%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO112^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n017.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 08:08:36 PM UTC 2025 % Result : Theorem 4.62s 4.79s % Output : Proof 4.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SYO112^5 : TPTP v9.2.0. Released v4.0.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n017.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 : Fri Oct 3 13:53:38 EDT 2025 % 0.13/0.34 % CPUTime : % 4.62/4.79 SZS status Theorem for theBenchmark.p % 4.62/4.79 SZS output start Proof for theBenchmark.p % 4.62/4.79 Clause #0 (by assumption #[]): Eq (Not (Iff (∀ (X : Iota), Iff (cP X) (Exists fun Y => cP Y)) (Iff (∀ (X : Iota), cP X) (Exists fun Y => cP Y)))) True % 4.62/4.79 Clause #1 (by betaEtaReduce #[0]): Eq (Not (Iff (∀ (X : Iota), Iff (cP X) (Exists cP)) (Iff (∀ (X : Iota), cP X) (Exists cP)))) True % 4.62/4.79 Clause #2 (by clausification #[1]): Eq (Iff (∀ (X : Iota), Iff (cP X) (Exists cP)) (Iff (∀ (X : Iota), cP X) (Exists cP))) False % 4.62/4.79 Clause #3 (by clausification #[2]): Or (Eq (∀ (X : Iota), Iff (cP X) (Exists cP)) False) (Eq (Iff (∀ (X : Iota), cP X) (Exists cP)) False) % 4.62/4.79 Clause #4 (by clausification #[2]): Or (Eq (∀ (X : Iota), Iff (cP X) (Exists cP)) True) (Eq (Iff (∀ (X : Iota), cP X) (Exists cP)) True) % 4.62/4.79 Clause #5 (by clausification #[3]): ∀ (a : Iota), Or (Eq (Iff (∀ (X : Iota), cP X) (Exists cP)) False) (Eq (Not (Iff (cP (skS.0 0 a)) (Exists cP))) True) % 4.62/4.79 Clause #6 (by clausification #[5]): ∀ (a : Iota), % 4.62/4.79 Or (Eq (Not (Iff (cP (skS.0 0 a)) (Exists cP))) True) (Or (Eq (∀ (X : Iota), cP X) False) (Eq (Exists cP) False)) % 4.62/4.79 Clause #7 (by clausification #[5]): ∀ (a : Iota), % 4.62/4.79 Or (Eq (Not (Iff (cP (skS.0 0 a)) (Exists cP))) True) (Or (Eq (∀ (X : Iota), cP X) True) (Eq (Exists cP) True)) % 4.62/4.79 Clause #8 (by clausification #[6]): ∀ (a : Iota), % 4.62/4.79 Or (Eq (∀ (X : Iota), cP X) False) (Or (Eq (Exists cP) False) (Eq (Iff (cP (skS.0 0 a)) (Exists cP)) False)) % 4.62/4.79 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), % 4.62/4.79 Or (Eq (Exists cP) False) (Or (Eq (Iff (cP (skS.0 0 a)) (Exists cP)) False) (Eq (Not (cP (skS.0 1 a_1))) True)) % 4.62/4.79 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 4.62/4.79 Or (Eq (Iff (cP (skS.0 0 a)) (Exists cP)) False) (Or (Eq (Not (cP (skS.0 1 a_1))) True) (Eq (cP a_2) False)) % 4.62/4.79 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), % 4.62/4.79 Or (Eq (Not (cP (skS.0 1 a))) True) (Or (Eq (cP a_1) False) (Or (Eq (cP (skS.0 0 a_2)) False) (Eq (Exists cP) False))) % 4.62/4.79 Clause #13 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), % 4.62/4.79 Or (Eq (cP a) False) (Or (Eq (cP (skS.0 0 a_1)) False) (Or (Eq (Exists cP) False) (Eq (cP (skS.0 1 a_2)) False))) % 4.62/4.79 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 a_3 : Iota), % 4.62/4.79 Or (Eq (cP a) False) (Or (Eq (cP (skS.0 0 