%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN332+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n015.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 08:07:25 PM UTC 2025 % Result : Theorem 3.87s 4.02s % Output : Proof 3.89s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SYN332+1 : TPTP v9.2.0. Released v2.0.0. % 0.11/0.13 % Command : duper %s % 0.15/0.35 % Computer : n015.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Thu Oct 2 15:13:08 EDT 2025 % 0.15/0.35 % CPUTime : % 3.87/4.02 SZS status Theorem for theBenchmark.p % 3.87/4.02 SZS output start Proof for theBenchmark.p % 3.87/4.02 Clause #0 (by assumption #[]): Eq % 3.87/4.02 (Not % 3.87/4.02 (Exists fun X => % 3.87/4.02 Exists fun Y => % 3.87/4.02 ∀ (Z : Iota), % 3.87/4.02 Not (Iff (And (big_f X Y) (big_f Y X)) (big_f X Z)) → % 3.87/4.02 Iff (big_f X Z) (big_f Z X) → % 3.87/4.02 Iff (big_f X Z) (big_f Y Z) → % 3.87/4.02 Iff (big_f Y X → big_f X Y) (big_f Z Z) → Iff (Iff (big_f X Y) (big_f Y X)) (big_f Z Y))) % 3.87/4.02 True % 3.87/4.02 Clause #1 (by clausification #[0]): Eq % 3.87/4.02 (Exists fun X => % 3.87/4.02 Exists fun Y => % 3.87/4.02 ∀ (Z : Iota), % 3.87/4.02 Not (Iff (And (big_f X Y) (big_f Y X)) (big_f X Z)) → % 3.87/4.02 Iff (big_f X Z) (big_f Z X) → % 3.87/4.02 Iff (big_f X Z) (big_f Y Z) → % 3.87/4.02 Iff (big_f Y X → big_f X Y) (big_f Z Z) → Iff (Iff (big_f X Y) (big_f Y X)) (big_f Z Y)) % 3.87/4.02 False % 3.87/4.02 Clause #2 (by clausification #[1]): ∀ (a : Iota), % 3.87/4.02 Eq % 3.87/4.02 (Exists fun Y => % 3.87/4.02 ∀ (Z : Iota), % 3.87/4.02 Not (Iff (And (big_f a Y) (big_f Y a)) (big_f a Z)) → % 3.87/4.02 Iff (big_f a Z) (big_f Z a) → % 3.87/4.02 Iff (big_f a Z) (big_f Y Z) → % 3.87/4.02 Iff (big_f Y a → big_f a Y) (big_f Z Z) → Iff (Iff (big_f a Y) (big_f Y a)) (big_f Z Y)) % 3.87/4.02 False % 3.87/4.02 Clause #3 (by clausification #[2]): ∀ (a a_1 : Iota), % 3.87/4.02 Eq % 3.87/4.02 (∀ (Z : Iota), % 3.87/4.02 Not (Iff (And (big_f a a_1) (big_f a_1 a)) (big_f a Z)) → % 3.87/4.02 Iff (big_f a Z) (big_f Z a) → % 3.87/4.02 Iff (big_f a Z) (big_f a_1 Z) → % 3.87/4.02 Iff (big_f a_1 a → big_f a a_1) (big_f Z Z) → Iff (Iff (big_f a a_1) (big_f a_1 a)) (big_f Z a_1)) % 3.87/4.02 False % 3.87/4.02 Clause #4 (by clausification #[3]): ∀ (a a_1 a_2 : Iota), % 3.87/4.02 Eq % 3.87/4.02 (Not % 3.87/4.02 (Not (Iff (And (big_f a a_1) (big_f a_1 a)) (big_f a (skS.0 0 a a_1 a_2))) → % 3.87/4.02 Iff (big_f a (skS.0 0 a a_1 a_2)) (big_f (skS.0 0 a a_1 a_2) a) → % 3.87/4.02 Iff (big_f a (skS.0 0 a a_1 a_2)) (big_f a_1 (skS.0 0 a a_1 a_2)) → % 3.87/4.02 Iff (big_f a_1 a → big_f a a_1) (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) → % 3.87/4.02 Iff (Iff (big_f a a_1) (big_f a_1 a)) (big_f (skS.0 0 a a_1 a_2) a_1))) % 3.87/4.02 True % 3.87/4.02 Clause #5 (by clausification #[4]): ∀ (a a_1 a_2 : Iota), % 3.87/4.02 Eq % 3.87/4.02 (Not (Iff (And (big_f a a_1) (big_f a_1 a)) (big_f a (skS.0 0 a a_1 a_2))) → % 3.87/4.02 Iff (big_f a (skS.0 0 a a_1 a_2)) (big_f (skS.0 0 a a_1 a_2) a) → % 3.87/4.02 Iff (big_f a (skS.0 0 a a_1 a_2)) (big_f a_1 (skS.0 0 a a_1 a_2)) → % 3.87/4.02 Iff (big_f a_1 a → big_f a a_1) (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) → % 3.87/4.02 Iff (Iff (big_f a a_1) (big_f a_1 a)) (big_f (skS.0 0 a a_1 a_2) a_1)) % 3.87/4.02 False % 3.87/4.02 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Iota), Eq (Not (Iff (And (big_f a a_1) (big_f a_1 a)) (big_f a (skS.0 0 a a_1 a_2)))) True % 3.87/4.02 Clause #7 (by clausification #[5]): ∀ (a a_1 a_2 : Iota), % 3.87/4.02 Eq % 3.87/4.02 (Iff (big_f a (skS.0 0 a a_1 a_2)) (big_f (skS.0 0 a a_1 a_2) a) → % 3.87/4.02 Iff (big_f a (skS.0 0 a a_1 a_2)) (big_f a_1 (skS.0 0 a a_1 a_2)) → % 3.87/4.02 Iff (big_f a_1 a → big_f a a_1) (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) → % 3.87/4.02 Iff (Iff (big_f a a_1) (big_f a_1 a)) (big_f (skS.0 0 a a_1 a_2) a_1)) % 3.87/4.02 False % 3.87/4.02 Clause #8 (by clausification #[6]): ∀ (a a_1 a_2 : Iota), Eq (Iff (And (big_f a a_1) (big_f a_1 a)) (big_f a (skS.0 0 a a_1 a_2))) False % 3.87/4.02 Clause #10 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (big_f a a_1) (big_f a_1 a)) True) (Eq (big_f a (skS.0 0 a a_1 a_2)) True) % 3.87/4.02 Clause #13 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a (skS.0 0 a a_1 a_2)) True) (Eq (big_f a a_1) True) % 3.87/4.02 Clause #18 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), Eq (Iff (big_f a (skS.0 0 a a_1 a_2)) (big_f (skS.0 0 a a_1 a_2) a)) True % 3.87/4.02 Clause #19 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), % 3.87/4.02 Eq % 3.87/4.02 (Iff (big_f a (skS.0 0 a a_1 a_2)) (big_f a_1 (skS.0 0 a a_1 a_2)) → % 3.87/4.02 Iff (big_f a_1 a → big_f a a_1) (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) → % 3.87/4.02 Iff (Iff (big_f a a_1) (big_f a_1 a)) (big_f (skS.0 0 a a_1 a_2) a_1)) % 3.87/4.02 False % 3.87/4.02 Clause #21 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a (skS.0 0 a a_1 a_2)) False) (Eq (big_f (skS.0 0 a a_1 a_2) a) True) % 3.89/4.05 Clause #22 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), Eq (Iff (big_f a (skS.0 0 a a_1 a_2)) (big_f a_1 (skS.0 0 a a_1 a_2))) True % 3.89/4.05 Clause #23 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), % 3.89/4.05 Eq % 3.89/4.05 (Iff (big_f a a_1 → big_f a_1 a) (big_f (skS.0 0 a_1 a a_2) (skS.0 0 a_1 a a_2)) → % 3.89/4.05 Iff (Iff (big_f a_1 a) (big_f a a_1)) (big_f (skS.0 0 a_1 a a_2) a)) % 3.89/4.05 False % 3.89/4.05 Clause #25 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a (skS.0 0 a a_1 a_2)) False) (Eq (big_f a_1 (skS.0 0 a a_1 a_2)) True) % 3.89/4.05 Clause #28 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Eq (Iff (big_f a a_1 → big_f a_1 a) (big_f (skS.0 0 a_1 a a_2) (skS.0 0 a_1 a a_2))) True % 3.89/4.05 Clause #29 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Eq (Iff (Iff (big_f a a_1) (big_f a_1 a)) (big_f (skS.0 0 a a_1 a_2) a_1)) False % 3.89/4.05 Clause #30 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), % 3.89/4.05 Or (Eq (big_f a a_1 → big_f a_1 a) True) (Eq (big_f (skS.0 0 a_1 a a_2) (skS.0 0 a_1 a a_2)) False) % 3.89/4.05 Clause #32 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), % 3.89/4.05 Or (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) False) (Or (Eq (big_f a_1 a) False) (Eq (big_f a a_1) True)) % 3.89/4.05 Clause #33 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Or (Eq (Iff (big_f a a_1) (big_f a_1 a)) False) (Eq (big_f (skS.0 0 a a_1 a_2) a_1) False) % 3.89/4.05 Clause #35 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), % 3.89/4.05 Or (Eq (big_f (skS.0 0 a a_1 a_2) a_1) False) (Or (Eq (big_f a a_1) False) (Eq (big_f a_1 a) False)) % 3.89/4.05 Clause #36 