%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS106+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n018.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 07:52:38 PM UTC 2025 % Result : Unsatisfiable 4.41s 4.62s % Output : Proof 4.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : KRS106+1 : TPTP v9.2.0. Released v3.1.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n018.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 10:16:38 EDT 2025 % 0.13/0.34 % CPUTime : % 4.41/4.62 SZS status Theorem for theBenchmark.p % 4.41/4.62 SZS output start Proof for theBenchmark.p % 4.41/4.62 Clause #18 (by assumption #[]): Eq % 4.41/4.62 (∀ (X : Iota), % 4.41/4.62 Iff (cUnsatisfiable X) % 4.41/4.62 (And (And (Exists fun Y => And (rf3 X Y) (cp2 Y)) (Exists fun Y => And (rf1 X Y) (cp1 Y))) % 4.41/4.62 (Exists fun Y => And (rf2 X Y) (cp1xcomp Y)))) % 4.41/4.62 True % 4.41/4.62 Clause #19 (by assumption #[]): Eq (∀ (X : Iota), Iff (cp1 X) (Not (Exists fun Y => ra_Px1 X Y))) True % 4.41/4.62 Clause #20 (by assumption #[]): Eq (∀ (X : Iota), Iff (cp1xcomp X) (Exists fun Y0 => ra_Px1 X Y0)) True % 4.41/4.62 Clause #21 (by assumption #[]): Eq (∀ (X Y Z : Iota), And (rf1 X Y) (rf1 X Z) → Eq Y Z) True % 4.41/4.62 Clause #22 (by assumption #[]): Eq (∀ (X Y Z : Iota), And (rf2 X Y) (rf2 X Z) → Eq Y Z) True % 4.41/4.62 Clause #24 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_20_57644) True % 4.41/4.62 Clause #25 (by assumption #[]): Eq (∀ (X Y : Iota), rf3 X Y → rf1 X Y) True % 4.41/4.62 Clause #26 (by assumption #[]): Eq (∀ (X Y : Iota), rf3 X Y → rf2 X Y) True % 4.41/4.62 Clause #75 (by clausification #[25]): ∀ (a : Iota), Eq (∀ (Y : Iota), rf3 a Y → rf1 a Y) True % 4.41/4.62 Clause #76 (by clausification #[75]): ∀ (a a_1 : Iota), Eq (rf3 a a_1 → rf1 a a_1) True % 4.41/4.62 Clause #77 (by clausification #[76]): ∀ (a a_1 : Iota), Or (Eq (rf3 a a_1) False) (Eq (rf1 a a_1) True) % 4.41/4.62 Clause #78 (by clausification #[26]): ∀ (a : Iota), Eq (∀ (Y : Iota), rf3 a Y → rf2 a Y) True % 4.41/4.62 Clause #79 (by clausification #[78]): ∀ (a a_1 : Iota), Eq (rf3 a a_1 → rf2 a a_1) True % 4.41/4.62 Clause #80 (by clausification #[79]): ∀ (a a_1 : Iota), Or (Eq (rf3 a a_1) False) (Eq (rf2 a a_1) True) % 4.41/4.62 Clause #150 (by clausification #[22]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), And (rf2 a Y) (rf2 a Z) → Eq Y Z) True % 4.41/4.62 Clause #151 (by clausification #[150]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), And (rf2 a a_1) (rf2 a Z) → Eq a_1 Z) True % 4.41/4.62 Clause #152 (by clausification #[151]): ∀ (a a_1 a_2 : Iota), Eq (And (rf2 a a_1) (rf2 a a_2) → Eq a_1 a_2) True % 4.41/4.62 Clause #153 (by clausification #[152]): ∀ (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) % 4.41/4.62 Clause #154 (by clausification #[153]): ∀ (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)) % 4.41/4.62 Clause #155 (by clausification #[154]): ∀ (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)) % 4.41/4.62 Clause #156 (by clausification #[21]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), And (rf1 a Y) (rf1 a Z) → Eq Y Z) True % 4.41/4.62 Clause #157 (by clausification #[156]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), And (rf1 a a_1) (rf1 a Z) → Eq a_1 Z) True % 4.41/4.62 Clause #158 (by clausification #[157]): ∀ (a a_1 a_2 : Iota), Eq (And (rf1 a a_1) (rf1 a a_2) → Eq a_1 a_2) True % 4.41/4.62 Clause #159 (by clausification #[158]): ∀ (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) % 4.41/4.62 Clause #160 (by clausification #[159]): ∀ (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)) % 4.41/4.62 Clause #161 (by clausification #[160]): ∀ (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)) % 4.41/4.62 Clause #162 (by betaEtaReduce #[20]): Eq (∀ (X : Iota), Iff (cp1xcomp X) (Exists (ra_Px1 X))) True % 4.41/4.62 Clause #163 (by clausification #[162]): ∀ (a : Iota), Eq (Iff (cp1xcomp a) (Exists (ra_Px1 a))) True % 4.41/4.62 Clause #165 (by clausification #[163]): ∀ (a : Iota), Or (Eq (cp1xcomp a) False) (Eq (Exists (ra_Px1 a)) True) % 4.41/4.62 Clause #167 (by clausification #[165]): ∀ (a a_1 : Iota), Or (Eq (cp1xcomp a) False) (Eq (ra_Px1 a (skS.0 0 a a_1)) True) % 4.41/4.62 Clause #168 (by clausification #[18]): ∀ (a : Iota), % 4.41/4.62 Eq % 4.41/4.62 (Iff (cUnsatisfiable a) % 4.41/4.62 (And (And (Exists fun Y => And (rf3 a Y) (cp2 Y)) (Exists fun Y => And (rf1 a Y) (cp1 Y))) % 4.41/4.62 (Exists fun Y => And (rf2 a Y) (cp1xcomp Y)))) % 4.41/4.62 True % 4.41/4.62 Clause #170 (by clausification #[168]): ∀ (a : Iota), % 4.41/4.62 Or (Eq (cUnsatisfiable a) False) % 4.41/4.62 (Eq % 4.41/4.62 (And (And (Exists fun Y => And (rf3 a Y) (cp2 Y)) (Exists fun Y => And (rf1 a Y) (cp1 Y))) % 4.41/4.62 (Exists fun Y => And (rf2 a Y) (cp1xcomp Y))) % 4.41/4.62 True) % 4.41/4.62 Clause #179 (by betaEtaReduce #[19]): Eq (∀ (X : Iota), Iff (cp1 X) (Not (Exists (ra_Px1 X)))) True % 4.41/4.64 Clause #180 (by clausification #[179]): ∀ (a : Iota), Eq (Iff (cp1 a) (Not (Exists (ra_Px1 a)))) True % 4.41/4.64 Clause #182 (by clausification #[180]): ∀ (a : Iota), Or (Eq (cp1 a) False) (Eq (Not (Exists (ra_Px1 a))) True) % 4.41/4.64 Clause #188 (by clausification #[182]): ∀ (a : Iota), Or (Eq (cp1 a) False) (Eq (Exists (ra_Px1 a)) False) % 4.41/4.64 Clause #189 (by clausification #[188]): ∀ (a a_1 : Iota), Or (Eq (cp1 a) False) (Eq (ra_Px1 a a_1) False) % 4.41/4.64 Clause #191 (by clausification #[170]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rf2 a Y) (cp1xcomp Y)) True) % 4.41/4.64 Clause #192 (by clausification #[170]): ∀ (a : Iota), % 4.41/4.64 Or (Eq (cUnsatisfiable a) False) % 4.41/4.64 (Eq (And (Exists fun Y => And (rf3 a Y) (cp2 Y)) (Exists fun Y => And (rf1 a Y) (cp1 Y))) True) % 4.41/4.64 Clause #193 (by clausification #[191]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rf2 