%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN920+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n023.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 08:08:14 PM UTC 2025 % Result : Theorem 4.13s 4.32s % Output : Proof 4.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SYN920+1 : TPTP v9.2.0. Released v3.1.0. % 0.13/0.14 % Command : duper %s % 0.14/0.35 % Computer : n023.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 15:29:23 EDT 2025 % 0.14/0.35 % CPUTime : % 4.13/4.32 SZS status Theorem for theBenchmark.p % 4.13/4.32 SZS output start Proof for theBenchmark.p % 4.13/4.32 Clause #0 (by assumption #[]): Eq % 4.13/4.32 (Not % 4.13/4.32 (And ((∀ (X : Iota), And (f X) (g X) → h X) → Exists fun X => And (f X) (Not (g X))) % 4.13/4.32 (Or (∀ (W : Iota), f W → g W) (∀ (Z : Iota), f Z → h Z)) → % 4.13/4.32 (∀ (R : Iota), And (f R) (h R) → g R) → Exists fun V => And (And (f V) (g V)) (Not (h V)))) % 4.13/4.32 True % 4.13/4.32 Clause #1 (by clausification #[0]): Eq % 4.13/4.32 (And ((∀ (X : Iota), And (f X) (g X) → h X) → Exists fun X => And (f X) (Not (g X))) % 4.13/4.32 (Or (∀ (W : Iota), f W → g W) (∀ (Z : Iota), f Z → h Z)) → % 4.13/4.32 (∀ (R : Iota), And (f R) (h R) → g R) → Exists fun V => And (And (f V) (g V)) (Not (h V))) % 4.13/4.32 False % 4.13/4.32 Clause #2 (by clausification #[1]): Eq % 4.13/4.32 (And ((∀ (X : Iota), And (f X) (g X) → h X) → Exists fun X => And (f X) (Not (g X))) % 4.13/4.32 (Or (∀ (W : Iota), f W → g W) (∀ (Z : Iota), f Z → h Z))) % 4.13/4.32 True % 4.13/4.32 Clause #3 (by clausification #[1]): Eq ((∀ (R : Iota), And (f R) (h R) → g R) → Exists fun V => And (And (f V) (g V)) (Not (h V))) False % 4.13/4.32 Clause #4 (by clausification #[2]): Eq (Or (∀ (W : Iota), f W → g W) (∀ (Z : Iota), f Z → h Z)) True % 4.13/4.32 Clause #5 (by clausification #[2]): Eq ((∀ (X : Iota), And (f X) (g X) → h X) → Exists fun X => And (f X) (Not (g X))) True % 4.13/4.32 Clause #6 (by clausification #[4]): Or (Eq (∀ (W : Iota), f W → g W) True) (Eq (∀ (Z : Iota), f Z → h Z) True) % 4.13/4.32 Clause #7 (by clausification #[6]): ∀ (a : Iota), Or (Eq (∀ (Z : Iota), f Z → h Z) True) (Eq (f a → g a) True) % 4.13/4.32 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (f a → g a) True) (Eq (f a_1 → h a_1) True) % 4.13/4.32 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq (f a → h a) True) (Or (Eq (f a_1) False) (Eq (g a_1) True)) % 4.13/4.32 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Or (Eq (f a) False) (Or (Eq (g a) True) (Or (Eq (f a_1) False) (Eq (h a_1) True))) % 4.13/4.32 Clause #11 (by clausification #[5]): Or (Eq (∀ (X : Iota), And (f X) (g X) → h X) False) (Eq (Exists fun X => And (f X) (Not (g X))) True) % 4.13/4.32 Clause #12 (by