TSTP Solution File: COM012+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : COM012+1 : 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 18:38:06 EDT 2023
% Result : Theorem 3.94s 4.23s
% Output : Proof 4.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COM012+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n031.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 : Tue Aug 29 13:53:41 EDT 2023
% 0.13/0.34 % CPUTime :
% 3.94/4.23 SZS status Theorem for theBenchmark.p
% 3.94/4.23 SZS output start Proof for theBenchmark.p
% 3.94/4.23 Clause #6 (by assumption #[]): Eq
% 3.94/4.23 (∀ (W0 W1 W2 W3 : Iota),
% 3.94/4.23 And (And (And (aElement0 W0) (aRewritingSystem0 W1)) (aElement0 W2)) (aElement0 W3) →
% 3.94/4.23 And (sdtmndtplgtdt0 W0 W1 W2) (sdtmndtplgtdt0 W2 W1 W3) → sdtmndtplgtdt0 W0 W1 W3)
% 3.94/4.23 True
% 3.94/4.23 Clause #7 (by assumption #[]): Eq
% 3.94/4.23 (∀ (W0 W1 W2 : Iota),
% 3.94/4.23 And (And (aElement0 W0) (aRewritingSystem0 W1)) (aElement0 W2) →
% 3.94/4.23 Iff (sdtmndtasgtdt0 W0 W1 W2) (Or (Eq W0 W2) (sdtmndtplgtdt0 W0 W1 W2)))
% 3.94/4.23 True
% 3.94/4.23 Clause #8 (by assumption #[]): Eq (And (And (And (aElement0 xx) (aRewritingSystem0 xR)) (aElement0 xy)) (aElement0 xz)) True
% 3.94/4.23 Clause #9 (by assumption #[]): Eq (Not (And (sdtmndtasgtdt0 xx xR xy) (sdtmndtasgtdt0 xy xR xz) → sdtmndtasgtdt0 xx xR xz)) True
% 3.94/4.23 Clause #19 (by clausification #[9]): Eq (And (sdtmndtasgtdt0 xx xR xy) (sdtmndtasgtdt0 xy xR xz) → sdtmndtasgtdt0 xx xR xz) False
% 3.94/4.23 Clause #20 (by clausification #[19]): Eq (And (sdtmndtasgtdt0 xx xR xy) (sdtmndtasgtdt0 xy xR xz)) True
% 3.94/4.23 Clause #21 (by clausification #[19]): Eq (sdtmndtasgtdt0 xx xR xz) False
% 3.94/4.23 Clause #22 (by clausification #[20]): Eq (sdtmndtasgtdt0 xy xR xz) True
% 3.94/4.23 Clause #23 (by clausification #[20]): Eq (sdtmndtasgtdt0 xx xR xy) True
% 3.94/4.23 Clause #37 (by clausification #[6]): ∀ (a : Iota),
% 3.94/4.23 Eq
% 3.94/4.23 (∀ (W1 W2 W3 : Iota),
% 3.94/4.23 And (And (And (aElement0 a) (aRewritingSystem0 W1)) (aElement0 W2)) (aElement0 W3) →
% 3.94/4.23 And (sdtmndtplgtdt0 a W1 W2) (sdtmndtplgtdt0 W2 W1 W3) → sdtmndtplgtdt0 a W1 W3)
% 3.94/4.23 True
% 3.94/4.23 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota),
% 3.94/4.23 Eq
% 3.94/4.23 (∀ (W2 W3 : Iota),
% 3.94/4.23 And (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 W2)) (aElement0 W3) →
% 3.94/4.23 And (sdtmndtplgtdt0 a a_1 W2) (sdtmndtplgtdt0 W2 a_1 W3) → sdtmndtplgtdt0 a a_1 W3)
% 3.94/4.23 True
% 3.94/4.23 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota),
% 3.94/4.23 Eq
% 3.94/4.23 (∀ (W3 : Iota),
% 3.94/4.23 And (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2)) (aElement0 W3) →
% 3.94/4.23 And (sdtmndtplgtdt0 a a_1 a_2) (sdtmndtplgtdt0 a_2 a_1 W3) → sdtmndtplgtdt0 a a_1 W3)
% 3.94/4.23 True
% 3.94/4.23 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.94/4.23 Eq
