%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN078+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n005.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 08:07:08 PM UTC 2025 % Result : Theorem 4.44s 4.65s % Output : Proof 4.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYN078+1 : TPTP v9.2.0. Released v2.0.0. % 0.07/0.13 % Command : duper %s % 0.14/0.35 % Computer : n005.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 15:42:38 EDT 2025 % 0.14/0.35 % CPUTime : % 4.44/4.65 SZS status Theorem for theBenchmark.p % 4.44/4.65 SZS output start Proof for theBenchmark.p % 4.44/4.65 Clause #0 (by assumption #[]): Eq % 4.44/4.65 (Not % 4.44/4.65 (Iff (∀ (X : Iota), (Exists fun Y => And (big_p Y) (Eq X (f Y))) → big_p X) (∀ (U : Iota), big_p U → big_p (f U)))) % 4.44/4.65 True % 4.44/4.65 Clause #1 (by clausification #[0]): Eq (Iff (∀ (X : Iota), (Exists fun Y => And (big_p Y) (Eq X (f Y))) → big_p X) (∀ (U : Iota), big_p U → big_p (f U))) % 4.44/4.65 False % 4.44/4.65 Clause #2 (by clausification #[1]): Or (Eq (∀ (X : Iota), (Exists fun Y => And (big_p Y) (Eq X (f Y))) → big_p X) False) % 4.44/4.65 (Eq (∀ (U : Iota), big_p U → big_p (f U)) False) % 4.44/4.65 Clause #3 (by clausification #[1]): Or (Eq (∀ (X : Iota), (Exists fun Y => And (big_p Y) (Eq X (f Y))) → big_p X) True) % 4.44/4.65 (Eq (∀ (U : Iota), big_p U → big_p (f U)) True) % 4.44/4.65 Clause #4 (by clausification #[2]): ∀ (a : Iota), % 4.44/4.65 Or (Eq (∀ (U : Iota), big_p U → big_p (f U)) False) % 4.44/4.65 (Eq (Not ((Exists fun Y => And (big_p Y) (Eq (skS.0 0 a) (f Y))) → big_p (skS.0 0 a))) True) % 4.44/4.65 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), % 4.44/4.65 Or (Eq (Not ((Exists fun Y => And (big_p Y) (Eq (skS.0 0 a) (f Y))) → big_p (skS.0 0 a))) True) % 4.44/4.65 (Eq (Not (big_p (skS.0 1 a_1) → big_p (f (skS.0 1 a_1)))) True) % 4.44/4.65 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), % 4.44/4.65 Or (Eq (Not (big_p (skS.0 1 a) → big_p (f (skS.0 1 a)))) True) % 4.44/4.65 (Eq ((Exists fun Y => And (big_p Y) (Eq (skS.0 0 a_1) (f Y))) → big_p (skS.0 0 a_1)) False) % 4.44/4.65 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), % 4.44/4.65 Or (Eq ((Exists fun Y => And (big_p Y) (Eq (skS.0 0 a) (f Y))) → big_p (skS.0 0 a)) False) % 4.44/4.65 (Eq (big_p (skS.0 1 a_1) → big_p (f (skS.0 1 a_1))) False) % 4.44/4.65 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), % 4.44/4.65 Or (Eq (big_p (skS.0 1 a) → big_p (f (skS.0 1 a))) False) % 4.44/4.65 (Eq (Exists fun Y => And (big_p Y) (Eq (skS.0 0 a_1) (f Y))) True) % 4.44/4.65 Clause #9 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 1 a) → big_p (f (skS.0 1 a))) False) (Eq (big_p (skS.0 0 a_1)) False) % 4.44/4.65 Clause #10 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq (Exists fun Y => And (big_p Y) (Eq (skS.0 0 a) (f Y))) True) (Eq (big_p (skS.0 1 a_1)) True) % 4.44/4.65 Clause #11 (by clausification #[8]): ∀ (a a_1 : Iota), % 4.44/4.65 Or (Eq (Exists fun Y => And (big_p Y) (Eq (skS.0 0 a) (f Y))) True) (Eq (big_p (f (skS.0 1 a_1))) False) % 4.44/4.65 Clause #12 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), % 4.44/4.65 Or (Eq (big_p (skS.0 1 a)) True) (Eq (And (big_p (skS.0 2 a_1 a_2)) (Eq (skS.0 0 a_1) (f (skS.0 2 a_1 a_2)))) True) % 4.44/4.65 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p (skS.0 1 a)) True) (Eq (Eq (skS.0 0 a_1) (f (skS.0 2 a_1 a_2))) True) % 4.44/4.65 Clause #14 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p (skS.0 1 a)) True) (Eq (big_p (skS.0 2 a_1 a_2)) True) % 4.44/4.65 Clause #15 (by clausification #[13]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p (skS.0 1 a)) True) (Eq (skS.0 0 a_1) (f (skS.0 2 a_1 a_2))) % 4.44/4.65 Clause #16 (by clausification #[3]): ∀ (a : Iota), % 4.44/4.65 Or (Eq (∀ (U : Iota), big_p U → big_p (f U)) True) (Eq ((Exists fun Y => And (big_p Y) (Eq a (f Y))) → big_p a) True) % 4.44/4.65 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), % 4.44/4.65 Or (Eq ((Exists fun Y => And (big_p Y) (Eq a (f Y))) → big_p a) True) (Eq (big_p a_1 → big_p (f a_1)) True) % 4.44/4.65 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), % 4.44/4.65 Or (Eq (big_p a → big_p (f a)) True) % 4.44/4.65 (Or (Eq (Exists fun Y => And (big_p Y) (Eq a_1 (f Y))) False) (Eq (big_p a_1) True)) % 4.44/4.65 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), % 4.44/4.65 Or (Eq (Exists fun Y => And (big_p Y) (Eq a (f Y))) False) % 4.44/4.65 (Or (Eq (big_p a) True) (Or (Eq (big_p a_1) False) (Eq (big_p (f a_1)) True))) % 4.44/4.65 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), % 4.44/4.65 Or (Eq (big_p a) True) % 4.44/4.65 (Or (Eq (big_p a_1) False) (Or (Eq (big_p (f a_1)) True) (Eq (And (big_p a_2) (Eq a (f a_2))) False))) % 4.44/4.65 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), % 4.44/4.65 Or (Eq (big_p a) True) % 4.44/4.65 (Or (Eq (big_p a_1) False) (Or (Eq (big_p (f a_1)) True) (Or (Eq (big_p a_2) False) (Eq (Eq a (f a_2)) False)))) % 4.44/4.65 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), % 4.44/4.68 Or (Eq (big_p a) True) % 4.44/4.68 (Or (Eq (big_p a_1) False) (Or (Eq (big_p (f a_1)) True) (Or (Eq (big_p a_2) False) (Ne a (f a_2))))) % 4.44/4.68 Clause #23 (by destructive equality resolution #[22]): ∀ (a a_1 : Iota), % 4.44/4.68 Or (Eq (big_p (f a)) True) (Or (Eq (big_p a_1) False) (Or (Eq (big_p (f a_1)) True) (Eq (big_p a) False))) % 4.44/4.68 Clause #25 (by clausification #[9]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 0 a)) False) (Eq (big_p (skS.0 1 a_1)) True) % 4.44/4.68 Clause #26 (by clausification #[9]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 0 a)) False) (Eq (big_p (f (skS.0 1 a_1))) False) % 4.44/4.68 Clause #28 (by superposition #[14, 23]): ∀ (a a_1 a_2 a_3 : Iota), % 4.44/4.68 Or (Eq (big_p (f a)) True) % 4.44/4.68 (Or (Eq (big_p (f (skS.0 2 a_1 a_2))) True) % 4.44/4.68 (Or (Eq (big_p a) False) (Or (Eq (big_p (skS.0 1 a_3)) True) (Eq False True)))) % 4.44/4.68 Clause #29 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), % 4.44/4.68 Or (Eq (big_p (f (skS.0 1 a))) False) % 4.44/4.68 (Eq (And (big_p (skS.0 3 a_1 a_2)) (Eq (skS.0 0 a_1) (f (skS.0 3 a_1 a_2)))) True) % 4.44/4.68 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p (f (skS.0 1 a))) False) (Eq (Eq (skS.0 0 a_1) (f (skS.0 3 a_1 a_2))) True) % 4.44/4.68 Clause #31 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p (f (skS.0 1 a))) False) (Eq (big_p (skS.0 3 a_1 a_2)) True) % 4.44/4.68 Clause #32 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p (f (skS.0 1 a))) False) (Eq (skS.0 0 a_1) (f (skS.0 3 a_1 a_2))) % 4.44/4.68 Clause #37 (by clausification #[28]): ∀ (a a_1 a_2 a_3 : Iota), % 4.44/4.68 Or (Eq (big_p (f a)) True) % 4.44/4.68 (Or (Eq (big_p (f (skS.0 2 a_1 a_2))) True) (Or (Eq (big_p a) False) (Eq (big_p (skS.0 1 a_3)) True))) % 4.44/4.68 Clause #40 (by superposition #[37, 14]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.44/4.68 Or (Eq (big_p (f (skS.0 2 a a_1))) True) % 4.44/4.68 (Or (Eq (big_p (f (skS.0 2 a_2 a_3))) True) % 4.44/4.68 (Or (Eq (big_p (skS.0 1 a_4)) True) (Or (Eq (big_p (skS.0 1 a_5)) True) (Eq False True)))) % 4.44/4.68 Clause #45 (by clausification #[40]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.44/4.68 Or (Eq (big_p (f (skS.0 2 a a_1))) True) % 4.44/4.68 (Or (Eq (big_p (f (skS.0 2 a_2 a_3))) True) (Or (Eq (big_p (skS.0 1 a_4)) True) (Eq (big_p (skS.0 1 a_5)) True))) % 4.44/4.68 Clause #56 (by equality factoring #[45]): ∀ (a a_1 a_2 a_3 : Iota), % 4.44/4.68 Or (Eq (big_p (skS.0 1 a)) True) % 4.44/4.68 (Or (Eq (big_p (skS.0 1 a_1)) True) (Or (Ne True True) (Eq (big_p (f (skS.0 2 a_2 a_3))) True))) % 4.44/4.68 Clause #72 (by clausification #[56]): ∀ (a a_1 a_2 a_3 : Iota), % 4.44/4.68 Or (Eq (big_p (skS.0 1 a)) True) % 4.44/4.68 (Or (Eq (big_p (skS.0 1 a_1)) True) % 4.44/4.68 (Or (Eq (big_p (f (skS.0 2 a_2 a_3))) True) (Or (Eq True False) (Eq True False)))) % 4.44/4.68 Clause #74 (by clausification #[72]): ∀ (a a_1 a_2 a_3 : Iota), % 4.44/4.68 Or (Eq (big_p (skS.0 1 a)) True) % 4.44/4.68 (Or (Eq (big_p (skS.0 1 a_1)) True) (Or (Eq (big_p (f (skS.0 2 a_2 a_3))) True) (Eq True False))) % 4.44/4.68 Clause #75 (by clausification #[74]): ∀ (a a_1 a_2 a_3 : Iota), % 4.44/4.68 Or (Eq (big_p (skS.0 1 a)) True) (Or (Eq (big_p (skS.0 1 a_1)) True) (Eq (big_p (f (skS.0 2 a_2 a_3))) True)) % 4.44/4.68 Clause #86 (by equality factoring #[75]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p (f (skS.0 2 a a_1))) True) (Or (Ne True True) (Eq (big_p (skS.0 1 a_2)) True)) % 4.44/4.68 Clause #87 (by clausification #[86]): ∀ (a a_1 a_2 : Iota), % 4.44/4.68 Or (Eq (big_p (f (skS.0 2 a a_1))) True) (Or (Eq (big_p (skS.0 1 a_2)) True) (Or (Eq True False) (Eq True False))) % 4.44/4.68 Clause #89 (by clausification #[87]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p (f (skS.0 2 a a_1))) True) (Or (Eq (big_p (skS.0 1 a_2)) True) (Eq True False)) % 4.44/4.68 Clause #90 (by clausification #[89]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p (f (skS.0 2 a a_1))) True) (Eq (big_p (skS.0 1 a_2)) True) % 4.44/4.68 Clause #97 (by superposition #[90, 15]): ∀ (a a_1 a_2 : Iota), % 4.44/4.68 Or (Eq (big_p (skS.0 1 a)) True) (Or (Eq (big_p (skS.0 0 a_1)) True) (Eq (big_p (skS.0 1 a_2)) True)) % 4.44/4.68 Clause #110 (by equality factoring #[97]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 0 a)) True) (Or (Ne True True) (Eq (big_p (skS.0 1 a_1)) True)) % 4.44/4.68 Clause #111 (by clausification #[110]): ∀ (a a_1 : Iota), % 4.44/4.68 Or (Eq (big_p (skS.0 0 a)) True) (Or (Eq (big_p (skS.0 1 a_1)) True) (Or (Eq True False) (Eq True False))) % 4.44/4.68 Clause #113 (by clausification #[111]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 0 a)) True) (Or (Eq (big_p (skS.0 1 a_1)) True) (Eq True False)) % 4.53/4.70 Clause #114 (by clausification #[113]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 0 a)) True) (Eq (big_p (skS.0 1 a_1)) True) % 4.53/4.70 Clause #115 (by superposition #[114, 25]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 1 a)) True) (Or (Eq True False) (Eq (big_p (skS.0 1 a_1)) True)) % 4.53/4.70 Clause #134 (by clausification #[115]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 1 a)) True) (Eq (big_p (skS.0 1 a_1)) True) % 4.53/4.70 Clause #138 (by equality factoring #[134]): ∀ (a : Iota), Or (Ne True True) (Eq (big_p (skS.0 1 a)) True) % 4.53/4.70 Clause #139 (by clausification #[138]): ∀ (a : Iota), Or (Eq (big_p (skS.0 1 a)) True) (Or (Eq True False) (Eq True False)) % 4.53/4.70 Clause #141 (by clausification #[139]): ∀ (a : Iota), Or (Eq (big_p (skS.0 1 a)) True) (Eq True False) % 4.53/4.70 Clause #142 (by clausification #[141]): ∀ (a : Iota), Eq (big_p (skS.0 1 a)) True % 4.53/4.70 Clause #143 (by superposition #[142, 23]): ∀ (a a_1 : Iota), % 4.53/4.70 Or (Eq (big_p (f a)) True) (Or (Eq True False) (Or (Eq (big_p (f (skS.0 1 a_1))) True) (Eq (big_p a) False))) % 4.53/4.70 Clause #146 (by clausification #[143]): ∀ (a a_1 : Iota), Or (Eq (big_p (f a)) True) (Or (Eq (big_p (f (skS.0 1 a_1))) True) (Eq (big_p a) False)) % 4.53/4.70 Clause #154 (by superposition #[146, 142]): ∀ (a a_1 : Iota), Or (Eq (big_p (f (skS.0 1 a))) True) (Or (Eq (big_p (f (skS.0 1 a_1))) True) (Eq False True)) % 4.53/4.70 Clause #157 (by clausification #[154]): ∀ (a a_1 : Iota), Or (Eq (big_p (f (skS.0 1 a))) True) (Eq (big_p (f (skS.0 1 a_1))) True) % 4.53/4.70 Clause #162 (by equality factoring #[157]): ∀ (a : Iota), Or (Ne True True) (Eq (big_p (f (skS.0 1 a))) True) % 4.53/4.70 Clause #163 (by clausification #[162]): ∀ (a : Iota), Or (Eq (big_p (f (skS.0 1 a))) True) (Or (Eq True False) (Eq True False)) % 4.53/4.70 Clause #165 (by clausification #[163]): ∀ (a : Iota), Or (Eq (big_p (f (skS.0 1 a))) True) (Eq True False) % 4.53/4.70 Clause #166 (by clausification #[165]): ∀ (a : Iota), Eq (big_p (f (skS.0 1 a))) True % 4.53/4.70 Clause #167 (by superposition #[166, 32]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (skS.0 0 a) (f (skS.0 3 a a_1))) % 4.53/4.70 Clause #168 (by superposition #[166, 31]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (big_p (skS.0 3 a a_1)) True) % 4.53/4.70 Clause #170 (by clausification #[168]): ∀ (a a_1 : Iota), Eq (big_p (skS.0 3 a a_1)) True % 4.53/4.70 Clause #171 (by superposition #[170, 23]): ∀ (a a_1 a_2 : Iota), % 4.53/4.70 Or (Eq (big_p (f a)) True) (Or (Eq True False) (Or (Eq (big_p (f (skS.0 3 a_1 a_2))) True) (Eq (big_p a) False))) % 4.53/4.70 Clause #173 (by clausification #[167]): ∀ (a a_1 : Iota), Eq (skS.0 0 a) (f (skS.0 3 a a_1)) % 4.53/4.70 Clause #178 (by clausification #[171]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p (f a)) True) (Or (Eq (big_p (f (skS.0 3 a_1 a_2))) True) (Eq (big_p a) False)) % 4.53/4.70 Clause #179 (by forward demodulation #[178, 173]): ∀ (a a_1 : Iota), Or (Eq (big_p (f a)) True) (Or (Eq (big_p (skS.0 0 a_1)) True) (Eq (big_p a) False)) % 4.53/4.70 Clause #182 (by superposition #[179, 170]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p (f (skS.0 3 a a_1))) True) (Or (Eq (big_p (skS.0 0 a_2)) True) (Eq False True)) % 4.53/4.70 Clause #193 (by clausification #[182]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p (f (skS.0 3 a a_1))) True) (Eq (big_p (skS.0 0 a_2)) True) % 4.53/4.70 Clause #194 (by forward demodulation #[193, 173]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 0 a)) True) (Eq (big_p (skS.0 0 a_1)) True) % 4.53/4.70 Clause #199 (by equality factoring #[194]): ∀ (a : Iota), Or (Ne True True) (Eq (big_p (skS.0 0 a)) True) % 4.53/4.70 Clause #200 (by clausification #[199]): ∀ (a : Iota), Or (Eq (big_p (skS.0 0 a)) True) (Or (Eq True False) (Eq True False)) % 4.53/4.70 Clause #202 (by clausification #[200]): ∀ (a : Iota), Or (Eq (big_p (skS.0 0 a)) True) (Eq True False) % 4.53/4.70 Clause #203 (by clausification #[202]): ∀ (a : Iota), Eq (big_p (skS.0 0 a)) True % 4.53/4.70 Clause #204 (by superposition #[203, 26]): ∀ (a : Iota), Or (Eq True False) (Eq (big_p (f (skS.0 1 a))) False) % 4.53/4.70 Clause #207 (by clausification #[204]): ∀ (a : Iota), Eq (big_p (f (skS.0 1 a))) False % 4.53/4.70 Clause #208 (by superposition #[207, 166]): Eq False True % 4.53/4.70 Clause #209 (by clausification #[208]): False % 4.53/4.70 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------