TSTP Solution File: SYO578+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYO578+1 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n024.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 Sep 1 04:23:04 EDT 2023
% Result : Theorem 27.87s 28.08s
% Output : Proof 27.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SYO578+1 : TPTP v8.1.2. Released v5.5.0.
% 0.12/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n024.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 : Sat Aug 26 05:52:54 EDT 2023
% 0.14/0.36 % CPUTime :
% 27.87/28.08 SZS status Theorem for theBenchmark.p
% 27.87/28.08 SZS output start Proof for theBenchmark.p
% 27.87/28.08 Clause #1 (by assumption #[]): Eq (∀ (X1 : Iota), k04_buttercup10622 X1 → k04_buttercup10619 X1) True
% 27.87/28.08 Clause #3 (by assumption #[]): Eq (∀ (X3 : Iota), b48_buttercup10104 X3 → b48_buttercup10098 X3) True
% 27.87/28.08 Clause #12 (by assumption #[]): Eq
% 27.87/28.08 (And (∀ (X27 : Iota), k04_buttercup10619 X27 → b48_buttercup10098 X27)
% 27.87/28.08 (Exists fun X28 => And (b48_buttercup10098 X28) (Not (k04_buttercup10619 X28))))
% 27.87/28.08 True
% 27.87/28.08 Clause #17 (by assumption #[]): Eq
% 27.87/28.08 (And (∀ (X55 : Iota), b48_buttercup10104 X55 → k04_buttercup10622 X55)
% 27.87/28.08 (Exists fun X56 => And (k04_buttercup10622 X56) (Not (b48_buttercup10104 X56))))
% 27.87/28.08 True
% 27.87/28.08 Clause #19 (by assumption #[]): Eq
% 27.87/28.08 (And (∀ (X59 : Iota), b48_buttercup10108 X59 → k04_buttercup10622 X59)
% 27.87/28.08 (Exists fun X60 => And (k04_buttercup10622 X60) (Not (b48_buttercup10108 X60))))
% 27.87/28.08 True
% 27.87/28.08 Clause #20 (by assumption #[]): Eq
% 27.87/28.08 (And (∀ (X61 : Iota), k04_buttercup10100 X61 → b48_buttercup10098 X61)
% 27.87/28.08 (Exists fun X62 => And (b48_buttercup10098 X62) (Not (k04_buttercup10100 X62))))
% 27.87/28.08 True
% 27.87/28.08 Clause #33 (by assumption #[]): Eq (Exists fun X90 => b48_buttercup10104 X90) True
% 27.87/28.08 Clause #37 (by assumption #[]): Eq (∀ (X94 : Iota), k04_buttercup10100 X94 → Not (k04_buttercup10619 X94)) True
% 27.87/28.08 Clause #85 (by assumption #[]): Eq
% 27.87/28.08 (Not
% 27.87/28.08 (Or
% 27.87/28.08 (Or
% 27.87/28.08 (Or
% 27.87/28.08 (And (∀ (X142 : Iota), b48_buttercup10098 X142 → k04_buttercup10100 X142)
% 27.87/28.08 (Exists fun X143 => And (k04_buttercup10100 X143) (Not (b48_buttercup10098 X143))))
% 27.87/28.08 (And (∀ (X144 : Iota), k04_buttercup10100 X144 → b48_buttercup10098 X144)
% 27.87/28.08 (Exists fun X145 => And (b48_buttercup10098 X145) (Not (k04_buttercup10100 X145)))))
% 27.87/28.08 (Exists fun X146 =>
% 27.87/28.08 Exists fun X147 =>
% 27.87/28.08 Exists fun X148 =>
% 27.87/28.08 And
% 27.87/28.08 (And
% 27.87/28.08 (And (And (And (k04_buttercup10100 X146) (b48_buttercup10098 X146)) (k04_buttercup10100 X147))