a_1)) False) (Or (Eq (cP (skS.0 1 a_2)) False) (Eq (cP a_3) False))) % 4.62/4.79 Clause #15 (by clausification #[4]): ∀ (a : Iota), Or (Eq (Iff (∀ (X : Iota), cP X) (Exists cP)) True) (Eq (Iff (cP a) (Exists cP)) True) % 4.62/4.79 Clause #16 (by clausification #[15]): ∀ (a : Iota), Or (Eq (Iff (cP a) (Exists cP)) True) (Or (Eq (∀ (X : Iota), cP X) True) (Eq (Exists cP) False)) % 4.62/4.79 Clause #18 (by clausification #[16]): ∀ (a : Iota), Or (Eq (∀ (X : Iota), cP X) True) (Or (Eq (Exists cP) False) (Or (Eq (cP a) True) (Eq (Exists cP) False))) % 4.62/4.79 Clause #20 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (Exists cP) False) (Or (Eq (cP a) True) (Or (Eq (Exists cP) False) (Eq (cP a_1) True))) % 4.62/4.79 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a) True) (Or (Eq (Exists cP) False) (Or (Eq (cP a_1) True) (Eq (cP a_2) False))) % 4.62/4.79 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cP a) True) (Or (Eq (cP a_1) True) (Or (Eq (cP a_2) False) (Eq (cP a_3) False))) % 4.62/4.79 Clause #36 (by clausification #[7]): ∀ (a : Iota), Or (Eq (∀ (X : Iota), cP X) True) (Or (Eq (Exists cP) True) (Eq (Iff (cP (skS.0 0 a)) (Exists cP)) False)) % 4.62/4.79 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (Exists cP) True) (Or (Eq (Iff (cP (skS.0 0 a)) (Exists cP)) False) (Eq (cP a_1) True)) % 4.62/4.79 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), % 4.62/4.79 Or (Eq (Iff (cP (skS.0 0 a)) (Exists cP)) False) (Or (Eq (cP a_1) True) (Eq (cP (skS.0 8 a_2)) True)) % 4.62/4.79 Clause #40 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), % 4.62/4.79 Or (Eq (cP a) True) (Or (Eq (cP (skS.0 8 a_1)) True) (Or (Eq (cP (skS.0 0 a_2)) True) (Eq (Exists cP) True))) % 4.62/4.79 Clause #42 (by clausification #[40]): ∀ (a a_1 a_2 a_3 : Iota), % 4.62/4.79 Or (Eq (cP a) True) (Or (Eq (cP (skS.0 8 a_1)) True) (Or (Eq (cP (skS.0 0 a_2)) True) (Eq (cP (skS.0 9 a_3)) True))) % 4.62/4.79 Clause #53 (by equality factoring #[42]): ∀ (a a_1 a_2 : Iota), % 4.62/4.82 Or (Eq (cP (skS.0 8 a)) True) (Or (Eq (cP (skS.0 0 a_1)) True) (Or (Ne True True) (Eq (cP (skS.0 9 a_2)) True))) % 4.62/4.82 Clause #56 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), % 4.62/4.82 Or (Eq (cP (skS.0 8 a)) True) % 4.62/4.82 (Or (Eq (cP (skS.0 0 a_1)) True) (Or (Eq (cP (skS.0 9 a_2)) True) (Or (Eq True False) (Eq True False)))) % 4.62/4.82 Clause #58 (by clausification #[56]): ∀ (a a_1 a_2 : Iota), % 4.62/4.82 Or (Eq (cP (skS.0 8 a)) True) (Or (Eq (cP (skS.0 0 a_1)) True) (Or (Eq (cP (skS.0 9 a_2)) True) (Eq True False))) % 4.62/4.82 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP (skS.0 8 a)) True) (Or (Eq (cP (skS.0 0 a_1)) True) (Eq (cP (skS.0 9 a_2)) True)) % 4.62/4.82 Clause #63 (by superposition #[59, 22]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.62/4.82 Or (Eq (cP (skS.0 8 a)) True) % 4.62/4.82 (Or (Eq (cP (skS.0 9 a_1)) True) % 4.62/4.82 (Or (Eq (cP a_2) True) (Or (Eq (cP a_3) True) (Or (Eq True False) (Eq (cP a_4) False))))) % 4.62/4.82 