clausification #[11]): ∀ (a : Iota), % 4.13/4.32 Or (Eq (Exists fun X => And (f X) (Not (g X))) True) % 4.13/4.32 (Eq (Not (And (f (skS.0 0 a)) (g (skS.0 0 a)) → h (skS.0 0 a))) True) % 4.13/4.32 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), % 4.13/4.32 Or (Eq (Not (And (f (skS.0 0 a)) (g (skS.0 0 a)) → h (skS.0 0 a))) True) % 4.13/4.32 (Eq (And (f (skS.0 1 a_1)) (Not (g (skS.0 1 a_1)))) True) % 4.13/4.32 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), % 4.13/4.32 Or (Eq (And (f (skS.0 1 a)) (Not (g (skS.0 1 a)))) True) % 4.13/4.32 (Eq (And (f (skS.0 0 a_1)) (g (skS.0 0 a_1)) → h (skS.0 0 a_1)) False) % 4.13/4.32 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (And (f (skS.0 0 a)) (g (skS.0 0 a)) → h (skS.0 0 a)) False) (Eq (Not (g (skS.0 1 a_1))) True) % 4.13/4.32 Clause #16 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (And (f (skS.0 0 a)) (g (skS.0 0 a)) → h (skS.0 0 a)) False) (Eq (f (skS.0 1 a_1)) True) % 4.13/4.32 Clause #17 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (Not (g (skS.0 1 a))) True) (Eq (And (f (skS.0 0 a_1)) (g (skS.0 0 a_1))) True) % 4.13/4.32 Clause #18 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (Not (g (skS.0 1 a))) True) (Eq (h (skS.0 0 a_1)) False) % 4.13/4.32 Clause #19 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (And (f (skS.0 0 a)) (g (skS.0 0 a))) True) (Eq (g (skS.0 1 a_1)) False) % 4.13/4.32 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Or (Eq (g (skS.0 1 a)) False) (Eq (g (skS.0 0 a_1)) True) % 4.13/4.32 Clause #21 (by clausification #[19]): ∀ (a a_1 : Iota), Or (Eq (g (skS.0 1 a)) False) (Eq (f (skS.0 0 a_1)) True) % 4.13/4.32 Clause #22 (by clausification #[3]): Eq (∀ (R : Iota), And (f R) (h R) → g R) True % 4.13/4.32 Clause #23 (by clausification #[3]): Eq (Exists fun V => And (And (f V) (g V)) (Not (h V))) False % 4.13/4.32 Clause #24 (by clausification #[22]): ∀ (a : Iota), Eq (And (f a) (h a) → g a) True % 4.13/4.32 Clause #25 (by clausification #[24]): ∀ (a : Iota), Or (Eq (And (f a) (h a)) False) (Eq (g a) True) % 4.13/4.32 Clause #26 (by clausification #[25]): ∀ (a : Iota), Or (Eq (g a) True) (Or (Eq (f a) False) (Eq (h a) False)) % 4.13/4.32 Clause #27 (by clausification #[23]): ∀ (a : Iota), Eq (And (And (f a) (g a)) (Not (h a))) False % 4.18/4.35 Clause #28 (by clausification #[27]): ∀ (a : Iota), Or (Eq (And (f a) (g a)) False) (Eq (Not (h a)) False) % 4.18/4.35 Clause #29 (by clausification #[28]): ∀ (a : Iota), Or (Eq (Not (h a)) False) (Or (Eq (f a) False) (Eq (g a) False)) % 4.18/4.35 Clause #30 (by clausification #[29]): ∀ (a : Iota), Or (Eq (f a) False) (Or (Eq (g a) False) (Eq (h a) True)) % 4.18/4.35 Clause #31 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (f (skS.0 1 a)) True) (Eq (And (f (skS.0 0 a_1)) (g (skS.0 0 a_1))) True) % 4.18/4.35 Clause #32 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (f (skS.0 1 a)) True) (Eq (h (skS.0 0 a_1)) False) % 4.18/4.35 Clause #33 (by clausification #[31]): ∀ (a a_1 : Iota), Or (Eq (f (skS.0 1 a)) True) (Eq (g (skS.0 0 a_1)) True) % 4.18/4.35 Clause #34 (by clausification #[31]): ∀ (a a_1 : Iota), Or (Eq (f (skS.0 1 a)) True) (Eq (f (skS.0 0 a_1)) True) % 4.18/4.35 Clause #43 (by superposition #[34, 30]): ∀ (a a_1 : Iota), % 4.18/4.35 Or (Eq (f (skS.0 1 a)) True) (Or (Eq True False) (Or (Eq (g (skS.0 0 a_1)) False) (Eq (h (skS.0 0 a_1)) True))) % 4.18/4.35 Clause #44 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (h (skS.0 0 a)) False) (Eq (g (skS.0 1 a_1)) False) % 4.18/4.35 Clause #56 (by clausification #[43]): ∀ (a a_1 : Iota), Or (Eq (f (skS.0 1 a)) True) (Or (Eq (g (skS.0 0 a_1)) False) (Eq (h (skS.0 0 a_1)) True)) % 4.18/4.35 Clause #57 (by superposition #[56, 33]): ∀ (a a_1 a_2 : Iota), % 4.18/4.35 Or (Eq (f (skS.0 1 a)) True) (Or (Eq (h (skS.0 0 a_1)) True) (Or (Eq (f (skS.0 1 a_2)) True) (Eq False True))) % 4.18/4.35 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), Or (Eq (f (skS.0 1 a)) True) (Or (Eq (h (skS.0 0 a_1)) True) (Eq (f (skS.0 1 a_2)) True)) % 4.18/4.35 Clause #71 (by equality factoring #[58]): ∀ (a a_1 : Iota), Or (Eq (h (skS.0 0 a)) True) (Or (Ne True True) (Eq (f (skS.0 1 a_1)) True)) % 4.18/4.35 Clause #72 (by clausification #[71]): ∀ (a a_1 : Iota), Or (Eq (h (skS.0 0 a)) True) (Or (Eq (f (skS.0 1 a_1)) True) (Or (Eq True False) (Eq True False))) % 4.18/4.35 Clause #74 (by clausification #[72]): ∀ (a a_1 : Iota), Or (Eq (h (skS.0 0 a)) True) (Or (Eq (f (skS.0 1 a_1)) True) (Eq True False)) % 4.18/4.35 Clause #75 (by clausification #[74]): ∀ (a a_1 : Iota), Or (Eq (h (skS.0 0 a)) True) (Eq (f (skS.0 1 a_1)) True) % 4.18/4.35 Clause #76 (by superposition #[75, 32]): ∀ (a a_1 : Iota), Or (Eq (f (skS.0 1 a)) True) (Or (Eq (f (skS.0 1 a_1)) True) (Eq True False)) % 4.18/4.35 Clause #85 (by clausification #[76]): ∀ (a a_1 : Iota), Or (Eq (f (skS.0 1 a)) True) (Eq (f (skS.0 1 a_1)) True) % 4.18/4.35 Clause #91 (by equality factoring #[85]): ∀ (a : Iota), Or (Ne True True) (Eq (f (skS.0 1 a)) True) % 4.18/4.35 Clause #92 (by clausification #[91]): ∀ (a : Iota), Or (Eq (f (skS.0 1 a)) True) (Or (Eq True False) (Eq True False)) % 4.18/4.35 Clause #94 (by clausification #[92]): ∀ (a : Iota), Or (Eq (f (skS.0 1 a)) True) (Eq True False) % 4.18/4.35 Clause #95 (by clausification #[94]): ∀ (a : Iota), Eq (f (skS.0 1 a)) True % 4.18/4.35 Clause #96 (by superposition #[95, 10]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (g (skS.0 1 a)) True) (Or (Eq (f a_1) False) (Eq (h a_1) True))) % 4.18/4.35 Clause #97 (by superposition #[95, 26]): ∀ (a : Iota), Or (Eq (g (skS.0 1 a)) True) (Or (Eq True False) (Eq (h (skS.0 1 a)) False)) % 4.18/4.35 Clause #101 (by clausification #[96]): ∀ (a a_1 : Iota), Or (Eq (g (skS.0 1 a)) True) (Or (Eq (f a_1) False) (Eq (h a_1) True)) % 4.18/4.35 Clause #102 (by superposition #[101, 95]): ∀ (a a_1 : Iota), Or (Eq (g (skS.0 1 a)) True) (Or (Eq (h (skS.0 1 a_1)) True) (Eq False True)) % 4.18/4.35 Clause #104 (by clausification #[97]): ∀ (a : Iota), Or (Eq (g (skS.0 1 a)) True) (Eq (h (skS.0 1 a)) False) % 4.18/4.35 Clause #106 (by clausification #[102]): ∀ (a a_1 : Iota), Or (Eq (g (skS.0 1 a)) True) (Eq (h (skS.0 1 a_1)) True) % 4.18/4.35 Clause #110 (by superposition #[106, 104]): ∀ (a a_1 : Iota), Or (Eq (g (skS.0 1 a)) True) (Or (Eq (g (skS.0 1 a_1)) True) (Eq True False)) % 4.18/4.35 Clause #111 (by clausification #[110]): ∀ (a a_1 : Iota), Or (Eq (g (skS.0 1 a)) True) (Eq (g (skS.0 1 a_1)) True) % 4.18/4.35 Clause #115 (by equality factoring #[111]): ∀ (a : Iota), Or (Ne True True) (Eq (g (skS.0 1 a)) True) % 4.18/4.35 Clause #116 (by clausification #[115]): ∀ (a : Iota), Or (Eq (g (skS.0 1 a)) True) (Or (Eq True False) (Eq True False)) % 4.18/4.36 Clause #118 (by clausification #[116]): ∀ (a : Iota), Or (Eq (g (skS.0 1 a)) True) (Eq True False) % 4.18/4.36 Clause #119 (by clausification #[118]): ∀ (a : Iota), Eq (g (skS.0 1 a)) True % 4.18/4.36 Clause #122 (by superposition #[119, 20]): ∀ (a : Iota), Or (Eq True False) (Eq (g (skS.0 0 a)) True) % 4.18/4.36 Clause #123 (by superposition #[119, 21]): ∀ (a : Iota), Or (Eq True False) (Eq (f (skS.0 0 a)) True) % 4.18/4.36 Clause #130 (by clausification #[123]): ∀ (a : Iota), Eq (f (skS.0 0 a)) True % 4.18/4.36 Clause #133 (by superposition #[130, 30]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (g (skS.0 0 a)) False) (Eq (h (skS.0 0 a)) True)) % 4.18/4.36 Clause #134 (by clausification #[122]): ∀ (a : Iota), Eq (g (skS.0 0 a)) True % 4.18/4.36 Clause #142 (by clausification #[133]): ∀ (a : Iota), Or (Eq (g (skS.0 0 a)) False) (Eq (h (skS.0 0 a)) True) % 4.18/4.36 Clause #143 (by forward demodulation #[142, 134]): ∀ (a : Iota), Or (Eq True False) (Eq (h (skS.0 0 a)) True) % 4.18/4.36 Clause #144 (by clausification #[143]): ∀ (a : Iota), Eq (h (skS.0 0 a)) True % 4.18/4.36 Clause #145 (by superposition #[144, 44]): ∀ (a : Iota), Or (Eq True False) (Eq (g (skS.0 1 a)) False) % 4.18/4.36 Clause #146 (by clausification #[145]): ∀ (a : Iota), Eq (g (skS.0 1 a)) False % 4.18/4.36 Clause #147 (by superposition #[146, 119]): Eq False True % 4.18/4.36 Clause #148 (by clausification #[147]): False % 4.18/4.36 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------