TSTP Solution File: ALG254^2 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : ALG254^2 : TPTP v8.1.2. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n021.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 : Wed Aug 30 16:11:52 EDT 2023
% Result : Theorem 166.23s 166.39s
% Output : Proof 167.77s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ALG254^2 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.00/0.14 % Command : duper %s
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 03:29:28 EDT 2023
% 0.14/0.34 % CPUTime :
% 166.23/166.39 SZS status Theorem for theBenchmark.p
% 166.23/166.39 SZS output start Proof for theBenchmark.p
% 166.23/166.39 Clause #5 (by assumption #[]): Eq (Eq axidl (∀ (M : subst), Eq (comp id M) M)) True
% 166.23/166.39 Clause #7 (by assumption #[]): Eq (Eq axassoc (∀ (M N K : subst), Eq (comp (comp M N) K) (comp M (comp N K)))) True
% 166.23/166.39 Clause #9 (by assumption #[]): Eq (Eq axidr (∀ (M : subst), Eq (comp M id) M)) True
% 166.23/166.39 Clause #48 (by assumption #[]): Eq
% 166.23/166.39 (Eq substmonoid
% 166.23/166.39 (And (And (∀ (M N K : subst), Eq (comp (comp M N) K) (comp M (comp N K))) (∀ (M : subst), Eq (comp id M) M))
% 166.23/166.39 (∀ (M : subst), Eq (comp M id) M)))
% 166.23/166.39 True
% 166.23/166.39 Clause #50 (by assumption #[]): Eq (Eq substmonoid_lthm (axidl → axassoc → axidr → substmonoid)) True
% 166.23/166.39 Clause #113 (by assumption #[]): Eq (Not substmonoid_lthm) True
% 166.23/166.39 Clause #114 (by clausification #[113]): Eq substmonoid_lthm False
% 166.23/166.39 Clause #179 (by clausification #[5]): Eq axidl (∀ (M : subst), Eq (comp id M) M)
% 166.23/166.39 Clause #224 (by clausification #[7]): Eq axassoc (∀ (M N K : subst), Eq (comp (comp M N) K) (comp M (comp N K)))
% 166.23/166.39 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)
% 166.23/166.39 Clause #270 (by clausification #[9]): Eq axidr (∀ (M : subst), Eq (comp M id) M)
% 166.23/166.39 Clause #333 (by clausification #[50]): Eq substmonoid_lthm (axidl → axassoc → axidr → substmonoid)
% 166.23/166.39 Clause #334 (by forward demodulation #[333, 114]): Eq False (axidl → axassoc → axidr → substmonoid)
% 166.23/166.39 Clause #335 (by clausification #[334]): Eq axidl True
% 166.23/166.39 Clause #336 (by clausification #[334]): Eq (axassoc → axidr → substmonoid) False
% 166.23/166.39 Clause #337 (by backward demodulation #[335, 179]): Eq True (∀ (M : subst), Eq (comp id M) M)
% 166.23/166.39 Clause #342 (by clausification #[336]): Eq axassoc True
% 166.23/166.39 Clause #343 (by clausification #[336]): Eq (axidr → substmonoid) False
% 166.23/166.39 Clause #345 (by clausification #[343]): Eq axidr True
% 166.23/166.39 Clause #346 (by clausification #[343]): Eq substmonoid False
% 166.23/166.39 Clause #347 (by backward demodulation #[345, 270]): Eq True (∀ (M : subst), Eq (comp M id) M)
% 166.23/166.39 Clause #348 (by clausification #[337]): ∀ (a : subst), Eq (Eq (comp id a) a) True
% 166.23/166.39 Clause #349 (by clausification #[348]): ∀ (a : subst), Eq (comp id a) a
% 166.23/166.39 Clause #350 (by clausification #[347]): ∀ (a : subst), Eq (Eq (comp a id) a) True
% 166.23/166.39 Clause #351 (by clausification #[350]): ∀ (a : subst), Eq (comp a id) a
% 166.23/166.39 Clause #1321 (by clausification #[48]): Eq substmonoid
% 166.23/166.39 (And (And (∀ (M N K : subst), Eq (comp (comp M N) K) (comp M (comp N K))) (∀ (M : subst), Eq (comp id M) M))
% 166.23/166.39 (∀ (M : subst), Eq (comp M id) M))
% 166.23/166.39 Clause #1322 (by forward demodulation #[1321, 346]): Eq False
