%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO580+1 : TPTP v9.2.0. Released v7.5.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n025.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 07:48:43 PM UTC 2025 % Result : Theorem 10.46s 10.64s % Output : Proof 10.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GEO580+1 : TPTP v9.2.0. Released v7.5.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n025.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 11:27:38 EDT 2025 % 0.13/0.34 % CPUTime : % 10.46/10.64 SZS status Theorem for theBenchmark.p % 10.46/10.64 SZS output start Proof for theBenchmark.p % 10.46/10.64 Clause #0 (by assumption #[]): Eq (∀ (A B C : Iota), coll A B C → coll A C B) True % 10.46/10.64 Clause #1 (by assumption #[]): Eq (∀ (A B C : Iota), coll A B C → coll B A C) True % 10.46/10.64 Clause #2 (by assumption #[]): Eq (∀ (A B C D : Iota), And (coll A B C) (coll A B D) → coll C D A) True % 10.46/10.64 Clause #3 (by assumption #[]): Eq (∀ (A B C D : Iota), para A B C D → para A B D C) True % 10.46/10.64 Clause #4 (by assumption #[]): Eq (∀ (A B C D : Iota), para A B C D → para C D A B) True % 10.46/10.64 Clause #10 (by assumption #[]): Eq (∀ (A B M : Iota), midp M B A → midp M A B) True % 10.46/10.64 Clause #14 (by assumption #[]): Eq (∀ (A B C D : Iota), cyclic A B C D → cyclic A C B D) True % 10.46/10.64 Clause #16 (by assumption #[]): Eq (∀ (A B C D E : Iota), And (cyclic A B C D) (cyclic A B C E) → cyclic B C D E) True % 10.46/10.64 Clause #17 (by assumption #[]): Eq (∀ (A B C D P Q U V : Iota), eqangle A B C D P Q U V → eqangle B A C D P Q U V) True % 10.46/10.64 Clause #18 (by assumption #[]): Eq (∀ (A B C D P Q U V : Iota), eqangle A B C D P Q U V → eqangle C D A B U V P Q) True % 10.46/10.64 Clause #19 (by assumption #[]): Eq (∀ (A B C D P Q U V : Iota), eqangle A B C D P Q U V → eqangle P Q U V A B C D) True % 10.46/10.64 Clause #20 (by assumption #[]): Eq (∀ (A B C D P Q U V : Iota), eqangle A B C D P Q U V → eqangle A B P Q C D U V) True % 10.46/10.64 Clause #38 (by assumption #[]): Eq (∀ (A B C D P Q : Iota), eqangle A B P Q C D P Q → para A B C D) True % 10.46/10.64 Clause #39 (by assumption #[]): Eq (∀ (A B C D P Q : Iota), para A B C D → eqangle A B P Q C D P Q) True % 10.46/10.64 Clause #42 (by assumption #[]): Eq (∀ (A B P Q : Iota), And (eqangle P A P B Q A Q B) (coll P Q B) → cyclic A B P Q) True % 10.46/10.64 Clause #63 (by assumption #[]): Eq (∀ (A B C D M : Iota), And (midp M A B) (midp M C D) → para A C B D) True % 10.46/10.64 Clause #66 (by assumption #[]): Eq (∀ (A B C : Iota), para A B A C → coll A B C) True % 10.46/10.64 Clause #94 (by assumption #[]): Eq % 10.46/10.64 (Not % 10.46/10.64 (∀ (A B C D E F G H : Iota), % 10.46/10.64 And % 10.46/10.64 (And % 10.46/10.64 (And % 10.46/10.64 (And % 10.46/10.64 (And % 10.46/10.64 (And % 10.46/10.64 (And (And (And (eqangle D A A B D A A C) (eqangle D B B C D B B A)) (eqangle D C C A D C C B)) % 10.46/10.64 (perp E A B C)) % 10.46/10.64 (coll E B C)) % 10.46/10.64 (perp F B A D)) % 10.46/10.64 (coll F A D)) % 10.46/10.64 (perp G C A D)) % 10.46/10.64 (coll G A D)) % 10.46/10.64 (midp H C B) → % 10.46/10.64 cyclic E F G H)) % 10.46/10.64 True % 10.46/10.64 Clause #104 (by clausification #[66]): ∀ (a : Iota), Eq (∀ (B C : Iota), para a B a C → coll a B C) True % 10.46/10.64 Clause #105 (by clausification #[104]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), para a a_1 a C → coll a a_1 C) True % 10.46/10.64 Clause #106 (by clausification #[105]): ∀ (a a_1 a_2 : Iota), Eq (para a a_1 a a_2 → coll a a_1 a_2) True % 10.46/10.64 Clause #107 (by clausification #[106]): ∀ (a a_1 a_2 : Iota), Or (Eq (para a a_1 a a_2) False) (Eq (coll a a_1 a_2) True) % 10.46/10.64 Clause #108 (by clausification #[10]): ∀ (a : Iota), Eq (∀ (B M : Iota), midp M B a → midp M a B) True % 10.46/10.64 Clause #109 (by clausification #[108]): ∀ (a a_1 : Iota), Eq (∀ (M : Iota), midp M a a_1 → midp M a_1 a) True % 10.46/10.64 Clause #110 (by clausification #[109]): ∀ (a a_1 a_2 : Iota), Eq (midp a a_1 a_2 → midp a a_2 a_1) True % 10.46/10.64 Clause #111 (by clausification #[110]): ∀ (a a_1 a_2 : Iota), Or (Eq (midp a a_1 a_2) False) (Eq (midp a a_2 a_1) True) % 10.46/10.64 Clause #112 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B C : Iota), coll a B C → coll B a C) True % 10.46/10.64 Clause #113 (by clausification #[112]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), coll a a_1 C → coll a_1 a C) True % 10.46/10.64 Clause #114 (by clausification #[113]): ∀ (a a_1 a_2 : Iota), Eq (coll a a_1 a_2 → coll a_1 a a_2) True % 10.46/10.64 Clause #115 (by clausification #[114]): ∀ (a a_1 a_2 : Iota), Or (Eq (coll a a_1 a_2) False) (Eq (coll a_1 a a_2) True) % 10.46/10.64 Clause #116 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (B C : Iota), coll a B C → coll a C B) True % 10.46/10.64 Clause #117 (by clausification #[116]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), coll a a_1 C → coll a C a_1) True % 10.46/10.64 Clause #118 (by clausification #[117]): ∀ (a a_1 a_2 : Iota), Eq (coll a a_1 a_2 → coll a a_2 a_1) True % 10.46/10.67 Clause #119 (by clausification #[118]): ∀ (a a_1 a_2 : Iota), Or (Eq (coll a a_1 a_2) False) (Eq (coll a a_2 a_1) True) % 10.46/10.67 Clause #120 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B C D : Iota), And (coll a B C) (coll a B D) → coll C D a) True % 10.46/10.67 Clause #121 (by clausification #[120]): ∀ (a a_1 : Iota), Eq (∀ (C D : Iota), And (coll a a_1 C) (coll a a_1 D) → coll C D a) True % 10.46/10.67 Clause #122 (by clausification #[121]): ∀ (a a_1 a_2 : Iota), Eq (∀ (D : Iota), And (coll a a_1 a_2) (coll a a_1 D) → coll a_2 D a) True % 10.46/10.67 Clause #123 (by clausification #[122]): ∀ (a a_1 a_2 a_3 : Iota), Eq (And (coll a a_1 a_2) (coll a a_1 a_3) → coll a_2 a_3 a) True % 10.46/10.67 Clause #124 (by clausification #[123]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (And (coll a a_1 a_2) (coll a a_1 a_3)) False) (Eq (coll a_2 a_3 a) True) % 10.46/10.67 Clause #125 (by clausification #[124]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (coll a a_1 a_2) True) (Or (Eq (coll a_2 a_3 a) False) (Eq (coll a_2 a_3 a_1) False)) % 10.46/10.67 Clause #152 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (B C D : Iota), para a B C D → para a B D C) True % 10.46/10.67 Clause #153 (by clausification #[152]): ∀ (a a_1 : Iota), Eq (∀ (C D : Iota), para a a_1 C D → para a a_1 D C) True % 10.46/10.67 Clause #154 (by clausification #[153]): ∀ (a a_1 a_2 : Iota), Eq (∀ (D : Iota), para a a_1 a_2 D → para a a_1 D a_2) True % 10.46/10.67 Clause #155 (by clausification #[154]): ∀ (a a_1 a_2 a_3 : Iota), Eq (para a a_1 a_2 a_3 → para a a_1 a_3 a_2) True % 10.46/10.67 Clause #156 (by clausification #[155]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (para a a_1 a_2 a_3) False) (Eq (para a a_1 a_3 a_2) True) % 10.46/10.67 Clause #157 (by clausification #[42]): ∀ (a : Iota), Eq (∀ (B P Q : Iota), And (eqangle P a P B Q a Q B) (coll P Q B) → cyclic a B P Q) True % 10.46/10.67 Clause #158 (by clausification #[157]): ∀ (a a_1 : Iota), Eq (∀ (P Q : Iota), And (eqangle P a P a_1 Q a Q a_1) (coll P Q a_1) → cyclic a a_1 P Q) True % 10.46/10.67 Clause #159 (by clausification #[158]): ∀ (a a_1 a_2 : Iota), Eq (∀ (Q : Iota), And (eqangle a