TSTP Solution File: COM022+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : COM022+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n002.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 18:38:10 EDT 2023
% Result : Theorem 37.70s 37.87s
% Output : Proof 37.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COM022+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % Command : duper %s
% 0.13/0.34 % Computer : n002.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 13:48:50 EDT 2023
% 0.13/0.34 % CPUTime :
% 37.70/37.87 SZS status Theorem for theBenchmark.p
% 37.70/37.87 SZS output start Proof for theBenchmark.p
% 37.70/37.87 Clause #7 (by assumption #[]): Eq
% 37.70/37.87 (∀ (W0 W1 W2 : Iota),
% 37.70/37.87 And (And (aElement0 W0) (aRewritingSystem0 W1)) (aElement0 W2) →
% 37.70/37.87 Iff (sdtmndtasgtdt0 W0 W1 W2) (Or (Eq W0 W2) (sdtmndtplgtdt0 W0 W1 W2)))
% 37.70/37.87 True
% 37.70/37.87 Clause #12 (by assumption #[]): Eq
% 37.70/37.87 (∀ (W0 W1 : Iota),
% 37.70/37.87 And (aElement0 W0) (aRewritingSystem0 W1) →
% 37.70/37.87 ∀ (W2 : Iota),
% 37.70/37.87 Iff (aNormalFormOfIn0 W2 W0 W1)
% 37.70/37.87 (And (And (aElement0 W2) (sdtmndtasgtdt0 W0 W1 W2)) (Not (Exists fun W3 => aReductOfIn0 W3 W2 W1))))
% 37.70/37.87 True
% 37.70/37.87 Clause #14 (by assumption #[]): Eq (aRewritingSystem0 xR) True
% 37.70/37.87 Clause #16 (by assumption #[]): Eq (And (And (aElement0 xa) (aElement0 xb)) (aElement0 xc)) True
% 37.70/37.87 Clause #18 (by assumption #[]): Eq
% 37.70/37.87 (Not
% 37.70/37.87 ((And (sdtmndtplgtdt0 xa xR xb) (sdtmndtplgtdt0 xa xR xc) →
% 37.70/37.87 Exists fun W0 =>
% 37.70/37.87 And (And (And (aElement0 W0) (aReductOfIn0 W0 xa xR)) (sdtmndtasgtdt0 W0 xR xb))
% 37.70/37.87 (Exists fun W1 =>
% 37.70/37.87 And (And (And (aElement0 W1) (aReductOfIn0 W1 xa xR)) (sdtmndtasgtdt0 W1 xR xc))
% 37.70/37.87 (Exists fun W2 =>
% 37.70/37.87 And (And (And (aElement0 W2) (sdtmndtasgtdt0 W0 xR W2)) (sdtmndtasgtdt0 W1 xR W2))
% 37.70/37.87 (Exists fun W3 =>
% 37.70/37.87 And (And (aNormalFormOfIn0 W3 W2 xR) (sdtmndtasgtdt0 xb xR W3)) (sdtmndtasgtdt0 xc xR W3))))) →
% 37.70/37.87 And (sdtmndtasgtdt0 xa xR xb) (sdtmndtasgtdt0 xa xR xc) →
% 37.70/37.87 Exists fun W0 => And (And (aElement0 W0) (sdtmndtasgtdt0 xb xR W0)) (sdtmndtasgtdt0 xc xR W0)))
% 37.70/37.87 True
% 37.70/37.87 Clause #43 (by clausification #[16]): Eq (aElement0 xc) True
% 37.70/37.87 Clause #44 (by clausification #[16]): Eq (And (aElement0 xa) (aElement0 xb)) True
% 37.70/37.87 Clause #46 (by clausification #[44]): Eq (aElement0 xb) True
% 37.70/37.87 Clause #47 (by clausification #[44]): Eq (aElement0 xa) True
% 37.70/37.87 Clause #102 (by clausification #[7]): ∀ (a : Iota),
% 37.70/37.87 Eq
% 37.70/37.87 (∀ (W1 W2 : Iota),
% 37.70/37.87 And (And (aElement0 a) (aRewritingSystem0 W1)) (aElement0 W2) →
% 37.70/37.87 Iff (sdtmndtasgtdt0 a W1 W2) (Or (Eq a W2) (sdtmndtplgtdt0 a W1 W2)))
% 37.70/37.87 True
% 37.70/37.87 Clause #103 (by clausification #[102]): ∀ (a a_1 : Iota),
% 37.70/37.87 Eq
% 37.70/37.87 (∀ (W2 : Iota),
% 37.70/37.87 And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 W2) →
% 37.70/37.87 Iff (sdtmndtasgtdt0 a a_1 W2) (Or (Eq a W2) (sdtmndtplgtdt0 a a_1 W2)))
% 37.70/37.87 True
% 37.70/37.87 Clause #104 (by clausification #[103]): ∀ (a a_1 a_2 : Iota),
% 37.70/37.87 Eq
% 37.70/37.87 (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2) →
% 37.70/37.87 Iff (sdtmndtasgtdt0 a a_1 a_2) (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2)))
% 37.70/37.87 True
% 37.70/37.87 Clause #105 (by clausification #[104]): ∀ (a a_1 a_2 : Iota),
% 37.70/37.87 Or (Eq (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2)) False)
% 37.70/37.87 (Eq (Iff (sdtmndtasgtdt0 a a_1 a_2) (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2))) True)
% 37.70/37.87 Clause #106 (by clausification #[105]): ∀ (a a_1 a_2 : Iota),
% 37.70/37.87 Or (Eq (Iff (sdtmndtasgtdt0 a a_1 a_2) (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2))) True)
% 37.70/37.87 (Or (Eq (And (aElement0 a) (aRewritingSystem0 a_1)) False) (Eq (aElement0 a_2) False))
% 37.70/37.87 Clause #107 (by clausification #[106]): ∀ (a a_1 a_2 : Iota),
% 37.70/37.87 Or (Eq (And (aElement0 a) (aRewritingSystem0 a_1)) False)
% 37.70/37.87 (Or (Eq (aElement0 a_2) False)
