%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN729+1 : TPTP v9.2.0. Released v2.5.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n026.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 178.92s 179.21s % Output : Proof 178.92s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SYN729+1 : TPTP v9.2.0. Released v2.5.0. % 0.08/0.13 % Command : duper %s % 0.13/0.35 % Computer : n026.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 15:04:53 EDT 2025 % 0.13/0.35 % CPUTime : % 178.92/179.21 SZS status Theorem for theBenchmark.p % 178.92/179.21 SZS output start Proof for theBenchmark.p % 178.92/179.21 Clause #0 (by assumption #[]): Eq % 178.92/179.21 (Not % 178.92/179.21 (And (∀ (X : Iota), Exists fun Y => p X → And (l X (g (h Y))) (p Y)) (∀ (W : Iota), p W → And (p (g W)) (p (h W))) → % 178.92/179.21 ∀ (X : Iota), p X → Exists fun Y => And (l X Y) (p Y))) % 178.92/179.21 True % 178.92/179.21 Clause #1 (by clausification #[0]): Eq % 178.92/179.21 (And (∀ (X : Iota), Exists fun Y => p X → And (l X (g (h Y))) (p Y)) (∀ (W : Iota), p W → And (p (g W)) (p (h W))) → % 178.92/179.21 ∀ (X : Iota), p X → Exists fun Y => And (l X Y) (p Y)) % 178.92/179.21 False % 178.92/179.21 Clause #2 (by clausification #[1]): Eq (And (∀ (X : Iota), Exists fun Y => p X → And (l X (g (h Y))) (p Y)) (∀ (W : Iota), p W → And (p (g W)) (p (h W)))) % 178.92/179.21 True % 178.92/179.21 Clause #3 (by clausification #[1]): Eq (∀ (X : Iota), p X → Exists fun Y => And (l X Y) (p Y)) False % 178.92/179.21 Clause #4 (by clausification #[2]): Eq (∀ (W : Iota), p W → And (p (g W)) (p (h W))) True % 178.92/179.21 Clause #5 (by clausification #[2]): Eq (∀ (X : Iota), Exists fun Y => p X → And (l X (g (h Y))) (p Y)) True % 178.92/179.21 Clause #6 (by clausification #[4]): ∀ (a : Iota), Eq (p a → And (p (g a)) (p (h a))) True % 178.92/179.21 Clause #7 (by clausification #[6]): ∀ (a : Iota), Or (Eq (p a) False) (Eq (And (p (g a)) (p (h a))) True) % 178.92/179.21 Clause #8 (by clausification #[7]): ∀ (a : Iota), Or (Eq (p a) False) (Eq (p (h a)) True) % 178.92/179.21 Clause #9 (by clausification #[7]): ∀ (a : Iota), Or (Eq (p a) False) (Eq (p (g a)) True) % 178.92/179.21 Clause #10 (by clausification #[3]): ∀ (a : Iota), Eq (Not (p (skS.0 0 a) → Exists fun Y => And (l (skS.0 0 a) Y) (p Y))) True % 178.92/179.21 Clause #11 (by clausification #[10]): ∀ (a : Iota), Eq (p (skS.0 0 a) → Exists fun Y => And (l (skS.0 0 a) Y) (p Y)) False % 178.92/179.21 Clause #12 (by clausification #[11]): ∀ (a : Iota), Eq (p (skS.0 0 a)) True % 178.92/179.21 Clause #13 (by clausification #[11]): ∀ (a : Iota), Eq (Exists fun Y => And (l (skS.0 0 a) Y) (p Y)) False % 178.92/179.21 Clause #22 (by clausification #[5]): ∀ (a : Iota), Eq (Exists fun Y => p a → And (l a (g (h Y))) (p Y)) True % 178.92/179.21 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Eq (p a → And (l a (g (h (skS.0 1 a a_1)))) (p (skS.0 1 a a_1))) True % 178.92/179.21 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (p a) False) (Eq (And (l a (g (h (skS.0 1 a a_1)))) (p (skS.0 1 a a_1))) True) % 178.92/179.21 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (p a) False) (Eq (p (skS.0 1 a a_1)) True) % 178.92/179.21 Clause #26 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (p a) False) (Eq (l a (g (h (skS.0 1 a a_1)))) True) % 178.92/179.21 Clause #27 (by superposition #[25, 12]): ∀ (a a_1 : Iota), Or (Eq (p (skS.0 1 (skS.0 0 a) a_1)) True) (Eq False True) % 178.92/179.21 Clause #50 (by clausification #[13]): ∀ (a a_1 : Iota), Eq (And (l (skS.0 0 a) a_1) (p a_1)) False % 178.92/179.21 Clause #51 (by clausification #[50]): ∀ (a a_1 : Iota), Or (Eq (l (skS.0 0 a) a_1) False) (Eq (p a_1) False) % 178.92/179.21 Clause #72 (by superposition #[26, 12]): ∀ (a a_1 : Iota), Or (Eq (l (skS.0 0 a) (g (h (skS.0 1 (skS.0 0 a) a_1)))) True) (Eq False True) % 178.92/179.21 Clause #110 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (p (skS.0 1 (skS.0 0 a) a_1)) True % 178.92/179.21 Clause #111 (by superposition #[110, 8]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (p (h (skS.0 1 (skS.0 0 a) a_1))) True) % 178.92/179.21 Clause #500 (by clausification #[72]): ∀ (a a_1 : Iota), Eq (l (skS.0 0 a) (g (h (skS.0 1 (skS.0 0 a) a_1)))) True % 178.92/179.21 Clause #501 (by superposition #[500, 51]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (p (g (h (skS.0 1 (skS.0 0 a) a_1)))) False) % 178.92/179.21 Clause #1119 (by clausification #[111]): ∀ (a a_1 : Iota), Eq (p (h (skS.0 1 (skS.0 0 a) a_1))) True % 178.92/179.21 Clause #1121 (by superposition #[1119, 9]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (p (g (h (skS.0 1 (skS.0 0 a) a_1)))) True) % 178.92/179.21 Clause #4262 (by clausification #[501]): ∀ (a a_1 : Iota), Eq (p (g (h (skS.0 1 (skS.0 0 a) a_1)))) False % 178.92/179.21 Clause #4674 (by clausification #[1121]): ∀ (a a_1 : Iota), Eq (p (g (h (skS.0 1 (skS.0 0 a) a_1)))) True % 178.92/179.21 Clause #4675 (by superposition #[4674, 4262]): Eq True False % 178.92/179.21 Clause #4685 (by clausification #[4675]): False % 178.92/179.21 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------