%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : COM012+3 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n028.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 07:45:47 PM UTC 2025 % Result : Theorem 4.49s 4.67s % Output : Proof 4.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : COM012+3 : TPTP v9.2.0. Released v4.0.0. % 0.06/0.13 % Command : duper %s % 0.13/0.34 % Computer : n028.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 15:51:23 EDT 2025 % 0.13/0.34 % CPUTime : % 4.49/4.67 SZS status Theorem for theBenchmark.p % 4.49/4.67 SZS output start Proof for theBenchmark.p % 4.49/4.67 Clause #6 (by assumption #[]): Eq % 4.49/4.67 (∀ (W0 W1 W2 W3 : Iota), % 4.49/4.67 And (And (And (aElement0 W0) (aRewritingSystem0 W1)) (aElement0 W2)) (aElement0 W3) → % 4.49/4.67 And (sdtmndtplgtdt0 W0 W1 W2) (sdtmndtplgtdt0 W2 W1 W3) → sdtmndtplgtdt0 W0 W1 W3) % 4.49/4.67 True % 4.49/4.67 Clause #7 (by assumption #[]): Eq % 4.49/4.67 (∀ (W0 W1 W2 : Iota), % 4.49/4.67 And (And (aElement0 W0) (aRewritingSystem0 W1)) (aElement0 W2) → % 4.49/4.67 Iff (sdtmndtasgtdt0 W0 W1 W2) (Or (Eq W0 W2) (sdtmndtplgtdt0 W0 W1 W2))) % 4.49/4.67 True % 4.49/4.67 Clause #8 (by assumption #[]): Eq (And (And (And (aElement0 xx) (aRewritingSystem0 xR)) (aElement0 xy)) (aElement0 xz)) True % 4.49/4.67 Clause #9 (by assumption #[]): Eq % 4.49/4.67 (Not % 4.49/4.67 (And % 4.49/4.67 (And % 4.49/4.67 (And % 4.49/4.67 (Or (Eq xx xy) % 4.49/4.67 (And % 4.49/4.67 (Or (aReductOfIn0 xy xx xR) % 4.49/4.67 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xx xR)) (sdtmndtplgtdt0 W0 xR xy))) % 4.49/4.67 (sdtmndtplgtdt0 xx xR xy))) % 4.49/4.67 (sdtmndtasgtdt0 xx xR xy)) % 4.49/4.67 (Or (Eq xy xz) % 4.49/4.67 (And % 4.49/4.67 (Or (aReductOfIn0 xz xy xR) % 4.49/4.67 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xy xR)) (sdtmndtplgtdt0 W0 xR xz))) % 4.49/4.67 (sdtmndtplgtdt0 xy xR xz)))) % 4.49/4.67 (sdtmndtasgtdt0 xy xR xz) → % 4.49/4.67 Or % 4.49/4.67 (Or % 4.49/4.67 (Or (Or (Eq xx xz) (aReductOfIn0 xz xx xR)) % 4.49/4.67 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xx xR)) (sdtmndtplgtdt0 W0 xR xz))) % 4.49/4.67 (sdtmndtplgtdt0 xx xR xz)) % 4.49/4.67 (sdtmndtasgtdt0 xx xR xz))) % 4.49/4.67 True % 4.49/4.67 Clause #45 (by clausification #[6]): ∀ (a : Iota), % 4.49/4.67 Eq % 4.49/4.67 (∀ (W1 W2 W3 : Iota), % 4.49/4.67 And (And (And (aElement0 a) (aRewritingSystem0 W1)) (aElement0 W2)) (aElement0 W3) → % 4.49/4.67 And (sdtmndtplgtdt0 a W1 W2) (sdtmndtplgtdt0 W2 W1 W3) → sdtmndtplgtdt0 a W1 W3) % 4.49/4.67 True % 4.49/4.67 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), % 4.49/4.67 Eq % 4.49/4.67 (∀ (W2 W3 : Iota), % 4.49/4.67 And (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 W2)) (aElement0 W3) → % 4.49/4.67 And (sdtmndtplgtdt0 a a_1 W2) (sdtmndtplgtdt0 W2 a_1 W3) → sdtmndtplgtdt0 a a_1 W3) % 4.49/4.67 True % 4.49/4.67 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 : Iota), % 4.49/4.67 Eq % 4.49/4.67 (∀ (W3 : Iota), % 4.49/4.67 And (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2)) (aElement0 