%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO109^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n018.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 08:08:36 PM UTC 2025 % Result : Theorem 4.86s 5.08s % Output : Proof 4.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SYO109^5 : TPTP v9.2.0. Released v4.0.0. % 0.12/0.13 % Command : duper %s % 0.13/0.34 % Computer : n018.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 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Oct 3 13:22:53 EDT 2025 % 0.13/0.35 % CPUTime : % 4.86/5.08 SZS status Theorem for theBenchmark.p % 4.86/5.08 SZS output start Proof for theBenchmark.p % 4.86/5.08 Clause #0 (by assumption #[]): Eq % 4.86/5.08 (Not % 4.86/5.08 (And % 4.86/5.08 (And (∀ (Xx : Iota), (Exists fun Xy => Or (cM Xx Xy) (cN Xx Xy)) → cP Xx) % 4.86/5.08 (∀ (Xw : Iota), Exists fun Xu => Or (∀ (Xv : Iota), cM Xu Xv) (cN Xu Xw))) % 4.86/5.08 (∀ (Xw Xz : Iota), Or (cM Xw Xz) (cN Xw Xz) → Or (Or (Or (cM Xz Xw) (cN Xz Xw)) (cM Xz Xz)) (cN Xz Xz)) → % 4.86/5.08 ∀ (Xz : Iota), cP Xz)) % 4.86/5.08 True % 4.86/5.08 Clause #1 (by clausification #[0]): Eq % 4.86/5.08 (And % 4.86/5.08 (And (∀ (Xx : Iota), (Exists fun Xy => Or (cM Xx Xy) (cN Xx Xy)) → cP Xx) % 4.86/5.08 (∀ (Xw : Iota), Exists fun Xu => Or (∀ (Xv : Iota), cM Xu Xv) (cN Xu Xw))) % 4.86/5.08 (∀ (Xw Xz : Iota), Or (cM Xw Xz) (cN Xw Xz) → Or (Or (Or (cM Xz Xw) (cN Xz Xw)) (cM Xz Xz)) (cN Xz Xz)) → % 4.86/5.08 ∀ (Xz : Iota), cP Xz) % 4.86/5.08 False % 4.86/5.08 Clause #2 (by clausification #[1]): Eq % 4.86/5.08 (And % 4.86/5.08 (And (∀ (Xx : Iota), (Exists fun Xy => Or (cM Xx Xy) (cN Xx Xy)) → cP Xx) % 4.86/5.08 (∀ (Xw : Iota), Exists fun Xu => Or (∀ (Xv : Iota), cM Xu Xv) (cN Xu Xw))) % 4.86/5.08 (∀ (Xw Xz : Iota), Or (cM Xw Xz) (cN Xw Xz) → Or (Or (Or (cM Xz Xw) (cN Xz Xw)) (cM Xz Xz)) (cN Xz Xz))) % 4.86/5.08 True % 4.86/5.08 Clause #3 (by clausification #[1]): Eq (∀ (Xz : Iota), cP Xz) False % 4.86/5.08 Clause #4 (by clausification #[2]): Eq (∀ (Xw Xz : Iota), Or (cM Xw Xz) (cN Xw Xz) → Or (Or (Or (cM Xz Xw) (cN Xz Xw)) (cM Xz Xz)) (cN Xz Xz)) True % 4.86/5.08 Clause #5 (by clausification #[2]): Eq % 4.86/5.08 (And (∀ (Xx : Iota), (Exists fun Xy => Or (cM Xx Xy) (cN Xx Xy)) → cP Xx) % 4.86/5.08 (∀ (Xw : Iota), Exists fun Xu => Or (∀ (Xv : Iota), cM Xu Xv) (cN Xu Xw))) % 4.86/5.08 True % 4.86/5.08 Clause #6 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (Xz : Iota), Or (cM a Xz) (cN a Xz) → Or (Or (Or (cM Xz a) (cN Xz a)) (cM Xz Xz)) (cN Xz Xz)) True % 4.86/5.08 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (Or (cM a a_1) (cN a a_1) → Or (Or (Or (cM a_1 a) (cN a_1 a)) (cM a_1 a_1)) (cN a_1 a_1)) True % 4.86/5.08 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), % 4.86/5.08 Or (Eq (Or (cM a a_1) (cN a a_1)) False) (Eq (Or (Or (Or (cM a_1 a) (cN