% 37.70/37.87 (Or (Eq (sdtmndtasgtdt0 a a_1 a_2) True) (Eq (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2)) False)))
% 37.70/37.87 Clause #108 (by clausification #[106]): ∀ (a a_1 a_2 : Iota),
% 37.70/37.87 Or (Eq (And (aElement0 a) (aRewritingSystem0 a_1)) False)
% 37.70/37.87 (Or (Eq (aElement0 a_2) False)
% 37.70/37.87 (Or (Eq (sdtmndtasgtdt0 a a_1 a_2) False) (Eq (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2)) True)))
% 37.70/37.87 Clause #109 (by clausification #[107]): ∀ (a a_1 a_2 : Iota),
% 37.70/37.87 Or (Eq (aElement0 a) False)
% 37.70/37.87 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) True)
% 37.70/37.87 (Or (Eq (Or (Eq a_1 a) (sdtmndtplgtdt0 a_1 a_2 a)) False)
% 37.70/37.87 (Or (Eq (aElement0 a_1) False) (Eq (aRewritingSystem0 a_2) False))))
% 37.70/37.87 Clause #110 (by clausification #[109]): ∀ (a a_1 a_2 : Iota),
% 37.70/37.87 Or (Eq (aElement0 a) False)
% 37.70/37.87 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) True)
% 37.70/37.87 (Or (Eq (aElement0 a_1) False) (Or (Eq (aRewritingSystem0 a_2) False) (Eq (sdtmndtplgtdt0 a_1 a_2 a) False))))
% 37.71/37.89 Clause #111 (by clausification #[109]): ∀ (a a_1 a_2 : Iota),
% 37.71/37.89 Or (Eq (aElement0 a) False)
% 37.71/37.89 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) True)
% 37.71/37.89 (Or (Eq (aElement0 a_1) False) (Or (Eq (aRewritingSystem0 a_2) False) (Eq (Eq a_1 a) False))))
% 37.71/37.89 Clause #112 (by superposition #[110, 43]): ∀ (a a_1 : Iota),
% 37.71/37.89 Or (Eq (sdtmndtasgtdt0 a a_1 xc) True)
% 37.71/37.89 (Or (Eq (aElement0 a) False)
% 37.71/37.89 (Or (Eq (aRewritingSystem0 a_1) False) (Or (Eq (sdtmndtplgtdt0 a a_1 xc) False) (Eq False True))))
% 37.71/37.89 Clause #187 (by clausification #[12]): ∀ (a : Iota),
% 37.71/37.89 Eq
% 37.71/37.89 (∀ (W1 : Iota),
% 37.71/37.89 And (aElement0 a) (aRewritingSystem0 W1) →
% 37.71/37.89 ∀ (W2 : Iota),
% 37.71/37.89 Iff (aNormalFormOfIn0 W2 a W1)
% 37.71/37.89 (And (And (aElement0 W2) (sdtmndtasgtdt0 a W1 W2)) (Not (Exists fun W3 => aReductOfIn0 W3 W2 W1))))
% 37.71/37.89 True
% 37.71/37.89 Clause #188 (by clausification #[187]): ∀ (a a_1 : Iota),
% 37.71/37.89 Eq
% 37.71/37.89 (And (aElement0 a) (aRewritingSystem0 a_1) →
% 37.71/37.89 ∀ (W2 : Iota),
% 37.71/37.89 Iff (aNormalFormOfIn0 W2 a a_1)
% 37.71/37.89 (And (And (aElement0 W2) (sdtmndtasgtdt0 a a_1 W2)) (Not (Exists fun W3 => aReductOfIn0 W3 W2 a_1))))
% 37.71/37.89 True
% 37.71/37.89 Clause #189 (by clausification #[188]): ∀ (a a_1 : Iota),
% 37.71/37.89 Or (Eq (And (aElement0 a) (aRewritingSystem0 a_1)) False)
% 37.71/37.89 (Eq
% 37.71/37.89 (∀ (W2 : Iota),
% 37.71/37.89 Iff (aNormalFormOfIn0 W2 a a_1)
% 37.71/37.89 (And (And (aElement0 W2) (sdtmndtasgtdt0 a a_1 W2)) (Not (Exists fun W3 => aReductOfIn0 W3 W2 a_1))))
% 37.71/37.89 True)
% 37.71/37.89 Clause #190 (by clausification #[189]): ∀ (a a_1 : Iota),
% 37.71/37.89 Or
% 37.71/37.89 (Eq
% 37.71/37.89 (∀ (W2 : Iota),
% 37.71/37.89 Iff (aNormalFormOfIn0 W2 a a_1)
% 37.71/37.89 (And (And (aElement0 W2) (sdtmndtasgtdt0 a a_1 W2)) (Not (Exists fun W3 => aReductOfIn0 W3 W2 a_1))))
% 37.71/37.89 True)
% 37.71/37.89 (Or (Eq (aElement0 a) False) (Eq (aRewritingSystem0 a_1) False))
% 37.71/37.89 Clause #191 (by clausification #[190]): ∀ (a a_1 a_2 : Iota),
% 37.71/37.89 Or (Eq (aElement0 a) False)
% 37.71/37.89 (Or (Eq (aRewritingSystem0 a_1) False)
% 37.71/37.89 (Eq
% 37.71/37.89 (Iff (aNormalFormOfIn0 a_2 a a_1)
% 37.71/37.89 (And (And (aElement0 a_2) (sdtmndtasgtdt0 a a_1 a_2)) (Not (Exists fun W3 => aReductOfIn0 W3 a_2 a_1))))
% 37.71/37.89 True))
% 37.71/37.89 Clause #193 (by clausification #[191]): ∀ (a a_1 a_2 : Iota),
% 37.71/37.89 Or (Eq (aElement0 a) False)
% 37.71/37.89 (Or (Eq (aRewritingSystem0 a_1) False)
% 37.71/37.89 (Or (Eq (aNormalFormOfIn0 a_2 a a_1) False)
% 37.71/37.89 (Eq (And (And (aElement0 a_2) (sdtmndtasgtdt0 a a_1 a_2)) (Not (Exists fun W3 => aReductOfIn0 W3 a_2 a_1)))
% 37.71/37.89 True)))
% 37.71/37.89 Clause #202 (by clausification #[112]): ∀ (a a_1 : Iota),
% 37.71/37.89 Or (Eq (sdtmndtasgtdt0 a a_1 xc) True)
% 37.71/37.89 (Or (Eq (aElement0 a) False) (Or (Eq (aRewritingSystem0 a_1) False) (Eq (sdtmndtplgtdt0 a a_1 xc) False)))
% 37.71/37.89 Clause #204 (by superposition #[202, 46]): ∀ (a : Iota),
% 37.71/37.89 Or (Eq (sdtmndtasgtdt0 xb a xc) True)