% 3.94/4.23 (And (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2)) (aElement0 a_3) →
% 3.94/4.23 And (sdtmndtplgtdt0 a a_1 a_2) (sdtmndtplgtdt0 a_2 a_1 a_3) → sdtmndtplgtdt0 a a_1 a_3)
% 3.94/4.23 True
% 3.94/4.23 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.94/4.23 Or (Eq (And (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2)) (aElement0 a_3)) False)
% 3.94/4.23 (Eq (And (sdtmndtplgtdt0 a a_1 a_2) (sdtmndtplgtdt0 a_2 a_1 a_3) → sdtmndtplgtdt0 a a_1 a_3) True)
% 3.94/4.23 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.94/4.23 Or (Eq (And (sdtmndtplgtdt0 a a_1 a_2) (sdtmndtplgtdt0 a_2 a_1 a_3) → sdtmndtplgtdt0 a a_1 a_3) True)
% 3.94/4.23 (Or (Eq (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2)) False) (Eq (aElement0 a_3) False))
% 3.94/4.23 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.94/4.23 Or (Eq (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2)) False)
% 3.94/4.23 (Or (Eq (aElement0 a_3) False)
% 3.94/4.23 (Or (Eq (And (sdtmndtplgtdt0 a a_1 a_2) (sdtmndtplgtdt0 a_2 a_1 a_3)) False)
% 3.94/4.23 (Eq (sdtmndtplgtdt0 a a_1 a_3) True)))
% 3.94/4.23 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.94/4.23 Or (Eq (aElement0 a) False)
% 3.94/4.23 (Or (Eq (And (sdtmndtplgtdt0 a_1 a_2 a_3) (sdtmndtplgtdt0 a_3 a_2 a)) False)
% 3.94/4.23 (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a) True)
% 3.94/4.23 (Or (Eq (And (aElement0 a_1) (aRewritingSystem0 a_2)) False) (Eq (aElement0 a_3) False))))
% 3.94/4.23 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.94/4.23 Or (Eq (aElement0 a) False)
% 3.94/4.23 (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a) True)
% 3.94/4.23 (Or (Eq (And (aElement0 a_1) (aRewritingSystem0 a_2)) False)
% 3.94/4.23 (Or (Eq (aElement0 a_3) False)
% 3.94/4.23 (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a_3) False) (Eq (sdtmndtplgtdt0 a_3 a_2 a) False)))))
% 3.94/4.23 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.94/4.23 Or (Eq (aElement0 a) False)
% 3.94/4.23 (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a) True)
% 3.94/4.23 (Or (Eq (aElement0 a_3) False)
% 4.09/4.25 (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a_3) False)
% 4.09/4.25 (Or (Eq (sdtmndtplgtdt0 a_3 a_2 a) False)
% 4.09/4.25 (Or (Eq (aElement0 a_1) False) (Eq (aRewritingSystem0 a_2) False))))))
% 4.09/4.25 Clause #47 (by clausification #[8]): Eq (aElement0 xz) True
% 4.09/4.25 Clause #48 (by clausification #[8]): Eq (And (And (aElement0 xx) (aRewritingSystem0 xR)) (aElement0 xy)) True
% 4.09/4.25 Clause #50 (by superposition #[47, 46]): ∀ (a a_1 a_2 : Iota),
% 4.09/4.25 Or (Eq True False)
% 4.09/4.25 (Or (Eq (sdtmndtplgtdt0 a a_1 xz) True)
% 4.09/4.25 (Or (Eq (aElement0 a_2) False)
% 4.09/4.25 (Or (Eq (sdtmndtplgtdt0 a a_1 a_2) False)
% 4.09/4.25 (Or (Eq (sdtmndtplgtdt0 a_2 a_1 xz) False)
% 4.09/4.25 (Or (Eq (aElement0 a) False) (Eq (aRewritingSystem0 a_1) False))))))
