%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS079+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n016.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 3.77s 4.04s % Output : Proof 3.86s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.16 % Problem : KRS079+1 : TPTP v9.2.0. Released v3.1.0. % 0.12/0.17 % Command : duper %s % 0.14/0.38 % Computer : n016.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 10:20:38 EDT 2025 % 0.14/0.38 % CPUTime : % 3.77/4.04 SZS status Theorem for theBenchmark.p % 3.77/4.04 SZS output start Proof for theBenchmark.p % 3.77/4.04 Clause #13 (by assumption #[]): Eq (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) True % 3.77/4.04 Clause #15 (by assumption #[]): Eq % 3.77/4.04 (∀ (X : Iota), % 3.77/4.04 Iff (cUnsatisfiable X) % 3.77/4.04 (And (And (Exists fun Y => And (rf2 X Y) (cp2 Y)) (Exists fun Y => And (rf1 X Y) (cp1 Y))) % 3.77/4.04 (Exists fun Y => And (rr X Y) (cowlThing Y)))) % 3.77/4.04 True % 3.77/4.04 Clause #16 (by assumption #[]): Eq (∀ (X : Iota), cp1 X → Not (cp2 X)) True % 3.77/4.04 Clause #17 (by assumption #[]): Eq (∀ (X : Iota), cowlThing X → ∀ (Y0 Y1 : Iota), And (rf1 X Y0) (rf1 X Y1) → Eq Y0 Y1) True % 3.77/4.04 Clause #18 (by assumption #[]): Eq (∀ (X : Iota), cowlThing X → ∀ (Y0 Y1 : Iota), And (rf2 X Y0) (rf2 X Y1) → Eq Y0 Y1) True % 3.77/4.04 Clause #19 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_19_17492) True % 3.77/4.04 Clause #20 (by assumption #[]): Eq (∀ (X Y : Iota), rr X Y → rf1 X Y) True % 3.77/4.04 Clause #21 (by assumption #[]): Eq (∀ (X Y : Iota), rr X Y → rf2 X Y) True % 3.77/4.04 Clause #22 (by clausification #[16]): ∀ (a : Iota), Eq (cp1 a → Not (cp2 a)) True % 3.77/4.04 Clause #23 (by clausification #[22]): ∀ (a : Iota), Or (Eq (cp1 a) False) (Eq (Not (cp2 a)) True) % 3.77/4.04 Clause #24 (by clausification #[23]): ∀ (a : Iota), Or (Eq (cp1 a) False) (Eq (cp2 a) False) % 3.77/4.04 Clause #67 (by clausification #[21]): ∀ (a : Iota), Eq (∀ (Y : Iota), rr a Y → rf2 a Y) True % 3.77/4.04 Clause #68 (by clausification #[67]): ∀ (a a_1 : Iota), Eq (rr a a_1 → rf2 a a_1) True % 3.77/4.04 Clause #69 (by clausification #[68]): ∀ (a a_1 : Iota), Or (Eq (rr a a_1) False) (Eq (rf2 a a_1) True) % 3.77/4.04 Clause #70 (by clausification #[20]): ∀ (a : Iota), Eq (∀ (Y : Iota), rr a Y → rf1 a Y) True % 3.77/4.04 Clause #71 (by clausification #[70]): ∀ (a a_1 : Iota), Eq (rr a a_1 → rf1 a a_1) True % 3.77/4.04 Clause #72 (by clausification #[71]): ∀ (a a_1 : Iota), Or (Eq (rr a a_1) False) (Eq (rf1 a a_1) True) % 3.77/4.04 Clause #112 (by clausification #[13]): ∀ (a : Iota), Eq (And (cowlThing a) (Not (cowlNothing a))) True % 3.77/4.04 Clause #114 (by clausification #[112]): ∀ (a : Iota), Eq (cowlThing a) True % 3.77/4.04 Clause #121 (by clausification #[17]): ∀ (a : Iota), Eq (cowlThing a → ∀ (Y0 Y1 : Iota), And (rf1 a Y0) (rf1 a Y1) → Eq Y0 Y1) True % 3.77/4.04 Clause #122 (by clausification #[121]): ∀ (a : Iota), Or (Eq (cowlThing a) False) (Eq (∀ (Y0 