%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : TOP022+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n003.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 08:09:53 PM UTC 2025 % Result : Theorem 4.90s 5.08s % Output : Proof 4.93s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : TOP022+1 : TPTP v9.2.0. Released v3.1.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n003.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 01:59:08 EDT 2025 % 0.13/0.34 % CPUTime : % 4.90/5.08 SZS status Theorem for theBenchmark.p % 4.90/5.08 SZS output start Proof for theBenchmark.p % 4.90/5.08 Clause #0 (by assumption #[]): Eq (∀ (A B : Iota), Iff (isomorphic_groups A B) (Exists fun F => a_group_isomorphism_from_to F A B)) True % 4.90/5.08 Clause #1 (by assumption #[]): Eq % 4.90/5.08 (∀ (X X0 X1 : Iota), % 4.90/5.08 Iff (path_connected X) (And (a_member_of X0 X) (a_member_of X1 X) → Exists fun P => a_path_from_to_in P X0 X1 X)) % 4.90/5.08 True % 4.90/5.08 Clause #2 (by assumption #[]): Eq % 4.90/5.08 (∀ (A X0 X1 X : Iota), % 4.90/5.08 a_path_from_to_in A X0 X1 X → % 4.90/5.08 a_group_isomorphism_from_to (alpha_hat A) (first_homotop_grp X X0) (first_homotop_grp X X1)) % 4.90/5.08 True % 4.90/5.08 Clause #3 (by assumption #[]): Eq % 4.90/5.08 (Not % 4.90/5.08 (∀ (X X0 X1 : Iota), % 4.90/5.08 And (And (path_connected X) (a_member_of X0 X)) (a_member_of X1 X) → % 4.90/5.08 isomorphic_groups (first_homotop_grp X X0) (first_homotop_grp X X1))) % 4.90/5.08 True % 4.90/5.08 Clause #4 (by clausification #[3]): Eq % 4.90/5.08 (∀ (X X0 X1 : Iota), % 4.90/5.08 And (And (path_connected X) (a_member_of X0 X)) (a_member_of X1 X) → % 4.90/5.08 isomorphic_groups (first_homotop_grp X X0) (first_homotop_grp X X1)) % 4.90/5.08 False % 4.90/5.08 Clause #5 (by clausification #[4]): ∀ (a : Iota), % 4.90/5.08 Eq % 4.90/5.08 (Not % 4.90/5.08 (∀ (X0 X1 : Iota), % 4.90/5.08 And (And (path_connected (skS.0 0 a)) (a_member_of X0 (skS.0 0 a))) (a_member_of X1 (skS.0 0 a)) → % 4.90/5.08 isomorphic_groups (first_homotop_grp (skS.0 0 a) X0) (first_homotop_grp (skS.0 0 a) X1))) % 4.90/5.08 True % 4.90/5.08 Clause #6 (by clausification #[5]): ∀ (a : Iota), % 4.90/5.08 Eq % 4.90/5.08 (∀ (X0 X1 : Iota), % 4.90/5.08 And (And (path_connected (skS.0 0 a)) (a_member_of X0 (skS.0 0 a))) (a_member_of X1 (skS.0 0 a)) → % 4.90/5.08 isomorphic_groups (first_homotop_grp (skS.0 0 a) X0) (first_homotop_grp (skS.0 0 a) X1)) % 4.90/5.08 False % 4.90/5.08 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), % 4.90/5.08 Eq % 4.90/5.08 (Not % 4.90/5.08 (∀ (X1 : Iota), % 4.90/5.08 And (And (path_connected (skS.0 0 a)) (a_member_of (skS.0 1 a a_1) (skS.0 0 a))) (a_member_of X1 (skS.0 0 a)) → % 4.90/5.08 isomorphic_groups (first_homotop_grp (skS.0 0 a) (skS.0 1 a a_1)) (first_homotop_grp (skS.0 0 a) X1))) % 4.90/5.08 True % 4.90/5.08 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), % 4.90/5.08 Eq % 4.90/5.08 (∀ (X1 : Iota), % 4.90/5.08 And (And (path_connected (skS.0 0 a)) (a_member_of (skS.0 1 a a_1) (skS.0 0 a))) (a_member_of