% 37.71/37.89 (Or (Eq (aRewritingSystem0 a) False) (Or (Eq (sdtmndtplgtdt0 xb a xc) False) (Eq False True)))
% 37.71/37.89 Clause #209 (by clausification #[204]): ∀ (a : Iota),
% 37.71/37.89 Or (Eq (sdtmndtasgtdt0 xb a xc) True) (Or (Eq (aRewritingSystem0 a) False) (Eq (sdtmndtplgtdt0 xb a xc) False))
% 37.71/37.89 Clause #210 (by superposition #[209, 14]): Or (Eq (sdtmndtasgtdt0 xb xR xc) True) (Or (Eq (sdtmndtplgtdt0 xb xR xc) False) (Eq False True))
% 37.71/37.89 Clause #223 (by clausification #[210]): Or (Eq (sdtmndtasgtdt0 xb xR xc) True) (Eq (sdtmndtplgtdt0 xb xR xc) False)
% 37.71/37.89 Clause #233 (by clausification #[18]): Eq
% 37.71/37.89 ((And (sdtmndtplgtdt0 xa xR xb) (sdtmndtplgtdt0 xa xR xc) →
% 37.71/37.89 Exists fun W0 =>
% 37.71/37.89 And (And (And (aElement0 W0) (aReductOfIn0 W0 xa xR)) (sdtmndtasgtdt0 W0 xR xb))
% 37.71/37.89 (Exists fun W1 =>
% 37.71/37.89 And (And (And (aElement0 W1) (aReductOfIn0 W1 xa xR)) (sdtmndtasgtdt0 W1 xR xc))
% 37.71/37.89 (Exists fun W2 =>
% 37.71/37.89 And (And (And (aElement0 W2) (sdtmndtasgtdt0 W0 xR W2)) (sdtmndtasgtdt0 W1 xR W2))
% 37.71/37.89 (Exists fun W3 =>
% 37.71/37.89 And (And (aNormalFormOfIn0 W3 W2 xR) (sdtmndtasgtdt0 xb xR W3)) (sdtmndtasgtdt0 xc xR W3))))) →
% 37.71/37.89 And (sdtmndtasgtdt0 xa xR xb) (sdtmndtasgtdt0 xa xR xc) →
% 37.71/37.89 Exists fun W0 => And (And (aElement0 W0) (sdtmndtasgtdt0 xb xR W0)) (sdtmndtasgtdt0 xc xR W0))
% 37.71/37.89 False
% 37.71/37.89 Clause #234 (by clausification #[233]): Eq
% 37.71/37.89 (And (sdtmndtplgtdt0 xa xR xb) (sdtmndtplgtdt0 xa xR xc) →
% 37.74/37.91 Exists fun W0 =>
% 37.74/37.91 And (And (And (aElement0 W0) (aReductOfIn0 W0 xa xR)) (sdtmndtasgtdt0 W0 xR xb))
% 37.74/37.91 (Exists fun W1 =>
% 37.74/37.91 And (And (And (aElement0 W1) (aReductOfIn0 W1 xa xR)) (sdtmndtasgtdt0 W1 xR xc))
% 37.74/37.91 (Exists fun W2 =>
% 37.74/37.91 And (And (And (aElement0 W2) (sdtmndtasgtdt0 W0 xR W2)) (sdtmndtasgtdt0 W1 xR W2))
% 37.74/37.91 (Exists fun W3 =>
% 37.74/37.91 And (And (aNormalFormOfIn0 W3 W2 xR) (sdtmndtasgtdt0 xb xR W3)) (sdtmndtasgtdt0 xc xR W3)))))
% 37.74/37.91 True
% 37.74/37.91 Clause #235 (by clausification #[233]): Eq
% 37.74/37.91 (And (sdtmndtasgtdt0 xa xR xb) (sdtmndtasgtdt0 xa xR xc) →
% 37.74/37.91 Exists fun W0 => And (And (aElement0 W0) (sdtmndtasgtdt0 xb xR W0)) (sdtmndtasgtdt0 xc xR W0))
% 37.74/37.91 False
% 37.74/37.91 Clause #236 (by clausification #[234]): Or (Eq (And (sdtmndtplgtdt0 xa xR xb) (sdtmndtplgtdt0 xa xR xc)) False)
% 37.74/37.91 (Eq
% 37.74/37.91 (Exists fun W0 =>
% 37.74/37.91 And (And (And (aElement0 W0) (aReductOfIn0 W0 xa xR)) (sdtmndtasgtdt0 W0 xR xb))
% 37.74/37.91 (Exists fun W1 =>
% 37.74/37.91 And (And (And (aElement0 W1) (aReductOfIn0 W1 xa xR)) (sdtmndtasgtdt0 W1 xR xc))
% 37.74/37.91 (Exists fun W2 =>
% 37.74/37.91 And (And (And (aElement0 W2) (sdtmndtasgtdt0 W0 xR W2)) (sdtmndtasgtdt0 W1 xR W2))
% 37.74/37.91 (Exists fun W3 =>
% 37.74/37.91 And (And (aNormalFormOfIn0 W3 W2 xR) (sdtmndtasgtdt0 xb xR W3)) (sdtmndtasgtdt0 xc xR W3)))))
% 37.74/37.91 True)
% 37.74/37.91 Clause #237 (by clausification #[236]): Or
% 37.74/37.91 (Eq
% 37.74/37.91 (Exists fun W0 =>
% 37.74/37.91 And (And (And (aElement0 W0) (aReductOfIn0 W0 xa xR)) (sdtmndtasgtdt0 W0 xR xb))
% 37.74/37.91 (Exists fun W1 =>
% 37.74/37.91 And (And (And (aElement0 W1) (aReductOfIn0 W1 xa xR)) (sdtmndtasgtdt0 W1 xR xc))
% 37.74/37.91 (Exists fun W2 =>
% 37.74/37.91 And (And (And (aElement0 W2) (sdtmndtasgtdt0 W0 xR W2)) (sdtmndtasgtdt0 W1 xR W2))
% 37.74/37.91 (Exists fun W3 =>
% 37.74/37.91 And (And (aNormalFormOfIn0 W3 W2 xR) (sdtmndtasgtdt0 xb xR W3)) (sdtmndtasgtdt0 xc xR W3)))))
% 37.74/37.91 True)
% 37.74/37.91 (Or (Eq (sdtmndtplgtdt0 xa xR xb) False) (Eq (sdtmndtplgtdt0 xa xR xc) False))
% 37.74/37.91 Clause #238 (by clausification #[237]): ∀ (a : Iota),
% 37.74/37.91 Or (Eq (sdtmndtplgtdt0 xa xR xb) False)
% 37.74/37.91 (Or (Eq (sdtmndtplgtdt0 xa xR xc) False)
% 37.74/37.91 (Eq
% 37.74/37.91 (And (And (And (aElement0 (skS.0 11 a)) (aReductOfIn0 (skS.0 11 a) xa xR)) (sdtmndtasgtdt0 (skS.0 11 a) xR xb))
% 37.74/37.91 (Exists fun W1 =>
% 37.74/37.91 And (And (And (aElement0 W1) (aReductOfIn0 W1 xa xR)) (sdtmndtasgtdt0 W1 xR xc))
% 37.74/37.91 (Exists fun W2 =>
% 37.74/37.91 And (And (And (aElement0 W2) (sdtmndtasgtdt0 (skS.0 11 a) xR W2)) (sdtmndtasgtdt0 W1 xR W2))
