%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO567+1 : TPTP v9.2.0. Released v7.5.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n031.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 07:48:42 PM UTC 2025 % Result : Theorem 13.63s 13.82s % Output : Proof 13.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : GEO567+1 : TPTP v9.2.0. Released v7.5.0. % 0.10/0.13 % Command : duper %s % 0.14/0.34 % Computer : n031.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Oct 3 12:02:08 EDT 2025 % 0.14/0.34 % CPUTime : % 13.63/13.82 SZS status Theorem for theBenchmark.p % 13.63/13.82 SZS output start Proof for theBenchmark.p % 13.63/13.82 Clause #0 (by assumption #[]): Eq (∀ (A B C : Iota), coll A B C → coll A C B) True % 13.63/13.82 Clause #1 (by assumption #[]): Eq (∀ (A B C : Iota), coll A B C → coll B A C) True % 13.63/13.82 Clause #2 (by assumption #[]): Eq (∀ (A B C D : Iota), And (coll A B C) (coll A B D) → coll C D A) True % 13.63/13.82 Clause #3 (by assumption #[]): Eq (∀ (A B C D : Iota), para A B C D → para A B D C) True % 13.63/13.82 Clause #6 (by assumption #[]): Eq (∀ (A B C D : Iota), perp A B C D → perp A B D C) True % 13.63/13.82 Clause #7 (by assumption #[]): Eq (∀ (A B C D : Iota), perp A B C D → perp C D A B) True % 13.63/13.82 Clause #8 (by assumption #[]): Eq (∀ (A B C D E F : Iota), And (perp A B C D) (perp C D E F) → para A B E F) True % 13.63/13.82 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 % 13.63/13.82 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 % 13.63/13.82 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 % 13.63/13.82 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 % 13.63/13.82 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 % 13.63/13.82 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 % 13.63/13.82 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 % 13.63/13.82 Clause #66 (by assumption #[]): Eq (∀ (A B C : Iota), para A B A C → coll A B C) True % 13.63/13.82 Clause #94 (by assumption #[]): Eq % 13.63/13.82 (Not % 13.63/13.82 (∀ (A B C D Q P : Iota), % 13.63/13.82 And (And (And (And (And (perp D A B C) (coll D B C)) (perp Q D A B)) (coll Q A B)) (perp P D A C)) (coll P A C) → % 13.63/13.82 cyclic B Q P C)) % 13.63/13.82 True % 13.63/13.82 Clause #104 (by clausification #[66]): ∀ (a : Iota), Eq (∀ (B C : Iota), para a B a C → coll a B C) True % 13.63/13.82 Clause #105 (by clausification #[104]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), para a a_1 a C → coll a a_1 C) True % 13.63/13.82 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 % 13.63/13.82 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) % 13.63/13.82 Clause #112 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B C : Iota), coll a B C → coll B a C) True % 13.63/13.82 Clause #113 (by clausification #[112]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), coll a a_1 C → coll a_1 a C) True % 13.63/13.82 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 % 13.63/13.82 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) % 13.63/13.82 Clause #116 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (B C : Iota), coll a B C → coll a C B) True % 13.63/13.82 Clause #117 (by clausification #[116]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), coll a a_1 C → coll a C a_1) True % 13.63/13.82 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 % 13.63/13.82 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) % 13.63/13.82 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 % 13.63/13.82 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 % 13.63/13.82 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 % 13.63/13.82 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 % 13.63/13.82 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) % 13.63/13.82 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)) % 13.63/13.84 Clause #152 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (B C D : Iota), para a B C D → para a B D C) True % 13.63/13.84 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 % 13.63/13.84 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 % 13.63/13.84 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 % 13.63/13.84 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) % 13.63/13.84 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 % 13.63/13.84 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 % 13.63/13.84 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 % 13.63/13.84 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 % 13.63/13.84 Clause #161 (by clausification #[160]): ∀ (a a_1 a_2 a_3 : Iota), % 13.63/13.84 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) % 13.63/13.84 Clause #162 (by clausification #[161]): ∀ (a a_1 a_2 a_3 : Iota), % 13.63/13.84 Or (Eq (cyclic a a_1 a_2 a_3) True) % 13.63/13.84 (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)) % 13.63/13.84 Clause #261 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (B C D : Iota), perp a B C D → perp a B D C) True % 13.63/13.84 Clause #262 (by clausification #[261]): ∀ (a a_1 : Iota), Eq (∀ (C D : Iota), perp a a_1 C D → perp a a_1 D C) True % 13.63/13.84 Clause #263 (by clausification #[262]): ∀ (a a_1 a_2 : Iota), Eq (∀ (D : Iota), perp a a_1 a_2 D → perp a a_1 D a_2) True % 13.63/13.84 Clause #264 (by clausification #[263]): ∀ (a a_1 a_2 a_3 : Iota), Eq (perp a a_1 a_2 a_3 → perp a a_1 a_3 a_2) True % 13.63/13.84 Clause #265 (by clausification #[264]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (perp a a_1 a_2 a_3) False) (Eq (perp a a_1 a_3 a_2) True) % 13.63/13.84 Clause #266 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (B C D : Iota), perp a B C D → perp C D a B) True % 13.63/13.84 Clause #267 (by clausification #[266]): ∀ (a a_1 : Iota), Eq (∀ (C D : Iota), perp a a_1 C D → perp C D a a_1) True % 13.63/13.84 Clause #268 (by clausification #[267]): ∀ (a a_1 a_2 : Iota), Eq (∀ (D : Iota), perp a a_1 a_2 D → perp a_2 D a a_1) True % 13.63/13.84 Clause #269 (by clausification #[268]): ∀ (a a_1 a_2 a_3 : Iota), Eq (perp a a_1 a_2 a_3 → perp a_2 a_3 a a_1) True % 13.63/13.84 Clause #270 (by clausification #[269]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (perp a a_1 a_2 a_3) False) (Eq (perp a_2 a_3 a a_1) True) % 13.63/13.84 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 % 13.63/13.84 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 % 13.63/13.84 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 % 13.63/13.84 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 % 13.63/13.84 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 % 13.63/13.84 Clause #289 (by clausification #[288]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 13.63/13.84 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) % 13.63/13.84 Clause #290 (by clausification #[289]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 13.63/13.84 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)) % 13.63/13.84 Clause #298 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (B C D E F : Iota), And (perp a B C D) (perp C D E F) → para a B E F) True % 13.63/13.87 Clause #299 (by clausification #[298]): ∀ (a a_1 : Iota), Eq (∀ (C D E F : Iota), And (perp a a_1 C D) (perp C D E F) → para a a_1 E F) True % 13.63/13.87 Clause #300 (by clausification #[299]): ∀ (a a_1 a_2 : Iota), Eq (∀ (D E F : Iota), And (perp a a_1 a_2 D) (perp a_2 D E F) → para a a_1 E F) True % 13.63/13.87 Clause #301 (by clausification #[300]): ∀ (a a_1 a_2 a_3 : Iota), Eq (∀ (E F : Iota), And (perp a a_1 a_2 a_3) (perp a_2 a_3 E F) → para a a_1 E F) True % 13.63/13.87 Clause #302 (by clausification #[301]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (∀ (F : Iota), And (perp a a_1 a_2 a_3) (perp a_2 a_3 a_4 F) → para a a_1 a_4 F) True % 13.63/13.87 Clause #303 (by clausification #[302]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), Eq (And (perp a a_1 a_2 a_3) (perp a_2 a_3 a_4 a_5) → para a a_1 a_4 a_5) True % 13.63/13.87 Clause #304 (by clausification #[303]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 13.63/13.87 Or (Eq (And (perp a a_1 a_2 a_3) (perp a_2 a_3 a_4 a_5)) False) (Eq (para a a_1 a_4 a_5) True) % 13.63/13.87 Clause #305 (by clausification #[304]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 13.63/13.87 Or (Eq (para a a_1 a_2 a_3) True) (Or (Eq (perp a a_1 a_4 a_5) False) (Eq (perp a_4 a_5 a_2 a_3) False)) % 13.63/13.87 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 % 13.63/13.87 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 % 13.63/13.87 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 % 13.63/13.87 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 % 13.63/13.87 Clause #348 (by clausification #[347]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 13.63/13.87 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 % 13.63/13.87 Clause #349 (by clausification #[348]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 13.63/13.87 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 % 13.63/13.87 Clause #350 (by clausification #[349]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 13.63/13.87 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 % 13.63/13.87 Clause #351 (by clausification #[350]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 13.63/13.87 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 % 13.63/13.87 Clause #352 (by clausification #[351]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 13.63/13.87 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) % 13.63/13.87 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 % 13.63/13.87 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 % 13.63/13.87 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 % 13.63/13.87 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 % 13.63/13.87 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 % 13.63/13.87 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 % 13.63/13.87 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) % 13.63/13.87 Clause #398 (by clausification #[94]): Eq % 13.63/13.87 (∀ (A B C D Q P : Iota), % 13.63/13.87 And (And (And (And (And (perp D A B C) (coll D B C)) (perp Q D A B)) (coll Q A B)) (perp P D A C)) (coll P A C) → % 13.63/13.87 cyclic B Q P C) % 13.63/13.87 False % 13.63/13.87 Clause #399 (by clausification #[398]): ∀ (a : Iota), % 13.63/13.87 Eq % 13.63/13.87 (Not % 13.63/13.87 (∀ (B C D Q P : Iota), % 13.63/13.87 And % 13.70/13.89 (And (And (And (And (perp D (skS.0 2 a) B C) (coll D B C)) (perp Q D (skS.0 2 a) B)) (coll Q (skS.0 2 a) B)) % 13.70/13.89 (perp P D (skS.0 2 a) C)) % 13.70/13.89 (coll P (skS.0 2 a) C) → % 13.70/13.89 cyclic B Q P C)) % 13.70/13.89 True % 13.70/13.89 Clause #400 (by clausification #[399]): ∀ (a : Iota), % 13.70/13.89 Eq % 13.70/13.89 (∀ (B C D Q P : Iota), % 13.70/13.89 And % 13.70/13.89 (And (And (And (And (perp D (skS.0 2 a) B C) (coll D B C)) (perp Q D (skS.0 2 a) B)) (coll Q (skS.0 2 a) B)) % 13.70/13.89 (perp P D (skS.0 2 a) C)) % 13.70/13.89 (coll P (skS.0 2 a) C) → % 13.70/13.89 cyclic B Q P C) % 13.70/13.89 False % 13.70/13.89 Clause #401 (by clausification #[400]): ∀ (a a_1 : Iota), % 13.70/13.89 Eq % 13.70/13.89 (Not % 13.70/13.89 (∀ (C D Q P : Iota), % 13.70/13.89 And % 13.70/13.89 (And % 13.70/13.89 (And % 13.70/13.89 (And (And (perp D (skS.0 2 a) (skS.0 3 a a_1) C) (coll D (skS.0 3 a a_1) C)) % 13.70/13.89 (perp Q D (skS.0 2 a) (skS.0 3 a a_1))) % 13.70/13.89 (coll Q (skS.0 2 a) (skS.0 3 a a_1))) % 13.70/13.89 (perp P D (skS.0 2 a) C)) % 13.70/13.89 (coll P (skS.0 2 a) C) → % 13.70/13.89 cyclic (skS.0 3 a a_1) Q P C)) % 13.70/13.89 True % 13.70/13.89 Clause #402 (by clausification #[401]): ∀ (a a_1 : Iota), % 13.70/13.89 Eq % 13.70/13.89 (∀ (C D Q P : Iota), % 13.70/13.89 And % 13.70/13.89 (And % 13.70/13.89 (And % 13.70/13.89 (And (And (perp D (skS.0 2 a) (skS.0 3 a a_1) C) (coll D (skS.0 3 a a_1) C)) % 13.70/13.89 (perp Q D (skS.0 2 a) (skS.0 3 a a_1))) % 13.70/13.89 (coll Q (skS.0 2 a) (skS.0 3 a a_1))) % 13.70/13.89 (perp P D (skS.0 2 a) C)) % 13.70/13.89 (coll P (skS.0 2 a) C) → % 13.70/13.89 cyclic (skS.0 3 a a_1) Q P C) % 13.70/13.89 False % 13.70/13.89 Clause #403 (by clausification #[402]): ∀ (a a_1 a_2 : Iota), % 13.70/13.89 Eq % 13.70/13.89 (Not % 13.70/13.89 (∀ (D Q P : Iota), % 13.70/13.89 And % 13.70/13.89 (And % 13.70/13.89 (And % 13.70/13.89 (And % 13.70/13.89 (And (perp D (skS.0 2 a) (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) % 13.70/13.89 (coll D (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 13.70/13.89 (perp Q D (skS.0 2 a) (skS.0 3 a a_1))) % 13.70/13.89 (coll Q (skS.0 2 a) (skS.0 3 a a_1))) % 13.70/13.89 (perp P D (skS.0 2 a) (skS.0 4 a a_1 a_2))) % 13.70/13.89 (coll P (skS.0 2 a) (skS.0 4 a a_1 a_2)) → % 13.70/13.89 cyclic (skS.0 3 a a_1) Q P (skS.0 4 a a_1 a_2))) % 13.70/13.89 True % 13.70/13.89 Clause #404 (by clausification #[403]): ∀ (a a_1 a_2 : Iota), % 13.70/13.89 Eq % 13.70/13.89 (∀ (D Q P : Iota), % 13.70/13.89 And % 13.70/13.89 (And % 13.70/13.89 (And % 13.70/13.89 (And % 13.70/13.89 (And (perp D (skS.0 2 a) (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) % 13.70/13.89 (coll D (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 13.70/13.89 (perp Q D (skS.0 2 a) (skS.0 3 a a_1))) % 13.70/13.89 (coll Q (skS.0 2 a) (skS.0 3 a a_1))) % 13.70/13.89 (perp P D (skS.0 2 a) (skS.0 4 a a_1 a_2))) % 13.70/13.89 (coll P (skS.0 2 a) (skS.0 4 a a_1 a_2)) → % 13.70/13.89 cyclic (skS.0 3 a a_1) Q P (skS.0 4 a a_1 a_2)) % 13.70/13.89 False % 13.70/13.89 Clause #405 (by clausification #[404]): ∀ (a a_1 a_2 a_3 : Iota), % 13.70/13.89 Eq % 13.70/13.89 (Not % 13.70/13.89 (∀ (Q P : Iota), % 13.70/13.89 And % 13.70/13.89 (And % 13.70/13.89 (And % 13.70/13.89 (And % 13.70/13.89 (And (perp (skS.0 5 a a_1 a_2 a_3) (skS.0 2 a) (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) % 13.70/13.89 (coll (skS.0 5 a a_1 a_2 a_3) (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 13.70/13.89 (perp Q (skS.0 5 a a_1 a_2 a_3) (skS.0 2 a) (skS.0 3 a a_1))) % 13.70/13.89 (coll Q (skS.0 2 a) (skS.0 3 a a_1))) % 13.70/13.89 (perp P (skS.0 5 a a_1 a_2 a_3) (skS.0 2 a) (skS.0 4 a a_1 a_2))) % 13.70/13.89 (coll P (skS.0 2 a) (skS.0 4 a a_1 a_2)) → % 13.70/13.89 cyclic (skS.0 3 a a_1) Q P (skS.0 4 a a_1 a_2))) % 13.70/13.89 True % 13.70/13.89 Clause #406 (by clausification #[405]): ∀ (a a_1 a_2 a_3 : Iota), % 13.70/13.89 Eq % 13.70/13.89 (∀ (Q P : Iota), % 13.70/13.89 And % 13.70/13.89 (And % 13.70/13.89 (And % 13.70/13.89 (And % 13.70/13.89 (And (perp (skS.0 5 a a_1 a_2 a_3) (skS.0 2 a) (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) % 13.70/13.89 (coll (skS.0 5 a a_1 a_2 a_3) (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 13.70/13.89 (perp Q (skS.0 5 a a_1 a_2 a_3) (skS.0 2 a) (skS.0 3 a a_1))) % 13.70/13.89 (coll Q (skS.0 2 a) (skS.0 3 a a_1))) % 13.70/13.89 (perp P (skS.0 5 a a_1 a_2 a_3) (skS.0 2 a) (skS.0 4 a a_1 a_2))) % 13.70/13.89 (coll P (skS.0 2 a) (skS.0 4 a a_1 a_2)) → % 13.70/13.89 cyclic (skS.0 3 a a_1) Q P (skS.0 4 a a_1 a_2)) % 13.70/13.89 False % 13.70/13.89 Clause #407 (by clausification #[406]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 13.70/13.91 Eq % 13.70/13.91 (Not % 13.70/13.91 (∀ (P : Iota), % 13.70/13.91 And % 13.70/13.91 (And % 13.70/13.91 (And % 13.70/13.91 (And % 13.70/13.91 (And (perp (skS.0 5 a a_1 a_2 a_3) (skS.0 2 a) (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) % 13.70/13.91 (coll (skS.0 5 a a_1 a_2 a_3) (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 13.70/13.91 (perp (skS.0 6 a a_1 a_2 a_3 a_4) (skS.0 5 a a_1 a_2 a_3) (skS.0 2 a) (skS.0 3 a a_1))) % 13.70/13.91 (coll (skS.0 6 a a_1 a_2 a_3 a_4) (skS.0 2 a) (skS.0 3 a a_1))) % 13.70/13.91 (perp P (skS.0 5 a a_1 a_2 a_3) (skS.0 2 a) (skS.0 4 a a_1 a_2))) % 13.70/13.91 (coll P (skS.0 2 a) (skS.0 4 a a_1 a_2)) → % 13.70/13.91 cyclic (skS.0 3 a a_1) (skS.0 6 a a_1 a_2 a_3 a_4) P (skS.0 4 a a_1 a_2))) % 13.70/13.91 True % 13.70/13.91 Clause #408 (by clausification #[407]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 13.70/13.91 Eq % 13.70/13.91 (∀ (P : Iota), % 13.70/13.91 And % 13.70/13.91 (And % 13.70/13.91 (And % 13.70/13.91 (And % 13.70/13.91 (And (perp (skS.0 5 a a_1 a_2 a_3) (skS.0 2 a) (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) % 13.70/13.91 (coll (skS.0 5 a a_1 a_2 a_3) (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 13.70/13.91 (perp (skS.0 6 a a_1 a_2 a_3 a_4) (skS.0 5 a a_1 a_2 a_3) (skS.0 2 a) (skS.0 3 