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f (skS.0 0 a a_1 a_2) a_1) False) (Or (Eq (big_f a a_1) True) (Eq (big_f a_1 a) True)) % 3.89/4.05 Clause #38 (by superposition #[21, 13]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f (skS.0 0 a a_1 a_2) a) True) (Or (Eq False True) (Eq (big_f a a_1) True)) % 3.89/4.05 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f (skS.0 0 a a_1 a_2) a) True) (Eq (big_f a a_1) True) % 3.89/4.05 Clause #42 (by superposition #[39, 36]): ∀ (a : Iota), Or (Eq (big_f a a) True) (Or (Eq True False) (Or (Eq (big_f a a) True) (Eq (big_f a a) True))) % 3.89/4.05 Clause #43 (by clausification #[42]): ∀ (a : Iota), Or (Eq (big_f a a) True) (Or (Eq (big_f a a) True) (Eq (big_f a a) True)) % 3.89/4.05 Clause #44 (by eliminate duplicate literals #[43]): ∀ (a : Iota), Eq (big_f a a) True % 3.89/4.05 Clause #45 (by superposition #[44, 32]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (big_f a a_1) False) (Eq (big_f a_1 a) True)) % 3.89/4.05 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1) False) (Eq (big_f a_1 a) True) % 3.89/4.05 Clause #51 (by superposition #[25, 13]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a (skS.0 0 a_1 a a_2)) True) (Or (Eq False True) (Eq (big_f a_1 a) True)) % 3.89/4.05 Clause #55 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a (skS.0 0 a_1 a a_2)) True) (Eq (big_f a_1 a) True) % 3.89/4.05 Clause #56 (by superposition #[55, 46]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a a_1) True) (Or (Eq True False) (Eq (big_f (skS.0 0 a a_1 a_2) a_1) True)) % 3.89/4.05 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a a_1) True) (Eq (big_f (skS.0 0 a a_1 a_2) a_1) True) % 3.89/4.05 Clause #58 (by superposition #[57, 36]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1) True) (Or (Eq True False) (Or (Eq (big_f a a_1) True) (Eq (big_f a_1 a) True))) % 3.89/4.05 Clause #60 (by clausification #[58]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1) True) (Or (Eq (big_f a a_1) True) (Eq (big_f a_1 a) True)) % 3.89/4.05 Clause #61 (by eliminate duplicate literals #[60]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1) True) (Eq (big_f a_1 a) True) % 3.89/4.05 Clause #63 (by superposition #[61, 46]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1) True) (Or (Eq True False) (Eq (big_f a a_1) True)) % 3.89/4.05 Clause #70 (by clausification #[63]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1) True) (Eq (big_f a a_1) True) % 3.89/4.05 Clause #71 (by eliminate duplicate literals #[70]): ∀ (a a_1 : Iota), Eq (big_f a a_1) True % 3.89/4.05 Clause #75 (by backward demodulation #[71, 35]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f (skS.0 0 a a_1 a_2) a_1) False) (Or (Eq True False) (Eq (big_f a_1 a) False)) % 3.89/4.05 Clause #84 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f (skS.0 0 a a_1 a_2) a_1) False) (Eq (big_f a_1 a) False) % 3.89/4.05 Clause #85 (by forward demodulation #[84, 71]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f (skS.0 0 a a_1 a_2) a_1) False) (Eq True False) % 3.89/4.05 Clause #86 (by clausification #[85]): ∀ (a a_1 a_2 : Iota), Eq (big_f (skS.0 0 a a_1 a_2) a_1) False % 3.89/4.05 Clause #87 (by superposition #[86, 71]): Eq False True % 3.89/4.05 Clause #88 (by clausification #[87]): False % 3.89/4.05 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------