a_1 a)) (cM a_1 a_1)) (cN a_1 a_1)) True) % 4.86/5.08 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq (Or (Or (Or (cM a a_1) (cN a a_1)) (cM a a)) (cN a a)) True) (Eq (cN a_1 a) False) % 4.86/5.08 Clause #10 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq (Or (Or (Or (cM a a_1) (cN a a_1)) (cM a a)) (cN a a)) True) (Eq (cM a_1 a) False) % 4.86/5.08 Clause #11 (by clausification #[9]): ∀ (a a_1 : Iota), % 4.86/5.08 Or (Eq (cN a a_1) False) (Or (Eq (Or (Or (cM a_1 a) (cN a_1 a)) (cM a_1 a_1)) True) (Eq (cN a_1 a_1) True)) % 4.86/5.08 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), % 4.86/5.08 Or (Eq (cN a a_1) False) (Or (Eq (cN a_1 a_1) True) (Or (Eq (Or (cM a_1 a) (cN a_1 a)) True) (Eq (cM a_1 a_1) True))) % 4.86/5.08 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), % 4.86/5.08 Or (Eq (cN a a_1) False) % 4.86/5.08 (Or (Eq (cN a_1 a_1) True) (Or (Eq (cM a_1 a_1) True) (Or (Eq (cM a_1 a) True) (Eq (cN a_1 a) True)))) % 4.86/5.08 Clause #14 (by clausification #[3]): ∀ (a : Iota), Eq (Not (cP (skS.0 0 a))) True % 4.86/5.08 Clause #15 (by clausification #[14]): ∀ (a : Iota), Eq (cP (skS.0 0 a)) False % 4.86/5.08 Clause #16 (by clausification #[5]): Eq (∀ (Xw : Iota), Exists fun Xu => Or (∀ (Xv : Iota), cM Xu Xv) (cN Xu Xw)) True % 4.86/5.08 Clause #17 (by clausification #[5]): Eq (∀ (Xx : Iota), (Exists fun Xy => Or (cM Xx Xy) (cN Xx Xy)) → cP Xx) True % 4.86/5.08 Clause #18 (by clausification #[16]): ∀ (a : Iota), Eq (Exists fun Xu => Or (∀ (Xv : Iota), cM Xu Xv) (cN Xu a)) True % 4.86/5.08 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Eq (Or (∀ (Xv : Iota), cM (skS.0 1 a a_1) Xv) (cN (skS.0 1 a a_1) a)) True % 4.86/5.08 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Or (Eq (∀ (Xv : Iota), cM (skS.0 1 a a_1) Xv) True) (Eq (cN (skS.0 1 a a_1) a) True) % 4.86/5.08 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), Or (Eq (cN (skS.0 1 a a_1) a) True) (Eq (cM (skS.0 1 a a_1) a_2) True) % 4.86/5.08 Clause #23 (by clausification #[17]): ∀ (a : Iota), Eq ((Exists fun Xy => Or (cM a Xy) (cN a Xy)) → cP a) True % 4.86/5.08 Clause #24 (by clausification #[23]): ∀ (a : Iota), Or (Eq (Exists fun Xy => Or (cM a Xy) (cN a Xy)) False) (Eq (cP a) True) % 4.95/5.11 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (cP a) True) (Eq (Or (cM a a_1) (cN a a_1)) False) % 4.95/5.11 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Or (Eq (cP a) True) (Eq (cN a a_1) False) % 4.95/5.11 Clause #27 (by clausification #[25]): ∀ (a a_1 : Iota), Or (Eq (cP a) True) (Eq (cM a a_1) False) % 4.95/5.11 Clause #30 (by clausification #[10]): ∀ (a a_1 : Iota), % 4.95/5.11 Or (Eq (cM a a_1) False) (Or (Eq (Or (Or (cM a_1 a) (cN a_1 a)) (cM a_1 a_1)) True) (Eq (cN a_1 a_1) True)) % 4.95/5.11 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), % 4.95/5.11 Or (Eq (cM