%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS083+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 4.13s 4.29s % Output : Proof 4.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : KRS083+1 : TPTP v9.2.0. Released v3.1.0. % 0.07/0.13 % Command : duper %s % 0.14/0.35 % Computer : n016.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Thu Oct 2 10:16:23 EDT 2025 % 0.14/0.35 % CPUTime : % 4.13/4.29 SZS status Theorem for theBenchmark.p % 4.13/4.29 SZS output start Proof for theBenchmark.p % 4.13/4.29 Clause #15 (by assumption #[]): Eq (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) True % 4.13/4.29 Clause #17 (by assumption #[]): Eq % 4.13/4.29 (∀ (X : Iota), % 4.13/4.29 Iff (cUnsatisfiable X) % 4.13/4.29 (And (And (∀ (Y : Iota), rinvR X Y → Exists fun Z => And (rinvF Y Z) (cd Z)) (Not (cc X))) % 4.13/4.29 (Exists fun Y => And (rinvF X Y) (cd Y)))) % 4.13/4.29 True % 4.13/4.29 Clause #18 (by assumption #[]): Eq (∀ (X : Iota), Iff (cd X) (And (Exists fun Y => And (rf X Y) (Not (cc Y))) (cc X))) True % 4.13/4.29 Clause #19 (by assumption #[]): Eq (∀ (X : Iota), cowlThing X → ∀ (Y0 Y1 : Iota), And (rf X Y0) (rf X Y1) → Eq Y0 Y1) True % 4.13/4.29 Clause #20 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (rinvF X Y) (rf Y X)) True % 4.13/4.29 Clause #21 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (rinvR X Y) (rr Y X)) True % 4.13/4.29 Clause #23 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_19_32337) True % 4.13/4.29 Clause #24 (by assumption #[]): Eq (∀ (X Y : Iota), rf X Y → rr X Y) True % 4.13/4.29 Clause #67 (by clausification #[24]): ∀ (a : Iota), Eq (∀ (Y : Iota), rf a Y → rr a Y) True % 4.13/4.29 Clause #68 (by clausification #[67]): ∀ (a a_1 : Iota), Eq (rf a a_1 → rr a a_1) True % 4.13/4.29 Clause #69 (by clausification #[68]): ∀ (a a_1 : Iota), Or (Eq (rf a a_1) False) (Eq (rr a a_1) True) % 4.13/4.29 Clause #122 (by clausification #[15]): ∀ (a : Iota), Eq (And (cowlThing a) (Not (cowlNothing a))) True % 4.13/4.29 Clause #124 (by clausification #[122]): ∀ (a : Iota), Eq (cowlThing a) True % 4.13/4.29 Clause #136 (by clausification #[21]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (rinvR a Y) (rr Y a)) True % 4.13/4.29 Clause #137 (by clausification #[136]): ∀ (a a_1 : Iota), Eq (Iff (rinvR a a_1) (rr a_1 a)) True % 4.13/4.29 Clause #138 (by clausification #[137]): ∀ (a a_1 : Iota), Or (Eq (rinvR a a_1) True) (Eq (rr a_1 a) False) % 4.13/4.29 Clause #140 (by clausification #[17]): ∀ (a : Iota), % 4.13/4.29 Eq % 4.13/4.29 (Iff (cUnsatisfiable a) % 4.13/4.29 (And (And (∀ (Y : Iota), rinvR a Y → Exists fun Z => And (rinvF Y Z) (cd Z)) (Not (cc a))) % 4.13/4.29 (Exists fun Y => And (rinvF a Y) (cd Y)))) % 4.13/4.29 True % 4.13/4.29 Clause #142 (by clausification #[140]): ∀ (a : Iota), % 4.13/4.29 Or (Eq (cUnsatisfiable a) False) % 4.13/4.29 (Eq % 4.13/4.29 (And (And (∀ (Y : Iota), rinvR a Y → Exists fun Z => And (rinvF Y Z) (cd Z)) (Not (cc a))) % 4.13/4.29 (Exists fun Y => And (rinvF a Y) (cd Y))) % 4.13/4.29 True) % 4.13/4.29 Clause #152 (by clausification #[20]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (rinvF a Y) (rf Y a)) True % 4.13/4.29 Clause #153 (by clausification #[152]): ∀ (a a_1 : Iota), Eq (Iff (rinvF a a_1) (rf a_1 a)) True % 4.13/4.29 Clause #155 (by clausification #[153]): ∀ (a a_1 : Iota), Or (Eq (rinvF a a_1) False) (Eq (rf a_1 a) True) % 4.13/4.29 Clause #156 (by clausification #[19]): ∀ (a : Iota), Eq (cowlThing a → ∀ (Y0 Y1 : Iota), And (rf a Y0) (rf a Y1) → Eq Y0 Y1) True % 4.13/4.29 Clause #157 (by clausification #[156]): ∀ (a : Iota), Or (Eq (cowlThing a) False) (Eq (∀ (Y0 Y1 : Iota), And (rf a Y0) (rf a Y1) → Eq Y0 Y1) True) % 4.13/4.29 Clause #158 (by clausification #[157]): ∀ (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) % 4.13/4.29 Clause #159 (by clausification #[158]): ∀ (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) % 4.13/4.29 Clause #160 (by clausification #[159]): ∀ (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)) % 4.13/4.29 Clause #161 (by clausification #[160]): ∀ (a a_1 a_2 : Iota), % 4.13/4.29 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))) % 4.13/4.29 Clause #162 (by clausification #[161]): ∀ (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))) % 4.13/4.29 Clause #163 (by forward demodulation #[162, 124]): ∀ (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))) % 4.13/4.29 Clause #164 (by clausification #[163]): ∀ (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)) % 4.13/4.29 Clause #165 (by clausification #[18]): ∀ (a : Iota), Eq (Iff (cd a) (And (Exists fun Y => And (rf a Y) (Not (cc Y))) (cc a))) True % 4.13/4.31 Clause #167 (by clausification #[165]): ∀ (a : Iota), Or (Eq (cd a) False) (Eq (And (Exists fun Y => And (rf a Y) (Not (cc Y))) (cc a)) True) % 4.13/4.31 Clause #172 (by clausification #[142]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rinvF a Y) (cd Y)) True) % 4.13/4.31 Clause #173 (by clausification #[142]): ∀ (a : Iota), % 4.13/4.31 Or (Eq (cUnsatisfiable a) False) % 4.13/4.31 (Eq (And (∀ (Y : Iota), rinvR a Y → Exists fun Z => And (rinvF Y Z) (cd Z)) (Not (cc a))) True) % 4.13/4.31 Clause #174 (by clausification #[172]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rinvF a (skS.0 1 a a_1)) (cd (skS.0 1 a a_1))) True) % 4.13/4.31 Clause #175 (by clausification #[174]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cd (skS.0 1 a a_1)) True) % 4.13/4.31 Clause #176 (by clausification #[174]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rinvF a (skS.0 1 a a_1)) True) % 4.13/4.31 Clause #177 (by superposition #[175, 23]): ∀ (a : Iota), Or (Eq (cd (skS.0 1 i2003_11_14_17_19_32337 a)) True) (Eq False True) % 4.13/4.31 Clause #178 (by clausification #[177]): ∀ (a : Iota), Eq (cd (skS.0 1 i2003_11_14_17_19_32337 a)) True % 4.13/4.31 Clause #179 (by superposition #[176, 23]): ∀ (a : Iota), Or (Eq (rinvF i2003_11_14_17_19_32337 (skS.0 1 i2003_11_14_17_19_32337 a)) True) (Eq False True) % 4.13/4.31 Clause #180 (by clausification #[179]): ∀ (a : Iota), Eq (rinvF i2003_11_14_17_19_32337 (skS.0 1 i2003_11_14_17_19_32337 a)) True % 4.13/4.31 Clause #182 (by superposition #[180, 155]): ∀ (a : Iota), Or (Eq True False) (Eq (rf (skS.0 1 i2003_11_14_17_19_32337 a) i2003_11_14_17_19_32337) True) % 4.13/4.31 Clause #183 (by clausification #[182]): ∀ (a : Iota), Eq (rf (skS.0 1 i2003_11_14_17_19_32337 a) i2003_11_14_17_19_32337) True % 4.13/4.31 Clause #184 (by superposition #[183, 69]): ∀ (a : Iota), Or (Eq True False) (Eq (rr (skS.0 1 i2003_11_14_17_19_32337 