%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : COM016+1 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n003.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 37.93s 38.12s % Output : Proof 38.08s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : COM016+1 : TPTP v9.2.0. Released v4.0.0. % 0.06/0.13 % Command : duper %s % 0.14/0.34 % Computer : n003.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Thu Oct 2 16:01:38 EDT 2025 % 0.14/0.34 % CPUTime : % 37.93/38.12 SZS status Theorem for theBenchmark.p % 37.93/38.12 SZS output start Proof for theBenchmark.p % 37.93/38.12 Clause #5 (by assumption #[]): Eq % 37.93/38.12 (∀ (W0 W1 W2 : Iota), % 37.93/38.12 And (And (aElement0 W0) (aRewritingSystem0 W1)) (aElement0 W2) → % 37.93/38.12 Iff (sdtmndtplgtdt0 W0 W1 W2) % 37.93/38.12 (Or (aReductOfIn0 W2 W0 W1) % 37.93/38.12 (Exists fun W3 => And (And (aElement0 W3) (aReductOfIn0 W3 W0 W1)) (sdtmndtplgtdt0 W3 W1 W2)))) % 37.93/38.12 True % 37.93/38.12 Clause #7 (by assumption #[]): Eq % 37.93/38.12 (∀ (W0 W1 W2 : Iota), % 37.93/38.12 And (And (aElement0 W0) (aRewritingSystem0 W1)) (aElement0 W2) → % 37.93/38.12 Iff (sdtmndtasgtdt0 W0 W1 W2) (Or (Eq W0 W2) (sdtmndtplgtdt0 W0 W1 W2))) % 37.93/38.12 True % 37.93/38.12 Clause #14 (by assumption #[]): Eq (aRewritingSystem0 xR) True % 37.93/38.12 Clause #16 (by assumption #[]): Eq (And (And (aElement0 xa) (aElement0 xb)) (aElement0 xc)) True % 37.93/38.12 Clause #18 (by assumption #[]): Eq (And (sdtmndtplgtdt0 xa xR xb) (sdtmndtplgtdt0 xa xR xc)) True % 37.93/38.12 Clause #19 (by assumption #[]): Eq (Not (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xa xR)) (sdtmndtasgtdt0 W0 xR xb))) True % 37.93/38.12 Clause #45 (by clausification #[16]): Eq (And (aElement0 xa) (aElement0 xb)) True % 37.93/38.12 Clause #47 (by clausification #[45]): Eq (aElement0 xb) True % 37.93/38.12 Clause #48 (by clausification #[45]): Eq (aElement0 xa) True % 37.93/38.12 Clause #51 (by clausification #[5]): ∀ (a : Iota), % 37.93/38.12 Eq % 37.93/38.12 (∀ (W1 W2 : Iota), % 37.93/38.12 And (And (aElement0 a) (aRewritingSystem0 W1)) (aElement0 W2) → % 37.93/38.12 Iff (sdtmndtplgtdt0 a W1 W2) % 37.93/38.12 (Or (aReductOfIn0 W2 a W1) % 37.93/38.12 (Exists fun W3 => And (And (aElement0 W3) (aReductOfIn0 W3 a W1)) (sdtmndtplgtdt0 W3 W1 W2)))) % 37.93/38.12 True % 37.93/38.12 Clause #52 (by clausification #[51]): ∀ (a a_1 : Iota), % 37.93/38.12 Eq % 37.93/38.12 (∀ (W2 : Iota), % 37.93/38.12 And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 W2) → % 37.93/38.12 Iff (sdtmndtplgtdt0 a a_1 W2) % 37.93/38.12 (Or (aReductOfIn0 W2 a a_1) % 37.93/38.12 (Exists fun W3 => And (And (aElement0 W3) (aReductOfIn0 W3 a a_1)) (sdtmndtplgtdt0 W3 a_1 W2)))) % 37.93/38.12 True % 37.93/38.12 Clause #53 (by clausification #[52]): ∀ (a a_1 a_2 : Iota), % 37.93/38.12 