Y1 : Iota), And (rf1 a Y0) (rf1 a Y1) → Eq Y0 Y1) True) % 3.77/4.04 Clause #123 (by clausification #[122]): ∀ (a a_1 : Iota), Or (Eq (cowlThing a) False) (Eq (∀ (Y1 : Iota), And (rf1 a a_1) (rf1 a Y1) → Eq a_1 Y1) True) % 3.77/4.04 Clause #124 (by clausification #[123]): ∀ (a a_1 a_2 : Iota), Or (Eq (cowlThing a) False) (Eq (And (rf1 a a_1) (rf1 a a_2) → Eq a_1 a_2) True) % 3.77/4.04 Clause #125 (by clausification #[124]): ∀ (a a_1 a_2 : Iota), Or (Eq (cowlThing a) False) (Or (Eq (And (rf1 a a_1) (rf1 a a_2)) False) (Eq (Eq a_1 a_2) True)) % 3.77/4.04 Clause #126 (by clausification #[125]): ∀ (a a_1 a_2 : Iota), % 3.77/4.04 Or (Eq (cowlThing a) False) (Or (Eq (Eq a_1 a_2) True) (Or (Eq (rf1 a a_1) False) (Eq (rf1 a a_2) False))) % 3.77/4.04 Clause #127 (by clausification #[126]): ∀ (a a_1 a_2 : Iota), Or (Eq (cowlThing a) False) (Or (Eq (rf1 a a_1) False) (Or (Eq (rf1 a a_2) False) (Eq a_1 a_2))) % 3.77/4.04 Clause #128 (by forward demodulation #[127, 114]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (rf1 a a_1) False) (Or (Eq (rf1 a a_2) False) (Eq a_1 a_2))) % 3.77/4.04 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)) % 3.77/4.04 Clause #130 (by clausification #[18]): ∀ (a : Iota), Eq (cowlThing a → ∀ (Y0 Y1 : Iota), And (rf2 a Y0) (rf2 a Y1) → Eq Y0 Y1) True % 3.77/4.04 Clause #131 (by clausification #[130]): ∀ (a : Iota), Or (Eq (cowlThing a) False) (Eq (∀ (Y0 Y1 : Iota), And (rf2 a Y0) (rf2 a Y1) → Eq Y0 Y1) True) % 3.77/4.04 Clause #132 (by clausification #[131]): ∀ (a a_1 : Iota), Or (Eq (cowlThing a) False) (Eq (∀ (Y1 : Iota), And (rf2 a a_1) (rf2 a Y1) → Eq a_1 Y1) True) % 3.77/4.04 Clause #133 (by clausification #[132]): ∀ (a a_1 a_2 : Iota), Or (Eq (cowlThing a) False) (Eq (And (rf2 a a_1) (rf2 a a_2) → Eq a_1 a_2) True) % 3.77/4.04 Clause #134 (by clausification #[133]): ∀ (a a_1 a_2 : Iota), Or (Eq (cowlThing a) False) (Or (Eq (And (rf2 a a_1) (rf2 a a_2)) False) (Eq (Eq a_1 a_2) True)) % 3.84/4.06 Clause #135 (by clausification #[134]): ∀ (a a_1 a_2 : Iota), % 3.84/4.06 Or (Eq (cowlThing a) False) (Or (Eq (Eq a_1 a_2) True) (Or (Eq (rf2 a a_1) False) (Eq (rf2 a a_2) False))) % 3.84/4.06 Clause #136 (by clausification #[135]): ∀ (a a_1 a_2 : Iota), Or (Eq (cowlThing a) False) (Or (Eq (rf2 a a_1) False) (Or (Eq (rf2 a a_2) False) (Eq a_1 a_2))) % 3.84/4.06 Clause #137 (by forward demodulation #[136, 114]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (rf2 a a_1) False) (Or (Eq (rf2 a a_2) False) (Eq a_1 a_2))) % 3.84/4.06 Clause #138 (by clausification #[137]): ∀ (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)) % 3.84/4.06 Clause #139 (by clausification #[15]): ∀ (a : Iota), % 3.84/4.06 Eq % 3.84/4.06 (Iff (cUnsatisfiable a) % 3.84/4.06 (And (And (Exists fun Y => And (rf2 a Y) (cp2 Y)) (Exists fun Y => And (rf1 a Y) (cp1 Y))) % 3.84/4.06 (Exists fun Y => And (rr a Y) (cowlThing Y)))) % 3.84/4.06 True % 3.84/4.06 Clause #141 (by clausification #[139]): ∀ (a : Iota), % 3.84/4.06 Or (Eq (cUnsatisfiable a) False) % 