%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN918+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n022.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 6.03s 6.24s % Output : Proof 6.08s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.05/0.10 % Problem : SYN918+1 : TPTP v9.2.0. Released v3.1.0. % 0.05/0.11 % Command : duper %s % 0.10/0.31 % Computer : n022.cluster.edu % 0.10/0.31 % Model : x86_64 x86_64 % 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.31 % Memory : 8042.1875MB % 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.31 % CPULimit : 300 % 0.10/0.31 % WCLimit : 300 % 0.10/0.31 % DateTime : Thu Oct 2 15:39:38 EDT 2025 % 0.16/0.31 % CPUTime : % 6.03/6.24 SZS status Theorem for theBenchmark.p % 6.03/6.24 SZS output start Proof for theBenchmark.p % 6.03/6.24 Clause #0 (by assumption #[]): Eq % 6.03/6.24 (Not % 6.03/6.24 (And (∀ (X : Iota), (And (f X) (g X) → h X) → Exists fun Y => And (f Y) (Not (g Y))) % 6.03/6.24 (Or (∀ (W : Iota), f W → g W) (∀ (Z : Iota), f Z → h Z)) → % 6.03/6.24 (∀ (R : Iota), And (f R) (h R) → g R) → Exists fun V => And (And (f V) (g V)) (Not (h V)))) % 6.03/6.24 True % 6.03/6.24 Clause #1 (by clausification #[0]): Eq % 6.03/6.24 (And (∀ (X : Iota), (And (f X) (g X) → h X) → Exists fun Y => And (f Y) (Not (g Y))) % 6.03/6.24 (Or (∀ (W : Iota), f W → g W) (∀ (Z : Iota), f Z → h Z)) → % 6.03/6.24 (∀ (R : Iota), And (f R) (h R) → g R) → Exists fun V => And (And (f V) (g V)) (Not (h V))) % 6.03/6.24 False % 6.03/6.24 Clause #2 (by clausification #[1]): Eq % 6.03/6.24 (And (∀ (X : Iota), (And (f X) (g X) → h X) → Exists fun Y => And (f Y) (Not (g Y))) % 6.03/6.24 (Or (∀ (W : Iota), f W → g W) (∀ (Z : Iota), f Z → h Z))) % 6.03/6.24 True % 6.03/6.24 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 % 6.03/6.24 Clause #4 (by clausification #[2]): Eq (Or (∀ (W : Iota), f W → g W) (∀ (Z : Iota), f Z → h Z)) True % 6.03/6.24 Clause #5 (by clausification #[2]): Eq (∀ (X : Iota), (And (f X) (g X) → h X) → Exists fun Y => And (f Y) (Not (g Y))) True % 6.03/6.24 Clause #6 (by clausification #[4]): Or (Eq (∀ (W : Iota), f W → g W) True) (Eq (∀ (Z : Iota), f Z → h Z) True) % 6.03/6.24 Clause #7 (by clausification #[6]): ∀ (a : Iota), Or (Eq (∀ (Z : Iota), f Z → h Z) True) (Eq (f a → g a) True) % 6.03/6.24 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (f a → g a) True) (Eq (f a_1 → h a_1) True) % 6.03/6.24 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)) % 6.03/6.24 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))) % 6.03/6.24 Clause #11 (by clausification #[5]): ∀ (a : Iota), Eq ((And (f a) (g a) → h a) → Exists fun Y => And (f Y) (Not (g Y))) True % 6.03/6.24 Clause #12 (by clausification #[11]): ∀ (a : Iota), Or (Eq (And (f a) (g a) → h a) False) (Eq (Exists fun Y => And (f Y) (Not (g Y))) True) % 6.03/6.24 Clause #13 (by clausification #[12]): ∀ (a : Iota), Or (Eq (Exists fun Y => And (f Y) (Not (g Y))) True) (Eq (And (f a) (g a)) True) % 6.03/6.24 Clause #14 (by clausification #[12]): ∀ (a : Iota), Or (Eq (Exists fun Y => And (f Y) (Not (g Y))) True) (Eq (h a) False) % 6.03/6.24 Clause #15 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (And (f a) (g a)) True) (Eq (And (f (skS.0 0 a_1)) (Not (g (skS.0 0 a_1)))) True) % 6.03/6.24 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (And (f (skS.0 0 a)) (Not (g (skS.0 0 a)))) True) (Eq (g a_1) True) % 6.03/6.24 Clause #17 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (And (f (skS.0 0 a)) (Not (g (skS.0 0 a)))) True) (Eq (f a_1) True) % 6.03/6.24 Clause #18 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (g a) True) (Eq (Not (g (skS.0 0 a_1))) True) % 6.03/6.24 Clause #20 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (g a) True) (Eq (g (skS.0 0 a_1)) False) % 6.03/6.24 Clause #23 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (h a) False) (Eq (And (f (skS.0 1 a_1)) (Not (g (skS.0 1 a_1)))) True) % 6.03/6.24 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (h a) False) (Eq (Not (g (skS.0 1 a_1))) True) % 6.03/6.24 Clause #26 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (h a) False) (Eq (g (skS.0 1 a_1)) False) % 6.03/6.24 Clause #27 (by clausification #[3]): Eq (∀ (R : Iota), And (f R) (h R) → g R) True % 6.03/6.24 Clause #28 (by clausification #[3]): Eq (Exists fun V => And (And (f V) (g V)) (Not (h V))) False % 6.03/6.24 Clause #29 (by clausification #[27]): ∀ (a : Iota), Eq (And (f a) (h a) → g a) True % 6.03/6.24 Clause #30 (by clausification #[29]): ∀ (a : Iota), Or (Eq (And (f a) (h a)) False) (Eq (g a) True) % 6.03/6.24 Clause #31 (by clausification #[30]): ∀ (a : Iota), Or (Eq (g a) True) (Or (Eq (f a) False) (Eq (h a) False)) % 6.03/6.24 Clause #33 (by clausification #[28]): ∀ (a : Iota), Eq (And (And (f a) (g a)) (Not (h a))) False % 6.03/6.24 Clause #34 (by clausification #[33]): ∀ (a : Iota), Or (Eq (And (f a) (g a)) False) (Eq (Not (h a)) False) % 6.08/6.29 Clause #35 (by clausification #[34]): ∀ (a : Iota), Or (Eq (Not (h a)) False) (Or (Eq (f a) False) (Eq (g a) False)) % 6.08/6.29 Clause #36 (by clausification #[35]): ∀ (a : Iota), Or (Eq (f a) False) (Or (Eq (g a) False) (Eq (h a) True)) % 6.08/6.29 Clause #40 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (f a) True) (Eq (Not (g (skS.0 0 a_1))) True) % 6.08/6.29 Clause #41 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (f a) True) (Eq (f (skS.0 0 a_1)) True) % 6.08/6.29 Clause #42 (by clausification #[40]): ∀ (a a_1 : Iota), Or (Eq (f a) True) (Eq (g (skS.0 0 a_1)) False) % 6.08/6.29 Clause #52 (by equality factoring #[41]): ∀ (a : Iota), Or (Ne True True) (Eq (f (skS.0 0 a)) True) % 6.08/6.29 Clause #54 (by clausification #[52]): ∀ (a : Iota), Or (Eq (f (skS.0 0 a)) True) (Or (Eq True False) (Eq True False)) % 6.08/6.29 Clause #56 (by clausification #[54]): ∀ (a : Iota), Or (Eq (f (skS.0 0 a)) True) (Eq True False) % 6.08/6.29 Clause #57 (by clausification #[56]): ∀ (a : Iota), Eq (f (skS.0 0 a)) True % 6.08/6.29 Clause #58 (by superposition #[57, 10]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (g (skS.0 0 a)) True) (Or (Eq (f a_1) False) (Eq (h a_1) True))) % 6.08/6.29 Clause #59 (by superposition #[57, 31]): ∀ (a : Iota), Or (Eq (g (skS.0 0 a)) True) (Or (Eq True False) (Eq (h (skS.0 0 a)) False)) % 6.08/6.29 Clause #63 (by clausification #[58]): ∀ (a a_1 : Iota), Or (Eq (g (skS.0 0 a)) True) (Or (Eq (f a_1) False) (Eq (h a_1) True)) % 6.08/6.29 Clause #64 (by superposition #[63, 