a a_1))) % 13.70/13.91 (coll (skS.0 6 a a_1 a_2 a_3 a_4) (skS.0 2 a) (skS.0 3 a a_1))) % 13.70/13.91 (perp P (skS.0 5 a a_1 a_2 a_3) (skS.0 2 a) (skS.0 4 a a_1 a_2))) % 13.70/13.91 (coll P (skS.0 2 a) (skS.0 4 a a_1 a_2)) → % 13.70/13.91 cyclic (skS.0 3 a a_1) (skS.0 6 a a_1 a_2 a_3 a_4) P (skS.0 4 a a_1 a_2)) % 13.70/13.91 False % 13.70/13.91 Clause #409 (by clausification #[408]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 13.70/13.91 Eq % 13.70/13.91 (Not % 13.70/13.91 (And % 13.70/13.91 (And % 13.70/13.91 (And % 13.70/13.91 (And % 13.70/13.91 (And (perp (skS.0 5 a a_1 a_2 a_3) (skS.0 2 a) (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) % 13.70/13.91 (coll (skS.0 5 a a_1 a_2 a_3) (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 13.70/13.91 (perp (skS.0 6 a a_1 a_2 a_3 a_4) (skS.0 5 a a_1 a_2 a_3) (skS.0 2 a) (skS.0 3 a a_1))) % 13.70/13.91 (coll (skS.0 6 a a_1 a_2 a_3 a_4) (skS.0 2 a) (skS.0 3 a a_1))) % 13.70/13.91 (perp (skS.0 7 a a_1 a_2 a_3 a_4 a_5) (skS.0 5 a a_1 a_2 a_3) (skS.0 2 a) (skS.0 4 a a_1 a_2))) % 13.70/13.91 (coll (skS.0 7 a a_1 a_2 a_3 a_4 a_5) (skS.0 2 a) (skS.0 4 a a_1 a_2)) → % 13.70/13.91 cyclic (skS.0 3 a a_1) (skS.0 6 a a_1 a_2 a_3 a_4) (skS.0 7 a a_1 a_2 a_3 a_4 a_5) (skS.0 4 a a_1 a_2))) % 13.70/13.91 True % 13.70/13.91 Clause #410 (by clausification #[409]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 13.70/13.91 Eq % 13.70/13.91 (And % 13.70/13.91 (And % 13.70/13.91 (And % 13.70/13.91 (And % 13.70/13.91 (And (perp (skS.0 5 a a_1 a_2 a_3) (skS.0 2 a) (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) % 13.70/13.91 (coll (skS.0 5 a a_1 a_2 a_3) (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 13.70/13.91 (perp (skS.0 6 a a_1 a_2 a_3 a_4) (skS.0 5 a a_1 a_2 a_3) (skS.0 2 a) (skS.0 3 a a_1))) % 13.70/13.91 (coll (skS.0 6 a a_1 a_2 a_3 a_4) (skS.0 2 a) (skS.0 3 a a_1))) % 13.70/13.91 (perp (skS.0 7 a a_1 a_2 a_3 a_4 a_5) (skS.0 5 a a_1 a_2 a_3) (skS.0 2 a) (skS.0 4 a a_1 a_2))) % 13.70/13.91 (coll (skS.0 7 a a_1 a_2 a_3 a_4 a_5) (skS.0 2 a) (skS.0 4 a a_1 a_2)) → % 13.70/13.91 cyclic (skS.0 3 a a_1) (skS.0 6 a a_1 a_2 a_3 a_4) (skS.0 7 a a_1 a_2 a_3 a_4 a_5) (skS.0 4 a a_1 a_2)) % 13.70/13.91 False % 13.70/13.91 Clause #411 (by clausification #[410]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 13.70/13.91 Eq % 13.70/13.91 (And % 13.70/13.91 (And % 13.70/13.91 (And % 13.70/13.91 (And % 13.70/13.91 (And (perp (skS.0 5 a a_1 a_2 a_3) (skS.0 2 a) (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) % 13.70/13.91 (coll (skS.0 5 a a_1 a_2 a_3) (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 13.70/13.91 (perp (skS.0 6 a a_1 a_2 a_3 a_4) (skS.0 5 a a_1 a_2 a_3) (skS.0 2 a) (skS.0 3 a a_1))) % 13.70/13.91 (coll (skS.0 6 a a_1 a_2 a_3 a_4) (skS.0 2 a) (skS.0 3 a a_1))) % 13.70/13.91 (perp (skS.0 7 a a_1 a_2 a_3 a_4 a_5) (skS.0 5 a a_1 a_2 a_3) (skS.0 2 a) (skS.0 4 a a_1 a_2))) % 13.70/13.91 (coll (skS.0 7 a a_1 a_2 a_3 a_4 a_5) (skS.0 2 a) (skS.0 4 a a_1 a_2))) % 13.70/13.91 True % 13.70/13.91 Clause #412 (by clausification #[410]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 13.70/13.91 Eq (cyclic (skS.0 3 a a_1) (skS.0 6 a a_1 a_2 a_3 a_4) (skS.0 7 a a_1 a_2 a_3 a_4 a_5) (skS.0 4 a a_1 a_2)) False % 13.70/13.91 Clause #414 (by clausification #[411]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 13.70/13.93 Eq % 13.70/13.93 (And % 13.70/13.93 (And % 13.70/13.93 (And % 13.70/13.93 (And (perp (skS.0 5 a a_1 a_2 a_3) (skS.0 2 a) (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) % 13.70/13.93 (coll (skS.0 5 a a_1 a_2 a_3) (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 13.70/13.93 (perp (skS.0 6 a a_1 a_2 a_3 a_4) (skS.0 5 a a_1 a_2 a_3) (skS.0 2 a) (skS.0 3 a a_1))) % 13.70/13.93 (coll (skS.0 6 a a_1 a_2 a_3 a_4) (skS.0 2 a) (skS.0 3 a a_1))) % 13.70/13.93 (perp (skS.0 7 a a_1 a_2 a_3 a_4 a_5) (skS.0 5 a a_1 a_2 a_3) (skS.0 2 a) (skS.0 4 a a_1 a_2))) % 13.70/13.93 True % 13.70/13.93 Clause #449 (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 % 13.70/13.93 Clause #450 (by clausification #[449]): ∀ (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 % 13.70/13.93 Clause #451 (by clausification #[450]): ∀ (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 % 13.70/13.93 Clause #452 (by clausification #[451]): ∀ (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 % 13.70/13.93 Clause #453 (by clausification #[452]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 13.70/13.93 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 % 13.70/13.93 Clause #454 (by clausification #[453]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 13.70/13.93 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 % 13.70/13.93 Clause #455 (by clausification #[454]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 13.70/13.93 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 % 13.70/13.93 Clause #456 (by clausification #[455]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 13.70/13.93 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 % 13.70/13.93 Clause #457 (by clausification #[456]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 13.70/13.93 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) % 13.70/13.93 Clause #499 (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 % 13.70/13.93 Clause #500 (by clausification #[499]): ∀ (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 % 13.70/13.93 Clause #501 (by clausification #[500]): ∀ (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 % 13.70/13.93 Clause #502 (by clausification #[501]): ∀ (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 % 13.70/13.93 Clause #503 (by clausification #[502]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 13.70/13.93 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 % 13.70/13.93 Clause #504 (by clausification #[503]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 13.70/13.93 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 % 13.70/13.93 Clause #505 (by clausification #[504]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 13.70/13.93 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 % 13.70/13.93 Clause #506 (by clausification #[505]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 13.70/13.93 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 % 13.70/13.93 Clause #507 (by clausification #[506]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 13.70/13.93 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) % 13.70/13.93 Clause #635 (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 % 13.70/13.93 Clause #636 (by clausification #[635]): ∀ (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 % 13.70/13.93 Clause #637 (by clausification #[636]): ∀ (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 % 13.70/13.93 Clause #638 (by clausification #[637]): ∀ (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 % 13.70/13.96 Clause #639 (by clausification #[638]): ∀ (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 % 13.70/13.96 Clause #640 (by clausification #[639]): ∀ (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 % 13.70/13.96 Clause #641 (by clausification #[640]): ∀ (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) % 13.70/13.96 Clause #884 (by clausification #[414]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 13.70/13.96 Eq (perp (skS.0 7 a a_1 a_2 a_3 a_4 a_5) (skS.0 5 a a_1 a_2 a_3) (skS.0 2 a) (skS.0 4 a a_1 a_2)) True % 13.70/13.96 Clause #887 (by superposition #[884, 270]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 13.70/13.96 Or (Eq True False) % 13.70/13.96 (Eq (perp (skS.0 2 a) (skS.0 4 a a_1 a_2) (skS.0 7 a a_1 a_2 a_3 a_4 a_5) (skS.0 5 a a_1 a_2 a_3)) True) % 13.70/13.96 Clause #1434 (by clausification #[887]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 13.70/13.96 Eq (perp (skS.0 2 a) (skS.0 4 a a_1 a_2) (skS.0 7 a a_1 a_2 a_3 a_4 a_5) (skS.0 5 a a_1 a_2 a_3)) True % 13.70/13.96 Clause #1435 (by superposition #[1434, 265]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 13.70/13.96 Or (Eq True False) % 13.70/13.96 (Eq (perp (skS.0 2 a) (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3) (skS.0 7 a a_1 a_2 a_3 a_4 a_5)) True) % 13.70/13.96 Clause #1444 (by