TSTP Solution File: PUZ005+1 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : PUZ005+1 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n003.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 : Thu Aug 31 13:14:21 EDT 2023
% Result : Theorem 31.39s 31.69s
% Output : Proof 31.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : PUZ005+1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n003.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 : Sat Aug 26 22:17:24 EDT 2023
% 0.13/0.34 % CPUTime :
% 31.39/31.69 SZS status Theorem for theBenchmark.p
% 31.39/31.69 SZS output start Proof for theBenchmark.p
% 31.39/31.69 Clause #3 (by assumption #[]): Eq (thursday a_thursday) True
% 31.39/31.69 Clause #9 (by assumption #[]): Eq (∀ (X : Iota), wednesday X → day X) True
% 31.39/31.69 Clause #10 (by assumption #[]): Eq (∀ (X : Iota), thursday X → day X) True
% 31.39/31.69 Clause #17 (by assumption #[]): Eq (∀ (X : Iota), thursday X → wednesday (yesterday X)) True
% 31.39/31.69 Clause #23 (by assumption #[]): Eq (∀ (X : Iota), wednesday X → lion_lies X) True
% 31.39/31.69 Clause #24 (by assumption #[]): Eq (∀ (X : Iota), thursday X → Not (lion_lies X)) True
% 31.39/31.69 Clause #30 (by assumption #[]): Eq (∀ (X : Iota), wednesday X → Not (unicorn_lies X)) True
% 31.39/31.69 Clause #31 (by assumption #[]): Eq (∀ (X : Iota), thursday X → unicorn_lies X) True
% 31.39/31.69 Clause #39 (by assumption #[]): Eq
% 31.39/31.69 (∀ (X : Iota),
% 31.39/31.69 day X → ∀ (Y : Iota), day Y → And (Not (lion_lies X)) (Not (lies_on_one_of a_lion X Y)) → Not (lion_lies Y))
% 31.39/31.69 True
% 31.39/31.69 Clause #44 (by assumption #[]): Eq
% 31.39/31.69 (∀ (X : Iota),
% 31.39/31.69 day X → ∀ (Y : Iota), day Y → And (unicorn_lies X) (Not (lies_on_one_of a_unicorn X Y)) → unicorn_lies Y)
% 31.39/31.69 True
% 31.39/31.69 Clause #45 (by assumption #[]): Eq
% 31.39/31.69 (Not
% 31.39/31.69 (Exists fun X =>
% 31.39/31.69 And (And (day X) (lies_on_one_of a_lion X (yesterday X))) (lies_on_one_of a_unicorn X (yesterday X))))
% 31.39/31.69 True
% 31.39/31.69 Clause #50 (by clausification #[31]): ∀ (a : Iota), Eq (thursday a → unicorn_lies a) True
% 31.39/31.69 Clause #51 (by clausification #[50]): ∀ (a : Iota), Or (Eq (thursday a) False) (Eq (unicorn_lies a) True)
% 31.39/31.69 Clause #52 (by superposition #[51, 3]): Or (Eq (unicorn_lies a_thursday) True) (Eq False True)
% 31.39/31.69 Clause #53 (by clausification #[52]): Eq (unicorn_lies a_thursday) True
% 31.39/31.69 Clause #66 (by clausification #[9]): ∀ (a : Iota), Eq (wednesday a → day a) True
% 31.39/31.69 Clause #67 (by clausification #[66]): ∀ (a : Iota), Or (Eq (wednesday a) False) (Eq (day a) True)
% 31.39/31.69 Clause #70 (by clausification #[23]): ∀ (a : Iota), Eq (wednesday a → lion_lies a) True
% 31.39/31.69 Clause #71 (by clausification #[70]): ∀ (a : Iota), Or (Eq (wednesday a) False) (Eq (lion_lies a) True)