% 27.87/28.08 (Not (b48_buttercup10098 X147)))
% 27.87/28.08 (Not (k04_buttercup10100 X148)))
% 27.87/28.08 (b48_buttercup10098 X148)))
% 27.87/28.08 (∀ (X149 : Iota), k04_buttercup10100 X149 → Not (b48_buttercup10098 X149))))
% 27.87/28.08 True
% 27.87/28.08 Clause #98 (by clausification #[3]): ∀ (a : Iota), Eq (b48_buttercup10104 a → b48_buttercup10098 a) True
% 27.87/28.08 Clause #99 (by clausification #[98]): ∀ (a : Iota), Or (Eq (b48_buttercup10104 a) False) (Eq (b48_buttercup10098 a) True)
% 27.87/28.08 Clause #100 (by clausification #[1]): ∀ (a : Iota), Eq (k04_buttercup10622 a → k04_buttercup10619 a) True
% 27.87/28.08 Clause #101 (by clausification #[100]): ∀ (a : Iota), Or (Eq (k04_buttercup10622 a) False) (Eq (k04_buttercup10619 a) True)
% 27.87/28.08 Clause #209 (by clausification #[12]): Eq (∀ (X27 : Iota), k04_buttercup10619 X27 → b48_buttercup10098 X27) True
% 27.87/28.08 Clause #214 (by clausification #[209]): ∀ (a : Iota), Eq (k04_buttercup10619 a → b48_buttercup10098 a) True
% 27.87/28.08 Clause #215 (by clausification #[214]): ∀ (a : Iota), Or (Eq (k04_buttercup10619 a) False) (Eq (b48_buttercup10098 a) True)
% 27.87/28.08 Clause #257 (by clausification #[37]): ∀ (a : Iota), Eq (k04_buttercup10100 a → Not (k04_buttercup10619 a)) True
% 27.87/28.08 Clause #258 (by clausification #[257]): ∀ (a : Iota), Or (Eq (k04_buttercup10100 a) False) (Eq (Not (k04_buttercup10619 a)) True)
% 27.87/28.08 Clause #259 (by clausification #[258]): ∀ (a : Iota), Or (Eq (k04_buttercup10100 a) False) (Eq (k04_buttercup10619 a) False)
% 27.87/28.08 Clause #330 (by betaEtaReduce #[33]): Eq (Exists b48_buttercup10104) True
% 27.87/28.08 Clause #331 (by clausification #[330]): ∀ (a : Iota), Eq (b48_buttercup10104 (skS.0 33 a)) True
% 27.87/28.08 Clause #332 (by superposition #[331, 99]): ∀ (a : Iota), Or (Eq True False) (Eq (b48_buttercup10098 (skS.0 33 a)) True)
% 27.87/28.08 Clause #386 (by clausification #[17]): Eq (∀ (X55 : Iota), b48_buttercup10104 X55 → k04_buttercup10622 X55) True
% 27.87/28.08 Clause #391 (by clausification #[386]): ∀ (a : Iota), Eq (b48_buttercup10104 a → k04_buttercup10622 a) True
% 27.87/28.08 Clause #392 (by clausification #[391]): ∀ (a : Iota), Or (Eq (b48_buttercup10104 a) False) (Eq (k04_buttercup10622 a) True)
% 27.87/28.08 Clause #393 (by superposition #[392, 331]): ∀ (a : Iota), Or (Eq (k04_buttercup10622 (skS.0 33 a)) True) (Eq False True)
% 27.87/28.10 Clause #429 (by clausification #[19]): Eq (Exists fun X60 => And (k04_buttercup10622 X60) (Not (b48_buttercup10108 X60))) True
% 27.87/28.10 Clause #431 (by clausification #[429]): ∀ (a : Iota), Eq (And (k04_buttercup10622 (skS.0 42 a)) (Not (b48_buttercup10108 (skS.0 42 a)))) True
% 27.87/28.10 Clause #433 (by clausification #[431]): ∀ (a : Iota), Eq (k04_buttercup10622 (skS.0 42 a)) True