Eq % 37.93/38.12 (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2) → % 37.93/38.12 Iff (sdtmndtplgtdt0 a a_1 a_2) % 37.93/38.12 (Or (aReductOfIn0 a_2 a a_1) % 37.93/38.12 (Exists fun W3 => And (And (aElement0 W3) (aReductOfIn0 W3 a a_1)) (sdtmndtplgtdt0 W3 a_1 a_2)))) % 37.93/38.12 True % 37.93/38.12 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), % 37.93/38.12 Or (Eq (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2)) False) % 37.93/38.12 (Eq % 37.93/38.12 (Iff (sdtmndtplgtdt0 a a_1 a_2) % 37.93/38.12 (Or (aReductOfIn0 a_2 a a_1) % 37.93/38.12 (Exists fun W3 => And (And (aElement0 W3) (aReductOfIn0 W3 a a_1)) (sdtmndtplgtdt0 W3 a_1 a_2)))) % 37.93/38.12 True) % 37.93/38.12 Clause #55 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), % 37.93/38.12 Or % 37.93/38.12 (Eq % 37.93/38.12 (Iff (sdtmndtplgtdt0 a a_1 a_2) % 37.93/38.12 (Or (aReductOfIn0 a_2 a a_1) % 37.93/38.12 (Exists fun W3 => And (And (aElement0 W3) (aReductOfIn0 W3 a a_1)) (sdtmndtplgtdt0 W3 a_1 a_2)))) % 37.93/38.12 True) % 37.93/38.12 (Or (Eq (And (aElement0 a) (aRewritingSystem0 a_1)) False) (Eq (aElement0 a_2) False)) % 37.93/38.12 Clause #57 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), % 37.93/38.12 Or (Eq (And (aElement0 a) (aRewritingSystem0 a_1)) False) % 37.93/38.12 (Or (Eq (aElement0 a_2) False) % 37.93/38.12 (Or (Eq (sdtmndtplgtdt0 a a_1 a_2) False) % 37.93/38.12 (Eq % 37.93/38.12 (Or (aReductOfIn0 a_2 a a_1) % 37.93/38.12 (Exists fun W3 => And (And (aElement0 W3) (aReductOfIn0 W3 a a_1)) (sdtmndtplgtdt0 W3 a_1 a_2))) % 37.93/38.12 True))) % 37.93/38.12 Clause #68 (by clausification #[18]): Eq (sdtmndtplgtdt0 xa xR xb) True % 37.93/38.12 Clause #102 (by clausification #[7]): ∀ (a : Iota), % 37.93/38.12 Eq % 37.93/38.12 (∀ (W1 W2 : Iota), % 37.93/38.12 And (And (aElement0 a) (aRewritingSystem0 W1)) (aElement0 W2) → % 37.93/38.12 Iff (sdtmndtasgtdt0 a W1 W2) (Or (Eq a W2) (sdtmndtplgtdt0 a W1 W2))) % 37.93/38.12 True % 37.93/38.12 Clause #103 (by clausification #[102]): ∀ (a a_1 : Iota), % 37.93/38.12 Eq % 37.93/38.12 (∀ (W2 : Iota), % 37.93/38.12 And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 W2) → % 37.93/38.12 Iff (sdtmndtasgtdt0 a a_1 W2) (Or (Eq a W2) (sdtmndtplgtdt0 a a_1 W2))) % 37.93/38.12 True % 37.93/38.12 Clause #104 (by clausification #[103]): ∀ (a a_1 a_2 : Iota), % 37.93/38.12 Eq % 37.93/38.12 (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2) → % 37.93/38.12 Iff (sdtmndtasgtdt0 a a_1 a_2) (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2))) % 37.93/38.14 True % 37.93/38.14 Clause #105 (by clausification #[104]): ∀ (a a_1 a_2 : Iota), % 37.93/38.14 Or (Eq (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2)) False) % 37.93/38.14 (Eq (Iff (sdtmndtasgtdt0 a a_1 a_2) (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2))) True) % 