clausification #[1435]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 13.70/13.96 Eq (perp (skS.0 2 a) (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3) (skS.0 7 a a_1 a_2 a_3 a_4 a_5)) True % 13.70/13.96 Clause #1445 (by superposition #[1444, 270]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 13.70/13.96 Or (Eq True False) % 13.70/13.96 (Eq (perp (skS.0 5 a a_1 a_2 a_3) (skS.0 7 a a_1 a_2 a_3 a_4 a_5) (skS.0 2 a) (skS.0 4 a a_1 a_2)) True) % 13.70/13.96 Clause #1446 (by superposition #[1444, 305]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 13.70/13.96 Or (Eq (para (skS.0 2 a) (skS.0 4 a a_1 a_2) a_3 a_4) True) % 13.70/13.96 (Or (Eq True False) (Eq (perp (skS.0 5 a a_1 a_2 a_5) (skS.0 7 a a_1 a_2 a_5 a_6 a_7) a_3 a_4) False)) % 13.70/13.96 Clause #1453 (by clausification #[1445]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 13.70/13.96 Eq (perp (skS.0 5 a a_1 a_2 a_3) (skS.0 7 a a_1 a_2 a_3 a_4 a_5) (skS.0 2 a) (skS.0 4 a a_1 a_2)) True % 13.70/13.96 Clause #1454 (by superposition #[1453, 265]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 13.70/13.96 Or (Eq True False) % 13.70/13.96 (Eq (perp (skS.0 5 a a_1 a_2 a_3) (skS.0 7 a a_1 a_2 a_3 a_4 a_5) (skS.0 4 a a_1 a_2) (skS.0 2 a)) True) % 13.70/13.96 Clause #1462 (by clausification #[1454]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 13.70/13.96 Eq (perp (skS.0 5 a a_1 a_2 a_3) (skS.0 7 a a_1 a_2 a_3 a_4 a_5) (skS.0 4 a a_1 a_2) (skS.0 2 a)) True % 13.70/13.96 Clause #1597 (by clausification #[1446]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 13.70/13.96 Or (Eq (para (skS.0 2 a) (skS.0 4 a a_1 a_2) a_3 a_4) True) % 13.70/13.96 (Eq (perp (skS.0 5 a a_1 a_2 a_5) (skS.0 7 a a_1 a_2 a_5 a_6 a_7) a_3 a_4) False) % 13.70/13.96 Clause #1599 (by superposition #[1597, 1462]): ∀ (a a_1 a_2 : Iota), % 13.70/13.96 Or (Eq (para (skS.0 2 a) (skS.0 4 a a_1 a_2) (skS.0 4 a a_1 a_2) (skS.0 2 a)) True) (Eq False True) % 13.70/13.96 Clause #1600 (by clausification #[1599]): ∀ (a a_1 a_2 : Iota), Eq (para (skS.0 2 a) (skS.0 4 a a_1 a_2) (skS.0 4 a a_1 a_2) (skS.0 2 a)) True % 13.70/13.96 Clause #1602 (by superposition #[1600, 156]): ∀ (a a_1 a_2 : Iota), % 13.70/13.96 Or (Eq True False) (Eq (para (skS.0 2 a) (skS.0 4 a a_1 a_2) (skS.0 2 a) (skS.0 4 a a_1 a_2)) True) % 13.70/13.96 Clause #1630 (by clausification #[1602]): ∀ (a a_1 a_2 : Iota), Eq (para (skS.0 2 a) (skS.0 4 a a_1 a_2) (skS.0 2 a) (skS.0 4 a a_1 a_2)) True % 13.70/13.96 Clause #1634 (by superposition #[1630, 641]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 13.70/13.96 Or (Eq True False) (Eq (eqangle (skS.0 2 a) (skS.0 4 a a_1 a_2) a_3 a_4 (skS.0 2 a) (skS.0 4 a a_1 a_2) a_3 a_4) True) % 13.70/13.96 Clause #1635 (by clausification #[1634]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 13.70/13.96 Eq (eqangle (skS.0 2 a) (skS.0 4 a a_1 a_2) a_3 a_4 (skS.0 2 a) (skS.0 4 a a_1 a_2) a_3 a_4) True % 13.70/13.96 Clause #1642 (by superposition #[1635, 507]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 13.70/13.96 Or (Eq True False) (Eq (eqangle (skS.0 2 a) (skS.0 4 a a_1 a_2) (skS.0 2 a) (skS.0 4 a a_1 a_2) a_3 a_4 a_3 a_4) True) % 13.70/13.96 Clause #1647 (by clausification #[1642]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 13.70/13.96 Eq (eqangle (skS.0 2 a) (skS.0 4 a a_1 a_2) (skS.0 2 a) (skS.0 4 a a_1 a_2) a_3 a_4 a_3 a_4) True % 13.79/13.99 Clause #1653 (by superposition #[1647, 457]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 13.79/13.99 Or (Eq True False) % 13.79/13.99 (Eq (eqangle a a_1 a a_1 (skS.0 2 a_2) (skS.0 4 a_2 a_3 a_4) (skS.0 2 a_2) (skS.0 4 a_2 a_3 a_4)) True) % 13.79/13.99 Clause #1659 (by clausification #[1653]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 13.79/13.99 Eq (eqangle a a_1 a a_1 (skS.0 2 a_2) (skS.0 4 a_2 a_3 a_4) (skS.0 2 a_2) (skS.0 4 a_2 a_3 a_4)) True % 13.79/13.99 Clause #1663 (by superposition #[1659, 352]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 13.79/13.99 Or (Eq True False) % 13.79/13.99 (Eq (eqangle a a_1 a_1 a (skS.0 2 a_2) (skS.0 4 a_2 a_3 a_4) (skS.0 2 a_2) (skS.0 4 a_2 a_3 a_4)) True) % 