TSTP Solution File: SEV045^5 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEV045^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n013.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 19:24:07 EDT 2023
% Result : Theorem 4.36s 4.53s
% Output : Proof 4.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15 % Problem : SEV045^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.16 % Command : duper %s
% 0.16/0.38 % Computer : n013.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Thu Aug 24 02:50:47 EDT 2023
% 0.16/0.39 % CPUTime :
% 4.36/4.53 SZS status Theorem for theBenchmark.p
% 4.36/4.53 SZS output start Proof for theBenchmark.p
% 4.36/4.53 Clause #0 (by assumption #[]): Eq
% 4.36/4.53 (Not
% 4.36/4.53 ((∀ (Xx : a), cP Xx Xx → cQ Xx (f Xx) (g Xx)) →
% 4.36/4.53 (∀ (Xx Xy : a), cP Xx Xy → cQ Xx (f Xx) (f Xy)) →
% 4.36/4.53 And (∀ (Xx Xy : a), cP Xx Xy → cP Xy Xx) (∀ (Xx Xy Xz : a), And (cP Xx Xy) (cP Xy Xz) → cP Xx Xz) →
% 4.36/4.53 And
% 4.36/4.53 (∀ (Xx : a),
% 4.36/4.53 cP Xx Xx →
% 4.36/4.53 And (∀ (Xx0 Xy : b), cQ Xx Xx0 Xy → cQ Xx Xy Xx0)
% 4.36/4.53 (∀ (Xx0 Xy Xz : b), And (cQ Xx Xx0 Xy) (cQ Xx Xy Xz) → cQ Xx Xx0 Xz))
% 4.36/4.53 (∀ (Xx Xy : a), cP Xx Xy → Eq (cQ Xx) (cQ Xy)) →
% 4.36/4.53 ∀ (Xx Xy : a), cP Xx Xy → cQ Xx (f Xx) (g Xy)))
% 4.36/4.53 True
% 4.36/4.53 Clause #1 (by clausification #[0]): Eq
% 4.36/4.53 ((∀ (Xx : a), cP Xx Xx → cQ Xx (f Xx) (g Xx)) →
% 4.36/4.53 (∀ (Xx Xy : a), cP Xx Xy → cQ Xx (f Xx) (f Xy)) →
% 4.36/4.53 And (∀ (Xx Xy : a), cP Xx Xy → cP Xy Xx) (∀ (Xx Xy Xz : a), And (cP Xx Xy) (cP Xy Xz) → cP Xx Xz) →
% 4.36/4.53 And
% 4.36/4.53 (∀ (Xx : a),
% 4.36/4.53 cP Xx Xx →
% 4.36/4.53 And (∀ (Xx0 Xy : b), cQ Xx Xx0 Xy → cQ Xx Xy Xx0)
% 4.36/4.53 (∀ (Xx0 Xy Xz : b), And (cQ Xx Xx0 Xy) (cQ Xx Xy Xz) → cQ Xx Xx0 Xz))
% 4.36/4.53 (∀ (Xx Xy : a), cP Xx Xy → Eq (cQ Xx) (cQ Xy)) →
% 4.36/4.53 ∀ (Xx Xy : a), cP Xx Xy → cQ Xx (f Xx) (g Xy))
% 4.36/4.53 False
% 4.36/4.53 Clause #2 (by clausification #[1]): Eq (∀ (Xx : a), cP Xx Xx → cQ Xx (f Xx) (g Xx)) True
% 4.36/4.53 Clause #3 (by clausification #[1]): Eq
% 4.36/4.53 ((∀ (Xx Xy : a), cP Xx Xy → cQ Xx (f Xx) (f Xy)) →