% 4.09/4.25 Clause #51 (by clausification #[48]): Eq (aElement0 xy) True
% 4.09/4.25 Clause #52 (by clausification #[48]): Eq (And (aElement0 xx) (aRewritingSystem0 xR)) True
% 4.09/4.25 Clause #70 (by clausification #[52]): Eq (aRewritingSystem0 xR) True
% 4.09/4.25 Clause #71 (by clausification #[52]): Eq (aElement0 xx) True
% 4.09/4.25 Clause #80 (by clausification #[7]): ∀ (a : Iota),
% 4.09/4.25 Eq
% 4.09/4.25 (∀ (W1 W2 : Iota),
% 4.09/4.25 And (And (aElement0 a) (aRewritingSystem0 W1)) (aElement0 W2) →
% 4.09/4.25 Iff (sdtmndtasgtdt0 a W1 W2) (Or (Eq a W2) (sdtmndtplgtdt0 a W1 W2)))
% 4.09/4.25 True
% 4.09/4.25 Clause #81 (by clausification #[80]): ∀ (a a_1 : Iota),
% 4.09/4.25 Eq
% 4.09/4.25 (∀ (W2 : Iota),
% 4.09/4.25 And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 W2) →
% 4.09/4.25 Iff (sdtmndtasgtdt0 a a_1 W2) (Or (Eq a W2) (sdtmndtplgtdt0 a a_1 W2)))
% 4.09/4.25 True
% 4.09/4.25 Clause #82 (by clausification #[81]): ∀ (a a_1 a_2 : Iota),
% 4.09/4.25 Eq
% 4.09/4.25 (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2) →
% 4.09/4.25 Iff (sdtmndtasgtdt0 a a_1 a_2) (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2)))
% 4.09/4.25 True
% 4.09/4.25 Clause #83 (by clausification #[82]): ∀ (a a_1 a_2 : Iota),
% 4.09/4.25 Or (Eq (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2)) False)
% 4.09/4.25 (Eq (Iff (sdtmndtasgtdt0 a a_1 a_2) (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2))) True)
% 4.09/4.25 Clause #84 (by clausification #[83]): ∀ (a a_1 a_2 : Iota),
% 4.09/4.25 Or (Eq (Iff (sdtmndtasgtdt0 a a_1 a_2) (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2))) True)
% 4.09/4.25 (Or (Eq (And (aElement0 a) (aRewritingSystem0 a_1)) False) (Eq (aElement0 a_2) False))
% 4.09/4.25 Clause #85 (by clausification #[84]): ∀ (a a_1 a_2 : Iota),
% 4.09/4.25 Or (Eq (And (aElement0 a) (aRewritingSystem0 a_1)) False)
% 4.09/4.25 (Or (Eq (aElement0 a_2) False)
% 4.09/4.25 (Or (Eq (sdtmndtasgtdt0 a a_1 a_2) True) (Eq (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2)) False)))
% 4.09/4.25 Clause #86 (by clausification #[84]): ∀ (a a_1 a_2 : Iota),
% 4.09/4.25 Or (Eq (And (aElement0 a) (aRewritingSystem0 a_1)) False)
% 4.09/4.25 (Or (Eq (aElement0 a_2) False)
% 4.09/4.25 (Or (Eq (sdtmndtasgtdt0 a a_1 a_2) False) (Eq (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2)) True)))
% 4.09/4.25 Clause #87 (by clausification #[85]): ∀ (a a_1 a_2 : Iota),
% 4.09/4.25 Or (Eq (aElement0 a) False)
% 4.09/4.25 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) True)
% 4.09/4.25 (Or (Eq (Or (Eq a_1 a) (sdtmndtplgtdt0 a_1 a_2 a)) False)
% 4.09/4.25 (Or (Eq (aElement0 a_1) False) (Eq (aRewritingSystem0 a_2) False))))
% 4.09/4.25 Clause #88 (by clausification #[87]): ∀ (a a_1 a_2 : Iota),
% 4.09/4.25 Or (Eq (aElement0 a) False)
% 4.09/4.25 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) True)
