%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS078+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n025.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 3.78s 3.95s % Output : Proof 3.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : KRS078+1 : TPTP v9.2.0. Released v3.1.0. % 0.03/0.13 % Command : duper %s % 0.12/0.34 % Computer : n025.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Thu Oct 2 10:22:08 EDT 2025 % 0.12/0.34 % CPUTime : % 3.78/3.95 SZS status Theorem for theBenchmark.p % 3.78/3.95 SZS output start Proof for theBenchmark.p % 3.78/3.95 Clause #15 (by assumption #[]): Eq % 3.78/3.95 (∀ (X : Iota), % 3.78/3.95 Iff (cUnsatisfiable X) % 3.78/3.95 (And % 3.78/3.95 (Exists fun Y => % 3.78/3.95 And (And (rr X Y) (Exists fun Z => And (rinvR Y Z) (∀ (W : Iota), rs Z W → cp W))) % 3.78/3.95 (∀ (Z0 Z1 : Iota), And (rinvR Y Z0) (rinvR Y Z1) → Eq Z0 Z1)) % 3.78/3.95 (Exists fun Y => And (And (rs X Y) (Not (cq Y))) (Not (cp Y))))) % 3.78/3.95 True % 3.78/3.95 Clause #16 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (rinvR X Y) (rr Y X)) True % 3.78/3.95 Clause #17 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_19_13721) True % 3.78/3.95 Clause #108 (by clausification #[16]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (rinvR a Y) (rr Y a)) True % 3.78/3.95 Clause #109 (by clausification #[108]): ∀ (a a_1 : Iota), Eq (Iff (rinvR a a_1) (rr a_1 a)) True % 3.78/3.95 Clause #110 (by clausification #[109]): ∀ (a a_1 : Iota), Or (Eq (rinvR a a_1) True) (Eq (rr a_1 a) False) % 3.78/3.95 Clause #112 (by clausification #[15]): ∀ (a : Iota), % 3.78/3.95 Eq % 3.78/3.95 (Iff (cUnsatisfiable a) % 3.78/3.95 (And % 3.78/3.95 (Exists fun Y => % 3.78/3.95 And (And (rr a Y) (Exists fun Z => And (rinvR Y Z) (∀ (W : Iota), rs Z W → cp W))) % 3.78/3.95 (∀ (Z0 Z1 : Iota), And (rinvR Y Z0) (rinvR Y Z1) → Eq Z0 Z1)) % 3.78/3.95 (Exists fun Y => And (And (rs a Y) (Not (cq Y))) (Not (cp Y))))) % 3.78/3.95 True % 3.78/3.95 Clause #114 (by clausification #[112]): ∀ (a : Iota), % 3.78/3.95 Or (Eq (cUnsatisfiable a) False) % 3.78/3.95 (Eq % 3.78/3.95 (And % 3.78/3.95 (Exists fun Y => % 3.78/3.95 And (And (rr a Y) (Exists fun Z => And (rinvR Y Z) (∀ (W : Iota), rs Z W → cp W))) % 3.78/3.95 (∀ (Z0 Z1 : Iota), And (rinvR Y Z0) (rinvR Y Z1) → Eq Z0 Z1)) % 3.78/3.95 (Exists fun Y => And (And (rs a Y) (Not (cq Y))) (Not (cp Y)))) % 3.78/3.95 True) % 3.78/3.95 Clause #138 (by clausification #[114]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (And (rs a Y) (Not (cq Y))) (Not (cp Y))) True) % 3.78/3.95 Clause #139 (by clausification #[114]): ∀ (a : Iota), % 3.78/3.95 Or (Eq (cUnsatisfiable