a (skS.0 2 a a_1)) (cp1xcomp (skS.0 2 a a_1))) True) % 4.41/4.64 Clause #194 (by clausification #[193]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cp1xcomp (skS.0 2 a a_1)) True) % 4.41/4.64 Clause #195 (by clausification #[193]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rf2 a (skS.0 2 a a_1)) True) % 4.41/4.64 Clause #196 (by superposition #[194, 24]): ∀ (a : Iota), Or (Eq (cp1xcomp (skS.0 2 i2003_11_14_17_20_57644 a)) True) (Eq False True) % 4.41/4.64 Clause #197 (by clausification #[192]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rf1 a Y) (cp1 Y)) True) % 4.41/4.64 Clause #198 (by clausification #[192]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rf3 a Y) (cp2 Y)) True) % 4.41/4.64 Clause #199 (by clausification #[197]): ∀ (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) % 4.41/4.64 Clause #200 (by clausification #[199]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cp1 (skS.0 3 a a_1)) True) % 4.41/4.64 Clause #201 (by clausification #[199]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rf1 a (skS.0 3 a a_1)) True) % 4.41/4.64 Clause #202 (by superposition #[200, 24]): ∀ (a : Iota), Or (Eq (cp1 (skS.0 3 i2003_11_14_17_20_57644 a)) True) (Eq False True) % 4.41/4.64 Clause #203 (by clausification #[202]): ∀ (a : Iota), Eq (cp1 (skS.0 3 i2003_11_14_17_20_57644 a)) True % 4.41/4.64 Clause #204 (by superposition #[203, 189]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (ra_Px1 (skS.0 3 i2003_11_14_17_20_57644 a) a_1) False) % 4.41/4.64 Clause #205 (by clausification #[196]): ∀ (a : Iota), Eq (cp1xcomp (skS.0 2 i2003_11_14_17_20_57644 a)) True % 4.41/4.64 Clause #206 (by superposition #[205, 167]): ∀ (a a_1 : Iota), % 4.41/4.64 Or (Eq True False) % 4.41/4.64 (Eq (ra_Px1 (skS.0 2 i2003_11_14_17_20_57644 a) (skS.0 0 (skS.0 2 i2003_11_14_17_20_57644 a) a_1)) True) % 4.41/4.64 Clause #207 (by clausification #[204]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 3 i2003_11_14_17_20_57644 a) a_1) False % 4.41/4.64 Clause #208 (by clausification #[198]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rf3 a (skS.0 4 a a_1)) (cp2 (skS.0 4 a a_1))) True) % 4.41/4.64 Clause #210 (by clausification #[208]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rf3 a (skS.0 4 a a_1)) True) % 4.41/4.64 Clause #213 (by superposition #[195, 24]): ∀ (a : Iota), Or (Eq (rf2 i2003_11_14_17_20_57644 (skS.0 2 i2003_11_14_17_20_57644 a)) True) (Eq False True) % 4.41/4.64 Clause #214 (by clausification #[213]): ∀ (a : Iota), Eq (rf2 i2003_11_14_17_20_57644 (skS.0 2 i2003_11_14_17_20_57644 a)) True % 4.41/4.64 Clause #215 (by superposition #[214, 155]): ∀ (a a_1 : Iota), % 4.41/4.64 Or (Eq True False) (Or (Eq (rf2 i2003_11_14_17_20_57644 a) False) (Eq (skS.0 2 i2003_11_14_17_20_57644 a_1) a)) % 4.41/4.64 Clause #217 (by superposition #[210, 24]): ∀ (a : Iota), Or (Eq (rf3 i2003_11_14_17_20_57644 (skS.0 4 i2003_11_14_17_20_57644 