%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : COM022+1 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n005.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 : Fri Oct 3 07:45:48 PM UTC 2025 % Result : Theorem 34.83s 35.06s % Output : Proof 35.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : COM022+1 : TPTP v9.2.0. Released v4.0.0. % 0.06/0.13 % Command : duper %s % 0.13/0.34 % Computer : n005.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 Oct 2 16:08:38 EDT 2025 % 0.13/0.34 % CPUTime : % 34.83/35.06 SZS status Theorem for theBenchmark.p % 34.83/35.06 SZS output start Proof for theBenchmark.p % 34.83/35.06 Clause #7 (by assumption #[]): Eq % 34.83/35.06 (∀ (W0 W1 W2 : Iota), % 34.83/35.06 And (And (aElement0 W0) (aRewritingSystem0 W1)) (aElement0 W2) → % 34.83/35.06 Iff (sdtmndtasgtdt0 W0 W1 W2) (Or (Eq W0 W2) (sdtmndtplgtdt0 W0 W1 W2))) % 34.83/35.06 True % 34.83/35.06 Clause #12 (by assumption #[]): Eq % 34.83/35.06 (∀ (W0 W1 : Iota), % 34.83/35.06 And (aElement0 W0) (aRewritingSystem0 W1) → % 34.83/35.06 ∀ (W2 : Iota), % 34.83/35.06 Iff (aNormalFormOfIn0 W2 W0 W1) % 34.83/35.06 (And (And (aElement0 W2) (sdtmndtasgtdt0 W0 W1 W2)) (Not (Exists fun W3 => aReductOfIn0 W3 W2 W1)))) % 34.83/35.06 True % 34.83/35.06 Clause #14 (by assumption #[]): Eq (aRewritingSystem0 xR) True % 34.83/35.06 Clause #16 (by assumption #[]): Eq (And (And (aElement0 xa) (aElement0 xb)) (aElement0 xc)) True % 34.83/35.06 Clause #18 (by assumption #[]): Eq % 34.83/35.06 (Not % 34.83/35.06 ((And (sdtmndtplgtdt0 xa xR xb) (sdtmndtplgtdt0 xa xR xc) → % 34.83/35.06 Exists fun W0 => % 34.83/35.06 And (And (And (aElement0 W0) (aReductOfIn0 W0 xa xR)) (sdtmndtasgtdt0 W0 xR xb)) % 34.83/35.06 (Exists fun W1 => % 34.83/35.06 And (And (And (aElement0 W1) (aReductOfIn0 W1 xa xR)) (sdtmndtasgtdt0 W1 xR xc)) % 34.83/35.06 (Exists fun W2 => % 34.83/35.06 And (And (And (aElement0 W2) (sdtmndtasgtdt0 W0 xR W2)) (sdtmndtasgtdt0 W1 xR W2)) % 34.83/35.06 (Exists fun W3 => % 34.83/35.06 And (And (aNormalFormOfIn0 W3 W2 xR) (sdtmndtasgtdt0 xb xR W3)) (sdtmndtasgtdt0 xc xR W3))))) → % 34.83/35.06 And (sdtmndtasgtdt0 xa xR xb) (sdtmndtasgtdt0 xa xR xc) → % 34.83/35.06 Exists fun W0 => And (And (aElement0 W0) (sdtmndtasgtdt0 xb xR W0)) (sdtmndtasgtdt0 xc xR W0))) % 34.83/35.06 True % 34.83/35.06 Clause #43 (by clausification #[16]): Eq (aElement0 xc) True % 34.83/35.06 Clause #44 (by clausification #[16]): Eq (And (aElement0 xa) (aElement0 xb)) True % 34.83/35.06 Clause #46 (by clausification #[44]): Eq (aElement0 xb) True % 34.83/35.06 Clause #47 (by clausification #[44]): Eq (aElement0 xa) True % 34.83/35.06 Clause #102 (by clausification #[7]): ∀ (a : Iota), % 34.83/35.06 Eq % 34.83/35.06 (∀ (W1 W2 : Iota), % 34.83/35.06 And (And (aElement0 a) (aRewritingSystem0 W1)) (aElement0 W2) → % 34.83/35.06 Iff (sdtmndtasgtdt0 a W1 W2) (Or (Eq a W2) (sdtmndtplgtdt0 a W1 W2))) % 34.83/35.06 True % 34.83/35.06 Clause #103 (by clausification #[102]): ∀ (a a_1 : Iota), % 34.83/35.06 Eq % 34.83/35.06 (∀ (W2 : Iota), % 34.83/35.06 And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 W2) → % 34.83/35.06 Iff (sdtmndtasgtdt0 a a_1 W2) (Or (Eq a W2) (sdtmndtplgtdt0 a a_1 W2))) % 34.83/35.06 True % 34.83/35.06 Clause #104 (by clausification #[103]): ∀ (a a_1 a_2 : Iota), % 34.83/35.06 Eq % 34.83/35.06 (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2) → % 34.83/35.06 Iff (sdtmndtasgtdt0 a a_1 a_2) (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2))) % 34.83/35.06 True % 34.83/35.06 Clause #105 (by clausification #[104]): ∀ (a a_1 a_2 : Iota), % 34.83/35.06 Or (Eq (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2)) False) % 34.83/35.06 (Eq (Iff (sdtmndtasgtdt0 a a_1 a_2) (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2))) True) % 34.83/35.06 Clause #106 (by clausification #[105]): ∀ (a a_1 a_2 : Iota), % 34.83/35.06 Or (Eq (Iff (sdtmndtasgtdt0 a a_1 a_2) (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2))) True) % 34.83/35.06 (Or (Eq (And (aElement0 a) (aRewritingSystem0 a_1)) False) (Eq (aElement0 a_2) False)) % 34.83/35.06 Clause #107 (by clausification #[106]): ∀ (a a_1 a_2 : Iota), % 34.83/35.06 Or (Eq (And (aElement0 a) (aRewritingSystem0 a_1)) False) % 34.83/35.06 (Or (Eq (aElement0 a_2) False) % 34.83/35.06 (Or (Eq (sdtmndtasgtdt0 a a_1 a_2) True) (Eq (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2)) False))) % 34.83/35.06 Clause #108 (by clausification #[106]): ∀ (a a_1 a_2 : Iota), % 34.83/35.06 Or (Eq (And (aElement0 a) (aRewritingSystem0 a_1)) False) % 34.83/35.06 (Or (Eq (aElement0 a_2) False) % 34.83/35.06 (Or (Eq (sdtmndtasgtdt0 a a_1 a_2) False) (Eq (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2)) True))) % 34.83/35.06 Clause #109 (by clausification #[107]): ∀ (a a_1 a_2 : Iota), % 34.83/35.06 Or (Eq (aElement0 a) False) % 34.83/35.06 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) True) % 34.83/35.06 (Or (Eq (Or (Eq a_1 a) (sdtmndtplgtdt0 a_1 a_2 a)) False) % 34.83/35.06 (Or (Eq (aElement0 a_1) False) (Eq (aRewritingSystem0 a_2) False)))) % 34.83/35.06 Clause #110 (by clausification #[109]): ∀ (a a_1 a_2 : Iota), % 34.83/35.06 Or (Eq (aElement0 a) False) % 34.83/35.06 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) True) % 34.83/35.06 (Or (Eq (aElement0 a_1) False) (Or (Eq (aRewritingSystem0 a_2) False) (Eq (sdtmndtplgtdt0 a_1 a_2 a) False)))) % 34.92/35.08 Clause #111 (by clausification #[109]): ∀ (a a_1 a_2 : Iota), % 34.92/35.08 Or (Eq (aElement0 a) False) % 34.92/35.08 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) True) % 34.92/35.08 (Or (Eq (aElement0 a_1) False) (Or (Eq (aRewritingSystem0 a_2) False) (Eq (Eq a_1 a) False)))) % 34.92/35.08 Clause #112 (by superposition #[110, 43]): ∀ (a a_1 : Iota), % 34.92/35.08 Or (Eq (sdtmndtasgtdt0 a a_1 xc) True) % 34.92/35.08 (Or (Eq (aElement0 a) False) % 34.92/35.08 (Or (Eq (aRewritingSystem0 a_1) False) (Or (Eq (sdtmndtplgtdt0 a a_1 xc) False) (Eq False True)))) % 34.92/35.08 Clause #187 (by clausification #[12]): ∀ (a : Iota), % 34.92/35.08 Eq % 34.92/35.08 (∀ (W1 : Iota), % 34.92/35.08 And (aElement0 a) (aRewritingSystem0 W1) → % 34.92/35.08 ∀ (W2 : Iota), % 34.92/35.08 Iff (aNormalFormOfIn0 W2 a W1) % 34.92/35.08 (And (And (aElement0 W2) (sdtmndtasgtdt0 a W1 W2)) (Not (Exists fun W3 => aReductOfIn0 W3 W2 W1)))) % 34.92/35.08 True % 34.92/35.08 Clause #188 (by clausification #[187]): ∀ (a a_1 : Iota), % 34.92/35.08 Eq % 34.92/35.08 (And (aElement0 a) (aRewritingSystem0 a_1) → % 34.92/35.08 ∀ (W2 : Iota), % 34.92/35.08 Iff (aNormalFormOfIn0 W2 a a_1) % 34.92/35.08 (And (And (aElement0 W2) (sdtmndtasgtdt0 a a_1 W2)) (Not (Exists fun W3 => aReductOfIn0 W3 W2 a_1)))) % 34.92/35.08 True % 34.92/35.08 Clause #189 (by clausification #[188]): ∀ (a a_1 : Iota), % 34.92/35.08 Or (Eq (And (aElement0 a) (aRewritingSystem0 a_1)) False) % 34.92/35.08 (Eq % 34.92/35.08 (∀ (W2 : Iota), % 34.92/35.08 Iff (aNormalFormOfIn0 W2 a a_1) % 34.92/35.08 (And (And (aElement0 W2) (sdtmndtasgtdt0 a a_1 W2)) (Not (Exists fun W3 => aReductOfIn0 W3 W2 a_1)))) % 34.92/35.08 True) % 34.92/35.08 Clause #190 (by clausification #[189]): ∀ (a a_1 : Iota), % 34.92/35.08 Or % 34.92/35.08 (Eq % 34.92/35.08 (∀ (W2 : Iota), % 34.92/35.08 Iff (aNormalFormOfIn0 W2 a a_1) % 34.92/35.08 (And (And (aElement0 W2) (sdtmndtasgtdt0 a a_1 W2)) (Not (Exists fun W3 => aReductOfIn0 W3 W2 a_1)))) % 34.92/35.08 True) % 34.92/35.08 (Or (Eq (aElement0 a) False) (Eq (aRewritingSystem0 a_1) False)) % 34.92/35.08 Clause #191 (by clausification #[190]): ∀ (a a_1 a_2 : Iota), % 34.92/35.08 Or (Eq (aElement0 a) False) % 34.92/35.08 (Or (Eq (aRewritingSystem0 a_1) False) % 34.92/35.08 (Eq % 34.92/35.08 (Iff (aNormalFormOfIn0 a_2 a a_1) % 34.92/35.08 (And (And (aElement0 a_2) (sdtmndtasgtdt0 a a_1 a_2)) (Not (Exists fun W3 => aReductOfIn0 W3 a_2 a_1)))) % 34.92/35.08 True)) % 34.92/35.08 Clause #193 (by clausification #[191]): ∀ (a a_1 a_2 : Iota), % 34.92/35.08 Or (Eq (aElement0 a) False) % 34.92/35.08 (Or (Eq (aRewritingSystem0 a_1) False) % 