a_1 a a_2 Q a_1 Q a_2) (coll a Q a_2) → cyclic a_1 a_2 a Q) True % 10.46/10.67 Clause #160 (by clausification #[159]): ∀ (a a_1 a_2 a_3 : Iota), Eq (And (eqangle a a_1 a a_2 a_3 a_1 a_3 a_2) (coll a a_3 a_2) → cyclic a_1 a_2 a a_3) True % 10.46/10.67 Clause #161 (by clausification #[160]): ∀ (a a_1 a_2 a_3 : Iota), % 10.46/10.67 Or (Eq (And (eqangle a a_1 a a_2 a_3 a_1 a_3 a_2) (coll a a_3 a_2)) False) (Eq (cyclic a_1 a_2 a a_3) True) % 10.46/10.67 Clause #162 (by clausification #[161]): ∀ (a a_1 a_2 a_3 : Iota), % 10.46/10.67 Or (Eq (cyclic a a_1 a_2 a_3) True) % 10.46/10.67 (Or (Eq (eqangle a_2 a a_2 a_1 a_3 a a_3 a_1) False) (Eq (coll a_2 a_3 a_1) False)) % 10.46/10.67 Clause #175 (by clausification #[14]): ∀ (a : Iota), Eq (∀ (B C D : Iota), cyclic a B C D → cyclic a C B D) True % 10.46/10.67 Clause #176 (by clausification #[175]): ∀ (a a_1 : Iota), Eq (∀ (C D : Iota), cyclic a a_1 C D → cyclic a C a_1 D) True % 10.46/10.67 Clause #177 (by clausification #[176]): ∀ (a a_1 a_2 : Iota), Eq (∀ (D : Iota), cyclic a a_1 a_2 D → cyclic a a_2 a_1 D) True % 10.46/10.67 Clause #178 (by clausification #[177]): ∀ (a a_1 a_2 a_3 : Iota), Eq (cyclic a a_1 a_2 a_3 → cyclic a a_2 a_1 a_3) True % 10.46/10.67 Clause #179 (by clausification #[178]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cyclic a a_1 a_2 a_3) False) (Eq (cyclic a a_2 a_1 a_3) True) % 10.46/10.67 Clause #185 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B C D : Iota), para a B C D → para C D a B) True % 10.46/10.67 Clause #186 (by clausification #[185]): ∀ (a a_1 : Iota), Eq (∀ (C D : Iota), para a a_1 C D → para C D a a_1) True % 10.46/10.67 Clause #187 (by clausification #[186]): ∀ (a a_1 a_2 : Iota), Eq (∀ (D : Iota), para a a_1 a_2 D → para a_2 D a a_1) True % 10.46/10.67 Clause #188 (by clausification #[187]): ∀ (a a_1 a_2 a_3 : Iota), Eq (para a a_1 a_2 a_3 → para a_2 a_3 a a_1) True % 10.46/10.67 Clause #189 (by clausification #[188]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (para a a_1 a_2 a_3) False) (Eq (para a_2 a_3 a a_1) True) % 10.46/10.67 Clause #277 (by clausification #[63]): ∀ (a : Iota), Eq (∀ (B C D M : Iota), And (midp M a B) (midp M C D) → para a C B D) True % 10.46/10.67 Clause #278 (by clausification #[277]): ∀ (a a_1 : Iota), Eq (∀ (C D M : Iota), And (midp M a a_1) (midp M C D) → para a C a_1 D) True % 10.53/10.69 Clause #279 (by clausification #[278]): ∀ (a a_1 a_2 : Iota), Eq (∀ (D M : Iota), And (midp M a a_1) (midp M a_2 D) → para a a_2 a_1 D) True % 10.53/10.69 Clause #280 (by clausification #[279]): ∀ (a a_1 a_2 a_3 : Iota), Eq (∀ (M : Iota), And (midp M a a_1) (midp M a_2 a_3) → para a a_2 a_1 a_3) True % 10.53/10.69 Clause #281 (by clausification #[280]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (And (midp a a_1 a_2) (midp a a_3 a_4) → para a_1 a_3 a_2 a_4) True % 10.53/10.69 Clause #282 (by clausification #[281]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq (And (midp a a_1 a_2) (midp a a_3 a_4)) False) (Eq (para a_1 a_3 a_2 a_4) True) % 10.53/10.69 Clause #283 (by clausification #[282]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.53/10.69 Or (Eq (para a a_1 a_2 a_3) True) (Or (Eq (midp a_4 a a_2) False) (Eq (midp a_4 a_1 a_3) False)) % 10.53/10.69 Clause #284 (by clausification #[16]): ∀ (a : Iota), Eq (∀ (B C D E : Iota), And (cyclic a B C D) (cyclic a B C E) → cyclic B C D E) True % 10.53/10.69 Clause #285 (by clausification #[284]): ∀ (a a_1 : Iota), Eq (∀ (C D E : Iota), And (cyclic a a_1 C D) (cyclic a a_1 C E) → cyclic a_1 C D E) True % 10.53/10.69 Clause #286 (by clausification #[285]): ∀ (a a_1 a_2 : Iota), Eq (∀ (D E : Iota), And (cyclic a a_1 a_2 D) (cyclic a a_1 a_2 E) → cyclic a_1 a_2 D E) True % 10.53/10.69 Clause #287 (by clausification #[286]): ∀ (a a_1 a_2 a_3 : Iota), Eq (∀ (E : Iota), And (cyclic a a_1 a_2 a_3) (cyclic a a_1 a_2 E) → cyclic a_1 a_2 a_3 E) True % 10.53/10.69 Clause #288 (by clausification #[287]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (And (cyclic a a_1 a_2 a_3) (cyclic a a_1 a_2 a_4) → cyclic a_1 a_2 a_3 a_4) True % 10.53/10.69 Clause #289 (by clausification #[288]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.53/10.69 Or (Eq (And (cyclic a a_1 a_2 a_3) (cyclic a a_1 a_2 a_4)) False) (Eq (cyclic a_1 a_2 a_3 a_4) True) % 10.53/10.69 Clause #290 (by clausification #[289]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.53/10.69 Or (Eq (cyclic a a_1 a_2 a_3) True) (Or (Eq (cyclic a_4 a a_1 a_2) False) (Eq (cyclic a_4 a a_1 a_3) False)) % 10.53/10.69 Clause #344 (by clausification #[17]): ∀ (a : Iota), Eq (∀ (B C D P Q U V : Iota), eqangle a B C D P Q U V → eqangle B a C D P Q U V) True % 10.53/10.69 Clause #345 (by clausification #[344]): ∀ (a a_1 : Iota), Eq (∀ (C D P Q U V : Iota), eqangle a a_1 C D P Q U V → eqangle a_1 a C D P Q U V) True % 10.53/10.69 Clause #346 (by clausification #[345]): ∀ (a a_1 a_2 : Iota), Eq (∀ (D P Q U V : Iota), eqangle a a_1 a_2 D P Q U V → eqangle a_1 a a_2 D P Q U V) True % 10.53/10.69 Clause #347 (by clausification #[346]): ∀ (a a_1 a_2 a_3 : Iota), Eq (∀ (P Q U V : Iota), eqangle a a_1 a_2 a_3 P Q U V → eqangle a_1 a a_2 a_3 P Q U V) True % 10.53/10.69 Clause #348 (by clausification #[347]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.53/10.69 Eq (∀ (Q U V : Iota), eqangle a a_1 a_2 a_3 a_4 Q U V → eqangle a_1 a a_2 a_3 a_4 Q U V) True % 10.53/10.69 Clause #349 (by clausification #[348]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 10.53/10.69 Eq (∀ (U V : Iota), eqangle a a_1 a_2 a_3 a_4 a_5 U V → eqangle a_1 a a_2 a_3 a_4 a_5 U V) True % 10.53/10.69 Clause #350 (by clausification #[349]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 10.53/10.69 Eq (∀ (V : Iota), eqangle a a_1 a_2 a_3 a_4 a_5 a_6 V → eqangle a_1 a a_2 a_3 a_4 a_5 a_6 V) True % 10.53/10.69 Clause #351 (by clausification #[350]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 10.53/10.69 Eq (eqangle a a_1 a_2 a_3 a_4 a_5 a_6 a_7 → eqangle a_1 a a_2 a_3 a_4 a_5 a_6 a_7) True % 10.53/10.69 Clause #352 (by clausification #[351]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 10.53/10.69 Or (Eq (eqangle a a_1 a_2 a_3 a_4 a_5 a_6 a_7) False) (Eq (eqangle a_1 a a_2 a_3 a_4 a_5 a_6 a_7) True) % 10.53/10.69 Clause #353 (by clausification #[38]): ∀ (a : Iota), Eq (∀ (B C D P Q : Iota), eqangle a B P Q C D P Q → para a B C D) True % 10.53/10.69 Clause #354 (by clausification #[353]): ∀ (a a_1 : Iota), Eq (∀ (C D P Q : Iota), eqangle a a_1 P Q C D P Q → para a a_1 C D) True % 10.53/10.69 Clause #355 (by clausification #[354]): ∀ (a a_1 a_2 : Iota), Eq (∀ (D P Q : Iota), eqangle a a_1 P Q a_2 D P Q → para a a_1 a_2 D) True % 10.53/10.69 Clause #356 (by clausification #[355]): ∀ (a a_1 a_2 a_3 : Iota), Eq (∀ (P Q : Iota), eqangle a a_1 P Q a_2 a_3 P Q → para a a_1 a_2 a_3) True % 10.53/10.69 Clause #357 (by clausification #[356]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (∀ (Q : Iota), eqangle a a_1 a_2 Q a_3 a_4 a_2 Q → para a a_1 a_3 a_4) True % 10.53/10.71 Clause #358 (by clausification #[357]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), Eq (eqangle a a_1 a_2 a_3 a_4 a_5 a_2 a_3 → para a a_1 a_4 a_5) True % 10.53/10.71 Clause #359 (by clausification #[358]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), Or (Eq (eqangle a a_1 a_2 a_3 a_4 a_5 a_2 