% 37.74/37.91 (Exists fun W3 =>
% 37.74/37.91 And (And (aNormalFormOfIn0 W3 W2 xR) (sdtmndtasgtdt0 xb xR W3)) (sdtmndtasgtdt0 xc xR W3)))))
% 37.74/37.91 True))
% 37.74/37.91 Clause #239 (by clausification #[238]): ∀ (a : Iota),
% 37.74/37.91 Or (Eq (sdtmndtplgtdt0 xa xR xb) False)
% 37.74/37.91 (Or (Eq (sdtmndtplgtdt0 xa xR xc) False)
% 37.74/37.91 (Eq
% 37.74/37.91 (Exists fun W1 =>
% 37.74/37.91 And (And (And (aElement0 W1) (aReductOfIn0 W1 xa xR)) (sdtmndtasgtdt0 W1 xR xc))
% 37.74/37.91 (Exists fun W2 =>
% 37.74/37.91 And (And (And (aElement0 W2) (sdtmndtasgtdt0 (skS.0 11 a) xR W2)) (sdtmndtasgtdt0 W1 xR W2))
% 37.74/37.91 (Exists fun W3 =>
% 37.74/37.91 And (And (aNormalFormOfIn0 W3 W2 xR) (sdtmndtasgtdt0 xb xR W3)) (sdtmndtasgtdt0 xc xR W3))))
% 37.74/37.91 True))
% 37.74/37.91 Clause #241 (by clausification #[239]): ∀ (a a_1 : Iota),
% 37.74/37.91 Or (Eq (sdtmndtplgtdt0 xa xR xb) False)
% 37.74/37.91 (Or (Eq (sdtmndtplgtdt0 xa xR xc) False)
% 37.74/37.91 (Eq
% 37.74/37.91 (And
% 37.74/37.91 (And (And (aElement0 (skS.0 12 a a_1)) (aReductOfIn0 (skS.0 12 a a_1) xa xR))
% 37.74/37.91 (sdtmndtasgtdt0 (skS.0 12 a a_1) xR xc))
% 37.74/37.91 (Exists fun W2 =>
% 37.74/37.91 And (And (And (aElement0 W2) (sdtmndtasgtdt0 (skS.0 11 a) xR W2)) (sdtmndtasgtdt0 (skS.0 12 a a_1) xR W2))
% 37.74/37.91 (Exists fun W3 =>
% 37.74/37.91 And (And (aNormalFormOfIn0 W3 W2 xR) (sdtmndtasgtdt0 xb xR W3)) (sdtmndtasgtdt0 xc xR W3))))
% 37.74/37.91 True))
% 37.74/37.91 Clause #242 (by clausification #[241]): ∀ (a a_1 : Iota),
% 37.74/37.91 Or (Eq (sdtmndtplgtdt0 xa xR xb) False)
% 37.74/37.91 (Or (Eq (sdtmndtplgtdt0 xa xR xc) False)
% 37.74/37.91 (Eq
% 37.74/37.91 (Exists fun W2 =>
% 37.74/37.91 And (And (And (aElement0 W2) (sdtmndtasgtdt0 (skS.0 11 a) xR W2)) (sdtmndtasgtdt0 (skS.0 12 a a_1) xR W2))
% 37.77/37.93 (Exists fun W3 =>
% 37.77/37.93 And (And (aNormalFormOfIn0 W3 W2 xR) (sdtmndtasgtdt0 xb xR W3)) (sdtmndtasgtdt0 xc xR W3)))
% 37.77/37.93 True))
% 37.77/37.93 Clause #244 (by clausification #[242]): ∀ (a a_1 a_2 : Iota),
% 37.77/37.93 Or (Eq (sdtmndtplgtdt0 xa xR xb) False)
% 37.77/37.93 (Or (Eq (sdtmndtplgtdt0 xa xR xc) False)
% 37.77/37.93 (Eq
% 37.77/37.93 (And
% 37.77/37.93 (And (And (aElement0 (skS.0 13 a a_1 a_2)) (sdtmndtasgtdt0 (skS.0 11 a) xR (skS.0 13 a a_1 a_2)))
% 37.77/37.93 (sdtmndtasgtdt0 (skS.0 12 a a_1) xR (skS.0 13 a a_1 a_2)))
% 37.77/37.93 (Exists fun W3 =>
% 37.77/37.93 And (And (aNormalFormOfIn0 W3 (skS.0 13 a a_1 a_2) xR) (sdtmndtasgtdt0 xb xR W3))
% 37.77/37.93 (sdtmndtasgtdt0 xc xR W3)))
% 37.77/37.93 True))
% 37.77/37.93 Clause #245 (by clausification #[244]): ∀ (a a_1 a_2 : Iota),
% 37.77/37.93 Or (Eq (sdtmndtplgtdt0 xa xR xb) False)
% 37.77/37.93 (Or (Eq (sdtmndtplgtdt0 xa xR xc) False)
% 37.77/37.93 (Eq
% 37.77/37.93 (Exists fun W3 =>
% 37.77/37.93 And (And (aNormalFormOfIn0 W3 (skS.0 13 a a_1 a_2) xR) (sdtmndtasgtdt0 xb xR W3)) (sdtmndtasgtdt0 xc xR W3))
% 37.77/37.93 True))
% 37.77/37.93 Clause #246 (by clausification #[244]): ∀ (a a_1 a_2 : Iota),
% 37.77/37.93 Or (Eq (sdtmndtplgtdt0 xa xR xb) False)
% 37.77/37.93 (Or (Eq (sdtmndtplgtdt0 xa xR xc) False)
% 37.77/37.93 (Eq
% 37.77/37.93 (And (And (aElement0 (skS.0 13 a a_1 a_2)) (sdtmndtasgtdt0 (skS.0 11 a) xR (skS.0 13 a a_1 a_2)))
% 37.77/37.93 (sdtmndtasgtdt0 (skS.0 12 a a_1) xR (skS.0 13 a a_1 a_2)))
% 37.77/37.93 True))
% 37.77/37.93 Clause #247 (by clausification #[245]): ∀ (a a_1 a_2 a_3 : Iota),
% 37.77/37.93 Or (Eq (sdtmndtplgtdt0 xa xR xb) False)
% 37.77/37.93 (Or (Eq (sdtmndtplgtdt0 xa xR xc) False)
% 37.77/37.93 (Eq
% 37.77/37.93 (And
% 37.77/37.93 (And (aNormalFormOfIn0 (skS.0 14 a a_1 a_2 a_3) (skS.0 13 a a_1 a_2) xR)
% 37.77/37.93 (sdtmndtasgtdt0 xb xR (skS.0 14 a a_1 a_2 a_3)))
% 37.77/37.93 (sdtmndtasgtdt0 xc xR (skS.0 14 a a_1 a_2 a_3)))
% 37.77/37.93 True))
% 37.77/37.93 Clause #248 (by clausification #[247]): ∀ (a a_1 a_2 a_3 : Iota),
% 37.77/37.93 Or (Eq (sdtmndtplgtdt0 xa xR xb) False)
% 37.77/37.93 (Or (Eq (sdtmndtplgtdt0 xa xR xc) False) (Eq (sdtmndtasgtdt0 xc xR (skS.0 14 a a_1 a_2 a_3)) True))
% 37.77/37.93 Clause #249 (by clausification #[247]): ∀ (a a_1 a_2 a_3 : Iota),
% 37.77/37.93 Or (Eq (sdtmndtplgtdt0 xa xR xb) False)
% 37.77/37.93 (Or (Eq (sdtmndtplgtdt0 xa xR xc) False)
% 37.77/37.93 (Eq
