%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO102^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n029.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 08:08:35 PM UTC 2025 % Result : Theorem 4.09s 4.25s % Output : Proof 4.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SYO102^5 : TPTP v9.2.0. Released v4.0.0. % 0.13/0.14 % Command : duper %s % 0.13/0.35 % Computer : n029.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Oct 3 13:18:08 EDT 2025 % 0.20/0.35 % CPUTime : % 4.09/4.25 SZS status Theorem for theBenchmark.p % 4.09/4.25 SZS output start Proof for theBenchmark.p % 4.09/4.25 Clause #0 (by assumption #[]): Eq % 4.09/4.25 (Not % 4.09/4.25 (And (∀ (Xx : Iota), cP Xx Xx) (∀ (Xx Xy Xz : Iota), And (cP Xx Xy) (cP Xz Xy) → cP Xx Xz) → % 4.09/4.25 ∀ (Xu Xv Xw : Iota), And (cP Xu Xv) (cP Xv Xw) → cP Xu Xw)) % 4.09/4.25 True % 4.09/4.25 Clause #1 (by clausification #[0]): Eq % 4.09/4.25 (And (∀ (Xx : Iota), cP Xx Xx) (∀ (Xx Xy Xz : Iota), And (cP Xx Xy) (cP Xz Xy) → cP Xx Xz) → % 4.09/4.25 ∀ (Xu Xv Xw : Iota), And (cP Xu Xv) (cP Xv Xw) → cP Xu Xw) % 4.09/4.25 False % 4.09/4.25 Clause #2 (by clausification #[1]): Eq (And (∀ (Xx : Iota), cP Xx Xx) (∀ (Xx Xy Xz : Iota), And (cP Xx Xy) (cP Xz Xy) → cP Xx Xz)) True % 4.09/4.25 Clause #3 (by clausification #[1]): Eq (∀ (Xu Xv Xw : Iota), And (cP Xu Xv) (cP Xv Xw) → cP Xu Xw) False % 4.09/4.25 Clause #4 (by clausification #[2]): Eq (∀ (Xx Xy Xz : Iota), And (cP Xx Xy) (cP Xz Xy) → cP Xx Xz) True % 4.09/4.25 Clause #5 (by clausification #[2]): Eq (∀ (Xx : Iota), cP Xx Xx) True % 4.09/4.25 Clause #6 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (Xy Xz : Iota), And (cP a Xy) (cP Xz Xy) → cP a Xz) True % 4.09/4.25 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (∀ (Xz : Iota), And (cP a a_1) (cP Xz a_1) → cP a Xz) True % 4.09/4.25 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), Eq (And (cP a a_1) (cP a_2 a_1) → cP a a_2) True % 4.09/4.25 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (cP a a_1) (cP a_2 a_1)) False) (Eq (cP a a_2) True) % 4.09/4.25 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a a_1) True) (Or (Eq (cP a a_2) False) (Eq (cP a_1 a_2) False)) % 4.09/4.25 Clause #11 (by clausification #[5]): ∀ (a : Iota), Eq (cP a a) True % 4.09/4.25 Clause #12 (by superposition #[11, 10]): ∀ (a a_1 : Iota), Or (Eq (cP a a_1) True) (Or (Eq True False) (Eq (cP a_1 a) False)) % 4.09/4.25 Clause #13 (by clausification #[3]): ∀ (a : Iota), Eq (Not (∀ (Xv Xw : Iota), And (cP (skS.0 0 a) Xv) (cP Xv Xw) → cP (skS.0 0 a) Xw)) True % 4.09/4.25 Clause #14 (by clausification #[13]): ∀ (a : Iota), Eq (∀ (Xv Xw : Iota), And (cP (skS.0 0 a) Xv) (cP Xv Xw) → cP (skS.0 0 a) Xw) False % 4.09/4.25 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), % 4.09/4.25 Eq (Not (∀ (Xw : Iota), And (cP (skS.0 0 a) (skS.0 1 a a_1)) (cP (skS.0 1 a a_1) Xw) → cP (skS.0 0 a) Xw)) True % 4.09/4.25 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), % 4.09/4.25 Eq (∀ (Xw : Iota), And (cP (skS.0 0 a) (skS.0 1 a a_1)) (cP (skS.0 1 a a_1) Xw) → cP (skS.0 0 a) Xw) False % 4.09/4.25 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 : Iota), % 4.09/4.25 Eq % 4.09/4.25 (Not % 4.09/4.25 (And (cP (skS.0 0 a) (skS.0 1 a a_1)) (cP (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → % 4.09/4.25 cP (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 4.09/4.25 True % 4.09/4.25 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), % 4.09/4.25 Eq % 4.09/4.25 (And (cP (skS.0 0 a) (skS.0 1 a a_1)) (cP (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → cP (skS.0 0 a) (skS.0 2 a a_1 a_2)) % 4.09/4.25 False % 4.09/4.25 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), Eq (And (cP (skS.0 0 a) (skS.0 1 a a_1)) (cP (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) True % 4.09/4.25 Clause #20 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), Eq (cP (skS.0 0 a) (skS.0 2 a a_1 a_2)) False % 4.09/4.25 Clause #21 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), Eq (cP (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) True % 4.09/4.25 Clause #22 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (cP (skS.0 0 a) (skS.0 1 a a_1)) True % 4.09/4.25 Clause #24 (by clausification #[12]): ∀ (a a_1 : Iota), Or (Eq (cP a a_1) True) (Eq (cP a_1 a) False) % 4.09/4.25 Clause #25 (by superposition #[24, 21]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True) (Eq False True) % 4.09/4.25 Clause #27 (by superposition #[22, 10]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP (skS.0 0 a) a_1) True) (Or (Eq True False) (Eq (cP a_1 (skS.0 1 a a_2)) False)) % 4.09/4.25 Clause #32 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), Eq (cP (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True % 4.09/4.25 Clause #39 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP (skS.0 0 a) a_1) True) (Eq (cP a_1 (skS.0 1 a a_2)) False) % 4.09/4.25 Clause #41 (by superposition #[39, 32]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) (Eq False True) % 4.09/4.25 Clause #46 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), Eq (cP (skS.0 0 a) (skS.0 2 a a_1 a_2)) True % 4.09/4.25 Clause #47 (by superposition #[46, 20]): Eq True False % 4.09/4.25 Clause #51 (by clausification #[47]): False % 4.09/4.25 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------