Clause #75 (by clausification #[63]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.62/4.82 Or (Eq (cP (skS.0 8 a)) True) % 4.62/4.82 (Or (Eq (cP (skS.0 9 a_1)) True) (Or (Eq (cP a_2) True) (Or (Eq (cP a_3) True) (Eq (cP a_4) False)))) % 4.62/4.82 Clause #77 (by superposition #[75, 59]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.62/4.82 Or (Eq (cP (skS.0 8 a)) True) % 4.62/4.82 (Or (Eq (cP (skS.0 9 a_1)) True) % 4.62/4.82 (Or (Eq (cP a_2) True) % 4.62/4.82 (Or (Eq (cP a_3) True) (Or (Eq (cP (skS.0 8 a_4)) True) (Or (Eq False True) (Eq (cP (skS.0 9 a_5)) True)))))) % 4.62/4.82 Clause #98 (by clausification #[77]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.62/4.82 Or (Eq (cP (skS.0 8 a)) True) % 4.62/4.82 (Or (Eq (cP (skS.0 9 a_1)) True) % 4.62/4.82 (Or (Eq (cP a_2) True) (Or (Eq (cP a_3) True) (Or (Eq (cP (skS.0 8 a_4)) True) (Eq (cP (skS.0 9 a_5)) True))))) % 4.62/4.82 Clause #127 (by equality factoring #[98]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.62/4.82 Or (Eq (cP (skS.0 8 a)) True) % 4.62/4.82 (Or (Eq (cP a_1) True) % 4.62/4.82 (Or (Eq (cP a_2) True) (Or (Eq (cP (skS.0 8 a_3)) True) (Or (Ne True True) (Eq (cP (skS.0 9 a_4)) True))))) % 4.62/4.82 Clause #131 (by clausification #[127]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.62/4.82 Or (Eq (cP (skS.0 8 a)) True) % 4.62/4.82 (Or (Eq (cP a_1) True) % 4.62/4.82 (Or (Eq (cP a_2) True) % 4.62/4.82 (Or (Eq (cP (skS.0 8 a_3)) True) (Or (Eq (cP (skS.0 9 a_4)) True) (Or (Eq True False) (Eq True False)))))) % 4.62/4.82 Clause #133 (by clausification #[131]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.62/4.82 Or (Eq (cP (skS.0 8 a)) True) % 4.62/4.82 (Or (Eq (cP a_1) True) % 4.62/4.82 (Or (Eq (cP a_2) True) (Or (Eq (cP (skS.0 8 a_3)) True) (Or (Eq (cP (skS.0 9 a_4)) True) (Eq True False))))) % 4.62/4.82 Clause #134 (by clausification #[133]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.62/4.82 Or (Eq (cP (skS.0 8 a)) True) % 4.62/4.82 (Or (Eq (cP a_1) True) (Or (Eq (cP a_2) True) (Or (Eq (cP (skS.0 8 a_3)) True) (Eq (cP (skS.0 9 a_4)) True)))) % 4.62/4.82 Clause #156 (by equality factoring #[134]): ∀ (a a_1 a_2 a_3 : Iota), % 4.62/4.82 Or (Eq (cP a) True) % 4.62/4.82 (Or (Eq (cP a_1) True) (Or (Eq (cP (skS.0 9 a_2)) True) (Or (Ne True True) (Eq (cP (skS.0 8 a_3)) True)))) % 4.62/4.82 Clause #160 (by clausification #[156]): ∀ (a a_1 a_2 a_3 : Iota), % 4.62/4.82 Or (Eq (cP a) True) % 4.62/4.82 (Or (Eq (cP a_1) True) % 4.62/4.82 (Or (Eq (cP (skS.0 9 a_2)) True) (Or (Eq (cP (skS.0 8 a_3)) True) (Or (Eq True False) (Eq True False))))) % 4.62/4.82 Clause #162 (by clausification #[160]): ∀ (a a_1 a_2 a_3 : Iota), % 4.62/4.82 Or (Eq (cP a) True) % 4.62/4.82 (Or (Eq (cP a_1) True) (Or (Eq (cP (skS.0 9 a_2)) True) (Or (Eq (cP (skS.0 8 a_3)) True) (Eq True False)))) % 4.62/4.82 Clause #163 (by clausification #[162]): ∀ (a a_1 a_2 a_3 : Iota), % 4.62/4.82 Or (Eq (cP a) True) (Or (Eq (cP a_1) True) (Or (Eq (cP (skS.0 9 a_2)) True) (Eq (cP (skS.0 8 