%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS082+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n021.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 07:52:35 PM UTC 2025 % Result : Unsatisfiable 4.29s 4.48s % Output : Proof 4.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : KRS082+1 : TPTP v9.2.0. Released v3.1.0. % 0.03/0.13 % Command : duper %s % 0.12/0.33 % Computer : n021.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Thu Oct 2 10:14:23 EDT 2025 % 0.12/0.34 % CPUTime : % 4.29/4.48 SZS status Theorem for theBenchmark.p % 4.29/4.48 SZS output start Proof for theBenchmark.p % 4.29/4.48 Clause #2 (by assumption #[]): Eq % 4.29/4.48 (∀ (X : Iota), % 4.29/4.48 cUnsatisfiable X → % 4.29/4.48 Exists fun Y => % 4.29/4.48 And % 4.29/4.48 (And % 4.29/4.48 (And % 4.29/4.48 (And (And (And (rs X Y) (Exists fun Z => And (rp Y Z) (cowlThing Z))) (∀ (Z : Iota), rr Y Z → cc Z)) % 4.29/4.48 (∀ (Z : Iota), rp Y Z → Exists fun W => And (rr Z W) (cowlThing W))) % 4.29/4.48 (∀ (Z : Iota), rp Y Z → Exists fun W => And (rp Z W) (cowlThing W))) % 4.29/4.48 (∀ (Z : Iota), rp Y Z → ∀ (W : Iota), rr Z W → cc W)) % 4.29/4.48 (Exists fun Z => And (rr Y Z) (cowlThing Z))) % 4.29/4.48 True % 4.29/4.48 Clause #3 (by assumption #[]): Eq (∀ (X : Iota), cUnsatisfiable X → ca X) True % 4.29/4.48 Clause #4 (by assumption #[]): Eq (∀ (X : Iota), Iff (cc X) (∀ (Y : Iota), rinvR X Y → ∀ (Z : Iota), rinvP Y Z → ∀ (W : Iota), rinvS Z W → Not (ca W))) % 4.29/4.48 True % 4.29/4.48 Clause #5 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (rinvP X Y) (rp Y X)) True % 4.29/4.48 Clause #6 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (rinvR X Y) (rr Y X)) True % 4.29/4.48 Clause #7 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (rinvS X Y) (rs Y X)) True % 4.29/4.48 Clause #9 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_19_28752) True % 4.29/4.48 Clause #10 (by clausification #[3]): ∀ (a : Iota), Eq (cUnsatisfiable a → ca a) True % 4.29/4.48 Clause #11 (by clausification #[10]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (ca a) True) % 4.29/4.48 Clause #12 (by superposition #[11, 9]): Or (Eq (ca i2003_11_14_17_19_28752) True) (Eq False True) % 4.29/4.48 Clause #13 (by clausification #[12]): Eq (ca i2003_11_14_17_19_28752) True % 4.29/4.48 Clause #28 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (rinvS a Y) (rs Y a)) True % 4.29/4.48 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (Iff (rinvS a a_1) (rs a_1 a)) True % 4.29/4.48 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Or (Eq (rinvS a a_1) True) (Eq (rs a_1 a) False) % 4.29/4.48 Clause #32 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (rinvP a Y) (rp Y a)) True % 4.29/4.48 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Eq (Iff (rinvP a a_1) (rp a_1 a)) True % 4.29/4.48 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Or (Eq (rinvP a a_1) True) (Eq (rp a_1 a) False) % 4.29/4.48 Clause #36 (by clausification #[2]): ∀ (a : Iota), % 4.29/4.48 Eq % 4.29/4.48 (cUnsatisfiable a → % 4.29/4.48 Exists fun Y => % 4.29/4.48 And % 4.29/4.48 (And % 4.29/4.48 (And % 4.29/4.48 (And (And (And (rs a Y) (Exists fun Z => And (rp Y Z) (cowlThing Z))) (∀ (Z : Iota), rr Y Z → cc Z)) % 4.29/4.48 (∀ (Z : Iota), rp Y Z → Exists fun W => And (rr Z W) (cowlThing W))) % 4.29/4.48 (∀ (Z : Iota), rp Y Z → Exists fun W => And (rp Z W) (cowlThing W))) % 4.29/4.48 (∀ (Z : Iota), rp Y Z → ∀ (W : Iota), rr Z W → cc W)) % 4.29/4.48 (Exists fun Z => And (rr Y Z) (cowlThing Z))) % 4.29/4.48 True % 4.29/4.48 Clause #37 (by clausification #[36]): ∀ (a : Iota), % 4.29/4.48 Or (Eq (cUnsatisfiable a) False) % 4.29/4.48 (Eq % 4.29/4.48 (Exists fun Y => % 4.29/4.48 And % 4.29/4.48 (And % 4.29/4.48 (And % 4.29/4.48 (And (And (And (rs a Y) (Exists fun Z => And (rp Y Z) (cowlThing Z))) (∀ (Z : Iota), rr Y Z → cc Z)) % 4.29/4.48 (∀ (Z : Iota), rp Y Z → Exists fun W => And (rr Z W) (cowlThing W))) % 4.29/4.48 (∀ (Z : Iota), rp Y Z → Exists fun W => And (rp Z W) (cowlThing W))) % 4.29/4.48 (∀ (Z : Iota), rp Y Z → ∀ (W : Iota), rr Z W → cc W)) % 4.29/4.48 (Exists fun Z => And (rr Y Z) (cowlThing Z))) % 4.29/4.48 True) % 4.29/4.48 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), % 4.29/4.48 Or (Eq (cUnsatisfiable a) False) % 4.29/4.48 (Eq % 4.29/4.48 (And % 4.29/4.48 (And % 4.29/4.48 (And % 4.29/4.48 (And % 4.29/4.48 (And (And (rs a (skS.0 0 a a_1)) (Exists fun Z => And (rp (skS.0 0 a a_1) Z) (cowlThing Z))) % 4.29/4.48 (∀ (Z : Iota), rr (skS.0 0 a a_1) Z → cc Z)) % 4.29/4.48 (∀ (Z : Iota), rp (skS.0 0 a a_1) Z → Exists fun W => And (rr Z W) (cowlThing W))) % 4.29/4.48 (∀ (Z : Iota), rp (skS.0 0 a a_1) Z → Exists fun W => And (rp Z W) (cowlThing W))) % 4.29/4.48 (∀ (Z : Iota), rp (skS.0 0 a a_1) Z → ∀ (W : Iota), rr Z W → cc W)) % 4.29/4.48 (Exists fun Z => And (rr (skS.0 0 a a_1) Z) (cowlThing Z))) % 4.29/4.48 True) % 4.33/4.50 Clause #40 (by clausification #[38]): ∀ (a a_1 : Iota), % 4.33/4.50 Or (Eq (cUnsatisfiable a) False) % 4.33/4.50 (Eq % 4.33/4.50 (And % 4.33/4.50 (And % 4.33/4.50 (And % 4.33/4.50 (And (And (rs a (skS.0 0 a a_1)) (Exists fun Z => And (rp (skS.0 0 a a_1) Z) (cowlThing Z))) % 4.33/4.50 (∀ (Z : Iota), rr (skS.0 0 a a_1) Z → cc Z)) % 4.33/4.50 (∀ (Z : Iota), rp (skS.0 0 a a_1) Z → Exists fun W => And (rr Z W) (cowlThing W))) % 4.33/4.50 (∀ (Z : Iota), rp (skS.0 0 a a_1) Z → Exists fun W => And (rp Z W) (cowlThing W))) % 4.33/4.50 (∀ (Z : Iota), rp (skS.0 0 a a_1) Z → ∀ (W : Iota), rr Z W → cc W)) % 4.33/4.50 True) % 4.33/4.50 Clause #44 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (rinvR a Y) (rr Y a)) True % 4.33/4.50 Clause #45 (by clausification #[44]): ∀ (a a_1 : Iota), Eq (Iff (rinvR a a_1) (rr a_1 a)) True % 4.33/4.50 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), Or (Eq (rinvR a a_1) True) (Eq (rr a_1 