%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN328+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n009.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 08:07:24 PM UTC 2025 % Result : Theorem 5.90s 6.08s % Output : Proof 5.98s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SYN328+1 : TPTP v9.2.0. Released v2.0.0. % 0.03/0.13 % Command : duper %s % 0.13/0.35 % Computer : n009.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % 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 : Thu Oct 2 15:37:38 EDT 2025 % 0.13/0.35 % CPUTime : % 5.90/6.08 SZS status Theorem for theBenchmark.p % 5.90/6.08 SZS output start Proof for theBenchmark.p % 5.90/6.08 Clause #0 (by assumption #[]): Eq % 5.90/6.08 (Not % 5.90/6.08 (Exists fun X => % 5.90/6.08 ∀ (Y Z : Iota), % 5.90/6.08 Iff (big_f Y → big_g Y) (big_f X) → % 5.90/6.08 Iff (big_f Y → big_h Y) (big_g X) → % 5.90/6.08 Iff ((big_f Y → big_g Y) → big_h Y) (big_h X) → And (And (big_f Z) (big_g Z)) (big_h Z))) % 5.90/6.08 True % 5.90/6.08 Clause #1 (by clausification #[0]): Eq % 5.90/6.08 (Exists fun X => % 5.90/6.08 ∀ (Y Z : Iota), % 5.90/6.08 Iff (big_f Y → big_g Y) (big_f X) → % 5.90/6.08 Iff (big_f Y → big_h Y) (big_g X) → % 5.90/6.08 Iff ((big_f Y → big_g Y) → big_h Y) (big_h X) → And (And (big_f Z) (big_g Z)) (big_h Z)) % 5.90/6.08 False % 5.90/6.08 Clause #2 (by clausification #[1]): ∀ (a : Iota), % 5.90/6.08 Eq % 5.90/6.08 (∀ (Y Z : Iota), % 5.90/6.08 Iff (big_f Y → big_g Y) (big_f a) → % 5.90/6.08 Iff (big_f Y → big_h Y) (big_g a) → % 5.90/6.08 Iff ((big_f Y → big_g Y) → big_h Y) (big_h a) → And (And (big_f Z) (big_g Z)) (big_h Z)) % 5.90/6.08 False % 5.90/6.08 Clause #3 (by clausification #[2]): ∀ (a a_1 : Iota), % 5.90/6.08 Eq % 5.90/6.08 (Not % 5.90/6.08 (∀ (Z : Iota), % 5.90/6.08 Iff (big_f (skS.0 0 a a_1) → big_g (skS.0 0 a a_1)) (big_f a) → % 5.90/6.08 Iff (big_f (skS.0 0 a a_1) → big_h (skS.0 0 a a_1)) (big_g a) → % 5.90/6.08 Iff ((big_f (skS.0 0 a a_1) → big_g (skS.0 0 a a_1)) → big_h (skS.0 0 a a_1)) (big_h a) → % 5.90/6.08 And (And (big_f Z) (big_g Z)) (big_h Z))) % 5.90/6.08 True % 5.90/6.08 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota), % 5.90/6.08 Eq % 5.90/6.08 (∀ (Z : Iota), % 5.90/6.08 Iff (big_f (skS.0 0 a a_1) → big_g (skS.0 0 a a_1)) (big_f a) → % 5.90/6.08 Iff (big_f (skS.0 0 a a_1) → big_h (skS.0 0 a a_1)) (big_g a) → % 5.90/6.08 Iff ((big_f (skS.0 0 a a_1) → big_g (skS.0 0 a a_1)) → big_h (skS.0 0 a a_1)) (big_h a) → % 5.90/6.08 And (And (big_f Z) (big_g Z)) (big_h Z)) % 5.90/6.08 False % 5.90/6.08 Clause #5 (by clausification #[4]): ∀ (a a_1 a_2 : Iota), % 5.90/6.08 Eq % 5.90/6.08 (Not % 5.90/6.08 (Iff (big_f (skS.0 0 a a_1) → big_g (skS.0 0 a a_1)) (big_f a) → % 5.90/6.08 Iff (big_f (skS.0 0 a a_1) → big_h (skS.0 0 a a_1)) (big_g a) → % 5.90/6.08 Iff ((big_f (skS.0 0 a