% 27.87/28.10 Clause #451 (by clausification #[20]): Eq (∀ (X61 : Iota), k04_buttercup10100 X61 → b48_buttercup10098 X61) True
% 27.87/28.10 Clause #456 (by clausification #[451]): ∀ (a : Iota), Eq (k04_buttercup10100 a → b48_buttercup10098 a) True
% 27.87/28.10 Clause #457 (by clausification #[456]): ∀ (a : Iota), Or (Eq (k04_buttercup10100 a) False) (Eq (b48_buttercup10098 a) True)
% 27.87/28.10 Clause #558 (by superposition #[433, 101]): ∀ (a : Iota), Or (Eq True False) (Eq (k04_buttercup10619 (skS.0 42 a)) True)
% 27.87/28.10 Clause #587 (by clausification #[85]): Eq
% 27.87/28.10 (Or
% 27.87/28.10 (Or
% 27.87/28.10 (Or
% 27.87/28.10 (And (∀ (X142 : Iota), b48_buttercup10098 X142 → k04_buttercup10100 X142)
% 27.87/28.10 (Exists fun X143 => And (k04_buttercup10100 X143) (Not (b48_buttercup10098 X143))))
% 27.87/28.10 (And (∀ (X144 : Iota), k04_buttercup10100 X144 → b48_buttercup10098 X144)
% 27.87/28.10 (Exists fun X145 => And (b48_buttercup10098 X145) (Not (k04_buttercup10100 X145)))))
% 27.87/28.10 (Exists fun X146 =>
% 27.87/28.10 Exists fun X147 =>
% 27.87/28.10 Exists fun X148 =>
% 27.87/28.10 And
% 27.87/28.10 (And
% 27.87/28.10 (And (And (And (k04_buttercup10100 X146) (b48_buttercup10098 X146)) (k04_buttercup10100 X147))
% 27.87/28.10 (Not (b48_buttercup10098 X147)))
% 27.87/28.10 (Not (k04_buttercup10100 X148)))
% 27.87/28.10 (b48_buttercup10098 X148)))
% 27.87/28.10 (∀ (X149 : Iota), k04_buttercup10100 X149 → Not (b48_buttercup10098 X149)))
% 27.87/28.10 False
% 27.87/28.10 Clause #589 (by clausification #[587]): Eq
% 27.87/28.10 (Or
% 27.87/28.10 (Or
% 27.87/28.10 (And (∀ (X142 : Iota), b48_buttercup10098 X142 → k04_buttercup10100 X142)
% 27.87/28.10 (Exists fun X143 => And (k04_buttercup10100 X143) (Not (b48_buttercup10098 X143))))
% 27.87/28.10 (And (∀ (X144 : Iota), k04_buttercup10100 X144 → b48_buttercup10098 X144)
% 27.87/28.10 (Exists fun X145 => And (b48_buttercup10098 X145) (Not (k04_buttercup10100 X145)))))
% 27.87/28.10 (Exists fun X146 =>
% 27.87/28.10 Exists fun X147 =>
% 27.87/28.10 Exists fun X148 =>
% 27.87/28.10 And
% 27.87/28.10 (And
% 27.87/28.10 (And (And (And (k04_buttercup10100 X146) (b48_buttercup10098 X146)) (k04_buttercup10100 X147))
% 27.87/28.10 (Not (b48_buttercup10098 X147)))
% 27.87/28.10 (Not (k04_buttercup10100 X148)))
% 27.87/28.10 (b48_buttercup10098 X148)))
% 27.87/28.10 False
% 27.87/28.10 Clause #664 (by clausification #[332]): ∀ (a : Iota), Eq (b48_buttercup10098 (skS.0 33 a)) True
% 27.87/28.10 Clause #886 (by clausification #[558]): ∀ (a : Iota), Eq (k04_buttercup10619 (skS.0 42 a)) True
% 27.87/28.10 Clause #888 (by superposition #[886, 215]): ∀ (a : Iota), Or (Eq True False) (Eq (b48_buttercup10098 (skS.0 42 a)) True)
% 27.87/28.10 Clause #896 (by clausification #[888]): ∀ (a : Iota), Eq (b48_buttercup10098 (skS.0 42 a)) True
