TSTP Solution File: SYN920+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYN920+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n004.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 02:13:16 EDT 2023
% Result : Theorem 3.87s 4.17s
% Output : Proof 3.87s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYN920+1 : TPTP v8.1.2. Released v3.1.0.
% 0.14/0.15 % Command : duper %s
% 0.16/0.36 % Computer : n004.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sat Aug 26 19:07:08 EDT 2023
% 0.16/0.36 % CPUTime :
% 3.87/4.17 SZS status Theorem for theBenchmark.p
% 3.87/4.17 SZS output start Proof for theBenchmark.p
% 3.87/4.17 Clause #0 (by assumption #[]): Eq
% 3.87/4.17 (Not
% 3.87/4.17 (And ((∀ (X : Iota), And (f X) (g X) → h X) → Exists fun X => And (f X) (Not (g X)))
% 3.87/4.17 (Or (∀ (W : Iota), f W → g W) (∀ (Z : Iota), f Z → h Z)) →
% 3.87/4.17 (∀ (R : Iota), And (f R) (h R) → g R) → Exists fun V => And (And (f V) (g V)) (Not (h V))))
% 3.87/4.17 True
% 3.87/4.17 Clause #1 (by clausification #[0]): Eq
% 3.87/4.17 (And ((∀ (X : Iota), And (f X) (g X) → h X) → Exists fun X => And (f X) (Not (g X)))
% 3.87/4.17 (Or (∀ (W : Iota), f W → g W) (∀ (Z : Iota), f Z → h Z)) →
% 3.87/4.17 (∀ (R : Iota), And (f R) (h R) → g R) → Exists fun V => And (And (f V) (g V)) (Not (h V)))
% 3.87/4.17 False
% 3.87/4.17 Clause #2 (by clausification #[1]): Eq
% 3.87/4.17 (And ((∀ (X : Iota), And (f X) (g X) → h X) → Exists fun X => And (f X) (Not (g X)))
% 3.87/4.17 (Or (∀ (W : Iota), f W → g W) (∀ (Z : Iota), f Z → h Z)))
% 3.87/4.17 True
% 3.87/4.17 Clause #3 (by clausification #[1]): Eq ((∀ (R : Iota), And (f R) (h R) → g R) → Exists fun V => And (And (f V) (g V)) (Not (h V))) False
% 3.87/4.17 Clause #4 (by clausification #[2]): Eq (Or (∀ (W : Iota), f W → g W) (∀ (Z : Iota), f Z → h Z)) True
% 3.87/4.17 Clause #5 (by clausification #[2]): Eq ((∀ (X : Iota), And (f X) (g X) → h X) → Exists fun X => And (f X) (Not (g X))) True
% 3.87/4.17 Clause #6 (by clausification #[4]): Or (Eq (∀ (W : Iota), f W → g W) True) (Eq (∀ (Z : Iota), f Z → h Z) True)
% 3.87/4.17 Clause #7 (by clausification #[6]): ∀ (a : Iota), Or (Eq (∀ (Z : Iota), f Z → h Z) True) (Eq (f a → g a) True)
% 3.87/4.17 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (f a → g a) True) (Eq (f a_1 → h a_1) True)
% 3.87/4.17 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq (f a → h a) True) (Or (Eq (f a_1) False) (Eq (g a_1) True))
% 3.87/4.17 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Or (Eq (f a) False) (Or (Eq (g a) True) (Or (Eq (f a_1) False) (Eq (h a_1) True)))
% 3.87/4.17 Clause #11 (by clausification #[5]): Or (Eq (∀ (X : Iota), And (f X) (g X) → h X) False) (Eq (Exists fun X => And (f X) (Not (g X))) True)