37.93/38.14 Clause #106 (by clausification #[105]): ∀ (a a_1 a_2 : Iota), % 37.93/38.14 Or (Eq (Iff (sdtmndtasgtdt0 a a_1 a_2) (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2))) True) % 37.93/38.14 (Or (Eq (And (aElement0 a) (aRewritingSystem0 a_1)) False) (Eq (aElement0 a_2) False)) % 37.93/38.14 Clause #107 (by clausification #[106]): ∀ (a a_1 a_2 : Iota), % 37.93/38.14 Or (Eq (And (aElement0 a) (aRewritingSystem0 a_1)) False) % 37.93/38.14 (Or (Eq (aElement0 a_2) False) % 37.93/38.14 (Or (Eq (sdtmndtasgtdt0 a a_1 a_2) True) (Eq (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2)) False))) % 37.93/38.14 Clause #109 (by clausification #[107]): ∀ (a a_1 a_2 : Iota), % 37.93/38.14 Or (Eq (aElement0 a) False) % 37.93/38.14 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) True) % 37.93/38.14 (Or (Eq (Or (Eq a_1 a) (sdtmndtplgtdt0 a_1 a_2 a)) False) % 37.93/38.14 (Or (Eq (aElement0 a_1) False) (Eq (aRewritingSystem0 a_2) False)))) % 37.93/38.14 Clause #110 (by clausification #[109]): ∀ (a a_1 a_2 : Iota), % 37.93/38.14 Or (Eq (aElement0 a) False) % 37.93/38.14 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) True) % 37.93/38.14 (Or (Eq (aElement0 a_1) False) (Or (Eq (aRewritingSystem0 a_2) False) (Eq (sdtmndtplgtdt0 a_1 a_2 a) False)))) % 37.93/38.14 Clause #111 (by clausification #[109]): ∀ (a a_1 a_2 : Iota), % 37.93/38.14 Or (Eq (aElement0 a) False) % 37.93/38.14 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) True) % 37.93/38.14 (Or (Eq (aElement0 a_1) False) (Or (Eq (aRewritingSystem0 a_2) False) (Eq (Eq a_1 a) False)))) % 37.93/38.14 Clause #113 (by superposition #[110, 47]): ∀ (a a_1 : Iota), % 37.93/38.14 Or (Eq (sdtmndtasgtdt0 a a_1 xb) True) % 37.93/38.14 (Or (Eq (aElement0 a) False) % 37.93/38.14 (Or (Eq (aRewritingSystem0 a_1) False) (Or (Eq (sdtmndtplgtdt0 a a_1 xb) False) (Eq False True)))) % 37.93/38.14 Clause #178 (by clausification #[19]): Eq (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xa xR)) (sdtmndtasgtdt0 W0 xR xb)) False % 37.93/38.14 Clause #179 (by clausification #[178]): ∀ (a : Iota), Eq (And (And (aElement0 a) (aReductOfIn0 a xa xR)) (sdtmndtasgtdt0 a xR xb)) False % 37.93/38.14 Clause #180 (by clausification #[179]): ∀ (a : Iota), Or (Eq (And (aElement0 a) (aReductOfIn0 a xa xR)) False) (Eq (sdtmndtasgtdt0 a xR xb) False) % 37.93/38.14 Clause #181 (by clausification #[180]): ∀ (a : Iota), Or (Eq (sdtmndtasgtdt0 a xR xb) False) (Or (Eq (aElement0 a) False) (Eq (aReductOfIn0 a xa xR) False)) % 37.93/38.14 Clause #182 (by clausification #[113]): ∀ (a a_1 : Iota), % 37.93/38.14 Or (Eq (sdtmndtasgtdt0 a a_1 xb) True) % 37.93/38.14 (Or (Eq (aElement0 a) False) (Or (Eq (aRewritingSystem0 a_1) False) (Eq (sdtmndtplgtdt0 a a_1 xb) False))) % 37.93/38.14 Clause #237 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), % 37.93/38.14 