%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : PUZ081^2 : TPTP v9.2.0. Bugfixed v7.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n025.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 07:58:19 PM UTC 2025 % Result : Theorem 3.61s 3.75s % Output : Proof 3.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : PUZ081^2 : TPTP v9.2.0. Bugfixed v7.1.0. % 0.03/0.13 % Command : duper %s % 0.14/0.35 % Computer : n025.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Thu Oct 2 20:56:23 EDT 2025 % 0.14/0.35 % CPUTime : % 3.61/3.75 SZS status Theorem for theBenchmark.p % 3.61/3.75 SZS output start Proof for theBenchmark.p % 3.61/3.75 Clause #0 (by assumption #[]): Eq (∀ (P : Iota), Not (Iff (knight P) (knave P))) True % 3.61/3.75 Clause #2 (by assumption #[]): Eq (∀ (P : Iota) (S : Prop), And (knave P) (says P S) → Not S) True % 3.61/3.75 Clause #3 (by assumption #[]): Eq (says zoey (knave mel)) True % 3.61/3.75 Clause #5 (by assumption #[]): Eq % 3.61/3.75 (Not % 3.61/3.75 (Exists fun TZ => % 3.61/3.75 Exists fun TM => % 3.61/3.75 And (And (And (Or (Eq TZ knight) (Eq TZ knave)) (Or (Eq TM knight) (Eq TM knave))) (TZ zoey)) (TM mel))) % 3.61/3.75 True % 3.61/3.75 Clause #6 (by identity loobHoist #[3]): Or (Eq (says zoey True) True) (Eq (knave mel) False) % 3.61/3.75 Clause #14 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (S : Prop), And (knave a) (says a S) → Not S) True % 3.61/3.75 Clause #15 (by clausification #[14]): ∀ (a : Iota) (a_1 : Prop), Eq (And (knave a) (says a a_1) → Not a_1) True % 3.61/3.75 Clause #16 (by clausification #[15]): ∀ (a : Iota) (a_1 : Prop), Or (Eq (And (knave a) (says a a_1)) False) (Eq (Not a_1) True) % 3.61/3.75 Clause #17 (by clausification #[16]): ∀ (a : Prop) (a_1 : Iota), Or (Eq (Not a) True) (Or (Eq (knave a_1) False) (Eq (says a_1 a) False)) % 3.61/3.75 Clause #18 (by clausification #[17]): ∀ (a : Iota) (a_1 : Prop), Or (Eq (knave a) False) (Or (Eq (says a a_1) False) (Eq a_1 False)) % 3.61/3.75 Clause #19 (by identity loobHoist #[18]): ∀ (a : Iota) (a_1 : Prop), Or (Eq (knave a) False) (Or (Eq a_1 False) (Or (Eq (says a True) False) (Eq a_1 False))) % 3.61/3.75 Clause #21 (by eliminate duplicate literals #[19]): ∀ (a : Iota) (a_1 : Prop), Or (Eq (knave a) False) (Or (Eq a_1 False) (Eq (says a True) False)) % 3.61/3.75 Clause #22 (by clausification #[0]): ∀ (a : Iota), Eq (Not (Iff (knight a) (knave a))) True % 3.61/3.75 Clause #23 (by clausification #[22]): ∀ (a : Iota), Eq (Iff (knight a) (knave a)) False % 3.61/3.75 Clause #25 (by clausification #[23]): ∀ (a : Iota), Or (Eq (knight a) True) (Eq (knave a) True) % 3.61/3.75 Clause #31 (by superposition #[25, 6]): Or (Eq (knight mel) True) (Or (Eq (says zoey True) True) (Eq True False)) % 3.61/3.75 Clause #32 (by superposition #[25, 21]): ∀ (a : Iota) (a_1 : Prop), Or (Eq (knight a) True) (Or (Eq True False) (Or (Eq a_1 False) (Eq (says a True) False))) % 3.61/3.75 Clause #33 (by clausification #[31]): Or (Eq (knight mel) True) (Eq (says