13.79/13.99 Clause #1672 (by clausification #[1663]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 13.79/13.99 Eq (eqangle a a_1 a_1 a (skS.0 2 a_2) (skS.0 4 a_2 a_3 a_4) (skS.0 2 a_2) (skS.0 4 a_2 a_3 a_4)) True % 13.79/13.99 Clause #1679 (by superposition #[1672, 507]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 13.79/13.99 Or (Eq True False) % 13.79/13.99 (Eq (eqangle a a_1 (skS.0 2 a_2) (skS.0 4 a_2 a_3 a_4) a_1 a (skS.0 2 a_2) (skS.0 4 a_2 a_3 a_4)) True) % 13.79/13.99 Clause #1684 (by clausification #[1679]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 13.79/13.99 Eq (eqangle a a_1 (skS.0 2 a_2) (skS.0 4 a_2 a_3 a_4) a_1 a (skS.0 2 a_2) (skS.0 4 a_2 a_3 a_4)) True % 13.79/13.99 Clause #1688 (by superposition #[1684, 359]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (para a a_1 a_1 a) True) % 13.79/13.99 Clause #1697 (by clausification #[1688]): ∀ (a a_1 : Iota), Eq (para a a_1 a_1 a) True % 13.79/13.99 Clause #1706 (by superposition #[1697, 156]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (para a a_1 a a_1) True) % 13.79/13.99 Clause #1726 (by clausification #[1706]): ∀ (a a_1 : Iota), Eq (para a a_1 a a_1) True % 13.79/13.99 Clause #1727 (by superposition #[1726, 107]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (coll a a_1 a_1) True) % 13.79/13.99 Clause #1731 (by superposition #[1726, 641]): ∀ (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) % 13.79/13.99 Clause #1733 (by clausification #[1727]): ∀ (a a_1 : Iota), Eq (coll a a_1 a_1) True % 13.79/13.99 Clause #1746 (by superposition #[1733, 115]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (coll a a_1 a) True) % 13.79/13.99 Clause #1755 (by clausification #[1746]): ∀ (a a_1 : Iota), Eq (coll a a_1 a) True % 13.79/13.99 Clause #1769 (by superposition #[1755, 119]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (coll a a a_1) True) % 13.79/13.99 Clause #1778 (by clausification #[1769]): ∀ (a a_1 : Iota), Eq (coll a a a_1) True % 13.79/13.99 Clause #1790 (by superposition #[1778, 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)) % 13.79/13.99 Clause #1798 (by clausification #[1731]): ∀ (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 % 13.79/13.99 Clause #1805 (by superposition #[1798, 507]): ∀ (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) % 13.79/13.99 Clause #1810 (by clausification #[1805]): ∀ (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 % 13.79/13.99 Clause #1811 (by superposition #[1810, 162]): ∀ (a a_1 a_2 : Iota), Or (Eq (cyclic a a a_1 a_2) True) (Or (Eq True False) (Eq (coll a_1 a_2 a) False)) % 13.79/13.99 Clause #1894 (by clausification #[1790]): ∀ (a a_1 a_2 : Iota), Or (Eq (coll a a_1 a_2) True) (Eq (coll a_2 a_2 a_1) False) % 13.79/13.99 Clause #1900 (by superposition #[1894, 1778]): ∀ (a a_1 a_2 : Iota), Or (Eq (coll a a_1 a_2) True) (Eq False True) % 13.79/13.99 Clause #1909 (by clausification #[1900]): ∀ (a a_1 a_2 : Iota), Eq (coll a a_1 a_2) True % 13.79/13.99 Clause #1957 (by clausification #[1811]): ∀ (a a_1 a_2 : Iota), Or (Eq (cyclic a a a_1 a_2) True) (Eq (coll a_1 a_2 a) False) % 13.79/13.99 Clause #1958 (by forward demodulation #[1957, 1909]): ∀ (a a_1 a_2 : Iota), Or (Eq (cyclic a a a_1 a_2) True) (Eq True False) % 13.79/13.99 Clause #1959 (by clausification #[1958]): ∀ (a a_1 a_2 : Iota), Eq (cyclic a a a_1 a_2) True % 13.79/13.99 Clause #1963 (by superposition #[1959, 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 a a_1 a_3) False)) % 13.79/13.99 Clause #2230 (by clausification #[1963]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cyclic a a_1 a_2 a_3) True) (Eq (cyclic a a a_1 a_3) False) % 13.79/13.99 Clause #2231 (by superposition #[2230, 1959]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cyclic a a_1 a_2 a_3) True) (Eq False True) % 13.79/13.99 Clause #2240 (by clausification #[2231]): ∀ (a a_1 a_2 a_3 : Iota), Eq (cyclic a a_1 a_2 a_3) True % 13.79/14.00 Clause #2246 (by superposition #[2240, 412]): Eq True False % 13.79/14.00 Clause #2248 (by clausification #[2246]): False % 13.79/14.00 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------