a a_1) False) (Or (Eq (cN a_1 a_1) True) (Or (Eq (Or (cM a_1 a) (cN a_1 a)) True) (Eq (cM a_1 a_1) True))) % 4.95/5.11 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), % 4.95/5.11 Or (Eq (cM a a_1) False) % 4.95/5.11 (Or (Eq (cN a_1 a_1) True) (Or (Eq (cM a_1 a_1) True) (Or (Eq (cM a_1 a) True) (Eq (cN a_1 a) True)))) % 4.95/5.11 Clause #33 (by superposition #[32, 21]): ∀ (a a_1 a_2 : Iota), % 4.95/5.11 Or (Eq (cN a a) True) % 4.95/5.11 (Or (Eq (cM a a) True) % 4.95/5.11 (Or (Eq (cM a (skS.0 1 a_1 a_2)) True) % 4.95/5.11 (Or (Eq (cN a (skS.0 1 a_1 a_2)) True) (Or (Eq (cN (skS.0 1 a_1 a_2) a_1) True) (Eq False True))))) % 4.95/5.11 Clause #69 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), % 4.95/5.11 Or (Eq (cN a a) True) % 4.95/5.11 (Or (Eq (cM a a) True) % 4.95/5.11 (Or (Eq (cM a (skS.0 1 a_1 a_2)) True) % 4.95/5.11 (Or (Eq (cN a (skS.0 1 a_1 a_2)) True) (Eq (cN (skS.0 1 a_1 a_2) a_1) True)))) % 4.95/5.11 Clause #72 (by superposition #[69, 26]): ∀ (a a_1 a_2 : Iota), % 4.95/5.11 Or (Eq (cN a a) True) % 4.95/5.11 (Or (Eq (cM a a) True) % 4.95/5.11 (Or (Eq (cM a (skS.0 1 a_1 a_2)) True) % 4.95/5.11 (Or (Eq (cN (skS.0 1 a_1 a_2) a_1) True) (Or (Eq (cP a) True) (Eq True False))))) % 4.95/5.11 Clause #80 (by clausification #[72]): ∀ (a a_1 a_2 : Iota), % 4.95/5.11 Or (Eq (cN a a) True) % 4.95/5.11 (Or (Eq (cM a a) True) % 4.95/5.11 (Or (Eq (cM a (skS.0 1 a_1 a_2)) True) (Or (Eq (cN (skS.0 1 a_1 a_2) a_1) True) (Eq (cP a) True)))) % 4.95/5.11 Clause #82 (by superposition #[80, 27]): ∀ (a a_1 a_2 : Iota), % 4.95/5.11 Or (Eq (cN a a) True) % 4.95/5.11 (Or (Eq (cM a a) True) % 4.95/5.11 (Or (Eq (cN (skS.0 1 a_1 a_2) a_1) True) (Or (Eq (cP a) True) (Or (Eq (cP a) True) (Eq True False))))) % 4.95/5.11 Clause #86 (by clausification #[82]): ∀ (a a_1 a_2 : Iota), % 4.95/5.11 Or (Eq (cN a a) True) % 4.95/5.11 (Or (Eq (cM a a) True) (Or (Eq (cN (skS.0 1 a_1 a_2) a_1) True) (Or (Eq (cP a) True) (Eq (cP a) True)))) % 4.95/5.11 Clause #87 (by eliminate duplicate literals #[86]): ∀ (a a_1 a_2 : Iota), % 4.95/5.11 Or (Eq (cN a a) True) (Or (Eq (cM a a) True) (Or (Eq (cN (skS.0 1 a_1 a_2) a_1) True) (Eq (cP a) True))) % 4.95/5.11 Clause #88 (by superposition #[87, 26]): ∀ (a a_1 a_2 : Iota), % 4.95/5.11 Or (Eq (cM a a) True) % 4.95/5.11 (Or (Eq (cN (skS.0 1 a_1 a_2) a_1) True) (Or (Eq (cP a) True) (Or (Eq (cP a) True) (Eq True False)))) % 4.95/5.11 Clause #94 (by clausification #[88]): ∀ (a a_1 a_2 : Iota), % 4.95/5.11 Or (Eq (cM a a) True) (Or (Eq (cN (skS.0 1 a_1 a_2) a_1) True) (Or (Eq (cP a) True) (Eq (cP a) True))) % 4.95/5.11 Clause #95 (by eliminate duplicate literals #[94]): ∀ (a a_1 a_2 : Iota), Or (Eq (cM a a) True) (Or (Eq (cN (skS.0 1 a_1 a_2) a_1) True) (Eq (cP a) True)) % 4.95/5.11 Clause #96 (by superposition #[95, 27]): ∀ (a a_1 a_2 : Iota), % 4.95/5.11 Or (Eq (cN (skS.0 