% 4.36/4.53 And (∀ (Xx Xy : a), cP Xx Xy → cP Xy Xx) (∀ (Xx Xy Xz : a), And (cP Xx Xy) (cP Xy Xz) → cP Xx Xz) →
% 4.36/4.53 And
% 4.36/4.53 (∀ (Xx : a),
% 4.36/4.53 cP Xx Xx →
% 4.36/4.53 And (∀ (Xx0 Xy : b), cQ Xx Xx0 Xy → cQ Xx Xy Xx0)
% 4.36/4.53 (∀ (Xx0 Xy Xz : b), And (cQ Xx Xx0 Xy) (cQ Xx Xy Xz) → cQ Xx Xx0 Xz))
% 4.36/4.53 (∀ (Xx Xy : a), cP Xx Xy → Eq (cQ Xx) (cQ Xy)) →
% 4.36/4.53 ∀ (Xx Xy : a), cP Xx Xy → cQ Xx (f Xx) (g Xy))
% 4.36/4.53 False
% 4.36/4.53 Clause #4 (by clausification #[2]): ∀ (a : a), Eq (cP a a → cQ a (f a) (g a)) True
% 4.36/4.53 Clause #5 (by clausification #[4]): ∀ (a : a), Or (Eq (cP a a) False) (Eq (cQ a (f a) (g a)) True)
% 4.36/4.53 Clause #6 (by clausification #[3]): Eq (∀ (Xx Xy : a), cP Xx Xy → cQ Xx (f Xx) (f Xy)) True
% 4.36/4.53 Clause #7 (by clausification #[3]): Eq
% 4.36/4.53 (And (∀ (Xx Xy : a), cP Xx Xy → cP Xy Xx) (∀ (Xx Xy Xz : a), And (cP Xx Xy) (cP Xy Xz) → cP Xx Xz) →
% 4.36/4.53 And
% 4.36/4.53 (∀ (Xx : a),
% 4.36/4.53 cP Xx Xx →
% 4.36/4.53 And (∀ (Xx0 Xy : b), cQ Xx Xx0 Xy → cQ Xx Xy Xx0)
% 4.36/4.53 (∀ (Xx0 Xy Xz : b), And (cQ Xx Xx0 Xy) (cQ Xx Xy Xz) → cQ Xx Xx0 Xz))
% 4.36/4.53 (∀ (Xx Xy : a), cP Xx Xy → Eq (cQ Xx) (cQ Xy)) →
% 4.36/4.53 ∀ (Xx Xy : a), cP Xx Xy → cQ Xx (f Xx) (g Xy))
% 4.36/4.53 False
% 4.36/4.53 Clause #8 (by clausification #[6]): ∀ (a_1 : a), Eq (∀ (Xy : a), cP a_1 Xy → cQ a_1 (f a_1) (f Xy)) True
% 4.36/4.53 Clause #9 (by clausification #[8]): ∀ (a_1 a : a), Eq (cP a_1 a → cQ a_1 (f a_1) (f a)) True
% 4.36/4.53 Clause #10 (by clausification #[9]): ∀ (a_1 a : a), Or (Eq (cP a_1 a) False) (Eq (cQ a_1 (f a_1) (f a)) True)
% 4.36/4.53 Clause #11 (by clausification #[7]): Eq (And (∀ (Xx Xy : a), cP Xx Xy → cP Xy Xx) (∀ (Xx Xy Xz : a), And (cP Xx Xy) (cP Xy Xz) → cP Xx Xz)) True
% 4.36/4.53 Clause #12 (by clausification #[7]): Eq
% 4.36/4.53 (And
% 4.36/4.53 (∀ (Xx : a),
% 4.36/4.53 cP Xx Xx →
% 4.36/4.53 And (∀ (Xx0 Xy : b), cQ Xx Xx0 Xy → cQ Xx Xy Xx0)
% 4.36/4.53 (∀ (Xx0 Xy Xz : b), And (cQ Xx Xx0 Xy) (cQ Xx Xy Xz) → cQ Xx Xx0 Xz))
% 4.36/4.53 (∀ (Xx Xy : a), cP Xx Xy → Eq (cQ Xx) (cQ Xy)) →
% 4.36/4.53 ∀ (Xx Xy : a), cP Xx Xy → cQ Xx (f Xx) (g Xy))
% 4.36/4.53 False
% 4.36/4.53 Clause #13 (by clausification #[11]): Eq (∀ (Xx Xy Xz : a), And (cP Xx Xy) (cP Xy Xz) → cP Xx Xz) True