a) i2003_11_14_17_19_32337) True) % 4.13/4.31 Clause #190 (by clausification #[184]): ∀ (a : Iota), Eq (rr (skS.0 1 i2003_11_14_17_19_32337 a) i2003_11_14_17_19_32337) True % 4.13/4.31 Clause #192 (by superposition #[190, 138]): ∀ (a : Iota), Or (Eq (rinvR i2003_11_14_17_19_32337 (skS.0 1 i2003_11_14_17_19_32337 a)) True) (Eq True False) % 4.13/4.31 Clause #193 (by clausification #[192]): ∀ (a : Iota), Eq (rinvR i2003_11_14_17_19_32337 (skS.0 1 i2003_11_14_17_19_32337 a)) True % 4.13/4.31 Clause #198 (by clausification #[167]): ∀ (a : Iota), Or (Eq (cd a) False) (Eq (cc a) True) % 4.13/4.31 Clause #199 (by clausification #[167]): ∀ (a : Iota), Or (Eq (cd a) False) (Eq (Exists fun Y => And (rf a Y) (Not (cc Y))) True) % 4.13/4.31 Clause #200 (by superposition #[198, 178]): ∀ (a : Iota), Or (Eq (cc (skS.0 1 i2003_11_14_17_19_32337 a)) True) (Eq False True) % 4.13/4.31 Clause #201 (by clausification #[200]): ∀ (a : Iota), Eq (cc (skS.0 1 i2003_11_14_17_19_32337 a)) True % 4.13/4.31 Clause #203 (by clausification #[199]): ∀ (a a_1 : Iota), Or (Eq (cd a) False) (Eq (And (rf a (skS.0 2 a a_1)) (Not (cc (skS.0 2 a a_1)))) True) % 4.13/4.31 Clause #204 (by clausification #[203]): ∀ (a a_1 : Iota), Or (Eq (cd a) False) (Eq (Not (cc (skS.0 2 a a_1))) True) % 4.13/4.31 Clause #205 (by clausification #[203]): ∀ (a a_1 : Iota), Or (Eq (cd a) False) (Eq (rf a (skS.0 2 a a_1)) True) % 4.13/4.31 Clause #206 (by clausification #[204]): ∀ (a a_1 : Iota), Or (Eq (cd a) False) (Eq (cc (skS.0 2 a a_1)) False) % 4.13/4.31 Clause #211 (by clausification #[173]): ∀ (a : Iota), % 4.13/4.31 Or (Eq (cUnsatisfiable a) False) (Eq (∀ (Y : Iota), rinvR a Y → Exists fun Z => And (rinvF Y Z) (cd Z)) True) % 4.13/4.31 Clause #217 (by clausification #[211]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rinvR a a_1 → Exists fun Z => And (rinvF a_1 Z) (cd Z)) True) % 4.13/4.31 Clause #218 (by clausification #[217]): ∀ (a a_1 : Iota), % 4.13/4.31 Or (Eq (cUnsatisfiable a) False) (Or (Eq (rinvR a a_1) False) (Eq (Exists fun Z => And (rinvF a_1 Z) (cd Z)) True)) % 4.13/4.31 Clause #219 (by clausification #[218]): ∀ (a a_1 a_2 : Iota), % 4.13/4.31 Or (Eq (cUnsatisfiable a) False) % 4.13/4.31 (Or (Eq (rinvR a a_1) False) (Eq (And (rinvF a_1 (skS.0 3 a_1 a_2)) (cd (skS.0 3 a_1 a_2))) True)) % 4.13/4.31 Clause #220 (by clausification #[219]): ∀ (a a_1 a_2 : Iota), Or (Eq (cUnsatisfiable a) False) (Or (Eq (rinvR a a_1) False) (Eq (cd (skS.0 3 a_1 a_2)) True)) % 4.13/4.33 Clause #221 (by clausification #[219]): ∀ (a a_1 a_2 : Iota), % 4.13/4.33 Or (Eq (cUnsatisfiable a) False) (Or (Eq (rinvR a a_1) False) (Eq (rinvF a_1 (skS.0 3 a_1 a_2)) True)) % 4.13/4.33 Clause #222 (by superposition #[220, 23]): ∀ (a a_1 : Iota), Or (Eq (rinvR i2003_11_14_17_19_32337 a) False) (Or (Eq (cd (skS.0 3 a a_1)) True) (Eq False True)) % 4.13/4.33 Clause #223 (by clausification #[222]): ∀ (a a_1 : Iota), Or (Eq (rinvR i2003_11_14_17_19_32337 a) False) (Eq (cd (skS.0 3 a a_1)) True) % 4.13/4.33 Clause #224 (by superposition #[223, 193]): ∀ (a a_1 : Iota), Or (Eq (cd (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1)) True) (Eq False True) % 4.13/4.33 Clause #225 (by superposition #[221, 23]): ∀ (a a_1 : Iota), % 4.13/4.33 Or (Eq (rinvR i2003_11_14_17_19_32337 a) False) (Or (Eq (rinvF a (skS.0 3 a a_1)) True) (Eq False True)) % 4.13/4.33 Clause #226 (by clausification #[225]): ∀ (a a_1 : Iota), Or (Eq (rinvR i2003_11_14_17_19_32337 a) False) (Eq (rinvF a (skS.0 3 a a_1)) True) % 4.13/4.33 Clause #227 (by superposition #[226, 193]): ∀ (a a_1 : Iota), % 4.13/4.33 Or (Eq (rinvF (skS.0 1 i2003_11_14_17_19_32337 a) (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1)) True) % 4.13/4.33 (Eq False True) % 4.13/4.33 Clause #230 (by clausification #[224]): ∀ (a a_1 : Iota), Eq (cd (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1)) True % 4.13/4.33 Clause #232 (by superposition #[230, 206]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (cc (skS.0 2 (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1) a_2)) False) % 4.13/4.33 Clause #233 (by superposition #[230, 205]): ∀ (a a_1 a_2 : Iota), % 4.13/4.33 Or (Eq True False) % 4.13/4.33 (Eq % 4.13/4.33 (rf (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1) % 4.13/4.33 (skS.0 2 (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1) a_2)) % 4.13/4.33 True) % 4.13/4.33 Clause #238 (by clausification #[232]): ∀ (a a_1 a_2 : Iota), Eq (cc (skS.0 2 (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1) a_2)) False % 4.13/4.33 Clause #239 (by clausification #[227]): ∀ (a a_1 : Iota), Eq (rinvF (skS.0 1 i2003_11_14_17_19_32337 a) (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1)) True % 4.13/4.33 Clause #241 (by superposition #[239, 155]): ∀ (a a_1 : Iota), % 4.13/4.33 Or (Eq True False) % 4.13/4.33 (Eq (rf (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1) (skS.0 1 i2003_11_14_17_19_32337 a)) True) % 4.13/4.33 Clause #251 (by clausification #[241]): ∀ (a a_1 : Iota), Eq (rf (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1) (skS.0 1 i2003_11_14_17_19_32337 a)) True % 4.13/4.33 Clause #254 (by superposition #[251, 164]): ∀ (a a_1 a_2 : Iota), % 4.13/4.33 Or (Eq True False) % 4.13/4.33 (Or (Eq (rf (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1) a_2) False) % 4.13/4.33 (Eq (skS.0 1 i2003_11_14_17_19_32337 a) a_2)) % 4.13/4.33 Clause #255 (by clausification #[233]): ∀ (a a_1 a_2 : Iota), % 4.13/4.33 Eq % 4.13/4.33 (rf (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1) % 4.13/4.33 (skS.0 2 (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1) a_2)) % 4.13/4.33 True % 4.13/4.33 Clause #264 (by clausification #[254]): ∀ (a a_1 a_2 : Iota), % 4.13/4.33 Or (Eq (rf (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1) a_2) False) (Eq (skS.0 1 i2003_11_14_17_19_32337 a) a_2) % 4.13/4.33 Clause #266 (by superposition #[264, 255]): ∀ (a a_1 a_2 : Iota), % 4.13/4.33 Or (Eq (skS.0 1 i2003_11_14_17_19_32337 a) (skS.0 2 (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1) a_2)) % 4.13/4.33 (Eq False True) % 4.13/4.33 Clause #288 (by clausification #[266]): ∀ (a a_1 a_2 : Iota), % 4.13/4.33 Eq (skS.0 1 i2003_11_14_17_19_32337 a) (skS.0 2 (skS.0 3 (skS.0 1 i2003_11_14_17_19_32337 a) a_1) a_2) % 4.13/4.33 Clause #289 (by backward demodulation #[288, 238]): ∀ (a : Iota), Eq (cc (skS.0 1 i2003_11_14_17_19_32337 a)) False % 4.13/4.33 Clause #290 (by superposition #[289, 201]): Eq False True % 4.13/4.33 Clause #291 (by clausification #[290]): False % 4.13/4.33 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------