%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN051^5 : TPTP v9.2.0. Released v4.0.0. % 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 08:07:03 PM UTC 2025 % Result : Theorem 3.56s 3.71s % Output : Proof 3.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SYN051^5 : TPTP v9.2.0. Released v4.0.0. % 0.11/0.14 % Command : duper %s % 0.14/0.35 % Computer : n021.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Thu Oct 2 15:16:23 EDT 2025 % 0.14/0.35 % CPUTime : % 3.56/3.71 SZS status Theorem for theBenchmark.p % 3.56/3.71 SZS output start Proof for theBenchmark.p % 3.56/3.71 Clause #0 (by assumption #[]): Eq (Not (And (Exists fun Xx => p → cF Xx) (Exists fun Xx => cF Xx → p) → Exists fun Xx => And (p → cF Xx) (cF Xx → p))) % 3.56/3.71 True % 3.56/3.71 Clause #1 (by clausification #[0]): Eq (And (Exists fun Xx => p → cF Xx) (Exists fun Xx => cF Xx → p) → Exists fun Xx => And (p → cF Xx) (cF Xx → p)) False % 3.56/3.71 Clause #2 (by clausification #[1]): Eq (And (Exists fun Xx => p → cF Xx) (Exists fun Xx => cF Xx → p)) True % 3.56/3.71 Clause #3 (by clausification #[1]): Eq (Exists fun Xx => And (p → cF Xx) (cF Xx → p)) False % 3.56/3.71 Clause #4 (by clausification #[2]): Eq (Exists fun Xx => cF Xx → p) True % 3.56/3.71 Clause #5 (by clausification #[2]): Eq (Exists fun Xx => p → cF Xx) True % 3.56/3.71 Clause #6 (by clausification #[4]): ∀ (a : Iota), Eq (cF (skS.0 0 a) → p) True % 3.56/3.71 Clause #7 (by clausification #[6]): ∀ (a : Iota), Or (Eq (cF (skS.0 0 a)) False) (Eq p True) % 3.56/3.71 Clause #8 (by clausification #[5]): ∀ (a : Iota), Eq (p → cF (skS.0 1 a)) True % 3.56/3.71 Clause #9 (by clausification #[8]): ∀ (a : Iota), Or (Eq p False) (Eq (cF (skS.0 1 a)) True) % 3.56/3.71 Clause #10 (by clausification #[3]): ∀ (a : Iota), Eq (And (p → cF a) (cF a → p)) False % 3.56/3.71 Clause #11 (by clausification #[10]): ∀ (a : Iota), Or (Eq (p → cF a) False) (Eq (cF a → p) False) % 3.56/3.71 Clause #12 (by clausification #[11]): ∀ (a : Iota), Or (Eq (cF a → p) False) (Eq p True) % 3.56/3.71 Clause #13 (by clausification #[11]): ∀ (a : Iota), Or (Eq (cF a → p) False) (Eq (cF a) False) % 3.56/3.71 Clause #14 (by clausification #[12]): ∀ (a : Iota), Or (Eq p True) (Eq (cF a) True) % 3.56/3.71 Clause #16 (by superposition #[14, 7]): Or (Eq p True) (Or (Eq True False) (Eq p True)) % 3.56/3.71 Clause #18 (by clausification #[13]): ∀ (a : Iota), Or (Eq (cF a) False) (Eq p False) % 3.56/3.71 Clause #19 (by clausification #[16]): Or (Eq p True) (Eq p True) % 3.56/3.71 Clause #20 (by eliminate duplicate literals #[19]): Eq p True % 3.56/3.71 Clause #22 (by backward demodulation #[20, 9]): ∀ (a : Iota), Or (Eq True False) (Eq (cF (skS.0 1 a)) True) % 3.56/3.71 Clause #24 (by forward demodulation #[18, 20]): ∀ (a : Iota), Or (Eq (cF a) False) (Eq True False) % 3.56/3.71 Clause #25 (by clausification #[24]): ∀ (a : Iota), Eq (cF a) False % 3.56/3.71 Clause #26 (by clausification #[22]): ∀ (a : Iota), Eq (cF (skS.0 1 a)) True % 3.56/3.71 Clause #27 (by superposition #[26, 25]): Eq True False % 3.56/3.71 Clause #28 (by clausification #[27]): False % 3.56/3.71 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------