%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : ALG254^2 : TPTP v9.2.0. Bugfixed v5.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n015.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 07:44:13 PM UTC 2025 % Result : Theorem 186.11s 186.35s % Output : Proof 187.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : ALG254^2 : TPTP v9.2.0. Bugfixed v5.2.0. % 0.07/0.14 % Command : duper %s % 0.14/0.35 % Computer : n015.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 : Fri Oct 3 09:11:23 EDT 2025 % 0.14/0.36 % CPUTime : % 186.11/186.35 SZS status Theorem for theBenchmark.p % 186.11/186.35 SZS output start Proof for theBenchmark.p % 186.11/186.35 Clause #5 (by assumption #[]): Eq (Eq axidl (∀ (M : subst), Eq (comp id M) M)) True % 186.11/186.35 Clause #7 (by assumption #[]): Eq (Eq axassoc (∀ (M N K : subst), Eq (comp (comp M N) K) (comp M (comp N K)))) True % 186.11/186.35 Clause #9 (by assumption #[]): Eq (Eq axidr (∀ (M : subst), Eq (comp M id) M)) True % 186.11/186.35 Clause #48 (by assumption #[]): Eq % 186.11/186.35 (Eq substmonoid % 186.11/186.35 (And (And (∀ (M N K : subst), Eq (comp (comp M N) K) (comp M (comp N K))) (∀ (M : subst), Eq (comp id M) M)) % 186.11/186.35 (∀ (M : subst), Eq (comp M id) M))) % 186.11/186.35 True % 186.11/186.35 Clause #50 (by assumption #[]): Eq (Eq substmonoid_lthm (axidl → axassoc → axidr → substmonoid)) True % 186.11/186.35 Clause #113 (by assumption #[]): Eq (Not substmonoid_lthm) True % 186.11/186.35 Clause #114 (by clausification #[113]): Eq substmonoid_lthm False % 186.11/186.35 Clause #179 (by clausification #[5]): Eq axidl (∀ (M : subst), Eq (comp id M) M) % 186.11/186.35 Clause #224 (by clausification #[7]): Eq axassoc (∀ (M N K : subst), Eq (comp (comp M N) K) (comp M (comp N K))) % 186.11/186.35 Clause #226 (by clausify Prop equality #[224]): Or (Eq axassoc False) (Eq (∀ (M N K : subst), Eq (comp (comp M N) K) (comp M (comp N K))) True) % 186.11/186.35 Clause #270 (by clausification #[9]): Eq axidr (∀ (M : subst), Eq (comp M id) M) % 186.11/186.35 Clause #333 (by clausification #[50]): Eq substmonoid_lthm (axidl → axassoc → axidr → substmonoid) % 186.11/186.35 Clause #334 (by forward demodulation #[333, 114]): Eq False (axidl → axassoc → axidr → substmonoid) % 186.11/186.35 Clause #335 (by clausification #[334]): Eq axidl True % 186.11/186.35 Clause #336 (by clausification #[334]): Eq (axassoc → axidr → substmonoid) False % 186.11/186.35 Clause #337 (by backward demodulation #[335, 179]): Eq True (∀ (M : subst), Eq (comp id M) M) % 186.11/186.35 Clause #342 (by clausification #[336]): Eq axassoc True % 186.11/186.35 Clause #343 (by clausification #[336]): Eq (axidr → substmonoid) False % 186.11/186.35 Clause #345 (by clausification #[343]): Eq axidr True % 186.11/186.35 Clause #346 (by clausification #[343]): Eq substmonoid False % 186.11/186.35 Clause #347 (by backward demodulation #[345, 270]): Eq True (∀ (M : subst), Eq (comp M id) M) % 186.11/186.35 Clause #348 (by clausification #[337]): ∀ (a : subst), Eq (Eq (comp id a) a) True % 186.11/186.35 Clause #349 (by clausification #[348]): ∀ (a : subst), Eq (comp id a) a % 186.11/186.35 Clause #350 (by clausification #[347]): ∀ (a : subst), Eq (Eq (comp a id) a) True % 186.11/186.35 Clause #351 (by clausification #[350]): ∀ (a : subst), Eq (comp a id) a % 186.11/186.35 Clause #1321 (by clausification #[48]): Eq substmonoid % 186.11/186.35 (And (And (∀ (M N K : subst), Eq (comp (comp M N) K) (comp M (comp N K))) (∀ (M : subst), Eq (comp id M) M)) % 186.11/186.35 (∀ (M : subst), Eq (comp M id) M)) % 186.11/186.35 Clause #1322 (by forward demodulation #[1321, 346]): Eq False % 186.11/186.35 (And (And (∀ (M N K : subst), Eq (comp (comp M N) K) (comp M (comp N K))) (∀ (M : subst), Eq (comp id M) M)) % 186.11/186.35 (∀ (M : subst), Eq (comp M id) M)) % 186.11/186.35 Clause #1323 (by clausification #[1322]): Or (Eq (And (∀ (M N K : subst), Eq (comp (comp M N) K) (comp M (comp N K))) (∀ (M : subst), Eq (comp id M) M)) False) % 186.11/186.35 (Eq (∀ (M : subst), Eq (comp M id) M) False) % 186.11/186.35 Clause #1324 (by clausification #[1323]): Or (Eq (∀ (M : subst), Eq (comp M id) M) False) % 186.11/186.35 (Or (Eq (∀ (M N K : subst), Eq (comp (comp M N) K) (comp M (comp N K))) False) % 186.11/186.35 (Eq (∀ (M : subst), Eq (comp id M) M) False)) % 186.11/186.35 Clause #1325 (by clausification #[1324]): ∀ (a : subst), % 186.11/186.35 Or (Eq (∀ (M N K : subst), Eq (comp (comp M N) K) (comp M (comp N K))) False) % 186.11/186.35 (Or (Eq (∀ (M : subst), Eq (comp id M) M) False) (Eq (Not (Eq (comp (skS.0 39 a) id) (skS.0 39 a))) True)) % 186.11/186.35 Clause #1326 (by clausification #[1325]): ∀ (a a_1 : subst), % 186.11/186.35 Or (Eq (∀ (M : subst), Eq (comp id M) M) False) % 186.11/186.35 (Or (Eq (Not (Eq (comp (skS.0 39 a) id) (skS.0 39 a))) True) % 186.11/186.35 (Eq (Not (∀ (N K : subst), Eq (comp (comp (skS.0 40 a_1) N) K) (comp (skS.0 40 a_1) (comp N K)))) True)) % 186.11/186.35 Clause #1327 (by clausification #[1326]): ∀ (a a_1 a_2 : subst), % 186.11/186.35 Or (Eq (Not (Eq (comp (skS.0 39 a) id) (skS.0 39 a))) True) % 186.11/186.35 (Or (Eq (Not (∀ (N K : subst), Eq (comp (comp (skS.0 40 a_1) N) K) (comp (skS.0 40 a_1) (comp N K)))) True) % 186.11/186.35 (Eq (Not (Eq (comp id (skS.0 41 a_2)) (skS.0 41 a_2))) True)) % 186.11/186.35 Clause #1328 (by clausification #[1327]): ∀ (a a_1 a_2 : subst), % 186.21/186.38 Or (Eq (Not (∀ (N K : subst), Eq (comp (comp (skS.0 40 a) N) K) (comp (skS.0 40 a) (comp N K)))) True) % 186.21/186.38 (Or (Eq (Not (Eq (comp id (skS.0 41 a_1)) (skS.0 41 a_1))) True) % 186.21/186.38 (Eq (Eq (comp (skS.0 39 a_2) id) (skS.0 39 a_2)) False)) % 186.21/186.38 Clause #1329 (by clausification #[1328]): ∀ (a a_1 a_2 : subst), % 186.21/186.38 Or (Eq (Not (Eq (comp id (skS.0 41 a)) (skS.0 41 a))) True) % 186.21/186.38 (Or (Eq (Eq (comp (skS.0 39 a_1) id) (skS.0 39 a_1)) False) % 186.21/186.38 (Eq (∀ (N K : subst), Eq (comp (comp (skS.0 40 a_2) N) K) (comp (skS.0 40 a_2) (comp N K))) False)) % 186.21/186.38 Clause #1330 (by clausification #[1329]): ∀ (a a_1 a_2 : subst), % 186.21/186.38 Or (Eq (Eq (comp (skS.0 39 a) id) (skS.0 39 a)) False) % 186.21/186.38 (Or (Eq (∀ (N K : subst), Eq (comp (comp (skS.0 40 a_1) N) K) (comp (skS.0 40 a_1) (comp N K))) False) % 186.21/186.38 (Eq (Eq (comp id (skS.0 41 a_2)) (skS.0 41 a_2)) False)) % 186.21/186.38 Clause #1331 (by clausification #[1330]): ∀ (a a_1 a_2 : subst), % 186.21/186.38 Or (Eq (∀ (N K : subst), Eq (comp (comp (skS.0 40 a) N) K) (comp (skS.0 40 a) (comp N K))) False) % 186.21/186.38 (Or (Eq (Eq (comp id (skS.0 41 a_1)) (skS.0 41 a_1)) False) (Ne (comp (skS.0 39 a_2) id) (skS.0 39 a_2))) % 186.21/186.38 Clause #1332 (by clausification #[1331]): ∀ (a a_1 a_2 a_3 : subst), % 186.21/186.38 Or (Eq (Eq (comp id (skS.0 41 a)) (skS.0 41 a)) False) % 186.21/186.38 (Or (Ne (comp (skS.0 39 a_1) id) (skS.0 39 a_1)) % 186.21/186.38 (Eq % 186.21/186.38 (Not % 186.21/186.38 (∀ (K : subst), % 186.21/186.38 Eq (comp (comp (skS.0 40 a_2) (skS.0 42 a_2 a_3)) K) (comp (skS.0 40 a_2) (comp (skS.0 42 a_2 a_3) K)))) % 186.21/186.38 True)) % 186.21/186.38 Clause #1333 (by clausification #[1332]): ∀ (a a_1 a_2 a_3 : subst), % 186.21/186.38 Or (Ne (comp (skS.0 39 a) id) (skS.0 39 a)) % 186.21/186.38 (Or % 186.21/186.38 (Eq % 186.21/186.38 (Not % 186.21/186.38 (∀ (K : subst), % 186.21/186.38 Eq (comp (comp (skS.0 40 a_1) (skS.0 42 a_1 a_2)) K) (comp (skS.0 40 a_1) (comp (skS.0 42 a_1 a_2) K)))) % 186.21/186.38 True) % 186.21/186.38 (Ne (comp id (skS.0 41 a_3)) (skS.0 41 a_3))) % 186.21/186.38 Clause #1334 (by clausification #[1333]): ∀ (a a_1 a_2 a_3 : subst), % 186.21/186.38 Or (Ne (comp (skS.0 39 a) id) (skS.0 39 a)) % 186.21/186.38 (Or (Ne (comp id (skS.0 41 a_1)) (skS.0 41 a_1)) % 186.21/186.38 (Eq % 186.21/186.38 (∀ (K : subst), % 186.21/186.38 Eq (comp (comp (skS.0 40 a_2) (skS.0 42 a_2 a_3)) K) (comp (skS.0 40 a_2) (comp (skS.0 42 a_2 a_3) K))) % 186.21/186.38 False)) % 186.21/186.38 Clause #1335 (by clausification #[1334]): ∀ (a a_1 a_2 a_3 a_4 : subst), % 186.21/186.38 Or (Ne (comp (skS.0 39 a) id) (skS.0 39 a)) % 186.21/186.38 (Or (Ne (comp id (skS.0 41 a_1)) (skS.0 41 a_1)) % 186.21/186.38 (Eq % 186.21/186.38 (Not % 186.21/186.38 (Eq (comp (comp (skS.0 40 a_2) (skS.0 42 a_2 a_3)) (skS.0 43 a_2 a_3 a_4)) % 186.21/186.38 (comp (skS.0 40 a_2) (comp (skS.0 42 a_2 a_3) (skS.0 43 a_2 a_3 a_4))))) % 186.21/186.38 True)) % 186.21/186.38 Clause #1336 (by clausification #[1335]): ∀ (a a_1 a_2 a_3 a_4 : subst), % 186.21/186.38 Or (Ne (comp (skS.0 39 a) id) (skS.0 39 a)) % 186.21/186.38 (Or (Ne (comp id (skS.0 41 a_1)) (skS.0 41 a_1)) % 186.21/186.38 (Eq % 186.21/186.38 (Eq (comp (comp (skS.0 40 a_2) (skS.0 42 a_2 a_3)) (skS.0 43 a_2 a_3 a_4)) % 186.21/186.38 (comp (skS.0 