%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS086+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n007.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 07:52:36 PM UTC 2025 % Result : Unsatisfiable 3.90s 4.06s % Output : Proof 3.90s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : KRS086+1 : TPTP v9.2.0. Released v3.1.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n007.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 : Thu Oct 2 10:13:53 EDT 2025 % 0.13/0.34 % CPUTime : % 3.90/4.06 SZS status Theorem for theBenchmark.p % 3.90/4.06 SZS output start Proof for theBenchmark.p % 3.90/4.06 Clause #14 (by assumption #[]): Eq (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) True % 3.90/4.06 Clause #16 (by assumption #[]): Eq % 3.90/4.06 (∀ (X : Iota), % 3.90/4.06 Iff (cUnsatisfiable X) % 3.90/4.06 (Exists fun Y => % 3.90/4.06 And (And (rf X Y) (Exists fun Z => And (rinvF Y Z) (Exists fun W => And (rf Z W) (Not (cp1 W))))) (cp1 Y))) % 3.90/4.06 True % 3.90/4.06 Clause #17 (by assumption #[]): Eq (∀ (X : Iota), cowlThing X → ∀ (Y0 Y1 : Iota), And (rf X Y0) (rf X Y1) → Eq Y0 Y1) True % 3.90/4.06 Clause #18 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (rinvF X Y) (rf Y X)) True % 3.90/4.06 Clause #21 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_19_42328) True % 3.90/4.06 Clause #68 (by clausification #[14]): ∀ (a : Iota), Eq (And (cowlThing a) (Not (cowlNothing a))) True % 3.90/4.06 Clause #70 (by clausification #[68]): ∀ (a : Iota), Eq (cowlThing a) True % 3.90/4.06 Clause #128 (by clausification #[18]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (rinvF a Y) (rf Y a)) True % 3.90/4.06 Clause #129 (by clausification #[128]): ∀ (a a_1 : Iota), Eq (Iff (rinvF a a_1) (rf a_1 a)) True % 3.90/4.06 Clause #131 (by clausification #[129]): ∀ (a a_1 : Iota), Or (Eq (rinvF a a_1) False) (Eq (rf a_1 a) True) % 3.90/4.06 Clause #132 (by clausification #[16]): ∀ (a : Iota), % 3.90/4.06 Eq % 3.90/4.06 (Iff (cUnsatisfiable a) % 3.90/4.06 (Exists fun Y => % 3.90/4.06 And (And (rf a Y) (Exists fun Z => And (rinvF Y Z) (Exists fun W => And (rf Z W) (Not (cp1 W))))) (cp1 Y))) % 3.90/4.06 True % 3.90/4.06 Clause #134 (by clausification #[132]): ∀ (a : Iota), % 3.90/4.06 Or (Eq (cUnsatisfiable a) False) % 3.90/4.06 (Eq % 3.90/4.06 (Exists fun Y => % 3.90/4.06 And (And (rf a Y) (Exists fun Z => And (rinvF Y Z) (Exists fun W => And (rf Z W) (Not (cp1 W))))) (cp1 Y)) % 3.90/4.06 True) % 3.90/4.06 Clause #143 (by clausification #[17]): ∀ (a : Iota), Eq (cowlThing a → ∀ (Y0 Y1 : Iota), And (rf a Y0) (rf a Y1) → Eq Y0 Y1) True % 3.90/4.06 Clause #144 (by clausification #[143]): ∀ (a : Iota), Or (Eq (cowlThing a) False) (Eq (∀ (Y0 Y1 : Iota), And (rf a Y0) (rf a Y1) → Eq Y0 Y1) True) % 3.90/4.06 Clause #145 (by clausification #[144]): ∀ (a a_1 : Iota), Or (Eq (cowlThing a) False) (Eq (∀ (Y1 : Iota), And (rf a a_1) (rf a Y1) → Eq a_1 Y1) True) % 3.90/4.06 Clause #146 (by clausification #[145]): ∀ (a a_1 a_2 : Iota), Or (Eq (cowlThing a) False) (Eq (And (rf a a_1) (rf a a_2) → Eq a_1 a_2) True) % 3.90/4.06 Clause #147 (by clausification #[146]): ∀ (a a_1 a_2 : Iota), Or (Eq (cowlThing a) False) (Or (Eq (And (rf a a_1) (rf a a_2)) False) (Eq (Eq a_1 a_2) True)) % 3.90/4.06 Clause #148 (by clausification #[147]): ∀ (a a_1 a_2 : Iota), % 3.90/4.06 Or (Eq (cowlThing a) False) (Or (Eq (Eq a_1 a_2) True) (Or (Eq (rf a a_1) False) (Eq (rf