% 31.39/31.69 Clause #78 (by clausification #[10]): ∀ (a : Iota), Eq (thursday a → day a) True
% 31.39/31.69 Clause #79 (by clausification #[78]): ∀ (a : Iota), Or (Eq (thursday a) False) (Eq (day a) True)
% 31.39/31.69 Clause #80 (by superposition #[79, 3]): Or (Eq (day a_thursday) True) (Eq False True)
% 31.39/31.69 Clause #81 (by clausification #[80]): Eq (day a_thursday) True
% 31.39/31.69 Clause #129 (by clausification #[17]): ∀ (a : Iota), Eq (thursday a → wednesday (yesterday a)) True
% 31.39/31.69 Clause #130 (by clausification #[129]): ∀ (a : Iota), Or (Eq (thursday a) False) (Eq (wednesday (yesterday a)) True)
% 31.39/31.69 Clause #131 (by superposition #[130, 3]): Or (Eq (wednesday (yesterday a_thursday)) True) (Eq False True)
% 31.39/31.69 Clause #132 (by clausification #[131]): Eq (wednesday (yesterday a_thursday)) True
% 31.39/31.69 Clause #133 (by superposition #[132, 67]): Or (Eq True False) (Eq (day (yesterday a_thursday)) True)
% 31.39/31.69 Clause #134 (by superposition #[132, 71]): Or (Eq True False) (Eq (lion_lies (yesterday a_thursday)) True)
% 31.39/31.69 Clause #136 (by clausification #[134]): Eq (lion_lies (yesterday a_thursday)) True
% 31.39/31.69 Clause #137 (by clausification #[133]): Eq (day (yesterday a_thursday)) True
% 31.39/31.69 Clause #152 (by clausification #[30]): ∀ (a : Iota), Eq (wednesday a → Not (unicorn_lies a)) True
% 31.39/31.69 Clause #153 (by clausification #[152]): ∀ (a : Iota), Or (Eq (wednesday a) False) (Eq (Not (unicorn_lies a)) True)
% 31.39/31.69 Clause #154 (by clausification #[153]): ∀ (a : Iota), Or (Eq (wednesday a) False) (Eq (unicorn_lies a) False)
% 31.39/31.69 Clause #156 (by superposition #[154, 132]): Or (Eq (unicorn_lies (yesterday a_thursday)) False) (Eq False True)
% 31.39/31.69 Clause #161 (by clausification #[156]): Eq (unicorn_lies (yesterday a_thursday)) False
% 31.39/31.69 Clause #171 (by clausification #[24]): ∀ (a : Iota), Eq (thursday a → Not (lion_lies a)) True
% 31.39/31.69 Clause #172 (by clausification #[171]): ∀ (a : Iota), Or (Eq (thursday a) False) (Eq (Not (lion_lies a)) True)
% 31.39/31.69 Clause #173 (by clausification #[172]): ∀ (a : Iota), Or (Eq (thursday a) False) (Eq (lion_lies a) False)
% 31.39/31.69 Clause #174 (by superposition #[173, 3]): Or (Eq (lion_lies a_thursday) False) (Eq False True)
% 31.53/31.72 Clause #176 (by clausification #[174]): Eq (lion_lies a_thursday) False
% 31.53/31.72 Clause #292 (by clausification #[39]): ∀ (a : Iota),
% 31.53/31.72 Eq (day a → ∀ (Y : Iota), day Y → And (Not (lion_lies a)) (Not (lies_on_one_of a_lion a Y)) → Not (lion_lies Y)) True
% 31.53/31.72 Clause #293 (by clausification #[292]): ∀ (a : Iota),
% 31.53/31.72 Or (Eq (day a) False)
% 31.53/31.72 (Eq (∀ (Y : Iota), day Y → And (Not (lion_lies a)) (Not (lies_on_one_of a_lion a Y)) → Not (lion_lies Y)) True)