40 a_2) (comp (skS.0 42 a_2 a_3) (skS.0 43 a_2 a_3 a_4)))) % 186.21/186.38 False)) % 186.21/186.38 Clause #1337 (by clausification #[1336]): ∀ (a a_1 a_2 a_3 a_4 : subst), % 186.21/186.38 Or (Ne (comp (skS.0 39 a) id) (skS.0 39 a)) % 186.21/186.38 (Or (Ne (comp id (skS.0 41 a_1)) (skS.0 41 a_1)) % 186.21/186.38 (Ne (comp (comp (skS.0 40 a_2) (skS.0 42 a_2 a_3)) (skS.0 43 a_2 a_3 a_4)) % 186.21/186.38 (comp (skS.0 40 a_2) (comp (skS.0 42 a_2 a_3) (skS.0 43 a_2 a_3 a_4))))) % 186.21/186.38 Clause #1338 (by forward demodulation #[1337, 351]): ∀ (a a_1 a_2 a_3 a_4 : subst), % 186.21/186.38 Or (Ne (skS.0 39 a) (skS.0 39 a)) % 186.21/186.38 (Or (Ne (comp id (skS.0 41 a_1)) (skS.0 41 a_1)) % 186.21/186.38 (Ne (comp (comp (skS.0 40 a_2) (skS.0 42 a_2 a_3)) (skS.0 43 a_2 a_3 a_4)) % 186.21/186.38 (comp (skS.0 40 a_2) (comp (skS.0 42 a_2 a_3) (skS.0 43 a_2 a_3 a_4))))) % 186.21/186.38 Clause #1339 (by eliminate resolved literals #[1338]): ∀ (a a_1 a_2 a_3 : subst), % 186.21/186.38 Or (Ne (comp id (skS.0 41 a)) (skS.0 41 a)) % 186.21/186.38 (Ne (comp (comp (skS.0 40 a_1) (skS.0 42 a_1 a_2)) (skS.0 43 a_1 a_2 a_3)) % 186.21/186.38 (comp (skS.0 40 a_1) (comp (skS.0 42 a_1 a_2) (skS.0 43 a_1 a_2 a_3)))) % 186.21/186.38 Clause #1340 (by forward demodulation #[1339, 349]): ∀ (a a_1 a_2 a_3 : subst), % 186.21/186.38 Or (Ne (skS.0 41 a) (skS.0 41 a)) % 186.21/186.38 (Ne (comp (comp (skS.0 40 a_1) (skS.0 42 a_1 a_2)) (skS.0 43 a_1 a_2 a_3)) % 187.60/187.83 (comp (skS.0 40 a_1) (comp (skS.0 42 a_1 a_2) (skS.0 43 a_1 a_2 a_3)))) % 187.60/187.83 Clause #1341 (by eliminate resolved literals #[1340]): ∀ (a a_1 a_2 : subst), % 187.60/187.83 Ne (comp (comp (skS.0 40 a) (skS.0 42 a a_1)) (skS.0 43 a a_1 a_2)) % 187.60/187.83 (comp (skS.0 40 a) (comp (skS.0 42 a a_1) (skS.0 43 a a_1 a_2))) % 187.60/187.83 Clause #13696 (by clausification #[226]): ∀ (a : subst), Or (Eq axassoc False) (Eq (∀ (N K : subst), Eq (comp (comp a N) K) (comp a (comp N K))) True) % 187.60/187.83 Clause #13697 (by clausification #[13696]): ∀ (a a_1 : subst), Or (Eq axassoc False) (Eq (∀ (K : subst), Eq (comp (comp a a_1) K) (comp a (comp a_1 K))) True) % 187.60/187.83 Clause #13698 (by clausification #[13697]): ∀ (a a_1 a_2 : subst), Or (Eq axassoc False) (Eq (Eq (comp (comp a a_1) a_2) (comp a (comp a_1 a_2))) True) % 187.60/187.83 Clause #13699 (by clausification #[13698]): ∀ (a a_1 a_2 : subst), Or (Eq axassoc False) (Eq (comp (comp a a_1) a_2) (comp a (comp a_1 a_2))) % 187.60/187.83 Clause #13700 (by forward demodulation #[13699, 342]): ∀ (a a_1 a_2 : subst), Or (Eq True False) (Eq (comp (comp a a_1) a_2) (comp a (comp a_1 a_2))) % 187.60/187.83 Clause #13701 (by clausification #[13700]): ∀ (a a_1 a_2 : subst), Eq (comp (comp a a_1) a_2) (comp a (comp a_1 a_2)) % 187.60/187.83 Clause #13703 (by backward contextual literal cutting #[13701, 1341]): False % 187.60/187.83 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------