57]): ∀ (a a_1 : Iota), Or (Eq (g (skS.0 0 a)) True) (Or (Eq (h (skS.0 0 a_1)) True) (Eq False True)) % 6.08/6.29 Clause #67 (by clausification #[59]): ∀ (a : Iota), Or (Eq (g (skS.0 0 a)) True) (Eq (h (skS.0 0 a)) False) % 6.08/6.29 Clause #69 (by clausification #[64]): ∀ (a a_1 : Iota), Or (Eq (g (skS.0 0 a)) True) (Eq (h (skS.0 0 a_1)) True) % 6.08/6.29 Clause #70 (by superposition #[69, 20]): ∀ (a a_1 : Iota), Or (Eq (h (skS.0 0 a)) True) (Or (Eq (g a_1) True) (Eq True False)) % 6.08/6.29 Clause #103 (by clausification #[70]): ∀ (a a_1 : Iota), Or (Eq (h (skS.0 0 a)) True) (Eq (g a_1) True) % 6.08/6.29 Clause #104 (by superposition #[103, 67]): ∀ (a a_1 : Iota), Or (Eq (g a) True) (Or (Eq (g (skS.0 0 a_1)) True) (Eq True False)) % 6.08/6.29 Clause #110 (by clausification #[104]): ∀ (a a_1 : Iota), Or (Eq (g a) True) (Eq (g (skS.0 0 a_1)) True) % 6.08/6.29 Clause #114 (by superposition #[110, 20]): ∀ (a a_1 : Iota), Or (Eq (g a) True) (Or (Eq (g a_1) True) (Eq True False)) % 6.08/6.29 Clause #115 (by superposition #[110, 42]): ∀ (a a_1 : Iota), Or (Eq (g a) True) (Or (Eq (f a_1) True) (Eq True False)) % 6.08/6.29 Clause #118 (by clausification #[115]): ∀ (a a_1 : Iota), Or (Eq (g a) True) (Eq (f a_1) True) % 6.08/6.29 Clause #120 (by superposition #[118, 42]): ∀ (a a_1 : Iota), Or (Eq (f a) True) (Or (Eq (f a_1) True) (Eq True False)) % 6.08/6.29 Clause #126 (by clausification #[120]): ∀ (a a_1 : Iota), Or (Eq (f a) True) (Eq (f a_1) True) % 6.08/6.29 Clause #131 (by equality factoring #[126]): ∀ (a : Iota), Or (Ne True True) (Eq (f a) True) % 6.08/6.29 Clause #132 (by clausification #[131]): ∀ (a : Iota), Or (Eq (f a) True) (Or (Eq True False) (Eq True False)) % 6.08/6.29 Clause #134 (by clausification #[132]): ∀ (a : Iota), Or (Eq (f a) True) (Eq True False) % 6.08/6.29 Clause #135 (by clausification #[134]): ∀ (a : Iota), Eq (f a) True % 6.08/6.29 Clause #138 (by backward demodulation #[135, 36]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (g a) False) (Eq (h a) True)) % 6.08/6.29 Clause #141 (by clausification #[138]): ∀ (a : Iota), Or (Eq (g a) False) (Eq (h a) True) % 6.08/6.29 Clause #148 (by clausification #[114]): ∀ (a a_1 : Iota), Or (Eq (g a) True) (Eq (g a_1) True) % 6.08/6.29 Clause #150 (by equality factoring #[148]): ∀ (a : Iota), Or (Ne True True) (Eq (g a) True) % 6.08/6.29 Clause #153 (by clausification #[150]): ∀ (a : Iota), Or (Eq (g a) True) (Or (Eq True False) (Eq True False)) % 6.08/6.29 Clause #155 (by clausification #[153]): ∀ (a : Iota), Or (Eq (g a) True) (Eq True False) % 6.08/6.29 Clause #156 (by clausification #[155]): ∀ (a : Iota), Eq (g a) True % 6.08/6.29 Clause #157 (by backward demodulation #[156, 141]): ∀ (a : Iota), Or (Eq True False) (Eq (h a) True) % 6.08/6.29 Clause #159 (by clausification #[157]): ∀ (a : Iota), Eq (h a) True % 6.08/6.29 Clause #160 (by superposition #[159, 26]): ∀ (a : Iota), Or (Eq True False) (Eq (g (skS.0 1 a)) False) % 6.08/6.29 Clause #164 (by clausification #[160]): ∀ (a : Iota), Eq (g (skS.0 1 a)) False % 6.08/6.29 Clause #165 (by superposition #[164, 156]): Eq False True % 6.08/6.29 Clause #166 (by clausification #[165]): False % 6.08/6.29 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------