% 31.53/31.72 Clause #294 (by clausification #[293]): ∀ (a a_1 : Iota),
% 31.53/31.72 Or (Eq (day a) False)
% 31.53/31.72 (Eq (day a_1 → And (Not (lion_lies a)) (Not (lies_on_one_of a_lion a a_1)) → Not (lion_lies a_1)) True)
% 31.53/31.72 Clause #295 (by clausification #[294]): ∀ (a a_1 : Iota),
% 31.53/31.72 Or (Eq (day a) False)
% 31.53/31.72 (Or (Eq (day a_1) False)
% 31.53/31.72 (Eq (And (Not (lion_lies a)) (Not (lies_on_one_of a_lion a a_1)) → Not (lion_lies a_1)) True))
% 31.53/31.72 Clause #296 (by clausification #[295]): ∀ (a a_1 : Iota),
% 31.53/31.72 Or (Eq (day a) False)
% 31.53/31.72 (Or (Eq (day a_1) False)
% 31.53/31.72 (Or (Eq (And (Not (lion_lies a)) (Not (lies_on_one_of a_lion a a_1))) False) (Eq (Not (lion_lies a_1)) True)))
% 31.53/31.72 Clause #297 (by clausification #[296]): ∀ (a a_1 : Iota),
% 31.53/31.72 Or (Eq (day a) False)
% 31.53/31.72 (Or (Eq (day a_1) False)
% 31.53/31.72 (Or (Eq (Not (lion_lies a_1)) True)
% 31.53/31.72 (Or (Eq (Not (lion_lies a)) False) (Eq (Not (lies_on_one_of a_lion a a_1)) False))))
% 31.53/31.72 Clause #298 (by clausification #[297]): ∀ (a a_1 : Iota),
% 31.53/31.72 Or (Eq (day a) False)
% 31.53/31.72 (Or (Eq (day a_1) False)
% 31.53/31.72 (Or (Eq (Not (lion_lies a)) False)
% 31.53/31.72 (Or (Eq (Not (lies_on_one_of a_lion a a_1)) False) (Eq (lion_lies a_1) False))))
% 31.53/31.72 Clause #299 (by clausification #[298]): ∀ (a a_1 : Iota),
% 31.53/31.72 Or (Eq (day a) False)
% 31.53/31.72 (Or (Eq (day a_1) False)
% 31.53/31.72 (Or (Eq (Not (lies_on_one_of a_lion a a_1)) False) (Or (Eq (lion_lies a_1) False) (Eq (lion_lies a) True))))
% 31.53/31.72 Clause #300 (by clausification #[299]): ∀ (a a_1 : Iota),
% 31.53/31.72 Or (Eq (day a) False)
% 31.53/31.72 (Or (Eq (day a_1) False)
% 31.53/31.72 (Or (Eq (lion_lies a_1) False) (Or (Eq (lion_lies a) True) (Eq (lies_on_one_of a_lion a a_1) True))))
% 31.53/31.72 Clause #306 (by superposition #[300, 81]): ∀ (a : Iota),
% 31.53/31.72 Or (Eq (day a) False)
% 31.53/31.72 (Or (Eq (lion_lies a) False)
% 31.53/31.72 (Or (Eq (lion_lies a_thursday) True) (Or (Eq (lies_on_one_of a_lion a_thursday a) True) (Eq False True))))
% 31.53/31.72 Clause #507 (by clausification #[44]): ∀ (a : Iota),
% 31.53/31.72 Eq (day a → ∀ (Y : Iota), day Y → And (unicorn_lies a) (Not (lies_on_one_of a_unicorn a Y)) → unicorn_lies Y) True
% 31.53/31.72 Clause #508 (by clausification #[507]): ∀ (a : Iota),
% 31.53/31.72 Or (Eq (day a) False)
% 31.53/31.72 (Eq (∀ (Y : Iota), day Y → And (unicorn_lies a) (Not (lies_on_one_of a_unicorn a Y)) → unicorn_lies Y) True)
% 31.53/31.72 Clause #509 (by clausification #[508]): ∀ (a a_1 : Iota),
% 31.53/31.72 Or (Eq (day a) False)
% 31.53/31.72 (Eq (day a_1 → And (unicorn_lies a) (Not (lies_on_one_of a_unicorn a a_1)) → unicorn_lies a_1) True)
