%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN083+1 : TPTP v9.2.0. Released v2.0.0. % 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 08:07:09 PM UTC 2025 % Result : Theorem 4.94s 5.11s % Output : Proof 4.94s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SYN083+1 : TPTP v9.2.0. Released v2.0.0. % 0.12/0.13 % Command : duper %s % 0.13/0.34 % Computer : n017.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 15:34:23 EDT 2025 % 0.13/0.34 % CPUTime : % 4.94/5.11 SZS status Theorem for theBenchmark.p % 4.94/5.11 SZS output start Proof for theBenchmark.p % 4.94/5.11 Clause #0 (by assumption #[]): Eq (∀ (X Y Z : Iota), Eq (f X (f Y Z)) (f (f X Y) Z)) True % 4.94/5.11 Clause #1 (by assumption #[]): Eq (Not (∀ (X Y Z W : Iota), Eq (f X (f Y (f Z W))) (f (f (f X Y) Z) W))) True % 4.94/5.11 Clause #2 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), Eq (f a (f Y Z)) (f (f a Y) Z)) True % 4.94/5.11 Clause #3 (by clausification #[2]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), Eq (f a (f a_1 Z)) (f (f a a_1) Z)) True % 4.94/5.11 Clause #4 (by clausification #[3]): ∀ (a a_1 a_2 : Iota), Eq (Eq (f a (f a_1 a_2)) (f (f a a_1) a_2)) True % 4.94/5.11 Clause #5 (by clausification #[4]): ∀ (a a_1 a_2 : Iota), Eq (f a (f a_1 a_2)) (f (f a a_1) a_2) % 4.94/5.11 Clause #31 (by clausification #[1]): Eq (∀ (X Y Z W : Iota), Eq (f X (f Y (f Z W))) (f (f (f X Y) Z) W)) False % 4.94/5.11 Clause #32 (by clausification #[31]): ∀ (a : Iota), Eq (Not (∀ (Y Z W : Iota), Eq (f (skS.0 0 a) (f Y (f Z W))) (f (f (f (skS.0 0 a) Y) Z) W))) True % 4.94/5.11 Clause #33 (by clausification #[32]): ∀ (a : Iota), Eq (∀ (Y Z W : Iota), Eq (f (skS.0 0 a) (f Y (f Z W))) (f (f (f (skS.0 0 a) Y) Z) W)) False % 4.94/5.11 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), % 4.94/5.11 Eq (Not (∀ (Z W : Iota), Eq (f (skS.0 0 a) (f (skS.0 1 a a_1) (f Z W))) (f (f (f (skS.0 0 a) (skS.0 1 a a_1)) Z) W))) % 4.94/5.11 True % 4.94/5.11 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), % 4.94/5.11 Eq (∀ (Z W : Iota), Eq (f (skS.0 0 a) (f (skS.0 1 a a_1) (f Z W))) (f (f (f (skS.0 0 a) (skS.0 1 a a_1)) Z) W)) False % 4.94/5.11 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), % 4.94/5.11 Eq % 4.94/5.11 (Not % 4.94/5.11 (∀ (W : Iota), % 4.94/5.11 Eq (f (skS.0 0 a) (f (skS.0 1 a a_1) (f (skS.0 2 a a_1 a_2) W))) % 4.94/5.11 (f (f (f (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2)) W))) % 4.94/5.11 True % 4.94/5.11 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), % 4.94/5.11 Eq % 4.94/5.11 (∀ (W : Iota), % 4.94/5.11 Eq (f (skS.0 0 a) (f (skS.0 1 a a_1) (f (skS.0 2 a a_1 a_2) W))) % 4.94/5.11 (f (f (f (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2)) W)) % 4.94/5.11 False % 4.94/5.11 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 a_3 : Iota), % 4.94/5.11 Eq % 4.94/5.11 (Not % 4.94/5.11 (Eq (f (skS.0 0 a) (f (skS.0 1 a a_1) (f (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)))) % 4.94/5.11 (f (f (f (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2)) (skS.0 3 a a_1 a_2 a_3)))) % 4.94/5.11 True % 4.94/5.11 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 a_3 : Iota), % 4.94/5.11 Eq % 4.94/5.11 (Eq (f (skS.0 0 a) (f (skS.0 1 a a_1) (f (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)))) % 4.94/5.11 (f (f (f (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2)) (skS.0 3 a a_1 a_2 a_3))) % 4.94/5.11 False % 4.94/5.11 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 a_3 : Iota), % 4.94/5.11 Ne (f (skS.0 0 a) (f (skS.0 1 a a_1) (f (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)))) % 4.94/5.11 (f (f (f (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2)) (skS.0 3 a a_1 a_2 a_3)) % 4.94/5.11 Clause #41 (by forward demodulation #[40, 5]): ∀ (a a_1 a_2 a_3 : Iota), % 4.94/5.11 Ne (f (skS.0 0 a) (f (skS.0 1 a a_1) (f (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)))) % 4.94/5.11 (f (f (skS.0 0 a) (skS.0 1 a a_1)) (f (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) % 4.94/5.11 Clause #42 (by forward demodulation #[41, 5]): ∀ (a a_1 a_2 a_3 : Iota), % 4.94/5.11 Ne (f (skS.0 0 a) (f (skS.0 1 a a_1) (f (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)))) % 4.94/5.11 (f (skS.0 0 a) (f (skS.0 1 a a_1) (f (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)))) % 4.94/5.11 Clause #43 (by eliminate resolved literals #[42]): False % 4.94/5.11 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------