TSTP Solution File: SYN328+1 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYN328+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n016.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 02:11:12 EDT 2023
% Result : Theorem 3.76s 3.93s
% Output : Proof 3.76s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN328+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.12 % Command : duper %s
% 0.13/0.33 % Computer : n016.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Aug 26 21:48:27 EDT 2023
% 0.13/0.33 % CPUTime :
% 3.76/3.93 SZS status Theorem for theBenchmark.p
% 3.76/3.93 SZS output start Proof for theBenchmark.p
% 3.76/3.93 Clause #0 (by assumption #[]): Eq
% 3.76/3.93 (Not
% 3.76/3.93 (Exists fun X =>
% 3.76/3.93 ∀ (Y Z : Iota),
% 3.76/3.93 Iff (big_f Y → big_g Y) (big_f X) →
% 3.76/3.93 Iff (big_f Y → big_h Y) (big_g X) →
% 3.76/3.93 Iff ((big_f Y → big_g Y) → big_h Y) (big_h X) → And (And (big_f Z) (big_g Z)) (big_h Z)))
% 3.76/3.93 True
% 3.76/3.93 Clause #1 (by clausification #[0]): Eq
% 3.76/3.93 (Exists fun X =>
% 3.76/3.93 ∀ (Y Z : Iota),
% 3.76/3.93 Iff (big_f Y → big_g Y) (big_f X) →
% 3.76/3.93 Iff (big_f Y → big_h Y) (big_g X) →
% 3.76/3.93 Iff ((big_f Y → big_g Y) → big_h Y) (big_h X) → And (And (big_f Z) (big_g Z)) (big_h Z))
% 3.76/3.93 False
% 3.76/3.93 Clause #2 (by clausification #[1]): ∀ (a : Iota),
% 3.76/3.93 Eq
% 3.76/3.93 (∀ (Y Z : Iota),
% 3.76/3.93 Iff (big_f Y → big_g Y) (big_f a) →
% 3.76/3.93 Iff (big_f Y → big_h Y) (big_g a) →
% 3.76/3.93 Iff ((big_f Y → big_g Y) → big_h Y) (big_h a) → And (And (big_f Z) (big_g Z)) (big_h Z))
% 3.76/3.93 False
% 3.76/3.93 Clause #3 (by clausification #[2]): ∀ (a a_1 : Iota),
% 3.76/3.93 Eq
% 3.76/3.93 (Not
% 3.76/3.93 (∀ (Z : Iota),
% 3.76/3.93 Iff (big_f (skS.0 0 a a_1) → big_g (skS.0 0 a a_1)) (big_f a) →
% 3.76/3.93 Iff (big_f (skS.0 0 a a_1) → big_h (skS.0 0 a a_1)) (big_g a) →
% 3.76/3.93 Iff ((big_f (skS.0 0 a a_1) → big_g (skS.0 0 a a_1)) → big_h (skS.0 0 a a_1)) (big_h a) →
% 3.76/3.93 And (And (big_f Z) (big_g Z)) (big_h Z)))
% 3.76/3.93 True
% 3.76/3.93 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota),
% 3.76/3.93 Eq
% 3.76/3.93 (∀ (Z : Iota),
% 3.76/3.93 Iff (big_f (skS.0 0 a a_1) → big_g (skS.0 0 a a_1)) (big_f a) →
% 3.76/3.93 Iff (big_f (skS.0 0 a a_1) → big_h (skS.0 0 a a_1)) (big_g a) →
% 3.76/3.93 Iff ((big_f (skS.0 0 a a_1) → big_g (skS.0 0 a a_1)) → big_h (skS.0 0 a a_1)) (big_h a) →
% 3.76/3.93 And (And (big_f Z) (big_g Z)) (big_h Z))
% 3.76/3.93 False
% 3.76/3.93 Clause #5 (by clausification #[4]): ∀ (a a_1 a_2 : Iota),
% 3.76/3.93 Eq
% 3.76/3.93 (Not
% 3.76/3.93 (Iff (big_f (skS.0 0 a a_1) → big_g (skS.0 0 a a_1)) (big_f a) →
% 3.76/3.93 Iff (big_f (skS.0 0 a a_1) → big_h (skS.0 0 a a_1)) (big_g a) →
% 3.76/3.93 Iff ((big_f (skS.0 0 a a_1) → big_g (skS.0 0 a a_1)) → big_h (skS.0 0 a a_1)) (big_h a) →