3.84/4.06 (Eq % 3.84/4.06 (And (And (Exists fun Y => And (rf2 a Y) (cp2 Y)) (Exists fun Y => And (rf1 a Y) (cp1 Y))) % 3.84/4.06 (Exists fun Y => And (rr a Y) (cowlThing Y))) % 3.84/4.06 True) % 3.84/4.06 Clause #152 (by clausification #[141]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rr a Y) (cowlThing Y)) True) % 3.84/4.06 Clause #153 (by clausification #[141]): ∀ (a : Iota), % 3.84/4.06 Or (Eq (cUnsatisfiable a) False) % 3.84/4.06 (Eq (And (Exists fun Y => And (rf2 a Y) (cp2 Y)) (Exists fun Y => And (rf1 a Y) (cp1 Y))) True) % 3.84/4.06 Clause #154 (by clausification #[152]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rr a (skS.0 0 a a_1)) (cowlThing (skS.0 0 a a_1))) True) % 3.84/4.06 Clause #156 (by clausification #[154]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rr a (skS.0 0 a a_1)) True) % 3.84/4.06 Clause #157 (by superposition #[156, 19]): ∀ (a : Iota), Or (Eq (rr i2003_11_14_17_19_17492 (skS.0 0 i2003_11_14_17_19_17492 a)) True) (Eq False True) % 3.84/4.06 Clause #158 (by clausification #[157]): ∀ (a : Iota), Eq (rr i2003_11_14_17_19_17492 (skS.0 0 i2003_11_14_17_19_17492 a)) True % 3.84/4.06 Clause #159 (by superposition #[158, 69]): ∀ (a : Iota), Or (Eq True False) (Eq (rf2 i2003_11_14_17_19_17492 (skS.0 0 i2003_11_14_17_19_17492 a)) True) % 3.84/4.06 Clause #160 (by superposition #[158, 72]): ∀ (a : Iota), Or (Eq True False) (Eq (rf1 i2003_11_14_17_19_17492 (skS.0 0 i2003_11_14_17_19_17492 a)) True) % 3.84/4.06 Clause #162 (by clausification #[160]): ∀ (a : Iota), Eq (rf1 i2003_11_14_17_19_17492 (skS.0 0 i2003_11_14_17_19_17492 a)) True % 3.84/4.06 Clause #164 (by clausification #[159]): ∀ (a : Iota), Eq (rf2 i2003_11_14_17_19_17492 (skS.0 0 i2003_11_14_17_19_17492 a)) True % 3.84/4.06 Clause #165 (by superposition #[164, 138]): ∀ (a a_1 : Iota), % 3.84/4.06 Or (Eq True False) (Or (Eq (rf2 i2003_11_14_17_19_17492 a) False) (Eq (skS.0 0 i2003_11_14_17_19_17492 a_1) a)) % 3.84/4.06 Clause #166 (by clausification #[153]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rf1 a Y) (cp1 Y)) True) % 3.84/4.06 Clause #167 (by clausification #[153]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rf2 a Y) (cp2 Y)) True) % 3.84/4.06 Clause #168 (by clausification #[166]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rf1 a (skS.0 1 a a_1)) (cp1 (skS.0 1 a a_1))) True) % 3.84/4.06 Clause #169 (by clausification #[168]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cp1 (skS.0 1 a a_1)) True) % 3.84/4.06 Clause #170 (by clausification #[168]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rf1 a (skS.0 1 a a_1)) True) % 3.84/4.06 Clause #171 (by superposition #[169, 19]): ∀ (a : Iota), Or (Eq (cp1 (skS.0 1 i2003_11_14_17_19_17492 a)) True) (Eq False True) % 3.84/4.06 Clause #172 (by clausification #[171]): ∀ (a : Iota), Eq (cp1 (skS.0 1 i2003_11_14_17_19_17492 a)) True % 3.84/4.06 Clause #173 (by superposition #[172, 24]): ∀ (a : Iota), Or (Eq True False) (Eq (cp2 (skS.0 1 i2003_11_14_17_19_17492 