%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN726+1 : TPTP v9.2.0. Released v2.5.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n008.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 08:08:02 PM UTC 2025 % Result : Theorem 7.84s 8.06s % Output : Proof 7.94s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SYN726+1 : TPTP v9.2.0. Released v2.5.0. % 0.12/0.13 % Command : duper %s % 0.13/0.34 % Computer : n008.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 15:46:38 EDT 2025 % 0.13/0.34 % CPUTime : % 7.84/8.06 SZS status Theorem for theBenchmark.p % 7.84/8.06 SZS output start Proof for theBenchmark.p % 7.84/8.06 Clause #0 (by assumption #[]): Eq % 7.84/8.06 (Not % 7.84/8.06 (Or % 7.84/8.06 (And % 7.84/8.06 (And (And (∀ (X Y Z : Iota), And (p X Y) (p Y Z) → p X Z) (∀ (X Y Z : Iota), And (q X Y) (q Y Z) → q X Z)) % 7.84/8.06 (∀ (X Y : Iota), q X Y → q Y X)) % 7.84/8.06 (∀ (X Y : Iota), Or (p X Y) (q X Y)) → % 7.84/8.06 ∀ (X Y : Iota), p X Y) % 7.84/8.06 (∀ (X Y : Iota), q X Y))) % 7.84/8.06 True % 7.84/8.06 Clause #1 (by clausification #[0]): Eq % 7.84/8.06 (Or % 7.84/8.06 (And % 7.84/8.06 (And (And (∀ (X Y Z : Iota), And (p X Y) (p Y Z) → p X Z) (∀ (X Y Z : Iota), And (q X Y) (q Y Z) → q X Z)) % 7.84/8.06 (∀ (X Y : Iota), q X Y → q Y X)) % 7.84/8.06 (∀ (X Y : Iota), Or (p X Y) (q X Y)) → % 7.84/8.06 ∀ (X Y : Iota), p X Y) % 7.84/8.06 (∀ (X Y : Iota), q X Y)) % 7.84/8.06 False % 7.84/8.06 Clause #2 (by clausification #[1]): Eq (∀ (X Y : Iota), q X Y) False % 7.84/8.06 Clause #3 (by clausification #[1]): Eq % 7.84/8.06 (And % 7.84/8.06 (And (And (∀ (X Y Z : Iota), And (p X Y) (p Y Z) → p X Z) (∀ (X Y Z : Iota), And (q X Y) (q Y Z) → q X Z)) % 7.84/8.06 (∀ (X Y : Iota), q X Y → q Y X)) % 7.84/8.06 (∀ (X Y : Iota), Or (p X Y) (q X Y)) → % 7.84/8.06 ∀ (X Y : Iota), p X Y) % 7.84/8.06 False % 7.84/8.06 Clause #4 (by clausification #[2]): ∀ (a : Iota), Eq (Not (∀ (Y : Iota), q (skS.0 0 a) Y)) True % 7.84/8.06 Clause #5 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (Y : Iota), q (skS.0 0 a) Y) False % 7.84/8.06 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), Eq (Not (q (skS.0 0 a) (skS.0 1 a a_1))) True % 7.84/8.06 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (q (skS.0 0 a) (skS.0 1 a a_1)) False % 7.84/8.06 Clause #8 (by clausification #[3]): Eq % 7.84/8.06 (And % 7.84/8.06 (And (And (∀ (X Y Z : Iota), And (p X Y) (p Y Z) → p X Z) (∀ (X Y Z : Iota), And (q X Y) (q Y Z) → q X Z)) % 7.84/8.06 (∀ (X Y : Iota), q X Y → q Y X)) % 7.84/8.06 (∀ (X Y : Iota), Or (p X Y) (q X Y))) % 7.84/8.06 True % 7.84/8.06 Clause #9 (by clausification #[3]): Eq (∀ (X Y : Iota), p X Y) False % 7.84/8.06 Clause #10 (by clausification #[8]): Eq (∀ (X Y : Iota), Or (p X Y) (q X Y)) True % 7.84/8.06 Clause #11 (by clausification #[8]): Eq % 7.84/8.06 (And (And (∀ (X Y Z : Iota), And (p X Y) (p Y Z) → p X Z) (∀ (X Y Z : Iota), And (q X Y) (q Y Z) → q X Z)) % 7.84/8.06 (∀ (X Y : Iota), q X Y → q Y X)) % 7.84/8.06 True % 7.84/8.06 Clause #12 (by clausification #[10]): ∀ (a : Iota), Eq (∀ (Y : Iota), Or (p a Y) (q a Y)) True % 7.84/8.06 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Eq (Or (p a a_1) (q a a_1)) True % 7.84/8.06 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (p a a_1) True) (Eq (q a a_1) True) % 7.84/8.06 Clause #15 (by clausification #[9]): ∀ (a : Iota), Eq (Not (∀ (Y : Iota), p (skS.0 2 a) Y)) True % 7.84/8.06 Clause #16 (by clausification #[15]): ∀ (a : Iota), Eq (∀ (Y : Iota), p (skS.0 2 a) Y) False % 7.84/8.06 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (Not (p (skS.0 2 a) (skS.0 3 a a_1))) True % 7.84/8.06 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (p (skS.0 2 a) (skS.0 3 a a_1)) False % 7.84/8.06 Clause #19 (by superposition #[18, 14]): ∀ (a a_1 : Iota), Or (Eq False True) (Eq (q (skS.0 2 a) (skS.0 3 a a_1)) True) % 7.84/8.06 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (q (skS.0 2 a) (skS.0 3 a a_1)) True % 7.84/8.06 Clause #21 (by clausification #[11]): Eq (∀ (X Y : Iota), q X Y → q Y X) True % 7.84/8.06 Clause #22 (by clausification #[11]): Eq (And (∀ (X Y Z : Iota), And (p X Y) (p Y Z) → p X Z) (∀ (X Y Z : Iota), And (q X Y) (q Y Z) → q X Z)) True % 7.84/8.06 Clause #23 (by clausification #[21]): ∀ (a : Iota), Eq (∀ (Y : Iota), q a Y → q Y a) True % 7.84/8.06 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (q a a_1 → q a_1 a) True % 7.84/8.06 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (q a a_1) False) (Eq (q a_1 a) True) % 7.84/8.06 Clause #27 (by clausification #[22]): Eq (∀ (X Y Z : Iota), And (q X Y) (q Y Z) → q X Z) True % 7.84/8.06 Clause #28 (by clausification #[22]): Eq (∀ (X Y Z : Iota), And (p X Y) (p Y Z) → p X Z) True % 7.84/8.06 Clause #29 (by clausification #[27]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), And (q a Y) (q Y Z) → q a Z) True % 7.84/8.06 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), And (q a a_1) (q a_1 Z) → q a Z) True % 7.84/8.06 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), Eq (And (q a a_1) (q a_1 a_2) → q a a_2) True % 7.94/8.10 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (q a a_1) (q a_1 a_2)) False) (Eq (q a a_2) True) % 7.94/8.10 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Or (Eq (q a a_1) True) (Or (Eq (q a a_2) False) (Eq (q a_2 a_1) False)) % 7.94/8.10 Clause #34 (by superposition #[33, 20]): ∀ (a a_1 a_2 : Iota), Or (Eq (q (skS.0 2 a) a_1) True) (Or (Eq (q (skS.0 3 a a_2) a_1) False) (Eq False True)) % 7.94/8.10 Clause #35 (by clausification #[28]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), And (p a Y) (p Y Z) → p a Z) True % 7.94/8.10 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), And (p a a_1) (p a_1 Z) → p a Z) True % 7.94/8.10 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Eq (And (p a a_1) (p a_1 a_2) → p a a_2) True % 7.94/8.10 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (p a a_1) (p a_1 a_2)) False) (Eq (p a a_2) True) % 7.94/8.10 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), Or (Eq (p a a_1) True) (Or (Eq (p a a_2) False) (Eq (p a_2 a_1) False)) % 7.94/8.10 Clause #40 (by superposition #[39, 14]): ∀ (a a_1 a_2 : Iota), Or (Eq (p a a_1) True) (Or (Eq (p a_2 a_1) False) (Or (Eq False True) (Eq (q a a_2) True))) % 7.94/8.10 