a a_2) False))) % 3.90/4.06 Clause #149 (by clausification #[148]): ∀ (a a_1 a_2 : Iota), Or (Eq (cowlThing a) False) (Or (Eq (rf a a_1) False) (Or (Eq (rf a a_2) False) (Eq a_1 a_2))) % 3.90/4.06 Clause #150 (by forward demodulation #[149, 70]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (rf a a_1) False) (Or (Eq (rf a a_2) False) (Eq a_1 a_2))) % 3.90/4.06 Clause #151 (by clausification #[150]): ∀ (a a_1 a_2 : Iota), Or (Eq (rf a a_1) False) (Or (Eq (rf a a_2) False) (Eq a_1 a_2)) % 3.90/4.06 Clause #152 (by clausification #[134]): ∀ (a a_1 : Iota), % 3.90/4.06 Or (Eq (cUnsatisfiable a) False) % 3.90/4.06 (Eq % 3.90/4.06 (And % 3.90/4.06 (And (rf a (skS.0 0 a a_1)) % 3.90/4.06 (Exists fun Z => And (rinvF (skS.0 0 a a_1) Z) (Exists fun W => And (rf Z W) (Not (cp1 W))))) % 3.90/4.06 (cp1 (skS.0 0 a a_1))) % 3.90/4.06 True) % 3.90/4.06 Clause #153 (by clausification #[152]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cp1 (skS.0 0 a a_1)) True) % 3.90/4.06 Clause #154 (by clausification #[152]): ∀ (a a_1 : Iota), % 3.90/4.06 Or (Eq (cUnsatisfiable a) False) % 3.90/4.06 (Eq % 3.90/4.06 (And (rf a (skS.0 0 a a_1)) % 3.90/4.06 (Exists fun Z => And (rinvF (skS.0 0 a a_1) Z) (Exists fun W => And (rf Z W) (Not (cp1 W))))) % 3.90/4.06 True) % 3.90/4.06 Clause #155 (by superposition #[153, 21]): ∀ (a : Iota), Or (Eq (cp1 (skS.0 0 i2003_11_14_17_19_42328 a)) True) (Eq False True) % 3.90/4.06 Clause #156 (by clausification #[155]): ∀ (a : Iota), Eq (cp1 (skS.0 0 i2003_11_14_17_19_42328 a)) True % 3.90/4.06 Clause #159 (by clausification #[154]): ∀ (a a_1 : Iota), % 3.90/4.06 Or (Eq (cUnsatisfiable a) False) % 3.90/4.06 (Eq (Exists fun Z => And (rinvF (skS.0 0 a a_1) Z) (Exists fun W => And (rf Z W) (Not (cp1 W)))) True) % 3.90/4.08 Clause #160 (by clausification #[154]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rf a (skS.0 0 a a_1)) True) % 3.90/4.08 Clause #161 (by clausification #[159]): ∀ (a a_1 a_2 : Iota), % 3.90/4.08 Or (Eq (cUnsatisfiable a) False) % 3.90/4.08 (Eq (And (rinvF (skS.0 0 a a_1) (skS.0 1 a a_1 a_2)) (Exists fun W => And (rf (skS.0 1 a a_1 a_2) W) (Not (cp1 W)))) % 3.90/4.08 True) % 3.90/4.08 Clause #162 (by clausification #[161]): ∀ (a a_1 a_2 : Iota), % 3.90/4.08 Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun W => And (rf (skS.0 1 a a_1 a_2) W) (Not (cp1 W))) True) % 3.90/4.08 Clause #163 (by clausification #[161]): ∀ (a a_1 a_2 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rinvF (skS.0 0 a a_1) (skS.0 1 a a_1 a_2)) True) % 3.90/4.08 Clause #164 (by clausification #[162]): ∀ (a a_1 a_2 a_3 : Iota), % 3.90/4.08 Or (Eq (cUnsatisfiable a) False) % 3.90/4.08 (Eq (And (rf (skS.0 1 a a_1 a_2) (skS.0 2 a a_1 a_2 a_3)) (Not (cp1 (skS.0 2 a a_1 a_2 a_3)))) True) % 3.90/4.08 Clause #165 (by clausification #[164]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Not (cp1 (skS.0 2 a a_1 a_2 a_3))) True) % 3.90/4.08 Clause #166 (by clausification #[164]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rf (skS.0 1 a a_1 a_2) (skS.0 2 a a_1 a_2 a_3)) True) % 3.90/4.08 Clause #167 (by clausification #[165]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cp1 (skS.0 2 a a_1 a_2 a_3)) False) % 3.90/4.08 Clause #168 (by superposition #[167, 21]): ∀ (a a_1 a_2 : Iota), Or (Eq (cp1 (skS.0 2 i2003_11_14_17_19_42328 a a_1 a_2)) False) (Eq False True) % 3.90/4.08 Clause #169 (by superposition #[160, 21]): ∀ (a : Iota), Or (Eq (rf i2003_11_14_17_19_42328 (skS.0 0 i2003_11_14_17_19_42328 a)) True) (Eq False True) % 3.90/4.08 Clause #170 (by clausification #[169]): ∀ (a : Iota), Eq (rf i2003_11_14_17_19_42328 (skS.0 0 i2003_11_14_17_19_42328 a)) True % 3.90/4.08 Clause #173 (by superposition #[170, 151]): ∀ (a a_1 : Iota), % 3.90/4.08 Or (Eq True False) (Or (Eq (rf i2003_11_14_17_19_42328 a) False) (Eq (skS.0 0 i2003_11_14_17_19_42328 a_1) a)) % 3.90/4.08 Clause #176 (by clausification #[173]): ∀ (a a_1 : Iota), Or (Eq (rf i2003_11_14_17_19_42328 a) False) (Eq (skS.0 0 i2003_11_14_17_19_42328 a_1) a) % 3.90/4.08 Clause #177 (by superposition #[176, 170]): ∀ (a a_1 : Iota), Or (Eq (skS.0 0 i2003_11_14_17_19_42328 a) (skS.0 0 i2003_11_14_17_19_42328 a_1)) (Eq False True) % 3.90/4.08 Clause #178 (by superposition #[163, 21]): ∀ (a a_1 : Iota), % 3.90/4.08 Or (Eq (rinvF (skS.0 0 i2003_11_14_17_19_42328 a) (skS.0 1 i2003_11_14_17_19_42328 a a_1)) True) (Eq False True) % 3.90/4.08 Clause #179 (by clausification #[168]): ∀ (a a_1 a_2 : Iota), Eq (cp1 (skS.0 2 i2003_11_14_17_19_42328 a a_1 a_2)) False % 3.90/4.08 Clause #180 (by clausification #[177]): ∀ (a a_1 : Iota), Eq (skS.0 0 i2003_11_14_17_19_42328 a) (skS.0 0 i2003_11_14_17_19_42328 a_1) % 3.90/4.08 Clause #181 (by clausification #[178]): ∀ (a a_1 : Iota), Eq (rinvF (skS.0 0 i2003_11_14_17_19_42328 a) (skS.0 1 i2003_11_14_17_19_42328 a a_1)) True % 3.90/4.08 Clause #182 (by superposition #[181, 131]): ∀ (a a_1 : Iota), % 3.90/4.08 Or (Eq True False) (Eq (rf (skS.0 1 i2003_11_14_17_19_42328 a a_1) (skS.0 0 i2003_11_14_17_19_42328 a)) True) % 3.90/4.08 Clause #185 (by clausification #[182]): ∀ (a a_1 : Iota), Eq (rf (skS.0 1 i2003_11_14_17_19_42328 a a_1) (skS.0 0 i2003_11_14_17_19_42328 a)) True % 3.90/4.08 Clause #189 (by superposition #[185, 180]): ∀ (a a_1 a_2 : Iota), Eq (rf (skS.0 1 i2003_11_14_17_19_42328 a a_1) (skS.0 0 i2003_11_14_17_19_42328 a_2)) True % 3.90/4.08 Clause #190 (by superposition #[166, 21]): ∀ (a a_1 a_2 : Iota), % 3.90/4.08 Or (Eq (rf (skS.0 1 i2003_11_14_17_19_42328 a a_1) (skS.0 2 i2003_11_14_17_19_42328 a a_1 a_2)) True) (Eq False True) % 3.90/4.08 Clause #193 (by superposition #[189, 151]): ∀ (a a_1 a_2 a_3 : Iota), % 3.90/4.08 Or (Eq True False) % 3.90/4.08 (Or (Eq (rf (skS.0 1 i2003_11_14_17_19_42328 a a_1) a_2) False) (Eq (skS.0 0 i2003_11_14_17_19_42328 a_3) a_2)) % 3.90/4.08 Clause #202 (by clausification #[193]): ∀ (a a_1 a_2 a_3 : Iota), % 3.90/4.08 Or (Eq (rf (skS.0 1 i2003_11_14_17_19_42328 a a_1) a_2) False) (Eq (skS.0 0 i2003_11_14_17_19_42328 a_3) a_2) % 3.90/4.08 Clause #205 (by clausification #[190]): ∀ (a a_1 a_2 : Iota), Eq (rf (skS.0 1 i2003_11_14_17_19_42328 a a_1) (skS.0 2 i2003_11_14_17_19_42328 a a_1 a_2)) True % 3.90/4.09 Clause #206 (by superposition #[205, 202]): ∀ (a a_1 a_2 a_3 : Iota), % 3.90/4.09 Or (Eq True False) (Eq (skS.0 0 i2003_11_14_17_19_42328 a) (skS.0 2 i2003_11_14_17_19_42328 a_1 a_2 a_3)) % 3.90/4.09 Clause #209 (by clausification #[206]): ∀ (a a_1 a_2 a_3 : Iota), Eq (skS.0 0 i2003_11_14_17_19_42328 a) (skS.0 2 i2003_11_14_17_19_42328 a_1 a_2 a_3) % 3.90/4.09 Clause #219 (by superposition #[209, 179]): ∀ (a : Iota), Eq (cp1 (skS.0 0 i2003_11_14_17_19_42328 a)) False % 3.90/4.09 Clause #220 (by superposition #[219, 156]): Eq False True % 3.90/4.09 Clause #221 (by clausification #[220]): False % 3.90/4.09 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------