% 37.77/37.93 (And (aNormalFormOfIn0 (skS.0 14 a a_1 a_2 a_3) (skS.0 13 a a_1 a_2) xR)
% 37.77/37.93 (sdtmndtasgtdt0 xb xR (skS.0 14 a a_1 a_2 a_3)))
% 37.77/37.93 True))
% 37.77/37.93 Clause #265 (by clausification #[235]): Eq (And (sdtmndtasgtdt0 xa xR xb) (sdtmndtasgtdt0 xa xR xc)) True
% 37.77/37.93 Clause #266 (by clausification #[235]): Eq (Exists fun W0 => And (And (aElement0 W0) (sdtmndtasgtdt0 xb xR W0)) (sdtmndtasgtdt0 xc xR W0)) False
% 37.77/37.93 Clause #267 (by clausification #[265]): Eq (sdtmndtasgtdt0 xa xR xc) True
% 37.77/37.93 Clause #268 (by clausification #[265]): Eq (sdtmndtasgtdt0 xa xR xb) True
% 37.77/37.93 Clause #273 (by clausification #[266]): ∀ (a : Iota), Eq (And (And (aElement0 a) (sdtmndtasgtdt0 xb xR a)) (sdtmndtasgtdt0 xc xR a)) False
% 37.77/37.93 Clause #274 (by clausification #[273]): ∀ (a : Iota), Or (Eq (And (aElement0 a) (sdtmndtasgtdt0 xb xR a)) False) (Eq (sdtmndtasgtdt0 xc xR a) False)
% 37.77/37.93 Clause #275 (by clausification #[274]): ∀ (a : Iota), Or (Eq (sdtmndtasgtdt0 xc xR a) False) (Or (Eq (aElement0 a) False) (Eq (sdtmndtasgtdt0 xb xR a) False))
% 37.77/37.93 Clause #334 (by clausification #[111]): ∀ (a a_1 a_2 : Iota),
% 37.77/37.93 Or (Eq (aElement0 a) False)
% 37.77/37.93 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) True)
% 37.77/37.93 (Or (Eq (aElement0 a_1) False) (Or (Eq (aRewritingSystem0 a_2) False) (Ne a_1 a))))
% 37.77/37.93 Clause #335 (by destructive equality resolution #[334]): ∀ (a a_1 : Iota),
% 37.77/37.93 Or (Eq (aElement0 a) False)
% 37.77/37.93 (Or (Eq (sdtmndtasgtdt0 a a_1 a) True) (Or (Eq (aElement0 a) False) (Eq (aRewritingSystem0 a_1) False)))
% 37.77/37.93 Clause #336 (by eliminate duplicate literals #[335]): ∀ (a a_1 : Iota), Or (Eq (aElement0 a) False) (Or (Eq (sdtmndtasgtdt0 a a_1 a) True) (Eq (aRewritingSystem0 a_1) False))
% 37.77/37.93 Clause #337 (by superposition #[336, 43]): ∀ (a : Iota), Or (Eq (sdtmndtasgtdt0 xc a xc) True) (Or (Eq (aRewritingSystem0 a) False) (Eq False True))
% 37.77/37.93 Clause #338 (by superposition #[336, 46]): ∀ (a : Iota), Or (Eq (sdtmndtasgtdt0 xb a xb) True) (Or (Eq (aRewritingSystem0 a) False) (Eq False True))
% 37.77/37.95 Clause #349 (by clausification #[338]): ∀ (a : Iota), Or (Eq (sdtmndtasgtdt0 xb a xb) True) (Eq (aRewritingSystem0 a) False)
% 37.77/37.95 Clause #350 (by superposition #[349, 14]): Or (Eq (sdtmndtasgtdt0 xb xR xb) True) (Eq False True)
% 37.77/37.95 Clause #351 (by clausification #[350]): Eq (sdtmndtasgtdt0 xb xR xb) True
% 37.77/37.95 Clause #354 (by clausification #[337]): ∀ (a : Iota), Or (Eq (sdtmndtasgtdt0 xc a xc) True) (Eq (aRewritingSystem0 a) False)
% 37.77/37.95 Clause #355 (by superposition #[354, 14]): Or (Eq (sdtmndtasgtdt0 xc xR xc) True) (Eq False True)
% 37.77/37.95 Clause #356 (by clausification #[355]): Eq (sdtmndtasgtdt0 xc xR xc) True
% 37.77/37.95 Clause #359 (by superposition #[356, 275]): Or (Eq True False) (Or (Eq (aElement0 xc) False) (Eq (sdtmndtasgtdt0 xb xR xc) False))
% 37.77/37.95 Clause #364 (by clausification #[359]): Or (Eq (aElement0 xc) False) (Eq (sdtmndtasgtdt0 xb xR xc) False)
% 37.77/37.95 Clause #365 (by forward demodulation #[364, 43]): Or (Eq True False) (Eq (sdtmndtasgtdt0 xb xR xc) False)
% 37.77/37.95 Clause #366 (by clausification #[365]): Eq (sdtmndtasgtdt0 xb xR xc) False
% 37.77/37.95 Clause #367 (by backward demodulation #[366, 223]): Or (Eq False True) (Eq (sdtmndtplgtdt0 xb xR xc) False)
% 37.77/37.95 Clause #368 (by clausification #[367]): Eq (sdtmndtplgtdt0 xb xR xc) False
% 37.77/37.95 Clause #418 (by clausification #[108]): ∀ (a a_1 a_2 : Iota),
% 37.77/37.95 Or (Eq (aElement0 a) False)
% 37.77/37.95 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) False)
% 37.77/37.95 (Or (Eq (Or (Eq a_1 a) (sdtmndtplgtdt0 a_1 a_2 a)) True)
% 37.77/37.95 (Or (Eq (aElement0 a_1) False) (Eq (aRewritingSystem0 a_2) False))))
% 37.77/37.95 Clause #419 (by clausification #[418]): ∀ (a a_1 a_2 : Iota),
% 37.77/37.95 Or (Eq (aElement0 a) False)
% 37.77/37.95 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) False)
% 37.77/37.95 (Or (Eq (aElement0 a_1) False)
% 37.77/37.95 (Or (Eq (aRewritingSystem0 a_2) False) (Or (Eq (Eq a_1 a) True) (Eq (sdtmndtplgtdt0 a_1 a_2 a) True)))))
% 37.77/37.95 Clause #420 (by clausification #[419]): ∀ (a a_1 a_2 : Iota),
