%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN922+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n017.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 08:08:15 PM UTC 2025 % Result : Theorem 3.44s 3.64s % Output : Proof 3.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYN922+1 : TPTP v9.2.0. Released v3.1.0. % 0.07/0.13 % Command : duper %s % 0.12/0.34 % Computer : n017.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 15:38:38 EDT 2025 % 0.12/0.34 % CPUTime : % 3.44/3.64 SZS status Theorem for theBenchmark.p % 3.44/3.64 SZS output start Proof for theBenchmark.p % 3.44/3.64 Clause #0 (by assumption #[]): Eq (Not (Iff (∀ (X : Iota), And (p X) (q X)) (And (∀ (X : Iota), p X) (∀ (X : Iota), q X)))) True % 3.44/3.64 Clause #1 (by clausification #[0]): Eq (Iff (∀ (X : Iota), And (p X) (q X)) (And (∀ (X : Iota), p X) (∀ (X : Iota), q X))) False % 3.44/3.64 Clause #2 (by clausification #[1]): Or (Eq (∀ (X : Iota), And (p X) (q X)) False) (Eq (And (∀ (X : Iota), p X) (∀ (X : Iota), q X)) False) % 3.44/3.64 Clause #3 (by clausification #[1]): Or (Eq (∀ (X : Iota), And (p X) (q X)) True) (Eq (And (∀ (X : Iota), p X) (∀ (X : Iota), q X)) True) % 3.44/3.64 Clause #4 (by clausification #[2]): ∀ (a : Iota), % 3.44/3.64 Or (Eq (And (∀ (X : Iota), p X) (∀ (X : Iota), q X)) False) (Eq (Not (And (p (skS.0 0 a)) (q (skS.0 0 a)))) True) % 3.44/3.64 Clause #5 (by clausification #[4]): ∀ (a : Iota), % 3.44/3.64 Or (Eq (Not (And (p (skS.0 0 a)) (q (skS.0 0 a)))) True) % 3.44/3.64 (Or (Eq (∀ (X : Iota), p X) False) (Eq (∀ (X : Iota), q X) False)) % 3.44/3.64 Clause #6 (by clausification #[5]): ∀ (a : Iota), % 3.44/3.64 Or (Eq (∀ (X : Iota), p X) False) (Or (Eq (∀ (X : Iota), q X) False) (Eq (And (p (skS.0 0 a)) (q (skS.0 0 a))) False)) % 3.44/3.64 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), % 3.44/3.64 Or (Eq (∀ (X : Iota), q X) False) % 3.44/3.64 (Or (Eq (And (p (skS.0 0 a)) (q (skS.0 0 a))) False) (Eq (Not (p (skS.0 1 a_1))) True)) % 3.44/3.64 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), % 3.44/3.64 Or (Eq (And (p (skS.0 0 a)) (q (skS.0 0 a))) False) % 3.44/3.64 (Or (Eq (Not (p (skS.0 1 a_1))) True) (Eq (Not (q (skS.0 2 a_2))) True)) % 3.44/3.64 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), % 3.44/3.64 Or (Eq (Not (p (skS.0 1 a))) True) % 3.44/3.64 (Or (Eq (Not (q (skS.0 2 a_1))) True) (Or (Eq (p (skS.0 0 a_2)) False) (Eq (q (skS.0 0 a_2)) False))) % 3.44/3.64 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 3.44/3.64 Or (Eq (Not (q (skS.0 2 a))) True) % 3.44/3.64 (Or (Eq (p (skS.0 0 a_1)) False) (Or (Eq (q (skS.0 0 a_1)) False) (Eq (p (skS.0 1 a_2)) False))) % 3.44/3.64 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), % 3.44/3.64 Or (Eq (p (skS.0 0 a)) False) % 3.44/3.64 (Or (Eq (q (skS.0 0 a)) False) (Or (Eq (p (skS.0 1 a_1)) False) (Eq (q (skS.0 2 a_2)) False))) % 3.44/3.64 Clause #12 (by clausification #[3]): ∀ (a : Iota), Or (Eq (And (∀ (X : Iota), p X) (∀ (X : Iota), q X)) True) (Eq (And (p a) (q a)) True) % 3.44/3.64 Clause #13 (by clausification #[12]): ∀ (a : Iota), Or (Eq (And (p a) (q a)) True) (Eq (∀ (X : Iota), q X) True) % 3.44/3.64 Clause #14 (by clausification #[12]): ∀ (a : Iota), Or (Eq (And (p a) (q a)) True) (Eq (∀ (X : Iota), p X) True) % 3.44/3.64 Clause #15 (by clausification #[13]): ∀ (a : Iota), Or (Eq (∀ (X : Iota), q X) True) (Eq (q a) True) % 3.44/3.64 Clause #17 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (q a) True) (Eq (q a_1) True) % 3.44/3.64 Clause #18 (by equality factoring #[17]): ∀ (a : Iota), Or (Ne True True) (Eq (q a) True) % 3.44/3.64 Clause #19 (by clausification #[18]): ∀ (a : Iota), Or (Eq (q a) True) (Or (Eq True False) (Eq True False)) % 3.44/3.64 Clause #21 (by clausification #[19]): ∀ (a : Iota), Or (Eq (q a) True) (Eq True False) % 3.44/3.64 Clause #22 (by clausification #[21]): ∀ (a : Iota), Eq (q a) True % 3.44/3.64 Clause #23 (by backward demodulation #[22, 11]): ∀ (a a_1 a_2 : Iota), % 3.44/3.64 Or (Eq (p (skS.0 0 a)) False) (Or (Eq True False) (Or (Eq (p (skS.0 1 a_1)) False) (Eq (q (skS.0 2 a_2)) False))) % 3.44/3.64 Clause #26 (by clausification #[14]): ∀ (a : Iota), Or (Eq (∀ (X : Iota), p X) True) (Eq (p a) True) % 3.44/3.64 Clause #28 (by clausification #[26]): ∀ (a a_1 : Iota), Or (Eq (p a) True) (Eq (p a_1) True) % 3.44/3.64 Clause #29 (by equality factoring #[28]): ∀ (a : Iota), Or (Ne True True) (Eq (p a) True) % 3.44/3.64 Clause #30 (by clausification #[29]): ∀ (a : Iota), Or (Eq (p a) True) (Or (Eq True False) (Eq True False)) % 3.44/3.64 Clause #32 (by clausification #[30]): ∀ (a : Iota), Or (Eq (p a) True) (Eq True False) % 3.44/3.64 Clause #33 (by clausification #[32]): ∀ (a : Iota), Eq (p a) True % 3.44/3.64 Clause #34 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Or (Eq (p (skS.0 0 a)) False) (Or (Eq (p (skS.0 1 a_1)) False) (Eq (q (skS.0 2 a_2)) False)) % 3.44/3.64 Clause #35 (by superposition #[34, 33]): ∀ (a a_1 : Iota), Or (Eq (p (skS.0 1 a)) False) (Or (Eq (q (skS.0 2 a_1)) False) (Eq False True)) % 3.44/3.64 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Or (Eq (p (skS.0 1 a)) False) (Eq (q (skS.0 2 a_1)) False) % 3.44/3.64 Clause #37 (by superposition #[36, 33]): ∀ (a : Iota), Or (Eq (q (skS.0 2 a)) False) (Eq False True) % 3.44/3.64 Clause #38 (by clausification #[37]): ∀ (a : Iota), Eq (q (skS.0 2 a)) False % 3.44/3.64 Clause #39 (by superposition #[38, 22]): Eq False True % 3.44/3.64 Clause #40 (by clausification #[39]): False % 3.44/3.64 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------