% 4.36/4.53 Clause #14 (by clausification #[11]): Eq (∀ (Xx Xy : a), cP Xx Xy → cP Xy Xx) True
% 4.36/4.53 Clause #15 (by clausification #[13]): ∀ (a_1 : a), Eq (∀ (Xy Xz : a), And (cP a_1 Xy) (cP Xy Xz) → cP a_1 Xz) True
% 4.36/4.53 Clause #16 (by clausification #[15]): ∀ (a_1 a_2 : a), Eq (∀ (Xz : a), And (cP a_1 a_2) (cP a_2 Xz) → cP a_1 Xz) True
% 4.36/4.53 Clause #17 (by clausification #[16]): ∀ (a_1 a_2 a : a), Eq (And (cP a_1 a_2) (cP a_2 a) → cP a_1 a) True
% 4.39/4.56 Clause #18 (by clausification #[17]): ∀ (a_1 a_2 a : a), Or (Eq (And (cP a_1 a_2) (cP a_2 a)) False) (Eq (cP a_1 a) True)
% 4.39/4.56 Clause #19 (by clausification #[18]): ∀ (a_1 a_2 a : a), Or (Eq (cP a_1 a_2) True) (Or (Eq (cP a_1 a) False) (Eq (cP a a_2) False))
% 4.39/4.56 Clause #20 (by clausification #[14]): ∀ (a_1 : a), Eq (∀ (Xy : a), cP a_1 Xy → cP Xy a_1) True
% 4.39/4.56 Clause #21 (by clausification #[20]): ∀ (a_1 a : a), Eq (cP a_1 a → cP a a_1) True
% 4.39/4.56 Clause #22 (by clausification #[21]): ∀ (a_1 a : a), Or (Eq (cP a_1 a) False) (Eq (cP a a_1) True)
% 4.39/4.56 Clause #23 (by clausification #[12]): Eq
% 4.39/4.56 (And
% 4.39/4.56 (∀ (Xx : a),
% 4.39/4.56 cP Xx Xx →
% 4.39/4.56 And (∀ (Xx0 Xy : b), cQ Xx Xx0 Xy → cQ Xx Xy Xx0)
% 4.39/4.56 (∀ (Xx0 Xy Xz : b), And (cQ Xx Xx0 Xy) (cQ Xx Xy Xz) → cQ Xx Xx0 Xz))
% 4.39/4.56 (∀ (Xx Xy : a), cP Xx Xy → Eq (cQ Xx) (cQ Xy)))
% 4.39/4.56 True
% 4.39/4.56 Clause #24 (by clausification #[12]): Eq (∀ (Xx Xy : a), cP Xx Xy → cQ Xx (f Xx) (g Xy)) False
% 4.39/4.56 Clause #25 (by clausification #[23]): Eq (∀ (Xx Xy : a), cP Xx Xy → Eq (cQ Xx) (cQ Xy)) True
% 4.39/4.56 Clause #26 (by clausification #[23]): Eq
% 4.39/4.56 (∀ (Xx : a),
% 4.39/4.56 cP Xx Xx →
% 4.39/4.56 And (∀ (Xx0 Xy : b), cQ Xx Xx0 Xy → cQ Xx Xy Xx0)
% 4.39/4.56 (∀ (Xx0 Xy Xz : b), And (cQ Xx Xx0 Xy) (cQ Xx Xy Xz) → cQ Xx Xx0 Xz))
% 4.39/4.56 True
% 4.39/4.56 Clause #27 (by clausification #[25]): ∀ (a_1 : a), Eq (∀ (Xy : a), cP a_1 Xy → Eq (cQ a_1) (cQ Xy)) True
% 4.39/4.56 Clause #28 (by clausification #[27]): ∀ (a_1 a : a), Eq (cP a_1 a → Eq (cQ a_1) (cQ a)) True
% 4.39/4.56 Clause #29 (by clausification #[28]): ∀ (a_1 a : a), Or (Eq (cP a_1 a) False) (Eq (Eq (cQ a_1) (cQ a)) True)