% 3.76/3.93 And (And (big_f (skS.0 1 a a_1 a_2)) (big_g (skS.0 1 a a_1 a_2))) (big_h (skS.0 1 a a_1 a_2))))
% 3.76/3.93 True
% 3.76/3.93 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Iota),
% 3.76/3.93 Eq
% 3.76/3.93 (Iff (big_f (skS.0 0 a a_1) → big_g (skS.0 0 a a_1)) (big_f a) →
% 3.76/3.93 Iff (big_f (skS.0 0 a a_1) → big_h (skS.0 0 a a_1)) (big_g a) →
% 3.76/3.93 Iff ((big_f (skS.0 0 a a_1) → big_g (skS.0 0 a a_1)) → big_h (skS.0 0 a a_1)) (big_h a) →
% 3.76/3.93 And (And (big_f (skS.0 1 a a_1 a_2)) (big_g (skS.0 1 a a_1 a_2))) (big_h (skS.0 1 a a_1 a_2)))
% 3.76/3.93 False
% 3.76/3.93 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (Iff (big_f (skS.0 0 a a_1) → big_g (skS.0 0 a a_1)) (big_f a)) True
% 3.76/3.93 Clause #8 (by clausification #[6]): ∀ (a a_1 a_2 : Iota),
% 3.76/3.93 Eq
% 3.76/3.93 (Iff (big_f (skS.0 0 a a_1) → big_h (skS.0 0 a a_1)) (big_g a) →
% 3.76/3.93 Iff ((big_f (skS.0 0 a a_1) → big_g (skS.0 0 a a_1)) → big_h (skS.0 0 a a_1)) (big_h a) →
% 3.76/3.93 And (And (big_f (skS.0 1 a a_1 a_2)) (big_g (skS.0 1 a a_1 a_2))) (big_h (skS.0 1 a a_1 a_2)))
% 3.76/3.93 False
% 3.76/3.93 Clause #10 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (big_f (skS.0 0 a a_1) → big_g (skS.0 0 a a_1)) False) (Eq (big_f a) True)
% 3.76/3.93 Clause #12 (by clausification #[10]): ∀ (a a_1 : Iota), Or (Eq (big_f a) True) (Eq (big_f (skS.0 0 a a_1)) True)
% 3.76/3.93 Clause #13 (by clausification #[10]): ∀ (a a_1 : Iota), Or (Eq (big_f a) True) (Eq (big_g (skS.0 0 a a_1)) False)
% 3.76/3.93 Clause #15 (by clausification #[8]): ∀ (a a_1 : Iota), Eq (Iff (big_f (skS.0 0 a a_1) → big_h (skS.0 0 a a_1)) (big_g a)) True
% 3.76/3.93 Clause #16 (by clausification #[8]): ∀ (a a_1 a_2 : Iota),
% 3.76/3.93 Eq
% 3.76/3.93 (Iff ((big_f (skS.0 0 a a_1) → big_g (skS.0 0 a a_1)) → big_h (skS.0 0 a a_1)) (big_h a) →
% 3.76/3.93 And (And (big_f (skS.0 1 a a_1 a_2)) (big_g (skS.0 1 a a_1 a_2))) (big_h (skS.0 1 a a_1 a_2)))
% 3.76/3.93 False
% 3.76/3.93 Clause #17 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (big_f (skS.0 0 a a_1) → big_h (skS.0 0 a a_1)) True) (Eq (big_g a) False)
% 3.76/3.93 Clause #18 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (big_f (skS.0 0 a a_1) → big_h (skS.0 0 a a_1)) False) (Eq (big_g a) True)
% 3.76/3.95 Clause #19 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (big_g a) False) (Or (Eq (big_f (skS.0 0 a a_1)) False) (Eq (big_h (skS.0 0 a a_1)) True))
% 3.76/3.95 Clause #21 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (big_g a) True) (Eq (big_h (skS.0 0 a a_1)) False)
% 3.76/3.95 Clause #31 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (Iff ((big_f (skS.0 0 a a_1) → big_g (skS.0 0 a a_1)) → big_h (skS.0 0 a a_1)) (big_h a)) True
% 3.76/3.95 Clause #32 (by clausification #[16]): ∀ (a a_1 a_2 : Iota),