a) False) % 4.33/4.50 Clause #48 (by clausification #[4]): ∀ (a : Iota), % 4.33/4.50 Eq (Iff (cc a) (∀ (Y : Iota), rinvR a Y → ∀ (Z : Iota), rinvP Y Z → ∀ (W : Iota), rinvS Z W → Not (ca W))) True % 4.33/4.50 Clause #50 (by clausification #[48]): ∀ (a : Iota), % 4.33/4.50 Or (Eq (cc a) False) % 4.33/4.50 (Eq (∀ (Y : Iota), rinvR a Y → ∀ (Z : Iota), rinvP Y Z → ∀ (W : Iota), rinvS Z W → Not (ca W)) True) % 4.33/4.50 Clause #61 (by clausification #[40]): ∀ (a a_1 : Iota), % 4.33/4.50 Or (Eq (cUnsatisfiable a) False) (Eq (∀ (Z : Iota), rp (skS.0 0 a a_1) Z → ∀ (W : Iota), rr Z W → cc W) True) % 4.33/4.50 Clause #62 (by clausification #[40]): ∀ (a a_1 : Iota), % 4.33/4.50 Or (Eq (cUnsatisfiable a) False) % 4.33/4.50 (Eq % 4.33/4.50 (And % 4.33/4.50 (And % 4.33/4.50 (And (And (rs a (skS.0 0 a a_1)) (Exists fun Z => And (rp (skS.0 0 a a_1) Z) (cowlThing Z))) % 4.33/4.50 (∀ (Z : Iota), rr (skS.0 0 a a_1) Z → cc Z)) % 4.33/4.50 (∀ (Z : Iota), rp (skS.0 0 a a_1) Z → Exists fun W => And (rr Z W) (cowlThing W))) % 4.33/4.50 (∀ (Z : Iota), rp (skS.0 0 a a_1) Z → Exists fun W => And (rp Z W) (cowlThing W))) % 4.33/4.50 True) % 4.33/4.50 Clause #63 (by clausification #[61]): ∀ (a a_1 a_2 : Iota), % 4.33/4.50 Or (Eq (cUnsatisfiable a) False) (Eq (rp (skS.0 0 a a_1) a_2 → ∀ (W : Iota), rr a_2 W → cc W) True) % 4.33/4.50 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 : Iota), % 4.33/4.50 Or (Eq (cUnsatisfiable a) False) (Or (Eq (rp (skS.0 0 a a_1) a_2) False) (Eq (∀ (W : Iota), rr a_2 W → cc W) True)) % 4.33/4.50 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 a_3 : Iota), % 4.33/4.50 Or (Eq (cUnsatisfiable a) False) (Or (Eq (rp (skS.0 0 a a_1) a_2) False) (Eq (rr a_2 a_3 → cc a_3) True)) % 4.33/4.50 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 a_3 : Iota), % 4.33/4.50 Or (Eq (cUnsatisfiable a) False) % 4.33/4.50 (Or (Eq (rp (skS.0 0 a a_1) a_2) False) (Or (Eq (rr a_2 a_3) False) (Eq (cc a_3) True))) % 4.33/4.50 Clause #67 (by superposition #[66, 9]): ∀ (a a_1 a_2 : Iota), % 4.33/4.50 Or (Eq (rp (skS.0 0 i2003_11_14_17_19_28752 a) a_1) False) % 4.33/4.50 (Or (Eq (rr a_1 a_2) False) (Or (Eq (cc a_2) True) (Eq False True))) % 4.33/4.50 Clause #73 (by clausification #[50]): ∀ (a a_1 : Iota), % 4.33/4.50 Or (Eq (cc a) False) (Eq (rinvR a a_1 → ∀ (Z : Iota), rinvP a_1 Z → ∀ (W : Iota), rinvS Z W → Not (ca W)) True) % 4.33/4.50 Clause #74 (by clausification #[73]): ∀ (a a_1 : Iota), % 4.33/4.50 Or (Eq (cc a) False) % 4.33/4.50 (Or (Eq (rinvR a a_1) False) (Eq (∀ (Z : Iota), rinvP a_1 Z → ∀ (W : Iota), rinvS Z W → Not (ca W)) True)) % 4.33/4.50 Clause #75 (by clausification #[74]): ∀ (a a_1 a_2 : Iota), % 4.33/4.50 Or (Eq (cc a) False) (Or (Eq (rinvR a a_1) False) (Eq (rinvP a_1 a_2 → ∀ (W : Iota), rinvS a_2 W → Not (ca W)) True)) % 4.33/4.50 Clause #76 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), % 4.33/4.50 Or (Eq (cc a) False) % 4.33/4.50 (Or (Eq (rinvR a a_1) False) (Or (Eq (rinvP a_1 a_2) False) (Eq (∀ (W : Iota), rinvS a_2 W → Not (ca W)) True))) % 4.33/4.50 Clause #77 (by clausification #[76]): ∀ (a a_1 a_2 a_3 : Iota), % 4.33/4.50 Or (Eq (cc a) False) % 4.33/4.50 (Or (Eq (rinvR a a_1) False) (Or (Eq (rinvP a_1 a_2) False) (Eq (rinvS a_2 a_3 → Not (ca a_3)) True))) % 4.33/4.50 Clause #78 (by clausification #[77]): ∀ (a a_1 a_2 a_3 : Iota), % 4.33/4.50 Or (Eq (cc a) False) % 4.33/4.50 (Or (Eq (rinvR a a_1) False) % 4.33/4.50 (Or (Eq (rinvP a_1 a_2) False) (Or (Eq (rinvS a_2 a_3) False) (Eq (Not (ca a_3)) True)))) % 4.33/4.50 Clause #79 (by clausification #[78]): ∀ (a a_1 a_2 a_3 : Iota), % 4.33/4.53 Or (Eq (cc a) False) % 4.33/4.53 (Or (Eq (rinvR a a_1) False) (Or (Eq (rinvP a_1 a_2) False) (Or (Eq (rinvS a_2 a_3) False) (Eq (ca a_3) False)))) % 4.33/4.53 Clause #84 (by clausification #[67]): ∀ (a a_1 a_2 : Iota), % 4.33/4.53 Or (Eq (rp (skS.0 0 i2003_11_14_17_19_28752 a) a_1) False) (Or (Eq (rr a_1 a_2) False) (Eq (cc a_2) True)) % 4.33/4.53 Clause #93 (by clausification #[62]): ∀ (a a_1 : Iota), % 4.33/4.53 Or (Eq (cUnsatisfiable a) False) % 4.33/4.53 (Eq % 4.33/4.53 (And % 4.33/4.53 (And (And (rs a (skS.0 0 a a_1)) (Exists fun Z => And (rp (skS.0 0 a a_1) Z) (cowlThing Z))) % 4.33/4.53 (∀ (Z : Iota), rr (skS.0 0 a a_1) Z → cc Z)) % 4.33/4.53 (∀ (Z : Iota), rp (skS.0 0 a a_1) Z → Exists fun W => And (rr Z W) (cowlThing W))) % 4.33/4.53 True) % 4.33/4.53 Clause #104 (by clausification #[93]): ∀ (a a_1 : Iota), % 4.33/4.53 Or (Eq (cUnsatisfiable a) False) % 4.33/4.53 (Eq (∀ (Z : Iota), rp (skS.0 0 a a_1) Z → Exists fun W => And (rr Z W) (cowlThing W)) True) % 4.33/4.53 Clause #105 (by clausification #[93]): ∀ (a a_1 : Iota), % 4.33/4.53 Or (Eq (cUnsatisfiable a) False) % 4.33/4.53 (Eq % 4.33/4.53 (And (And (rs a (skS.0 0 a a_1)) (Exists fun Z => And (rp (skS.0 0 a a_1) Z) (cowlThing Z))) % 4.33/4.53 (∀ (Z : Iota), rr (skS.0 0 a a_1) Z → cc Z)) % 4.33/4.53 True) % 4.33/4.53 Clause #106 (by clausification #[104]): ∀ (a a_1 a_2 : Iota), % 4.33/4.53 Or (Eq (cUnsatisfiable a) False) (Eq (rp (skS.0 0 a a_1) a_2 → Exists fun W => And (rr a_2 W) (cowlThing W)) True) % 4.33/4.53 Clause #107 (by clausification #[106]): ∀ (a a_1 a_2 : Iota), % 4.33/4.53 Or (Eq (cUnsatisfiable a) False) % 4.33/4.53 (Or (Eq (rp (skS.0 0 a a_1) a_2) False) (Eq (Exists fun W => And (rr a_2 W) (cowlThing W)) True)) % 4.33/4.53 Clause #108 (by clausification #[107]): ∀ (a a_1 a_2 a_3 : Iota), % 4.33/4.53 Or (Eq (cUnsatisfiable a) False) % 4.33/4.53 (Or (Eq (rp (skS.0 0 a a_1) a_2) False) (Eq (And (rr a_2 (skS.0 6 a_2 a_3)) (cowlThing (skS.0 6 a_2 a_3))) True)) % 4.33/4.53 Clause #110 (by clausification #[108]): ∀ (a a_1 a_2 a_3 : Iota), % 4.33/4.53 Or (Eq (cUnsatisfiable a) False) (Or (Eq (rp (skS.0 0 a a_1) a_2) False) (Eq (rr a_2 (skS.0 6 a_2 a_3)) True)) % 4.33/4.53 Clause #111 (by superposition #[110, 9]): ∀ (a a_1 a_2 : Iota), % 