X1 (skS.0 0 a)) → % 4.90/5.08 isomorphic_groups (first_homotop_grp (skS.0 0 a) (skS.0 1 a a_1)) (first_homotop_grp (skS.0 0 a) X1)) % 4.90/5.08 False % 4.90/5.08 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), % 4.90/5.08 Eq % 4.90/5.08 (Not % 4.90/5.08 (And (And (path_connected (skS.0 0 a)) (a_member_of (skS.0 1 a a_1) (skS.0 0 a))) % 4.90/5.08 (a_member_of (skS.0 2 a a_1 a_2) (skS.0 0 a)) → % 4.90/5.08 isomorphic_groups (first_homotop_grp (skS.0 0 a) (skS.0 1 a a_1)) % 4.90/5.08 (first_homotop_grp (skS.0 0 a) (skS.0 2 a a_1 a_2)))) % 4.90/5.08 True % 4.90/5.08 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 4.90/5.08 Eq % 4.90/5.08 (And (And (path_connected (skS.0 0 a)) (a_member_of (skS.0 1 a a_1) (skS.0 0 a))) % 4.90/5.08 (a_member_of (skS.0 2 a a_1 a_2) (skS.0 0 a)) → % 4.90/5.08 isomorphic_groups (first_homotop_grp (skS.0 0 a) (skS.0 1 a a_1)) % 4.90/5.08 (first_homotop_grp (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 4.90/5.08 False % 4.90/5.08 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), % 4.90/5.08 Eq % 4.90/5.08 (And (And (path_connected (skS.0 0 a)) (a_member_of (skS.0 1 a a_1) (skS.0 0 a))) % 4.90/5.08 (a_member_of (skS.0 2 a a_1 a_2) (skS.0 0 a))) % 4.90/5.08 True % 4.90/5.08 Clause #12 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), % 4.90/5.08 Eq % 4.90/5.08 (isomorphic_groups (first_homotop_grp (skS.0 0 a) (skS.0 1 a a_1)) % 4.90/5.08 (first_homotop_grp (skS.0 0 a) (skS.0 2 a a_1 a_2))) % 4.90/5.08 False % 4.90/5.08 Clause #13 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Eq (a_member_of (skS.0 2 a a_1 a_2) (skS.0 0 a)) True % 4.90/5.08 Clause #14 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (And (path_connected (skS.0 0 a)) (a_member_of (skS.0 1 a a_1) (skS.0 0 a))) True % 4.90/5.08 Clause #15 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (isomorphic_groups a B) (Exists fun F => a_group_isomorphism_from_to F a B)) True % 4.90/5.08 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (Iff (isomorphic_groups a a_1) (Exists fun F => a_group_isomorphism_from_to F a a_1)) True % 4.90/5.08 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), % 4.93/5.10 Or (Eq (isomorphic_groups a a_1) True) (Eq (Exists fun F => a_group_isomorphism_from_to F a a_1) False) % 4.93/5.10 Clause #19 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), Or (Eq (isomorphic_groups a a_1) True) (Eq (a_group_isomorphism_from_to a_2 a a_1) False) % 4.93/5.10 Clause #21 (by clausification #[2]): ∀ (a : Iota), % 4.93/5.10 Eq % 4.93/5.10 (∀ (X0 X1 X : Iota), % 4.93/5.10 a_path_from_to_in a X0 X1 X → % 4.93/5.10 a_group_isomorphism_from_to (alpha_hat a) (first_homotop_grp X X0) (first_homotop_grp X X1)) % 4.93/5.10 True % 4.93/5.10 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), % 4.93/5.10 Eq % 4.93/5.10 (∀ (X1 X : Iota), % 4.93/5.10 a_path_from_to_in a a_1 X1 X → % 4.93/5.10 a_group_isomorphism_from_to (alpha_hat a) (first_homotop_grp X a_1) (first_homotop_grp X X1)) % 4.93/5.10 True % 4.93/5.10 