%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU886^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n003.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 08:02:35 PM UTC 2025 % Result : Theorem 3.77s 4.00s % Output : Proof 3.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU886^5 : TPTP v9.2.0. Released v4.0.0. % 0.11/0.13 % Command : duper %s % 0.13/0.35 % Computer : n003.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 : Fri Oct 3 04:19:23 EDT 2025 % 0.13/0.35 % CPUTime : % 3.77/4.00 SZS status Theorem for theBenchmark.p % 3.77/4.00 SZS output start Proof for theBenchmark.p % 3.77/4.00 Clause #0 (by assumption #[]): Eq % 3.77/4.00 (Not % 3.77/4.00 (∀ (Xx0 : a), % 3.77/4.00 (Exists fun Xt => And (And (x Xt) (y Xt)) (Eq Xx0 (f Xt))) → % 3.77/4.00 And (Exists fun Xt => And (x Xt) (Eq Xx0 (f Xt))) (Exists fun Xt => And (y Xt) (Eq Xx0 (f Xt))))) % 3.77/4.00 True % 3.77/4.00 Clause #1 (by clausification #[0]): Eq % 3.77/4.00 (∀ (Xx0 : a), % 3.77/4.00 (Exists fun Xt => And (And (x Xt) (y Xt)) (Eq Xx0 (f Xt))) → % 3.77/4.00 And (Exists fun Xt => And (x Xt) (Eq Xx0 (f Xt))) (Exists fun Xt => And (y Xt) (Eq Xx0 (f Xt)))) % 3.77/4.00 False % 3.77/4.00 Clause #2 (by clausification #[1]): ∀ (a_1 : a), % 3.77/4.00 Eq % 3.77/4.00 (Not % 3.77/4.00 ((Exists fun Xt => And (And (x Xt) (y Xt)) (Eq (skS.0 0 a_1) (f Xt))) → % 3.77/4.00 And (Exists fun Xt => And (x Xt) (Eq (skS.0 0 a_1) (f Xt))) % 3.77/4.00 (Exists fun Xt => And (y Xt) (Eq (skS.0 0 a_1) (f Xt))))) % 3.77/4.00 True % 3.77/4.00 Clause #3 (by clausification #[2]): ∀ (a_1 : a), % 3.77/4.00 Eq % 3.77/4.00 ((Exists fun Xt => And (And (x Xt) (y Xt)) (Eq (skS.0 0 a_1) (f Xt))) → % 3.77/4.00 And (Exists fun Xt => And (x Xt) (Eq (skS.0 0 a_1) (f Xt))) % 3.77/4.00 (Exists fun Xt => And (y Xt) (Eq (skS.0 0 a_1) (f Xt)))) % 3.77/4.00 False % 3.77/4.00 Clause #4 (by clausification #[3]): ∀ (a_1 : a), Eq (Exists fun Xt => And (And (x Xt) (y Xt)) (Eq (skS.0 0 a_1) (f Xt))) True % 3.77/4.00 Clause #5 (by clausification #[3]): ∀ (a_1 : a), % 3.77/4.00 Eq % 3.77/4.00 (And (Exists fun Xt => And (x Xt) (Eq (skS.0 0 a_1) (f Xt))) % 3.77/4.00 (Exists fun Xt => And (y Xt) (Eq (skS.0 0 a_1) (f Xt)))) % 3.77/4.00 False % 3.77/4.00 Clause #6 (by clausification #[4]): ∀ (a_1 : a) (a_2 : b), % 3.77/4.00 Eq (And (And (x (skS.0 1 a_1 a_2)) (y (skS.0 1 a_1 a_2))) (Eq (skS.0 0 a_1) (f (skS.0 1 a_1 a_2)))) True % 3.77/4.00 Clause #7 (by clausification #[6]): ∀ (a_1 : a) (a_2 : b), Eq (Eq (skS.0 0 a_1) (f (skS.0 1 a_1 a_2))) True % 3.77/4.00 Clause #8 (by clausification #[6]): ∀ (a_1 : a) (a_2 : b), Eq (And (x (skS.0 1 a_1 a_2)) (y (skS.0 1 a_1 a_2))) True % 3.77/4.00 Clause #9 (by clausification #[7]): ∀ (a_1 : a) (a_2 : b), Eq (skS.0 0 a_1) (f (skS.0 1 a_1 a_2)) % 3.77/4.00 Clause #10 (by clausification #[8]): ∀ (a_1 : a) (a_2 : b), Eq (y (skS.0 1 a_1 a_2)) True % 3.77/4.00 Clause #11 (by