%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN407+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n004.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 08:07:36 PM UTC 2025 % Result : Theorem 3.32s 3.54s % Output : Proof 3.32s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SYN407+1 : TPTP v9.2.0. Released v2.0.0. % 0.06/0.13 % Command : duper %s % 0.13/0.36 % Computer : n004.cluster.edu % 0.13/0.36 % Model : x86_64 x86_64 % 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.36 % Memory : 8042.1875MB % 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.36 % CPULimit : 300 % 0.13/0.36 % WCLimit : 300 % 0.13/0.36 % DateTime : Thu Oct 2 15:46:08 EDT 2025 % 0.13/0.36 % CPUTime : % 3.32/3.54 SZS status Theorem for theBenchmark.p % 3.32/3.54 SZS output start Proof for theBenchmark.p % 3.32/3.54 Clause #0 (by assumption #[]): Eq (Not ((∀ (X : Iota), f X → Or (g X) (h X)) → Or (∀ (Y : Iota), f Y → g Y) (Exists fun Z => And (f Z) (h Z)))) True % 3.32/3.54 Clause #1 (by clausification #[0]): Eq ((∀ (X : Iota), f X → Or (g X) (h X)) → Or (∀ (Y : Iota), f Y → g Y) (Exists fun Z => And (f Z) (h Z))) False % 3.32/3.54 Clause #2 (by clausification #[1]): Eq (∀ (X : Iota), f X → Or (g X) (h X)) True % 3.32/3.54 Clause #3 (by clausification #[1]): Eq (Or (∀ (Y : Iota), f Y → g Y) (Exists fun Z => And (f Z) (h Z))) False % 3.32/3.54 Clause #4 (by clausification #[2]): ∀ (a : Iota), Eq (f a → Or (g a) (h a)) True % 3.32/3.54 Clause #5 (by clausification #[4]): ∀ (a : Iota), Or (Eq (f a) False) (Eq (Or (g a) (h a)) True) % 3.32/3.54 Clause #6 (by clausification #[5]): ∀ (a : Iota), Or (Eq (f a) False) (Or (Eq (g a) True) (Eq (h a) True)) % 3.32/3.54 Clause #7 (by clausification #[3]): Eq (Exists fun Z => And (f Z) (h Z)) False % 3.32/3.54 Clause #8 (by clausification #[3]): Eq (∀ (Y : Iota), f Y → g Y) False % 3.32/3.54 Clause #9 (by clausification #[7]): ∀ (a : Iota), Eq (And (f a) (h a)) False % 3.32/3.54 Clause #10 (by clausification #[9]): ∀ (a : Iota), Or (Eq (f a) False) (Eq (h a) False) % 3.32/3.54 Clause #11 (by clausification #[8]): ∀ (a : Iota), Eq (Not (f (skS.0 0 a) → g (skS.0 0 a))) True % 3.32/3.54 Clause #12 (by clausification #[11]): ∀ (a : Iota), Eq (f (skS.0 0 a) → g (skS.0 0 a)) False % 3.32/3.54 Clause #13 (by clausification #[12]): ∀ (a : Iota), Eq (f (skS.0 0 a)) True % 3.32/3.54 Clause #14 (by clausification #[12]): ∀ (a : Iota), Eq (g (skS.0 0 a)) False % 3.32/3.54 Clause #15 (by superposition #[13, 6]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (g (skS.0 0 a)) True) (Eq (h (skS.0 0 a)) True)) % 3.32/3.54 Clause #16 (by superposition #[13, 10]): ∀ (a : Iota), Or (Eq True False) (Eq (h (skS.0 0 a)) False) % 3.32/3.54 Clause #17 (by clausification #[16]): ∀ (a : Iota), Eq (h (skS.0 0 a)) False % 3.32/3.54 Clause #18 (by clausification #[15]): ∀ (a : Iota), Or (Eq (g (skS.0 0 a)) True) (Eq (h (skS.0 0 a)) True) % 3.32/3.54 Clause #19 (by forward demodulation #[18, 17]): ∀ (a : Iota), Or (Eq (g (skS.0 0 a)) True) (Eq False True) % 3.32/3.54 Clause #20 (by clausification #[19]): ∀ (a : Iota), Eq (g (skS.0 0 a)) True % 3.32/3.54 Clause #21 (by superposition #[20, 14]): Eq True False % 3.32/3.54 Clause #22 (by clausification #[21]): False % 3.32/3.54 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------