% 37.77/37.95 Or (Eq (aElement0 a) False)
% 37.77/37.95 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) False)
% 37.77/37.95 (Or (Eq (aElement0 a_1) False)
% 37.77/37.95 (Or (Eq (aRewritingSystem0 a_2) False) (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a) True) (Eq a_1 a)))))
% 37.77/37.95 Clause #421 (by superposition #[420, 43]): ∀ (a a_1 : Iota),
% 37.77/37.95 Or (Eq (sdtmndtasgtdt0 a a_1 xc) False)
% 37.77/37.95 (Or (Eq (aElement0 a) False)
% 37.77/37.95 (Or (Eq (aRewritingSystem0 a_1) False) (Or (Eq (sdtmndtplgtdt0 a a_1 xc) True) (Or (Eq a xc) (Eq False True)))))
% 37.77/37.95 Clause #422 (by superposition #[420, 46]): ∀ (a a_1 : Iota),
% 37.77/37.95 Or (Eq (sdtmndtasgtdt0 a a_1 xb) False)
% 37.77/37.95 (Or (Eq (aElement0 a) False)
% 37.77/37.95 (Or (Eq (aRewritingSystem0 a_1) False) (Or (Eq (sdtmndtplgtdt0 a a_1 xb) True) (Or (Eq a xb) (Eq False True)))))
% 37.77/37.95 Clause #428 (by clausification #[422]): ∀ (a a_1 : Iota),
% 37.77/37.95 Or (Eq (sdtmndtasgtdt0 a a_1 xb) False)
% 37.77/37.95 (Or (Eq (aElement0 a) False)
% 37.77/37.95 (Or (Eq (aRewritingSystem0 a_1) False) (Or (Eq (sdtmndtplgtdt0 a a_1 xb) True) (Eq a xb))))
% 37.77/37.95 Clause #429 (by superposition #[428, 268]): Or (Eq (aElement0 xa) False)
% 37.77/37.95 (Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xa xR xb) True) (Or (Eq xa xb) (Eq False True))))
% 37.77/37.95 Clause #435 (by clausification #[429]): Or (Eq (aElement0 xa) False) (Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xa xR xb) True) (Eq xa xb)))
% 37.77/37.95 Clause #436 (by forward demodulation #[435, 47]): Or (Eq True False) (Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xa xR xb) True) (Eq xa xb)))
% 37.77/37.95 Clause #437 (by clausification #[436]): Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xa xR xb) True) (Eq xa xb))
% 37.77/37.95 Clause #438 (by forward demodulation #[437, 14]): Or (Eq True False) (Or (Eq (sdtmndtplgtdt0 xa xR xb) True) (Eq xa xb))
% 37.77/37.95 Clause #439 (by clausification #[438]): Or (Eq (sdtmndtplgtdt0 xa xR xb) True) (Eq xa xb)
% 37.77/37.95 Clause #440 (by superposition #[439, 248]): ∀ (a a_1 a_2 a_3 : Iota),
% 37.77/37.95 Or (Eq xa xb)
% 37.77/37.95 (Or (Eq True False)
% 37.77/37.95 (Or (Eq (sdtmndtplgtdt0 xa xR xc) False) (Eq (sdtmndtasgtdt0 xc xR (skS.0 14 a a_1 a_2 a_3)) True)))
% 37.77/37.95 Clause #443 (by clausification #[421]): ∀ (a a_1 : Iota),
% 37.77/37.95 Or (Eq (sdtmndtasgtdt0 a a_1 xc) False)
% 37.77/37.95 (Or (Eq (aElement0 a) False)
% 37.77/37.95 (Or (Eq (aRewritingSystem0 a_1) False) (Or (Eq (sdtmndtplgtdt0 a a_1 xc) True) (Eq a xc))))
% 37.77/37.98 Clause #444 (by superposition #[443, 267]): Or (Eq (aElement0 xa) False)
% 37.77/37.98 (Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xa xR xc) True) (Or (Eq xa xc) (Eq False True))))
% 37.77/37.98 Clause #447 (by clausification #[444]): Or (Eq (aElement0 xa) False) (Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xa xR xc) True) (Eq xa xc)))
% 37.77/37.98 Clause #448 (by forward demodulation #[447, 47]): Or (Eq True False) (Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xa xR xc) True) (Eq xa xc)))
% 37.77/37.98 Clause #449 (by clausification #[448]): Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xa xR xc) True) (Eq xa xc))
% 37.77/37.98 Clause #450 (by forward demodulation #[449, 14]): Or (Eq True False) (Or (Eq (sdtmndtplgtdt0 xa xR xc) True) (Eq xa xc))
% 37.77/37.98 Clause #451 (by clausification #[450]): Or (Eq (sdtmndtplgtdt0 xa xR xc) True) (Eq xa xc)
% 37.77/37.98 Clause #584 (by clausification #[193]): ∀ (a a_1 a_2 : Iota),
% 37.77/37.98 Or (Eq (aElement0 a) False)
% 37.77/37.98 (Or (Eq (aRewritingSystem0 a_1) False)
% 37.77/37.98 (Or (Eq (aNormalFormOfIn0 a_2 a a_1) False) (Eq (And (aElement0 a_2) (sdtmndtasgtdt0 a a_1 a_2)) True)))
% 37.77/37.98 Clause #608 (by clausification #[584]): ∀ (a a_1 a_2 : Iota),
% 37.77/37.98 Or (Eq (aElement0 a) False)
% 37.77/37.98 (Or (Eq (aRewritingSystem0 a_1) False) (Or (Eq (aNormalFormOfIn0 a_2 a a_1) False) (Eq (aElement0 a_2) True)))
% 37.77/37.98 Clause #790 (by clausification #[246]): ∀ (a a_1 a_2 : Iota),
% 37.77/37.98 Or (Eq (sdtmndtplgtdt0 xa xR xb) False)
% 37.77/37.98 (Or (Eq (sdtmndtplgtdt0 xa xR xc) False)
% 37.77/37.98 (Eq (And (aElement0 (skS.0 13 a a_1 a_2)) (sdtmndtasgtdt0 (skS.0 11 a) xR (skS.0 13 a a_1 a_2))) True))