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), % 4.93/5.10 Eq % 4.93/5.10 (∀ (X : Iota), % 4.93/5.10 a_path_from_to_in a a_1 a_2 X → % 4.93/5.10 a_group_isomorphism_from_to (alpha_hat a) (first_homotop_grp X a_1) (first_homotop_grp X a_2)) % 4.93/5.10 True % 4.93/5.10 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 a_3 : Iota), % 4.93/5.10 Eq % 4.93/5.10 (a_path_from_to_in a a_1 a_2 a_3 → % 4.93/5.10 a_group_isomorphism_from_to (alpha_hat a) (first_homotop_grp a_3 a_1) (first_homotop_grp a_3 a_2)) % 4.93/5.10 True % 4.93/5.10 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 a_3 : Iota), % 4.93/5.10 Or (Eq (a_path_from_to_in a a_1 a_2 a_3) False) % 4.93/5.10 (Eq (a_group_isomorphism_from_to (alpha_hat a) (first_homotop_grp a_3 a_1) (first_homotop_grp a_3 a_2)) True) % 4.93/5.10 Clause #26 (by clausification #[1]): ∀ (a : Iota), % 4.93/5.10 Eq % 4.93/5.10 (∀ (X0 X1 : Iota), % 4.93/5.10 Iff (path_connected a) (And (a_member_of X0 a) (a_member_of X1 a) → Exists fun P => a_path_from_to_in P X0 X1 a)) % 4.93/5.10 True % 4.93/5.10 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), % 4.93/5.10 Eq % 4.93/5.10 (∀ (X1 : Iota), % 4.93/5.10 Iff (path_connected a) % 4.93/5.10 (And (a_member_of a_1 a) (a_member_of X1 a) → Exists fun P => a_path_from_to_in P a_1 X1 a)) % 4.93/5.10 True % 4.93/5.10 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), % 4.93/5.10 Eq % 4.93/5.10 (Iff (path_connected a) % 4.93/5.10 (And (a_member_of a_1 a) (a_member_of a_2 a) → Exists fun P => a_path_from_to_in P a_1 a_2 a)) % 4.93/5.10 True % 4.93/5.10 Clause #30 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), % 4.93/5.10 Or (Eq (path_connected a) False) % 4.93/5.10 (Eq (And (a_member_of a_1 a) (a_member_of a_2 a) → Exists fun P => a_path_from_to_in P a_1 a_2 a) True) % 4.93/5.10 Clause #35 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), % 4.93/5.10 Or (Eq (path_connected a) False) % 4.93/5.10 (Or (Eq (And (a_member_of a_1 a) (a_member_of a_2 a)) False) % 4.93/5.10 (Eq (Exists fun P => a_path_from_to_in P a_1 a_2 a) True)) % 4.93/5.10 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), % 4.93/5.10 Or (Eq (path_connected a) False) % 4.93/5.10 (Or (Eq (Exists fun P => a_path_from_to_in P a_1 a_2 a) True) % 4.93/5.10 (Or (Eq (a_member_of a_1 a) False) (Eq (a_member_of a_2 a) False))) % 4.93/5.10 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 a_3 : Iota), % 4.93/5.10 Or (Eq (path_connected a) False) % 4.93/5.10 (Or (Eq (a_member_of a_1 a) False) % 4.93/5.10 (Or (Eq (a_member_of a_2 a) False) (Eq (a_path_from_to_in (skS.0 4 a_1 a_2 a a_3) a_1 a_2 a) True))) % 4.93/5.10 Clause #38 (by clausification #[14]): ∀ (a a_1 : Iota), Eq (a_member_of (skS.0 1 a a_1) (skS.0 0 a)) True % 4.93/5.10 Clause #39 (by clausification #[14]): ∀ (a : Iota), Eq (path_connected (skS.0 0 a)) True % 4.93/5.10 Clause #40 (by superposition #[39, 37]): ∀ (a a_1 a_2 a_3 : Iota), % 4.93/5.10 Or (Eq True False) % 4.93/5.10 (Or (Eq (a_member_of a (skS.0 0 a_1)) False) % 4.93/5.10 (Or (Eq (a_member_of a_2 (skS.0 0 a_1)) False) % 4.93/5.10 (Eq (a_path_from_to_in (skS.0 4 a a_2 (skS.0 0 a_1) a_3) a a_2 (skS.0 0 a_1)) True))) % 4.93/5.10 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 a_3 : Iota), % 4.93/5.10 Or (Eq (a_member_of a (skS.0 0 a_1)) False) % 4.93/5.10 (Or (Eq (a_member_of a_2 (skS.0 0 a_1)) False) % 4.93/5.10 (Eq (a_path_from_to_in (skS.0 4 a a_2 (skS.0 0 a_1) a_3) a a_2 (skS.0 0 a_1)) True)) % 4.93/5.10 Clause #43 (by superposition #[41, 38]): ∀ (a a_1 a_2 a_3 : Iota), % 4.93/5.10 Or (Eq (a_member_of a (skS.0 0 a_1)) False) % 4.93/5.10 (Or (Eq (a_path_from_to_in (skS.0 4 (skS.0 1 a_1 a_2) a (skS.0 0 a_1) a_3) (skS.0 1 a_1 a_2) a (skS.0 0 a_1)) True) % 4.93/5.10 (Eq False True)) % 4.93/5.10 Clause #51 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota), % 4.93/5.10 Or (Eq (a_member_of a (skS.0 0 a_1)) False) % 4.93/5.11 (Eq (a_path_from_to_in (skS.0 4 (skS.0 1 a_1 a_2) a (skS.0 0 a_1) a_3) (skS.0 1 a_1 a_2) a (skS.0 0 a_1)) True) % 4.93/5.11 Clause #52 (by superposition #[51, 13]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.93/5.11 Or % 4.93/5.11 (Eq % 4.93/5.11 (a_path_from_to_in (skS.0 4 (skS.0 1 a a_1) (skS.0 2 a a_2 a_3) (skS.0 0 a) a_4) (skS.0 1 a a_1) % 4.93/5.11 (skS.0 2 a a_2 a_3) (skS.0 0 a)) % 4.93/5.11 True) % 4.93/5.11 (Eq False True) % 4.93/5.11 Clause #64 (by clausification #[52]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.93/5.11 Eq % 4.93/5.11 (a_path_from_to_in (skS.0 4 (skS.0 1 a a_1) (skS.0 2 a a_2 a_3) (skS.0 0 a) a_4) (skS.0 1 a a_1) (skS.0 2 a a_2 a_3) % 4.93/5.11 (skS.0 0 a)) % 4.93/5.11 True % 4.93/5.11 Clause #65 (by superposition #[64, 25]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.93/5.11 Or (Eq True False) % 4.93/5.11 (Eq % 4.93/5.11 (a_group_isomorphism_from_to (alpha_hat (skS.0 4 (skS.0 1 a a_1) (skS.0 2 a a_2 a_3) (skS.0 0 a) a_4)) % 4.93/5.11 (first_homotop_grp (skS.0 0 a) (skS.0 1 a a_1)) (first_homotop_grp (skS.0 0 a) (skS.0 2 a a_2 a_3))) % 4.93/5.11 True) % 4.93/5.11 Clause #80 (by clausification #[65]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.93/5.11 Eq % 4.93/5.11 (a_group_isomorphism_from_to (alpha_hat (skS.0 4 (skS.0 1 a a_1) (skS.0 2 a a_2 a_3) (skS.0 0 a) a_4)) % 4.93/5.11 (first_homotop_grp (skS.0 0 a) (skS.0 1 a a_1)) (first_homotop_grp (skS.0 0 a) (skS.0 2 a a_2 a_3))) % 4.93/5.11 True % 4.93/5.11 Clause #81 (by superposition #[80, 19]): ∀ (a a_1 a_2 a_3 : Iota), % 4.93/5.11 Or % 4.93/5.11 (Eq % 4.93/5.11 (isomorphic_groups (first_homotop_grp (skS.0 0 a) (skS.0 1 a a_1)) % 4.93/5.11 (first_homotop_grp (skS.0 0 a) (skS.0 2 a a_2 a_3))) % 4.93/5.11 True) % 4.93/5.11 (Eq True False) % 4.93/5.11 Clause #82 (by clausification #[81]): ∀ (a a_1 a_2 a_3 : Iota), % 4.93/5.11 Eq % 4.93/5.11 (isomorphic_groups (first_homotop_grp (skS.0 0 a) (skS.0 1 a a_1)) % 4.93/5.11 (first_homotop_grp (skS.0 0 a) (skS.0 2 a a_2 a_3))) % 4.93/5.11 True % 4.93/5.11 Clause #83 (by superposition #[82, 12]): Eq True False % 4.93/5.11 Clause #86 (by clausification #[83]): False % 4.93/5.11 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------