34.92/35.08 (Or (Eq (aNormalFormOfIn0 a_2 a a_1) False) % 34.92/35.08 (Eq (And (And (aElement0 a_2) (sdtmndtasgtdt0 a a_1 a_2)) (Not (Exists fun W3 => aReductOfIn0 W3 a_2 a_1))) % 34.92/35.08 True))) % 34.92/35.08 Clause #202 (by clausification #[112]): ∀ (a a_1 : Iota), % 34.92/35.08 Or (Eq (sdtmndtasgtdt0 a a_1 xc) True) % 34.92/35.08 (Or (Eq (aElement0 a) False) (Or (Eq (aRewritingSystem0 a_1) False) (Eq (sdtmndtplgtdt0 a a_1 xc) False))) % 34.92/35.08 Clause #204 (by superposition #[202, 46]): ∀ (a : Iota), % 34.92/35.08 Or (Eq (sdtmndtasgtdt0 xb a xc) True) % 34.92/35.08 (Or (Eq (aRewritingSystem0 a) False) (Or (Eq (sdtmndtplgtdt0 xb a xc) False) (Eq False True))) % 34.92/35.08 Clause #209 (by clausification #[204]): ∀ (a : Iota), % 34.92/35.08 Or (Eq (sdtmndtasgtdt0 xb a xc) True) (Or (Eq (aRewritingSystem0 a) False) (Eq (sdtmndtplgtdt0 xb a xc) False)) % 34.92/35.08 Clause #210 (by superposition #[209, 14]): Or (Eq (sdtmndtasgtdt0 xb xR xc) True) (Or (Eq (sdtmndtplgtdt0 xb xR xc) False) (Eq False True)) % 34.92/35.08 Clause #223 (by clausification #[210]): Or (Eq (sdtmndtasgtdt0 xb xR xc) True) (Eq (sdtmndtplgtdt0 xb xR xc) False) % 34.92/35.08 Clause #233 (by clausification #[18]): Eq % 34.92/35.08 ((And (sdtmndtplgtdt0 xa xR xb) (sdtmndtplgtdt0 xa xR xc) → % 34.92/35.08 Exists fun W0 => % 34.92/35.08 And (And (And (aElement0 W0) (aReductOfIn0 W0 xa xR)) (sdtmndtasgtdt0 W0 xR xb)) % 34.92/35.08 (Exists fun W1 => % 34.92/35.08 And (And (And (aElement0 W1) (aReductOfIn0 W1 xa xR)) (sdtmndtasgtdt0 W1 xR xc)) % 34.92/35.08 (Exists fun W2 => % 34.92/35.08 And (And (And (aElement0 W2) (sdtmndtasgtdt0 W0 xR W2)) (sdtmndtasgtdt0 W1 xR W2)) % 34.92/35.08 (Exists fun W3 => % 34.92/35.08 And (And (aNormalFormOfIn0 W3 W2 xR) (sdtmndtasgtdt0 xb xR W3)) (sdtmndtasgtdt0 xc xR W3))))) → % 34.92/35.08 And (sdtmndtasgtdt0 xa xR xb) (sdtmndtasgtdt0 xa xR xc) → % 34.92/35.08 Exists fun W0 => And (And (aElement0 W0) (sdtmndtasgtdt0 xb xR W0)) (sdtmndtasgtdt0 xc xR W0)) % 34.92/35.08 False % 34.92/35.08 Clause #234 (by clausification #[233]): Eq % 34.92/35.08 (And (sdtmndtplgtdt0 xa xR xb) (sdtmndtplgtdt0 xa xR xc) → % 34.92/35.10 Exists fun W0 => % 34.92/35.10 And (And (And (aElement0 W0) (aReductOfIn0 W0 xa xR)) (sdtmndtasgtdt0 W0 xR xb)) % 34.92/35.10 (Exists fun W1 => % 34.92/35.10 And (And (And (aElement0 W1) (aReductOfIn0 W1 xa xR)) (sdtmndtasgtdt0 W1 xR xc)) % 34.92/35.10 (Exists fun W2 => % 34.92/35.10 And (And (And (aElement0 W2) (sdtmndtasgtdt0 W0 xR W2)) (sdtmndtasgtdt0 W1 xR W2)) % 34.92/35.10 (Exists fun W3 => % 34.92/35.10 And (And (aNormalFormOfIn0 W3 W2 xR) (sdtmndtasgtdt0 xb xR W3)) (sdtmndtasgtdt0 xc xR W3))))) % 34.92/35.10 True % 34.92/35.10 Clause #235 (by clausification #[233]): Eq % 34.92/35.10 (And (sdtmndtasgtdt0 xa xR xb) (sdtmndtasgtdt0 xa xR xc) → % 34.92/35.10 Exists fun W0 => And (And (aElement0 W0) (sdtmndtasgtdt0 xb xR W0)) (sdtmndtasgtdt0 xc xR W0)) % 34.92/35.10 False % 34.92/35.10 Clause #236 (by clausification #[234]): Or (Eq (And (sdtmndtplgtdt0 xa xR xb) (sdtmndtplgtdt0 xa xR xc)) False) % 34.92/35.10 (Eq % 34.92/35.10 (Exists fun W0 => % 34.92/35.10 And (And (And (aElement0 W0) (aReductOfIn0 W0 xa xR)) (sdtmndtasgtdt0 W0 xR xb)) % 34.92/35.10 (Exists fun W1 => % 34.92/35.10 And (And (And (aElement0 W1) (aReductOfIn0 W1 xa xR)) (sdtmndtasgtdt0 W1 xR xc)) % 34.92/35.10 (Exists fun W2 => % 34.92/35.10 And (And (And (aElement0 W2) (sdtmndtasgtdt0 W0 xR W2)) (sdtmndtasgtdt0 W1 xR W2)) % 34.92/35.10 (Exists fun W3 => % 34.92/35.10 And (And (aNormalFormOfIn0 W3 W2 xR) (sdtmndtasgtdt0 xb xR W3)) (sdtmndtasgtdt0 xc xR W3))))) % 34.92/35.10 True) % 34.92/35.10 Clause #237 (by clausification #[236]): Or % 34.92/35.10 (Eq % 34.92/35.10 (Exists fun W0 => % 34.92/35.10 And (And (And (aElement0 W0) (aReductOfIn0 W0 xa xR)) (sdtmndtasgtdt0 W0 xR xb)) % 34.92/35.10 (Exists fun W1 => % 34.92/35.10 And (And (And (aElement0 W1) (aReductOfIn0 W1 xa xR)) (sdtmndtasgtdt0 W1 xR xc)) % 34.92/35.10 (Exists fun W2 => % 34.92/35.10 And (And (And (aElement0 W2) (sdtmndtasgtdt0 W0 xR W2)) (sdtmndtasgtdt0 W1 xR W2)) % 34.92/35.10 (Exists fun W3 => % 34.92/35.10 And (And (aNormalFormOfIn0 W3 W2 xR) (sdtmndtasgtdt0 xb xR W3)) (sdtmndtasgtdt0 xc xR W3))))) % 34.92/35.10 True) % 34.92/35.10 (Or (Eq (sdtmndtplgtdt0 xa xR xb) False) (Eq (sdtmndtplgtdt0 xa xR xc) False)) % 34.92/35.10 Clause #238 (by clausification #[237]): ∀ (a : Iota), % 34.92/35.10 Or (Eq (sdtmndtplgtdt0 xa xR xb) False) % 34.92/35.10 (Or (Eq (sdtmndtplgtdt0 xa xR xc) False) % 34.92/35.10 (Eq % 34.92/35.10 (And (And (And (aElement0 (skS.0 11 a)) (aReductOfIn0 (skS.0 11 a) xa xR)) (sdtmndtasgtdt0 (skS.0 11 a) xR xb)) % 34.92/35.10 (Exists fun W1 => % 34.92/35.10 And (And (And (aElement0 W1) (aReductOfIn0 W1 xa xR)) (sdtmndtasgtdt0 W1 xR xc)) % 34.92/35.10 (Exists fun W2 => % 34.92/35.10 And (And (And (aElement0 W2) (sdtmndtasgtdt0 (skS.0 11 a) xR W2)) (sdtmndtasgtdt0 W1 xR W2)) % 34.92/35.10 (Exists fun W3 => % 34.92/35.10 And (And (aNormalFormOfIn0 W3 W2 xR) (sdtmndtasgtdt0 xb xR W3)) (sdtmndtasgtdt0 xc xR W3))))) % 34.92/35.10 True)) % 34.92/35.10 Clause #239 (by clausification #[238]): ∀ (a : Iota), % 34.92/35.10 Or (Eq (sdtmndtplgtdt0 xa xR xb) False) % 34.92/35.10 (Or (Eq (sdtmndtplgtdt0 xa xR xc) False) % 34.92/35.10 (Eq % 34.92/35.10 (Exists fun W1 => % 34.92/35.10 And (And (And (aElement0 W1) (aReductOfIn0 W1 xa xR)) (sdtmndtasgtdt0 W1 xR xc)) % 34.92/35.10 (Exists fun W2 => % 34.92/35.10 And (And (And (aElement0 W2) (sdtmndtasgtdt0 (skS.0 11 a) xR W2)) (sdtmndtasgtdt0 W1 xR W2)) % 34.92/35.10 (Exists fun W3 => % 34.92/35.10 And (And (aNormalFormOfIn0 W3 W2 xR) (sdtmndtasgtdt0 xb xR W3)) (sdtmndtasgtdt0 xc xR W3)))) % 34.92/35.10 True)) % 34.92/35.10 Clause #241 (by clausification #[239]): ∀ (a a_1 : Iota), % 34.92/35.10 Or (Eq (sdtmndtplgtdt0 xa xR xb) False) % 34.92/35.10 (Or (Eq (sdtmndtplgtdt0 xa xR xc) False) % 34.92/35.10 (Eq % 34.92/35.10 (And % 34.92/35.10 (And (And (aElement0 (skS.0 12 a a_1)) (aReductOfIn0 (skS.0 12 a a_1) xa xR)) % 34.92/35.10 (sdtmndtasgtdt0 (skS.0 12 a a_1) xR xc)) % 34.92/35.10 (Exists fun W2 => % 34.92/35.10 And (And (And (aElement0 W2) (sdtmndtasgtdt0 (skS.0 11 a) xR W2)) (sdtmndtasgtdt0 (skS.0 12 a a_1) xR W2)) % 34.92/35.10 (Exists fun W3 => % 34.92/35.10 And (And (aNormalFormOfIn0 W3 W2 xR) (sdtmndtasgtdt0 xb xR W3)) (sdtmndtasgtdt0 xc xR W3)))) % 34.92/35.10 True)) % 34.92/35.10 Clause #242 (by clausification #[241]): ∀ (a a_1 : Iota), % 34.92/35.10 Or (Eq (sdtmndtplgtdt0 xa xR xb) False) % 34.92/35.10 (Or (Eq (sdtmndtplgtdt0 xa xR xc) False) % 34.92/35.10 (Eq % 34.92/35.10 (Exists fun W2 => % 34.92/35.10 And (And (And (aElement0 W2) (sdtmndtasgtdt0 (skS.0 11 a) xR W2)) (sdtmndtasgtdt0 (skS.0 12 a a_1) xR W2)) % 34.96/35.12 (Exists fun W3 => % 34.96/35.12 And (And (aNormalFormOfIn0 W3 W2 xR) (sdtmndtasgtdt0 xb xR W3)) (sdtmndtasgtdt0 xc xR W3))) % 34.96/35.12 True)) % 34.96/35.12 Clause #244 (by clausification #[242]): ∀ (a a_1 a_2 : Iota), % 34.96/35.12 Or (Eq (sdtmndtplgtdt0 xa xR xb) False) % 34.96/35.12 (Or (Eq (sdtmndtplgtdt0 xa xR xc) False) % 34.96/35.12 (Eq % 34.96/35.12 (And % 34.96/35.12 (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))) % 34.96/35.12 (sdtmndtasgtdt0 (skS.0 12 a a_1) xR (skS.0 13 a a_1 a_2))) % 34.96/35.12 (Exists fun W3 => % 34.96/35.12 And (And (aNormalFormOfIn0 W3 (skS.0 13 a a_1 a_2) xR) (sdtmndtasgtdt0 xb xR W3)) % 34.96/35.12 (sdtmndtasgtdt0 xc xR W3))) % 34.96/35.12 True)) % 34.96/35.12 Clause #245 (by clausification #[244]): ∀ (a a_1 a_2 : Iota), % 34.96/35.12 Or (Eq (sdtmndtplgtdt0 xa xR xb) False) % 34.96/35.12 (Or (Eq (sdtmndtplgtdt0 xa xR xc) False) % 34.96/35.12 (Eq % 34.96/35.12 (Exists fun W3 => % 34.96/35.12 And (And (aNormalFormOfIn0 W3 (skS.0 13 a a_1 a_2) xR) (sdtmndtasgtdt0 xb xR W3)) (sdtmndtasgtdt0 xc xR W3)) % 34.96/35.12 True)) % 34.96/35.12 Clause #246 (by clausification #[244]): ∀ (a a_1 a_2 : Iota), % 34.96/35.12 Or (Eq (sdtmndtplgtdt0 xa xR xb) False) % 34.96/35.12 (Or (Eq (sdtmndtplgtdt0 xa xR xc) False) % 