% 37.77/37.98 Clause #800 (by clausification #[249]): ∀ (a a_1 a_2 a_3 : Iota),
% 37.77/37.98 Or (Eq (sdtmndtplgtdt0 xa xR xb) False)
% 37.77/37.98 (Or (Eq (sdtmndtplgtdt0 xa xR xc) False) (Eq (sdtmndtasgtdt0 xb xR (skS.0 14 a a_1 a_2 a_3)) True))
% 37.77/37.98 Clause #801 (by clausification #[249]): ∀ (a a_1 a_2 a_3 : Iota),
% 37.77/37.98 Or (Eq (sdtmndtplgtdt0 xa xR xb) False)
% 37.77/37.98 (Or (Eq (sdtmndtplgtdt0 xa xR xc) False)
% 37.77/37.98 (Eq (aNormalFormOfIn0 (skS.0 14 a a_1 a_2 a_3) (skS.0 13 a a_1 a_2) xR) True))
% 37.77/37.98 Clause #802 (by superposition #[800, 439]): ∀ (a a_1 a_2 a_3 : Iota),
% 37.77/37.98 Or (Eq (sdtmndtplgtdt0 xa xR xc) False)
% 37.77/37.98 (Or (Eq (sdtmndtasgtdt0 xb xR (skS.0 14 a a_1 a_2 a_3)) True) (Or (Eq False True) (Eq xa xb)))
% 37.77/37.98 Clause #869 (by clausification #[440]): ∀ (a a_1 a_2 a_3 : Iota),
% 37.77/37.98 Or (Eq xa xb) (Or (Eq (sdtmndtplgtdt0 xa xR xc) False) (Eq (sdtmndtasgtdt0 xc xR (skS.0 14 a a_1 a_2 a_3)) True))
% 37.77/37.98 Clause #870 (by superposition #[869, 451]): ∀ (a a_1 a_2 a_3 : Iota),
% 37.77/37.98 Or (Eq xa xb) (Or (Eq (sdtmndtasgtdt0 xc xR (skS.0 14 a a_1 a_2 a_3)) True) (Or (Eq False True) (Eq xa xc)))
% 37.77/37.98 Clause #871 (by clausification #[870]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq xa xb) (Or (Eq (sdtmndtasgtdt0 xc xR (skS.0 14 a a_1 a_2 a_3)) True) (Eq xa xc))
% 37.77/37.98 Clause #873 (by superposition #[871, 275]): ∀ (a a_1 a_2 a_3 : Iota),
% 37.77/37.98 Or (Eq xa xb)
% 37.77/37.98 (Or (Eq xa xc)
% 37.77/37.98 (Or (Eq True False)
% 37.77/37.98 (Or (Eq (aElement0 (skS.0 14 a a_1 a_2 a_3)) False)
% 37.77/37.98 (Eq (sdtmndtasgtdt0 xb xR (skS.0 14 a a_1 a_2 a_3)) False))))
% 37.77/37.98 Clause #880 (by clausification #[802]): ∀ (a a_1 a_2 a_3 : Iota),
% 37.77/37.98 Or (Eq (sdtmndtplgtdt0 xa xR xc) False) (Or (Eq (sdtmndtasgtdt0 xb xR (skS.0 14 a a_1 a_2 a_3)) True) (Eq xa xb))
% 37.77/37.98 Clause #881 (by superposition #[880, 451]): ∀ (a a_1 a_2 a_3 : Iota),
% 37.77/37.98 Or (Eq (sdtmndtasgtdt0 xb xR (skS.0 14 a a_1 a_2 a_3)) True) (Or (Eq xa xb) (Or (Eq False True) (Eq xa xc)))
% 37.77/37.98 Clause #882 (by clausification #[881]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (sdtmndtasgtdt0 xb xR (skS.0 14 a a_1 a_2 a_3)) True) (Or (Eq xa xb) (Eq xa xc))
% 37.77/37.98 Clause #3557 (by clausification #[790]): ∀ (a a_1 a_2 : Iota),
% 37.77/37.98 Or (Eq (sdtmndtplgtdt0 xa xR xb) False)
% 37.77/37.98 (Or (Eq (sdtmndtplgtdt0 xa xR xc) False) (Eq (aElement0 (skS.0 13 a a_1 a_2)) True))
% 37.77/37.98 Clause #3559 (by superposition #[3557, 439]): ∀ (a a_1 a_2 : Iota),
% 37.77/37.98 Or (Eq (sdtmndtplgtdt0 xa xR xc) False)
% 37.77/37.98 (Or (Eq (aElement0 (skS.0 13 a a_1 a_2)) True) (Or (Eq False True) (Eq xa xb)))
% 37.77/37.98 Clause #3560 (by clausification #[3559]): ∀ (a a_1 a_2 : Iota), Or (Eq (sdtmndtplgtdt0 xa xR xc) False) (Or (Eq (aElement0 (skS.0 13 a a_1 a_2)) True) (Eq xa xb))
% 37.77/38.01 Clause #3561 (by superposition #[3560, 451]): ∀ (a a_1 a_2 : Iota), Or (Eq (aElement0 (skS.0 13 a a_1 a_2)) True) (Or (Eq xa xb) (Or (Eq False True) (Eq xa xc)))
% 37.77/38.01 Clause #3562 (by clausification #[3561]): ∀ (a a_1 a_2 : Iota), Or (Eq (aElement0 (skS.0 13 a a_1 a_2)) True) (Or (Eq xa xb) (Eq xa xc))
% 37.77/38.01 Clause #3595 (by superposition #[3562, 608]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 37.77/38.01 Or (Eq xa xb)
% 37.77/38.01 (Or (Eq xa xc)
% 37.77/38.01 (Or (Eq True False)
% 37.77/38.01 (Or (Eq (aRewritingSystem0 a) False)
% 37.77/38.01 (Or (Eq (aNormalFormOfIn0 a_1 (skS.0 13 a_2 a_3 a_4) a) False) (Eq (aElement0 a_1) True)))))
% 37.77/38.01 Clause #3627 (by clausification #[3595]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 37.77/38.01 Or (Eq xa xb)
% 37.77/38.01 (Or (Eq xa xc)
% 37.77/38.01 (Or (Eq (aRewritingSystem0 a) False)
% 37.77/38.01 (Or (Eq (aNormalFormOfIn0 a_1 (skS.0 13 a_2 a_3 a_4) a) False) (Eq (aElement0 a_1) True))))
% 37.77/38.01 Clause #3628 (by superposition #[3627, 14]): ∀ (a a_1 a_2 a_3 : Iota),
% 37.77/38.01 Or (Eq xa xb)
% 37.77/38.01 (Or (Eq xa xc)
% 37.77/38.01 (Or (Eq (aNormalFormOfIn0 a (skS.0 13 a_1 a_2 a_3) xR) False) (Or (Eq (aElement0 a) True) (Eq False True))))
% 37.77/38.01 Clause #3629 (by clausification #[3628]): ∀ (a a_1 a_2 a_3 : Iota),