a_1) → big_g (skS.0 0 a a_1)) → big_h (skS.0 0 a a_1)) (big_h a) → % 5.90/6.08 And (And (big_f (skS.0 1 a a_1 a_2)) (big_g (skS.0 1 a a_1 a_2))) (big_h (skS.0 1 a a_1 a_2)))) % 5.90/6.08 True % 5.90/6.08 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Iota), % 5.90/6.08 Eq % 5.90/6.08 (Iff (big_f (skS.0 0 a a_1) → big_g (skS.0 0 a a_1)) (big_f a) → % 5.90/6.08 Iff (big_f (skS.0 0 a a_1) → big_h (skS.0 0 a a_1)) (big_g a) → % 5.90/6.08 Iff ((big_f (skS.0 0 a a_1) → big_g (skS.0 0 a a_1)) → big_h (skS.0 0 a a_1)) (big_h a) → % 5.90/6.08 And (And (big_f (skS.0 1 a a_1 a_2)) (big_g (skS.0 1 a a_1 a_2))) (big_h (skS.0 1 a a_1 a_2))) % 5.90/6.08 False % 5.90/6.08 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (Iff (big_f (skS.0 0 a a_1) → big_g (skS.0 0 a a_1)) (big_f a)) True % 5.90/6.08 Clause #8 (by clausification #[6]): ∀ (a a_1 a_2 : Iota), % 5.90/6.08 Eq % 5.90/6.08 (Iff (big_f (skS.0 0 a a_1) → big_h (skS.0 0 a a_1)) (big_g a) → % 5.90/6.08 Iff ((big_f (skS.0 0 a a_1) → big_g (skS.0 0 a a_1)) → big_h (skS.0 0 a a_1)) (big_h a) → % 5.90/6.08 And (And (big_f (skS.0 1 a a_1 a_2)) (big_g (skS.0 1 a a_1 a_2))) (big_h (skS.0 1 a a_1 a_2))) % 5.90/6.08 False % 5.90/6.08 Clause #10 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (big_f (skS.0 0 a a_1) → big_g (skS.0 0 a a_1)) False) (Eq (big_f a) True) % 5.90/6.08 Clause #12 (by clausification #[10]): ∀ (a a_1 : Iota), Or (Eq (big_f a) True) (Eq (big_f (skS.0 0 a a_1)) True) % 5.90/6.08 Clause #13 (by clausification #[10]): ∀ (a a_1 : Iota), Or (Eq (big_f a) True) (Eq (big_g (skS.0 0 a a_1)) False) % 5.90/6.08 Clause #15 (by clausification #[8]): ∀ (a a_1 : Iota), Eq (Iff (big_f (skS.0 0 a a_1) → big_h (skS.0 0 a a_1)) (big_g a)) True % 5.90/6.08 Clause #16 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), % 5.90/6.08 Eq % 5.90/6.08 (Iff ((big_f (skS.0 0 a a_1) → big_g (skS.0 0 a a_1)) → big_h (skS.0 0 a a_1)) (big_h a) → % 5.90/6.08 And (And (big_f (skS.0 1 a a_1 a_2)) (big_g (skS.0 1 a a_1 a_2))) (big_h (skS.0 1 a a_1 a_2))) % 5.90/6.08 False % 5.90/6.08 Clause #17 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (big_f (skS.0 0 a a_1) → big_h (skS.0 0 a a_1)) True) (Eq (big_g a) False) % 5.90/6.08 Clause #18 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (big_f (skS.0 0 a a_1) → big_h (skS.0 0 a a_1)) False) (Eq (big_g a) True) % 5.90/6.14 Clause #19 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (big_g a) False) (Or (Eq (big_f (skS.0 0 a a_1)) False) (Eq (big_h (skS.0 0 a a_1)) True)) % 5.90/6.14 Clause #21 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (big_g a) True) (Eq (big_h (skS.0 0 a a_1)) False) % 5.90/6.14 Clause #31 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (Iff ((big_f (skS.0 0 a a_1) → big_g (skS.0 0 a a_1)) → big_h (skS.0 0 a a_1)) (big_h a)) True % 5.90/6.14 Clause #32 (by clausification #[16]): ∀ (a a_1 a_2 : Iota), % 5.90/6.14 Eq (And (And (big_f (skS.0 1 a a_1 a_2)) (big_g (skS.0 1 a a_1 a_2))) (big_h (skS.0 1 a a_1 a_2))) False % 5.90/6.14 Clause #34 (by clausification #[31]): ∀ (a a_1 : Iota), % 5.90/6.14 Or (Eq ((big_f (skS.0 0 a a_1) → big_g (skS.0 0 a a_1)) → big_h (skS.0 0 a a_1)) False) (Eq (big_h a) True) % 5.90/6.14 Clause #41 (by clausification #[34]): ∀ (a a_1 : Iota), Or (Eq (big_h a) True) (Eq (big_f (skS.0 0 a a_1) → big_g (skS.0 0 a a_1)) True) % 5.90/6.14 Clause #42 (by clausification #[34]): ∀ (a a_1 : Iota), Or (Eq (big_h a) True) (Eq (big_h (skS.0 0 a a_1)) False) % 5.90/6.14 Clause #43 (by clausification #[41]): ∀ (a a_1 : Iota), Or (Eq (big_h a) True) (Or (Eq (big_f (skS.0 0 a a_1)) False) (Eq (big_g (skS.0 0 a a_1)) True)) % 5.90/6.14 Clause #44 (by superposition #[43, 12]): ∀ (a a_1 : Iota), Or (Eq (big_h a) True) (Or (Eq (big_g (skS.0 0 a a_1)) True) (Or (Eq (big_f a) True) (Eq False True))) % 5.90/6.14 Clause #46 (by clausification #[44]): ∀ (a a_1 : Iota), Or (Eq (big_h a) True) (Or (Eq (big_g (skS.0 0 a a_1)) True) (Eq (big_f a) True)) % 5.90/6.14 Clause #47 (by superposition #[46, 13]): ∀ (a : Iota), Or (Eq (big_h a) True) (Or (Eq (big_f a) True) (Or (Eq (big_f a) True) (Eq True False))) % 5.90/6.14 Clause #49 (by clausification #[47]): ∀ (a : Iota), Or (Eq (big_h a) True) (Or (Eq (big_f a) True) (Eq (big_f a) True)) % 5.90/6.14 Clause #50 (by eliminate duplicate literals #[49]): ∀ (a : Iota), Or (Eq (big_h a) True) (Eq (big_f a) True) % 5.90/6.14 Clause #52 (by superposition #[50, 42]): ∀ (a a_1 : Iota), Or (Eq (big_f (skS.0 0 a a_1)) True) (Or (Eq (big_h a) True) (Eq True False)) % 5.90/6.14 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), Or (Eq (big_f (skS.0 0 a a_1)) True) (Eq (big_h a) True) % 5.90/6.14 Clause #56 (by superposition #[53, 43]): ∀ (a a_1 : Iota), Or (Eq (big_h a) True) (Or (Eq (big_h a) True) (Or (Eq True False) (Eq (big_g (skS.0 0 a a_1)) True))) % 5.90/6.14 Clause #67 (by clausification #[56]): ∀ (a a_1 : Iota), Or (Eq (big_h a) True) (Or (Eq (big_h a) True) (Eq (big_g (skS.0 0 a a_1)) True)) % 5.90/6.14 Clause #68 (by eliminate duplicate literals #[67]): ∀ (a a_1 : Iota), Or (Eq (big_h a) True) (Eq (big_g (skS.0 0 a a_1)) True) % 5.90/6.14 Clause #70 (by superposition #[68, 19]): ∀ (a a_1 a_2 : Iota), % 5.90/6.14 Or (Eq (big_h a) True) % 5.90/6.14 (Or (Eq True False) % 5.90/6.14 (Or (Eq (big_f (skS.0 0 (skS.0 0 a a_1) a_2)) False) (Eq (big_h (skS.0 0 (skS.0 0 a a_1) a_2)) True))) % 5.90/6.14 Clause #71 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), % 5.90/6.14 Or (Eq (And (big_f (skS.0 1 a a_1 a_2)) (big_g (skS.0 1 a a_1 a_2))) False) (Eq (big_h (skS.0 1 a a_1 a_2)) False) % 5.90/6.14 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 : Iota), % 5.90/6.14 Or (Eq (big_h (skS.0 1 a a_1 a_2)) False) % 5.90/6.14 (Or (Eq (big_f (skS.0 1 a a_1 a_2)) False) (Eq (big_g (skS.0 1 a a_1 a_2)) False)) % 5.90/6.14 Clause #85 (by clausification #[70]): ∀ (a a_1 a_2 : Iota), % 5.90/6.14 Or (Eq (big_h a) True) % 5.90/6.14 (Or (Eq (big_f (skS.0 0 (skS.0 0 a a_1) a_2)) False) (Eq (big_h (skS.0 0 (skS.0 0 a a_1) a_2)) True)) % 5.90/6.14 Clause #88 (by superposition #[85, 53]): ∀ (a a_1 a_2 : Iota), % 5.90/6.14 Or (Eq (big_h a) True) % 5.90/6.14 (Or (Eq (big_h (skS.0 0 (skS.0 0 a a_1) a_2)) True) (Or (Eq False True) (Eq (big_h (skS.0 0 a a_1)) True))) % 5.90/6.14 Clause #89 (by clausification #[88]): ∀ (a a_1 a_2 : Iota), % 5.90/6.14 Or (Eq (big_h a) True) (Or (Eq (big_h (skS.0 0 (skS.0 0 a a_1) a_2)) True) (Eq (big_h (skS.0 0 a a_1)) True)) % 5.90/6.14 Clause #91 (by superposition #[89, 42]): ∀ (a a_1 : Iota), % 5.90/6.14 Or (Eq (big_h a) True) (Or (Eq (big_h (skS.0 0 a a_1)) True) (Or (Eq (big_h (skS.0 0 a a_1)) True) (Eq True False))) % 5.90/6.14 Clause #97 (by clausification #[91]): ∀ (a a_1 : Iota), Or (Eq (big_h a) True) (Or (Eq (big_h (skS.0 0 a a_1)) True) (Eq (big_h (skS.0 0 a a_1)) True)) % 5.98/6.16 Clause #98 (by eliminate duplicate literals #[97]): ∀ (a a_1 : Iota), Or (Eq (big_h a) True) (Eq (big_h (skS.0 0 a a_1)) True) % 5.98/6.16 Clause #100 (by superposition #[98, 42]): ∀ (a : Iota), Or (Eq (big_h a) True) (Or (Eq (big_h a) True) (Eq True False)) % 5.98/6.16 Clause #102 (by clausification #[100]): ∀ (a : Iota), Or (Eq (big_h a) True) (Eq (big_h a) True) % 5.98/6.16 Clause #103 (by eliminate duplicate literals #[102]): ∀ (a : Iota), Eq (big_h a) True % 5.98/6.16 Clause #104 (by backward demodulation #[103, 72]): ∀ (a a_1 a_2 : Iota), % 5.98/6.16 Or (Eq True False) (Or (Eq (big_f (skS.0 1 a a_1 a_2)) False) (Eq (big_g (skS.0 1 a a_1 a_2)) False)) % 5.98/6.16 Clause #112 (by superposition #[103, 21]): ∀ (a : Iota), Or (Eq (big_g a) True) (Eq True False) % 5.98/6.16 Clause #113 (by clausification #[112]): ∀ (a : Iota), Eq (big_g a) True % 5.98/6.16 Clause #117 (by superposition #[113, 13]): ∀ (a : Iota), Or (Eq (big_f a) True) (Eq True False) % 5.98/6.16 Clause #118 (by clausification #[117]): ∀ (a : Iota), Eq (big_f a) True % 5.98/6.16 Clause #130 (by clausification #[104]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f (skS.0 1 a a_1 a_2)) False) (Eq (big_g (skS.0 1 a a_1 a_2)) False) % 5.98/6.16 Clause #131 (by forward demodulation #[130, 118]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (big_g (skS.0 1 a a_1 a_2)) False) % 5.98/6.16 Clause #132 (by clausification #[131]): ∀ (a a_1 a_2 : Iota), Eq (big_g (skS.0 1 a a_1 a_2)) False % 5.98/6.16 Clause #133 (by superposition #[132, 113]): Eq False True % 5.98/6.16 Clause #134 (by clausification #[133]): False % 5.98/6.16 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------