a_3) False) (Eq (para a a_1 a_4 a_5) True) % 10.53/10.71 Clause #389 (by clausification #[18]): ∀ (a : Iota), Eq (∀ (B C D P Q U V : Iota), eqangle a B C D P Q U V → eqangle C D a B U V P Q) True % 10.53/10.71 Clause #390 (by clausification #[389]): ∀ (a a_1 : Iota), Eq (∀ (C D P Q U V : Iota), eqangle a a_1 C D P Q U V → eqangle C D a a_1 U V P Q) True % 10.53/10.71 Clause #391 (by clausification #[390]): ∀ (a a_1 a_2 : Iota), Eq (∀ (D P Q U V : Iota), eqangle a a_1 a_2 D P Q U V → eqangle a_2 D a a_1 U V P Q) True % 10.53/10.71 Clause #392 (by clausification #[391]): ∀ (a a_1 a_2 a_3 : Iota), Eq (∀ (P Q U V : Iota), eqangle a a_1 a_2 a_3 P Q U V → eqangle a_2 a_3 a a_1 U V P Q) True % 10.53/10.71 Clause #393 (by clausification #[392]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.53/10.71 Eq (∀ (Q U V : Iota), eqangle a a_1 a_2 a_3 a_4 Q U V → eqangle a_2 a_3 a a_1 U V a_4 Q) True % 10.53/10.71 Clause #394 (by clausification #[393]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 10.53/10.71 Eq (∀ (U V : Iota), eqangle a a_1 a_2 a_3 a_4 a_5 U V → eqangle a_2 a_3 a a_1 U V a_4 a_5) True % 10.53/10.71 Clause #395 (by clausification #[394]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 10.53/10.71 Eq (∀ (V : Iota), eqangle a a_1 a_2 a_3 a_4 a_5 a_6 V → eqangle a_2 a_3 a a_1 a_6 V a_4 a_5) True % 10.53/10.71 Clause #396 (by clausification #[395]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 10.53/10.71 Eq (eqangle a a_1 a_2 a_3 a_4 a_5 a_6 a_7 → eqangle a_2 a_3 a a_1 a_6 a_7 a_4 a_5) True % 10.53/10.71 Clause #397 (by clausification #[396]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 10.53/10.71 Or (Eq (eqangle a a_1 a_2 a_3 a_4 a_5 a_6 a_7) False) (Eq (eqangle a_2 a_3 a a_1 a_6 a_7 a_4 a_5) True) % 10.53/10.71 Clause #433 (by clausification #[19]): ∀ (a : Iota), Eq (∀ (B C D P Q U V : Iota), eqangle a B C D P Q U V → eqangle P Q U V a B C D) True % 10.53/10.71 Clause #434 (by clausification #[433]): ∀ (a a_1 : Iota), Eq (∀ (C D P Q U V : Iota), eqangle a a_1 C D P Q U V → eqangle P Q U V a a_1 C D) True % 10.53/10.71 Clause #435 (by clausification #[434]): ∀ (a a_1 a_2 : Iota), Eq (∀ (D P Q U V : Iota), eqangle a a_1 a_2 D P Q U V → eqangle P Q U V a a_1 a_2 D) True % 10.53/10.71 Clause #436 (by clausification #[435]): ∀ (a a_1 a_2 a_3 : Iota), Eq (∀ (P Q U V : Iota), eqangle a a_1 a_2 a_3 P Q U V → eqangle P Q U V a a_1 a_2 a_3) True % 10.53/10.71 Clause #437 (by clausification #[436]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.53/10.71 Eq (∀ (Q U V : Iota), eqangle a a_1 a_2 a_3 a_4 Q U V → eqangle a_4 Q U V a a_1 a_2 a_3) True % 10.53/10.71 Clause #438 (by clausification #[437]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 10.53/10.71 Eq (∀ (U V : Iota), eqangle a a_1 a_2 a_3 a_4 a_5 U V → eqangle a_4 a_5 U V a a_1 a_2 a_3) True % 10.53/10.71 Clause #439 (by clausification #[438]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 10.53/10.71 Eq (∀ (V : Iota), eqangle a a_1 a_2 a_3 a_4 a_5 a_6 V → eqangle a_4 a_5 a_6 V a a_1 a_2 a_3) True % 10.53/10.71 Clause #440 (by clausification #[439]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 10.53/10.71 Eq (eqangle a a_1 a_2 a_3 a_4 a_5 a_6 a_7 → eqangle a_4 a_5 a_6 a_7 a a_1 a_2 a_3) True % 10.53/10.71 Clause #441 (by clausification #[440]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 10.53/10.71 Or (Eq (eqangle a a_1 a_2 a_3 a_4 a_5 a_6 a_7) False) (Eq (eqangle a_4 a_5 a_6 a_7 a a_1 a_2 a_3) True) % 10.53/10.71 Clause #488 (by clausification #[20]): ∀ (a : Iota), Eq (∀ (B C D P Q U V : Iota), eqangle a B C D P Q U V → eqangle a B P Q C D U V) True % 10.53/10.71 Clause #489 (by clausification #[488]): ∀ (a a_1 : Iota), Eq (∀ (C D P Q U V : Iota), eqangle a a_1 C D P Q U V → eqangle a a_1 P Q C D U V) True % 10.53/10.71 Clause #490 (by clausification #[489]): ∀ (a a_1 a_2 : Iota), Eq (∀ (D P Q U V : Iota), eqangle a a_1 a_2 D P Q U V → eqangle a a_1 P Q a_2 D U V) True % 10.53/10.71 Clause #491 (by clausification #[490]): ∀ (a a_1 a_2 a_3 : Iota), Eq (∀ (P Q U V : Iota), eqangle a a_1 a_2 a_3 P Q U V → eqangle a a_1 P Q a_2 a_3 U V) True % 10.53/10.74 Clause #492 (by clausification #[491]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.53/10.74 Eq (∀ (Q U V : Iota), eqangle a a_1 a_2 a_3 a_4 Q U V → eqangle a a_1 a_4 Q a_2 a_3 U V) True % 10.53/10.74 Clause #493 (by clausification #[492]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 10.53/10.74 Eq (∀ (U V : Iota), eqangle a a_1 a_2 a_3 a_4 a_5 U V → eqangle a a_1 a_4 a_5 a_2 a_3 U V) True % 10.53/10.74 Clause #494 (by clausification #[493]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 10.53/10.74 Eq (∀ (V : Iota), eqangle a a_1 a_2 a_3 a_4 a_5 a_6 V → eqangle a a_1 a_4 a_5 a_2 a_3 a_6 V) True % 10.53/10.74 Clause #495 (by clausification #[494]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 10.53/10.74 Eq (eqangle a a_1 a_2 a_3 a_4 a_5 a_6 a_7 → eqangle a a_1 a_4 a_5 a_2 a_3 a_6 a_7) True % 10.53/10.74 Clause #496 (by clausification #[495]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 10.53/10.74 Or (Eq (eqangle a a_1 a_2 a_3 a_4 a_5 a_6 a_7) False) (Eq (eqangle a a_1 a_4 a_5 a_2 a_3 a_6 a_7) True) % 10.53/10.74 Clause #547 (by clausification #[94]): Eq % 10.53/10.74 (∀ (A B C D E F G H : Iota), % 10.53/10.74 And % 10.53/10.74 (And % 10.53/10.74 (And % 10.53/10.74 (And % 10.53/10.74 (And % 10.53/10.74 (And % 10.53/10.74 (And (And (And (eqangle D A A B D A A C) (eqangle D B B C D B B A)) (eqangle D C C A D C C B)) % 10.53/10.74 (perp E A B C)) % 10.53/10.74 (coll E B C)) % 10.53/10.74 (perp F B A D)) % 10.53/10.74 (coll F A D)) % 10.53/10.74 (perp G C A D)) % 10.53/10.74 (coll G A D)) % 10.53/10.74 (midp H C B) → % 10.53/10.74 cyclic E F G H) % 10.53/10.74 False % 10.53/10.74 Clause #548 (by clausification #[547]): ∀ (a : Iota), % 10.53/10.74 Eq % 10.53/10.74 (Not % 10.53/10.74 (∀ (B C D E F G H : Iota), % 10.53/10.74 And % 10.53/10.74 (And % 10.53/10.74 (And % 10.53/10.74 (And % 10.53/10.74 (And % 10.53/10.74 (And % 10.53/10.74 (And % 10.53/10.74 (And % 10.53/10.74 (And (eqangle D (skS.0 4 a) (skS.0 4 a) B D (skS.0 4 a) (skS.0 4 a) C) % 10.53/10.74 (eqangle D B B C D B B (skS.0 4 a))) % 10.53/10.74 (eqangle D C C (skS.0 4 a) D C C B)) % 10.53/10.74 (perp E (skS.0 4 a) B C)) % 10.53/10.74 (coll E B C)) % 10.53/10.74 (perp F B (skS.0 4 a) D)) % 10.53/10.74 (coll F (skS.0 4 a) D)) % 10.53/10.74 (perp G C (skS.0 4 a) D)) % 10.53/10.74 (coll G (skS.0 4 a) D)) % 10.53/10.74 (midp H C B) → % 10.53/10.74 cyclic E F G H)) % 10.53/10.74 True % 10.53/10.74 Clause #549 (by clausification #[548]): ∀ (a : Iota), % 10.53/10.74 Eq % 10.53/10.74 (∀ (B C D E F G H : Iota), % 10.53/10.74 And % 10.53/10.74 (And % 10.53/10.74 (And % 10.53/10.74 (And % 10.53/10.74 (And % 10.53/10.74 (And % 10.53/10.74 (And % 10.53/10.74 (And % 10.53/10.74 (And (eqangle D (skS.0 4 a) (skS.0 4 a) B D (skS.0 4 a) (skS.0 4 a) C) % 10.53/10.74 (eqangle D B B C D B B (skS.0 4 a))) % 10.53/10.74 (eqangle D C C (skS.0 4 a) D C C B)) % 10.53/10.74 (perp E (skS.0 4 a) B C)) % 10.53/10.74 (coll E B C)) % 10.53/10.74 (perp F B (skS.0 4 a) D)) % 10.53/10.74 (coll F (skS.0 4 a) D)) % 10.53/10.74 (perp G C (skS.0 4 a) D)) % 10.53/10.74 (coll G (skS.0 4 a) D)) % 10.53/10.74 (midp H C B) → % 10.53/10.74 cyclic E F G H) % 10.53/10.74 False % 10.53/10.74 