% 3.76/3.95 Eq (And (And (big_f (skS.0 1 a a_1 a_2)) (big_g (skS.0 1 a a_1 a_2))) (big_h (skS.0 1 a a_1 a_2))) False
% 3.76/3.95 Clause #34 (by clausification #[31]): ∀ (a a_1 : Iota),
% 3.76/3.95 Or (Eq ((big_f (skS.0 0 a a_1) → big_g (skS.0 0 a a_1)) → big_h (skS.0 0 a a_1)) False) (Eq (big_h a) True)
% 3.76/3.95 Clause #41 (by clausification #[34]): ∀ (a a_1 : Iota), Or (Eq (big_h a) True) (Eq (big_f (skS.0 0 a a_1) → big_g (skS.0 0 a a_1)) True)
% 3.76/3.95 Clause #42 (by clausification #[34]): ∀ (a a_1 : Iota), Or (Eq (big_h a) True) (Eq (big_h (skS.0 0 a a_1)) False)
% 3.76/3.95 Clause #43 (by clausification #[41]): ∀ (a a_1 : Iota), Or (Eq (big_h a) True) (Or (Eq (big_f (skS.0 0 a a_1)) False) (Eq (big_g (skS.0 0 a a_1)) True))
% 3.76/3.95 Clause #44 (by superposition #[43, 12]): ∀ (a a_1 : Iota), Or (Eq (big_h a) True) (Or (Eq (big_g (skS.0 0 a a_1)) True) (Or (Eq (big_f a) True) (Eq False True)))
% 3.76/3.95 Clause #46 (by clausification #[44]): ∀ (a a_1 : Iota), Or (Eq (big_h a) True) (Or (Eq (big_g (skS.0 0 a a_1)) True) (Eq (big_f a) True))
% 3.76/3.95 Clause #47 (by superposition #[46, 13]): ∀ (a : Iota), Or (Eq (big_h a) True) (Or (Eq (big_f a) True) (Or (Eq (big_f a) True) (Eq True False)))
% 3.76/3.95 Clause #49 (by clausification #[47]): ∀ (a : Iota), Or (Eq (big_h a) True) (Or (Eq (big_f a) True) (Eq (big_f a) True))
% 3.76/3.95 Clause #50 (by eliminate duplicate literals #[49]): ∀ (a : Iota), Or (Eq (big_h a) True) (Eq (big_f a) True)
% 3.76/3.95 Clause #52 (by superposition #[50, 42]): ∀ (a a_1 : Iota), Or (Eq (big_f (skS.0 0 a a_1)) True) (Or (Eq (big_h a) True) (Eq True False))
% 3.76/3.95 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), Or (Eq (big_f (skS.0 0 a a_1)) True) (Eq (big_h a) True)
% 3.76/3.95 Clause #56 (by superposition #[53, 43]): ∀ (a a_1 : Iota), Or (Eq (big_h a) True) (Or (Eq (big_h a) True) (Or (Eq True False) (Eq (big_g (skS.0 0 a a_1)) True)))
% 3.76/3.95 Clause #67 (by clausification #[56]): ∀ (a a_1 : Iota), Or (Eq (big_h a) True) (Or (Eq (big_h a) True) (Eq (big_g (skS.0 0 a a_1)) True))
% 3.76/3.95 Clause #68 (by eliminate duplicate literals #[67]): ∀ (a a_1 : Iota), Or (Eq (big_h a) True) (Eq (big_g (skS.0 0 a a_1)) True)
% 3.76/3.95 Clause #70 (by superposition #[68, 19]): ∀ (a a_1 a_2 : Iota),
% 3.76/3.95 Or (Eq (big_h a) True)
% 3.76/3.95 (Or (Eq True False)
% 3.76/3.95 (Or (Eq (big_f (skS.0 0 (skS.0 0 a a_1) a_2)) False) (Eq (big_h (skS.0 0 (skS.0 0 a a_1) a_2)) True)))
% 3.76/3.95 Clause #71 (by clausification #[32]): ∀ (a a_1 a_2 : Iota),
% 3.76/3.95 Or (Eq (And (big_f (skS.0 1 a a_1 a_2)) (big_g (skS.0 1 a a_1 a_2))) False) (Eq (big_h (skS.0 1 a a_1 a_2)) False)
% 3.76/3.95 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 : Iota),
% 3.76/3.95 Or (Eq (big_h (skS.0 1 a a_1 a_2)) False)