a)) False) % 3.84/4.06 Clause #174 (by clausification #[173]): ∀ (a : Iota), Eq (cp2 (skS.0 1 i2003_11_14_17_19_17492 a)) False % 3.84/4.06 Clause #175 (by clausification #[167]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rf2 a (skS.0 2 a a_1)) (cp2 (skS.0 2 a a_1))) True) % 3.86/4.07 Clause #176 (by clausification #[175]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cp2 (skS.0 2 a a_1)) True) % 3.86/4.07 Clause #177 (by clausification #[175]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rf2 a (skS.0 2 a a_1)) True) % 3.86/4.07 Clause #178 (by superposition #[176, 19]): ∀ (a : Iota), Or (Eq (cp2 (skS.0 2 i2003_11_14_17_19_17492 a)) True) (Eq False True) % 3.86/4.07 Clause #179 (by clausification #[178]): ∀ (a : Iota), Eq (cp2 (skS.0 2 i2003_11_14_17_19_17492 a)) True % 3.86/4.07 Clause #180 (by superposition #[177, 19]): ∀ (a : Iota), Or (Eq (rf2 i2003_11_14_17_19_17492 (skS.0 2 i2003_11_14_17_19_17492 a)) True) (Eq False True) % 3.86/4.07 Clause #183 (by clausification #[180]): ∀ (a : Iota), Eq (rf2 i2003_11_14_17_19_17492 (skS.0 2 i2003_11_14_17_19_17492 a)) True % 3.86/4.07 Clause #185 (by superposition #[170, 19]): ∀ (a : Iota), Or (Eq (rf1 i2003_11_14_17_19_17492 (skS.0 1 i2003_11_14_17_19_17492 a)) True) (Eq False True) % 3.86/4.07 Clause #186 (by clausification #[185]): ∀ (a : Iota), Eq (rf1 i2003_11_14_17_19_17492 (skS.0 1 i2003_11_14_17_19_17492 a)) True % 3.86/4.07 Clause #187 (by superposition #[186, 129]): ∀ (a a_1 : Iota), % 3.86/4.07 Or (Eq True False) (Or (Eq (rf1 i2003_11_14_17_19_17492 a) False) (Eq (skS.0 1 i2003_11_14_17_19_17492 a_1) a)) % 3.86/4.07 Clause #188 (by clausification #[165]): ∀ (a a_1 : Iota), Or (Eq (rf2 i2003_11_14_17_19_17492 a) False) (Eq (skS.0 0 i2003_11_14_17_19_17492 a_1) a) % 3.86/4.07 Clause #190 (by superposition #[188, 183]): ∀ (a a_1 : Iota), Or (Eq (skS.0 0 i2003_11_14_17_19_17492 a) (skS.0 2 i2003_11_14_17_19_17492 a_1)) (Eq False True) % 3.86/4.07 Clause #196 (by clausification #[187]): ∀ (a a_1 : Iota), Or (Eq (rf1 i2003_11_14_17_19_17492 a) False) (Eq (skS.0 1 i2003_11_14_17_19_17492 a_1) a) % 3.86/4.07 Clause #197 (by superposition #[196, 162]): ∀ (a a_1 : Iota), Or (Eq (skS.0 1 i2003_11_14_17_19_17492 a) (skS.0 0 i2003_11_14_17_19_17492 a_1)) (Eq False True) % 3.86/4.07 Clause #200 (by clausification #[197]): ∀ (a a_1 : Iota), Eq (skS.0 1 i2003_11_14_17_19_17492 a) (skS.0 0 i2003_11_14_17_19_17492 a_1) % 3.86/4.07 Clause #202 (by superposition #[200, 174]): ∀ (a : Iota), Eq (cp2 (skS.0 0 i2003_11_14_17_19_17492 a)) False % 3.86/4.07 Clause #213 (by clausification #[190]): ∀ (a a_1 : Iota), Eq (skS.0 0 i2003_11_14_17_19_17492 a) (skS.0 2 i2003_11_14_17_19_17492 a_1) % 3.86/4.07 Clause #220 (by superposition #[213, 179]): ∀ (a : Iota), Eq (cp2 (skS.0 0 i2003_11_14_17_19_17492 a)) True % 3.86/4.07 Clause #221 (by superposition #[220, 202]): Eq True False % 3.86/4.07 Clause #222 (by clausification #[221]): False % 3.86/4.07 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------