Clause #550 (by clausification #[549]): ∀ (a a_1 : Iota), % 10.53/10.74 Eq % 10.53/10.74 (Not % 10.53/10.74 (∀ (C D E F G H : Iota), % 10.53/10.74 And % 10.53/10.74 (And % 10.53/10.74 (And % 10.53/10.74 (And % 10.53/10.74 (And % 10.53/10.74 (And % 10.53/10.74 (And % 10.53/10.74 (And % 10.53/10.74 (And (eqangle D (skS.0 4 a) (skS.0 4 a) (skS.0 5 a a_1) D (skS.0 4 a) (skS.0 4 a) C) % 10.53/10.74 (eqangle D (skS.0 5 a a_1) (skS.0 5 a a_1) C D (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 4 a))) % 10.53/10.74 (eqangle D C C (skS.0 4 a) D C C (skS.0 5 a a_1))) % 10.53/10.74 (perp E (skS.0 4 a) (skS.0 5 a a_1) C)) % 10.53/10.74 (coll E (skS.0 5 a a_1) C)) % 10.53/10.74 (perp F (skS.0 5 a a_1) (skS.0 4 a) D)) % 10.53/10.74 (coll F (skS.0 4 a) D)) % 10.53/10.74 (perp G C (skS.0 4 a) D)) % 10.53/10.74 (coll G (skS.0 4 a) D)) % 10.53/10.74 (midp H C (skS.0 5 a a_1)) → % 10.53/10.74 cyclic E F G H)) % 10.53/10.74 True % 10.53/10.74 Clause #551 (by clausification #[550]): ∀ (a a_1 : Iota), % 10.53/10.74 Eq % 10.53/10.74 (∀ (C D E F G H : Iota), % 10.53/10.74 And % 10.53/10.74 (And % 10.61/10.76 (And % 10.61/10.76 (And % 10.61/10.76 (And % 10.61/10.76 (And % 10.61/10.76 (And % 10.61/10.76 (And % 10.61/10.76 (And (eqangle D (skS.0 4 a) (skS.0 4 a) (skS.0 5 a a_1) D (skS.0 4 a) (skS.0 4 a) C) % 10.61/10.76 (eqangle D (skS.0 5 a a_1) (skS.0 5 a a_1) C D (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 4 a))) % 10.61/10.76 (eqangle D C C (skS.0 4 a) D C C (skS.0 5 a a_1))) % 10.61/10.76 (perp E (skS.0 4 a) (skS.0 5 a a_1) C)) % 10.61/10.76 (coll E (skS.0 5 a a_1) C)) % 10.61/10.76 (perp F (skS.0 5 a a_1) (skS.0 4 a) D)) % 10.61/10.76 (coll F (skS.0 4 a) D)) % 10.61/10.76 (perp G C (skS.0 4 a) D)) % 10.61/10.76 (coll G (skS.0 4 a) D)) % 10.61/10.76 (midp H C (skS.0 5 a a_1)) → % 10.61/10.76 cyclic E F G H) % 10.61/10.76 False % 10.61/10.76 Clause #552 (by clausification #[551]): ∀ (a a_1 a_2 : Iota), % 10.61/10.76 Eq % 10.61/10.76 (Not % 10.61/10.76 (∀ (D E F G H : Iota), % 10.61/10.76 And % 10.61/10.76 (And % 10.61/10.76 (And % 10.61/10.76 (And % 10.61/10.76 (And % 10.61/10.76 (And % 10.61/10.76 (And % 10.61/10.76 (And % 10.61/10.76 (And % 10.61/10.76 (eqangle D (skS.0 4 a) (skS.0 4 a) (skS.0 5 a a_1) D (skS.0 4 a) (skS.0 4 a) % 10.61/10.76 (skS.0 6 a a_1 a_2)) % 10.61/10.76 (eqangle D (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) D (skS.0 5 a a_1) % 10.61/10.76 (skS.0 5 a a_1) (skS.0 4 a))) % 10.61/10.76 (eqangle D (skS.0 6 a a_1 a_2) (skS.0 6 a a_1 a_2) (skS.0 4 a) D (skS.0 6 a a_1 a_2) % 10.61/10.76 (skS.0 6 a a_1 a_2) (skS.0 5 a a_1))) % 10.61/10.76 (perp E (skS.0 4 a) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2))) % 10.61/10.76 (coll E (skS.0 5 a a_1) (skS.0 6 a a_1 a_2))) % 10.61/10.76 (perp F (skS.0 5 a a_1) (skS.0 4 a) D)) % 10.61/10.76 (coll F (skS.0 4 a) D)) % 10.61/10.76 (perp G (skS.0 6 a a_1 a_2) (skS.0 4 a) D)) % 10.61/10.76 (coll G (skS.0 4 a) D)) % 10.61/10.76 (midp H (skS.0 6 a a_1 a_2) (skS.0 5 a a_1)) → % 10.61/10.76 cyclic E F G H)) % 10.61/10.76 True % 10.61/10.76 Clause #553 (by clausification #[552]): ∀ (a a_1 a_2 : Iota), % 10.61/10.76 Eq % 10.61/10.76 (∀ (D E F G H : Iota), % 10.61/10.76 And % 10.61/10.76 (And % 10.61/10.76 (And % 10.61/10.76 (And % 10.61/10.76 (And % 10.61/10.76 (And % 10.61/10.76 (And % 10.61/10.76 (And % 10.61/10.76 (And % 10.61/10.76 (eqangle D (skS.0 4 a) (skS.0 4 a) (skS.0 5 a a_1) D (skS.0 4 a) (skS.0 4 a) % 10.61/10.76 (skS.0 6 a a_1 a_2)) % 10.61/10.76 (eqangle D (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) D (skS.0 5 a a_1) % 10.61/10.76 (skS.0 5 a a_1) (skS.0 4 a))) % 10.61/10.76 (eqangle D (skS.0 6 a a_1 a_2) (skS.0 6 a a_1 a_2) (skS.0 4 a) D (skS.0 6 a a_1 a_2) % 10.61/10.76 (skS.0 6 a a_1 a_2) (skS.0 5 a a_1))) % 10.61/10.76 (perp E (skS.0 4 a) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2))) % 10.61/10.76 (coll E (skS.0 5 a a_1) (skS.0 6 a a_1 a_2))) % 10.61/10.76 (perp F (skS.0 5 a a_1) (skS.0 4 a) D)) % 10.61/10.76 (coll F (skS.0 4 a) D)) % 10.61/10.76 (perp G (skS.0 6 a a_1 a_2) (skS.0 4 a) D)) % 10.61/10.76 (coll G (skS.0 4 a) D)) % 10.61/10.76 (midp H (skS.0 6 a a_1 a_2) (skS.0 5 a a_1)) → % 10.61/10.76 cyclic E F G H) % 10.61/10.76 False % 10.61/10.76 Clause #554 (by clausification #[553]): ∀ (a a_1 a_2 a_3 : Iota), % 10.61/10.76 Eq % 10.61/10.76 (Not % 10.61/10.76 (∀ (E F G H : Iota), % 10.61/10.76 And % 10.61/10.76 (And % 10.61/10.76 (And % 10.61/10.76 (And % 10.61/10.76 (And % 10.61/10.76 (And % 10.61/10.76 (And % 10.61/10.76 (And % 10.61/10.76 (And % 10.61/10.76 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 4 a) (skS.0 4 a) (skS.0 5 a a_1) % 10.61/10.76 (skS.0 7 a a_1 a_2 a_3) (skS.0 4 a) (skS.0 4 a) (skS.0 6 a a_1 a_2)) % 10.61/10.76 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) % 10.61/10.76 (skS.0 7 a a_1 a_2 a_3) (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 4 a))) % 10.61/10.76 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2) (skS.0 6 a a_1 a_2) (skS.0 4 a) % 10.63/10.79 (skS.0 7 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2) (skS.0 6 a a_1 a_2) (skS.0 5 a a_1))) % 10.63/10.79 (perp E (skS.0 4 a) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2))) % 10.63/10.79 (coll E (skS.0 5 a a_1) (skS.0 6 a a_1 a_2))) % 10.63/10.79 (perp F (skS.0 5 a a_1) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.63/10.79 (coll F (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.63/10.79 (perp G (skS.0 6 a a_1 a_2) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.63/10.79 (coll G (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.63/10.79 (midp H (skS.0 6 a a_1 a_2) (skS.0 5 a a_1)) → % 10.63/10.79 cyclic E F G H)) % 10.63/10.79 True % 10.63/10.79 Clause #555 (by clausification #[554]): ∀ (a a_1 a_2 a_3 : Iota), % 10.63/10.79 Eq % 10.63/10.79 (∀ (E F G H : Iota), % 10.63/10.79 And % 10.63/10.79 (And % 10.63/10.79 (And % 10.63/10.79 (And % 10.63/10.79 (And % 10.63/10.79 (And % 10.63/10.79 (And % 10.63/10.79 (And % 10.63/10.79 (And % 10.63/10.79 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 4 a) (skS.0 4 a) (skS.0 5 a a_1) % 10.63/10.79 (skS.0 7 a a_1 a_2 a_3) (skS.0 4 a) (skS.0 4 a) (skS.0 6 a a_1 a_2)) % 10.63/10.79 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) % 10.63/10.79 (skS.0 7 a a_1 a_2 a_3) (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 4 a))) % 10.63/10.79 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2) (skS.0 6 a a_1 a_2) (skS.0 4 a) % 10.63/10.79 (skS.0 7 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2) (skS.0 6 a a_1 a_2) (skS.0 5 a a_1))) % 10.63/10.79 (perp E (skS.0 4 a) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2))) % 10.63/10.79 (coll E (skS.0 5 a a_1) (skS.0 6 a a_1 a_2))) % 10.63/10.79 (perp F (skS.0 5 a a_1) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.63/10.79 (coll F (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.63/10.79 (perp G (skS.0 6 a a_1 a_2) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.63/10.79 (coll G (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.63/10.79 (midp H (skS.0 6 a a_1 a_2) (skS.0 5 a a_1)) → % 10.63/10.79 cyclic E F G H) % 10.63/10.79 False % 10.63/10.79 Clause #556 (by clausification #[555]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.63/10.79 Eq % 10.63/10.79 (Not % 10.63/10.79 (∀ (F G H : Iota), % 