% 3.87/4.17 Clause #12 (by clausification #[11]): ∀ (a : Iota),
% 3.87/4.17 Or (Eq (Exists fun X => And (f X) (Not (g X))) True)
% 3.87/4.17 (Eq (Not (And (f (skS.0 0 a)) (g (skS.0 0 a)) → h (skS.0 0 a))) True)
% 3.87/4.17 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota),
% 3.87/4.17 Or (Eq (Not (And (f (skS.0 0 a)) (g (skS.0 0 a)) → h (skS.0 0 a))) True)
% 3.87/4.17 (Eq (And (f (skS.0 1 a_1)) (Not (g (skS.0 1 a_1)))) True)
% 3.87/4.17 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota),
% 3.87/4.17 Or (Eq (And (f (skS.0 1 a)) (Not (g (skS.0 1 a)))) True)
% 3.87/4.17 (Eq (And (f (skS.0 0 a_1)) (g (skS.0 0 a_1)) → h (skS.0 0 a_1)) False)
% 3.87/4.17 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (And (f (skS.0 0 a)) (g (skS.0 0 a)) → h (skS.0 0 a)) False) (Eq (Not (g (skS.0 1 a_1))) True)
% 3.87/4.17 Clause #16 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (And (f (skS.0 0 a)) (g (skS.0 0 a)) → h (skS.0 0 a)) False) (Eq (f (skS.0 1 a_1)) True)
% 3.87/4.17 Clause #17 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (Not (g (skS.0 1 a))) True) (Eq (And (f (skS.0 0 a_1)) (g (skS.0 0 a_1))) True)
% 3.87/4.17 Clause #18 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (Not (g (skS.0 1 a))) True) (Eq (h (skS.0 0 a_1)) False)
% 3.87/4.17 Clause #19 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (And (f (skS.0 0 a)) (g (skS.0 0 a))) True) (Eq (g (skS.0 1 a_1)) False)
% 3.87/4.17 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Or (Eq (g (skS.0 1 a)) False) (Eq (g (skS.0 0 a_1)) True)
% 3.87/4.17 Clause #21 (by clausification #[19]): ∀ (a a_1 : Iota), Or (Eq (g (skS.0 1 a)) False) (Eq (f (skS.0 0 a_1)) True)
% 3.87/4.17 Clause #22 (by clausification #[3]): Eq (∀ (R : Iota), And (f R) (h R) → g R) True
% 3.87/4.17 Clause #23 (by clausification #[3]): Eq (Exists fun V => And (And (f V) (g V)) (Not (h V))) False
% 3.87/4.17 Clause #24 (by clausification #[22]): ∀ (a : Iota), Eq (And (f a) (h a) → g a) True
% 3.87/4.17 Clause #25 (by clausification #[24]): ∀ (a : Iota), Or (Eq (And (f a) (h a)) False) (Eq (g a) True)
% 3.87/4.17 Clause #26 (by clausification #[25]): ∀ (a : Iota), Or (Eq (g a) True) (Or (Eq (f a) False) (Eq (h a) False))
% 3.87/4.17 Clause #27 (by clausification #[23]): ∀ (a : Iota), Eq (And (And (f a) (g a)) (Not (h a))) False
% 3.87/4.21 Clause #28 (by clausification #[27]): ∀ (a : Iota), Or (Eq (And (f a) (g a)) False) (Eq (Not (h a)) False)
% 3.87/4.21 Clause #29 (by clausification #[28]): ∀ (a : Iota), Or (Eq (Not (h a)) False) (Or (Eq (f a) False) (Eq (g a) False))
% 3.87/4.21 Clause #30 (by clausification #[29]): ∀ (a : Iota), Or (Eq (f a) False) (Or (Eq (g a) False) (Eq (h a) True))
% 3.87/4.21 Clause #31 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (f (skS.0 1 a)) True) (Eq (And (f (skS.0 0 a_1)) (g (skS.0 0 a_1))) True)