W3) → % 4.49/4.67 And (sdtmndtplgtdt0 a a_1 a_2) (sdtmndtplgtdt0 a_2 a_1 W3) → sdtmndtplgtdt0 a a_1 W3) % 4.49/4.67 True % 4.49/4.67 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 a_3 : Iota), % 4.49/4.67 Eq % 4.49/4.67 (And (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2)) (aElement0 a_3) → % 4.49/4.67 And (sdtmndtplgtdt0 a a_1 a_2) (sdtmndtplgtdt0 a_2 a_1 a_3) → sdtmndtplgtdt0 a a_1 a_3) % 4.49/4.67 True % 4.49/4.67 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 a_3 : Iota), % 4.49/4.67 Or (Eq (And (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2)) (aElement0 a_3)) False) % 4.49/4.67 (Eq (And (sdtmndtplgtdt0 a a_1 a_2) (sdtmndtplgtdt0 a_2 a_1 a_3) → sdtmndtplgtdt0 a a_1 a_3) True) % 4.49/4.67 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 a_3 : Iota), % 4.49/4.67 Or (Eq (And (sdtmndtplgtdt0 a a_1 a_2) (sdtmndtplgtdt0 a_2 a_1 a_3) → sdtmndtplgtdt0 a a_1 a_3) True) % 4.49/4.67 (Or (Eq (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2)) False) (Eq (aElement0 a_3) False)) % 4.49/4.67 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 a_3 : Iota), % 4.49/4.67 Or (Eq (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2)) False) % 4.49/4.67 (Or (Eq (aElement0 a_3) False) % 4.49/4.67 (Or (Eq (And (sdtmndtplgtdt0 a a_1 a_2) (sdtmndtplgtdt0 a_2 a_1 a_3)) False) % 4.49/4.67 (Eq (sdtmndtplgtdt0 a a_1 a_3) True))) % 4.49/4.67 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 a_3 : Iota), % 4.49/4.67 Or (Eq (aElement0 a) False) % 4.49/4.67 (Or (Eq (And (sdtmndtplgtdt0 a_1 a_2 a_3) (sdtmndtplgtdt0 a_3 a_2 a)) False) % 4.49/4.67 (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a) True) % 4.49/4.67 (Or (Eq (And (aElement0 a_1) (aRewritingSystem0 a_2)) False) (Eq (aElement0 a_3) False)))) % 4.49/4.67 Clause #53 (by clausification #[52]): ∀ (a a_1 a_2 a_3 : Iota), % 4.49/4.67 Or (Eq (aElement0 a) False) % 4.49/4.67 (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a) True) % 4.49/4.67 (Or (Eq (And (aElement0 a_1) (aRewritingSystem0 a_2)) False) % 4.49/4.69 (Or (Eq (aElement0 a_3) False) % 4.49/4.69 (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a_3) False) (Eq (sdtmndtplgtdt0 a_3 a_2 a) False))))) % 4.49/4.69 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 a_3 : Iota), % 4.49/4.69 Or (Eq (aElement0 a) False) % 4.49/4.69 (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a) True) % 4.49/4.69 (Or (Eq (aElement0 a_3) False) % 4.49/4.69 (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a_3) False) % 4.49/4.69 (Or (Eq (sdtmndtplgtdt0 a_3 a_2 a) False) % 4.49/4.69 (Or (Eq (aElement0 a_1) False) (Eq (aRewritingSystem0 a_2) False)))))) % 4.49/4.69 Clause #55 (by clausification #[8]): Eq (aElement0 xz) True % 4.49/4.69 Clause #56 (by clausification #[8]): Eq (And (And (aElement0 xx) (aRewritingSystem0 xR)) (aElement0 xy)) True % 4.49/4.69 Clause #59 (by superposition #[55, 54]): ∀ (a a_1 a_2 : Iota), % 4.49/4.69 Or (Eq True False) % 4.49/4.69 (Or (Eq (sdtmndtplgtdt0 a a_1 xz) True) % 4.49/4.69 (Or (Eq (aElement0 a_2) False) % 4.49/4.69 (Or (Eq (sdtmndtplgtdt0 a a_1 a_2) False) % 4.49/4.69 (Or (Eq (sdtmndtplgtdt0 a_2 a_1 xz) False) % 4.49/4.69 (Or (Eq (aElement0 a) False) (Eq (aRewritingSystem0 a_1) False)))))) % 4.49/4.69 Clause #60 (by clausification #[56]): Eq (aElement0 xy) True % 4.49/4.69 Clause #61 (by clausification #[56]): Eq (And (aElement0 xx) (aRewritingSystem0 xR)) True % 4.49/4.69 Clause #65 (by clausification #[61]): Eq (aRewritingSystem0 xR) True % 4.49/4.69 Clause #66 (by clausification #[61]): Eq (aElement0 xx) True % 4.49/4.69 Clause #70 (by clausification #[7]): ∀ (a : Iota), % 4.49/4.69 Eq % 4.49/4.69 (∀ (W1 W2 : Iota), % 4.49/4.69 And (And (aElement0 a) (aRewritingSystem0 W1)) (aElement0 W2) → % 4.49/4.69 Iff (sdtmndtasgtdt0 a W1 W2) (Or (Eq a W2) (sdtmndtplgtdt0 a W1 W2))) % 4.49/4.69 True % 4.49/4.69 Clause #71 (by clausification #[70]): ∀ (a a_1 : Iota), % 4.49/4.69 Eq % 4.49/4.69 (∀ (W2 : Iota), % 4.49/4.69 And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 W2) → % 4.49/4.69 Iff (sdtmndtasgtdt0 a a_1 W2) (Or (Eq a W2) (sdtmndtplgtdt0 a a_1 W2))) % 4.49/4.69 True % 4.49/4.69 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 : Iota), % 4.49/4.69 Eq % 4.49/4.69 (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2) → % 4.49/4.69 Iff (sdtmndtasgtdt0 a a_1 a_2) (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2))) % 4.49/4.69 True % 4.49/4.69 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 : Iota), % 4.49/4.69 Or (Eq (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2)) False) % 4.49/4.69 (Eq (Iff (sdtmndtasgtdt0 a a_1 a_2) (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2))) True) % 4.49/4.69 Clause #74 (by clausification #[73]): ∀ (a a_1 a_2 : Iota), % 4.49/4.69 Or (Eq (Iff (sdtmndtasgtdt0 a a_1 a_2) (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2))) True) % 4.49/4.69 (Or (Eq (And (aElement0 a) (aRewritingSystem0 a_1)) False) (Eq (aElement0 a_2) False)) % 4.49/4.69 Clause #76 (by clausification #[74]): ∀ (a a_1 a_2 : Iota), % 4.49/4.69 Or (Eq (And (aElement0 a) (aRewritingSystem0 a_1)) False) % 4.49/4.69 (Or (Eq (aElement0 a_2) False) % 4.49/4.69 (Or (Eq (sdtmndtasgtdt0 a a_1 a_2) False) (Eq (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2)) True))) % 4.49/4.69 Clause #91 (by clausification #[9]): Eq % 4.49/4.69 (And % 4.49/4.69 (And % 4.49/4.69 (And % 4.49/4.69 (Or (Eq xx xy) % 4.49/4.69 (And % 4.49/4.69 (Or (aReductOfIn0 xy xx xR) % 4.49/4.69 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xx xR)) (sdtmndtplgtdt0 W0 xR xy))) % 4.49/4.69 (sdtmndtplgtdt0 xx xR xy))) % 4.49/4.69 (sdtmndtasgtdt0 xx xR xy)) % 4.49/4.69 (Or (Eq xy xz) % 4.49/4.69 (And % 4.49/4.69 (Or (aReductOfIn0 xz xy xR) % 4.49/4.69 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xy xR)) (sdtmndtplgtdt0 W0 xR xz))) % 4.49/4.69 (sdtmndtplgtdt0 xy xR xz)))) % 4.49/4.69 (sdtmndtasgtdt0 xy xR xz) → % 4.49/4.69 Or % 4.49/4.69 (Or % 4.49/4.69 (Or (Or (Eq xx xz) (aReductOfIn0 xz xx xR)) % 4.49/4.69 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xx