Or (Eq (aElement0 a) False) % 37.93/38.14 (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a) False) % 37.93/38.14 (Or % 37.93/38.14 (Eq % 37.93/38.14 (Or (aReductOfIn0 a a_1 a_2) % 37.93/38.14 (Exists fun W3 => And (And (aElement0 W3) (aReductOfIn0 W3 a_1 a_2)) (sdtmndtplgtdt0 W3 a_2 a))) % 37.93/38.14 True) % 37.93/38.14 (Or (Eq (aElement0 a_1) False) (Eq (aRewritingSystem0 a_2) False)))) % 37.93/38.14 Clause #238 (by clausification #[237]): ∀ (a a_1 a_2 : Iota), % 37.93/38.14 Or (Eq (aElement0 a) False) % 37.93/38.14 (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a) False) % 37.93/38.14 (Or (Eq (aElement0 a_1) False) % 37.93/38.14 (Or (Eq (aRewritingSystem0 a_2) False) % 37.93/38.14 (Or (Eq (aReductOfIn0 a a_1 a_2) True) % 37.93/38.14 (Eq (Exists fun W3 => And (And (aElement0 W3) (aReductOfIn0 W3 a_1 a_2)) (sdtmndtplgtdt0 W3 a_2 a)) % 37.93/38.14 True))))) % 37.93/38.14 Clause #239 (by clausification #[238]): ∀ (a a_1 a_2 a_3 : Iota), % 37.93/38.14 Or (Eq (aElement0 a) False) % 37.93/38.14 (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a) False) % 37.93/38.14 (Or (Eq (aElement0 a_1) False) % 37.93/38.14 (Or (Eq (aRewritingSystem0 a_2) False) % 37.93/38.14 (Or (Eq (aReductOfIn0 a a_1 a_2) True) % 37.93/38.14 (Eq % 37.93/38.14 (And (And (aElement0 (skS.0 11 a_1 a_2 a a_3)) (aReductOfIn0 (skS.0 11 a_1 a_2 a a_3) a_1 a_2)) % 37.93/38.14 (sdtmndtplgtdt0 (skS.0 11 a_1 a_2 a a_3) a_2 a)) % 37.93/38.14 True))))) % 37.93/38.14 Clause #240 (by clausification #[239]): ∀ (a a_1 a_2 a_3 : Iota), % 37.93/38.14 Or (Eq (aElement0 a) False) % 37.93/38.14 (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a) False) % 37.93/38.14 (Or (Eq (aElement0 a_1) False) % 37.93/38.14 (Or (Eq (aRewritingSystem0 a_2) False) % 38.00/38.17 (Or (Eq (aReductOfIn0 a a_1 a_2) True) (Eq (sdtmndtplgtdt0 (skS.0 11 a_1 a_2 a a_3) a_2 a) True))))) % 38.00/38.17 Clause #241 (by clausification #[239]): ∀ (a a_1 a_2 a_3 : Iota), % 38.00/38.17 Or (Eq (aElement0 a) False) % 38.00/38.17 (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a) False) % 38.00/38.17 (Or (Eq (aElement0 a_1) False) % 38.00/38.17 (Or (Eq (aRewritingSystem0 a_2) False) % 38.00/38.17 (Or (Eq (aReductOfIn0 a a_1 a_2) True) % 38.00/38.17 (Eq (And (aElement0 (skS.0 11 a_1 a_2 a a_3)) (aReductOfIn0 (skS.0 11 a_1 a_2 a a_3) a_1 a_2)) True))))) % 38.00/38.17 Clause #243 (by superposition #[240, 47]): ∀ (a a_1 a_2 : Iota), % 38.00/38.17 Or (Eq (sdtmndtplgtdt0 a a_1 xb) False) % 38.00/38.17 (Or (Eq (aElement0 a) False) % 38.00/38.17 (Or (Eq (aRewritingSystem0 a_1) False) % 38.00/38.17 (Or (Eq (aReductOfIn0 xb a a_1) True) % 38.00/38.17 (Or (Eq (sdtmndtplgtdt0 (skS.0 11 a a_1 xb a_2) a_1 xb) True) (Eq False True))))) % 38.00/38.17 Clause #331 (by clausification #[111]): ∀ (a a_1 a_2 : Iota), % 38.00/38.17 Or (Eq (aElement0 a) False) % 