zoey True) True) % 3.61/3.75 Clause #35 (by clausification #[32]): ∀ (a : Iota) (a_1 : Prop), Or (Eq (knight a) True) (Or (Eq a_1 False) (Eq (says a True) False)) % 3.61/3.75 Clause #40 (by falseElim #[35]): ∀ (a : Iota), Or (Eq (knight a) True) (Eq (says a True) False) % 3.61/3.75 Clause #41 (by clausification #[5]): Eq % 3.61/3.75 (Exists fun TZ => % 3.61/3.75 Exists fun TM => % 3.61/3.75 And (And (And (Or (Eq TZ knight) (Eq TZ knave)) (Or (Eq TM knight) (Eq TM knave))) (TZ zoey)) (TM mel)) % 3.61/3.75 False % 3.61/3.75 Clause #42 (by clausification #[41]): ∀ (a : Iota → Prop), % 3.61/3.75 Eq % 3.61/3.75 (Exists fun TM => % 3.61/3.75 And (And (And (Or (Eq a knight) (Eq a knave)) (Or (Eq TM knight) (Eq TM knave))) (a zoey)) (TM mel)) % 3.61/3.75 False % 3.61/3.75 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota → Prop), % 3.61/3.75 Eq (And (And (And (Or (Eq a knight) (Eq a knave)) (Or (Eq a_1 knight) (Eq a_1 knave))) (a zoey)) (a_1 mel)) False % 3.61/3.75 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota → Prop), % 3.61/3.75 Or (Eq (And (And (Or (Eq a knight) (Eq a knave)) (Or (Eq a_1 knight) (Eq a_1 knave))) (a zoey)) False) % 3.61/3.75 (Eq (a_1 mel) False) % 3.61/3.75 Clause #45 (by clausification #[44]): ∀ (a a_1 : Iota → Prop), % 3.61/3.75 Or (Eq (a mel) False) % 3.61/3.75 (Or (Eq (And (Or (Eq a_1 knight) (Eq a_1 knave)) (Or (Eq a knight) (Eq a knave))) False) (Eq (a_1 zoey) False)) % 3.61/3.75 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota → Prop), % 3.61/3.75 Or (Eq (a mel) False) % 3.61/3.75 (Or (Eq (a_1 zoey) False) % 3.61/3.75 (Or (Eq (Or (Eq a_1 knight) (Eq a_1 knave)) False) (Eq (Or (Eq a knight) (Eq a knave)) False))) % 3.61/3.75 Clause #47 (by clausification #[46]): ∀ (a a_1 : Iota → Prop), % 3.61/3.75 Or (Eq (a mel) False) % 3.61/3.75 (Or (Eq (a_1 zoey) False) (Or (Eq (Or (Eq a knight) (Eq a knave)) False) (Eq (Eq a_1 knave) False))) % 3.61/3.75 Clause #48 (by clausification #[46]): ∀ (a a_1 : Iota → Prop), % 3.61/3.75 Or (Eq (a mel) False) % 3.61/3.75 (Or (Eq (a_1 zoey) False) (Or (Eq (Or (Eq a knight) (Eq a knave)) False) (Eq (Eq a_1 knight) False))) % 3.61/3.75 Clause #50 (by clausification #[47]): ∀ (a a_1 : Iota → Prop), % 3.61/3.77 Or (Eq (a mel) False) (Or (Eq (a_1 zoey) False) (Or (Eq (Eq a_1 knave) False) (Eq (Eq a knight) False))) % 3.61/3.77 Clause #57 (by superposition #[40, 33]): Or (Eq (knight zoey) True) (Or (Eq (knight mel) True) (Eq False True)) % 3.61/3.77 Clause #58 (by clausification #[57]): Or (Eq (knight zoey) True) (Eq (knight mel) True) % 3.61/3.77 Clause #81 (by clausification #[50]): ∀ (a a_1 : Iota → Prop), Or (Eq (a mel) False) (Or (Eq (a_1 zoey) False) (Or (Eq (Eq a knight) False) (Ne a_1 knave))) % 3.61/3.77 Clause #82 (by clausification #[81]): ∀ (a a_1 : Iota → Prop), Or (Eq (a mel) False) (Or (Eq (a_1 zoey) False) (Or (Ne a_1 knave) (Ne a knight))) % 3.61/3.77 Clause #83 (by destructive equality resolution #[82]): ∀ (a : Iota → Prop), Or (Eq (a mel) False) (Or (Eq (knave