10.63/10.79 And % 10.63/10.79 (And % 10.63/10.79 (And % 10.63/10.79 (And % 10.63/10.79 (And % 10.63/10.79 (And % 10.63/10.79 (And % 10.63/10.79 (And % 10.63/10.79 (And % 10.63/10.79 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 4 a) (skS.0 4 a) (skS.0 5 a a_1) % 10.63/10.79 (skS.0 7 a a_1 a_2 a_3) (skS.0 4 a) (skS.0 4 a) (skS.0 6 a a_1 a_2)) % 10.63/10.79 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) % 10.63/10.79 (skS.0 7 a a_1 a_2 a_3) (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 4 a))) % 10.63/10.79 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2) (skS.0 6 a a_1 a_2) (skS.0 4 a) % 10.63/10.79 (skS.0 7 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2) (skS.0 6 a a_1 a_2) (skS.0 5 a a_1))) % 10.63/10.79 (perp (skS.0 8 a a_1 a_2 a_3 a_4) (skS.0 4 a) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2))) % 10.63/10.79 (coll (skS.0 8 a a_1 a_2 a_3 a_4) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2))) % 10.63/10.79 (perp F (skS.0 5 a a_1) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.63/10.79 (coll F (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.63/10.79 (perp G (skS.0 6 a a_1 a_2) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.63/10.79 (coll G (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.63/10.79 (midp H (skS.0 6 a a_1 a_2) (skS.0 5 a a_1)) → % 10.63/10.79 cyclic (skS.0 8 a a_1 a_2 a_3 a_4) F G H)) % 10.63/10.79 True % 10.63/10.79 Clause #557 (by clausification #[556]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.63/10.79 Eq % 10.63/10.79 (∀ (F G H : Iota), % 10.63/10.79 And % 10.63/10.79 (And % 10.63/10.79 (And % 10.63/10.79 (And % 10.63/10.79 (And % 10.63/10.79 (And % 10.63/10.79 (And % 10.63/10.79 (And % 10.63/10.79 (And % 10.63/10.79 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 4 a) (skS.0 4 a) (skS.0 5 a a_1) % 10.63/10.79 (skS.0 7 a a_1 a_2 a_3) (skS.0 4 a) (skS.0 4 a) (skS.0 6 a a_1 a_2)) % 10.63/10.80 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) % 10.63/10.80 (skS.0 7 a a_1 a_2 a_3) (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 4 a))) % 10.63/10.80 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2) (skS.0 6 a a_1 a_2) (skS.0 4 a) % 10.63/10.80 (skS.0 7 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2) (skS.0 6 a a_1 a_2) (skS.0 5 a a_1))) % 10.63/10.80 (perp (skS.0 8 a a_1 a_2 a_3 a_4) (skS.0 4 a) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2))) % 10.63/10.80 (coll (skS.0 8 a a_1 a_2 a_3 a_4) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2))) % 10.63/10.80 (perp F (skS.0 5 a a_1) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.63/10.80 (coll F (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.63/10.80 (perp G (skS.0 6 a a_1 a_2) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.63/10.80 (coll G (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.63/10.80 (midp H (skS.0 6 a a_1 a_2) (skS.0 5 a a_1)) → % 10.63/10.80 cyclic (skS.0 8 a a_1 a_2 a_3 a_4) F G H) % 10.63/10.80 False % 10.63/10.80 Clause #558 (by clausification #[557]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 10.63/10.80 Eq % 10.63/10.80 (Not % 10.63/10.80 (∀ (G H : Iota), % 10.63/10.80 And % 10.63/10.80 (And % 10.63/10.80 (And % 10.63/10.80 (And % 10.63/10.80 (And % 10.63/10.80 (And % 10.63/10.80 (And % 10.63/10.80 (And % 10.63/10.80 (And % 10.63/10.80 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 4 a) (skS.0 4 a) (skS.0 5 a a_1) % 10.63/10.80 (skS.0 7 a a_1 a_2 a_3) (skS.0 4 a) (skS.0 4 a) (skS.0 6 a a_1 a_2)) % 10.63/10.80 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) % 10.63/10.80 (skS.0 7 a a_1 a_2 a_3) (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 4 a))) % 10.63/10.80 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2) (skS.0 6 a a_1 a_2) (skS.0 4 a) % 10.63/10.80 (skS.0 7 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2) (skS.0 6 a a_1 a_2) (skS.0 5 a a_1))) % 10.63/10.80 (perp (skS.0 8 a a_1 a_2 a_3 a_4) (skS.0 4 a) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2))) % 10.63/10.80 (coll (skS.0 8 a a_1 a_2 a_3 a_4) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2))) % 10.63/10.80 (perp (skS.0 9 a a_1 a_2 a_3 a_4 a_5) (skS.0 5 a a_1) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.63/10.80 (coll (skS.0 9 a a_1 a_2 a_3 a_4 a_5) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.63/10.80 (perp G (skS.0 6 a a_1 a_2) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.63/10.80 (coll G (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.63/10.80 (midp H (skS.0 6 a a_1 a_2) (skS.0 5 a a_1)) → % 10.63/10.80 cyclic (skS.0 8 a a_1 a_2 a_3 a_4) (skS.0 9 a a_1 a_2 a_3 a_4 a_5) G H)) % 10.63/10.80 True % 10.63/10.80 Clause #559 (by clausification #[558]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 10.63/10.80 Eq % 10.63/10.80 (∀ (G H : Iota), % 10.63/10.80 And % 10.63/10.80 (And % 10.63/10.80 (And % 10.63/10.80 (And % 10.63/10.80 (And % 10.63/10.80 (And % 10.63/10.80 (And % 10.63/10.80 (And % 10.63/10.80 (And % 10.63/10.80 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 4 a) (skS.0 4 a) (skS.0 5 a a_1) % 10.63/10.80 (skS.0 7 a a_1 a_2 a_3) (skS.0 4 a) (skS.0 4 a) (skS.0 6 a a_1 a_2)) % 10.63/10.80 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) % 10.63/10.80 (skS.0 7 a a_1 a_2 a_3) (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 4 a))) % 10.63/10.80 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2) (skS.0 6 a a_1 a_2) (skS.0 4 a) % 10.63/10.80 (skS.0 7 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2) (skS.0 6 a a_1 a_2) (skS.0 5 a a_1))) % 10.63/10.80 (perp (skS.0 8 a a_1 a_2 a_3 a_4) (skS.0 4 a) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2))) % 10.63/10.80 (coll (skS.0 8 a a_1 a_2 a_3 a_4) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2))) % 10.63/10.80 (perp (skS.0 9 a a_1 a_2 a_3 a_4 a_5) (skS.0 5 a a_1) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.63/10.80 (coll (skS.0 9 a a_1 a_2 a_3 a_4 a_5) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.63/10.80 (perp G (skS.0 6 a a_1 a_2) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.67/10.83 (coll G (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.67/10.83 (midp H (skS.0 6 a a_1 a_2) (skS.0 5 a a_1)) → % 10.67/10.83 cyclic (skS.0 8 a a_1 a_2 a_3 a_4) (skS.0 9 a a_1 a_2 a_3 a_4 a_5) G H) % 10.67/10.83 False % 10.67/10.83 Clause #560 (by clausification #[559]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 10.67/10.83 Eq % 10.67/10.83 (Not % 10.67/10.83 (∀ (H : Iota), % 10.67/10.83 And % 10.67/10.83 (And % 10.67/10.83 (And % 10.67/10.83 (And % 10.67/10.83 (And % 10.67/10.83 (And % 10.67/10.83 (And % 10.67/10.83 (And % 10.67/10.83 (And % 10.67/10.83 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 4 a) (skS.0 4 a) (skS.0 5 a a_1) % 10.67/10.83 (skS.0 7 a a_1 a_2 a_3) (skS.0 4 a) (skS.0 4 a) (skS.0 6 a a_1 a_2)) % 10.67/10.83 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) % 10.67/10.83 (skS.0 7 a a_1 a_2 a_3) (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 4 a))) % 10.67/10.83 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2) (skS.0 6 a a_1 a_2) (skS.0 4 a) % 10.67/10.83 (skS.0 7 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2) (skS.0 6 a a_1 a_2) (skS.0 5 a a_1))) % 10.67/10.83 (perp (skS.0 8 a a_1 a_2 a_3 a_4) (skS.0 4 a) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2))) % 10.67/10.83 (coll (skS.0 8 a a_1 a_2 a_3 a_4) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2))) % 10.67/10.83 (perp (skS.0 9 a a_1 a_2 a_3 a_4 a_5) (skS.0 5 a a_1) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.67/10.83 (coll (skS.0 9 a a_1 a_2 a_3 a_4 a_5) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.67/10.83 (perp (skS.0 10 a a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 6 a a_1 a_2) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.67/10.83 (coll (skS.0 10 a a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.67/10.83 (midp H (skS.0 6 a a_1 a_2) (skS.0 5 a a_1)) → % 10.67/10.83 cyclic (skS.0 8 a a_1 a_2 a_3 a_4) (skS.0 9 a a_1 a_2 a_3 a_4 a_5) (skS.0 10 a a_1 a_2 a_3 a_4 a_5 a_6) H)) % 10.67/10.83 True % 10.67/10.83 Clause #561 (by clausification #[560]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 10.67/10.83 Eq % 10.67/10.83 (∀ (H : Iota), % 10.67/10.83 And % 10.67/10.83 (And % 10.67/10.83 (And % 10.67/10.83 (And % 10.67/10.83 (And % 10.67/10.83 (And % 10.67/10.83 (And % 10.67/10.83 (And % 10.67/10.83 (And % 10.67/10.83 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 4 a) (skS.0 4 a) (skS.0 5 a a_1) % 10.67/10.83 (skS.0 7 a a_1 a_2 a_3) (skS.0 4 a) (skS.0 4 a) (skS.0 6 a a_1 a_2)) % 10.67/10.83 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) % 10.67/10.83 (skS.0 7 a a_1 a_2 a_3) (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 4 a))) % 10.67/10.83 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2) (skS.0 6 a a_1 a_2) (skS.0 4 a) % 10.67/10.83 (skS.0 7 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2) (skS.0 6 a a_1 a_2) (skS.0 5 a a_1))) % 10.67/10.83 (perp (skS.0 8 a a_1 a_2 a_3 a_4) (skS.0 4 a) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2))) % 10.67/10.83 (coll (skS.0 8 a a_1 a_2 a_3 a_4) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2))) % 10.67/10.83 (perp (skS.0 9 a a_1 a_2 a_3 a_4 a_5) (skS.0 5 a a_1) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.67/10.83 (coll (skS.0 9 a a_1 a_2 a_3 a_4 a_5) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.67/10.83 (perp (skS.0 10 a a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 6 a a_1 a_2) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.67/10.83 (coll (skS.0 10 a a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.67/10.83 (midp H (skS.0 6 a a_1 a_2) (skS.0 5 a a_1)) → % 10.67/10.83 cyclic (skS.0 8 a a_1 a_2 a_3 a_4) (skS.0 9 a a_1 a_2 a_3 a_4 a_5) (skS.0 10 a a_1 a_2 a_3 a_4 a_5 a_6) H) % 10.67/10.83 False % 10.67/10.83 Clause #562 (by clausification #[561]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 10.67/10.83 Eq % 10.67/10.83 (Not % 10.67/10.83 (And % 10.67/10.83 (And % 10.67/10.83 (And % 10.67/10.83 (And % 10.67/10.83 (And % 10.67/10.83 (And % 10.67/10.83 (And % 10.67/10.83 (And % 10.67/10.83 (And % 10.67/10.83 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 4 a) (skS.0 4 a) (skS.0 5 a a_1) % 10.67/10.83 (skS.0 7 a a_1 a_2 a_3) (skS.0 4 a) (skS.0 4 a) (skS.0 6 a a_1 a_2)) % 10.69/10.85 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) % 10.69/10.85 (skS.0 7 a a_1 a_2 a_3) (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 4 a))) % 10.69/10.85 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2) (skS.0 6 a a_1 a_2) (skS.0 4 a) % 10.69/10.85 (skS.0 7 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2) (skS.0 6 a a_1 a_2) (skS.0 5 a a_1))) % 10.69/10.85 (perp (skS.0 8 a a_1 a_2 a_3 a_4) (skS.0 4 a) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2))) % 10.69/10.85 (coll (skS.0 8 a a_1 a_2 a_3 a_4) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2))) % 10.69/10.85 (perp (skS.0 9 a a_1 a_2 a_3 a_4 a_5) (skS.0 5 a a_1) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.69/10.85 (coll (skS.0 9 a a_1 a_2 a_3 a_4 a_5) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.69/10.85 (perp (skS.0 10 a a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 6 a a_1 a_2) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.69/10.85 (coll (skS.0 10 a a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.69/10.85 (midp (skS.0 11 a a_1 a_2 a_3 a_4 a_5 a_6 a_7) (skS.0 6 a a_1 a_2) (skS.0 5 a a_1)) → % 10.69/10.85 cyclic (skS.0 8 a a_1 a_2 a_3 a_4) (skS.0 9 a a_1 a_2 a_3 a_4 a_5) (skS.0 10 a a_1 a_2 a_3 a_4 a_5 a_6) % 10.69/10.85 (skS.0 11 a a_1 a_2 a_3 a_4 a_5 a_6 a_7))) % 10.69/10.85 True % 10.69/10.85 Clause #563 (by clausification #[562]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 10.69/10.85 Eq % 10.69/10.85 (And % 10.69/10.85 (And % 10.69/10.85 (And % 10.69/10.85 (And % 10.69/10.85 (And % 10.69/10.85 (And % 10.69/10.85 (And % 10.69/10.85 (And % 10.69/10.85 (And % 10.69/10.85 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 4 a) (skS.0 4 a) (skS.0 5 a a_1) (skS.0 7 a a_1 a_2 a_3) % 10.69/10.85 (skS.0 4 a) (skS.0 4 a) (skS.0 6 a a_1 a_2)) % 10.69/10.85 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) % 10.69/10.85 (skS.0 7 a a_1 a_2 a_3) (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 4 a))) % 10.69/10.85 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2) (skS.0 6 a a_1 a_2) (skS.0 4 a) % 10.69/10.85 (skS.0 7 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2) (skS.0 6 a a_1 a_2) (skS.0 5 a a_1))) % 10.69/10.85 (perp (skS.0 8 a a_1 a_2 a_3 a_4) (skS.0 4 a) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2))) % 10.69/10.85 (coll (skS.0 8 a a_1 a_2 a_3 a_4) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2))) % 10.69/10.85 (perp (skS.0 9 a a_1 a_2 a_3 a_4 a_5) (skS.0 5 a a_1) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.69/10.85 (coll (skS.0 9 a a_1 a_2 a_3 a_4 a_5) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.69/10.85 (perp (skS.0 10 a a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 6 a a_1 a_2) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.69/10.85 (coll (skS.0 10 a a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.69/10.85 (midp (skS.0 11 a a_1 a_2 a_3 a_4 a_5 a_6 a_7) (skS.0 6 a a_1 a_2) (skS.0 5 a a_1)) → % 10.69/10.85 cyclic (skS.0 8 a a_1 a_2 a_3 a_4) (skS.0 9 a a_1 a_2 a_3 a_4 a_5) (skS.0 10 a a_1 a_2 a_3 a_4 a_5 a_6) % 10.69/10.85 (skS.0 11 a a_1 a_2 a_3 a_4 a_5 a_6 a_7)) % 10.69/10.85 False % 10.69/10.85 Clause #564 (by clausification #[563]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 10.69/10.85 Eq % 10.69/10.85 (And % 10.69/10.85 (And % 10.69/10.85 (And % 10.69/10.85 (And % 10.69/10.85 (And % 10.69/10.85 (And % 10.69/10.85 (And % 10.69/10.85 (And % 10.69/10.85 (And % 10.69/10.85 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 4 a) (skS.0 4 a) (skS.0 5 a a_1) (skS.0 7 a a_1 a_2 a_3) % 10.69/10.85 (skS.0 4 a) (skS.0 4 a) (skS.0 6 a a_1 a_2)) % 10.69/10.85 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) % 10.69/10.85 (skS.0 7 a a_1 a_2 a_3) (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 4 a))) % 10.69/10.85 (eqangle (skS.0 7 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2) (skS.0 6 a a_1 a_2) (skS.0 4 a) % 10.69/10.85 (skS.0 7 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2) (skS.0 6 a a_1 a_2) (skS.0 5 a a_1))) % 10.69/10.85 (perp (skS.0 8 a a_1 a_2 a_3 a_4) (skS.0 4 a) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2))) % 10.69/10.85 (coll (skS.0 8 a a_1 a_2 a_3 a_4) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2))) % 