38.00/38.17 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) True) % 38.00/38.17 (Or (Eq (aElement0 a_1) False) (Or (Eq (aRewritingSystem0 a_2) False) (Ne a_1 a)))) % 38.00/38.17 Clause #332 (by destructive equality resolution #[331]): ∀ (a a_1 : Iota), % 38.00/38.17 Or (Eq (aElement0 a) False) % 38.00/38.17 (Or (Eq (sdtmndtasgtdt0 a a_1 a) True) (Or (Eq (aElement0 a) False) (Eq (aRewritingSystem0 a_1) False))) % 38.00/38.17 Clause #333 (by eliminate duplicate literals #[332]): ∀ (a a_1 : Iota), Or (Eq (aElement0 a) False) (Or (Eq (sdtmndtasgtdt0 a a_1 a) True) (Eq (aRewritingSystem0 a_1) False)) % 38.00/38.17 Clause #335 (by superposition #[333, 47]): ∀ (a : Iota), Or (Eq (sdtmndtasgtdt0 xb a xb) True) (Or (Eq (aRewritingSystem0 a) False) (Eq False True)) % 38.00/38.17 Clause #346 (by clausification #[335]): ∀ (a : Iota), Or (Eq (sdtmndtasgtdt0 xb a xb) True) (Eq (aRewritingSystem0 a) False) % 38.00/38.17 Clause #347 (by superposition #[346, 14]): Or (Eq (sdtmndtasgtdt0 xb xR xb) True) (Eq False True) % 38.00/38.17 Clause #348 (by clausification #[347]): Eq (sdtmndtasgtdt0 xb xR xb) True % 38.00/38.17 Clause #350 (by superposition #[348, 181]): Or (Eq True False) (Or (Eq (aElement0 xb) False) (Eq (aReductOfIn0 xb xa xR) False)) % 38.00/38.17 Clause #356 (by clausification #[350]): Or (Eq (aElement0 xb) False) (Eq (aReductOfIn0 xb xa xR) False) % 38.00/38.17 Clause #357 (by forward demodulation #[356, 47]): Or (Eq True False) (Eq (aReductOfIn0 xb xa xR) False) % 38.00/38.17 Clause #358 (by clausification #[357]): Eq (aReductOfIn0 xb xa xR) False % 38.00/38.17 Clause #745 (by clausification #[241]): ∀ (a a_1 a_2 a_3 : Iota), % 38.00/38.17 Or (Eq (aElement0 a) False) % 38.00/38.17 (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a) False) % 38.00/38.17 (Or (Eq (aElement0 a_1) False) % 38.00/38.17 (Or (Eq (aRewritingSystem0 a_2) False) % 38.00/38.17 (Or (Eq (aReductOfIn0 a a_1 a_2) True) (Eq (aReductOfIn0 (skS.0 11 a_1 a_2 a a_3) a_1 a_2) True))))) % 38.00/38.17 Clause #746 (by clausification #[241]): ∀ (a a_1 a_2 a_3 : Iota), % 38.00/38.17 Or (Eq (aElement0 a) False) % 38.00/38.17 (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a) False) % 38.00/38.17 (Or (Eq (aElement0 a_1) False) % 38.00/38.17 (Or (Eq (aRewritingSystem0 a_2) False) % 38.00/38.17 (Or (Eq (aReductOfIn0 a a_1 a_2) True) (Eq (aElement0 (skS.0 11 a_1 a_2 a a_3)) True))))) % 38.00/38.17 Clause #748 (by superposition #[745, 47]): ∀ (a a_1 a_2 : Iota), % 38.00/38.17 Or (Eq (sdtmndtplgtdt0 a a_1 xb) False) % 38.00/38.17 (Or (Eq (aElement0 a) False) % 38.00/38.17 (Or (Eq (aRewritingSystem0 a_1) False) % 38.00/38.17 (Or (Eq (aReductOfIn0 xb a a_1) True) % 38.00/38.17 (Or (Eq (aReductOfIn0 (skS.0 11 a a_1 xb a_2) a a_1) True) (Eq False True))))) % 38.00/38.17 Clause #770 (by clausification #[243]): ∀ (a a_1 