a_3)) True))) % 4.62/4.82 Clause #181 (by equality factoring #[163]): ∀ (a a_1 a_2 : Iota), % 4.62/4.82 Or (Eq (cP a) True) (Or (Eq (cP (skS.0 9 a_1)) True) (Or (Ne True True) (Eq (cP (skS.0 8 a_2)) True))) % 4.62/4.82 Clause #182 (by clausification #[181]): ∀ (a a_1 a_2 : Iota), % 4.62/4.82 Or (Eq (cP a) True) % 4.62/4.82 (Or (Eq (cP (skS.0 9 a_1)) True) (Or (Eq (cP (skS.0 8 a_2)) True) (Or (Eq True False) (Eq True False)))) % 4.62/4.82 Clause #184 (by clausification #[182]): ∀ (a a_1 a_2 : Iota), % 4.62/4.82 Or (Eq (cP a) True) (Or (Eq (cP (skS.0 9 a_1)) True) (Or (Eq (cP (skS.0 8 a_2)) True) (Eq True False))) % 4.62/4.82 Clause #185 (by clausification #[184]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a) True) (Or (Eq (cP (skS.0 9 a_1)) True) (Eq (cP (skS.0 8 a_2)) True)) % 4.68/4.85 Clause #202 (by equality factoring #[185]): ∀ (a a_1 : Iota), Or (Eq (cP (skS.0 9 a)) True) (Or (Ne True True) (Eq (cP (skS.0 8 a_1)) True)) % 4.68/4.85 Clause #203 (by clausification #[202]): ∀ (a a_1 : Iota), Or (Eq (cP (skS.0 9 a)) True) (Or (Eq (cP (skS.0 8 a_1)) True) (Or (Eq True False) (Eq True False))) % 4.68/4.85 Clause #205 (by clausification #[203]): ∀ (a a_1 : Iota), Or (Eq (cP (skS.0 9 a)) True) (Or (Eq (cP (skS.0 8 a_1)) True) (Eq True False)) % 4.68/4.85 Clause #206 (by clausification #[205]): ∀ (a a_1 : Iota), Or (Eq (cP (skS.0 9 a)) True) (Eq (cP (skS.0 8 a_1)) True) % 4.68/4.85 Clause #212 (by superposition #[206, 22]): ∀ (a a_1 a_2 a_3 : Iota), % 4.68/4.85 Or (Eq (cP (skS.0 9 a)) True) (Or (Eq (cP a_1) True) (Or (Eq (cP a_2) True) (Or (Eq True False) (Eq (cP a_3) False)))) % 4.68/4.85 Clause #223 (by clausification #[212]): ∀ (a a_1 a_2 a_3 : Iota), % 4.68/4.85 Or (Eq (cP (skS.0 9 a)) True) (Or (Eq (cP a_1) True) (Or (Eq (cP a_2) True) (Eq (cP a_3) False))) % 4.68/4.85 Clause #225 (by superposition #[223, 206]): ∀ (a a_1 a_2 a_3 : Iota), % 4.68/4.85 Or (Eq (cP (skS.0 9 a)) True) % 4.68/4.85 (Or (Eq (cP a_1) True) (Or (Eq (cP a_2) True) (Or (Eq (cP (skS.0 9 a_3)) True) (Eq False True)))) % 4.68/4.85 Clause #267 (by clausification #[225]): ∀ (a a_1 a_2 a_3 : Iota), % 4.68/4.85 Or (Eq (cP (skS.0 9 a)) True) (Or (Eq (cP a_1) True) (Or (Eq (cP a_2) True) (Eq (cP (skS.0 9 a_3)) True))) % 4.68/4.85 Clause #279 (by equality factoring #[267]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a) True) (Or (Eq (cP a_1) True) (Or (Ne True True) (Eq (cP (skS.0 9 a_2)) True))) % 4.68/4.85 Clause #282 (by clausification #[279]): ∀ (a a_1 a_2 : Iota), % 4.68/4.85 Or (Eq (cP a) True) (Or (Eq (cP a_1) True) (Or (Eq (cP (skS.0 9 a_2)) True) (Or (Eq True False) (Eq True False)))) % 4.68/4.85 Clause #284 (by clausification #[282]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a) True) (Or (Eq (cP a_1) True) (Or (Eq (cP (skS.0 9 a_2)) True) (Eq True False))) % 4.68/4.85 Clause #285 (by clausification #[284]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a) True) (Or (Eq (cP a_1) True) (Eq (cP (skS.0 9 a_2)) True)) % 4.68/4.85 Clause #293 (by equality