%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN728+1 : TPTP v9.2.0. Released v2.5.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n021.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 08:08:03 PM UTC 2025 % Result : Theorem 5.83s 6.04s % Output : Proof 5.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : SYN728+1 : TPTP v9.2.0. Released v2.5.0. % 0.00/0.11 % Command : duper %s % 0.10/0.31 % Computer : n021.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 15:24:23 EDT 2025 % 0.16/0.31 % CPUTime : % 5.83/6.04 SZS status Theorem for theBenchmark.p % 5.83/6.04 SZS output start Proof for theBenchmark.p % 5.83/6.04 Clause #0 (by assumption #[]): Eq % 5.83/6.04 (Not % 5.83/6.04 (And % 5.83/6.04 (And (∀ (X : Iota), (Exists fun Y => p X Y) → ∀ (Z : Iota), p Z Z) % 5.83/6.04 (∀ (R : Iota), Exists fun S => Or (p R S) (And (m R) (q (f R S))))) % 5.83/6.04 (∀ (W : Iota), q W → Not (m (g W))) → % 5.83/6.04 ∀ (U : Iota), Exists fun V => And (p (g U) V) (p U U))) % 5.83/6.04 True % 5.83/6.04 Clause #1 (by betaEtaReduce #[0]): Eq % 5.83/6.04 (Not % 5.83/6.04 (And % 5.83/6.04 (And (∀ (X : Iota), Exists (p X) → ∀ (Z : Iota), p Z Z) % 5.83/6.04 (∀ (R : Iota), Exists fun S => Or (p R S) (And (m R) (q (f R S))))) % 5.83/6.04 (∀ (W : Iota), q W → Not (m (g W))) → % 5.83/6.04 ∀ (U : Iota), Exists fun V => And (p (g U) V) (p U U))) % 5.83/6.04 True % 5.83/6.04 Clause #2 (by clausification #[1]): Eq % 5.83/6.04 (And % 5.83/6.04 (And (∀ (X : Iota), Exists (p X) → ∀ (Z : Iota), p Z Z) % 5.83/6.04 (∀ (R : Iota), Exists fun S => Or (p R S) (And (m R) (q (f R S))))) % 5.83/6.04 (∀ (W : Iota), q W → Not (m (g W))) → % 5.83/6.04 ∀ (U : Iota), Exists fun V => And (p (g U) V) (p U U)) % 5.83/6.04 False % 5.83/6.04 Clause #3 (by clausification #[2]): Eq % 5.83/6.04 (And % 5.83/6.04 (And (∀ (X : Iota), Exists (p X) → ∀ (Z : Iota), p Z Z) % 5.83/6.04 (∀ (R : Iota), Exists fun S => Or (p R S) (And (m R) (q (f R S))))) % 5.83/6.04 (∀ (W : Iota), q W → Not (m (g W)))) % 5.83/6.04 True % 5.83/6.04 Clause #4 (by clausification #[2]): Eq (∀ (U : Iota), Exists fun V => And (p (g U) V) (p U U)) False % 5.83/6.04 Clause #5 (by clausification #[3]): Eq (∀ (W : Iota), q W → Not (m (g W))) True % 5.83/6.04 Clause #6 (by clausification #[3]): Eq % 5.83/6.04 (And (∀ (X : Iota), Exists (p X) → ∀ (Z : Iota), p Z Z) % 5.83/6.04 (∀ (R : Iota), Exists fun S => Or (p R S) (And (m R) (q (f R S))))) % 5.83/6.04 True % 5.83/6.04 Clause #7 (by clausification #[5]): ∀ (a : Iota), Eq (q a → Not (m (g a))) True % 5.83/6.04 Clause #8 (by clausification #[7]): ∀ (a : Iota), Or (Eq (q a) False) (Eq (Not (m (g a))) True) % 5.83/6.04 Clause #9 (by clausification #[8]): ∀ (a : Iota), Or (Eq (q a) False) (Eq (m (g a)) False) % 5.83/6.04 Clause #10 (by clausification #[4]): ∀ (a : Iota), Eq (Not (Exists fun V => And (p (g (skS.0 0 a)) V) (p (skS.0 0 a) (skS.0 0 a)))) True % 5.83/6.04 Clause #11 (by clausification #[10]): ∀ (a : Iota), Eq (Exists fun V => And (p (g (skS.0 0 a)) V) (p (skS.0 0 a) (skS.0 0 a))) False % 5.83/6.04 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (And (p (g (skS.0 0 a)) a_1) (p (skS.0 0 a) (skS.0 0 a))) False % 5.83/6.04 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Or (Eq (p (g (skS.0 0 a)) a_1) False) (Eq (p (skS.0 0 