a) False) % 3.78/3.95 (Eq % 3.78/3.95 (Exists fun Y => % 3.78/3.95 And (And (rr a Y) (Exists fun Z => And (rinvR Y Z) (∀ (W : Iota), rs Z W → cp W))) % 3.78/3.95 (∀ (Z0 Z1 : Iota), And (rinvR Y Z0) (rinvR Y Z1) → Eq Z0 Z1)) % 3.78/3.95 True) % 3.78/3.95 Clause #140 (by clausification #[138]): ∀ (a a_1 : Iota), % 3.78/3.95 Or (Eq (cUnsatisfiable a) False) % 3.78/3.95 (Eq (And (And (rs a (skS.0 3 a a_1)) (Not (cq (skS.0 3 a a_1)))) (Not (cp (skS.0 3 a a_1)))) True) % 3.78/3.95 Clause #141 (by clausification #[140]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Not (cp (skS.0 3 a a_1))) True) % 3.78/3.95 Clause #142 (by clausification #[140]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rs a (skS.0 3 a a_1)) (Not (cq (skS.0 3 a a_1)))) True) % 3.78/3.95 Clause #143 (by clausification #[141]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cp (skS.0 3 a a_1)) False) % 3.78/3.95 Clause #144 (by superposition #[143, 17]): ∀ (a : Iota), Or (Eq (cp (skS.0 3 i2003_11_14_17_19_13721 a)) False) (Eq False True) % 3.78/3.95 Clause #148 (by clausification #[144]): ∀ (a : Iota), Eq (cp (skS.0 3 i2003_11_14_17_19_13721 a)) False % 3.78/3.95 Clause #150 (by clausification #[142]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rs a (skS.0 3 a a_1)) True) % 3.78/3.95 Clause #154 (by superposition #[150, 17]): ∀ (a : Iota), Or (Eq (rs i2003_11_14_17_19_13721 (skS.0 3 i2003_11_14_17_19_13721 a)) True) (Eq False True) % 3.78/3.95 Clause #155 (by clausification #[154]): ∀ (a : Iota), Eq (rs i2003_11_14_17_19_13721 (skS.0 3 i2003_11_14_17_19_13721 a)) True % 3.78/3.95 Clause #158 (by clausification #[139]): ∀ (a a_1 : Iota), % 3.78/3.95 Or (Eq (cUnsatisfiable a) False) % 3.78/3.95 (Eq % 3.78/3.95 (And (And (rr a (skS.0 4 a a_1)) (Exists fun Z => And (rinvR (skS.0 4 a a_1) Z) (∀ (W : Iota), rs Z W → cp W))) % 3.78/3.95 (∀ (Z0 Z1 : Iota), And (rinvR (skS.0 4 a a_1) Z0) (rinvR (skS.0 4 a a_1) Z1) → Eq Z0 Z1)) % 3.78/3.95 True) % 3.78/3.95 Clause #159 (by clausification #[158]): ∀ (a a_1 : Iota), % 3.78/3.95 Or (Eq (cUnsatisfiable a) False) % 3.78/3.95 (Eq (∀ (Z0 Z1 : Iota), And (rinvR (skS.0 4 a a_1) Z0) (rinvR (skS.0 4 a a_1) Z1) → Eq Z0 Z1) True) % 3.78/3.95 Clause #160 (by clausification #[158]): ∀ (a a_1 : Iota), % 3.78/3.95 Or (Eq (cUnsatisfiable a) False) % 3.78/3.95 (Eq (And (rr a (skS.0 4 a a_1)) (Exists fun Z => And (rinvR (skS.0 4 a a_1) Z) (∀ (W : Iota), rs Z W → cp W))) True) % 3.82/3.97 Clause #161 (by clausification #[159]): ∀ (a a_1 a_2 : Iota), % 3.82/3.97 Or (Eq (cUnsatisfiable a) False) % 3.82/3.97 (Eq (∀ (Z1 : Iota), And (rinvR (skS.0 4 a a_1) a_2) (rinvR (skS.0 4 a a_1) Z1) → Eq a_2 Z1) True) % 