% 4.09/4.25 (Or (Eq (aElement0 a_1) False) (Or (Eq (aRewritingSystem0 a_2) False) (Eq (sdtmndtplgtdt0 a_1 a_2 a) False))))
% 4.09/4.25 Clause #90 (by superposition #[88, 47]): ∀ (a a_1 : Iota),
% 4.09/4.25 Or (Eq (sdtmndtasgtdt0 a a_1 xz) True)
% 4.09/4.25 (Or (Eq (aElement0 a) False)
% 4.09/4.25 (Or (Eq (aRewritingSystem0 a_1) False) (Or (Eq (sdtmndtplgtdt0 a a_1 xz) False) (Eq False True))))
% 4.09/4.25 Clause #97 (by clausification #[90]): ∀ (a a_1 : Iota),
% 4.09/4.25 Or (Eq (sdtmndtasgtdt0 a a_1 xz) True)
% 4.09/4.25 (Or (Eq (aElement0 a) False) (Or (Eq (aRewritingSystem0 a_1) False) (Eq (sdtmndtplgtdt0 a a_1 xz) False)))
% 4.09/4.25 Clause #100 (by superposition #[97, 71]): ∀ (a : Iota),
% 4.09/4.25 Or (Eq (sdtmndtasgtdt0 xx a xz) True)
% 4.09/4.25 (Or (Eq (aRewritingSystem0 a) False) (Or (Eq (sdtmndtplgtdt0 xx a xz) False) (Eq False True)))
% 4.09/4.25 Clause #101 (by clausification #[100]): ∀ (a : Iota),
% 4.09/4.25 Or (Eq (sdtmndtasgtdt0 xx a xz) True) (Or (Eq (aRewritingSystem0 a) False) (Eq (sdtmndtplgtdt0 xx a xz) False))
% 4.09/4.25 Clause #102 (by superposition #[101, 70]): Or (Eq (sdtmndtasgtdt0 xx xR xz) True) (Or (Eq (sdtmndtplgtdt0 xx xR xz) False) (Eq False True))
% 4.09/4.27 Clause #103 (by clausification #[50]): ∀ (a a_1 a_2 : Iota),
% 4.09/4.27 Or (Eq (sdtmndtplgtdt0 a a_1 xz) True)
% 4.09/4.27 (Or (Eq (aElement0 a_2) False)
% 4.09/4.27 (Or (Eq (sdtmndtplgtdt0 a a_1 a_2) False)
% 4.09/4.27 (Or (Eq (sdtmndtplgtdt0 a_2 a_1 xz) False) (Or (Eq (aElement0 a) False) (Eq (aRewritingSystem0 a_1) False)))))
% 4.09/4.27 Clause #105 (by superposition #[103, 51]): ∀ (a a_1 : Iota),
% 4.09/4.27 Or (Eq (sdtmndtplgtdt0 a a_1 xz) True)
% 4.09/4.27 (Or (Eq (sdtmndtplgtdt0 a a_1 xy) False)
% 4.09/4.27 (Or (Eq (sdtmndtplgtdt0 xy a_1 xz) False)
% 4.09/4.27 (Or (Eq (aElement0 a) False) (Or (Eq (aRewritingSystem0 a_1) False) (Eq False True)))))
% 4.09/4.27 Clause #107 (by clausification #[102]): Or (Eq (sdtmndtasgtdt0 xx xR xz) True) (Eq (sdtmndtplgtdt0 xx xR xz) False)
% 4.09/4.27 Clause #210 (by clausification #[86]): ∀ (a a_1 a_2 : Iota),
% 4.09/4.27 Or (Eq (aElement0 a) False)
% 4.09/4.27 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) False)
% 4.09/4.27 (Or (Eq (Or (Eq a_1 a) (sdtmndtplgtdt0 a_1 a_2 a)) True)
% 4.09/4.27 (Or (Eq (aElement0 a_1) False) (Eq (aRewritingSystem0 a_2) False))))
% 4.09/4.27 Clause #211 (by clausification #[210]): ∀ (a a_1 a_2 : Iota),
% 4.09/4.27 Or (Eq (aElement0 a) False)
% 4.09/4.27 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) False)
% 4.09/4.27 (Or (Eq (aElement0 a_1) False)
% 4.09/4.27 (Or (Eq (aRewritingSystem0 a_2) False) (Or (Eq (Eq a_1 a) True) (Eq (sdtmndtplgtdt0 a_1 a_2 a) True)))))
% 4.09/4.27 Clause #212 (by clausification #[211]): ∀ (a a_1 a_2 : Iota),
% 4.09/4.27 Or (Eq (aElement0 a) False)
% 4.09/4.27 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) False)
% 4.09/4.27 (Or (Eq (aElement0 a_1) False)