10.69/10.87 (perp (skS.0 9 a a_1 a_2 a_3 a_4 a_5) (skS.0 5 a a_1) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.69/10.87 (coll (skS.0 9 a a_1 a_2 a_3 a_4 a_5) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.69/10.87 (perp (skS.0 10 a a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 6 a a_1 a_2) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.69/10.87 (coll (skS.0 10 a a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 4 a) (skS.0 7 a a_1 a_2 a_3))) % 10.69/10.87 (midp (skS.0 11 a a_1 a_2 a_3 a_4 a_5 a_6 a_7) (skS.0 6 a a_1 a_2) (skS.0 5 a a_1))) % 10.69/10.87 True % 10.69/10.87 Clause #565 (by clausification #[563]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 10.69/10.87 Eq % 10.69/10.87 (cyclic (skS.0 8 a a_1 a_2 a_3 a_4) (skS.0 9 a a_1 a_2 a_3 a_4 a_5) (skS.0 10 a a_1 a_2 a_3 a_4 a_5 a_6) % 10.69/10.87 (skS.0 11 a a_1 a_2 a_3 a_4 a_5 a_6 a_7)) % 10.69/10.87 False % 10.69/10.87 Clause #566 (by clausification #[564]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 10.69/10.87 Eq (midp (skS.0 11 a a_1 a_2 a_3 a_4 a_5 a_6 a_7) (skS.0 6 a a_1 a_2) (skS.0 5 a a_1)) True % 10.69/10.87 Clause #569 (by superposition #[566, 111]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 10.69/10.88 Or (Eq True False) (Eq (midp (skS.0 11 a a_1 a_2 a_3 a_4 a_5 a_6 a_7) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2)) True) % 10.69/10.88 Clause #642 (by clausification #[39]): ∀ (a : Iota), Eq (∀ (B C D P Q : Iota), para a B C D → eqangle a B P Q C D P Q) True % 10.69/10.88 Clause #643 (by clausification #[642]): ∀ (a a_1 : Iota), Eq (∀ (C D P Q : Iota), para a a_1 C D → eqangle a a_1 P Q C D P Q) True % 10.69/10.88 Clause #644 (by clausification #[643]): ∀ (a a_1 a_2 : Iota), Eq (∀ (D P Q : Iota), para a a_1 a_2 D → eqangle a a_1 P Q a_2 D P Q) True % 10.69/10.88 Clause #645 (by clausification #[644]): ∀ (a a_1 a_2 a_3 : Iota), Eq (∀ (P Q : Iota), para a a_1 a_2 a_3 → eqangle a a_1 P Q a_2 a_3 P Q) True % 10.69/10.88 Clause #646 (by clausification #[645]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (∀ (Q : Iota), para a a_1 a_2 a_3 → eqangle a a_1 a_4 Q a_2 a_3 a_4 Q) True % 10.69/10.88 Clause #647 (by clausification #[646]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), Eq (para a a_1 a_2 a_3 → eqangle a a_1 a_4 a_5 a_2 a_3 a_4 a_5) True % 10.69/10.88 Clause #648 (by clausification #[647]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), Or (Eq (para a a_1 a_2 a_3) False) (Eq (eqangle a a_1 a_4 a_5 a_2 a_3 a_4 a_5) True) % 10.69/10.88 Clause #851 (by clausification #[569]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 10.69/10.88 Eq (midp (skS.0 11 a a_1 a_2 a_3 a_4 a_5 a_6 a_7) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2)) True % 10.69/10.88 Clause #856 (by superposition #[851, 283]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 : Iota), % 10.69/10.88 Or (Eq (para (skS.0 5 a a_1) a_2 (skS.0 6 a a_1 a_3) a_4) True) % 10.69/10.88 (Or (Eq True False) (Eq (midp (skS.0 11 a a_1 a_3 a_5 a_6 a_7 a_8 a_9) a_2 a_4) False)) % 10.69/10.88 Clause #998 (by clausification #[856]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 : Iota), % 10.69/10.88 Or (Eq (para (skS.0 5 a a_1) a_2 (skS.0 6 a a_1 a_3) a_4) True) % 10.69/10.88 (Eq (midp (skS.0 11 a a_1 a_3 a_5 a_6 a_7 a_8 a_9) a_2 a_4) False) % 10.69/10.88 Clause #999 (by superposition #[998, 566]): ∀ (a a_1 a_2 : Iota), % 10.69/10.88 Or (Eq (para (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) (skS.0 6 a a_1 a_2) (skS.0 5 a a_1)) True) (Eq False True) % 10.69/10.88 Clause #1013 (by clausification #[999]): ∀ (a a_1 a_2 : Iota), Eq (para (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) (skS.0 6 a a_1 a_2) (skS.0 5 a a_1)) True % 10.69/10.88 Clause #1016 (by superposition #[1013, 189]): ∀ (a a_1 a_2 : Iota), % 10.69/10.88 Or (Eq True False) (Eq (para (skS.0 6 a a_1 a_2) (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2)) True) % 10.69/10.88 Clause #1021 (by clausification #[1016]): ∀ (a a_1 a_2 : Iota), Eq (para (skS.0 6 a a_1 a_2) (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2)) True % 10.69/10.88 Clause #1027 (by superposition #[1021, 648]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.69/10.88 Or (Eq True False) % 10.69/10.88 (Eq (eqangle (skS.0 6 a a_1 a_2) (skS.0 5 a a_1) a_3 a_4 (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) a_3 a_4) True) % 10.69/10.88 Clause #1248 (by clausification #[1027]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.69/10.88 Eq (eqangle (skS.0 6 a a_1 a_2) (skS.0 5 a a_1) a_3 a_4 (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) a_3 a_4) True % 10.69/10.88 Clause #1250 (by superposition #[1248, 496]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.69/10.88 Or (Eq True False) % 10.69/10.88 (Eq (eqangle (skS.0 6 a a_1 a_2) (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) a_3 a_4 a_3 a_4) True) % 10.69/10.90 Clause #1258 (by clausification #[1250]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.69/10.90 Eq (eqangle (skS.0 6 a a_1 a_2) (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) a_3 a_4 a_3 a_4) True % 10.69/10.90 Clause #1261 (by superposition #[1258, 441]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.69/10.90 Or (Eq True False) % 10.69/10.90 (Eq (eqangle a a_1 a a_1 (skS.0 6 a_2 a_3 a_4) (skS.0 5 a_2 a_3) (skS.0 5 a_2 a_3) (skS.0 6 a_2 a_3 a_4)) True) % 10.69/10.90 Clause #1266 (by clausification #[1261]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.69/10.90 Eq (eqangle a a_1 a a_1 (skS.0 6 a_2 a_3 a_4) (skS.0 5 a_2 a_3) (skS.0 5 a_2 a_3) (skS.0 6 a_2 a_3 a_4)) True % 10.69/10.90 Clause #1268 (by superposition #[1266, 397]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.69/10.90 Or (Eq True False) % 10.69/10.90 (Eq (eqangle a a_1 a a_1 (skS.0 5 a_2 a_3) (skS.0 6 a_2 a_3 a_4) (skS.0 6 a_2 a_3 a_4) (skS.0 5 a_2 a_3)) True) % 10.69/10.90 Clause #1273 (by clausification #[1268]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.69/10.90 Eq (eqangle a a_1 a a_1 (skS.0 5 a_2 a_3) (skS.0 6 a_2 a_3 a_4) (skS.0 6 a_2 a_3 a_4) (skS.0 5 a_2 a_3)) True % 10.69/10.90 Clause #1277 (by superposition #[1273, 496]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.69/10.90 Or (Eq True False) % 10.69/10.90 (Eq (eqangle a a_1 (skS.0 5 a_2 a_3) (skS.0 6 a_2 a_3 a_4) a a_1 (skS.0 6 a_2 a_3 a_4) (skS.0 5 a_2 a_3)) True) % 10.69/10.90 Clause #1280 (by clausification #[1277]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.69/10.90 Eq (eqangle a a_1 (skS.0 5 a_2 a_3) (skS.0 6 a_2 a_3 a_4) a a_1 (skS.0 6 a_2 a_3 a_4) (skS.0 5 a_2 a_3)) True % 10.69/10.90 Clause #1281 (by superposition #[1280, 352]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.69/10.90 Or (Eq True False) % 10.69/10.90 (Eq (eqangle a a_1 (skS.0 5 a_2 a_3) (skS.0 6 a_2 a_3 a_4) a_1 a (skS.0 6 a_2 a_3 a_4) (skS.0 5 a_2 a_3)) True) % 10.69/10.90 Clause #1288 (by clausification #[1281]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.69/10.90 Eq (eqangle a a_1 (skS.0 5 a_2 a_3) (skS.0 6 a_2 a_3 a_4) a_1 a (skS.0 6 a_2 a_3 a_4) (skS.0 5 a_2 a_3)) True % 10.69/10.90 Clause #1292 (by superposition #[1288, 441]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.69/10.90 Or (Eq True False) % 10.69/10.90 (Eq (eqangle a a_1 (skS.0 6 a_2 a_3 a_4) (skS.0 5 a_2 a_3) a_1 a (skS.0 5 a_2 