% 166.23/166.39 (And (And (∀ (M N K : subst), Eq (comp (comp M N) K) (comp M (comp N K))) (∀ (M : subst), Eq (comp id M) M))
% 166.23/166.39 (∀ (M : subst), Eq (comp M id) M))
% 166.23/166.39 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)
% 166.23/166.39 (Eq (∀ (M : subst), Eq (comp M id) M) False)
% 166.23/166.39 Clause #1324 (by clausification #[1323]): Or (Eq (∀ (M : subst), Eq (comp M id) M) False)
% 166.23/166.39 (Or (Eq (∀ (M N K : subst), Eq (comp (comp M N) K) (comp M (comp N K))) False)
% 166.23/166.39 (Eq (∀ (M : subst), Eq (comp id M) M) False))
% 166.23/166.39 Clause #1325 (by clausification #[1324]): ∀ (a : subst),
% 166.23/166.39 Or (Eq (∀ (M N K : subst), Eq (comp (comp M N) K) (comp M (comp N K))) False)
% 166.23/166.39 (Or (Eq (∀ (M : subst), Eq (comp id M) M) False) (Eq (Not (Eq (comp (skS.0 39 a) id) (skS.0 39 a))) True))
% 166.23/166.39 Clause #1326 (by clausification #[1325]): ∀ (a a_1 : subst),
% 166.23/166.39 Or (Eq (∀ (M : subst), Eq (comp id M) M) False)
% 166.23/166.39 (Or (Eq (Not (Eq (comp (skS.0 39 a) id) (skS.0 39 a))) True)
% 166.23/166.39 (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))
% 166.23/166.39 Clause #1327 (by clausification #[1326]): ∀ (a a_1 a_2 : subst),
% 166.23/166.39 Or (Eq (Not (Eq (comp (skS.0 39 a) id) (skS.0 39 a))) True)
% 166.23/166.39 (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)
% 166.23/166.39 (Eq (Not (Eq (comp id (skS.0 41 a_2)) (skS.0 41 a_2))) True))
% 166.23/166.39 Clause #1328 (by clausification #[1327]): ∀ (a a_1 a_2 : subst),
% 166.23/166.42 Or (Eq (Not (∀ (N K : subst), Eq (comp (comp (skS.0 40 a) N) K) (comp (skS.0 40 a) (comp N K)))) True)
% 166.23/166.42 (Or (Eq (Not (Eq (comp id (skS.0 41 a_1)) (skS.0 41 a_1))) True)
% 166.23/166.42 (Eq (Eq (comp (skS.0 39 a_2) id) (skS.0 39 a_2)) False))
% 166.23/166.42 Clause #1329 (by clausification #[1328]): ∀ (a a_1 a_2 : subst),
% 166.23/166.42 Or (Eq (Not (Eq (comp id (skS.0 41 a)) (skS.0 41 a))) True)
% 166.23/166.42 (Or (Eq (Eq (comp (skS.0 39 a_1) id) (skS.0 39 a_1)) False)
% 166.23/166.42 (Eq (∀ (N K : subst), Eq (comp (comp (skS.0 40 a_2) N) K) (comp (skS.0 40 a_2) (comp N K))) False))
% 166.23/166.42 Clause #1330 (by clausification #[1329]): ∀ (a a_1 a_2 : subst),
% 166.23/166.42 Or (Eq (Eq (comp (skS.0 39 a) id) (skS.0 39 a)) False)
% 166.23/166.42 (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)
% 166.23/166.42 (Eq (Eq (comp id (skS.0 41 a_2)) (skS.0 41 a_2)) False))
% 166.23/166.42 Clause #1331 (by clausification #[1330]): ∀ (a a_1 a_2 : subst),
% 166.23/166.42 Or (Eq (∀ (N K : subst), Eq (comp (comp (skS.0 40 a) N) K) (comp (skS.0 40 a) (comp N K))) False)
% 166.23/166.42 (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)))
% 166.23/166.42 Clause #1332 (by clausification #[1331]): ∀ (a a_1 a_2 a_3 : subst),
% 166.23/166.42 Or (Eq (Eq (comp id (skS.0 41 a)) (skS.0 41 a)) False)
% 166.23/166.42 (Or (Ne (comp (skS.0 39 a_1) id) (skS.0 39 a_1))
% 166.23/166.42 (Eq
% 166.23/166.42 (Not
% 166.23/166.42 (∀ (K : subst),
% 166.23/166.42 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))))
% 166.23/166.42 True))
% 166.23/166.42 Clause #1333 (by clausification #[1332]): ∀ (a a_1 a_2 a_3 : subst),
% 166.23/166.42 Or (Ne (comp (skS.0 39 a) id) (skS.0 39 a))
% 166.23/166.42 (Or
% 166.23/166.42 (Eq
% 166.23/166.42 (Not
% 166.23/166.42 (∀ (K : subst),
% 166.23/166.42 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))))
% 166.23/166.42 True)
% 166.23/166.42 (Ne (comp id (skS.0 41 a_3)) (skS.0 41 a_3)))