% 31.53/31.72 Clause #510 (by clausification #[509]): ∀ (a a_1 : Iota),
% 31.53/31.72 Or (Eq (day a) False)
% 31.53/31.72 (Or (Eq (day a_1) False) (Eq (And (unicorn_lies a) (Not (lies_on_one_of a_unicorn a a_1)) → unicorn_lies a_1) True))
% 31.53/31.72 Clause #511 (by clausification #[510]): ∀ (a a_1 : Iota),
% 31.53/31.72 Or (Eq (day a) False)
% 31.53/31.72 (Or (Eq (day a_1) False)
% 31.53/31.72 (Or (Eq (And (unicorn_lies a) (Not (lies_on_one_of a_unicorn a a_1))) False) (Eq (unicorn_lies a_1) True)))
% 31.53/31.72 Clause #512 (by clausification #[511]): ∀ (a a_1 : Iota),
% 31.53/31.72 Or (Eq (day a) False)
% 31.53/31.72 (Or (Eq (day a_1) False)
% 31.53/31.72 (Or (Eq (unicorn_lies a_1) True)
% 31.53/31.72 (Or (Eq (unicorn_lies a) False) (Eq (Not (lies_on_one_of a_unicorn a a_1)) False))))
% 31.53/31.72 Clause #513 (by clausification #[512]): ∀ (a a_1 : Iota),
% 31.53/31.72 Or (Eq (day a) False)
% 31.53/31.72 (Or (Eq (day a_1) False)
% 31.53/31.72 (Or (Eq (unicorn_lies a_1) True) (Or (Eq (unicorn_lies a) False) (Eq (lies_on_one_of a_unicorn a a_1) True))))
% 31.53/31.72 Clause #519 (by superposition #[513, 81]): ∀ (a : Iota),
% 31.53/31.72 Or (Eq (day a) False)
% 31.53/31.72 (Or (Eq (unicorn_lies a) True)
% 31.53/31.72 (Or (Eq (unicorn_lies a_thursday) False) (Or (Eq (lies_on_one_of a_unicorn a_thursday a) True) (Eq False True))))
% 31.53/31.72 Clause #558 (by clausification #[45]): Eq
% 31.53/31.72 (Exists fun X => And (And (day X) (lies_on_one_of a_lion X (yesterday X))) (lies_on_one_of a_unicorn X (yesterday X)))
% 31.53/31.75 False
% 31.53/31.75 Clause #559 (by clausification #[558]): ∀ (a : Iota),
% 31.53/31.75 Eq (And (And (day a) (lies_on_one_of a_lion a (yesterday a))) (lies_on_one_of a_unicorn a (yesterday a))) False
% 31.53/31.75 Clause #560 (by clausification #[559]): ∀ (a : Iota),
% 31.53/31.75 Or (Eq (And (day a) (lies_on_one_of a_lion a (yesterday a))) False)
% 31.53/31.75 (Eq (lies_on_one_of a_unicorn a (yesterday a)) False)
% 31.53/31.75 Clause #561 (by clausification #[560]): ∀ (a : Iota),
% 31.53/31.75 Or (Eq (lies_on_one_of a_unicorn a (yesterday a)) False)
% 31.53/31.75 (Or (Eq (day a) False) (Eq (lies_on_one_of a_lion a (yesterday a)) False))
% 31.53/31.75 Clause #2202 (by clausification #[306]): ∀ (a : Iota),
% 31.53/31.75 Or (Eq (day a) False)
% 31.53/31.75 (Or (Eq (lion_lies a) False) (Or (Eq (lion_lies a_thursday) True) (Eq (lies_on_one_of a_lion a_thursday a) True)))
% 31.53/31.75 Clause #2203 (by forward demodulation #[2202, 176]): ∀ (a : Iota),
% 31.53/31.75 Or (Eq (day a) False)
% 31.53/31.75 (Or (Eq (lion_lies a) False) (Or (Eq False True) (Eq (lies_on_one_of a_lion a_thursday a) True)))
% 31.53/31.75 Clause #2204 (by clausification #[2203]): ∀ (a : Iota), Or (Eq (day a) False) (Or (Eq (lion_lies a) False) (Eq (lies_on_one_of a_lion a_thursday a) True))