% 4.09/4.27 (Or (Eq (aRewritingSystem0 a_2) False) (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a) True) (Eq a_1 a)))))
% 4.09/4.27 Clause #213 (by superposition #[212, 47]): ∀ (a a_1 : Iota),
% 4.09/4.27 Or (Eq (sdtmndtasgtdt0 a a_1 xz) False)
% 4.09/4.27 (Or (Eq (aElement0 a) False)
% 4.09/4.27 (Or (Eq (aRewritingSystem0 a_1) False) (Or (Eq (sdtmndtplgtdt0 a a_1 xz) True) (Or (Eq a xz) (Eq False True)))))
% 4.09/4.27 Clause #214 (by superposition #[212, 51]): ∀ (a a_1 : Iota),
% 4.09/4.27 Or (Eq (sdtmndtasgtdt0 a a_1 xy) False)
% 4.09/4.27 (Or (Eq (aElement0 a) False)
% 4.09/4.27 (Or (Eq (aRewritingSystem0 a_1) False) (Or (Eq (sdtmndtplgtdt0 a a_1 xy) True) (Or (Eq a xy) (Eq False True)))))
% 4.09/4.27 Clause #235 (by clausification #[214]): ∀ (a a_1 : Iota),
% 4.09/4.27 Or (Eq (sdtmndtasgtdt0 a a_1 xy) False)
% 4.09/4.27 (Or (Eq (aElement0 a) False)
% 4.09/4.27 (Or (Eq (aRewritingSystem0 a_1) False) (Or (Eq (sdtmndtplgtdt0 a a_1 xy) True) (Eq a xy))))
% 4.09/4.27 Clause #236 (by superposition #[235, 23]): Or (Eq (aElement0 xx) False)
% 4.09/4.27 (Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xx xR xy) True) (Or (Eq xx xy) (Eq False True))))
% 4.09/4.27 Clause #238 (by clausification #[105]): ∀ (a a_1 : Iota),
% 4.09/4.27 Or (Eq (sdtmndtplgtdt0 a a_1 xz) True)
% 4.09/4.27 (Or (Eq (sdtmndtplgtdt0 a a_1 xy) False)
% 4.09/4.27 (Or (Eq (sdtmndtplgtdt0 xy a_1 xz) False) (Or (Eq (aElement0 a) False) (Eq (aRewritingSystem0 a_1) False))))
% 4.09/4.27 Clause #240 (by clausification #[236]): Or (Eq (aElement0 xx) False) (Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xx xR xy) True) (Eq xx xy)))
% 4.09/4.27 Clause #241 (by forward demodulation #[240, 71]): Or (Eq True False) (Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xx xR xy) True) (Eq xx xy)))
% 4.09/4.27 Clause #242 (by clausification #[241]): Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xx xR xy) True) (Eq xx xy))
% 4.09/4.27 Clause #243 (by forward demodulation #[242, 70]): Or (Eq True False) (Or (Eq (sdtmndtplgtdt0 xx xR xy) True) (Eq xx xy))
% 4.09/4.27 Clause #244 (by clausification #[243]): Or (Eq (sdtmndtplgtdt0 xx xR xy) True) (Eq xx xy)
% 4.09/4.27 Clause #245 (by superposition #[244, 238]): Or (Eq xx xy)
% 4.09/4.27 (Or (Eq (sdtmndtplgtdt0 xx xR xz) True)
% 4.09/4.27 (Or (Eq True False)
% 4.09/4.27 (Or (Eq (sdtmndtplgtdt0 xy xR xz) False) (Or (Eq (aElement0 xx) False) (Eq (aRewritingSystem0 xR) False)))))
% 4.09/4.27 Clause #246 (by clausification #[245]): Or (Eq xx xy)
% 4.09/4.27 (Or (Eq (sdtmndtplgtdt0 xx xR xz) True)
% 4.09/4.27 (Or (Eq (sdtmndtplgtdt0 xy xR xz) False) (Or (Eq (aElement0 xx) False) (Eq (aRewritingSystem0 xR) False))))
% 4.09/4.27 Clause #247 (by forward demodulation #[246, 71]): Or (Eq xx xy)
% 4.09/4.27 (Or (Eq (sdtmndtplgtdt0 xx xR xz) True)
% 4.09/4.27 (Or (Eq (sdtmndtplgtdt0 xy xR xz) False) (Or (Eq True False) (Eq (aRewritingSystem0 xR) False))))
