%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO232+3 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n017.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 07:48:18 PM UTC 2025 % Result : Theorem 4.30s 4.48s % Output : Proof 4.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.09 % Problem : GEO232+3 : TPTP v9.2.0. Released v4.0.0. % 0.06/0.10 % Command : duper %s % 0.09/0.30 % Computer : n017.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 12:22:53 EDT 2025 % 0.09/0.30 % CPUTime : % 4.30/4.48 SZS status Theorem for theBenchmark.p % 4.30/4.48 SZS output start Proof for theBenchmark.p % 4.30/4.48 Clause #0 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (unequally_directed_opposite_lines X Y) (unequally_directed_lines X (reverse_line Y))) True % 4.30/4.48 Clause #3 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (equally_directed_lines X Y) (Not (unequally_directed_lines X Y))) True % 4.30/4.48 Clause #14 (by assumption #[]): Eq (∀ (L : Iota), equally_directed_lines L L) True % 4.30/4.48 Clause #15 (by assumption #[]): Eq (∀ (L M N : Iota), unequally_directed_lines L M → Or (unequally_directed_lines L N) (unequally_directed_lines M N)) % 4.30/4.48 True % 4.30/4.48 Clause #17 (by assumption #[]): Eq (∀ (L M : Iota), Or (unequally_directed_lines L M) (unequally_directed_lines L (reverse_line M))) True % 4.30/4.48 Clause #36 (by assumption #[]): Eq (Not (∀ (L : Iota), unequally_directed_opposite_lines L L)) True % 4.30/4.48 Clause #37 (by clausification #[14]): ∀ (a : Iota), Eq (equally_directed_lines a a) True % 4.30/4.48 Clause #40 (by clausification #[36]): Eq (∀ (L : Iota), unequally_directed_opposite_lines L L) False % 4.30/4.48 Clause #41 (by clausification #[40]): ∀ (a : Iota), Eq (Not (unequally_directed_opposite_lines (skS.0 0 a) (skS.0 0 a))) True % 4.30/4.48 Clause #42 (by clausification #[41]): ∀ (a : Iota), Eq (unequally_directed_opposite_lines (skS.0 0 a) (skS.0 0 a)) False % 4.30/4.48 Clause #47 (by clausification #[0]): ∀ (a : Iota), % 4.30/4.48 Eq (∀ (Y : Iota), Iff (unequally_directed_opposite_lines a Y) (unequally_directed_lines a (reverse_line Y))) True % 4.30/4.48 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota), % 4.30/4.48 Eq (Iff (unequally_directed_opposite_lines a a_1) (unequally_directed_lines a (reverse_line a_1))) True % 4.30/4.48 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota), % 4.30/4.48 Or (Eq (unequally_directed_opposite_lines a a_1) True) (Eq (unequally_directed_lines a (reverse_line a_1)) False) % 4.30/4.48 Clause #89 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (equally_directed_lines a Y) (Not (unequally_directed_lines a Y))) True % 4.30/4.48 Clause #90 (by clausification #[89]): ∀ (a a_1 : Iota), Eq (Iff (equally_directed_lines a a_1) (Not (unequally_directed_lines a a_1))) True % 4.30/4.48 Clause #92 (by clausification #[90]): ∀ (a a_1 : Iota), Or (Eq (equally_directed_lines a a_1) False) (Eq (Not (unequally_directed_lines a a_1)) True) % 4.30/4.48 Clause #94 (by clausification #[92]): ∀ (a a_1 : Iota), Or (Eq (equally_directed_lines a a_1) False) (Eq (unequally_directed_lines a a_1) False) % 4.30/4.48 Clause #96 (by superposition #[94, 37]): ∀ (a : Iota), Or (Eq (unequally_directed_lines a a) False) (Eq False True) % 4.30/4.48 Clause #98 (by clausification #[96]): ∀ (a : Iota), Eq (unequally_directed_lines a a) False % 4.30/4.48 Clause #107 (by clausification #[17]): ∀ (a : Iota), Eq (∀ (M : Iota), Or (unequally_directed_lines a M) (unequally_directed_lines a (reverse_line M))) True % 4.30/4.48 Clause #108 (by clausification #[107]): ∀ (a a_1 : Iota), Eq (Or (unequally_directed_lines a a_1) (unequally_directed_lines a (reverse_line a_1))) True % 4.30/4.48 Clause #109 (by clausification #[108]): ∀ (a a_1 : Iota), % 4.30/4.48 Or (Eq (unequally_directed_lines a a_1) True) (Eq (unequally_directed_lines a (reverse_line a_1)) True) % 4.30/4.48 Clause #113 (by superposition #[109, 98]): ∀ (a : Iota), Or (Eq (unequally_directed_lines (reverse_line a) a) True) (Eq True False) % 4.30/4.48 Clause #114 (by clausification #[113]): ∀ (a : Iota), Eq (unequally_directed_lines (reverse_line a) a) True % 4.30/4.48 Clause #190 (by clausification #[15]): ∀ (a : Iota), % 4.30/4.48 Eq (∀ (M N : Iota), unequally_directed_lines a M → Or (unequally_directed_lines a N) (unequally_directed_lines M N)) % 4.30/4.48 True % 4.30/4.48 Clause #191 (by clausification #[190]): ∀ (a a_1 : Iota), % 4.30/4.48 Eq (∀ (N : Iota), unequally_directed_lines a a_1 → Or (unequally_directed_lines a N) (unequally_directed_lines a_1 N)) % 4.30/4.48 True % 4.30/4.48 Clause #192 (by clausification #[191]): ∀ (a a_1 a_2 : Iota), % 4.30/4.48 Eq (unequally_directed_lines a a_1 → Or (unequally_directed_lines a a_2) (unequally_directed_lines a_1 a_2)) True % 4.30/4.48 Clause #193 (by clausification #[192]): ∀ (a a_1 a_2 : Iota), % 4.30/4.48 Or (Eq (unequally_directed_lines a a_1) False) % 4.30/4.48 (Eq (Or (unequally_directed_lines a a_2) (unequally_directed_lines a_1 a_2)) True) % 4.30/4.48 Clause #194 (by clausification #[193]): ∀ (a a_1 a_2 : Iota), % 4.30/4.49 Or (Eq (unequally_directed_lines a a_1) False) % 4.30/4.49 (Or (Eq (unequally_directed_lines a a_2) True) (Eq (unequally_directed_lines a_1 a_2) True)) % 4.30/4.49 Clause #196 (by superposition #[194, 114]): ∀ (a a_1 : Iota), % 4.30/4.49 Or (Eq (unequally_directed_lines (reverse_line a) a_1) True) % 4.30/4.49 (Or (Eq (unequally_directed_lines a a_1) True) (Eq False True)) % 4.30/4.49 Clause #198 (by clausification #[196]): ∀ (a a_1 : Iota), % 4.30/4.49 Or (Eq (unequally_directed_lines (reverse_line a) a_1) True) (Eq (unequally_directed_lines a a_1) True) % 4.30/4.49 Clause #201 (by superposition #[198, 98]): ∀ (a : Iota), Or (Eq (unequally_directed_lines a (reverse_line a)) True) (Eq True False) % 4.30/4.49 Clause #204 (by clausification #[201]): ∀ (a : Iota), Eq (unequally_directed_lines a (reverse_line a)) True % 4.30/4.49 Clause #205 (by superposition #[204, 49]): ∀ (a : Iota), Or (Eq (unequally_directed_opposite_lines a a) True) (Eq True False) % 4.30/4.49 Clause #214 (by clausification #[205]): ∀ (a : Iota), Eq (unequally_directed_opposite_lines a a) True % 4.30/4.49 Clause #215 (by superposition #[214, 42]): Eq True False % 4.30/4.49 Clause #217 (by clausification #[215]): False % 4.30/4.49 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------