% 166.23/166.42 Clause #1334 (by clausification #[1333]): ∀ (a a_1 a_2 a_3 : subst),
% 166.23/166.42 Or (Ne (comp (skS.0 39 a) id) (skS.0 39 a))
% 166.23/166.42 (Or (Ne (comp id (skS.0 41 a_1)) (skS.0 41 a_1))
% 166.23/166.42 (Eq
% 166.23/166.42 (∀ (K : subst),
% 166.23/166.42 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)))
% 166.23/166.42 False))
% 166.23/166.42 Clause #1335 (by clausification #[1334]): ∀ (a a_1 a_2 a_3 a_4 : subst),
% 166.23/166.42 Or (Ne (comp (skS.0 39 a) id) (skS.0 39 a))
% 166.23/166.42 (Or (Ne (comp id (skS.0 41 a_1)) (skS.0 41 a_1))
% 166.23/166.42 (Eq
% 166.23/166.42 (Not
% 166.23/166.42 (Eq (comp (comp (skS.0 40 a_2) (skS.0 42 a_2 a_3)) (skS.0 43 a_2 a_3 a_4))
% 166.23/166.42 (comp (skS.0 40 a_2) (comp (skS.0 42 a_2 a_3) (skS.0 43 a_2 a_3 a_4)))))
% 166.23/166.42 True))
% 166.23/166.42 Clause #1336 (by clausification #[1335]): ∀ (a a_1 a_2 a_3 a_4 : subst),
% 166.23/166.42 Or (Ne (comp (skS.0 39 a) id) (skS.0 39 a))
% 166.23/166.42 (Or (Ne (comp id (skS.0 41 a_1)) (skS.0 41 a_1))
% 166.23/166.42 (Eq
% 166.23/166.42 (Eq (comp (comp (skS.0 40 a_2) (skS.0 42 a_2 a_3)) (skS.0 43 a_2 a_3 a_4))
% 166.23/166.42 (comp (skS.0 40 a_2) (comp (skS.0 42 a_2 a_3) (skS.0 43 a_2 a_3 a_4))))
% 166.23/166.42 False))
% 166.23/166.42 Clause #1337 (by clausification #[1336]): ∀ (a a_1 a_2 a_3 a_4 : subst),
% 166.23/166.42 Or (Ne (comp (skS.0 39 a) id) (skS.0 39 a))
% 166.23/166.42 (Or (Ne (comp id (skS.0 41 a_1)) (skS.0 41 a_1))
% 166.23/166.42 (Ne (comp (comp (skS.0 40 a_2) (skS.0 42 a_2 a_3)) (skS.0 43 a_2 a_3 a_4))
% 166.23/166.42 (comp (skS.0 40 a_2) (comp (skS.0 42 a_2 a_3) (skS.0 43 a_2 a_3 a_4)))))
% 166.23/166.42 Clause #1338 (by forward demodulation #[1337, 351]): ∀ (a a_1 a_2 a_3 a_4 : subst),
% 166.23/166.42 Or (Ne (skS.0 39 a) (skS.0 39 a))
% 166.23/166.42 (Or (Ne (comp id (skS.0 41 a_1)) (skS.0 41 a_1))
% 166.23/166.42 (Ne (comp (comp (skS.0 40 a_2) (skS.0 42 a_2 a_3)) (skS.0 43 a_2 a_3 a_4))
% 166.23/166.42 (comp (skS.0 40 a_2) (comp (skS.0 42 a_2 a_3) (skS.0 43 a_2 a_3 a_4)))))
% 166.23/166.42 Clause #1339 (by eliminate resolved literals #[1338]): ∀ (a a_1 a_2 a_3 : subst),
% 166.23/166.42 Or (Ne (comp id (skS.0 41 a)) (skS.0 41 a))
% 166.23/166.42 (Ne (comp (comp (skS.0 40 a_1) (skS.0 42 a_1 a_2)) (skS.0 43 a_1 a_2 a_3))
% 166.23/166.42 (comp (skS.0 40 a_1) (comp (skS.0 42 a_1 a_2) (skS.0 43 a_1 a_2 a_3))))
% 166.23/166.42 Clause #1340 (by forward demodulation #[1339, 349]): ∀ (a a_1 a_2 a_3 : subst),
% 166.23/166.42 Or (Ne (skS.0 41 a) (skS.0 41 a))
% 166.23/166.42 (Ne (comp (comp (skS.0 40 a_1) (skS.0 42 a_1 a_2)) (skS.0 43 a_1 a_2 a_3))
% 167.77/167.98 (comp (skS.0 40 a_1) (comp (skS.0 42 a_1 a_2) (skS.0 43 a_1 a_2 a_3))))
% 167.77/167.98 Clause #1341 (by eliminate resolved literals #[1340]): ∀ (a a_1 a_2 : subst),
% 167.77/167.98 Ne (comp (comp (skS.0 40 a) (skS.0 42 a a_1)) (skS.0 43 a a_1 a_2))
% 167.77/167.98 (comp (skS.0 40 a) (comp (skS.0 42 a a_1) (skS.0 43 a a_1 a_2)))
% 167.77/167.98 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)
% 167.77/167.98 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)
% 167.77/167.98 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)
% 167.77/167.98 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)))
% 167.77/167.98 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)))
% 167.77/167.98 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))
% 167.77/167.98 Clause #13703 (by backward contextual literal cutting #[13701, 1341]): False
% 167.77/167.98 SZS output end Proof for theBenchmark.p
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