% 3.87/4.21 Clause #32 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (f (skS.0 1 a)) True) (Eq (h (skS.0 0 a_1)) False)
% 3.87/4.21 Clause #33 (by clausification #[31]): ∀ (a a_1 : Iota), Or (Eq (f (skS.0 1 a)) True) (Eq (g (skS.0 0 a_1)) True)
% 3.87/4.21 Clause #34 (by clausification #[31]): ∀ (a a_1 : Iota), Or (Eq (f (skS.0 1 a)) True) (Eq (f (skS.0 0 a_1)) True)
% 3.87/4.21 Clause #43 (by superposition #[34, 30]): ∀ (a a_1 : Iota),
% 3.87/4.21 Or (Eq (f (skS.0 1 a)) True) (Or (Eq True False) (Or (Eq (g (skS.0 0 a_1)) False) (Eq (h (skS.0 0 a_1)) True)))
% 3.87/4.21 Clause #44 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (h (skS.0 0 a)) False) (Eq (g (skS.0 1 a_1)) False)
% 3.87/4.21 Clause #56 (by clausification #[43]): ∀ (a a_1 : Iota), Or (Eq (f (skS.0 1 a)) True) (Or (Eq (g (skS.0 0 a_1)) False) (Eq (h (skS.0 0 a_1)) True))
% 3.87/4.21 Clause #57 (by superposition #[56, 33]): ∀ (a a_1 a_2 : Iota),
% 3.87/4.21 Or (Eq (f (skS.0 1 a)) True) (Or (Eq (h (skS.0 0 a_1)) True) (Or (Eq (f (skS.0 1 a_2)) True) (Eq False True)))
% 3.87/4.21 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), Or (Eq (f (skS.0 1 a)) True) (Or (Eq (h (skS.0 0 a_1)) True) (Eq (f (skS.0 1 a_2)) True))
% 3.87/4.21 Clause #71 (by equality factoring #[58]): ∀ (a a_1 : Iota), Or (Eq (h (skS.0 0 a)) True) (Or (Ne True True) (Eq (f (skS.0 1 a_1)) True))
% 3.87/4.21 Clause #72 (by clausification #[71]): ∀ (a a_1 : Iota), Or (Eq (h (skS.0 0 a)) True) (Or (Eq (f (skS.0 1 a_1)) True) (Or (Eq True False) (Eq True False)))
% 3.87/4.21 Clause #74 (by clausification #[72]): ∀ (a a_1 : Iota), Or (Eq (h (skS.0 0 a)) True) (Or (Eq (f (skS.0 1 a_1)) True) (Eq True False))
% 3.87/4.21 Clause #75 (by clausification #[74]): ∀ (a a_1 : Iota), Or (Eq (h (skS.0 0 a)) True) (Eq (f (skS.0 1 a_1)) True)
% 3.87/4.21 Clause #76 (by superposition #[75, 32]): ∀ (a a_1 : Iota), Or (Eq (f (skS.0 1 a)) True) (Or (Eq (f (skS.0 1 a_1)) True) (Eq True False))
% 3.87/4.21 Clause #85 (by clausification #[76]): ∀ (a a_1 : Iota), Or (Eq (f (skS.0 1 a)) True) (Eq (f (skS.0 1 a_1)) True)
% 3.87/4.21 Clause #91 (by equality factoring #[85]): ∀ (a : Iota), Or (Ne True True) (Eq (f (skS.0 1 a)) True)
% 3.87/4.21 Clause #92 (by clausification #[91]): ∀ (a : Iota), Or (Eq (f (skS.0 1 a)) True) (Or (Eq True False) (Eq True False))
% 3.87/4.21 Clause #94 (by clausification #[92]): ∀ (a : Iota), Or (Eq (f (skS.0 1 a)) True) (Eq True False)
% 3.87/4.21 Clause #95 (by clausification #[94]): ∀ (a : Iota), Eq (f (skS.0 1 a)) True
% 3.87/4.21 Clause #96 (by superposition #[95, 10]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (g (skS.0 1 a)) True) (Or (Eq (f a_1) False) (Eq (h a_1) True)))
