%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV091^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n022.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 08:02:50 PM UTC 2025 % Result : Theorem 8.20s 8.38s % Output : Proof 8.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEV091^5 : TPTP v9.2.0. Released v4.0.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n022.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 : Fri Oct 3 01:15:42 EDT 2025 % 0.13/0.34 % CPUTime : % 8.20/8.38 SZS status Theorem for theBenchmark.p % 8.20/8.38 SZS output start Proof for theBenchmark.p % 8.20/8.38 Clause #0 (by assumption #[]): Eq % 8.20/8.38 (Not % 8.20/8.38 (And % 8.20/8.38 (And % 8.20/8.38 (And (∀ (Xx Xy Xz : Iota), And (cP Xx Xy) (cP Xy Xz) → cP Xx Xz) % 8.20/8.38 (∀ (Xx Xy Xz : Iota), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz)) % 8.20/8.38 (∀ (Xx Xy : Iota), cQ Xx Xy → cQ Xy Xx)) % 8.20/8.38 (∀ (Xx Xy : Iota), Or (cP Xx Xy) (cQ Xx Xy)) → % 8.20/8.38 Or (∀ (Xx Xy : Iota), cP Xx Xy) (∀ (Xx Xy : Iota), cQ Xx Xy))) % 8.20/8.38 True % 8.20/8.38 Clause #1 (by clausification #[0]): Eq % 8.20/8.38 (And % 8.20/8.38 (And % 8.20/8.38 (And (∀ (Xx Xy Xz : Iota), And (cP Xx Xy) (cP Xy Xz) → cP Xx Xz) % 8.20/8.38 (∀ (Xx Xy Xz : Iota), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz)) % 8.20/8.38 (∀ (Xx Xy : Iota), cQ Xx Xy → cQ Xy Xx)) % 8.20/8.38 (∀ (Xx Xy : Iota), Or (cP Xx Xy) (cQ Xx Xy)) → % 8.20/8.38 Or (∀ (Xx Xy : Iota), cP Xx Xy) (∀ (Xx Xy : Iota), cQ Xx Xy)) % 8.20/8.38 False % 8.20/8.38 Clause #2 (by clausification #[1]): Eq % 8.20/8.38 (And % 8.20/8.38 (And % 8.20/8.38 (And (∀ (Xx Xy Xz : Iota), And (cP Xx Xy) (cP Xy Xz) → cP Xx Xz) % 8.20/8.38 (∀ (Xx Xy Xz : Iota), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz)) % 8.20/8.38 (∀ (Xx Xy : Iota), cQ Xx Xy → cQ Xy Xx)) % 8.20/8.38 (∀ (Xx Xy : Iota), Or (cP Xx Xy) (cQ Xx Xy))) % 8.20/8.38 True % 8.20/8.38 Clause #3 (by clausification #[1]): Eq (Or (∀ (Xx Xy : Iota), cP Xx Xy) (∀ (Xx Xy : Iota), cQ Xx Xy)) False % 8.20/8.38 Clause #4 (by clausification #[2]): Eq (∀ (Xx Xy : Iota), Or (cP Xx Xy) (cQ Xx Xy)) True % 8.20/8.38 Clause #5 (by clausification #[2]): Eq % 8.20/8.38 (And % 8.20/8.38 (And (∀ (Xx Xy Xz : Iota), And (cP Xx Xy) (cP Xy Xz) → cP Xx Xz) % 8.20/8.38 (∀ (Xx Xy Xz : Iota), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz)) % 8.20/8.38 (∀ (Xx Xy : Iota), cQ Xx Xy → cQ Xy Xx)) % 8.20/8.38 True % 8.20/8.38 Clause #6 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (Xy : Iota), Or (cP a Xy) (cQ a Xy)) True % 8.20/8.38 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (Or (cP a a_1) (cQ a a_1)) True % 8.20/8.38 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (cP a a_1) True) (Eq (cQ a a_1) True) % 8.20/8.38 Clause #9 (by clausification #[3]): Eq (∀ (Xx Xy : Iota), cQ Xx Xy) False % 8.20/8.38 Clause #10 (by clausification #[3]): Eq (∀ (Xx Xy : Iota), cP Xx Xy) False % 8.20/8.38 Clause #11 (by clausification #[9]): ∀ (a : Iota), Eq (Not (∀ (Xy : Iota), cQ (skS.0 0 a) Xy)) True % 8.20/8.38 Clause #12 (by clausification #[11]): ∀ (a : Iota), Eq (∀ (Xy : Iota), cQ (skS.0 0 a) Xy) False % 8.20/8.38 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Eq (Not (cQ (skS.0 0 a) (skS.0 1 a a_1))) True % 8.20/8.38 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Eq (cQ (skS.0 0 a) (skS.0 1 a a_1)) False % 8.20/8.38 Clause #15 (by clausification #[10]): ∀ (a : Iota), Eq (Not (∀ (Xy : Iota), cP (skS.0 2 a) Xy)) True % 8.20/8.38 Clause #16 (by clausification #[15]): ∀ (a : Iota), Eq (∀ (Xy : Iota), cP (skS.0 2 a) Xy) False % 8.20/8.38 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (Not (cP (skS.0 2 a) (skS.0 3 a a_1))) True % 8.20/8.38 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (cP (skS.0 2 a) (skS.0 3 a a_1)) False % 8.20/8.38 Clause #19 (by superposition #[18, 8]): ∀ (a a_1 : Iota), Or (Eq False True) (Eq (cQ (skS.0 2 a) (skS.0 3 a a_1)) True) % 8.20/8.38 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (cQ (skS.0 2 a) (skS.0 3 a a_1)) True % 8.20/8.38 Clause #21 (by clausification #[5]): Eq (∀ (Xx Xy : Iota), cQ Xx Xy → cQ Xy Xx) True % 8.20/8.38 Clause #22 (by clausification #[5]): Eq % 8.20/8.38 (And (∀ (Xx Xy Xz : Iota), And (cP Xx Xy) (cP Xy Xz) → cP Xx Xz) % 8.20/8.38 (∀ (Xx Xy Xz : Iota), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz)) % 8.20/8.38 True % 8.20/8.38 Clause #23 (by clausification #[21]): ∀ (a : Iota), Eq (∀ (Xy : Iota), cQ a Xy → cQ Xy a) True % 8.20/8.38 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (cQ a a_1 → cQ a_1 a) True % 8.20/8.38 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (cQ a a_1) False) (Eq (cQ a_1 a) True) % 8.20/8.38 Clause #27 (by clausification #[22]): Eq (∀ (Xx Xy Xz : Iota), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz) True % 8.20/8.38 Clause #28 (by clausification #[22]): Eq (∀ (Xx Xy Xz : Iota), And (cP Xx Xy) (cP Xy Xz) → cP Xx Xz) True % 8.20/8.38 Clause #29 (by clausification #[27]): ∀ (a : Iota), Eq (∀ (Xy Xz : Iota), And (cQ a Xy) (cQ Xy Xz) → cQ a Xz) True % 8.20/8.38 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Eq (∀ (Xz : Iota), And (cQ a a_1) (cQ a_1 Xz) → cQ a Xz) True % 8.20/8.40 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), Eq (And (cQ a a_1) (cQ a_1 a_2) → cQ a a_2) True % 8.20/8.40 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (cQ a a_1) (cQ a_1 a_2)) False) (Eq (cQ a a_2) True) % 8.20/8.40 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Or (Eq (cQ a a_1) True) (Or (Eq (cQ a a_2) False) (Eq (cQ a_2 a_1) False)) % 8.20/8.40 Clause #34 (by superposition #[33, 20]): ∀ (a a_1 a_2 : Iota), Or (Eq (cQ (skS.0 2 a) a_1) True) (Or (Eq (cQ (skS.0 3 a a_2) a_1) False) (Eq False True)) % 8.20/8.40 Clause #35 (by clausification #[28]): ∀ (a : Iota), Eq (∀ (Xy Xz : Iota), And (cP a Xy) (cP Xy Xz) → cP a Xz) True % 8.20/8.40 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Eq (∀ (Xz : Iota), And (cP a a_1) (cP a_1 Xz) → cP a Xz) True % 8.20/8.40 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Eq (And (cP a a_1) (cP a_1 a_2) → cP a a_2) True % 8.20/8.40 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (cP a a_1) (cP a_1 a_2)) False) (Eq (cP a a_2) True) % 8.20/8.40 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a a_1) True) (Or (Eq (cP a a_2) False) (Eq (cP a_2 a_1) False)) % 8.20/8.40 Clause #40 (by superposition #[39, 8]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a a_1) True) (Or (Eq (cP a_2 a_1) False) (Or (Eq False True) (Eq (cQ a