% 27.87/28.10 Clause #898 (by clausification #[393]): ∀ (a : Iota), Eq (k04_buttercup10622 (skS.0 33 a)) True
% 27.87/28.10 Clause #899 (by superposition #[898, 101]): ∀ (a : Iota), Or (Eq True False) (Eq (k04_buttercup10619 (skS.0 33 a)) True)
% 27.87/28.10 Clause #902 (by clausification #[899]): ∀ (a : Iota), Eq (k04_buttercup10619 (skS.0 33 a)) True
% 27.87/28.10 Clause #1586 (by clausification #[589]): Eq
% 27.87/28.10 (Or
% 27.87/28.10 (And (∀ (X142 : Iota), b48_buttercup10098 X142 → k04_buttercup10100 X142)
% 27.87/28.10 (Exists fun X143 => And (k04_buttercup10100 X143) (Not (b48_buttercup10098 X143))))
% 27.87/28.10 (And (∀ (X144 : Iota), k04_buttercup10100 X144 → b48_buttercup10098 X144)
% 27.87/28.10 (Exists fun X145 => And (b48_buttercup10098 X145) (Not (k04_buttercup10100 X145)))))
% 27.87/28.10 False
% 27.87/28.10 Clause #1597 (by clausification #[1586]): Eq
% 27.87/28.10 (And (∀ (X144 : Iota), k04_buttercup10100 X144 → b48_buttercup10098 X144)
% 27.87/28.10 (Exists fun X145 => And (b48_buttercup10098 X145) (Not (k04_buttercup10100 X145))))
% 27.87/28.10 False
% 27.87/28.10 Clause #1599 (by clausification #[1597]): Or (Eq (∀ (X144 : Iota), k04_buttercup10100 X144 → b48_buttercup10098 X144) False)
% 27.96/28.12 (Eq (Exists fun X145 => And (b48_buttercup10098 X145) (Not (k04_buttercup10100 X145))) False)
% 27.96/28.12 Clause #1600 (by clausification #[1599]): ∀ (a : Iota),
% 27.96/28.12 Or (Eq (Exists fun X145 => And (b48_buttercup10098 X145) (Not (k04_buttercup10100 X145))) False)
% 27.96/28.12 (Eq (Not (k04_buttercup10100 (skS.0 112 a) → b48_buttercup10098 (skS.0 112 a))) True)
% 27.96/28.12 Clause #1601 (by clausification #[1600]): ∀ (a a_1 : Iota),
% 27.96/28.12 Or (Eq (Not (k04_buttercup10100 (skS.0 112 a) → b48_buttercup10098 (skS.0 112 a))) True)
% 27.96/28.12 (Eq (And (b48_buttercup10098 a_1) (Not (k04_buttercup10100 a_1))) False)
% 27.96/28.12 Clause #1602 (by clausification #[1601]): ∀ (a a_1 : Iota),
% 27.96/28.12 Or (Eq (And (b48_buttercup10098 a) (Not (k04_buttercup10100 a))) False)
% 27.96/28.12 (Eq (k04_buttercup10100 (skS.0 112 a_1) → b48_buttercup10098 (skS.0 112 a_1)) False)
% 27.96/28.12 Clause #1603 (by clausification #[1602]): ∀ (a a_1 : Iota),
% 27.96/28.12 Or (Eq (k04_buttercup10100 (skS.0 112 a) → b48_buttercup10098 (skS.0 112 a)) False)
% 27.96/28.12 (Or (Eq (b48_buttercup10098 a_1) False) (Eq (Not (k04_buttercup10100 a_1)) False))
% 27.96/28.12 Clause #1604 (by clausification #[1603]): ∀ (a a_1 : Iota),
% 27.96/28.12 Or (Eq (b48_buttercup10098 a) False)
% 27.96/28.12 (Or (Eq (Not (k04_buttercup10100 a)) False) (Eq (k04_buttercup10100 (skS.0 112 a_1)) True))
% 27.96/28.12 Clause #1605 (by clausification #[1603]): ∀ (a a_1 : Iota),
% 27.96/28.12 Or (Eq (b48_buttercup10098 a) False)
% 27.96/28.12 (Or (Eq (Not (k04_buttercup10100 a)) False) (Eq (b48_buttercup10098 (skS.0 112 a_1)) False))
