%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO233+3 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n006.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 07:48:19 PM UTC 2025 % Result : Theorem 28.69s 28.93s % Output : Proof 28.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.09 % Problem : GEO233+3 : TPTP v9.2.0. Released v4.0.0. % 0.00/0.10 % Command : duper %s % 0.09/0.30 % Computer : n006.cluster.edu % 0.09/0.30 % Model : x86_64 x86_64 % 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.30 % Memory : 8042.1875MB % 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.30 % CPULimit : 300 % 0.09/0.30 % WCLimit : 300 % 0.09/0.30 % DateTime : Fri Oct 3 11:58:53 EDT 2025 % 0.09/0.30 % CPUTime : % 28.69/28.93 SZS status Theorem for theBenchmark.p % 28.69/28.93 SZS output start Proof for theBenchmark.p % 28.69/28.93 Clause #3 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (equally_directed_lines X Y) (Not (unequally_directed_lines X Y))) True % 28.69/28.93 Clause #14 (by assumption #[]): Eq (∀ (L : Iota), equally_directed_lines L L) True % 28.69/28.93 Clause #17 (by assumption #[]): Eq (∀ (L M : Iota), Or (unequally_directed_lines L M) (unequally_directed_lines L (reverse_line M))) True % 28.69/28.93 Clause #18 (by assumption #[]): Eq % 28.69/28.93 (∀ (L M : Iota), % 28.69/28.93 And (unequally_directed_lines L M) (unequally_directed_lines L (reverse_line M)) → % 28.69/28.93 Or (left_convergent_lines L M) (left_convergent_lines L (reverse_line M))) % 28.69/28.93 True % 28.69/28.93 Clause #20 (by assumption #[]): Eq (∀ (L M : Iota), Not (Or (left_convergent_lines L M) (left_convergent_lines L (reverse_line M)))) True % 28.69/28.93 Clause #36 (by assumption #[]): Eq (Not (∀ (L : Iota), equally_directed_lines (reverse_line (reverse_line L)) L)) True % 28.69/28.93 Clause #37 (by clausification #[14]): ∀ (a : Iota), Eq (equally_directed_lines a a) True % 28.69/28.93 Clause #54 (by clausification #[36]): Eq (∀ (L : Iota), equally_directed_lines (reverse_line (reverse_line L)) L) False % 28.69/28.93 Clause #55 (by clausification #[54]): ∀ (a : Iota), Eq (Not (equally_directed_lines (reverse_line (reverse_line (skS.0 0 a))) (skS.0 0 a))) True % 28.69/28.93 Clause #56 (by clausification #[55]): ∀ (a : Iota), Eq (equally_directed_lines (reverse_line (reverse_line (skS.0 0 a))) (skS.0 0 a)) False % 28.69/28.93 Clause #77 (by clausification #[17]): ∀ (a : Iota), Eq (∀ (M : Iota), Or (unequally_directed_lines a M) (unequally_directed_lines a (reverse_line M))) True % 28.69/28.93 Clause #78 (by clausification #[77]): ∀ (a a_1 : Iota), Eq (Or (unequally_directed_lines a a_1) (unequally_directed_lines a (reverse_line a_1))) True % 28.69/28.93 Clause #79 (by clausification #[78]): ∀ (a a_1 : Iota), % 28.69/28.93 Or (Eq (unequally_directed_lines a a_1) True) (Eq (unequally_directed_lines a (reverse_line a_1)) True) % 28.69/28.93 Clause #96 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (equally_directed_lines a Y) (Not (unequally_directed_lines a Y))) True % 28.69/28.93 Clause #97 (by clausification #[96]): ∀ (a a_1 : Iota), Eq (Iff (equally_directed_lines a a_1) (Not (unequally_directed_lines a a_1))) True % 28.69/28.93 Clause #98 (by clausification #[97]): ∀ (a a_1 : Iota), Or (Eq (equally_directed_lines a a_1) True) (Eq (Not (unequally_directed_lines a a_1)) False) % 28.69/28.93 Clause #99 (by clausification #[97]): ∀ (a a_1 : Iota), Or (Eq (equally_directed_lines a a_1) False) (Eq (Not (unequally_directed_lines a a_1)) True) % 28.69/28.93 Clause #100 (by clausification #[98]): ∀ (a a_1 : Iota), Or (Eq (equally_directed_lines a a_1) True) (Eq (unequally_directed_lines a a_1) True) % 28.69/28.93 Clause #101 (by superposition #[100, 56]): ∀ (a : Iota), % 28.69/28.93 Or (Eq (unequally_directed_lines (reverse_line (reverse_line (skS.0 0 a))) (skS.0 0 a)) True) (Eq True False) % 28.69/28.93 Clause #102 (by clausification #[99]): ∀ (a a_1 : Iota), Or (Eq (equally_directed_lines a a_1) False) (Eq (unequally_directed_lines a a_1) False) % 28.69/28.93 Clause #104 (by superposition #[102, 37]): ∀ (a : Iota), Or (Eq (unequally_directed_lines a a) False) (Eq False True) % 28.69/28.93 Clause #106 (by clausification #[104]): ∀ (a : Iota), Eq (unequally_directed_lines a a) False % 28.69/28.93 Clause #107 (by superposition #[106, 79]): ∀ (a : Iota), Or (Eq (unequally_directed_lines (reverse_line a) a) True) (Eq False True) % 28.69/28.93 Clause #108 (by clausification #[107]): ∀ (a : Iota), Eq (unequally_directed_lines (reverse_line a) a) True % 28.69/28.93 Clause #200 (by clausification #[20]): ∀ (a : Iota), Eq (∀ (M : Iota), Not (Or (left_convergent_lines a M) (left_convergent_lines a (reverse_line M)))) True % 28.69/28.93 Clause #201 (by clausification #[200]): ∀ (a a_1 : Iota), Eq (Not (Or (left_convergent_lines a a_1) (left_convergent_lines a (reverse_line a_1)))) True % 28.69/28.93 Clause #202 (by clausification #[201]): ∀ (a a_1 : Iota), Eq (Or (left_convergent_lines a a_1) (left_convergent_lines a (reverse_line a_1))) False % 28.69/28.93 Clause #204 (by clausification #[202]): ∀ (a a_1 : Iota), Eq (left_convergent_lines a a_1) False % 28.69/28.93 Clause #229 (by clausification #[18]): ∀ (a : Iota), % 28.69/28.93 Eq % 28.69/28.93 (∀ (M : Iota), % 28.69/28.93 And (unequally_directed_lines a M) (unequally_directed_lines a (reverse_line M)) → % 28.79/28.98 Or (left_convergent_lines a M) (left_convergent_lines a (reverse_line M))) % 28.79/28.98 True % 28.79/28.98 Clause #230 (by clausification #[229]): ∀ (a a_1 : Iota), % 28.79/28.98 Eq % 28.79/28.98 (And (unequally_directed_lines a a_1) (unequally_directed_lines a (reverse_line a_1)) → % 28.79/28.98 Or (left_convergent_lines a a_1) (left_convergent_lines a (reverse_line a_1))) % 28.79/28.98 True % 28.79/28.98 Clause #231 (by clausification #[230]): ∀ (a a_1 : Iota), % 28.79/28.98 Or (Eq (And (unequally_directed_lines a a_1) (unequally_directed_lines a (reverse_line a_1))) False) % 28.79/28.98 (Eq (Or (left_convergent_lines a a_1) (left_convergent_lines a (reverse_line a_1))) True) % 28.79/28.98 Clause #232 (by clausification #[231]): ∀ (a a_1 : Iota), % 28.79/28.98 Or (Eq (Or (left_convergent_lines a a_1) (left_convergent_lines a (reverse_line a_1))) True) % 28.79/28.98 (Or (Eq (unequally_directed_lines a a_1) False) (Eq (unequally_directed_lines a (reverse_line a_1)) False)) % 28.79/28.98 Clause #233 (by clausification #[232]): ∀ (a a_1 : Iota), % 28.79/28.98 Or (Eq (unequally_directed_lines a a_1) False) % 28.79/28.98 (Or (Eq (unequally_directed_lines a (reverse_line a_1)) False) % 28.79/28.98 (Or (Eq (left_convergent_lines a a_1) True) (Eq (left_convergent_lines a (reverse_line a_1)) True))) % 28.79/28.98 Clause #234 (by forward demodulation #[233, 204]): ∀ (a a_1 : Iota), % 28.79/28.98 Or (Eq (unequally_directed_lines a a_1) False) % 28.79/28.98 (Or (Eq (unequally_directed_lines a (reverse_line a_1)) False) % 28.79/28.98 (Or (Eq False True) (Eq (left_convergent_lines a (reverse_line a_1)) True))) % 28.79/28.98 Clause #235 (by clausification #[234]): ∀ (a a_1 : Iota), % 28.79/28.98 Or (Eq (unequally_directed_lines a a_1) False) % 28.79/28.98 (Or (Eq (unequally_directed_lines a (reverse_line a_1)) False) % 28.79/28.98 (Eq (left_convergent_lines a (reverse_line a_1)) True)) % 28.79/28.98 Clause #400 (by clausification #[101]): ∀ (a : Iota), Eq (unequally_directed_lines (reverse_line (reverse_line (skS.0 0 a))) (skS.0 0 a)) True % 28.79/28.98 Clause #403 (by superposition #[400, 235]): ∀ (a : Iota), % 28.79/28.98 Or (Eq True False) % 28.79/28.98 (Or (Eq (unequally_directed_lines (reverse_line (reverse_line (skS.0 0 a))) (reverse_line (skS.0 0 a))) False) % 28.79/28.98 (Eq (left_convergent_lines (reverse_line (reverse_line (skS.0 0 a))) (reverse_line (skS.0 0 a))) True)) % 28.79/28.98 Clause #5999 (by clausification #[403]): ∀ (a : Iota), % 28.79/28.98 Or (Eq (unequally_directed_lines (reverse_line (reverse_line (skS.0 0 a))) (reverse_line (skS.0 0 a))) False) % 28.79/28.98 (Eq (left_convergent_lines (reverse_line (reverse_line (skS.0 0 a))) (reverse_line (skS.0 0 a))) True) % 28.79/28.98 Clause #6000 (by forward demodulation #[5999, 108]): ∀ (a : Iota), % 28.79/28.98 Or (Eq True False) % 28.79/28.98 (Eq (left_convergent_lines (reverse_line (reverse_line (skS.0 0 a))) (reverse_line (skS.0 0 a))) True) % 28.79/28.98 Clause #6001 (by clausification #[6000]): ∀ (a : Iota), Eq (left_convergent_lines (reverse_line (reverse_line (skS.0 0 a))) (reverse_line (skS.0 0 a))) True % 28.79/28.98 Clause #6002 (by superposition #[6001, 204]): Eq True False % 28.79/28.98 Clause #6003 (by clausification #[6002]): False % 28.79/28.98 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------