a_3) (skS.0 6 a_2 a_3 a_4)) True) % 10.69/10.90 Clause #1297 (by clausification #[1292]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.69/10.90 Eq (eqangle a a_1 (skS.0 6 a_2 a_3 a_4) (skS.0 5 a_2 a_3) a_1 a (skS.0 5 a_2 a_3) (skS.0 6 a_2 a_3 a_4)) True % 10.69/10.90 Clause #1300 (by superposition #[1297, 397]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.69/10.90 Or (Eq True False) % 10.69/10.90 (Eq (eqangle (skS.0 6 a a_1 a_2) (skS.0 5 a a_1) a_3 a_4 (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) a_4 a_3) True) % 10.69/10.90 Clause #1305 (by clausification #[1300]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.69/10.90 Eq (eqangle (skS.0 6 a a_1 a_2) (skS.0 5 a a_1) a_3 a_4 (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) a_4 a_3) True % 10.69/10.90 Clause #1308 (by superposition #[1305, 496]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.69/10.90 Or (Eq True False) % 10.69/10.90 (Eq (eqangle (skS.0 6 a a_1 a_2) (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) a_3 a_4 a_4 a_3) True) % 10.69/10.90 Clause #1311 (by clausification #[1308]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.69/10.90 Eq (eqangle (skS.0 6 a a_1 a_2) (skS.0 5 a a_1) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) a_3 a_4 a_4 a_3) True % 10.69/10.90 Clause #1313 (by superposition #[1311, 397]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.69/10.90 Or (Eq True False) % 10.69/10.90 (Eq (eqangle (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) (skS.0 6 a a_1 a_2) (skS.0 5 a a_1) a_3 a_4 a_4 a_3) True) % 10.69/10.90 Clause #1318 (by clausification #[1313]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.69/10.90 Eq (eqangle (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) (skS.0 6 a a_1 a_2) (skS.0 5 a a_1) a_3 a_4 a_4 a_3) True % 10.69/10.90 Clause #1319 (by superposition #[1318, 352]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.69/10.90 Or (Eq True False) % 10.69/10.90 (Eq (eqangle (skS.0 6 a a_1 a_2) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) (skS.0 5 a a_1) a_3 a_4 a_4 a_3) True) % 10.69/10.90 Clause #1328 (by clausification #[1319]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.69/10.90 Eq (eqangle (skS.0 6 a a_1 a_2) (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) (skS.0 5 a a_1) a_3 a_4 a_4 a_3) True % 10.69/10.90 Clause #1335 (by superposition #[1328, 496]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.69/10.90 Or (Eq True False) % 10.69/10.90 (Eq (eqangle (skS.0 6 a a_1 a_2) (skS.0 5 a a_1) a_3 a_4 (skS.0 6 a a_1 a_2) (skS.0 5 a a_1) a_4 a_3) True) % 10.69/10.90 Clause #1340 (by clausification #[1335]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.69/10.90 Eq (eqangle (skS.0 6 a a_1 a_2) (skS.0 5 a a_1) a_3 a_4 (skS.0 6 a a_1 a_2) (skS.0 5 a a_1) a_4 a_3) True % 10.76/10.93 Clause #1345 (by superposition #[1340, 397]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.76/10.93 Or (Eq True False) % 10.76/10.93 (Eq (eqangle a a_1 (skS.0 6 a_2 a_3 a_4) (skS.0 5 a_2 a_3) a_1 a (skS.0 6 a_2 a_3 a_4) (skS.0 5 a_2 a_3)) True) % 10.76/10.93 Clause #1352 (by clausification #[1345]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 10.76/10.93 Eq (eqangle a a_1 (skS.0 6 a_2 a_3 a_4) (skS.0 5 a_2 a_3) a_1 a (skS.0 6 a_2 a_3 a_4) (skS.0 5 a_2 a_3)) True % 10.76/10.93 Clause #1357 (by superposition #[1352, 359]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (para a a_1 a_1 a) True) % 10.76/10.93 Clause #1365 (by clausification #[1357]): ∀ (a a_1 : Iota), Eq (para a a_1 a_1 a) True % 10.76/10.93 Clause #1368 (by superposition #[1365, 156]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (para a a_1 a a_1) True) % 10.76/10.93 Clause #1383 (by clausification #[1368]): ∀ (a a_1 : Iota), Eq (para a a_1 a a_1) True % 10.76/10.93 Clause #1384 (by superposition #[1383, 107]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (coll a a_1 a_1) True) % 10.76/10.93 Clause #1388 (by superposition #[1383, 648]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq True False) (Eq (eqangle a a_1 a_2 a_3 a a_1 a_2 a_3) True) % 10.76/10.93 Clause #1389 (by clausification #[1384]): ∀ (a a_1 : Iota), Eq (coll a a_1 a_1) True % 10.76/10.93 Clause #1391 (by superposition #[1389, 115]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (coll a a_1 a) True) % 10.76/10.93 Clause #1400 (by clausification #[1391]): ∀ (a a_1 : Iota), Eq (coll a a_1 a) True % 10.76/10.93 Clause #1402 (by superposition #[1400, 119]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (coll a a a_1) True) % 10.76/10.93 Clause #1411 (by clausification #[1402]): ∀ (a a_1 : Iota), Eq (coll a a a_1) True % 10.76/10.93 Clause #1413 (by superposition #[1411, 125]): ∀ (a a_1 a_2 : Iota), Or (Eq (coll a a_1 a_2) True) (Or (Eq True False) (Eq (coll a_2 a_2 a_1) False)) % 10.76/10.93 Clause #1427 (by clausification #[1413]): ∀ (a a_1 a_2 : Iota), Or (Eq (coll a a_1 a_2) True) (Eq (coll a_2 a_2 a_1) False) % 10.76/10.93 Clause #1430 (by superposition #[1427, 1411]): ∀ (a a_1 a_2 : Iota), Or (Eq (coll a a_1 a_2) True) (Eq False True) % 10.76/10.93 Clause #1431 (by clausification #[1430]): ∀ (a a_1 a_2 : Iota), Eq (coll a a_1 a_2) True % 10.76/10.93 Clause #1437 (by backward demodulation #[1431, 162]): ∀ (a a_1 a_2 a_3 : Iota), % 10.76/10.93 Or (Eq (cyclic a a_1 a_2 a_3) True) (Or (Eq (eqangle a_2 a a_2 a_1 a_3 a a_3 a_1) False) (Eq True False)) % 10.76/10.93 Clause #1463 (by clausification #[1388]): ∀ (a a_1 a_2 a_3 : Iota), Eq (eqangle a a_1 a_2 a_3 a a_1 a_2 a_3) True % 10.76/10.93 Clause #1466 (by superposition #[1463, 496]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq True False) (Eq (eqangle a a_1 a a_1 a_2 a_3 a_2 a_3) True) % 10.76/10.93 Clause #1468 (by clausification #[1466]): ∀ (a a_1 a_2 a_3 : Iota), Eq (eqangle a a_1 a a_1 a_2 a_3 a_2 a_3) True % 10.76/10.93 Clause #1555 (by clausification #[1437]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cyclic a a_1 a_2 a_3) True) (Eq (eqangle a_2 a a_2 a_1 a_3 a a_3 a_1) False) % 10.76/10.93 Clause #1557 (by superposition #[1555, 1468]): ∀ (a a_1 a_2 : Iota), Or (Eq (cyclic a a a_1 a_2) True) (Eq False True) % 10.76/10.93 Clause #1597 (by clausification #[1557]): ∀ (a a_1 a_2 : Iota), Eq (cyclic a a a_1 a_2) True % 10.76/10.93 Clause #1598 (by superposition #[1597, 179]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (cyclic a a_1 a a_2) True) % 10.76/10.93 Clause #1604 (by clausification #[1598]): ∀ (a a_1 a_2 : Iota), Eq (cyclic a a_1 a a_2) True % 10.76/10.93 Clause #1608 (by superposition #[1604, 290]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cyclic a a_1 a_2 a_3) True) (Or (Eq True False) (Eq (cyclic a_1 a a_1 a_3) False)) % 10.76/10.93 Clause #1867 (by clausification #[1608]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cyclic a a_1 a_2 a_3) True) (Eq (cyclic a_1 a a_1 a_3) False) % 10.76/10.93 Clause #1868 (by superposition #[1867, 1604]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cyclic a a_1 a_2 a_3) True) (Eq False True) % 10.76/10.93 Clause #1871 (by clausification #[1868]): ∀ (a a_1 a_2 a_3 : Iota), Eq (cyclic a a_1 a_2 a_3) True % 10.76/10.93 Clause #1880 (by superposition #[1871, 565]): Eq True False % 10.76/10.93 Clause #1882 (by clausification #[1880]): False % 10.76/10.93 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------