a) (skS.0 0 a)) False) % 5.83/6.04 Clause #14 (by clausification #[6]): Eq (∀ (R : Iota), Exists fun S => Or (p R S) (And (m R) (q (f R S)))) True % 5.83/6.04 Clause #15 (by clausification #[6]): Eq (∀ (X : Iota), Exists (p X) → ∀ (Z : Iota), p Z Z) True % 5.83/6.04 Clause #16 (by clausification #[14]): ∀ (a : Iota), Eq (Exists fun S => Or (p a S) (And (m a) (q (f a S)))) True % 5.83/6.04 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (Or (p a (skS.0 1 a a_1)) (And (m a) (q (f a (skS.0 1 a a_1))))) True % 5.83/6.04 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (p a (skS.0 1 a a_1)) True) (Eq (And (m a) (q (f a (skS.0 1 a a_1)))) True) % 5.83/6.04 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (p a (skS.0 1 a a_1)) True) (Eq (q (f a (skS.0 1 a a_1))) True) % 5.83/6.04 Clause #20 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (p a (skS.0 1 a a_1)) True) (Eq (m a) True) % 5.83/6.04 Clause #21 (by superposition #[19, 9]): ∀ (a a_1 : Iota), Or (Eq (p a (skS.0 1 a a_1)) True) (Or (Eq True False) (Eq (m (g (f a (skS.0 1 a a_1)))) False)) % 5.83/6.04 Clause #22 (by clausification #[15]): ∀ (a : Iota), Eq (Exists (p a) → ∀ (Z : Iota), p Z Z) True % 5.83/6.04 Clause #23 (by clausification #[22]): ∀ (a : Iota), Or (Eq (Exists (p a)) False) (Eq (∀ (Z : Iota), p Z Z) True) % 5.83/6.04 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (∀ (Z : Iota), p Z Z) True) (Eq (p a a_1) False) % 5.83/6.04 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), Or (Eq (p a a_1) False) (Eq (p a_2 a_2) True) % 5.83/6.04 Clause #27 (by superposition #[20, 25]): ∀ (a a_1 : Iota), Or (Eq (p a a) True) (Or (Eq False True) (Eq (m a_1) True)) % 5.83/6.04 Clause #28 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (p a (skS.0 1 a a_1)) True) (Eq (m (g (f a (skS.0 1 a a_1)))) False) % 5.83/6.06 Clause #29 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq (p a a) True) (Eq (m a_1) True) % 5.83/6.06 Clause #32 (by superposition #[29, 28]): ∀ (a a_1 a_2 : Iota), Or (Eq (p a a) True) (Or (Eq (p a_1 (skS.0 1 a_1 a_2)) True) (Eq True False)) % 5.83/6.06 Clause #34 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Or (Eq (p a a) True) (Eq (p a_1 (skS.0 1 a_1 a_2)) True) % 5.83/6.06 Clause #38 (by superposition #[34, 25]): ∀ (a a_1 : Iota), Or (Eq (p a a) True) (Or (Eq True False) (Eq (p a_1 a_1) True)) % 5.83/6.06 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Or (Eq (p a a) True) (Eq (p a_1 a_1) True) % 5.83/6.06 Clause #40 (by equality factoring #[39]): ∀ (a : Iota), Or (Ne True True) (Eq (p a a) True) % 5.83/6.06 Clause #41 (by clausification #[40]): ∀ (a : Iota), Or (Eq (p a a) True) (Or (Eq True False) (Eq True False)) % 5.83/6.06 Clause #43 (by clausification #[41]): ∀ (a : Iota), Or (Eq (p a a) True) (Eq True False) % 5.83/6.06 Clause #44 (by clausification #[43]): ∀ (a : Iota), Eq (p a a) True % 5.83/6.06 Clause #45 (by superposition #[44, 13]): ∀ (a : Iota), Or (Eq True False) (Eq (p (skS.0 0 a) (skS.0 0 a)) False) % 5.83/6.06 Clause #50 (by clausification #[45]): ∀ (a : Iota), Eq (p (skS.0 0 a) (skS.0 0 a)) False % 5.83/6.06 Clause #51 (by superposition #[50, 44]): Eq False True % 5.83/6.06 Clause #52 (by clausification #[51]): False % 5.83/6.06 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------