% 4.39/4.56 Clause #30 (by clausification #[29]): ∀ (a_1 a : a), Or (Eq (cP a_1 a) False) (Eq (cQ a_1) (cQ a))
% 4.39/4.56 Clause #31 (by clausification #[24]): ∀ (a_1 : a), Eq (Not (∀ (Xy : a), cP (skS.0 0 a_1) Xy → cQ (skS.0 0 a_1) (f (skS.0 0 a_1)) (g Xy))) True
% 4.39/4.56 Clause #32 (by clausification #[31]): ∀ (a_1 : a), Eq (∀ (Xy : a), cP (skS.0 0 a_1) Xy → cQ (skS.0 0 a_1) (f (skS.0 0 a_1)) (g Xy)) False
% 4.39/4.56 Clause #33 (by clausification #[32]): ∀ (a_1 a_2 : a),
% 4.39/4.56 Eq (Not (cP (skS.0 0 a_1) (skS.0 1 a_1 a_2) → cQ (skS.0 0 a_1) (f (skS.0 0 a_1)) (g (skS.0 1 a_1 a_2)))) True
% 4.39/4.56 Clause #34 (by clausification #[33]): ∀ (a_1 a_2 : a),
% 4.39/4.56 Eq (cP (skS.0 0 a_1) (skS.0 1 a_1 a_2) → cQ (skS.0 0 a_1) (f (skS.0 0 a_1)) (g (skS.0 1 a_1 a_2))) False
% 4.39/4.56 Clause #35 (by clausification #[34]): ∀ (a_1 a_2 : a), Eq (cP (skS.0 0 a_1) (skS.0 1 a_1 a_2)) True
% 4.39/4.56 Clause #36 (by clausification #[34]): ∀ (a_1 a_2 : a), Eq (cQ (skS.0 0 a_1) (f (skS.0 0 a_1)) (g (skS.0 1 a_1 a_2))) False
% 4.39/4.56 Clause #37 (by superposition #[35, 10]): ∀ (a_1 a_2 : a), Or (Eq True False) (Eq (cQ (skS.0 0 a_1) (f (skS.0 0 a_1)) (f (skS.0 1 a_1 a_2))) True)
% 4.39/4.56 Clause #38 (by superposition #[35, 19]): ∀ (a_1 a_2 a_3 : a), Or (Eq (cP (skS.0 0 a_1) a_2) True) (Or (Eq True False) (Eq (cP (skS.0 1 a_1 a_3) a_2) False))
% 4.39/4.56 Clause #39 (by superposition #[35, 22]): ∀ (a_1 a_2 : a), Or (Eq True False) (Eq (cP (skS.0 1 a_1 a_2) (skS.0 0 a_1)) True)
% 4.39/4.56 Clause #40 (by superposition #[35, 30]): ∀ (a_1 a_2 : a), Or (Eq True False) (Eq (cQ (skS.0 0 a_1)) (cQ (skS.0 1 a_1 a_2)))
% 4.39/4.56 Clause #41 (by clausification #[40]): ∀ (a_1 a_2 : a), Eq (cQ (skS.0 0 a_1)) (cQ (skS.0 1 a_1 a_2))
% 4.39/4.56 Clause #43 (by argument congruence #[41]): ∀ (a_1 : a) (a_2 a_3 : b) (a_4 : a), Eq (cQ (skS.0 0 a_1) a_2 a_3) (cQ (skS.0 1 a_1 a_4) a_2 a_3)
% 4.39/4.56 Clause #44 (by clausification #[39]): ∀ (a_1 a_2 : a), Eq (cP (skS.0 1 a_1 a_2) (skS.0 0 a_1)) True
% 4.39/4.56 Clause #46 (by superposition #[44, 19]): ∀ (a_1 a_2 a_3 : a), Or (Eq (cP (skS.0 1 a_1 a_2) a_3) True) (Or (Eq True False) (Eq (cP (skS.0 0 a_1) a_3) False))