% 27.96/28.12 Clause #1606 (by clausification #[1604]): ∀ (a a_1 : Iota),
% 27.96/28.12 Or (Eq (b48_buttercup10098 a) False)
% 27.96/28.12 (Or (Eq (k04_buttercup10100 (skS.0 112 a_1)) True) (Eq (k04_buttercup10100 a) True))
% 27.96/28.12 Clause #1627 (by superposition #[1606, 896]): ∀ (a a_1 : Iota),
% 27.96/28.12 Or (Eq (k04_buttercup10100 (skS.0 112 a)) True) (Or (Eq (k04_buttercup10100 (skS.0 42 a_1)) True) (Eq False True))
% 27.96/28.12 Clause #1628 (by clausification #[1605]): ∀ (a a_1 : Iota),
% 27.96/28.12 Or (Eq (b48_buttercup10098 a) False)
% 27.96/28.12 (Or (Eq (b48_buttercup10098 (skS.0 112 a_1)) False) (Eq (k04_buttercup10100 a) True))
% 27.96/28.12 Clause #1637 (by superposition #[1628, 664]): ∀ (a a_1 : Iota),
% 27.96/28.12 Or (Eq (b48_buttercup10098 (skS.0 112 a)) False) (Or (Eq (k04_buttercup10100 (skS.0 33 a_1)) True) (Eq False True))
% 27.96/28.12 Clause #1671 (by clausification #[1637]): ∀ (a a_1 : Iota), Or (Eq (b48_buttercup10098 (skS.0 112 a)) False) (Eq (k04_buttercup10100 (skS.0 33 a_1)) True)
% 27.96/28.12 Clause #1682 (by clausification #[1627]): ∀ (a a_1 : Iota), Or (Eq (k04_buttercup10100 (skS.0 112 a)) True) (Eq (k04_buttercup10100 (skS.0 42 a_1)) True)
% 27.96/28.12 Clause #1716 (by superposition #[1682, 259]): ∀ (a a_1 : Iota),
% 27.96/28.12 Or (Eq (k04_buttercup10100 (skS.0 112 a)) True) (Or (Eq True False) (Eq (k04_buttercup10619 (skS.0 42 a_1)) False))
% 27.96/28.12 Clause #1761 (by clausification #[1716]): ∀ (a a_1 : Iota), Or (Eq (k04_buttercup10100 (skS.0 112 a)) True) (Eq (k04_buttercup10619 (skS.0 42 a_1)) False)
% 27.96/28.12 Clause #1762 (by superposition #[1761, 886]): ∀ (a : Iota), Or (Eq (k04_buttercup10100 (skS.0 112 a)) True) (Eq False True)
% 27.96/28.12 Clause #1763 (by clausification #[1762]): ∀ (a : Iota), Eq (k04_buttercup10100 (skS.0 112 a)) True
% 27.96/28.12 Clause #1768 (by superposition #[1763, 457]): ∀ (a : Iota), Or (Eq True False) (Eq (b48_buttercup10098 (skS.0 112 a)) True)
% 27.96/28.12 Clause #1796 (by clausification #[1768]): ∀ (a : Iota), Eq (b48_buttercup10098 (skS.0 112 a)) True
% 27.96/28.12 Clause #1803 (by superposition #[1796, 1671]): ∀ (a : Iota), Or (Eq True False) (Eq (k04_buttercup10100 (skS.0 33 a)) True)
% 27.96/28.12 Clause #1847 (by clausification #[1803]): ∀ (a : Iota), Eq (k04_buttercup10100 (skS.0 33 a)) True
% 27.96/28.12 Clause #1849 (by superposition #[1847, 259]): ∀ (a : Iota), Or (Eq True False) (Eq (k04_buttercup10619 (skS.0 33 a)) False)
% 27.96/28.12 Clause #1879 (by clausification #[1849]): ∀ (a : Iota), Eq (k04_buttercup10619 (skS.0 33 a)) False
% 27.96/28.12 Clause #1880 (by superposition #[1879, 902]): Eq False True
% 27.96/28.12 Clause #1881 (by clausification #[1880]): False
% 27.96/28.12 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------