zoey) False) (Ne a knight)) % 3.61/3.77 Clause #84 (by destructive equality resolution #[83]): Or (Eq (knight mel) False) (Eq (knave zoey) False) % 3.61/3.77 Clause #85 (by clausification #[48]): ∀ (a a_1 : Iota → Prop), % 3.61/3.77 Or (Eq (a mel) False) (Or (Eq (a_1 zoey) False) (Or (Eq (Eq a_1 knight) False) (Eq (Eq a knave) False))) % 3.61/3.77 Clause #86 (by clausification #[48]): ∀ (a a_1 : Iota → Prop), % 3.61/3.77 Or (Eq (a mel) False) (Or (Eq (a_1 zoey) False) (Or (Eq (Eq a_1 knight) False) (Eq (Eq a knight) False))) % 3.61/3.77 Clause #87 (by clausification #[85]): ∀ (a a_1 : Iota → Prop), Or (Eq (a mel) False) (Or (Eq (a_1 zoey) False) (Or (Eq (Eq a knave) False) (Ne a_1 knight))) % 3.61/3.77 Clause #88 (by clausification #[87]): ∀ (a a_1 : Iota → Prop), Or (Eq (a mel) False) (Or (Eq (a_1 zoey) False) (Or (Ne a_1 knight) (Ne a knave))) % 3.61/3.77 Clause #89 (by destructive equality resolution #[88]): ∀ (a : Iota → Prop), Or (Eq (a mel) False) (Or (Eq (knight zoey) False) (Ne a knave)) % 3.61/3.77 Clause #90 (by destructive equality resolution #[89]): Or (Eq (knave mel) False) (Eq (knight zoey) False) % 3.61/3.77 Clause #91 (by superposition #[90, 25]): Or (Eq (knight zoey) False) (Or (Eq (knight mel) True) (Eq False True)) % 3.61/3.77 Clause #92 (by clausification #[91]): Or (Eq (knight zoey) False) (Eq (knight mel) True) % 3.61/3.77 Clause #93 (by superposition #[92, 58]): Or (Eq (knight mel) True) (Or (Eq False True) (Eq (knight mel) True)) % 3.61/3.77 Clause #94 (by clausification #[93]): Or (Eq (knight mel) True) (Eq (knight mel) True) % 3.61/3.77 Clause #95 (by eliminate duplicate literals #[94]): Eq (knight mel) True % 3.61/3.77 Clause #101 (by backward demodulation #[95, 84]): Or (Eq True False) (Eq (knave zoey) False) % 3.61/3.77 Clause #112 (by clausification #[86]): ∀ (a a_1 : Iota → Prop), Or (Eq (a mel) False) (Or (Eq (a_1 zoey) False) (Or (Eq (Eq a knight) False) (Ne a_1 knight))) % 3.61/3.77 Clause #113 (by clausification #[112]): ∀ (a a_1 : Iota → Prop), Or (Eq (a mel) False) (Or (Eq (a_1 zoey) False) (Or (Ne a_1 knight) (Ne a knight))) % 3.61/3.77 Clause #114 (by destructive equality resolution #[113]): ∀ (a : Iota → Prop), Or (Eq (a mel) False) (Or (Eq (knight zoey) False) (Ne a knight)) % 3.61/3.77 Clause #115 (by destructive equality resolution #[114]): Or (Eq (knight mel) False) (Eq (knight zoey) False) % 3.61/3.77 Clause #116 (by forward demodulation #[115, 95]): Or (Eq True False) (Eq (knight zoey) False) % 3.61/3.77 Clause #117 (by clausification #[116]): Eq (knight zoey) False % 3.61/3.77 Clause #119 (by clausification #[101]): Eq (knave zoey) False % 3.61/3.77 Clause #120 (by superposition #[119, 25]): Or (Eq (knight zoey) True) (Eq False True) % 3.61/3.77 Clause #121 (by clausification #[120]): Eq (knight zoey) True % 3.61/3.77 Clause #122 (by superposition #[121, 117]): Eq True False % 3.61/3.77 Clause #124 (by clausification #[122]): False % 3.61/3.77 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------