clausification #[8]): ∀ (a_1 : a) (a_2 : b), Eq (x (skS.0 1 a_1 a_2)) True % 3.77/4.00 Clause #12 (by clausification #[5]): ∀ (a_1 : a), % 3.77/4.00 Or (Eq (Exists fun Xt => And (x Xt) (Eq (skS.0 0 a_1) (f Xt))) False) % 3.77/4.00 (Eq (Exists fun Xt => And (y Xt) (Eq (skS.0 0 a_1) (f Xt))) False) % 3.77/4.00 Clause #13 (by clausification #[12]): ∀ (a_1 : a) (a_2 : b), % 3.77/4.00 Or (Eq (Exists fun Xt => And (y Xt) (Eq (skS.0 0 a_1) (f Xt))) False) % 3.77/4.00 (Eq (And (x a_2) (Eq (skS.0 0 a_1) (f a_2))) False) % 3.77/4.00 Clause #14 (by clausification #[13]): ∀ (a_1 : b) (a_2 : a) (a_3 : b), % 3.77/4.00 Or (Eq (And (x a_1) (Eq (skS.0 0 a_2) (f a_1))) False) (Eq (And (y a_3) (Eq (skS.0 0 a_2) (f a_3))) False) % 3.77/4.00 Clause #15 (by clausification #[14]): ∀ (a_1 : b) (a_2 : a) (a_3 : b), % 3.77/4.00 Or (Eq (And (y a_1) (Eq (skS.0 0 a_2) (f a_1))) False) (Or (Eq (x a_3) False) (Eq (Eq (skS.0 0 a_2) (f a_3)) False)) % 3.77/4.00 Clause #16 (by clausification #[15]): ∀ (a_1 : b) (a_2 : a) (a_3 : b), % 3.77/4.00 Or (Eq (x a_1) False) % 3.77/4.00 (Or (Eq (Eq (skS.0 0 a_2) (f a_1)) False) (Or (Eq (y a_3) False) (Eq (Eq (skS.0 0 a_2) (f a_3)) False))) % 3.77/4.00 Clause #17 (by clausification #[16]): ∀ (a_1 a_2 : b) (a_3 : a), % 3.77/4.00 Or (Eq (x a_1) False) (Or (Eq (y a_2) False) (Or (Eq (Eq (skS.0 0 a_3) (f a_2)) False) (Ne (skS.0 0 a_3) (f a_1)))) % 3.77/4.00 Clause #18 (by clausification #[17]): ∀ (a_1 a_2 : b) (a_3 : a), % 3.77/4.00 Or (Eq (x a_1) False) (Or (Eq (y a_2) False) (Or (Ne (skS.0 0 a_3) (f a_1)) (Ne (skS.0 0 a_3) (f a_2)))) % 3.77/4.00 Clause #19 (by superposition #[18, 11]): ∀ (a_1 : b) (a_2 a_3 : a) (a_4 : b), % 3.77/4.00 Or (Eq (y a_1) False) (Or (Ne (skS.0 0 a_2) (f (skS.0 1 a_3 a_4))) (Or (Ne (skS.0 0 a_2) (f a_1)) (Eq False True))) % 3.77/4.00 Clause #20 (by clausification #[19]): ∀ (a_1 : b) (a_2 a_3 : a) (a_4 : b), % 3.77/4.00 Or (Eq (y a_1) False) (Or (Ne (skS.0 0 a_2) (f (skS.0 1 a_3 a_4))) (Ne (skS.0 0 a_2) (f a_1))) % 3.77/4.00 Clause #21 (by forward demodulation #[20, 9]): ∀ (a_1 : b) (a_2 a_3 : a), Or (Eq (y a_1) False) (Or (Ne (skS.0 0 a_2) (skS.0 0 a_3)) (Ne (skS.0 0 a_2) (f a_1))) % 3.77/4.00 Clause #22 (by superposition #[21, 10]): ∀ (a_1 a_2 a_3 : a) (a_4 : b), % 3.77/4.00 Or (Ne (skS.0 0 a_1) (skS.0 0 a_2)) (Or (Ne (skS.0 0 a_1) (f (skS.0 1 a_3 a_4))) (Eq False True)) % 3.77/4.00 Clause #23 (by clausification #[22]): ∀ (a_1 a_2 a_3 : a) (a_4 : b), Or (Ne (skS.0 0 a_1) (skS.0 0 a_2)) (Ne (skS.0 0 a_1) (f (skS.0 1 a_3 a_4))) % 3.77/4.00 Clause #24 (by forward demodulation #[23, 9]): ∀ (a_1 a_2 a_3 : a), Or (Ne (skS.0 0 a_1) (skS.0 0 a_2)) (Ne (skS.0 0 a_1) (skS.0 0 a_3)) % 3.77/4.00 Clause #25 (by equality resolution #[24]): ∀ (a_1 a_2 : a), Ne (skS.0 0 a_1) (skS.0 0 a_2) % 3.77/4.00 Clause #26 (by equality resolution #[25]): False % 3.77/4.00 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------