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), Or (Eq (p a a_1) True) (Or (Eq (p a_2 a_1) False) (Eq (q a a_2) True)) % 7.94/8.10 Clause #42 (by superposition #[41, 14]): ∀ (a a_1 a_2 : Iota), Or (Eq (p a a_1) True) (Or (Eq (q a a_2) True) (Or (Eq False True) (Eq (q a_2 a_1) True))) % 7.94/8.10 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), Or (Eq (p a a_1) True) (Or (Eq (q a a_2) True) (Eq (q a_2 a_1) True)) % 7.94/8.10 Clause #51 (by superposition #[43, 25]): ∀ (a a_1 a_2 : Iota), Or (Eq (p a a_1) True) (Or (Eq (q a a_2) True) (Or (Eq True False) (Eq (q a_1 a_2) True))) % 7.94/8.10 Clause #53 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), Or (Eq (p a a_1) True) (Or (Eq (q a a_2) True) (Eq (q a_1 a_2) True)) % 7.94/8.10 Clause #58 (by superposition #[53, 25]): ∀ (a a_1 a_2 : Iota), Or (Eq (p a a_1) True) (Or (Eq (q a_1 a_2) True) (Or (Eq True False) (Eq (q a_2 a) True))) % 7.94/8.10 Clause #81 (by clausification #[58]): ∀ (a a_1 a_2 : Iota), Or (Eq (p a a_1) True) (Or (Eq (q a_1 a_2) True) (Eq (q a_2 a) True)) % 7.94/8.10 Clause #82 (by superposition #[81, 18]): ∀ (a a_1 a_2 : Iota), Or (Eq (q (skS.0 3 a a_1) a_2) True) (Or (Eq (q a_2 (skS.0 2 a)) True) (Eq True False)) % 7.94/8.10 Clause #91 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), Or (Eq (q (skS.0 2 a) a_1) True) (Eq (q (skS.0 3 a a_2) a_1) False) % 7.94/8.10 Clause #641 (by clausification #[82]): ∀ (a a_1 a_2 : Iota), Or (Eq (q (skS.0 3 a a_1) a_2) True) (Eq (q a_2 (skS.0 2 a)) True) % 7.94/8.10 Clause #642 (by superposition #[641, 91]): ∀ (a a_1 : Iota), Or (Eq (q a (skS.0 2 a_1)) True) (Or (Eq (q (skS.0 2 a_1) a) True) (Eq True False)) % 7.94/8.10 Clause #1777 (by clausification #[642]): ∀ (a a_1 : Iota), Or (Eq (q a (skS.0 2 a_1)) True) (Eq (q (skS.0 2 a_1) a) True) % 7.94/8.10 Clause #1780 (by superposition #[1777, 25]): ∀ (a a_1 : Iota), Or (Eq (q (skS.0 2 a) a_1) True) (Or (Eq True False) (Eq (q (skS.0 2 a) a_1) True)) % 7.94/8.10 Clause #1820 (by clausification #[1780]): ∀ (a a_1 : Iota), Or (Eq (q (skS.0 2 a) a_1) True) (Eq (q (skS.0 2 a) a_1) True) % 7.94/8.10 Clause #1821 (by eliminate duplicate literals #[1820]): ∀ (a a_1 : Iota), Eq (q (skS.0 2 a) a_1) True % 7.94/8.10 Clause #1826 (by superposition #[1821, 25]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (q a (skS.0 2 a_1)) True) % 7.94/8.10 Clause #1838 (by clausification #[1826]): ∀ (a a_1 : Iota), Eq (q a (skS.0 2 a_1)) True % 7.94/8.10 Clause #1841 (by superposition #[1838, 33]): ∀ (a a_1 a_2 : Iota), Or (Eq (q a a_1) True) (Or (Eq True False) (Eq (q (skS.0 2 a_2) a_1) False)) % 7.94/8.10 Clause #1879 (by clausification #[1841]): ∀ (a a_1 a_2 : Iota), Or (Eq (q a a_1) True) (Eq (q (skS.0 2 a_2) a_1) False) % 7.94/8.10 Clause #1884 (by superposition #[1879, 1821]): ∀ (a a_1 : Iota), Or (Eq (q a a_1) True) (Eq False True) % 7.94/8.10 Clause #1930 (by clausification #[1884]): ∀ (a a_1 : Iota), Eq (q a a_1) True % 7.94/8.10 Clause #1940 (by superposition #[1930, 7]): Eq True False % 7.94/8.10 Clause #1941 (by clausification #[1940]): False % 7.94/8.10 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------