a_2 : Iota), % 38.00/38.17 Or (Eq (sdtmndtplgtdt0 a a_1 xb) False) % 38.00/38.17 (Or (Eq (aElement0 a) False) % 38.00/38.17 (Or (Eq (aRewritingSystem0 a_1) False) % 38.00/38.17 (Or (Eq (aReductOfIn0 xb a a_1) True) (Eq (sdtmndtplgtdt0 (skS.0 11 a a_1 xb a_2) a_1 xb) True)))) % 38.00/38.17 Clause #771 (by superposition #[770, 68]): ∀ (a : Iota), % 38.00/38.17 Or (Eq (aElement0 xa) False) % 38.00/38.17 (Or (Eq (aRewritingSystem0 xR) False) % 38.00/38.17 (Or (Eq (aReductOfIn0 xb xa xR) True) % 38.00/38.17 (Or (Eq (sdtmndtplgtdt0 (skS.0 11 xa xR xb a) xR xb) True) (Eq False True)))) % 38.00/38.17 Clause #883 (by clausification #[771]): ∀ (a : Iota), % 38.00/38.17 Or (Eq (aElement0 xa) False) % 38.00/38.17 (Or (Eq (aRewritingSystem0 xR) False) % 38.00/38.17 (Or (Eq (aReductOfIn0 xb xa xR) True) (Eq (sdtmndtplgtdt0 (skS.0 11 xa xR xb a) xR xb) True))) % 38.00/38.19 Clause #884 (by forward demodulation #[883, 48]): ∀ (a : Iota), % 38.00/38.19 Or (Eq True False) % 38.00/38.19 (Or (Eq (aRewritingSystem0 xR) False) % 38.00/38.19 (Or (Eq (aReductOfIn0 xb xa xR) True) (Eq (sdtmndtplgtdt0 (skS.0 11 xa xR xb a) xR xb) True))) % 38.00/38.19 Clause #885 (by clausification #[884]): ∀ (a : Iota), % 38.00/38.19 Or (Eq (aRewritingSystem0 xR) False) % 38.00/38.19 (Or (Eq (aReductOfIn0 xb xa xR) True) (Eq (sdtmndtplgtdt0 (skS.0 11 xa xR xb a) xR xb) True)) % 38.00/38.19 Clause #886 (by forward demodulation #[885, 14]): ∀ (a : Iota), % 38.00/38.19 Or (Eq True False) (Or (Eq (aReductOfIn0 xb xa xR) True) (Eq (sdtmndtplgtdt0 (skS.0 11 xa xR xb a) xR xb) True)) % 38.00/38.19 Clause #887 (by clausification #[886]): ∀ (a : Iota), Or (Eq (aReductOfIn0 xb xa xR) True) (Eq (sdtmndtplgtdt0 (skS.0 11 xa xR xb a) xR xb) True) % 38.00/38.19 Clause #888 (by forward demodulation #[887, 358]): ∀ (a : Iota), Or (Eq False True) (Eq (sdtmndtplgtdt0 (skS.0 11 xa xR xb a) xR xb) True) % 38.00/38.19 Clause #889 (by clausification #[888]): ∀ (a : Iota), Eq (sdtmndtplgtdt0 (skS.0 11 xa xR xb a) xR xb) True % 38.00/38.19 Clause #1764 (by superposition #[746, 47]): ∀ (a a_1 a_2 : Iota), % 38.00/38.19 Or (Eq (sdtmndtplgtdt0 a a_1 xb) False) % 38.00/38.19 (Or (Eq (aElement0 a) False) % 38.00/38.19 (Or (Eq (aRewritingSystem0 a_1) False) % 38.00/38.19 (Or (Eq (aReductOfIn0 xb a a_1) True) (Or (Eq (aElement0 (skS.0 11 a a_1 xb a_2)) True) (Eq False True))))) % 38.00/38.19 Clause #1779 (by clausification #[1764]): ∀ (a a_1 a_2 : Iota), % 38.00/38.19 Or (Eq (sdtmndtplgtdt0 a a_1 xb) False) % 38.00/38.19 (Or (Eq (aElement0 a) False) % 38.00/38.19 (Or (Eq (aRewritingSystem0 a_1) False) % 38.00/38.19 (Or (Eq (aReductOfIn0 xb a a_1) True) (Eq (aElement0 (skS.0 11 a a_1 xb a_2)) True)))) % 38.00/38.19 Clause #1780 (by superposition #[1779, 68]): ∀ (a : Iota), % 38.00/38.19 Or (Eq (aElement0 xa) False) % 38.00/38.19 (Or (Eq (aRewritingSystem0 