%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN951+1 : TPTP v9.2.0. Released v3.1.0. % 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 08:08:18 PM UTC 2025 % Result : Theorem 3.51s 3.70s % Output : Proof 3.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYN951+1 : TPTP v9.2.0. Released v3.1.0. % 0.07/0.13 % Command : duper %s % 0.12/0.34 % Computer : n004.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Thu Oct 2 15:26:08 EDT 2025 % 0.12/0.34 % CPUTime : % 3.51/3.70 SZS status Theorem for theBenchmark.p % 3.51/3.70 SZS output start Proof for theBenchmark.p % 3.51/3.70 Clause #0 (by assumption #[]): Eq (Not ((Exists fun X => p X) → And (Exists fun X => p X) (a → And (Or b (Not b)) (q → q)))) True % 3.51/3.70 Clause #1 (by betaEtaReduce #[0]): Eq (Not (Exists p → And (Exists p) (a → And (Or b (Not b)) (q → q)))) True % 3.51/3.70 Clause #2 (by clausification #[1]): Eq (Exists p → And (Exists p) (a → And (Or b (Not b)) (q → q))) False % 3.51/3.70 Clause #3 (by clausification #[2]): Eq (Exists p) True % 3.51/3.70 Clause #4 (by clausification #[2]): Eq (And (Exists p) (a → And (Or b (Not b)) (q → q))) False % 3.51/3.70 Clause #5 (by clausification #[3]): ∀ (a : Iota), Eq (p (skS.0 0 a)) True % 3.51/3.70 Clause #6 (by clausification #[4]): Or (Eq (Exists p) False) (Eq (a → And (Or b (Not b)) (q → q)) False) % 3.51/3.70 Clause #7 (by clausification #[6]): ∀ (a_1 : Iota), Or (Eq (a → And (Or b (Not b)) (q → q)) False) (Eq (p a_1) False) % 3.51/3.70 Clause #9 (by clausification #[7]): ∀ (a : Iota), Or (Eq (p a) False) (Eq (And (Or b (Not b)) (q → q)) False) % 3.51/3.70 Clause #13 (by clausification #[9]): ∀ (a : Iota), Or (Eq (p a) False) (Or (Eq (Or b (Not b)) False) (Eq (q → q) False)) % 3.51/3.70 Clause #14 (by clausification #[13]): ∀ (a : Iota), Or (Eq (p a) False) (Or (Eq (q → q) False) (Eq (Not b) False)) % 3.51/3.70 Clause #15 (by clausification #[13]): ∀ (a : Iota), Or (Eq (p a) False) (Or (Eq (q → q) False) (Eq b False)) % 3.51/3.70 Clause #16 (by clausification #[14]): ∀ (a : Iota), Or (Eq (p a) False) (Or (Eq (Not b) False) (Eq q True)) % 3.51/3.70 Clause #17 (by clausification #[14]): ∀ (a : Iota), Or (Eq (p a) False) (Or (Eq (Not b) False) (Eq q False)) % 3.51/3.70 Clause #18 (by clausification #[16]): ∀ (a : Iota), Or (Eq (p a) False) (Or (Eq q True) (Eq b True)) % 3.51/3.70 Clause #19 (by superposition #[18, 5]): Or (Eq q True) (Or (Eq b True) (Eq False True)) % 3.51/3.70 Clause #20 (by clausification #[15]): ∀ (a : Iota), Or (Eq (p a) False) (Or (Eq b False) (Eq q True)) % 3.51/3.70 Clause #21 (by clausification #[15]): ∀ (a : Iota), Or (Eq (p a) False) (Or (Eq b False) (Eq q False)) % 3.51/3.70 Clause #22 (by superposition #[20, 5]): Or (Eq b False) (Or (Eq q True) (Eq False True)) % 3.51/3.70 Clause #23 (by clausification #[22]): Or (Eq b False) (Eq q True) % 3.51/3.70 Clause #24 (by clausification #[19]): Or (Eq q True) (Eq b True) % 3.51/3.70 Clause #25 (by superposition #[24, 23]): Or (Eq q True) (Or (Eq True False) (Eq q True)) % 3.51/3.70 Clause #26 (by clausification #[25]): Or (Eq q True) (Eq q True) % 3.51/3.70 Clause #27 (by eliminate duplicate literals #[26]): Eq q True % 3.51/3.70 Clause #30 (by clausification #[17]): ∀ (a : Iota), Or (Eq (p a) False) (Or (Eq q False) (Eq b True)) % 3.51/3.70 Clause #31 (by forward demodulation #[30, 27]): ∀ (a : Iota), Or (Eq (p a) False) (Or (Eq True False) (Eq b True)) % 3.51/3.70 Clause #32 (by clausification #[31]): ∀ (a : Iota), Or (Eq (p a) False) (Eq b True) % 3.51/3.70 Clause #33 (by superposition #[32, 5]): Or (Eq b True) (Eq False True) % 3.51/3.70 Clause #34 (by clausification #[33]): Eq b True % 3.51/3.70 Clause #35 (by forward demodulation #[21, 34]): ∀ (a : Iota), Or (Eq (p a) False) (Or (Eq True False) (Eq q False)) % 3.51/3.70 Clause #36 (by clausification #[35]): ∀ (a : Iota), Or (Eq (p a) False) (Eq q False) % 3.51/3.70 Clause #37 (by forward demodulation #[36, 27]): ∀ (a : Iota), Or (Eq (p a) False) (Eq True False) % 3.51/3.70 Clause #38 (by clausification #[37]): ∀ (a : Iota), Eq (p a) False % 3.51/3.70 Clause #39 (by superposition #[38, 5]): Eq False True % 3.51/3.70 Clause #40 (by clausification #[39]): False % 3.51/3.70 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------