xR)) (sdtmndtplgtdt0 W0 xR xz))) % 4.49/4.69 (sdtmndtplgtdt0 xx xR xz)) % 4.49/4.69 (sdtmndtasgtdt0 xx xR xz)) % 4.49/4.69 False % 4.49/4.69 Clause #92 (by clausification #[91]): Eq % 4.49/4.69 (And % 4.49/4.69 (And % 4.49/4.69 (And % 4.49/4.69 (Or (Eq xx xy) % 4.49/4.69 (And % 4.49/4.69 (Or (aReductOfIn0 xy xx xR) % 4.49/4.69 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xx xR)) (sdtmndtplgtdt0 W0 xR xy))) % 4.49/4.69 (sdtmndtplgtdt0 xx xR xy))) % 4.49/4.69 (sdtmndtasgtdt0 xx xR xy)) % 4.49/4.69 (Or (Eq xy xz) % 4.49/4.69 (And % 4.49/4.69 (Or (aReductOfIn0 xz xy xR) % 4.49/4.69 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xy xR)) (sdtmndtplgtdt0 W0 xR xz))) % 4.49/4.71 (sdtmndtplgtdt0 xy xR xz)))) % 4.49/4.71 (sdtmndtasgtdt0 xy xR xz)) % 4.49/4.71 True % 4.49/4.71 Clause #93 (by clausification #[91]): Eq % 4.49/4.71 (Or % 4.49/4.71 (Or % 4.49/4.71 (Or (Or (Eq xx xz) (aReductOfIn0 xz xx xR)) % 4.49/4.71 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xx xR)) (sdtmndtplgtdt0 W0 xR xz))) % 4.49/4.71 (sdtmndtplgtdt0 xx xR xz)) % 4.49/4.71 (sdtmndtasgtdt0 xx xR xz)) % 4.49/4.71 False % 4.49/4.71 Clause #94 (by clausification #[92]): Eq (sdtmndtasgtdt0 xy xR xz) True % 4.49/4.71 Clause #95 (by clausification #[92]): Eq % 4.49/4.71 (And % 4.49/4.71 (And % 4.49/4.71 (Or (Eq xx xy) % 4.49/4.71 (And % 4.49/4.71 (Or (aReductOfIn0 xy xx xR) % 4.49/4.71 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xx xR)) (sdtmndtplgtdt0 W0 xR xy))) % 4.49/4.71 (sdtmndtplgtdt0 xx xR xy))) % 4.49/4.71 (sdtmndtasgtdt0 xx xR xy)) % 4.49/4.71 (Or (Eq xy xz) % 4.49/4.71 (And % 4.49/4.71 (Or (aReductOfIn0 xz xy xR) % 4.49/4.71 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xy xR)) (sdtmndtplgtdt0 W0 xR xz))) % 4.49/4.71 (sdtmndtplgtdt0 xy xR xz)))) % 4.49/4.71 True % 4.49/4.71 Clause #148 (by clausification #[59]): ∀ (a a_1 a_2 : Iota), % 4.49/4.71 Or (Eq (sdtmndtplgtdt0 a a_1 xz) True) % 4.49/4.71 (Or (Eq (aElement0 a_2) False) % 4.49/4.71 (Or (Eq (sdtmndtplgtdt0 a a_1 a_2) False) % 4.49/4.71 (Or (Eq (sdtmndtplgtdt0 a_2 a_1 xz) False) (Or (Eq (aElement0 a) False) (Eq (aRewritingSystem0 a_1) False))))) % 4.49/4.71 Clause #150 (by superposition #[148, 60]): ∀ (a a_1 : Iota), % 4.49/4.71 Or (Eq (sdtmndtplgtdt0 a a_1 xz) True) % 4.49/4.71 (Or (Eq (sdtmndtplgtdt0 a a_1 xy) False) % 4.49/4.71 (Or (Eq (sdtmndtplgtdt0 xy a_1 xz) False) % 4.49/4.71 (Or (Eq (aElement0 a) False) (Or (Eq (aRewritingSystem0 a_1) False) (Eq False True))))) % 4.49/4.71 Clause #218 (by clausification #[76]): ∀ (a a_1 a_2 : Iota), % 4.49/4.71 Or (Eq (aElement0 a) False) % 4.49/4.71 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) False) % 4.49/4.71 (Or (Eq (Or (Eq a_1 a) (sdtmndtplgtdt0 a_1 a_2 a)) True) % 4.49/4.71 (Or (Eq (aElement0 a_1) False) (Eq (aRewritingSystem0 a_2) False)))) % 4.49/4.71 Clause #219 (by clausification #[218]): ∀ (a a_1 a_2 : Iota), % 4.49/4.71 Or (Eq (aElement0 a) False) % 4.49/4.71 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) False) % 4.49/4.71 (Or (Eq (aElement0 a_1) False) % 4.49/4.71 (Or (Eq (aRewritingSystem0 a_2) False) (Or (Eq (Eq a_1 a) True) (Eq (sdtmndtplgtdt0 a_1 a_2 a) True))))) % 4.49/4.71 Clause #220 (by clausification #[219]): ∀ (a a_1 a_2 : Iota), % 4.49/4.71 Or (Eq (aElement0 a) False) % 4.49/4.71 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) False) % 4.49/4.71 (Or (Eq (aElement0 a_1) False) % 4.49/4.71 (Or (Eq (aRewritingSystem0 a_2) False) (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a) True) (Eq a_1 a))))) % 4.49/4.71 Clause #222 (by superposition #[220, 60]): ∀ (a a_1 : Iota), % 4.49/4.71 Or (Eq (sdtmndtasgtdt0 a a_1 xy) False) % 4.49/4.71 (Or (Eq (aElement0 a) False) % 4.49/4.71 (Or (Eq (aRewritingSystem0 a_1) False) (Or (Eq (sdtmndtplgtdt0 a a_1 xy) True) (Or (Eq a xy) (Eq False True))))) % 4.49/4.71 Clause #231 (by clausification #[93]): Eq (sdtmndtasgtdt0 xx xR xz) False % 4.49/4.71 Clause #232 (by clausification #[93]): Eq % 4.49/4.71 (Or % 4.49/4.71 (Or (Or (Eq xx xz) (aReductOfIn0 xz xx xR)) % 4.49/4.71 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xx xR)) (sdtmndtplgtdt0 W0 xR xz))) % 4.49/4.71 (sdtmndtplgtdt0 xx xR xz)) % 4.49/4.71 False % 4.49/4.71 Clause #236 (by clausification #[222]): ∀ (a a_1 : Iota), % 4.49/4.71 Or (Eq (sdtmndtasgtdt0 a a_1 xy) False) % 4.49/4.71 (Or (Eq (aElement0 a) False) % 4.49/4.71 (Or (Eq (aRewritingSystem0 a_1) False) (Or (Eq (sdtmndtplgtdt0 a a_1 xy) True) (Eq a xy)))) % 4.49/4.71 Clause #242 (by clausification #[95]): Eq % 4.49/4.71 (Or (Eq xy xz) % 4.49/4.71 (And % 4.49/4.71 (Or (aReductOfIn0 xz xy xR) % 4.49/4.71 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xy xR)) (sdtmndtplgtdt0 W0 xR xz))) % 4.49/4.71 (sdtmndtplgtdt0 xy xR xz))) % 4.49/4.71 True % 4.49/4.71 Clause #243 (by clausification #[95]): Eq % 4.49/4.71 (And % 4.49/4.71 (Or (Eq xx xy) % 4.49/4.71 (And % 4.49/4.71 (Or (aReductOfIn0 xy xx xR) % 4.49/4.71 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xx xR)) (sdtmndtplgtdt0 W0 xR xy))) % 4.49/4.71 (sdtmndtplgtdt0 xx xR xy))) % 4.49/4.71 (sdtmndtasgtdt0 xx xR xy)) % 4.49/4.71 True % 4.49/4.71 Clause #244 (by clausification #[242]): Or (Eq (Eq xy xz) True) % 4.49/4.71 (Eq % 4.49/4.71 (And % 4.49/4.71 (Or (aReductOfIn0 xz xy xR) % 4.49/4.71 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xy xR)) (sdtmndtplgtdt0 W0 xR xz))) % 4.49/4.71 (sdtmndtplgtdt0 xy xR xz)) % 4.49/4.71 True) % 4.49/4.71 Clause #245 (by clausification #[244]): Or % 4.49/4.71 (Eq % 4.49/4.71 (And % 4.54/4.73 (Or (aReductOfIn0 xz xy xR) % 4.54/4.73 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xy xR)) (sdtmndtplgtdt0 W0 xR xz))) % 4.54/4.73 (sdtmndtplgtdt0 xy xR xz)) % 4.54/4.73 True) % 4.54/4.73 (Eq xy xz) % 4.54/4.73 Clause #246 (by clausification #[245]): Or (Eq xy xz) (Eq (sdtmndtplgtdt0 xy xR xz) True) % 4.54/4.73 Clause #270 (by clausification #[150]): ∀ (a a_1 : Iota), % 4.54/4.73 Or (Eq (sdtmndtplgtdt0 a a_1 xz) True) % 4.54/4.73 (Or (Eq (sdtmndtplgtdt0 a a_1 xy) False) % 4.54/4.73 (Or (Eq (sdtmndtplgtdt0 xy a_1 xz) False) (Or (Eq (aElement0 