Clause #218 (by clausification #[76]): ∀ (a a_1 a_2 : Iota),
% 4.45/4.70 Or (Eq (aElement0 a) False)
% 4.45/4.70 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) False)
% 4.45/4.70 (Or (Eq (Or (Eq a_1 a) (sdtmndtplgtdt0 a_1 a_2 a)) True)
% 4.45/4.70 (Or (Eq (aElement0 a_1) False) (Eq (aRewritingSystem0 a_2) False))))
% 4.45/4.70 Clause #219 (by clausification #[218]): ∀ (a a_1 a_2 : Iota),
% 4.45/4.70 Or (Eq (aElement0 a) False)
% 4.45/4.70 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) False)
% 4.45/4.70 (Or (Eq (aElement0 a_1) False)
% 4.45/4.70 (Or (Eq (aRewritingSystem0 a_2) False) (Or (Eq (Eq a_1 a) True) (Eq (sdtmndtplgtdt0 a_1 a_2 a) True)))))
% 4.45/4.70 Clause #220 (by clausification #[219]): ∀ (a a_1 a_2 : Iota),
% 4.45/4.70 Or (Eq (aElement0 a) False)
% 4.45/4.70 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) False)
% 4.45/4.70 (Or (Eq (aElement0 a_1) False)
% 4.45/4.70 (Or (Eq (aRewritingSystem0 a_2) False) (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a) True) (Eq a_1 a)))))
% 4.45/4.70 Clause #222 (by superposition #[220, 60]): ∀ (a a_1 : Iota),
% 4.45/4.70 Or (Eq (sdtmndtasgtdt0 a a_1 xy) False)
% 4.45/4.70 (Or (Eq (aElement0 a) False)
% 4.45/4.70 (Or (Eq (aRewritingSystem0 a_1) False) (Or (Eq (sdtmndtplgtdt0 a a_1 xy) True) (Or (Eq a xy) (Eq False True)))))
% 4.45/4.70 Clause #231 (by clausification #[93]): Eq (sdtmndtasgtdt0 xx xR xz) False
% 4.45/4.70 Clause #232 (by clausification #[93]): Eq
% 4.45/4.70 (Or
% 4.45/4.70 (Or (Or (Eq xx xz) (aReductOfIn0 xz xx xR))
% 4.45/4.70 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xx xR)) (sdtmndtplgtdt0 W0 xR xz)))
% 4.45/4.70 (sdtmndtplgtdt0 xx xR xz))
% 4.45/4.70 False
% 4.45/4.70 Clause #236 (by clausification #[222]): ∀ (a a_1 : Iota),
% 4.45/4.70 Or (Eq (sdtmndtasgtdt0 a a_1 xy) False)
% 4.45/4.70 (Or (Eq (aElement0 a) False)
% 4.45/4.70 (Or (Eq (aRewritingSystem0 a_1) False) (Or (Eq (sdtmndtplgtdt0 a a_1 xy) True) (Eq a xy))))
% 4.45/4.70 Clause #242 (by clausification #[95]): Eq
% 4.45/4.70 (Or (Eq xy xz)
% 4.45/4.70 (And
% 4.45/4.70 (Or (aReductOfIn0 xz xy xR)
% 4.45/4.70 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xy xR)) (sdtmndtplgtdt0 W0 xR xz)))
% 4.45/4.70 (sdtmndtplgtdt0 xy xR xz)))
% 4.45/4.70 True
% 4.45/4.70 Clause #243 (by clausification #[95]): Eq
% 4.45/4.70 (And
% 4.45/4.70 (Or (Eq xx xy)
% 4.45/4.70 (And
% 4.45/4.70 (Or (aReductOfIn0 xy xx xR)
% 4.45/4.70 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xx xR)) (sdtmndtplgtdt0 W0 xR xy)))
% 4.45/4.70 (sdtmndtplgtdt0 xx xR xy)))
% 4.45/4.70 (sdtmndtasgtdt0 xx xR xy))
% 4.45/4.70 True
% 4.45/4.70 Clause #244 (by clausification #[242]): Or (Eq (Eq xy xz) True)
% 4.45/4.70 (Eq
% 4.45/4.70 (And
% 4.45/4.70 (Or (aReductOfIn0 xz xy xR)
% 4.45/4.70 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xy xR)) (sdtmndtplgtdt0 W0 xR xz)))
% 4.45/4.70 (sdtmndtplgtdt0 xy xR xz))
% 4.45/4.70 True)
% 4.45/4.70 Clause #245 (by clausification #[244]): Or
% 4.45/4.70 (Eq
% 4.45/4.70 (And
% 4.56/4.72 (Or (aReductOfIn0 xz xy xR)
% 4.56/4.72 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xy xR)) (sdtmndtplgtdt0 W0 xR xz)))
% 4.56/4.72 (sdtmndtplgtdt0 xy xR xz))
% 4.56/4.72 True)
% 4.56/4.72 (Eq xy xz)
% 4.56/4.72 Clause #246 (by clausification #[245]): Or (Eq xy xz) (Eq (sdtmndtplgtdt0 xy xR xz) True)
% 4.56/4.72 Clause #270 (by clausification #[150]): ∀ (a a_1 : Iota),
% 4.56/4.72 Or (Eq (sdtmndtplgtdt0 a a_1 xz) True)
% 4.56/4.72 (Or (Eq (sdtmndtplgtdt0 a a_1 xy) False)