3.82/3.97 Clause #162 (by clausification #[161]): ∀ (a a_1 a_2 a_3 : Iota), % 3.82/3.97 Or (Eq (cUnsatisfiable a) False) (Eq (And (rinvR (skS.0 4 a a_1) a_2) (rinvR (skS.0 4 a a_1) a_3) → Eq a_2 a_3) True) % 3.82/3.97 Clause #163 (by clausification #[162]): ∀ (a a_1 a_2 a_3 : Iota), % 3.82/3.97 Or (Eq (cUnsatisfiable a) False) % 3.82/3.97 (Or (Eq (And (rinvR (skS.0 4 a a_1) a_2) (rinvR (skS.0 4 a a_1) a_3)) False) (Eq (Eq a_2 a_3) True)) % 3.82/3.97 Clause #164 (by clausification #[163]): ∀ (a a_1 a_2 a_3 : Iota), % 3.82/3.97 Or (Eq (cUnsatisfiable a) False) % 3.82/3.97 (Or (Eq (Eq a_1 a_2) True) (Or (Eq (rinvR (skS.0 4 a a_3) a_1) False) (Eq (rinvR (skS.0 4 a a_3) a_2) False))) % 3.82/3.97 Clause #165 (by clausification #[164]): ∀ (a a_1 a_2 a_3 : Iota), % 3.82/3.97 Or (Eq (cUnsatisfiable a) False) % 3.82/3.97 (Or (Eq (rinvR (skS.0 4 a a_1) a_2) False) (Or (Eq (rinvR (skS.0 4 a a_1) a_3) False) (Eq a_2 a_3))) % 3.82/3.97 Clause #166 (by superposition #[165, 17]): ∀ (a a_1 a_2 : Iota), % 3.82/3.97 Or (Eq (rinvR (skS.0 4 i2003_11_14_17_19_13721 a) a_1) False) % 3.82/3.97 (Or (Eq (rinvR (skS.0 4 i2003_11_14_17_19_13721 a) a_2) False) (Or (Eq a_1 a_2) (Eq False True))) % 3.82/3.97 Clause #167 (by clausification #[166]): ∀ (a a_1 a_2 : Iota), % 3.82/3.97 Or (Eq (rinvR (skS.0 4 i2003_11_14_17_19_13721 a) a_1) False) % 3.82/3.97 (Or (Eq (rinvR (skS.0 4 i2003_11_14_17_19_13721 a) a_2) False) (Eq a_1 a_2)) % 3.82/3.97 Clause #168 (by clausification #[160]): ∀ (a a_1 : Iota), % 3.82/3.97 Or (Eq (cUnsatisfiable a) False) % 3.82/3.97 (Eq (Exists fun Z => And (rinvR (skS.0 4 a a_1) Z) (∀ (W : Iota), rs Z W → cp W)) True) % 3.82/3.97 Clause #169 (by clausification #[160]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rr a (skS.0 4 a a_1)) True) % 3.82/3.97 Clause #170 (by clausification #[168]): ∀ (a a_1 a_2 : Iota), % 3.82/3.97 Or (Eq (cUnsatisfiable a) False) % 3.82/3.97 (Eq (And (rinvR (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)) (∀ (W : Iota), rs (skS.0 5 a a_1 a_2) W → cp W)) True) % 3.82/3.97 Clause #171 (by clausification #[170]): ∀ (a a_1 a_2 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (∀ (W : Iota), rs (skS.0 5 a a_1 a_2) W → cp W) True) % 3.82/3.97 Clause #172 (by clausification #[170]): ∀ (a a_1 a_2 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rinvR (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)) True) % 3.82/3.97 Clause #173 (by clausification #[171]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rs (skS.0 5 a a_1 a_2) a_3 → cp a_3) True) % 3.82/3.97 Clause #174 (by clausification #[173]): ∀ (a a_1 a_2 a_3 : Iota), % 3.82/3.97 Or (Eq (cUnsatisfiable a) False) (Or (Eq (rs (skS.0 5 a a_1 a_2) a_3) False) (Eq (cp a_3) True)) % 3.82/3.97 Clause #175 (by superposition #[174, 17]): ∀ (a a_1 a_2 : Iota), % 3.82/3.97 Or (Eq (rs (skS.0 5 i2003_11_14_17_19_13721 a a_1) a_2) False) (Or (Eq (cp a_2) True) (Eq False True)) % 3.82/3.97 Clause #176 (by superposition #[169, 17]): ∀ (a : Iota), Or (Eq (rr i2003_11_14_17_19_13721 (skS.0 4 i2003_11_14_17_19_13721 a)) True) (Eq False True) % 3.82/3.97 Clause #177 (by clausification #[176]): ∀ (a : Iota), Eq (rr i2003_11_14_17_19_13721 (skS.0 4 i2003_11_14_17_19_13721 a)) True % 3.82/3.97 Clause #178 (by superposition #[177, 110]): ∀ (a : Iota), Or (Eq (rinvR (skS.0 4 i2003_11_14_17_19_13721 a) i2003_11_14_17_19_13721) True) (Eq True False) % 3.82/3.97 Clause #185 (by clausification #[178]): ∀ (a : Iota), Eq (rinvR (skS.0 4 i2003_11_14_17_19_13721 a) i2003_11_14_17_19_13721) True % 3.82/3.97 Clause #186 (by superposition #[185, 167]): ∀ (a a_1 : Iota), % 3.82/3.97 Or (Eq True False) (Or (Eq (rinvR (skS.0 4 i2003_11_14_17_19_13721 a) a_1) False) (Eq i2003_11_14_17_19_13721 a_1)) % 3.82/3.97 Clause #188 (by clausification #[186]): ∀ (a a_1 : Iota), Or (Eq (rinvR (skS.0 4 i2003_11_14_17_19_13721 a) a_1) False) (Eq i2003_11_14_17_19_13721 a_1) % 3.82/3.97 Clause #191 (by clausification #[175]): ∀ (a a_1 a_2 : Iota), Or (Eq (rs (skS.0 5 i2003_11_14_17_19_13721 a a_1) a_2) False) (Eq (cp a_2) True) % 3.82/3.97 Clause #193 (by superposition #[172, 17]): ∀ (a a_1 : Iota), % 3.82/3.97 Or (Eq (rinvR (skS.0 4 i2003_11_14_17_19_13721 a) (skS.0 5 i2003_11_14_17_19_13721 a a_1)) True) (Eq False True) % 3.82/3.98 Clause #194 (by clausification #[193]): ∀ (a a_1 : Iota), Eq (rinvR (skS.0 4 i2003_11_14_17_19_13721 a) (skS.0 5 i2003_11_14_17_19_13721 a a_1)) True % 3.82/3.98 Clause #196 (by superposition #[194, 188]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq i2003_11_14_17_19_13721 (skS.0 5 i2003_11_14_17_19_13721 a a_1)) % 3.82/3.98 Clause #198 (by clausification #[196]): ∀ (a a_1 : Iota), Eq i2003_11_14_17_19_13721 (skS.0 5 i2003_11_14_17_19_13721 a a_1) % 3.82/3.98 Clause #199 (by backward demodulation #[198, 191]): ∀ (a : Iota), Or (Eq (rs i2003_11_14_17_19_13721 a) False) (Eq (cp a) True) % 3.82/3.98 Clause #200 (by superposition #[199, 155]): ∀ (a : Iota), Or (Eq (cp (skS.0 3 i2003_11_14_17_19_13721 a)) True) (Eq False True) % 3.82/3.98 Clause #201 (by clausification #[200]): ∀ (a : Iota), Eq (cp (skS.0 3 i2003_11_14_17_19_13721 a)) True % 3.82/3.98 Clause #202 (by superposition #[201, 148]): Eq True False % 3.82/3.98 Clause #205 (by clausification #[202]): False % 3.82/3.98 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------