% 4.39/4.56 Clause #50 (by clausification #[26]): ∀ (a : a),
% 4.39/4.56 Eq
% 4.39/4.56 (cP a a →
% 4.39/4.56 And (∀ (Xx0 Xy : b), cQ a Xx0 Xy → cQ a Xy Xx0) (∀ (Xx0 Xy Xz : b), And (cQ a Xx0 Xy) (cQ a Xy Xz) → cQ a Xx0 Xz))
% 4.39/4.56 True
% 4.39/4.56 Clause #51 (by clausification #[50]): ∀ (a : a),
% 4.39/4.56 Or (Eq (cP a a) False)
% 4.39/4.56 (Eq
% 4.39/4.56 (And (∀ (Xx0 Xy : b), cQ a Xx0 Xy → cQ a Xy Xx0)
% 4.39/4.56 (∀ (Xx0 Xy Xz : b), And (cQ a Xx0 Xy) (cQ a Xy Xz) → cQ a Xx0 Xz))
% 4.39/4.58 True)
% 4.39/4.58 Clause #52 (by clausification #[51]): ∀ (a : a), Or (Eq (cP a a) False) (Eq (∀ (Xx0 Xy Xz : b), And (cQ a Xx0 Xy) (cQ a Xy Xz) → cQ a Xx0 Xz) True)
% 4.39/4.58 Clause #54 (by clausification #[52]): ∀ (a : a) (a_1 : b), Or (Eq (cP a a) False) (Eq (∀ (Xy Xz : b), And (cQ a a_1 Xy) (cQ a Xy Xz) → cQ a a_1 Xz) True)
% 4.39/4.58 Clause #55 (by clausification #[54]): ∀ (a : a) (a_1 a_2 : b), Or (Eq (cP a a) False) (Eq (∀ (Xz : b), And (cQ a a_1 a_2) (cQ a a_2 Xz) → cQ a a_1 Xz) True)
% 4.39/4.58 Clause #56 (by clausification #[55]): ∀ (a : a) (a_1 a_2 a_3 : b), Or (Eq (cP a a) False) (Eq (And (cQ a a_1 a_2) (cQ a a_2 a_3) → cQ a a_1 a_3) True)
% 4.39/4.58 Clause #57 (by clausification #[56]): ∀ (a : a) (a_1 a_2 a_3 : b),
% 4.39/4.58 Or (Eq (cP a a) False) (Or (Eq (And (cQ a a_1 a_2) (cQ a a_2 a_3)) False) (Eq (cQ a a_1 a_3) True))
% 4.39/4.58 Clause #58 (by clausification #[57]): ∀ (a : a) (a_1 a_2 a_3 : b),
% 4.39/4.58 Or (Eq (cP a a) False) (Or (Eq (cQ a a_1 a_2) True) (Or (Eq (cQ a a_1 a_3) False) (Eq (cQ a a_3 a_2) False)))
% 4.39/4.58 Clause #64 (by clausification #[38]): ∀ (a_1 a_2 a_3 : a), Or (Eq (cP (skS.0 0 a_1) a_2) True) (Eq (cP (skS.0 1 a_1 a_3) a_2) False)
% 4.39/4.58 Clause #65 (by superposition #[64, 44]): ∀ (a_1 : a), Or (Eq (cP (skS.0 0 a_1) (skS.0 0 a_1)) True) (Eq False True)
% 4.39/4.58 Clause #66 (by clausification #[65]): ∀ (a_1 : a), Eq (cP (skS.0 0 a_1) (skS.0 0 a_1)) True
% 4.39/4.58 Clause #70 (by superposition #[66, 58]): ∀ (a_1 : a) (a_2 a_3 a_4 : b),
% 4.39/4.58 Or (Eq True False)
% 4.39/4.58 (Or (Eq (cQ (skS.0 0 a_1) a_2 a_3) True)
% 4.39/4.58 (Or (Eq (cQ (skS.0 0 a_1) a_2 a_4) False) (Eq (cQ (skS.0 0 a_1) a_4 a_3) False)))