% 3.76/3.95 (Or (Eq (big_f (skS.0 1 a a_1 a_2)) False) (Eq (big_g (skS.0 1 a a_1 a_2)) False))
% 3.76/3.95 Clause #85 (by clausification #[70]): ∀ (a a_1 a_2 : Iota),
% 3.76/3.95 Or (Eq (big_h a) True)
% 3.76/3.95 (Or (Eq (big_f (skS.0 0 (skS.0 0 a a_1) a_2)) False) (Eq (big_h (skS.0 0 (skS.0 0 a a_1) a_2)) True))
% 3.76/3.95 Clause #88 (by superposition #[85, 53]): ∀ (a a_1 a_2 : Iota),
% 3.76/3.95 Or (Eq (big_h a) True)
% 3.76/3.95 (Or (Eq (big_h (skS.0 0 (skS.0 0 a a_1) a_2)) True) (Or (Eq False True) (Eq (big_h (skS.0 0 a a_1)) True)))
% 3.76/3.95 Clause #89 (by clausification #[88]): ∀ (a a_1 a_2 : Iota),
% 3.76/3.95 Or (Eq (big_h a) True) (Or (Eq (big_h (skS.0 0 (skS.0 0 a a_1) a_2)) True) (Eq (big_h (skS.0 0 a a_1)) True))
% 3.76/3.95 Clause #91 (by superposition #[89, 42]): ∀ (a a_1 : Iota),
% 3.76/3.95 Or (Eq (big_h a) True) (Or (Eq (big_h (skS.0 0 a a_1)) True) (Or (Eq (big_h (skS.0 0 a a_1)) True) (Eq True False)))
% 3.76/3.95 Clause #97 (by clausification #[91]): ∀ (a a_1 : Iota), Or (Eq (big_h a) True) (Or (Eq (big_h (skS.0 0 a a_1)) True) (Eq (big_h (skS.0 0 a a_1)) True))
% 3.76/3.96 Clause #98 (by eliminate duplicate literals #[97]): ∀ (a a_1 : Iota), Or (Eq (big_h a) True) (Eq (big_h (skS.0 0 a a_1)) True)
% 3.76/3.96 Clause #100 (by superposition #[98, 42]): ∀ (a : Iota), Or (Eq (big_h a) True) (Or (Eq (big_h a) True) (Eq True False))
% 3.76/3.96 Clause #102 (by clausification #[100]): ∀ (a : Iota), Or (Eq (big_h a) True) (Eq (big_h a) True)
% 3.76/3.96 Clause #103 (by eliminate duplicate literals #[102]): ∀ (a : Iota), Eq (big_h a) True
% 3.76/3.96 Clause #104 (by backward demodulation #[103, 72]): ∀ (a a_1 a_2 : Iota),
% 3.76/3.96 Or (Eq True False) (Or (Eq (big_f (skS.0 1 a a_1 a_2)) False) (Eq (big_g (skS.0 1 a a_1 a_2)) False))
% 3.76/3.96 Clause #112 (by superposition #[103, 21]): ∀ (a : Iota), Or (Eq (big_g a) True) (Eq True False)
% 3.76/3.96 Clause #113 (by clausification #[112]): ∀ (a : Iota), Eq (big_g a) True
% 3.76/3.96 Clause #117 (by superposition #[113, 13]): ∀ (a : Iota), Or (Eq (big_f a) True) (Eq True False)
% 3.76/3.96 Clause #118 (by clausification #[117]): ∀ (a : Iota), Eq (big_f a) True
% 3.76/3.96 Clause #130 (by clausification #[104]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f (skS.0 1 a a_1 a_2)) False) (Eq (big_g (skS.0 1 a a_1 a_2)) False)
% 3.76/3.96 Clause #131 (by forward demodulation #[130, 118]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (big_g (skS.0 1 a a_1 a_2)) False)
% 3.76/3.96 Clause #132 (by clausification #[131]): ∀ (a a_1 a_2 : Iota), Eq (big_g (skS.0 1 a a_1 a_2)) False
% 3.76/3.96 Clause #133 (by superposition #[132, 113]): Eq False True
% 3.76/3.96 Clause #134 (by clausification #[133]): False
% 3.76/3.96 SZS output end Proof for theBenchmark.p
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