factoring #[285]): ∀ (a a_1 : Iota), Or (Eq (cP a) True) (Or (Ne True True) (Eq (cP (skS.0 9 a_1)) True)) % 4.68/4.85 Clause #295 (by clausification #[293]): ∀ (a a_1 : Iota), Or (Eq (cP a) True) (Or (Eq (cP (skS.0 9 a_1)) True) (Or (Eq True False) (Eq True False))) % 4.68/4.85 Clause #297 (by clausification #[295]): ∀ (a a_1 : Iota), Or (Eq (cP a) True) (Or (Eq (cP (skS.0 9 a_1)) True) (Eq True False)) % 4.68/4.85 Clause #298 (by clausification #[297]): ∀ (a a_1 : Iota), Or (Eq (cP a) True) (Eq (cP (skS.0 9 a_1)) True) % 4.68/4.85 Clause #305 (by equality factoring #[298]): ∀ (a : Iota), Or (Ne True True) (Eq (cP (skS.0 9 a)) True) % 4.68/4.85 Clause #306 (by clausification #[305]): ∀ (a : Iota), Or (Eq (cP (skS.0 9 a)) True) (Or (Eq True False) (Eq True False)) % 4.68/4.85 Clause #308 (by clausification #[306]): ∀ (a : Iota), Or (Eq (cP (skS.0 9 a)) True) (Eq True False) % 4.68/4.85 Clause #309 (by clausification #[308]): ∀ (a : Iota), Eq (cP (skS.0 9 a)) True % 4.68/4.85 Clause #310 (by superposition #[309, 14]): ∀ (a a_1 a_2 : Iota), % 4.68/4.85 Or (Eq True False) (Or (Eq (cP (skS.0 0 a)) False) (Or (Eq (cP (skS.0 1 a_1)) False) (Eq (cP a_2) False))) % 4.68/4.85 Clause #311 (by superposition #[309, 22]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a) True) (Or (Eq (cP a_1) True) (Or (Eq True False) (Eq (cP a_2) False))) % 4.68/4.85 Clause #313 (by clausification #[311]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a) True) (Or (Eq (cP a_1) True) (Eq (cP a_2) False)) % 4.68/4.85 Clause #314 (by superposition #[313, 309]): ∀ (a a_1 : Iota), Or (Eq (cP a) True) (Or (Eq (cP a_1) True) (Eq False True)) % 4.68/4.85 Clause #315 (by clausification #[314]): ∀ (a a_1 : Iota), Or (Eq (cP a) True) (Eq (cP a_1) True) % 4.68/4.85 Clause #316 (by equality factoring #[315]): ∀ (a : Iota), Or (Ne True True) (Eq (cP a) True) % 4.68/4.85 Clause #317 (by clausification #[316]): ∀ (a : Iota), Or (Eq (cP a) True) (Or (Eq True False) (Eq True False)) % 4.68/4.85 Clause #319 (by clausification #[317]): ∀ (a : Iota), Or (Eq (cP a) True) (Eq True False) % 4.68/4.85 Clause #320 (by clausification #[319]): ∀ (a : Iota), Eq (cP a) True % 4.68/4.85 Clause #333 (by clausification #[310]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP (skS.0 0 a)) False) (Or (Eq (cP (skS.0 1 a_1)) False) (Eq (cP a_2) False)) % 4.68/4.86 Clause #334 (by superposition #[333, 320]): ∀ (a a_1 : Iota), Or (Eq (cP (skS.0 1 a)) False) (Or (Eq (cP a_1) False) (Eq False True)) % 4.68/4.86 Clause #335 (by clausification #[334]): ∀ (a a_1 : Iota), Or (Eq (cP (skS.0 1 a)) False) (Eq (cP a_1) False) % 4.68/4.86 Clause #336 (by superposition #[335, 320]): ∀ (a : Iota), Or (Eq (cP a) False) (Eq False True) % 4.68/4.86 Clause #337 (by clausification #[336]): ∀ (a : Iota), Eq (cP a) False % 4.68/4.86 Clause #338 (by superposition #[337, 320]): Eq False True % 4.68/4.86 Clause #339 (by clausification #[338]): False % 4.68/4.86 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------