% 4.09/4.28 Clause #248 (by clausification #[247]): Or (Eq xx xy)
% 4.09/4.28 (Or (Eq (sdtmndtplgtdt0 xx xR xz) True) (Or (Eq (sdtmndtplgtdt0 xy xR xz) False) (Eq (aRewritingSystem0 xR) False)))
% 4.09/4.28 Clause #249 (by forward demodulation #[248, 70]): Or (Eq xx xy) (Or (Eq (sdtmndtplgtdt0 xx xR xz) True) (Or (Eq (sdtmndtplgtdt0 xy xR xz) False) (Eq True False)))
% 4.09/4.28 Clause #250 (by clausification #[249]): Or (Eq xx xy) (Or (Eq (sdtmndtplgtdt0 xx xR xz) True) (Eq (sdtmndtplgtdt0 xy xR xz) False))
% 4.09/4.28 Clause #251 (by clausification #[213]): ∀ (a a_1 : Iota),
% 4.09/4.28 Or (Eq (sdtmndtasgtdt0 a a_1 xz) False)
% 4.09/4.28 (Or (Eq (aElement0 a) False)
% 4.09/4.28 (Or (Eq (aRewritingSystem0 a_1) False) (Or (Eq (sdtmndtplgtdt0 a a_1 xz) True) (Eq a xz))))
% 4.09/4.28 Clause #252 (by superposition #[251, 22]): Or (Eq (aElement0 xy) False)
% 4.09/4.28 (Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xy xR xz) True) (Or (Eq xy xz) (Eq False True))))
% 4.09/4.28 Clause #256 (by clausification #[252]): Or (Eq (aElement0 xy) False) (Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xy xR xz) True) (Eq xy xz)))
% 4.09/4.28 Clause #257 (by forward demodulation #[256, 51]): Or (Eq True False) (Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xy xR xz) True) (Eq xy xz)))
% 4.09/4.28 Clause #258 (by clausification #[257]): Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xy xR xz) True) (Eq xy xz))
% 4.09/4.28 Clause #259 (by forward demodulation #[258, 70]): Or (Eq True False) (Or (Eq (sdtmndtplgtdt0 xy xR xz) True) (Eq xy xz))
% 4.09/4.28 Clause #260 (by clausification #[259]): Or (Eq (sdtmndtplgtdt0 xy xR xz) True) (Eq xy xz)
% 4.09/4.28 Clause #261 (by superposition #[260, 250]): Or (Eq xy xz) (Or (Eq xx xy) (Or (Eq (sdtmndtplgtdt0 xx xR xz) True) (Eq True False)))
% 4.09/4.28 Clause #262 (by clausification #[261]): Or (Eq xy xz) (Or (Eq xx xy) (Eq (sdtmndtplgtdt0 xx xR xz) True))
% 4.09/4.28 Clause #263 (by superposition #[262, 107]): Or (Eq xy xz) (Or (Eq xx xy) (Or (Eq (sdtmndtasgtdt0 xx xR xz) True) (Eq True False)))
% 4.09/4.28 Clause #264 (by clausification #[263]): Or (Eq xy xz) (Or (Eq xx xy) (Eq (sdtmndtasgtdt0 xx xR xz) True))
% 4.09/4.28 Clause #265 (by superposition #[264, 21]): Or (Eq xy xz) (Or (Eq xx xy) (Eq True False))
% 4.09/4.28 Clause #267 (by clausification #[265]): Or (Eq xy xz) (Eq xx xy)
% 4.09/4.28 Clause #269 (by superposition #[267, 21]): Or (Eq xx xy) (Eq (sdtmndtasgtdt0 xx xR xy) False)
% 4.09/4.28 Clause #283 (by superposition #[269, 23]): Or (Eq xx xy) (Eq False True)
% 4.09/4.28 Clause #284 (by clausification #[283]): Eq xx xy
% 4.09/4.28 Clause #285 (by backward demodulation #[284, 22]): Eq (sdtmndtasgtdt0 xx xR xz) True
% 4.09/4.28 Clause #317 (by superposition #[285, 21]): Eq True False
% 4.09/4.28 Clause #320 (by clausification #[317]): False
% 4.09/4.28 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------