xR) False) % 38.00/38.19 (Or (Eq (aReductOfIn0 xb xa xR) True) (Or (Eq (aElement0 (skS.0 11 xa xR xb a)) True) (Eq False True)))) % 38.00/38.19 Clause #1782 (by clausification #[1780]): ∀ (a : Iota), % 38.00/38.19 Or (Eq (aElement0 xa) False) % 38.00/38.19 (Or (Eq (aRewritingSystem0 xR) False) % 38.00/38.19 (Or (Eq (aReductOfIn0 xb xa xR) True) (Eq (aElement0 (skS.0 11 xa xR xb a)) True))) % 38.00/38.19 Clause #1783 (by forward demodulation #[1782, 48]): ∀ (a : Iota), % 38.00/38.19 Or (Eq True False) % 38.00/38.19 (Or (Eq (aRewritingSystem0 xR) False) % 38.00/38.19 (Or (Eq (aReductOfIn0 xb xa xR) True) (Eq (aElement0 (skS.0 11 xa xR xb a)) True))) % 38.00/38.19 Clause #1784 (by clausification #[1783]): ∀ (a : Iota), % 38.00/38.19 Or (Eq (aRewritingSystem0 xR) False) % 38.00/38.19 (Or (Eq (aReductOfIn0 xb xa xR) True) (Eq (aElement0 (skS.0 11 xa xR xb a)) True)) % 38.00/38.19 Clause #1785 (by forward demodulation #[1784, 14]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (aReductOfIn0 xb xa xR) True) (Eq (aElement0 (skS.0 11 xa xR xb a)) True)) % 38.00/38.19 Clause #1786 (by clausification #[1785]): ∀ (a : Iota), Or (Eq (aReductOfIn0 xb xa xR) True) (Eq (aElement0 (skS.0 11 xa xR xb a)) True) % 38.00/38.19 Clause #1787 (by forward demodulation #[1786, 358]): ∀ (a : Iota), Or (Eq False True) (Eq (aElement0 (skS.0 11 xa xR xb a)) True) % 38.00/38.19 Clause #1788 (by clausification #[1787]): ∀ (a : Iota), Eq (aElement0 (skS.0 11 xa xR xb a)) True % 38.00/38.19 Clause #1794 (by superposition #[1788, 182]): ∀ (a a_1 : Iota), % 38.00/38.19 Or (Eq (sdtmndtasgtdt0 (skS.0 11 xa xR xb a) a_1 xb) True) % 38.00/38.19 (Or (Eq True False) % 38.00/38.19 (Or (Eq (aRewritingSystem0 a_1) False) (Eq (sdtmndtplgtdt0 (skS.0 11 xa xR xb a) a_1 xb) False))) % 38.00/38.19 Clause #2846 (by clausification #[748]): ∀ (a a_1 a_2 : Iota), % 38.00/38.19 Or (Eq (sdtmndtplgtdt0 a a_1 xb) False) % 38.00/38.19 (Or (Eq (aElement0 a) False) % 38.00/38.19 (Or (Eq (aRewritingSystem0 a_1) False) % 38.00/38.19 (Or (Eq (aReductOfIn0 xb a a_1) True) (Eq (aReductOfIn0 (skS.0 11 a a_1 xb a_2) a a_1) True)))) % 38.00/38.19 Clause #2847 (by superposition #[2846, 68]): ∀ (a : Iota), % 38.00/38.19 Or (Eq (aElement0 xa) False) % 38.00/38.19 (Or (Eq (aRewritingSystem0 xR) False) % 38.00/38.19 (Or (Eq (aReductOfIn0 xb xa xR) True) (Or (Eq (aReductOfIn0 (skS.0 11 xa xR xb a) xa xR) True) (Eq False True)))) % 38.00/38.19 Clause #2849 (by clausification #[2847]): ∀ (a : Iota), % 38.00/38.19 Or (Eq (aElement0 xa) False) % 38.00/38.19 (Or (Eq (aRewritingSystem0 xR) False) % 38.00/38.19 (Or (Eq (aReductOfIn0 xb xa xR) True) (Eq (aReductOfIn0 (skS.0 11 xa xR xb a) xa xR) True))) % 38.00/38.19 Clause #2850 (by forward demodulation #[2849, 48]): ∀ (a : Iota), % 38.08/38.27 Or (Eq True False) % 38.08/38.27 (Or (Eq (aRewritingSystem0 