%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO247+1 : TPTP v9.2.0. Bugfixed v6.4.0. % 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 07:48:21 PM UTC 2025 % Result : Theorem 3.62s 3.84s % Output : Proof 3.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : GEO247+1 : TPTP v9.2.0. Bugfixed v6.4.0. % 0.12/0.14 % Command : duper %s % 0.14/0.35 % Computer : n022.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Fri Oct 3 11:52:38 EDT 2025 % 0.14/0.36 % CPUTime : % 3.62/3.84 SZS status Theorem for theBenchmark.p % 3.62/3.84 SZS output start Proof for theBenchmark.p % 3.62/3.84 Clause #14 (by assumption #[]): Eq (∀ (A L : Iota), Not (Or (left_apart_point A L) (left_apart_point A (reverse_line L)))) True % 3.62/3.84 Clause #31 (by assumption #[]): Eq % 3.62/3.84 (Not % 3.62/3.84 (∀ (A B C D L M : Iota), % 3.62/3.84 And % 3.62/3.84 (And % 3.62/3.84 (And % 3.62/3.84 (And % 3.62/3.84 (And (And (And (left_apart_point A L) (left_apart_point A M)) (left_apart_point B (reverse_line L))) % 3.62/3.84 (left_apart_point B (reverse_line M))) % 3.62/3.84 (left_apart_point C L)) % 3.62/3.84 (left_apart_point C (reverse_line M))) % 3.62/3.84 (left_apart_point D (reverse_line L))) % 3.62/3.84 (left_apart_point D M) → % 3.62/3.84 convergent_lines L M)) % 3.62/3.84 True % 3.62/3.84 Clause #79 (by clausification #[14]): ∀ (a : Iota), Eq (∀ (L : Iota), Not (Or (left_apart_point a L) (left_apart_point a (reverse_line L)))) True % 3.62/3.84 Clause #80 (by clausification #[79]): ∀ (a a_1 : Iota), Eq (Not (Or (left_apart_point a a_1) (left_apart_point a (reverse_line a_1)))) True % 3.62/3.84 Clause #81 (by clausification #[80]): ∀ (a a_1 : Iota), Eq (Or (left_apart_point a a_1) (left_apart_point a (reverse_line a_1))) False % 3.62/3.84 Clause #83 (by clausification #[81]): ∀ (a a_1 : Iota), Eq (left_apart_point a a_1) False % 3.62/3.84 Clause #140 (by clausification #[31]): Eq % 3.62/3.84 (∀ (A B C D L M : Iota), % 3.62/3.84 And % 3.62/3.84 (And % 3.62/3.84 (And % 3.62/3.84 (And % 3.62/3.84 (And (And (And (left_apart_point A L) (left_apart_point A M)) (left_apart_point B (reverse_line L))) % 3.62/3.84 (left_apart_point B (reverse_line M))) % 3.62/3.84 (left_apart_point C L)) % 3.62/3.84 (left_apart_point C (reverse_line M))) % 3.62/3.84 (left_apart_point D (reverse_line L))) % 3.62/3.84 (left_apart_point D M) → % 3.62/3.84 convergent_lines L M) % 3.62/3.84 False % 3.62/3.84 Clause #141 (by clausification #[140]): ∀ (a : Iota), % 3.62/3.84 Eq % 3.62/3.84 (Not % 3.62/3.84 (∀ (B C D L M : Iota), % 3.62/3.84 And % 3.62/3.84 (And % 3.62/3.84 (And % 3.62/3.84 (And % 3.62/3.84 (And % 3.62/3.84 (And (And (left_apart_point (skS.0 0 a) L) (left_apart_point (skS.0 0 a) M)) % 3.62/3.84 (left_apart_point B (reverse_line L))) % 3.62/3.84 (left_apart_point B (reverse_line M))) % 3.62/3.84 (left_apart_point C L)) % 3.62/3.84 (left_apart_point C (reverse_line M))) % 3.62/3.84 (left_apart_point D (reverse_line L))) % 3.62/3.84 (left_apart_point D M) → % 3.62/3.84 convergent_lines L M)) % 3.62/3.84 True % 3.62/3.84 Clause #142 (by clausification #[141]): ∀ (a : Iota), % 3.62/3.84 Eq % 3.62/3.84 (∀ (B C D L M : Iota), % 3.62/3.84 And % 3.62/3.84 (And % 3.62/3.84 (And % 3.62/3.84 (And % 3.62/3.84 (And % 3.62/3.84 (And (And (left_apart_point (skS.0 0 a) L) (left_apart_point (skS.0 0 a) M)) % 3.62/3.84 (left_apart_point B (reverse_line L))) % 3.62/3.84 (left_apart_point B (reverse_line M))) % 3.62/3.84 (left_apart_point C L)) % 3.62/3.84 (left_apart_point C (reverse_line M))) % 3.62/3.84 (left_apart_point D (reverse_line L))) % 3.62/3.84 (left_apart_point D M) → % 3.62/3.84 convergent_lines L M) % 3.62/3.84 False % 3.62/3.84 Clause #143 (by clausification #[142]): ∀ (a a_1 : Iota), % 3.62/3.84 Eq % 3.62/3.84 (Not % 3.62/3.84 (∀ (C D L M : Iota), % 3.62/3.84 And % 3.62/3.84 (And % 3.62/3.84 (And % 3.62/3.84 (And % 3.62/3.84 (And % 3.62/3.84 (And (And (left_apart_point (skS.0 0 a) L) (left_apart_point (skS.0 0 a) M)) % 3.62/3.84 (left_apart_point (skS.0 1 a a_1) (reverse_line L))) % 3.62/3.84 (left_apart_point (skS.0 1 a a_1) (reverse_line M))) % 3.62/3.84 (left_apart_point C L)) % 3.62/3.84 (left_apart_point C (reverse_line M))) % 3.62/3.84 (left_apart_point D (reverse_line L))) % 3.62/3.84 (left_apart_point D M) → % 3.62/3.84 convergent_lines L M)) % 3.62/3.84 True % 3.62/3.84 Clause #144 (by clausification #[143]): ∀ (a a_1 : Iota), % 3.62/3.84 Eq % 3.62/3.84 (∀ (C D L M : Iota), % 3.62/3.84 And % 3.62/3.84 (And % 3.62/3.84 (And % 3.62/3.84 (And % 3.62/3.84 (And % 3.62/3.84 (And (And (left_apart_point (skS.0 0 a) L) (left_apart_point (skS.0 0 a) M)) % 3.62/3.84 (left_apart_point (skS.0 1 a a_1) (reverse_line L))) % 3.62/3.84 (left_apart_point (skS.0 1 a a_1) (reverse_line M))) % 3.62/3.84 (left_apart_point C L)) % 3.70/3.86 (left_apart_point C (reverse_line M))) % 3.70/3.86 (left_apart_point D (reverse_line L))) % 3.70/3.86 (left_apart_point D M) → % 3.70/3.86 convergent_lines L M) % 3.70/3.86 False % 3.70/3.86 Clause #145 (by clausification #[144]): ∀ (a a_1 a_2 : Iota), % 3.70/3.86 Eq % 3.70/3.86 (Not % 3.70/3.86 (∀ (D L M : Iota), % 3.70/3.86 And % 3.70/3.86 (And % 3.70/3.86 (And % 3.70/3.86 (And % 3.70/3.86 (And % 3.70/3.86 (And (And (left_apart_point (skS.0 0 a) L) (left_apart_point (skS.0 0 a) M)) % 3.70/3.86 (left_apart_point (skS.0 1 a a_1) (reverse_line L))) % 3.70/3.86 (left_apart_point (skS.0 1 a a_1) (reverse_line M))) % 3.70/3.86 (left_apart_point (skS.0 2 a a_1 a_2) L)) % 3.70/3.86 (left_apart_point (skS.0 2 a a_1 a_2) (reverse_line M))) % 3.70/3.86 (left_apart_point D (reverse_line L))) % 3.70/3.86 (left_apart_point D M) → % 3.70/3.86 convergent_lines L M)) % 3.70/3.86 True % 3.70/3.86 Clause #146 (by clausification #[145]): ∀ (a a_1 a_2 : Iota), % 3.70/3.86 Eq % 3.70/3.86 (∀ (D L M : Iota), % 3.70/3.86 And % 3.70/3.86 (And % 3.70/3.86 (And % 3.70/3.86 (And % 3.70/3.86 (And % 3.70/3.86 (And (And (left_apart_point (skS.0 0 a) L) (left_apart_point (skS.0 0 a) M)) % 3.70/3.86 (left_apart_point (skS.0 1 a a_1) (reverse_line L))) % 3.70/3.86 (left_apart_point (skS.0 1 a a_1) (reverse_line M))) % 3.70/3.86 (left_apart_point (skS.0 2 a a_1 a_2) L)) % 3.70/3.86 (left_apart_point (skS.0 2 a a_1 a_2) (reverse_line M))) % 3.70/3.86 (left_apart_point D (reverse_line L))) % 3.70/3.86 (left_apart_point D M) → % 3.70/3.86 convergent_lines L M) % 3.70/3.86 False % 3.70/3.86 Clause #147 (by clausification #[146]): ∀ (a a_1 a_2 a_3 : Iota), % 3.70/3.86 Eq % 3.70/3.86 (Not % 3.70/3.86 (∀ (L M : Iota), % 3.70/3.86 And % 3.70/3.86 (And % 3.70/3.86 (And % 3.70/3.86 (And % 3.70/3.86 (And % 3.70/3.86 (And (And (left_apart_point (skS.0 0 a) L) (left_apart_point (skS.0 0 a) M)) % 3.70/3.86 (left_apart_point (skS.0 1 a a_1) (reverse_line L))) % 3.70/3.86 (left_apart_point (skS.0 1 a a_1) (reverse_line M))) % 3.70/3.86 (left_apart_point (skS.0 2 a a_1 a_2) L)) % 3.70/3.86 (left_apart_point (skS.0 2 a a_1 a_2) (reverse_line M))) % 3.70/3.86 (left_apart_point (skS.0 3 a a_1 a_2 a_3) (reverse_line L))) % 3.70/3.86 (left_apart_point (skS.0 3 a a_1 a_2 a_3) M) → % 3.70/3.86 convergent_lines L M)) % 3.70/3.86 True % 3.70/3.86 Clause #148 (by clausification #[147]): ∀ (a a_1 a_2 a_3 : Iota), % 3.70/3.86 Eq % 3.70/3.86 (∀ (L M : Iota), % 3.70/3.86 And % 3.70/3.86 (And % 3.70/3.86 (And % 3.70/3.86 (And % 3.70/3.86 (And % 3.70/3.86 (And (And (left_apart_point (skS.0 0 a) L) (left_apart_point (skS.0 0 a) M)) % 3.70/3.86 (left_apart_point (skS.0 1 a a_1) (reverse_line L))) % 3.70/3.86 (left_apart_point (skS.0 1 a a_1) (reverse_line M))) % 3.70/3.86 (left_apart_point (skS.0 2 a a_1 a_2) L)) % 3.70/3.86 (left_apart_point (skS.0 2 a a_1 a_2) (reverse_line M))) % 3.70/3.86 (left_apart_point (skS.0 3 a a_1 a_2 a_3) (reverse_line L))) % 3.70/3.86 (left_apart_point (skS.0 3 a a_1 a_2 a_3) M) → % 3.70/3.86 convergent_lines L M) % 3.70/3.86 False % 3.70/3.86 Clause #149 (by clausification #[148]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 3.70/3.86 Eq % 3.70/3.86 (Not % 3.70/3.86 (∀ (M : Iota), % 3.70/3.86 And % 3.70/3.86 (And % 3.70/3.86 (And % 3.70/3.86 (And % 3.70/3.86 (And % 3.70/3.86 (And % 3.70/3.86 (And (left_apart_point (skS.0 0 a) (skS.0 4 a a_1 a_2 a_3 a_4)) (left_apart_point (skS.0 0 a) M)) % 3.70/3.86 (left_apart_point (skS.0 1 a a_1) (reverse_line (skS.0 4 a a_1 a_2 a_3 a_4)))) % 3.70/3.86 (left_apart_point (skS.0 1 a a_1) (reverse_line M))) % 3.70/3.86 (left_apart_point (skS.0 2 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.70/3.86 (left_apart_point (skS.0 2 a a_1 a_2) (reverse_line M))) % 3.70/3.86 (left_apart_point (skS.0 3 a a_1 a_2 a_3) (reverse_line (skS.0 4 a a_1 a_2 a_3 a_4)))) % 3.70/3.86 (left_apart_point (skS.0 3 a a_1 a_2 a_3) M) → % 3.70/3.86 convergent_lines (skS.0 4 a a_1 a_2 a_3 a_4) M)) % 3.70/3.86 True % 3.70/3.86 Clause #150 (by clausification #[149]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 3.70/3.86 Eq % 3.70/3.86 (∀ (M : Iota), % 3.70/3.86 And % 3.70/3.86 (And % 3.72/3.88 (And % 3.72/3.88 (And % 3.72/3.88 (And % 3.72/3.88 (And (And (left_apart_point (skS.0 0 a) (skS.0 4 a a_1 a_2 a_3 a_4)) (left_apart_point (skS.0 0 a) M)) % 3.72/3.88 (left_apart_point (skS.0 1 a a_1) (reverse_line (skS.0 4 a a_1 a_2 a_3 a_4)))) % 3.72/3.88 (left_apart_point (skS.0 1 a a_1) (reverse_line M))) % 3.72/3.88 (left_apart_point (skS.0 2 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.72/3.88 (left_apart_point (skS.0 2 a a_1 a_2) (reverse_line M))) % 3.72/3.88 (left_apart_point (skS.0 3 a a_1 a_2 a_3) (reverse_line (skS.0 4 a a_1 a_2 a_3 a_4)))) % 3.72/3.88 (left_apart_point (skS.0 3 a a_1 a_2 a_3) M) → % 3.72/3.88 convergent_lines (skS.0 4 a a_1 a_2 a_3 a_4) M) % 3.72/3.88 False % 3.72/3.88 Clause #151 (by clausification #[150]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 3.72/3.88 Eq % 3.72/3.88 (Not % 3.72/3.88 (And % 3.72/3.88 (And % 3.72/3.88 (And % 3.72/3.88 (And % 3.72/3.88 (And % 3.72/3.88 (And % 3.72/3.88 (And (left_apart_point (skS.0 0 a) (skS.0 4 a a_1 a_2 a_3 a_4)) % 3.72/3.88 (left_apart_point (skS.0 0 a) (skS.0 5 a a_1 a_2 a_3 a_4 a_5))) % 3.72/3.88 (left_apart_point (skS.0 1 a a_1) (reverse_line (skS.0 4 a a_1 a_2 a_3 a_4)))) % 3.72/3.88 (left_apart_point (skS.0 1 a a_1) (reverse_line (skS.0 5 a a_1 a_2 a_3 a_4 a_5)))) % 3.72/3.88 (left_apart_point (skS.0 2 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.72/3.88 (left_apart_point (skS.0 2 a a_1 a_2) (reverse_line (skS.0 5 a a_1 a_2 a_3 a_4 a_5)))) % 3.72/3.88 (left_apart_point (skS.0 3 a a_1 a_2 a_3) (reverse_line (skS.0 4 a a_1 a_2 a_3 a_4)))) % 3.72/3.88 (left_apart_point (skS.0 3 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2 a_3 a_4 a_5)) → % 3.72/3.88 convergent_lines (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 5 a a_1 a_2 a_3 a_4 a_5))) % 3.72/3.88 True % 3.72/3.88 Clause #152 (by clausification #[151]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 3.72/3.88 Eq % 3.72/3.88 (And % 3.72/3.88 (And % 3.72/3.88 (And % 3.72/3.88 (And % 3.72/3.88 (And % 3.72/3.88 (And % 3.72/3.88 (And (left_apart_point (skS.0 0 a) (skS.0 4 a a_1 a_2 a_3 a_4)) % 3.72/3.88 (left_apart_point (skS.0 0 a) (skS.0 5 a a_1 a_2 a_3 a_4 a_5))) % 3.72/3.88 (left_apart_point (skS.0 1 a a_1) (reverse_line (skS.0 4 a a_1 a_2 a_3 a_4)))) % 3.72/3.88 (left_apart_point (skS.0 1 a a_1) (reverse_line (skS.0 5 a a_1 a_2 a_3 a_4 a_5)))) % 3.72/3.88 (left_apart_point (skS.0 2 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.72/3.88 (left_apart_point (skS.0 2 a a_1 a_2) (reverse_line (skS.0 5 a a_1 a_2 a_3 a_4 a_5)))) % 3.72/3.88 (left_apart_point (skS.0 3 a a_1 a_2 a_3) (reverse_line (skS.0 4 a a_1 a_2 a_3 a_4)))) % 3.72/3.88 (left_apart_point (skS.0 3 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2 a_3 a_4 a_5)) → % 3.72/3.88 convergent_lines (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 5 a a_1 a_2 a_3 a_4 a_5)) % 3.72/3.88 False % 3.72/3.88 Clause #153 (by clausification #[152]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 3.72/3.88 Eq % 3.72/3.88 (And % 3.72/3.88 (And % 3.72/3.88 (And % 3.72/3.88 (And % 3.72/3.88 (And % 3.72/3.88 (And % 3.72/3.88 (And (left_apart_point (skS.0 0 a) (skS.0 4 a a_1 a_2 a_3 a_4)) % 3.72/3.88 (left_apart_point (skS.0 0 a) (skS.0 5 a a_1 a_2 a_3 a_4 a_5))) % 3.72/3.88 (left_apart_point (skS.0 1 a a_1) (reverse_line (skS.0 4 a a_1 a_2 a_3 a_4)))) % 3.72/3.88 (left_apart_point (skS.0 1 a a_1) (reverse_line (skS.0 5 a a_1 a_2 a_3 a_4 a_5)))) % 3.72/3.88 (left_apart_point (skS.0 2 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.72/3.88 (left_apart_point (skS.0 2 a a_1 a_2) (reverse_line (skS.0 5 a a_1 a_2 a_3 a_4 a_5)))) % 3.72/3.88 (left_apart_point (skS.0 3 a a_1 a_2 a_3) (reverse_line (skS.0 4 a a_1 a_2 a_3 a_4)))) % 3.72/3.88 (left_apart_point (skS.0 3 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2 a_3 a_4 a_5))) % 3.72/3.88 True % 3.72/3.88 Clause #155 (by clausification #[153]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), Eq (left_apart_point (skS.0 3 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2 a_3 a_4 a_5)) True % 3.72/3.88 Clause #157 (by superposition #[155, 83]): Eq True False % 3.72/3.88 Clause #158 (by clausification #[157]): False % 3.72/3.88 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------