1 a a_1) a) True) (Or (Eq (cP a_2) True) (Or (Eq (cP a_2) True) (Eq True False))) % 4.95/5.11 Clause #100 (by clausification #[96]): ∀ (a a_1 a_2 : Iota), Or (Eq (cN (skS.0 1 a a_1) a) True) (Or (Eq (cP a_2) True) (Eq (cP a_2) True)) % 4.95/5.11 Clause #101 (by eliminate duplicate literals #[100]): ∀ (a a_1 a_2 : Iota), Or (Eq (cN (skS.0 1 a a_1) a) True) (Eq (cP a_2) True) % 4.95/5.11 Clause #104 (by superposition #[101, 15]): ∀ (a a_1 : Iota), Or (Eq (cN (skS.0 1 a a_1) a) True) (Eq True False) % 4.95/5.11 Clause #105 (by clausification #[104]): ∀ (a a_1 : Iota), Eq (cN (skS.0 1 a a_1) a) True % 4.95/5.11 Clause #106 (by superposition #[105, 13]): ∀ (a a_1 : Iota), % 4.95/5.11 Or (Eq True False) % 4.95/5.11 (Or (Eq (cN a a) True) % 4.95/5.11 (Or (Eq (cM a a) True) (Or (Eq (cM a (skS.0 1 a a_1)) True) (Eq (cN a (skS.0 1 a a_1)) True)))) % 4.95/5.11 Clause #117 (by clausification #[106]): ∀ (a a_1 : Iota), % 4.95/5.11 Or (Eq (cN a a) True) (Or (Eq (cM a a) True) (Or (Eq (cM a (skS.0 1 a a_1)) True) (Eq (cN a (skS.0 1 a a_1)) True))) % 4.95/5.11 Clause #119 (by superposition #[117, 26]): ∀ (a a_1 : Iota), % 4.95/5.11 Or (Eq (cN a a) True) % 4.95/5.11 (Or (Eq (cM a a) True) (Or (Eq (cM a (skS.0 1 a a_1)) True) (Or (Eq (cP a) True) (Eq True False)))) % 4.95/5.12 Clause #120 (by clausification #[119]): ∀ (a a_1 : Iota), Or (Eq (cN a a) True) (Or (Eq (cM a a) True) (Or (Eq (cM a (skS.0 1 a a_1)) True) (Eq (cP a) True))) % 4.95/5.12 Clause #121 (by superposition #[120, 27]): ∀ (a : Iota), Or (Eq (cN a a) True) (Or (Eq (cM a a) True) (Or (Eq (cP a) True) (Or (Eq (cP a) True) (Eq True False)))) % 4.95/5.12 Clause #123 (by clausification #[121]): ∀ (a : Iota), Or (Eq (cN a a) True) (Or (Eq (cM a a) True) (Or (Eq (cP a) True) (Eq (cP a) True))) % 4.95/5.12 Clause #124 (by eliminate duplicate literals #[123]): ∀ (a : Iota), Or (Eq (cN a a) True) (Or (Eq (cM a a) True) (Eq (cP a) True)) % 4.95/5.12 Clause #125 (by superposition #[124, 26]): ∀ (a : Iota), Or (Eq (cM a a) True) (Or (Eq (cP a) True) (Or (Eq (cP a) True) (Eq True False))) % 4.95/5.12 Clause #128 (by clausification #[125]): ∀ (a : Iota), Or (Eq (cM a a) True) (Or (Eq (cP a) True) (Eq (cP a) True)) % 4.95/5.12 Clause #129 (by eliminate duplicate literals #[128]): ∀ (a : Iota), Or (Eq (cM a a) True) (Eq (cP a) True) % 4.95/5.12 Clause #130 (by superposition #[129, 27]): ∀ (a : Iota), Or (Eq (cP a) True) (Or (Eq (cP a) True) (Eq True False)) % 4.95/5.12 Clause #131 (by clausification #[130]): ∀ (a : Iota), Or (Eq (cP a) True) (Eq (cP a) True) % 4.95/5.12 Clause #132 (by eliminate duplicate literals #[131]): ∀ (a : Iota), Eq (cP a) True % 4.95/5.12 Clause #137 (by superposition #[132, 15]): Eq True False % 4.95/5.12 Clause #138 (by clausification #[137]): False % 4.95/5.12 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------