xR) False) % 38.08/38.27 (Or (Eq (aReductOfIn0 xb xa xR) True) (Eq (aReductOfIn0 (skS.0 11 xa xR xb a) xa xR) True))) % 38.08/38.27 Clause #2851 (by clausification #[2850]): ∀ (a : Iota), % 38.08/38.27 Or (Eq (aRewritingSystem0 xR) False) % 38.08/38.27 (Or (Eq (aReductOfIn0 xb xa xR) True) (Eq (aReductOfIn0 (skS.0 11 xa xR xb a) xa xR) True)) % 38.08/38.27 Clause #2852 (by forward demodulation #[2851, 14]): ∀ (a : Iota), % 38.08/38.27 Or (Eq True False) (Or (Eq (aReductOfIn0 xb xa xR) True) (Eq (aReductOfIn0 (skS.0 11 xa xR xb a) xa xR) True)) % 38.08/38.27 Clause #2853 (by clausification #[2852]): ∀ (a : Iota), Or (Eq (aReductOfIn0 xb xa xR) True) (Eq (aReductOfIn0 (skS.0 11 xa xR xb a) xa xR) True) % 38.08/38.27 Clause #2854 (by forward demodulation #[2853, 358]): ∀ (a : Iota), Or (Eq False True) (Eq (aReductOfIn0 (skS.0 11 xa xR xb a) xa xR) True) % 38.08/38.27 Clause #2855 (by clausification #[2854]): ∀ (a : Iota), Eq (aReductOfIn0 (skS.0 11 xa xR xb a) xa xR) True % 38.08/38.27 Clause #3878 (by clausification #[1794]): ∀ (a a_1 : Iota), % 38.08/38.27 Or (Eq (sdtmndtasgtdt0 (skS.0 11 xa xR xb a) a_1 xb) True) % 38.08/38.27 (Or (Eq (aRewritingSystem0 a_1) False) (Eq (sdtmndtplgtdt0 (skS.0 11 xa xR xb a) a_1 xb) False)) % 38.08/38.27 Clause #3879 (by superposition #[3878, 14]): ∀ (a : Iota), % 38.08/38.27 Or (Eq (sdtmndtasgtdt0 (skS.0 11 xa xR xb a) xR xb) True) % 38.08/38.27 (Or (Eq (sdtmndtplgtdt0 (skS.0 11 xa xR xb a) xR xb) False) (Eq False True)) % 38.08/38.27 Clause #3880 (by clausification #[3879]): ∀ (a : Iota), % 38.08/38.27 Or (Eq (sdtmndtasgtdt0 (skS.0 11 xa xR xb a) xR xb) True) (Eq (sdtmndtplgtdt0 (skS.0 11 xa xR xb a) xR xb) False) % 38.08/38.27 Clause #3881 (by superposition #[3880, 889]): ∀ (a : Iota), Or (Eq (sdtmndtasgtdt0 (skS.0 11 xa xR xb a) xR xb) True) (Eq False True) % 38.08/38.27 Clause #3882 (by clausification #[3881]): ∀ (a : Iota), Eq (sdtmndtasgtdt0 (skS.0 11 xa xR xb a) xR xb) True % 38.08/38.27 Clause #3884 (by superposition #[3882, 181]): ∀ (a : Iota), % 38.08/38.27 Or (Eq True False) % 38.08/38.27 (Or (Eq (aElement0 (skS.0 11 xa xR xb a)) False) (Eq (aReductOfIn0 (skS.0 11 xa xR xb a) xa xR) False)) % 38.08/38.27 Clause #3892 (by clausification #[3884]): ∀ (a : Iota), Or (Eq (aElement0 (skS.0 11 xa xR xb a)) False) (Eq (aReductOfIn0 (skS.0 11 xa xR xb a) xa xR) False) % 38.08/38.27 Clause #3893 (by forward demodulation #[3892, 1788]): ∀ (a : Iota), Or (Eq True False) (Eq (aReductOfIn0 (skS.0 11 xa xR xb a) xa xR) False) % 38.08/38.27 Clause #3894 (by clausification #[3893]): ∀ (a : Iota), Eq (aReductOfIn0 (skS.0 11 xa xR xb a) xa xR) False % 38.08/38.27 Clause #3895 (by superposition #[3894, 2855]): Eq False True % 38.08/38.27 Clause #3896 (by clausification #[3895]): False % 38.08/38.27 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------