4.33/4.53 Or (Eq (rp (skS.0 0 i2003_11_14_17_19_28752 a) a_1) False) (Or (Eq (rr a_1 (skS.0 6 a_1 a_2)) True) (Eq False True)) % 4.33/4.53 Clause #112 (by clausification #[111]): ∀ (a a_1 a_2 : Iota), Or (Eq (rp (skS.0 0 i2003_11_14_17_19_28752 a) a_1) False) (Eq (rr a_1 (skS.0 6 a_1 a_2)) True) % 4.33/4.53 Clause #114 (by clausification #[105]): ∀ (a a_1 : Iota), % 4.33/4.53 Or (Eq (cUnsatisfiable a) False) % 4.33/4.53 (Eq (And (rs a (skS.0 0 a a_1)) (Exists fun Z => And (rp (skS.0 0 a a_1) Z) (cowlThing Z))) True) % 4.33/4.53 Clause #120 (by clausification #[114]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Z => And (rp (skS.0 0 a a_1) Z) (cowlThing Z)) True) % 4.33/4.53 Clause #121 (by clausification #[114]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rs a (skS.0 0 a a_1)) True) % 4.33/4.53 Clause #122 (by clausification #[120]): ∀ (a a_1 a_2 : Iota), % 4.33/4.53 Or (Eq (cUnsatisfiable a) False) % 4.33/4.53 (Eq (And (rp (skS.0 0 a a_1) (skS.0 7 a a_1 a_2)) (cowlThing (skS.0 7 a a_1 a_2))) True) % 4.33/4.53 Clause #124 (by clausification #[122]): ∀ (a a_1 a_2 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rp (skS.0 0 a a_1) (skS.0 7 a a_1 a_2)) True) % 4.33/4.53 Clause #125 (by superposition #[121, 9]): ∀ (a : Iota), Or (Eq (rs i2003_11_14_17_19_28752 (skS.0 0 i2003_11_14_17_19_28752 a)) True) (Eq False True) % 4.33/4.53 Clause #126 (by clausification #[125]): ∀ (a : Iota), Eq (rs i2003_11_14_17_19_28752 (skS.0 0 i2003_11_14_17_19_28752 a)) True % 4.33/4.53 Clause #127 (by superposition #[126, 30]): ∀ (a : Iota), Or (Eq (rinvS (skS.0 0 i2003_11_14_17_19_28752 a) i2003_11_14_17_19_28752) True) (Eq True False) % 4.33/4.53 Clause #128 (by clausification #[127]): ∀ (a : Iota), Eq (rinvS (skS.0 0 i2003_11_14_17_19_28752 a) i2003_11_14_17_19_28752) True % 4.33/4.53 Clause #132 (by superposition #[124, 9]): ∀ (a a_1 : Iota), % 4.33/4.53 Or (Eq (rp (skS.0 0 i2003_11_14_17_19_28752 a) (skS.0 7 i2003_11_14_17_19_28752 a a_1)) True) (Eq False True) % 4.33/4.53 Clause #133 (by clausification #[132]): ∀ (a a_1 : Iota), Eq (rp (skS.0 0 i2003_11_14_17_19_28752 a) (skS.0 7 i2003_11_14_17_19_28752 a a_1)) True % 4.33/4.53 Clause #134 (by superposition #[133, 84]): ∀ (a a_1 a_2 : Iota), % 4.39/4.55 Or (Eq True False) (Or (Eq (rr (skS.0 7 i2003_11_14_17_19_28752 a a_1) a_2) False) (Eq (cc a_2) True)) % 4.39/4.55 Clause #136 (by superposition #[133, 112]): ∀ (a a_1 a_2 : Iota), % 4.39/4.55 Or (Eq True False) % 4.39/4.55 (Eq (rr (skS.0 7 i2003_11_14_17_19_28752 a a_1) (skS.0 6 (skS.0 7 i2003_11_14_17_19_28752 a a_1) a_2)) True) % 4.39/4.55 Clause #138 (by superposition #[133, 34]): ∀ (a a_1 : Iota), % 4.39/4.55 Or (Eq (rinvP (skS.0 7 i2003_11_14_17_19_28752 a a_1) (skS.0 0 i2003_11_14_17_19_28752 a)) True) (Eq True False) % 4.39/4.55 Clause #139 (by clausification #[134]): ∀ (a a_1 a_2 : Iota), Or (Eq (rr (skS.0 7 i2003_11_14_17_19_28752 a a_1) a_2) False) (Eq (cc a_2) True) % 4.39/4.55 Clause #140 (by clausification #[138]): ∀ (a a_1 : Iota), Eq (rinvP (skS.0 7 i2003_11_14_17_19_28752 a a_1) (skS.0 0 i2003_11_14_17_19_28752 a)) True % 4.39/4.55 Clause #160 (by clausification #[136]): ∀ (a a_1 a_2 : Iota), % 4.39/4.55 Eq (rr (skS.0 7 i2003_11_14_17_19_28752 a a_1) (skS.0 6 (skS.0 7 i2003_11_14_17_19_28752 a a_1) a_2)) True % 4.39/4.55 Clause #161 (by superposition #[160, 139]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (cc (skS.0 6 (skS.0 7 i2003_11_14_17_19_28752 a a_1) a_2)) True) % 4.39/4.55 Clause #162 (by superposition #[160, 46]): ∀ (a a_1 a_2 : Iota), % 4.39/4.55 Or (Eq (rinvR (skS.0 6 (skS.0 7 i2003_11_14_17_19_28752 a a_1) a_2) (skS.0 7 i2003_11_14_17_19_28752 a a_1)) True) % 4.39/4.55 (Eq True False) % 4.39/4.55 Clause #163 (by clausification #[161]): ∀ (a a_1 a_2 : Iota), Eq (cc (skS.0 6 (skS.0 7 i2003_11_14_17_19_28752 a a_1) a_2)) True % 4.39/4.55 Clause #164 (by superposition #[163, 79]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.39/4.55 Or (Eq True False) % 4.39/4.55 (Or (Eq (rinvR (skS.0 6 (skS.0 7 i2003_11_14_17_19_28752 a a_1) a_2) a_3) False) % 4.39/4.55 (Or (Eq (rinvP a_3 a_4) False) (Or (Eq (rinvS a_4 a_5) False) (Eq (ca a_5) False)))) % 4.39/4.55 Clause #166 (by clausification #[162]): ∀ (a a_1 a_2 : Iota), % 4.39/4.55 Eq (rinvR (skS.0 6 (skS.0 7 i2003_11_14_17_19_28752 a a_1) a_2) (skS.0 7 i2003_11_14_17_19_28752 a a_1)) True % 4.39/4.55 Clause #167 (by clausification #[164]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.39/4.55 Or (Eq (rinvR (skS.0 6 (skS.0 7 i2003_11_14_17_19_28752 a a_1) a_2) a_3) False) % 4.39/4.55 (Or (Eq (rinvP a_3 a_4) False) (Or (Eq (rinvS a_4 a_5) False) (Eq (ca a_5) False))) % 4.39/4.55 Clause #168 (by superposition #[167, 166]): ∀ (a a_1 a_2 a_3 : Iota), % 4.39/4.55 Or (Eq (rinvP (skS.0 7 i2003_11_14_17_19_28752 a a_1) a_2) False) % 4.39/4.55 (Or (Eq (rinvS a_2 a_3) False) (Or (Eq (ca a_3) False) (Eq False True))) % 4.39/4.55 Clause #172 (by clausification #[168]): ∀ (a a_1 a_2 a_3 : Iota), % 4.39/4.55 Or (Eq (rinvP (skS.0 7 i2003_11_14_17_19_28752 a a_1) a_2) False) (Or (Eq (rinvS a_2 a_3) False) (Eq (ca a_3) False)) % 4.39/4.55 Clause #173 (by superposition #[172, 140]): ∀ (a a_1 : Iota), Or (Eq (rinvS (skS.0 0 i2003_11_14_17_19_28752 a) a_1) False) (Or (Eq (ca a_1) False) (Eq False True)) % 4.39/4.55 Clause #174 (by clausification #[173]): ∀ (a a_1 : Iota), Or (Eq (rinvS (skS.0 0 i2003_11_14_17_19_28752 a) a_1) False) (Eq (ca a_1) False) % 4.39/4.55 Clause #175 (by superposition #[174, 128]): Or (Eq (ca i2003_11_14_17_19_28752) False) (Eq False True) % 4.39/4.55 Clause #176 (by clausification #[175]): Eq (ca i2003_11_14_17_19_28752) False % 4.39/4.55 Clause #177 (by superposition #[176, 13]): Eq False True % 4.39/4.55 Clause #178 (by clausification #[177]): False % 4.39/4.55 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------