%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS115+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n020.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 07:52:39 PM UTC 2025 % Result : Unsatisfiable 3.86s 4.03s % Output : Proof 3.90s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : KRS115+1 : TPTP v9.2.0. Released v3.1.0. % 0.04/0.14 % Command : duper %s % 0.13/0.35 % Computer : n020.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Thu Oct 2 10:16:08 EDT 2025 % 0.13/0.35 % CPUTime : % 3.86/4.03 SZS status Theorem for theBenchmark.p % 3.86/4.03 SZS output start Proof for theBenchmark.p % 3.86/4.03 Clause #16 (by assumption #[]): Eq (∀ (X : Iota), And (cowlThing X) (Not (cowlNothing X))) True % 3.86/4.03 Clause #18 (by assumption #[]): Eq % 3.86/4.03 (∀ (X : Iota), % 3.86/4.03 Iff (cUnsatisfiable X) % 3.86/4.03 (And (And (Exists fun Y => And (rf2 X Y) (cp2 Y)) (Exists fun Y => And (rf1 X Y) (cp1 Y))) % 3.86/4.03 (Exists fun Y => And (rr X Y) (cowlThing Y)))) % 3.86/4.03 True % 3.86/4.03 Clause #19 (by assumption #[]): Eq (∀ (X : Iota), cp1 X → cp2xcomp X) True % 3.86/4.03 Clause #20 (by assumption #[]): Eq (∀ (X : Iota), Iff (cp2 X) (Not (Exists fun Y => ra_Px1 X Y))) True % 3.86/4.03 Clause #21 (by assumption #[]): Eq (∀ (X : Iota), Iff (cp2xcomp X) (Exists fun Y0 => ra_Px1 X Y0)) True % 3.86/4.03 Clause #22 (by assumption #[]): Eq (∀ (X : Iota), cowlThing X → ∀ (Y0 Y1 : Iota), And (rf1 X Y0) (rf1 X Y1) → Eq Y0 Y1) True % 3.86/4.03 Clause #23 (by assumption #[]): Eq (∀ (X : Iota), cowlThing X → ∀ (Y0 Y1 : Iota), And (rf2 X Y0) (rf2 X Y1) → Eq Y0 Y1) True % 3.86/4.03 Clause #24 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_21_30578) True % 3.86/4.03 Clause #25 (by assumption #[]): Eq (∀ (X Y : Iota), rr X Y → rf2 X Y) True % 3.86/4.03 Clause #26 (by assumption #[]): Eq (∀ (X Y : Iota), rr X Y → rf1 X Y) True % 3.86/4.03 Clause #27 (by clausification #[19]): ∀ (a : Iota), Eq (cp1 a → cp2xcomp a) True % 3.86/4.03 Clause #28 (by clausification #[27]): ∀ (a : Iota), Or (Eq (cp1 a) False) (Eq (cp2xcomp a) True) % 3.86/4.03 Clause #77 (by clausification #[25]): ∀ (a : Iota), Eq (∀ (Y : Iota), rr a Y → rf2 a Y) True % 3.86/4.03 Clause #78 (by clausification #[77]): ∀ (a a_1 : Iota), Eq (rr a a_1 → rf2 a a_1) True % 3.86/4.03 Clause #79 (by clausification #[78]): ∀ (a a_1 : Iota), Or (Eq (rr a a_1) False) (Eq (rf2 a a_1) True) % 3.86/4.03 Clause #87 (by clausification #[26]): ∀ (a : Iota), Eq (∀ (Y : Iota), rr a Y → rf1 a Y) True % 3.86/4.03 Clause #88 (by clausification #[87]): ∀ (a a_1 : Iota), Eq (rr a a_1 → rf1 a a_1) True % 3.86/4.03 Clause #89 (by clausification #[88]): ∀ (a a_1 : Iota), Or (Eq (rr a a_1) False) (Eq (rf1 a a_1) True) % 3.86/4.03 Clause #141 (by clausification #[16]): ∀ (a : Iota), Eq (And (cowlThing a) (Not (cowlNothing a))) True % 3.86/4.03 Clause #143 (by clausification #[141]): ∀ (a : Iota), Eq (cowlThing a) True % 3.86/4.03 Clause #145 (by clausification #[18]): ∀ (a : Iota), % 3.86/4.03 Eq % 3.86/4.03 (Iff (cUnsatisfiable a) % 3.86/4.03 (And (And (Exists fun Y => And (rf2 a Y) (cp2 Y)) (Exists fun Y => And (rf1 a Y) (cp1 Y))) % 3.86/4.03 (Exists fun Y => And (rr a Y) (cowlThing Y)))) % 3.86/4.03 True % 3.86/4.03 Clause #147 (by clausification #[145]): ∀ (a : Iota), % 3.86/4.03 Or (Eq (cUnsatisfiable a) False) % 3.86/4.03 (Eq % 3.86/4.03 (And (And (Exists fun Y => And (rf2 a Y) (cp2 Y)) (Exists fun Y => And (rf1 a Y) (cp1 Y))) % 3.86/4.03 (Exists fun Y => And (rr a Y) (cowlThing Y))) % 3.86/4.03 True) % 3.86/4.03 Clause #158 (by clausification #[23]): ∀ (a : Iota), Eq (cowlThing a → ∀ (Y0 Y1 : Iota), And (rf2 a Y0) (rf2 a Y1) → Eq Y0 Y1) True % 3.86/4.03 Clause #159 (by clausification #[158]): ∀ (a : Iota), Or (Eq (cowlThing a) False) (Eq (∀ (Y0 Y1 : Iota), And (rf2 a Y0) (rf2 a Y1) → Eq Y0 Y1) True) % 3.86/4.03 Clause #160 (by clausification #[159]): ∀ (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) % 3.86/4.03 Clause #161 (by clausification #[160]): ∀ (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) % 3.86/4.03 Clause #162 (by clausification #[161]): ∀ (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)) % 3.86/4.03 Clause #163 (by clausification #[162]): ∀ (a a_1 a_2 : Iota), % 3.86/4.03 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))) % 3.86/4.03 Clause #164 (by clausification #[163]): ∀ (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))) % 3.86/4.03 Clause #165 (by forward demodulation #[164, 143]): ∀ (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))) % 3.86/4.03 Clause #166 (by clausification #[165]): ∀ (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)) % 3.86/4.03 Clause #167 (by clausification #[22]): ∀ (a : Iota), Eq (cowlThing a → ∀ (Y0 Y1 : Iota), And (rf1 a Y0) (rf1 a Y1) → Eq Y0 Y1) True % 3.86/4.05 Clause #168 (by clausification #[167]): ∀ (a : Iota), Or (Eq (cowlThing a) False) (Eq (∀ (Y0 Y1 : Iota), And (rf1 a Y0) (rf1 a Y1) → Eq Y0 Y1) True) % 3.86/4.05 Clause #169 (by clausification #[168]): ∀ (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) % 3.86/4.05 Clause #170 (by clausification #[169]): ∀ (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) % 3.86/4.05 Clause #171 (by clausification #[170]): ∀ (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)) % 3.86/4.05 Clause #172 (by clausification #[171]): ∀ (a a_1 a_2 : Iota), % 3.86/4.05 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))) % 3.86/4.05 Clause #173 (by clausification #[172]): ∀ (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))) % 3.86/4.05 Clause #174 (by forward demodulation #[173, 143]): ∀ (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))) % 3.86/4.05 Clause #175 (by clausification #[174]): ∀ (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)) % 3.86/4.05 Clause #176 (by betaEtaReduce #[21]): Eq (∀ (X : Iota), Iff (cp2xcomp X) (Exists (ra_Px1 X))) True % 3.86/4.05 Clause #177 (by clausification #[176]): ∀ (a : Iota), Eq (Iff (cp2xcomp a) (Exists (ra_Px1 a))) True % 3.86/4.05 Clause #179 (by clausification #[177]): ∀ (a : Iota), Or (Eq (cp2xcomp a) False) (Eq (Exists (ra_Px1 a)) True) % 3.86/4.05 Clause #181 (by betaEtaReduce #[20]): Eq (∀ (X : Iota), Iff (cp2 X) (Not (Exists (ra_Px1 X)))) True % 3.86/4.05 Clause #182 (by clausification #[181]): ∀ (a : Iota), Eq (Iff (cp2 a) (Not (Exists (ra_Px1 a)))) True % 3.86/4.05 Clause #184 (by clausification #[182]): ∀ (a : Iota), Or (Eq (cp2 a) False) (Eq (Not (Exists (ra_Px1 a))) True) % 3.86/4.05 Clause #189 (by clausification #[179]): ∀ (a a_1 : Iota), Or (Eq (cp2xcomp a) False) (Eq (ra_Px1 a (skS.0 1 a a_1)) True) % 3.86/4.05 Clause #191 (by clausification #[184]): ∀ (a : Iota), Or (Eq (cp2 a) False) (Eq (Exists (ra_Px1 