a)) True) (Eq False True) % 4.41/4.64 Clause #218 (by clausification #[217]): ∀ (a : Iota), Eq (rf3 i2003_11_14_17_20_57644 (skS.0 4 i2003_11_14_17_20_57644 a)) True % 4.41/4.64 Clause #219 (by superposition #[218, 77]): ∀ (a : Iota), Or (Eq True False) (Eq (rf1 i2003_11_14_17_20_57644 (skS.0 4 i2003_11_14_17_20_57644 a)) True) % 4.41/4.64 Clause #220 (by superposition #[218, 80]): ∀ (a : Iota), Or (Eq True False) (Eq (rf2 i2003_11_14_17_20_57644 (skS.0 4 i2003_11_14_17_20_57644 a)) True) % 4.41/4.65 Clause #222 (by clausification #[220]): ∀ (a : Iota), Eq (rf2 i2003_11_14_17_20_57644 (skS.0 4 i2003_11_14_17_20_57644 a)) True % 4.41/4.65 Clause #225 (by clausification #[219]): ∀ (a : Iota), Eq (rf1 i2003_11_14_17_20_57644 (skS.0 4 i2003_11_14_17_20_57644 a)) True % 4.41/4.65 Clause #226 (by superposition #[225, 161]): ∀ (a a_1 : Iota), % 4.41/4.65 Or (Eq True False) (Or (Eq (rf1 i2003_11_14_17_20_57644 a) False) (Eq (skS.0 4 i2003_11_14_17_20_57644 a_1) a)) % 4.41/4.65 Clause #227 (by superposition #[201, 24]): ∀ (a : Iota), Or (Eq (rf1 i2003_11_14_17_20_57644 (skS.0 3 i2003_11_14_17_20_57644 a)) True) (Eq False True) % 4.41/4.65 Clause #228 (by clausification #[227]): ∀ (a : Iota), Eq (rf1 i2003_11_14_17_20_57644 (skS.0 3 i2003_11_14_17_20_57644 a)) True % 4.41/4.65 Clause #233 (by clausification #[215]): ∀ (a a_1 : Iota), Or (Eq (rf2 i2003_11_14_17_20_57644 a) False) (Eq (skS.0 2 i2003_11_14_17_20_57644 a_1) a) % 4.41/4.65 Clause #235 (by superposition #[233, 222]): ∀ (a a_1 : Iota), Or (Eq (skS.0 2 i2003_11_14_17_20_57644 a) (skS.0 4 i2003_11_14_17_20_57644 a_1)) (Eq False True) % 4.41/4.65 Clause #239 (by clausification #[226]): ∀ (a a_1 : Iota), Or (Eq (rf1 i2003_11_14_17_20_57644 a) False) (Eq (skS.0 4 i2003_11_14_17_20_57644 a_1) a) % 4.41/4.65 Clause #240 (by superposition #[239, 228]): ∀ (a a_1 : Iota), Or (Eq (skS.0 4 i2003_11_14_17_20_57644 a) (skS.0 3 i2003_11_14_17_20_57644 a_1)) (Eq False True) % 4.41/4.65 Clause #241 (by clausification #[206]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 2 i2003_11_14_17_20_57644 a) (skS.0 0 (skS.0 2 i2003_11_14_17_20_57644 a) a_1)) True % 4.41/4.65 Clause #244 (by clausification #[240]): ∀ (a a_1 : Iota), Eq (skS.0 4 i2003_11_14_17_20_57644 a) (skS.0 3 i2003_11_14_17_20_57644 a_1) % 4.41/4.65 Clause #250 (by superposition #[244, 207]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 4 i2003_11_14_17_20_57644 a) a_1) False % 4.41/4.65 Clause #269 (by clausification #[235]): ∀ (a a_1 : Iota), Eq (skS.0 2 i2003_11_14_17_20_57644 a) (skS.0 4 i2003_11_14_17_20_57644 a_1) % 4.41/4.65 Clause #277 (by superposition #[269, 250]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 2 i2003_11_14_17_20_57644 a) a_1) False % 4.41/4.65 Clause #290 (by superposition #[277, 241]): Eq False True % 4.41/4.65 Clause #292 (by clausification #[290]): False % 4.41/4.65 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------