% 31.53/31.75 Clause #2213 (by superposition #[2204, 137]): Or (Eq (lion_lies (yesterday a_thursday)) False)
% 31.53/31.75 (Or (Eq (lies_on_one_of a_lion a_thursday (yesterday a_thursday)) True) (Eq False True))
% 31.53/31.75 Clause #7101 (by clausification #[2213]): Or (Eq (lion_lies (yesterday a_thursday)) False) (Eq (lies_on_one_of a_lion a_thursday (yesterday a_thursday)) True)
% 31.53/31.75 Clause #7102 (by forward demodulation #[7101, 136]): Or (Eq True False) (Eq (lies_on_one_of a_lion a_thursday (yesterday a_thursday)) True)
% 31.53/31.75 Clause #7103 (by clausification #[7102]): Eq (lies_on_one_of a_lion a_thursday (yesterday a_thursday)) True
% 31.53/31.75 Clause #7912 (by clausification #[519]): ∀ (a : Iota),
% 31.53/31.75 Or (Eq (day a) False)
% 31.53/31.75 (Or (Eq (unicorn_lies a) True)
% 31.53/31.75 (Or (Eq (unicorn_lies a_thursday) False) (Eq (lies_on_one_of a_unicorn a_thursday a) True)))
% 31.53/31.75 Clause #7913 (by forward demodulation #[7912, 53]): ∀ (a : Iota),
% 31.53/31.75 Or (Eq (day a) False)
% 31.53/31.75 (Or (Eq (unicorn_lies a) True) (Or (Eq True False) (Eq (lies_on_one_of a_unicorn a_thursday a) True)))
% 31.53/31.75 Clause #7914 (by clausification #[7913]): ∀ (a : Iota), Or (Eq (day a) False) (Or (Eq (unicorn_lies a) True) (Eq (lies_on_one_of a_unicorn a_thursday a) True))
% 31.53/31.75 Clause #7923 (by superposition #[7914, 137]): Or (Eq (unicorn_lies (yesterday a_thursday)) True)
% 31.53/31.75 (Or (Eq (lies_on_one_of a_unicorn a_thursday (yesterday a_thursday)) True) (Eq False True))
% 31.53/31.75 Clause #8394 (by clausification #[7923]): Or (Eq (unicorn_lies (yesterday a_thursday)) True)
% 31.53/31.75 (Eq (lies_on_one_of a_unicorn a_thursday (yesterday a_thursday)) True)
% 31.53/31.75 Clause #8395 (by forward demodulation #[8394, 161]): Or (Eq False True) (Eq (lies_on_one_of a_unicorn a_thursday (yesterday a_thursday)) True)
% 31.53/31.75 Clause #8396 (by clausification #[8395]): Eq (lies_on_one_of a_unicorn a_thursday (yesterday a_thursday)) True
% 31.53/31.75 Clause #8397 (by superposition #[8396, 561]): Or (Eq True False) (Or (Eq (day a_thursday) False) (Eq (lies_on_one_of a_lion a_thursday (yesterday a_thursday)) False))
% 31.53/31.75 Clause #8398 (by clausification #[8397]): Or (Eq (day a_thursday) False) (Eq (lies_on_one_of a_lion a_thursday (yesterday a_thursday)) False)
% 31.53/31.75 Clause #8399 (by forward demodulation #[8398, 81]): Or (Eq True False) (Eq (lies_on_one_of a_lion a_thursday (yesterday a_thursday)) False)
% 31.53/31.75 Clause #8400 (by clausification #[8399]): Eq (lies_on_one_of a_lion a_thursday (yesterday a_thursday)) False
% 31.53/31.75 Clause #8401 (by superposition #[8400, 7103]): Eq False True
% 31.53/31.75 Clause #8402 (by clausification #[8401]): False
% 31.53/31.75 SZS output end Proof for theBenchmark.p
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