% 4.56/4.72 (Or (Eq (sdtmndtplgtdt0 xy a_1 xz) False) (Or (Eq (aElement0 a) False) (Eq (aRewritingSystem0 a_1) False))))
% 4.56/4.72 Clause #357 (by clausification #[232]): Eq (sdtmndtplgtdt0 xx xR xz) False
% 4.56/4.72 Clause #370 (by clausification #[243]): Eq (sdtmndtasgtdt0 xx xR xy) True
% 4.56/4.72 Clause #372 (by superposition #[370, 236]): Or (Eq True False)
% 4.56/4.72 (Or (Eq (aElement0 xx) False)
% 4.56/4.72 (Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xx xR xy) True) (Eq xx xy))))
% 4.56/4.72 Clause #373 (by clausification #[372]): Or (Eq (aElement0 xx) False) (Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xx xR xy) True) (Eq xx xy)))
% 4.56/4.72 Clause #374 (by forward demodulation #[373, 66]): Or (Eq True False) (Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xx xR xy) True) (Eq xx xy)))
% 4.56/4.72 Clause #375 (by clausification #[374]): Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xx xR xy) True) (Eq xx xy))
% 4.56/4.72 Clause #376 (by forward demodulation #[375, 65]): Or (Eq True False) (Or (Eq (sdtmndtplgtdt0 xx xR xy) True) (Eq xx xy))
% 4.56/4.72 Clause #377 (by clausification #[376]): Or (Eq (sdtmndtplgtdt0 xx xR xy) True) (Eq xx xy)
% 4.56/4.72 Clause #380 (by superposition #[377, 270]): Or (Eq xx xy)
% 4.56/4.72 (Or (Eq (sdtmndtplgtdt0 xx xR xz) True)
% 4.56/4.72 (Or (Eq True False)
% 4.56/4.72 (Or (Eq (sdtmndtplgtdt0 xy xR xz) False) (Or (Eq (aElement0 xx) False) (Eq (aRewritingSystem0 xR) False)))))
% 4.56/4.72 Clause #389 (by clausification #[380]): Or (Eq xx xy)
% 4.56/4.72 (Or (Eq (sdtmndtplgtdt0 xx xR xz) True)
% 4.56/4.72 (Or (Eq (sdtmndtplgtdt0 xy xR xz) False) (Or (Eq (aElement0 xx) False) (Eq (aRewritingSystem0 xR) False))))
% 4.56/4.72 Clause #390 (by forward demodulation #[389, 357]): Or (Eq xx xy)
% 4.56/4.72 (Or (Eq False True)
% 4.56/4.72 (Or (Eq (sdtmndtplgtdt0 xy xR xz) False) (Or (Eq (aElement0 xx) False) (Eq (aRewritingSystem0 xR) False))))
% 4.56/4.72 Clause #391 (by clausification #[390]): Or (Eq xx xy) (Or (Eq (sdtmndtplgtdt0 xy xR xz) False) (Or (Eq (aElement0 xx) False) (Eq (aRewritingSystem0 xR) False)))
% 4.56/4.72 Clause #392 (by forward demodulation #[391, 66]): Or (Eq xx xy) (Or (Eq (sdtmndtplgtdt0 xy xR xz) False) (Or (Eq True False) (Eq (aRewritingSystem0 xR) False)))
% 4.56/4.72 Clause #393 (by clausification #[392]): Or (Eq xx xy) (Or (Eq (sdtmndtplgtdt0 xy xR xz) False) (Eq (aRewritingSystem0 xR) False))
% 4.56/4.72 Clause #394 (by forward demodulation #[393, 65]): Or (Eq xx xy) (Or (Eq (sdtmndtplgtdt0 xy xR xz) False) (Eq True False))
% 4.56/4.72 Clause #395 (by clausification #[394]): Or (Eq xx xy) (Eq (sdtmndtplgtdt0 xy xR xz) False)
% 4.56/4.72 Clause #396 (by superposition #[395, 246]): Or (Eq xx xy) (Or (Eq xy xz) (Eq False True))
% 4.56/4.72 Clause #401 (by clausification #[396]): Or (Eq xx xy) (Eq xy xz)
% 4.56/4.72 Clause #415 (by superposition #[401, 357]): Or (Eq xx xy) (Eq (sdtmndtplgtdt0 xx xR xy) False)
% 4.56/4.72 Clause #420 (by superposition #[415, 377]): Or (Eq xx xy) (Or (Eq False True) (Eq xx xy))
% 4.56/4.72 Clause #421 (by clausification #[420]): Or (Eq xx xy) (Eq xx xy)
% 4.56/4.72 Clause #422 (by eliminate duplicate literals #[421]): Eq xx xy
% 4.56/4.72 Clause #423 (by backward demodulation #[422, 94]): Eq (sdtmndtasgtdt0 xx xR xz) True
% 4.56/4.72 Clause #478 (by superposition #[423, 231]): Eq True False
% 4.56/4.72 Clause #480 (by clausification #[478]): False
% 4.56/4.72 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------