%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS069+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 07:52:34 PM UTC 2025 % Result : Unsatisfiable 3.87s 4.12s % Output : Proof 3.94s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.15 % Problem : KRS069+1 : TPTP v9.2.0. Released v3.1.0. % 0.11/0.16 % Command : duper %s % 0.14/0.38 % Computer : n021.cluster.edu % 0.14/0.38 % Model : x86_64 x86_64 % 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.38 % Memory : 8042.1875MB % 0.14/0.38 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.38 % CPULimit : 300 % 0.14/0.38 % WCLimit : 300 % 0.14/0.38 % DateTime : Thu Oct 2 10:23:23 EDT 2025 % 0.14/0.38 % CPUTime : % 3.87/4.12 SZS status Theorem for theBenchmark.p % 3.87/4.12 SZS output start Proof for theBenchmark.p % 3.87/4.12 Clause #15 (by assumption #[]): Eq % 3.87/4.12 (∀ (X : Iota), % 3.87/4.12 Iff (cUnsatisfiable X) % 3.87/4.12 (And (And (Exists fun Y => And (rf1 X Y) (cp1 Y)) (Exists fun Y => And (rf2 X Y) (Not (cp1 Y)))) % 3.87/4.12 (Exists fun Y => And (rf3 X Y) (cp2 Y)))) % 3.87/4.12 True % 3.87/4.12 Clause #16 (by assumption #[]): Eq (∀ (X Y Z : Iota), And (rf1 X Y) (rf1 X Z) → Eq Y Z) True % 3.87/4.12 Clause #17 (by assumption #[]): Eq (∀ (X Y Z : Iota), And (rf2 X Y) (rf2 X Z) → Eq Y Z) True % 3.87/4.12 Clause #19 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_18_2750) True % 3.87/4.12 Clause #20 (by assumption #[]): Eq (∀ (X Y : Iota), rf3 X Y → rf1 X Y) True % 3.87/4.12 Clause #21 (by assumption #[]): Eq (∀ (X Y : Iota), rf3 X Y → rf2 X Y) True % 3.87/4.12 Clause #64 (by clausification #[21]): ∀ (a : Iota), Eq (∀ (Y : Iota), rf3 a Y → rf2 a Y) True % 3.87/4.12 Clause #65 (by clausification #[64]): ∀ (a a_1 : Iota), Eq (rf3 a a_1 → rf2 a a_1) True % 3.87/4.12 Clause #66 (by clausification #[65]): ∀ (a a_1 : Iota), Or (Eq (rf3 a a_1) False) (Eq (rf2 a a_1) True) % 3.87/4.12 Clause #67 (by clausification #[20]): ∀ (a : Iota), Eq (∀ (Y : Iota), rf3 a Y → rf1 a Y) True % 3.87/4.12 Clause #68 (by clausification #[67]): ∀ (a a_1 : Iota), Eq (rf3 a a_1 → rf1 a a_1) True % 3.87/4.12 Clause #69 (by clausification #[68]): ∀ (a a_1 : Iota), Or (Eq (rf3 a a_1) False) (Eq (rf1 a a_1) True) % 3.87/4.12 Clause #118 (by clausification #[17]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), And (rf2 a Y) (rf2 a Z) → Eq Y Z) True % 3.87/4.12 Clause #119 (by clausification #[118]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), And (rf2 a a_1) (rf2 a Z) → Eq a_1 Z) True % 3.87/4.12 Clause #120 (by clausification #[119]): ∀ (a a_1 a_2 : Iota), Eq (And (rf2 a a_1) (rf2 a a_2) → Eq a_1 a_2) True % 3.87/4.12 Clause #121 (by clausification #[120]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (rf2 a a_1) (rf2 a a_2)) False) (Eq (Eq a_1 a_2) True) % 3.87/4.12 Clause #122 (by clausification #[121]): ∀ (a a_1 a_2 : Iota), Or (Eq (Eq a a_1) True) (Or (Eq (rf2 a_2 a) False) (Eq (rf2 a_2 a_1) False)) % 3.87/4.12 Clause #123 (by clausification #[122]): ∀ (a a_1 a_2 : Iota), Or (Eq (rf2 a a_1) False) (Or (Eq (rf2 a a_2) False) (Eq a_1 a_2)) % 3.87/4.12 Clause #124 (by clausification #[16]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), And (rf1 a Y) (rf1 a Z) → Eq Y Z) True % 3.87/4.12 Clause #125 (by clausification #[124]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), And (rf1 a a_1) (rf1 a Z) → Eq a_1 Z) True % 3.87/4.12 Clause #126 (by clausification #[125]): ∀ (a a_1 a_2 : Iota), Eq (And (rf1 a a_1) (rf1 a a_2) → Eq a_1 a_2) True % 3.87/4.12 Clause #127 (by clausification #[126]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (rf1 a a_1) (rf1 a a_2)) False) (Eq (Eq a_1 a_2) True) % 3.87/4.12 Clause #128 (by clausification #[127]): ∀ (a a_1 a_2 : Iota), Or (Eq (Eq a a_1) True) (Or (Eq (rf1 a_2 a) False) (Eq (rf1 a_2 a_1) False)) % 3.87/4.12 Clause #129 (by clausification #[128]): ∀ (a a_1 a_2 : Iota), Or (Eq (rf1 a a_1) False) (Or (Eq (rf1 a a_2) False) (Eq a_1 a_2)) % 3.87/4.12 Clause #136 (by clausification #[15]): ∀ (a : Iota), % 3.87/4.12 Eq % 3.87/4.12 (Iff (cUnsatisfiable a) % 3.87/4.12 (And (And (Exists fun Y => And (rf1 a Y) (cp1 Y)) (Exists fun Y => And (rf2 a Y) (Not (cp1 Y)))) % 3.87/4.12 (Exists fun Y => And (rf3 a Y) (cp2 Y)))) % 3.87/4.12 True % 3.87/4.12 Clause #138 (by clausification #[136]): ∀ (a : Iota), % 3.87/4.12 Or (Eq (cUnsatisfiable a) False) % 3.87/4.12 (Eq % 3.87/4.12 (And (And (Exists fun Y => And (rf1 a Y) (cp1 Y)) (Exists fun Y => And (rf2 a Y) (Not (cp1 Y)))) % 3.87/4.12 (Exists fun Y => And (rf3 a Y) (cp2 Y))) % 3.87/4.12 True) % 3.87/4.12 Clause #148 (by clausification #[138]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rf3 a Y) (cp2 Y)) True) % 3.87/4.12 Clause #149 (by clausification #[138]): ∀ (a : Iota), % 3.87/4.12 Or (Eq (cUnsatisfiable a) False) % 3.87/4.12 (Eq (And (Exists fun Y => And (rf1 a Y) (cp1 Y)) (Exists fun Y => And (rf2 a Y) (Not (cp1 Y)))) True) % 3.87/4.12 Clause #150 (by clausification #[148]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rf3 a (skS.0 0 a a_1)) (cp2 (skS.0 0 a a_1))) True) % 3.87/4.12 Clause #152 (by clausification #[150]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rf3 a (skS.0 0 a a_1)) True) % 3.87/4.12 Clause #155 (by superposition #[152, 19]): ∀ (a : Iota), Or (Eq (rf3 i2003_11_14_17_18_2750 (skS.0 0 i2003_11_14_17_18_2750 a)) True) (Eq False True) % 3.94/4.14 Clause #156 (by clausification #[155]): ∀ (a : Iota), Eq (rf3 i2003_11_14_17_18_2750 (skS.0 0 i2003_11_14_17_18_2750 a)) True % 3.94/4.14 Clause #157 (by superposition #[156, 66]): ∀ (a : Iota), Or (Eq True False) (Eq (rf2 i2003_11_14_17_18_2750 (skS.0 0 i2003_11_14_17_18_2750 a)) True) % 3.94/4.14 Clause #158 (by superposition #[156, 69]): ∀ (a : Iota), Or (Eq True False) (Eq (rf1 i2003_11_14_17_18_2750 (skS.0 0 i2003_11_14_17_18_2750 a)) True) % 3.94/4.14 Clause #161 (by clausification #[158]): ∀ (a : Iota), Eq (rf1 i2003_11_14_17_18_2750 (skS.0 0 i2003_11_14_17_18_2750 a)) True % 3.94/4.14 Clause #163 (by clausification #[149]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rf2 a Y) (Not (cp1 Y))) True) % 3.94/4.14 Clause #164 (by clausification #[149]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rf1 a Y) (cp1 Y)) True) % 3.94/4.14 Clause #165 (by clausification #[163]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rf2 a (skS.0 1 a a_1)) (Not (cp1 (skS.0 1 a a_1)))) True) % 3.94/4.14 Clause #166 (by clausification #[165]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Not (cp1 (skS.0 1 a a_1))) True) % 3.94/4.14 Clause #167 (by clausification #[165]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rf2 a (skS.0 1 a a_1)) True) % 3.94/4.14 Clause #168 (by clausification #[166]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cp1 (skS.0 1 a a_1)) False) % 3.94/4.14 Clause #169 (by superposition #[168, 19]): ∀ (a : Iota), Or (Eq (cp1 (skS.0 1 i2003_11_14_17_18_2750 a)) False) (Eq False True) % 3.94/4.14 Clause #170 (by clausification #[169]): ∀ (a : Iota), Eq (cp1 (skS.0 1 i2003_11_14_17_18_2750 a)) False % 3.94/4.14 Clause #171 (by clausification #[164]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rf1 a (skS.0 2 a a_1)) (cp1 (skS.0 2 a a_1))) True) % 3.94/4.14 Clause #172 (by clausification #[171]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cp1 (skS.0 2 a a_1)) True) % 3.94/4.14 Clause #173 (by clausification #[171]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rf1 a (skS.0 2 a a_1)) True) % 3.94/4.14 Clause #174 (by superposition #[172, 19]): ∀ (a : Iota), Or (Eq (cp1 (skS.0 2 i2003_11_14_17_18_2750 a)) True) (Eq False True) % 3.94/4.14 Clause #175 (by clausification #[174]): ∀ (a : Iota), Eq (cp1 (skS.0 2 i2003_11_14_17_18_2750 a)) True % 3.94/4.14 Clause #176 (by clausification #[157]): ∀ (a : Iota), Eq (rf2 i2003_11_14_17_18_2750 (skS.0 0 i2003_11_14_17_18_2750 a)) True % 3.94/4.14 Clause #177 (by superposition #[176, 123]): ∀ (a a_1 : Iota), % 3.94/4.14 Or (Eq True False) (Or (Eq (rf2 i2003_11_14_17_18_2750 a) False) (Eq (skS.0 0 i2003_11_14_17_18_2750 a_1) a)) % 3.94/4.14 Clause #178 (by superposition #[167, 19]): ∀ (a : Iota), Or (Eq (rf2 i2003_11_14_17_18_2750 (skS.0 1 i2003_11_14_17_18_2750 a)) True) (Eq False True) % 3.94/4.14 Clause #181 (by clausification #[178]): ∀ (a : Iota), Eq (rf2 i2003_11_14_17_18_2750 (skS.0 1 i2003_11_14_17_18_2750 a)) True % 3.94/4.14 Clause #183 (by superposition #[173, 19]): ∀ (a : Iota), Or (Eq (rf1 i2003_11_14_17_18_2750 (skS.0 2 i2003_11_14_17_18_2750 a)) True) (Eq False True) % 3.94/4.14 Clause #184 (by clausification #[183]): ∀ (a : Iota), Eq (rf1 i2003_11_14_17_18_2750 (skS.0 2 i2003_11_14_17_18_2750 a)) True % 3.94/4.14 Clause #185 (by superposition #[184, 129]): ∀ (a a_1 : Iota), % 3.94/4.14 Or (Eq True False) (Or (Eq (rf1 i2003_11_14_17_18_2750 a) False) (Eq (skS.0 2 i2003_11_14_17_18_2750 a_1) a)) % 3.94/4.14 Clause #186 (by clausification #[185]): ∀ (a a_1 : Iota), Or (Eq (rf1 i2003_11_14_17_18_2750 a) False) (Eq (skS.0 2 i2003_11_14_17_18_2750 a_1) a) % 3.94/4.14 Clause #187 (by superposition #[186, 161]): ∀ (a a_1 : Iota), Or (Eq (skS.0 2 i2003_11_14_17_18_2750 a) (skS.0 0 i2003_11_14_17_18_2750 a_1)) (Eq False True) % 3.94/4.14 Clause #189 (by clausification #[177]): ∀ (a a_1 : Iota), Or (Eq (rf2 i2003_11_14_17_18_2750 a) False) (Eq (skS.0 0 i2003_11_14_17_18_2750 a_1) a) % 3.94/4.14 Clause #190 (by superposition #[189, 181]): ∀ (a a_1 : Iota), Or (Eq (skS.0 0 i2003_11_14_17_18_2750 a) (skS.0 1 i2003_11_14_17_18_2750 a_1)) (Eq False True) % 3.94/4.14 Clause #199 (by clausification #[190]): ∀ (a a_1 : Iota), Eq (skS.0 0 i2003_11_14_17_18_2750 a) (skS.0 1 i2003_11_14_17_18_2750 a_1) % 3.94/4.14 Clause #205 (by superposition #[199, 170]): ∀ (a : Iota), Eq (cp1 (skS.0 0 i2003_11_14_17_18_2750 a)) False % 3.94/4.14 Clause #206 (by clausification #[187]): ∀ (a a_1 : Iota), Eq (skS.0 2 i2003_11_14_17_18_2750 a) (skS.0 0 i2003_11_14_17_18_2750 a_1) % 3.94/4.14 Clause #212 (by superposition #[206, 205]): ∀ (a : Iota), Eq (cp1 (skS.0 2 i2003_11_14_17_18_2750 a)) False % 3.94/4.14 Clause #214 (by superposition #[212, 175]): Eq False True % 3.94/4.14 Clause #215 (by clausification #[214]): False % 3.94/4.14 SZS output end Proof for theBenchmark.p 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