a)) False) % 3.86/4.05 Clause #192 (by clausification #[191]): ∀ (a a_1 : Iota), Or (Eq (cp2 a) False) (Eq (ra_Px1 a a_1) False) % 3.86/4.05 Clause #195 (by clausification #[147]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rr a Y) (cowlThing Y)) True) % 3.86/4.05 Clause #196 (by clausification #[147]): ∀ (a : Iota), % 3.86/4.05 Or (Eq (cUnsatisfiable a) False) % 3.86/4.05 (Eq (And (Exists fun Y => And (rf2 a Y) (cp2 Y)) (Exists fun Y => And (rf1 a Y) (cp1 Y))) True) % 3.86/4.05 Clause #197 (by clausification #[195]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rr a (skS.0 2 a a_1)) (cowlThing (skS.0 2 a a_1))) True) % 3.86/4.05 Clause #199 (by clausification #[197]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rr a (skS.0 2 a a_1)) True) % 3.86/4.05 Clause #200 (by superposition #[199, 24]): ∀ (a : Iota), Or (Eq (rr i2003_11_14_17_21_30578 (skS.0 2 i2003_11_14_17_21_30578 a)) True) (Eq False True) % 3.86/4.05 Clause #201 (by clausification #[200]): ∀ (a : Iota), Eq (rr i2003_11_14_17_21_30578 (skS.0 2 i2003_11_14_17_21_30578 a)) True % 3.86/4.05 Clause #202 (by superposition #[201, 79]): ∀ (a : Iota), Or (Eq True False) (Eq (rf2 i2003_11_14_17_21_30578 (skS.0 2 i2003_11_14_17_21_30578 a)) True) % 3.86/4.05 Clause #203 (by superposition #[201, 89]): ∀ (a : Iota), Or (Eq True False) (Eq (rf1 i2003_11_14_17_21_30578 (skS.0 2 i2003_11_14_17_21_30578 a)) True) % 3.86/4.05 Clause #205 (by clausification #[203]): ∀ (a : Iota), Eq (rf1 i2003_11_14_17_21_30578 (skS.0 2 i2003_11_14_17_21_30578 a)) True % 3.86/4.05 Clause #206 (by superposition #[205, 175]): ∀ (a a_1 : Iota), % 3.86/4.05 Or (Eq True False) (Or (Eq (rf1 i2003_11_14_17_21_30578 a) False) (Eq (skS.0 2 i2003_11_14_17_21_30578 a_1) a)) % 3.86/4.05 Clause #207 (by clausification #[202]): ∀ (a : Iota), Eq (rf2 i2003_11_14_17_21_30578 (skS.0 2 i2003_11_14_17_21_30578 a)) True % 3.86/4.05 Clause #208 (by superposition #[207, 166]): ∀ (a a_1 : Iota), % 3.86/4.05 Or (Eq True False) (Or (Eq (rf2 i2003_11_14_17_21_30578 a) False) (Eq (skS.0 2 i2003_11_14_17_21_30578 a_1) a)) % 3.90/4.07 Clause #209 (by clausification #[208]): ∀ (a a_1 : Iota), Or (Eq (rf2 i2003_11_14_17_21_30578 a) False) (Eq (skS.0 2 i2003_11_14_17_21_30578 a_1) a) % 3.90/4.07 Clause #211 (by clausification #[196]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rf1 a Y) (cp1 Y)) True) % 3.90/4.07 Clause #212 (by clausification #[196]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rf2 a Y) (cp2 Y)) True) % 3.90/4.07 Clause #213 (by clausification #[211]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rf1 a (skS.0 3 a a_1)) (cp1 (skS.0 3 a a_1))) True) % 3.90/4.07 Clause #214 (by clausification #[213]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cp1 (skS.0 3 a a_1)) True) % 3.90/4.07 Clause #215 (by clausification #[213]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rf1 a (skS.0 3 a a_1)) True) % 3.90/4.07 Clause #216 (by superposition #[214, 24]): ∀ (a : Iota), Or (Eq (cp1 (skS.0 3 i2003_11_14_17_21_30578 a)) True) (Eq False True) % 3.90/4.07 Clause #217 (by clausification #[216]): ∀ (a : Iota), Eq (cp1 (skS.0 3 i2003_11_14_17_21_30578 a)) True % 3.90/4.07 Clause #218 (by superposition #[217, 28]): ∀ (a : Iota), Or (Eq True False) (Eq (cp2xcomp (skS.0 3 i2003_11_14_17_21_30578 a)) True) % 3.90/4.07 Clause #219 (by clausification #[218]): ∀ (a : Iota), Eq (cp2xcomp (skS.0 3 i2003_11_14_17_21_30578 a)) True % 3.90/4.07 Clause #220 (by superposition #[219, 189]): ∀ (a a_1 : Iota), % 3.90/4.07 Or (Eq True False) % 3.90/4.07 (Eq (ra_Px1 (skS.0 3 i2003_11_14_17_21_30578 a) (skS.0 1 (skS.0 3 i2003_11_14_17_21_30578 a) a_1)) True) % 3.90/4.07 Clause #221 (by clausification #[212]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rf2 a (skS.0 4 a a_1)) (cp2 (skS.0 4 a a_1))) True) % 3.90/4.07 Clause #222 (by clausification #[221]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cp2 (skS.0 4 a a_1)) True) % 3.90/4.07 Clause #223 (by clausification #[221]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rf2 a (skS.0 4 a a_1)) True) % 3.90/4.07 Clause #224 (by superposition #[222, 24]): ∀ (a : Iota), Or (Eq (cp2 (skS.0 4 i2003_11_14_17_21_30578 a)) True) (Eq False True) % 3.90/4.07 Clause #225 (by clausification #[224]): ∀ (a : Iota), Eq (cp2 (skS.0 4 i2003_11_14_17_21_30578 a)) True % 3.90/4.07 Clause #226 (by superposition #[225, 192]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (ra_Px1 (skS.0 4 i2003_11_14_17_21_30578 a) a_1) False) % 3.90/4.07 Clause #227 (by clausification #[226]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 4 i2003_11_14_17_21_30578 a) a_1) False % 3.90/4.07 Clause #231 (by superposition #[215, 24]): ∀ (a : Iota), Or (Eq (rf1 i2003_11_14_17_21_30578 (skS.0 3 i2003_11_14_17_21_30578 a)) True) (Eq False True) % 3.90/4.07 Clause #232 (by clausification #[231]): ∀ (a : Iota), Eq (rf1 i2003_11_14_17_21_30578 (skS.0 3 i2003_11_14_17_21_30578 a)) True % 3.90/4.07 Clause #234 (by superposition #[223, 24]): ∀ (a : Iota), Or (Eq (rf2 i2003_11_14_17_21_30578 (skS.0 4 i2003_11_14_17_21_30578 a)) True) (Eq False True) % 3.90/4.07 Clause #235 (by clausification #[234]): ∀ (a : Iota), Eq (rf2 i2003_11_14_17_21_30578 (skS.0 4 i2003_11_14_17_21_30578 a)) True % 3.90/4.07 Clause #236 (by superposition #[235, 209]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (skS.0 2 i2003_11_14_17_21_30578 a) (skS.0 4 i2003_11_14_17_21_30578 a_1)) % 3.90/4.07 Clause #238 (by clausification #[206]): ∀ (a a_1 : Iota), Or (Eq (rf1 i2003_11_14_17_21_30578 a) False) (Eq (skS.0 2 i2003_11_14_17_21_30578 a_1) a) % 3.90/4.07 Clause #239 (by superposition #[238, 232]): ∀ (a a_1 : Iota), Or (Eq (skS.0 2 i2003_11_14_17_21_30578 a) (skS.0 3 i2003_11_14_17_21_30578 a_1)) (Eq False True) % 3.90/4.07 Clause #246 (by clausification #[236]): ∀ (a a_1 : Iota), Eq (skS.0 2 i2003_11_14_17_21_30578 a) (skS.0 4 i2003_11_14_17_21_30578 a_1) % 3.90/4.07 Clause #251 (by superposition #[246, 227]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 2 i2003_11_14_17_21_30578 a) a_1) False % 3.90/4.07 Clause #260 (by clausification #[220]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 3 i2003_11_14_17_21_30578 a) (skS.0 1 (skS.0 3 i2003_11_14_17_21_30578 a) a_1)) True % 3.90/4.07 Clause #264 (by clausification #[239]): ∀ (a a_1 : Iota), Eq (skS.0 2 i2003_11_14_17_21_30578 a) (skS.0 3 i2003_11_14_17_21_30578 a_1) % 3.90/4.07 Clause #269 (by superposition #[264, 251]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 3 i2003_11_14_17_21_30578 a) a_1) False % 3.90/4.08 Clause #282 (by superposition #[269, 260]): Eq False True % 3.90/4.08 Clause #285 (by clausification #[282]): False % 3.90/4.08 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------