a) False) (Eq (aRewritingSystem0 a_1) False)))) % 4.54/4.73 Clause #357 (by clausification #[232]): Eq (sdtmndtplgtdt0 xx xR xz) False % 4.54/4.73 Clause #370 (by clausification #[243]): Eq (sdtmndtasgtdt0 xx xR xy) True % 4.54/4.73 Clause #372 (by superposition #[370, 236]): Or (Eq True False) % 4.54/4.73 (Or (Eq (aElement0 xx) False) % 4.54/4.73 (Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xx xR xy) True) (Eq xx xy)))) % 4.54/4.73 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))) % 4.54/4.73 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))) % 4.54/4.73 Clause #375 (by clausification #[374]): Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xx xR xy) True) (Eq xx xy)) % 4.54/4.73 Clause #376 (by forward demodulation #[375, 65]): Or (Eq True False) (Or (Eq (sdtmndtplgtdt0 xx xR xy) True) (Eq xx xy)) % 4.54/4.73 Clause #377 (by clausification #[376]): Or (Eq (sdtmndtplgtdt0 xx xR xy) True) (Eq xx xy) % 4.54/4.73 Clause #380 (by superposition #[377, 270]): Or (Eq xx xy) % 4.54/4.73 (Or (Eq (sdtmndtplgtdt0 xx xR xz) True) % 4.54/4.73 (Or (Eq True False) % 4.54/4.73 (Or (Eq (sdtmndtplgtdt0 xy xR xz) False) (Or (Eq (aElement0 xx) False) (Eq (aRewritingSystem0 xR) False))))) % 4.54/4.73 Clause #389 (by clausification #[380]): Or (Eq xx xy) % 4.54/4.73 (Or (Eq (sdtmndtplgtdt0 xx xR xz) True) % 4.54/4.73 (Or (Eq (sdtmndtplgtdt0 xy xR xz) False) (Or (Eq (aElement0 xx) False) (Eq (aRewritingSystem0 xR) False)))) % 4.54/4.73 Clause #390 (by forward demodulation #[389, 357]): Or (Eq xx xy) % 4.54/4.73 (Or (Eq False True) % 4.54/4.73 (Or (Eq (sdtmndtplgtdt0 xy xR xz) False) (Or (Eq (aElement0 xx) False) (Eq (aRewritingSystem0 xR) False)))) % 4.54/4.73 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))) % 4.54/4.73 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))) % 4.54/4.73 Clause #393 (by clausification #[392]): Or (Eq xx xy) (Or (Eq (sdtmndtplgtdt0 xy xR xz) False) (Eq (aRewritingSystem0 xR) False)) % 4.54/4.73 Clause #394 (by forward demodulation #[393, 65]): Or (Eq xx xy) (Or (Eq (sdtmndtplgtdt0 xy xR xz) False) (Eq True False)) % 4.54/4.73 Clause #395 (by clausification #[394]): Or (Eq xx xy) (Eq (sdtmndtplgtdt0 xy xR xz) False) % 4.54/4.73 Clause #396 (by superposition #[395, 246]): Or (Eq xx xy) (Or (Eq xy xz) (Eq False True)) % 4.54/4.73 Clause #401 (by clausification #[396]): Or (Eq xx xy) (Eq xy xz) % 4.54/4.73 Clause #415 (by superposition #[401, 357]): Or (Eq xx xy) (Eq (sdtmndtplgtdt0 xx xR xy) False) % 4.54/4.73 Clause #420 (by superposition #[415, 377]): Or (Eq xx xy) (Or (Eq False True) (Eq xx xy)) % 4.54/4.73 Clause #421 (by clausification #[420]): Or (Eq xx xy) (Eq xx xy) % 4.54/4.73 Clause #422 (by eliminate duplicate literals #[421]): Eq xx xy % 4.54/4.73 Clause #423 (by backward demodulation #[422, 94]): Eq (sdtmndtasgtdt0 xx xR xz) True % 4.54/4.73 Clause #478 (by superposition #[423, 231]): Eq True False % 4.54/4.73 Clause #480 (by clausification #[478]): False % 4.54/4.73 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------