%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN051+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n005.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 08:07:03 PM UTC 2025 % Result : Theorem 3.45s 3.68s % Output : Proof 3.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SYN051+1 : TPTP v9.2.0. Released v2.0.0. % 0.06/0.13 % Command : duper %s % 0.13/0.34 % Computer : n005.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Oct 2 15:26:38 EDT 2025 % 0.13/0.34 % CPUTime : % 3.45/3.68 SZS status Theorem for theBenchmark.p % 3.45/3.68 SZS output start Proof for theBenchmark.p % 3.45/3.68 Clause #0 (by assumption #[]): Eq (Exists fun X => p → big_f X) True % 3.45/3.68 Clause #1 (by assumption #[]): Eq (Exists fun X => big_f X → p) True % 3.45/3.68 Clause #2 (by assumption #[]): Eq (Not (Exists fun X => Iff p (big_f X))) True % 3.45/3.68 Clause #3 (by clausification #[1]): ∀ (a : Iota), Eq (big_f (skS.0 0 a) → p) True % 3.45/3.68 Clause #4 (by clausification #[3]): ∀ (a : Iota), Or (Eq (big_f (skS.0 0 a)) False) (Eq p True) % 3.45/3.68 Clause #5 (by clausification #[0]): ∀ (a : Iota), Eq (p → big_f (skS.0 1 a)) True % 3.45/3.68 Clause #6 (by clausification #[5]): ∀ (a : Iota), Or (Eq p False) (Eq (big_f (skS.0 1 a)) True) % 3.45/3.68 Clause #7 (by clausification #[2]): Eq (Exists fun X => Iff p (big_f X)) False % 3.45/3.68 Clause #8 (by clausification #[7]): ∀ (a : Iota), Eq (Iff p (big_f a)) False % 3.45/3.68 Clause #9 (by clausification #[8]): ∀ (a : Iota), Or (Eq p False) (Eq (big_f a) False) % 3.45/3.68 Clause #10 (by clausification #[8]): ∀ (a : Iota), Or (Eq p True) (Eq (big_f a) True) % 3.45/3.68 Clause #11 (by superposition #[10, 4]): Or (Eq p True) (Or (Eq True False) (Eq p True)) % 3.45/3.68 Clause #12 (by clausification #[11]): Or (Eq p True) (Eq p True) % 3.45/3.68 Clause #13 (by eliminate duplicate literals #[12]): Eq p True % 3.45/3.68 Clause #15 (by backward demodulation #[13, 6]): ∀ (a : Iota), Or (Eq True False) (Eq (big_f (skS.0 1 a)) True) % 3.45/3.68 Clause #16 (by backward demodulation #[13, 9]): ∀ (a : Iota), Or (Eq True False) (Eq (big_f a) False) % 3.45/3.68 Clause #18 (by clausification #[16]): ∀ (a : Iota), Eq (big_f a) False % 3.45/3.68 Clause #19 (by clausification #[15]): ∀ (a : Iota), Eq (big_f (skS.0 1 a)) True % 3.45/3.68 Clause #20 (by superposition #[19, 18]): Eq True False % 3.45/3.68 Clause #21 (by clausification #[20]): False % 3.45/3.68 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------