% 3.87/4.21 Clause #97 (by superposition #[95, 26]): ∀ (a : Iota), Or (Eq (g (skS.0 1 a)) True) (Or (Eq True False) (Eq (h (skS.0 1 a)) False))
% 3.87/4.21 Clause #101 (by clausification #[96]): ∀ (a a_1 : Iota), Or (Eq (g (skS.0 1 a)) True) (Or (Eq (f a_1) False) (Eq (h a_1) True))
% 3.87/4.21 Clause #102 (by superposition #[101, 95]): ∀ (a a_1 : Iota), Or (Eq (g (skS.0 1 a)) True) (Or (Eq (h (skS.0 1 a_1)) True) (Eq False True))
% 3.87/4.21 Clause #104 (by clausification #[97]): ∀ (a : Iota), Or (Eq (g (skS.0 1 a)) True) (Eq (h (skS.0 1 a)) False)
% 3.87/4.21 Clause #106 (by clausification #[102]): ∀ (a a_1 : Iota), Or (Eq (g (skS.0 1 a)) True) (Eq (h (skS.0 1 a_1)) True)
% 3.87/4.21 Clause #110 (by superposition #[106, 104]): ∀ (a a_1 : Iota), Or (Eq (g (skS.0 1 a)) True) (Or (Eq (g (skS.0 1 a_1)) True) (Eq True False))
% 3.87/4.21 Clause #111 (by clausification #[110]): ∀ (a a_1 : Iota), Or (Eq (g (skS.0 1 a)) True) (Eq (g (skS.0 1 a_1)) True)
% 3.87/4.21 Clause #115 (by equality factoring #[111]): ∀ (a : Iota), Or (Ne True True) (Eq (g (skS.0 1 a)) True)
% 3.87/4.21 Clause #116 (by clausification #[115]): ∀ (a : Iota), Or (Eq (g (skS.0 1 a)) True) (Or (Eq True False) (Eq True False))
% 3.87/4.22 Clause #118 (by clausification #[116]): ∀ (a : Iota), Or (Eq (g (skS.0 1 a)) True) (Eq True False)
% 3.87/4.22 Clause #119 (by clausification #[118]): ∀ (a : Iota), Eq (g (skS.0 1 a)) True
% 3.87/4.22 Clause #122 (by superposition #[119, 20]): ∀ (a : Iota), Or (Eq True False) (Eq (g (skS.0 0 a)) True)
% 3.87/4.22 Clause #123 (by superposition #[119, 21]): ∀ (a : Iota), Or (Eq True False) (Eq (f (skS.0 0 a)) True)
% 3.87/4.22 Clause #130 (by clausification #[123]): ∀ (a : Iota), Eq (f (skS.0 0 a)) True
% 3.87/4.22 Clause #133 (by superposition #[130, 30]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (g (skS.0 0 a)) False) (Eq (h (skS.0 0 a)) True))
% 3.87/4.22 Clause #134 (by clausification #[122]): ∀ (a : Iota), Eq (g (skS.0 0 a)) True
% 3.87/4.22 Clause #142 (by clausification #[133]): ∀ (a : Iota), Or (Eq (g (skS.0 0 a)) False) (Eq (h (skS.0 0 a)) True)
% 3.87/4.22 Clause #143 (by forward demodulation #[142, 134]): ∀ (a : Iota), Or (Eq True False) (Eq (h (skS.0 0 a)) True)
% 3.87/4.22 Clause #144 (by clausification #[143]): ∀ (a : Iota), Eq (h (skS.0 0 a)) True
% 3.87/4.22 Clause #145 (by superposition #[144, 44]): ∀ (a : Iota), Or (Eq True False) (Eq (g (skS.0 1 a)) False)
% 3.87/4.22 Clause #146 (by clausification #[145]): ∀ (a : Iota), Eq (g (skS.0 1 a)) False
% 3.87/4.22 Clause #147 (by superposition #[146, 119]): Eq False True
% 3.87/4.22 Clause #148 (by clausification #[147]): False
% 3.87/4.22 SZS output end Proof for theBenchmark.p
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