34.96/35.12 (Eq % 34.96/35.12 (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))) % 34.96/35.12 (sdtmndtasgtdt0 (skS.0 12 a a_1) xR (skS.0 13 a a_1 a_2))) % 34.96/35.12 True)) % 34.96/35.12 Clause #247 (by clausification #[245]): ∀ (a a_1 a_2 a_3 : Iota), % 34.96/35.12 Or (Eq (sdtmndtplgtdt0 xa xR xb) False) % 34.96/35.12 (Or (Eq (sdtmndtplgtdt0 xa xR xc) False) % 34.96/35.12 (Eq % 34.96/35.12 (And % 34.96/35.12 (And (aNormalFormOfIn0 (skS.0 14 a a_1 a_2 a_3) (skS.0 13 a a_1 a_2) xR) % 34.96/35.12 (sdtmndtasgtdt0 xb xR (skS.0 14 a a_1 a_2 a_3))) % 34.96/35.12 (sdtmndtasgtdt0 xc xR (skS.0 14 a a_1 a_2 a_3))) % 34.96/35.12 True)) % 34.96/35.12 Clause #248 (by clausification #[247]): ∀ (a a_1 a_2 a_3 : Iota), % 34.96/35.12 Or (Eq (sdtmndtplgtdt0 xa xR xb) False) % 34.96/35.12 (Or (Eq (sdtmndtplgtdt0 xa xR xc) False) (Eq (sdtmndtasgtdt0 xc xR (skS.0 14 a a_1 a_2 a_3)) True)) % 34.96/35.12 Clause #249 (by clausification #[247]): ∀ (a a_1 a_2 a_3 : Iota), % 34.96/35.12 Or (Eq (sdtmndtplgtdt0 xa xR xb) False) % 34.96/35.12 (Or (Eq (sdtmndtplgtdt0 xa xR xc) False) % 34.96/35.12 (Eq % 34.96/35.12 (And (aNormalFormOfIn0 (skS.0 14 a a_1 a_2 a_3) (skS.0 13 a a_1 a_2) xR) % 34.96/35.12 (sdtmndtasgtdt0 xb xR (skS.0 14 a a_1 a_2 a_3))) % 34.96/35.12 True)) % 34.96/35.12 Clause #265 (by clausification #[235]): Eq (And (sdtmndtasgtdt0 xa xR xb) (sdtmndtasgtdt0 xa xR xc)) True % 34.96/35.12 Clause #266 (by clausification #[235]): Eq (Exists fun W0 => And (And (aElement0 W0) (sdtmndtasgtdt0 xb xR W0)) (sdtmndtasgtdt0 xc xR W0)) False % 34.96/35.12 Clause #267 (by clausification #[265]): Eq (sdtmndtasgtdt0 xa xR xc) True % 34.96/35.12 Clause #268 (by clausification #[265]): Eq (sdtmndtasgtdt0 xa xR xb) True % 34.96/35.12 Clause #273 (by clausification #[266]): ∀ (a : Iota), Eq (And (And (aElement0 a) (sdtmndtasgtdt0 xb xR a)) (sdtmndtasgtdt0 xc xR a)) False % 34.96/35.12 Clause #274 (by clausification #[273]): ∀ (a : Iota), Or (Eq (And (aElement0 a) (sdtmndtasgtdt0 xb xR a)) False) (Eq (sdtmndtasgtdt0 xc xR a) False) % 34.96/35.12 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)) % 34.96/35.12 Clause #334 (by clausification #[111]): ∀ (a a_1 a_2 : Iota), % 34.96/35.12 Or (Eq (aElement0 a) False) % 34.96/35.12 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) True) % 34.96/35.12 (Or (Eq (aElement0 a_1) False) (Or (Eq (aRewritingSystem0 a_2) False) (Ne a_1 a)))) % 34.96/35.12 Clause #335 (by destructive equality resolution #[334]): ∀ (a a_1 : Iota), % 34.96/35.12 Or (Eq (aElement0 a) False) % 34.96/35.12 (Or (Eq (sdtmndtasgtdt0 a a_1 a) True) (Or (Eq (aElement0 a) False) (Eq (aRewritingSystem0 a_1) False))) % 34.96/35.12 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)) % 34.96/35.12 Clause #337 (by superposition #[336, 43]): ∀ (a : Iota), Or (Eq (sdtmndtasgtdt0 xc a xc) True) (Or (Eq (aRewritingSystem0 a) False) (Eq False True)) % 34.96/35.12 Clause #338 (by superposition #[336, 46]): ∀ (a : Iota), Or (Eq (sdtmndtasgtdt0 xb a xb) True) (Or (Eq (aRewritingSystem0 a) False) (Eq False True)) % 34.98/35.14 Clause #349 (by clausification #[338]): ∀ (a : Iota), Or (Eq (sdtmndtasgtdt0 xb a xb) True) (Eq (aRewritingSystem0 a) False) % 34.98/35.14 Clause #350 (by superposition #[349, 14]): Or (Eq (sdtmndtasgtdt0 xb xR xb) True) (Eq False True) % 34.98/35.14 Clause #351 (by clausification #[350]): Eq (sdtmndtasgtdt0 xb xR xb) True % 34.98/35.14 Clause #354 (by clausification #[337]): ∀ (a : Iota), Or (Eq (sdtmndtasgtdt0 xc a xc) True) (Eq (aRewritingSystem0 a) False) % 34.98/35.14 Clause #355 (by superposition #[354, 14]): Or (Eq (sdtmndtasgtdt0 xc xR xc) True) (Eq False True) % 34.98/35.14 Clause #356 (by clausification #[355]): Eq (sdtmndtasgtdt0 xc xR xc) True % 34.98/35.14 Clause #359 (by superposition #[356, 275]): Or (Eq True False) (Or (Eq (aElement0 xc) False) (Eq (sdtmndtasgtdt0 xb xR xc) False)) % 34.98/35.14 Clause #364 (by clausification #[359]): Or (Eq (aElement0 xc) False) (Eq (sdtmndtasgtdt0 xb xR xc) False) % 34.98/35.14 Clause #365 (by forward demodulation #[364, 43]): Or (Eq True False) (Eq (sdtmndtasgtdt0 xb xR xc) False) % 34.98/35.14 Clause #366 (by clausification #[365]): Eq (sdtmndtasgtdt0 xb xR xc) False % 34.98/35.14 Clause #367 (by backward demodulation #[366, 223]): Or (Eq False True) (Eq (sdtmndtplgtdt0 xb xR xc) False) % 34.98/35.14 Clause #368 (by clausification #[367]): Eq (sdtmndtplgtdt0 xb xR xc) False % 34.98/35.14 Clause #418 (by clausification #[108]): ∀ (a a_1 a_2 : Iota), % 34.98/35.14 Or (Eq (aElement0 a) False) % 34.98/35.14 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) False) % 34.98/35.14 (Or (Eq (Or (Eq a_1 a) (sdtmndtplgtdt0 a_1 a_2 a)) True) % 34.98/35.14 (Or (Eq (aElement0 a_1) False) (Eq (aRewritingSystem0 a_2) False)))) % 34.98/35.14 Clause #419 (by clausification #[418]): ∀ (a a_1 a_2 : Iota), % 34.98/35.14 Or (Eq (aElement0 a) False) % 34.98/35.14 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) False) % 34.98/35.14 (Or (Eq (aElement0 a_1) False) % 34.98/35.14 (Or (Eq (aRewritingSystem0 a_2) False) (Or (Eq (Eq a_1 a) True) (Eq (sdtmndtplgtdt0 a_1 a_2 a) True))))) % 34.98/35.14 Clause #420 (by clausification #[419]): ∀ (a a_1 a_2 : Iota), % 34.98/35.14 Or (Eq (aElement0 a) False) % 34.98/35.14 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) False) % 34.98/35.14 (Or (Eq (aElement0 a_1) False) % 34.98/35.14 (Or (Eq (aRewritingSystem0 a_2) False) (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a) True) (Eq a_1 a))))) % 34.98/35.14 Clause #421 (by superposition #[420, 43]): ∀ (a a_1 : Iota), % 34.98/35.14 Or (Eq (sdtmndtasgtdt0 a a_1 xc) False) % 34.98/35.14 (Or (Eq (aElement0 a) False) % 34.98/35.14 (Or (Eq (aRewritingSystem0 a_1) False) (Or (Eq (sdtmndtplgtdt0 a a_1 xc) True) (Or (Eq a xc) (Eq False True))))) % 34.98/35.14 Clause #422 (by superposition #[420, 46]): ∀ (a a_1 : Iota), % 34.98/35.14 Or (Eq (sdtmndtasgtdt0 a a_1 xb) False) % 34.98/35.14 (Or (Eq (aElement0 a) False) % 34.98/35.14 (Or (Eq (aRewritingSystem0 a_1) False) (Or (Eq (sdtmndtplgtdt0 a a_1 xb) True) (Or (Eq a xb) (Eq False True))))) % 34.98/35.14 Clause #428 (by clausification #[422]): ∀ (a a_1 : Iota), % 34.98/35.14 Or (Eq (sdtmndtasgtdt0 a a_1 xb) False) % 34.98/35.14 (Or (Eq (aElement0 a) False) % 34.98/35.14 (Or (Eq (aRewritingSystem0 a_1) False) (Or (Eq (sdtmndtplgtdt0 a a_1 xb) True) (Eq a xb)))) % 34.98/35.14 Clause #429 (by superposition #[428, 268]): Or (Eq (aElement0 xa) False) % 34.98/35.14 (Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xa xR xb) True) (Or (Eq xa xb) (Eq False True)))) % 34.98/35.14 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))) % 34.98/35.14 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))) % 34.98/35.14 Clause #437 (by clausification #[436]): Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xa xR xb) True) (Eq xa xb)) % 34.98/35.14 Clause #438 (by forward demodulation #[437, 14]): Or (Eq True False) (Or (Eq (sdtmndtplgtdt0 xa xR xb) True) (Eq xa xb)) % 34.98/35.14 Clause #439 (by clausification #[438]): Or (Eq (sdtmndtplgtdt0 xa xR xb) True) (Eq xa xb) % 34.98/35.14 Clause #440 (by superposition #[439, 248]): ∀ (a a_1 a_2 a_3 : Iota), % 34.98/35.14 Or (Eq xa xb) % 34.98/35.14 (Or (Eq True False) % 34.98/35.14 (Or (Eq (sdtmndtplgtdt0 xa xR xc) False) (Eq (sdtmndtasgtdt0 xc xR (skS.0 14 a a_1 a_2 a_3)) True))) % 34.98/35.14 Clause #443 (by clausification #[421]): ∀ (a a_1 : Iota), % 34.98/35.14 Or (Eq (sdtmndtasgtdt0 a a_1 xc) False) % 34.98/35.14 (Or (Eq (aElement0 a) False) % 34.98/35.14 (Or (Eq (aRewritingSystem0 a_1) False) (Or (Eq (sdtmndtplgtdt0 a a_1 xc) True) (Eq a xc)))) % 34.98/35.17 Clause #444 (by superposition #[443, 267]): Or (Eq (aElement0 xa) False) % 34.98/35.17 (Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xa xR xc) True) (Or (Eq xa xc) (Eq False True)))) % 34.98/35.17 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))) % 34.98/35.17 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))) % 34.98/35.17 Clause #449 (by clausification #[448]): Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xa xR xc) True) (Eq xa xc)) % 34.98/35.17 Clause #450 (by forward demodulation #[449, 14]): Or (Eq True False) (Or (Eq (sdtmndtplgtdt0 xa xR xc) True) (Eq xa xc)) % 34.98/35.17 Clause #451 (by clausification #[450]): Or (Eq (sdtmndtplgtdt0 xa xR xc) True) (Eq xa xc) % 34.98/35.17 Clause #584 (by clausification #[193]): ∀ (a a_1 a_2 : Iota), % 34.98/35.17 Or (Eq (aElement0 a) False) % 34.98/35.17 (Or (Eq (aRewritingSystem0 a_1) False) % 34.98/35.17 (Or (Eq (aNormalFormOfIn0 a_2 a a_1) False) (Eq (And (aElement0 a_2) (sdtmndtasgtdt0 a a_1 a_2)) True))) % 34.98/35.17 Clause #608 (by clausification #[584]): ∀ (a a_1 a_2 : Iota), % 34.98/35.17 Or (Eq (aElement0 a) False) % 34.98/35.17 (Or (Eq (aRewritingSystem0 a_1) False) (Or (Eq (aNormalFormOfIn0 a_2 a a_1) False) (Eq (aElement0 a_2) True))) % 34.98/35.17 Clause #790 (by clausification #[246]): ∀ (a a_1 a_2 : Iota), % 34.98/35.17 Or (Eq (sdtmndtplgtdt0 xa xR xb) False) % 34.98/35.17 (Or (Eq (sdtmndtplgtdt0 xa xR xc) False) % 34.98/35.17 (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)) % 34.98/35.17 Clause #800 (by clausification #[249]): ∀ (a a_1 a_2 a_3 : Iota), % 34.98/35.17 Or (Eq (sdtmndtplgtdt0 xa xR xb) False) % 34.98/35.17 (Or (Eq (sdtmndtplgtdt0 xa xR xc) False) (Eq (sdtmndtasgtdt0 xb xR (skS.0 14 a a_1 a_2 a_3)) True)) % 34.98/35.17 Clause #801 (by clausification #[249]): ∀ (a a_1 a_2 a_3 : Iota), % 34.98/35.17 Or (Eq (sdtmndtplgtdt0 xa xR xb) False) % 34.98/35.17 (Or (Eq (sdtmndtplgtdt0 xa xR xc) False) % 34.98/35.17 (Eq (aNormalFormOfIn0 (skS.0 14 a a_1 a_2 a_3) (skS.0 13 a a_1 a_2) xR) True)) % 34.98/35.17 Clause #802 (by superposition #[800, 439]): ∀ (a a_1 a_2 a_3 : Iota), % 34.98/35.17 Or (Eq (sdtmndtplgtdt0 xa xR xc) False) % 34.98/35.17 (Or (Eq (sdtmndtasgtdt0 xb xR (skS.0 14 a a_1 a_2 a_3)) True) (Or (Eq False True) (Eq xa xb))) % 34.98/35.17 Clause #869 (by clausification #[440]): ∀ (a a_1 a_2 a_3 : Iota), % 34.98/35.17 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)) % 34.98/35.17 Clause #870 (by superposition #[869, 451]): ∀ (a a_1 a_2 a_3 : Iota), % 34.98/35.17 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))) % 34.98/35.17 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)) % 34.98/35.17 Clause #873 (by superposition #[871, 275]): ∀ (a a_1 a_2 a_3 : Iota), % 34.98/35.17 Or (Eq xa xb) % 34.98/35.17 (Or (Eq xa xc) % 34.98/35.17 (Or (Eq True False) % 34.98/35.17 (Or (Eq (aElement0 (skS.0 14 a a_1 a_2 a_3)) False) % 34.98/35.17 (Eq (sdtmndtasgtdt0 xb xR (skS.0 14 a a_1 a_2 a_3)) False)))) % 34.98/35.17 Clause #880 (by clausification #[802]): ∀ (a a_1 a_2 a_3 : Iota), % 34.98/35.17 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)) % 34.98/35.17 Clause #881 (by superposition #[880, 451]): ∀ (a a_1 a_2 a_3 : Iota), % 34.98/35.17 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))) % 34.98/35.17 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)) % 34.98/35.17 Clause #3557 (by clausification #[790]): ∀ (a a_1 a_2 : Iota), % 34.98/35.17 Or (Eq (sdtmndtplgtdt0 xa xR xb) False) % 34.98/35.17 (Or (Eq (sdtmndtplgtdt0 xa xR xc) False) (Eq (aElement0 (skS.0 13 a a_1 a_2)) True)) % 34.98/35.17 Clause #3559 (by superposition #[3557, 439]): ∀ (a a_1 a_2 : Iota), % 34.98/35.17 Or (Eq (sdtmndtplgtdt0 xa xR xc) False) % 34.98/35.17 (Or (Eq (aElement0 (skS.0 13 a a_1 a_2)) True) (Or (Eq False True) (Eq xa xb))) % 34.98/35.17 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)) % 34.98/35.19 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))) % 34.98/35.19 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)) % 34.98/35.19 Clause #3595 (by superposition #[3562, 608]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 34.98/35.19 Or (Eq xa xb) % 34.98/35.19 (Or (Eq xa xc) % 34.98/35.19 (Or (Eq True False) % 34.98/35.19 (Or (Eq (aRewritingSystem0 a) False) % 34.98/35.19 (Or (Eq (aNormalFormOfIn0 a_1 (skS.0 13 a_2 a_3 a_4) a) False) (Eq (aElement0 a_1) True))))) % 34.98/35.19 Clause #3627 (by clausification #[3595]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 34.98/35.19 Or (Eq xa xb) % 34.98/35.19 (Or (Eq xa xc) % 34.98/35.19 (Or (Eq (aRewritingSystem0 a) False) % 34.98/35.19 (Or (Eq (aNormalFormOfIn0 a_1 (skS.0 13 a_2 a_3 a_4) a) False) (Eq (aElement0 a_1) True)))) % 34.98/35.19 Clause #3628 (by superposition #[3627, 14]): ∀ (a a_1 a_2 a_3 : Iota), % 34.98/35.19 Or (Eq xa xb) % 34.98/35.19 (Or (Eq xa xc) % 34.98/35.19 (Or (Eq (aNormalFormOfIn0 a (skS.0 13 a_1 a_2 a_3) xR) False) (Or (Eq (aElement0 a) True) (Eq False True)))) % 34.98/35.19 Clause #3629 (by clausification #[3628]): ∀ (a a_1 a_2 a_3 : Iota), % 34.98/35.19 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))) % 34.98/35.19 Clause #3630 (by superposition #[801, 439]): ∀ (a a_1 a_2 a_3 : Iota), % 34.98/35.19 Or (Eq (sdtmndtplgtdt0 xa xR xc) False) % 34.98/35.19 (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))) % 34.98/35.19 Clause #3656 (by clausification #[3630]): ∀ (a a_1 a_2 a_3 : Iota), % 34.98/35.19 Or (Eq (sdtmndtplgtdt0 xa xR xc) False) % 34.98/35.19 (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)) % 34.98/35.19 Clause #3657 (by superposition #[3656, 451]): ∀ (a a_1 a_2 a_3 : Iota), % 34.98/35.19 Or (Eq (aNormalFormOfIn0 (skS.0 14 a a_1 a_2 a_3) (skS.0 13 a a_1 a_2) xR) True) % 34.98/35.19 (Or (Eq xa xb) (Or (Eq False True) (Eq xa xc))) % 34.98/35.19 Clause #3658 (by clausification #[3657]): ∀ (a a_1 a_2 a_3 : Iota), % 34.98/35.19 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)) % 34.98/35.19 Clause #3659 (by superposition #[3658, 3629]): ∀ (a a_1 a_2 a_3 : Iota), % 34.98/35.19 Or (Eq xa xb) % 34.98/35.19 (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))))) % 34.98/35.19 Clause #3661 (by clausification #[3659]): ∀ (a a_1 a_2 a_3 : Iota), % 34.98/35.19 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)))) % 34.98/35.19 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)) % 34.98/35.19 Clause #3788 (by clausification #[873]): ∀ (a a_1 a_2 a_3 : Iota), % 34.98/35.19 Or (Eq xa xb) % 34.98/35.19 (Or (Eq xa xc) % 34.98/35.19 (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))) % 34.98/35.19 Clause #3789 (by superposition #[3788, 3662]): ∀ (a a_1 a_2 a_3 : Iota), % 34.98/35.19 Or (Eq xa xb) % 34.98/35.19 (Or (Eq xa xc) % 34.98/35.19 (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))))) % 34.98/35.19 Clause #3790 (by clausification #[3789]): ∀ (a a_1 a_2 a_3 : Iota), % 34.98/35.19 Or (Eq xa xb) % 34.98/35.19 (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)))) % 34.98/35.19 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)) % 34.98/35.19 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)))) % 34.98/35.19 Clause #3793 (by clausification #[3792]): Or (Eq xa xb) (Or (Eq xa xc) (Or (Eq xa xb) (Eq xa xc))) % 34.98/35.19 Clause #3794 (by eliminate duplicate literals #[3793]): Or (Eq xa xb) (Eq xa xc) % 34.98/35.19 Clause #3804 (by superposition #[3794, 368]): Or (Eq xa xc) (Eq (sdtmndtplgtdt0 xa xR xc) False) % 34.98/35.19 Clause #3903 (by superposition #[3804, 451]): Or (Eq xa xc) (Or (Eq False True) (Eq xa xc)) % 34.98/35.19 Clause #3907 (by clausification #[3903]): Or (Eq xa xc) (Eq xa xc) % 34.98/35.19 Clause #3908 (by eliminate duplicate literals #[3907]): Eq xa xc % 35.07/35.25 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)) % 35.07/35.25 Clause #4209 (by superposition #[3917, 268]): Or (Eq (aElement0 xb) False) (Or (Eq (sdtmndtasgtdt0 xb xR xb) False) (Eq False True)) % 35.07/35.25 Clause #4214 (by clausification #[4209]): Or (Eq (aElement0 xb) False) (Eq (sdtmndtasgtdt0 xb xR xb) False) % 35.07/35.25 Clause #4215 (by forward demodulation #[4214, 46]): Or (Eq True False) (Eq (sdtmndtasgtdt0 xb xR xb) False) % 35.07/35.25 Clause #4216 (by clausification #[4215]): Eq (sdtmndtasgtdt0 xb xR xb) False % 35.07/35.25 Clause #4217 (by superposition #[4216, 351]): Eq False True % 35.07/35.25 Clause #4218 (by clausification #[4217]): False % 35.07/35.25 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------