% 37.77/38.01 Or (Eq xa xb) (Or (Eq xa xc) (Or (Eq (aNormalFormOfIn0 a (skS.0 13 a_1 a_2 a_3) xR) False) (Eq (aElement0 a) True)))
% 37.77/38.01 Clause #3630 (by superposition #[801, 439]): ∀ (a a_1 a_2 a_3 : Iota),
% 37.77/38.01 Or (Eq (sdtmndtplgtdt0 xa xR xc) False)
% 37.77/38.01 (Or (Eq (aNormalFormOfIn0 (skS.0 14 a a_1 a_2 a_3) (skS.0 13 a a_1 a_2) xR) True) (Or (Eq False True) (Eq xa xb)))
% 37.77/38.01 Clause #3656 (by clausification #[3630]): ∀ (a a_1 a_2 a_3 : Iota),
% 37.77/38.01 Or (Eq (sdtmndtplgtdt0 xa xR xc) False)
% 37.77/38.01 (Or (Eq (aNormalFormOfIn0 (skS.0 14 a a_1 a_2 a_3) (skS.0 13 a a_1 a_2) xR) True) (Eq xa xb))
% 37.77/38.01 Clause #3657 (by superposition #[3656, 451]): ∀ (a a_1 a_2 a_3 : Iota),
% 37.77/38.01 Or (Eq (aNormalFormOfIn0 (skS.0 14 a a_1 a_2 a_3) (skS.0 13 a a_1 a_2) xR) True)
% 37.77/38.01 (Or (Eq xa xb) (Or (Eq False True) (Eq xa xc)))
% 37.77/38.01 Clause #3658 (by clausification #[3657]): ∀ (a a_1 a_2 a_3 : Iota),
% 37.77/38.01 Or (Eq (aNormalFormOfIn0 (skS.0 14 a a_1 a_2 a_3) (skS.0 13 a a_1 a_2) xR) True) (Or (Eq xa xb) (Eq xa xc))
% 37.77/38.01 Clause #3659 (by superposition #[3658, 3629]): ∀ (a a_1 a_2 a_3 : Iota),
% 37.77/38.01 Or (Eq xa xb)
% 37.77/38.01 (Or (Eq xa xc) (Or (Eq xa xb) (Or (Eq xa xc) (Or (Eq True False) (Eq (aElement0 (skS.0 14 a a_1 a_2 a_3)) True)))))
% 37.77/38.01 Clause #3661 (by clausification #[3659]): ∀ (a a_1 a_2 a_3 : Iota),
% 37.77/38.01 Or (Eq xa xb) (Or (Eq xa xc) (Or (Eq xa xb) (Or (Eq xa xc) (Eq (aElement0 (skS.0 14 a a_1 a_2 a_3)) True))))
% 37.77/38.01 Clause #3662 (by eliminate duplicate literals #[3661]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq xa xb) (Or (Eq xa xc) (Eq (aElement0 (skS.0 14 a a_1 a_2 a_3)) True))
% 37.77/38.01 Clause #3788 (by clausification #[873]): ∀ (a a_1 a_2 a_3 : Iota),
% 37.77/38.01 Or (Eq xa xb)
% 37.77/38.01 (Or (Eq xa xc)
% 37.77/38.01 (Or (Eq (aElement0 (skS.0 14 a a_1 a_2 a_3)) False) (Eq (sdtmndtasgtdt0 xb xR (skS.0 14 a a_1 a_2 a_3)) False)))
% 37.77/38.01 Clause #3789 (by superposition #[3788, 3662]): ∀ (a a_1 a_2 a_3 : Iota),
% 37.77/38.01 Or (Eq xa xb)
% 37.77/38.01 (Or (Eq xa xc)
% 37.77/38.01 (Or (Eq (sdtmndtasgtdt0 xb xR (skS.0 14 a a_1 a_2 a_3)) False) (Or (Eq xa xb) (Or (Eq xa xc) (Eq False True)))))
% 37.77/38.01 Clause #3790 (by clausification #[3789]): ∀ (a a_1 a_2 a_3 : Iota),
% 37.77/38.01 Or (Eq xa xb)
% 37.77/38.01 (Or (Eq xa xc) (Or (Eq (sdtmndtasgtdt0 xb xR (skS.0 14 a a_1 a_2 a_3)) False) (Or (Eq xa xb) (Eq xa xc))))
% 37.77/38.01 Clause #3791 (by eliminate duplicate literals #[3790]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq xa xb) (Or (Eq xa xc) (Eq (sdtmndtasgtdt0 xb xR (skS.0 14 a a_1 a_2 a_3)) False))
% 37.77/38.01 Clause #3792 (by superposition #[3791, 882]): Or (Eq xa xb) (Or (Eq xa xc) (Or (Eq False True) (Or (Eq xa xb) (Eq xa xc))))
% 37.77/38.01 Clause #3793 (by clausification #[3792]): Or (Eq xa xb) (Or (Eq xa xc) (Or (Eq xa xb) (Eq xa xc)))
% 37.77/38.01 Clause #3794 (by eliminate duplicate literals #[3793]): Or (Eq xa xb) (Eq xa xc)
% 37.77/38.01 Clause #3804 (by superposition #[3794, 368]): Or (Eq xa xc) (Eq (sdtmndtplgtdt0 xa xR xc) False)
% 37.77/38.01 Clause #3903 (by superposition #[3804, 451]): Or (Eq xa xc) (Or (Eq False True) (Eq xa xc))
% 37.77/38.01 Clause #3907 (by clausification #[3903]): Or (Eq xa xc) (Eq xa xc)
% 37.77/38.01 Clause #3908 (by eliminate duplicate literals #[3907]): Eq xa xc
% 37.86/38.07 Clause #3917 (by backward demodulation #[3908, 275]): ∀ (a : Iota), Or (Eq (sdtmndtasgtdt0 xa xR a) False) (Or (Eq (aElement0 a) False) (Eq (sdtmndtasgtdt0 xb xR a) False))
% 37.86/38.07 Clause #4209 (by superposition #[3917, 268]): Or (Eq (aElement0 xb) False) (Or (Eq (sdtmndtasgtdt0 xb xR xb) False) (Eq False True))
% 37.86/38.07 Clause #4214 (by clausification #[4209]): Or (Eq (aElement0 xb) False) (Eq (sdtmndtasgtdt0 xb xR xb) False)
% 37.86/38.07 Clause #4215 (by forward demodulation #[4214, 46]): Or (Eq True False) (Eq (sdtmndtasgtdt0 xb xR xb) False)
% 37.86/38.07 Clause #4216 (by clausification #[4215]): Eq (sdtmndtasgtdt0 xb xR xb) False
% 37.86/38.07 Clause #4217 (by superposition #[4216, 351]): Eq False True
% 37.86/38.07 Clause #4218 (by clausification #[4217]): False
% 37.86/38.07 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------