%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN411+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n031.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 08:07:37 PM UTC 2025 % Result : Theorem 3.45s 3.66s % Output : Proof 3.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : SYN411+1 : TPTP v9.2.0. Released v2.0.0. % 0.08/0.15 % Command : duper %s % 0.15/0.36 % Computer : n031.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 300 % 0.15/0.36 % DateTime : Thu Oct 2 15:22:08 EDT 2025 % 0.15/0.36 % CPUTime : % 3.45/3.66 SZS status Theorem for theBenchmark.p % 3.45/3.66 SZS output start Proof for theBenchmark.p % 3.45/3.66 Clause #0 (by assumption #[]): Eq (Not (Iff (∀ (X Y Z : Iota), f X Y Z) (Not (Exists fun U => Exists fun V => Exists fun W => Not (f U V W))))) True % 3.45/3.66 Clause #1 (by clausification #[0]): Eq (Iff (∀ (X Y Z : Iota), f X Y Z) (Not (Exists fun U => Exists fun V => Exists fun W => Not (f U V W)))) False % 3.45/3.66 Clause #2 (by clausification #[1]): Or (Eq (∀ (X Y Z : Iota), f X Y Z) False) % 3.45/3.66 (Eq (Not (Exists fun U => Exists fun V => Exists fun W => Not (f U V W))) False) % 3.45/3.66 Clause #3 (by clausification #[1]): Or (Eq (∀ (X Y Z : Iota), f X Y Z) True) (Eq (Not (Exists fun U => Exists fun V => Exists fun W => Not (f U V W))) True) % 3.45/3.66 Clause #4 (by clausification #[2]): ∀ (a : Iota), % 3.45/3.66 Or (Eq (Not (Exists fun U => Exists fun V => Exists fun W => Not (f U V W))) False) % 3.45/3.66 (Eq (Not (∀ (Y Z : Iota), f (skS.0 0 a) Y Z)) True) % 3.45/3.66 Clause #5 (by clausification #[4]): ∀ (a : Iota), % 3.45/3.66 Or (Eq (Not (∀ (Y Z : Iota), f (skS.0 0 a) Y Z)) True) % 3.45/3.66 (Eq (Exists fun U => Exists fun V => Exists fun W => Not (f U V W)) True) % 3.45/3.66 Clause #6 (by clausification #[5]): ∀ (a : Iota), % 3.45/3.66 Or (Eq (Exists fun U => Exists fun V => Exists fun W => Not (f U V W)) True) % 3.45/3.66 (Eq (∀ (Y Z : Iota), f (skS.0 0 a) Y Z) False) % 3.45/3.66 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), % 3.45/3.66 Or (Eq (∀ (Y Z : Iota), f (skS.0 0 a) Y Z) False) % 3.45/3.66 (Eq (Exists fun V => Exists fun W => Not (f (skS.0 1 a_1) V W)) True) % 3.45/3.66 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), % 3.45/3.66 Or (Eq (Exists fun V => Exists fun W => Not (f (skS.0 1 a) V W)) True) % 3.45/3.66 (Eq (Not (∀ (Z : Iota), f (skS.0 0 a_1) (skS.0 2 a_1 a_2) Z)) True) % 3.45/3.66 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 a_3 : Iota), % 3.45/3.66 Or (Eq (Not (∀ (Z : Iota), f (skS.0 0 a) (skS.0 2 a a_1) Z)) True) % 3.45/3.66 (Eq (Exists fun W => Not (f (skS.0 1 a_2) (skS.0 3 a_2 a_3) W)) True) % 3.45/3.66 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 a_3 : Iota), % 3.45/3.66 Or (Eq (Exists fun W => Not (f (skS.0 1 a) (skS.0 3 a a_1) W)) True) % 3.45/3.66 (Eq (∀ (Z : Iota), f (skS.0 0 a_2) (skS.0 2 a_2 a_3) Z) False) % 3.45/3.66 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 3.45/3.66 Or (Eq (∀ (Z : Iota), f (skS.0 0 a) (skS.0 2 a a_1) Z) False) % 3.45/3.66 (Eq (Not (f (skS.0 1 a_2) (skS.0 3 a_2 a_3) (skS.0 4 a_2 a_3 a_4))) True) % 3.45/3.66 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 3.45/3.66 Or (Eq (Not (f (skS.0 1 a) (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) True) % 3.45/3.66 (Eq (Not (f (skS.0 0 a_3) (skS.0 2 a_3 a_4) (skS.0 5 a_3 a_4 a_5))) True) % 3.45/3.66 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 3.45/3.66 Or (Eq (Not (f (skS.0 0 a) (skS.0 2 a a_1) (skS.0 5 a a_1 a_2))) True) % 3.45/3.66 (Eq (f (skS.0 1 a_3) (skS.0 3 a_3 a_4) (skS.0 4 a_3 a_4 a_5)) False) % 3.45/3.66 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 3.45/3.66 Or (Eq (f (skS.0 1 a) (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) False) % 3.45/3.66 (Eq (f (skS.0 0 a_3) (skS.0 2 a_3 a_4) (skS.0 5 a_3 a_4 a_5)) False) % 3.45/3.66 Clause #15 (by clausification #[3]): ∀ (a : Iota), % 3.45/3.66 Or (Eq (Not (Exists fun U => Exists fun V => Exists fun W => Not (f U V W))) True) (Eq (∀ (Y Z : Iota), f a Y Z) True) % 3.45/3.66 Clause #16 (by clausification #[15]): ∀ (a : Iota), % 3.45/3.66 Or (Eq (∀ (Y Z : Iota), f a Y Z) True) (Eq (Exists fun U => Exists fun V => Exists fun W => Not (f U V W)) False) % 3.45/3.66 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), % 3.45/3.66 Or (Eq (Exists fun U => Exists fun V => Exists fun W => Not (f U V W)) False) (Eq (∀ (Z : Iota), f a a_1 Z) True) % 3.45/3.66 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), % 3.45/3.66 Or (Eq (∀ (Z : Iota), f a a_1 Z) True) (Eq (Exists fun V => Exists fun W => Not (f a_2 V W)) False) % 3.45/3.66 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (Exists fun V => Exists fun W => Not (f a V W)) False) (Eq (f a_1 a_2 a_3) True) % 3.45/3.66 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq (f a a_1 a_2) True) (Eq (Exists fun W => Not (f a_3 a_4 W)) False) % 3.45/3.66 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), Or (Eq (f a a_1 a_2) True) (Eq (Not (f a_3 a_4 a_5)) False) % 3.45/3.66 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), Or (Eq (f a a_1 a_2) True) (Eq (f a_3 a_4 a_5) True) % 3.45/3.67 Clause #24 (by equality factoring #[22]): ∀ (a a_1 a_2 : Iota), Or (Ne True True) (Eq (f a a_1 a_2) True) % 3.45/3.67 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), Or (Eq (f a a_1 a_2) True) (Or (Eq True False) (Eq True False)) % 3.45/3.67 Clause #27 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), Or (Eq (f a a_1 a_2) True) (Eq True False) % 3.45/3.67 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), Eq (f a a_1 a_2) True % 3.45/3.67 Clause #29 (by superposition #[28, 14]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (f (skS.0 0 a) (skS.0 2 a a_1) (skS.0 5 a a_1 a_2)) False) % 3.45/3.67 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Eq (f (skS.0 0 a) (skS.0 2 a a_1) (skS.0 5 a a_1 a_2)) False % 3.45/3.67 Clause #31 (by superposition #[30, 28]): Eq False True % 3.45/3.67 Clause #33 (by clausification #[31]): False % 3.45/3.67 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------