% 4.39/4.58 Clause #73 (by clausification #[46]): ∀ (a_1 a_2 a_3 : a), Or (Eq (cP (skS.0 1 a_1 a_2) a_3) True) (Eq (cP (skS.0 0 a_1) a_3) False)
% 4.39/4.58 Clause #74 (by superposition #[73, 35]): ∀ (a_1 a_2 a_3 : a), Or (Eq (cP (skS.0 1 a_1 a_2) (skS.0 1 a_1 a_3)) True) (Eq False True)
% 4.39/4.58 Clause #76 (by clausification #[74]): ∀ (a_1 a_2 a_3 : a), Eq (cP (skS.0 1 a_1 a_2) (skS.0 1 a_1 a_3)) True
% 4.39/4.58 Clause #78 (by superposition #[76, 5]): ∀ (a_1 a_2 : a), Or (Eq True False) (Eq (cQ (skS.0 1 a_1 a_2) (f (skS.0 1 a_1 a_2)) (g (skS.0 1 a_1 a_2))) True)
% 4.39/4.58 Clause #86 (by clausification #[37]): ∀ (a_1 a_2 : a), Eq (cQ (skS.0 0 a_1) (f (skS.0 0 a_1)) (f (skS.0 1 a_1 a_2))) True
% 4.39/4.58 Clause #103 (by clausification #[70]): ∀ (a_1 : a) (a_2 a_3 a_4 : b),
% 4.39/4.58 Or (Eq (cQ (skS.0 0 a_1) a_2 a_3) True)
% 4.39/4.58 (Or (Eq (cQ (skS.0 0 a_1) a_2 a_4) False) (Eq (cQ (skS.0 0 a_1) a_4 a_3) False))
% 4.39/4.58 Clause #104 (by superposition #[103, 86]): ∀ (a_1 : a) (a_2 : b) (a_3 : a),
% 4.39/4.58 Or (Eq (cQ (skS.0 0 a_1) (f (skS.0 0 a_1)) a_2) True)
% 4.39/4.58 (Or (Eq (cQ (skS.0 0 a_1) (f (skS.0 1 a_1 a_3)) a_2) False) (Eq False True))
% 4.39/4.58 Clause #115 (by clausification #[78]): ∀ (a_1 a_2 : a), Eq (cQ (skS.0 1 a_1 a_2) (f (skS.0 1 a_1 a_2)) (g (skS.0 1 a_1 a_2))) True
% 4.39/4.58 Clause #116 (by superposition #[115, 43]): ∀ (a_1 a_2 : a), Eq (cQ (skS.0 0 a_1) (f (skS.0 1 a_1 a_2)) (g (skS.0 1 a_1 a_2))) True
% 4.39/4.58 Clause #158 (by clausification #[104]): ∀ (a_1 : a) (a_2 : b) (a_3 : a),
% 4.39/4.58 Or (Eq (cQ (skS.0 0 a_1) (f (skS.0 0 a_1)) a_2) True) (Eq (cQ (skS.0 0 a_1) (f (skS.0 1 a_1 a_3)) a_2) False)
% 4.39/4.58 Clause #160 (by superposition #[158, 116]): ∀ (a_1 a_2 : a), Or (Eq (cQ (skS.0 0 a_1) (f (skS.0 0 a_1)) (g (skS.0 1 a_1 a_2))) True) (Eq False True)
% 4.39/4.58 Clause #162 (by clausification #[160]): ∀ (a_1 a_2 : a), Eq (cQ (skS.0 0 a_1) (f (skS.0 0 a_1)) (g (skS.0 1 a_1 a_2))) True
% 4.39/4.58 Clause #163 (by superposition #[162, 36]): Eq True False
% 4.39/4.58 Clause #168 (by clausification #[163]): False
% 4.39/4.58 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------