a_2) True))) % 8.20/8.40 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a a_1) True) (Or (Eq (cP a_2 a_1) False) (Eq (cQ a a_2) True)) % 8.20/8.40 Clause #42 (by superposition #[41, 8]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a a_1) True) (Or (Eq (cQ a a_2) True) (Or (Eq False True) (Eq (cQ a_2 a_1) True))) % 8.20/8.40 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a a_1) True) (Or (Eq (cQ a a_2) True) (Eq (cQ a_2 a_1) True)) % 8.20/8.40 Clause #51 (by superposition #[43, 25]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a a_1) True) (Or (Eq (cQ a a_2) True) (Or (Eq True False) (Eq (cQ a_1 a_2) True))) % 8.20/8.40 Clause #53 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a a_1) True) (Or (Eq (cQ a a_2) True) (Eq (cQ a_1 a_2) True)) % 8.20/8.40 Clause #58 (by superposition #[53, 25]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a a_1) True) (Or (Eq (cQ a_1 a_2) True) (Or (Eq True False) (Eq (cQ a_2 a) True))) % 8.20/8.40 Clause #81 (by clausification #[58]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a a_1) True) (Or (Eq (cQ a_1 a_2) True) (Eq (cQ a_2 a) True)) % 8.20/8.40 Clause #82 (by superposition #[81, 18]): ∀ (a a_1 a_2 : Iota), Or (Eq (cQ (skS.0 3 a a_1) a_2) True) (Or (Eq (cQ a_2 (skS.0 2 a)) True) (Eq True False)) % 8.20/8.40 Clause #91 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), Or (Eq (cQ (skS.0 2 a) a_1) True) (Eq (cQ (skS.0 3 a a_2) a_1) False) % 8.20/8.40 Clause #641 (by clausification #[82]): ∀ (a a_1 a_2 : Iota), Or (Eq (cQ (skS.0 3 a a_1) a_2) True) (Eq (cQ a_2 (skS.0 2 a)) True) % 8.20/8.40 Clause #642 (by superposition #[641, 91]): ∀ (a a_1 : Iota), Or (Eq (cQ a (skS.0 2 a_1)) True) (Or (Eq (cQ (skS.0 2 a_1) a) True) (Eq True False)) % 8.20/8.40 Clause #1777 (by clausification #[642]): ∀ (a a_1 : Iota), Or (Eq (cQ a (skS.0 2 a_1)) True) (Eq (cQ (skS.0 2 a_1) a) True) % 8.20/8.40 Clause #1780 (by superposition #[1777, 25]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 2 a) a_1) True) (Or (Eq True False) (Eq (cQ (skS.0 2 a) a_1) True)) % 8.20/8.40 Clause #1820 (by clausification #[1780]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 2 a) a_1) True) (Eq (cQ (skS.0 2 a) a_1) True) % 8.20/8.40 Clause #1821 (by eliminate duplicate literals #[1820]): ∀ (a a_1 : Iota), Eq (cQ (skS.0 2 a) a_1) True % 8.20/8.40 Clause #1826 (by superposition #[1821, 25]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (cQ a (skS.0 2 a_1)) True) % 8.20/8.40 Clause #1838 (by clausification #[1826]): ∀ (a a_1 : Iota), Eq (cQ a (skS.0 2 a_1)) True % 8.20/8.40 Clause #1841 (by superposition #[1838, 33]): ∀ (a a_1 a_2 : Iota), Or (Eq (cQ a a_1) True) (Or (Eq True False) (Eq (cQ (skS.0 2 a_2) a_1) False)) % 8.20/8.40 Clause #1879 (by clausification #[1841]): ∀ (a a_1 a_2 : Iota), Or (Eq (cQ a a_1) True) (Eq (cQ (skS.0 2 a_2) a_1) False) % 8.20/8.40 Clause #1884 (by superposition #[1879, 1821]): ∀ (a a_1 : Iota), Or (Eq (cQ a a_1) True) (Eq False True) % 8.20/8.40 Clause #1930 (by clausification #[1884]): ∀ (a a_1 : Iota), Eq (cQ a a_1) True % 8.20/8.41 Clause #1940 (by superposition #[1930, 14]): Eq True False % 8.20/8.41 Clause #1941 (by clausification #[1940]): False % 8.20/8.41 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------