TSTP Solution File: SYN986+1.003 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYN986+1.003 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n011.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 02:13:33 EDT 2023
% Result : Theorem 3.90s 4.19s
% Output : Proof 3.90s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : SYN986+1.003 : TPTP v8.1.2. Released v4.0.0.
% 0.15/0.15 % Command : duper %s
% 0.15/0.37 % Computer : n011.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sat Aug 26 17:49:54 EDT 2023
% 0.15/0.37 % CPUTime :
% 3.90/4.19 SZS status Theorem for theBenchmark.p
% 3.90/4.19 SZS output start Proof for theBenchmark.p
% 3.90/4.19 Clause #0 (by assumption #[]): Eq (∀ (Y : Iota), r Y zero (succ Y)) True
% 3.90/4.19 Clause #1 (by assumption #[]): Eq (∀ (Y X Z Z1 : Iota), r Y X Z → r Z X Z1 → r Y (succ X) Z1) True
% 3.90/4.19 Clause #2 (by assumption #[]): Eq
% 3.90/4.19 (Not
% 3.90/4.19 (Exists fun Z3 =>
% 3.90/4.19 Exists fun Z2 =>
% 3.90/4.19 Exists fun Z1 =>
% 3.90/4.19 Exists fun Z0 => And (And (And (r zero zero Z3) (r zero Z3 Z2)) (r zero Z2 Z1)) (r zero Z1 Z0)))
% 3.90/4.19 True
% 3.90/4.19 Clause #3 (by clausification #[0]): ∀ (a : Iota), Eq (r a zero (succ a)) True
% 3.90/4.19 Clause #4 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (X Z Z1 : Iota), r a X Z → r Z X Z1 → r a (succ X) Z1) True
% 3.90/4.19 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), Eq (∀ (Z Z1 : Iota), r a a_1 Z → r Z a_1 Z1 → r a (succ a_1) Z1) True
% 3.90/4.19 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Iota), Eq (∀ (Z1 : Iota), r a a_1 a_2 → r a_2 a_1 Z1 → r a (succ a_1) Z1) True
% 3.90/4.19 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 a_3 : Iota), Eq (r a a_1 a_2 → r a_2 a_1 a_3 → r a (succ a_1) a_3) True
% 3.90/4.19 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r a a_1 a_2) False) (Eq (r a_2 a_1 a_3 → r a (succ a_1) a_3) True)
% 3.90/4.19 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r a a_1 a_2) False) (Or (Eq (r a_2 a_1 a_3) False) (Eq (r a (succ a_1) a_3) True))
% 3.90/4.19 Clause #10 (by superposition #[9, 3]): ∀ (a a_1 : Iota), Or (Eq (r (succ a) zero a_1) False) (Or (Eq (r a (succ zero) a_1) True) (Eq False True))
% 3.90/4.19 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Or (Eq (r (succ a) zero a_1) False) (Eq (r a (succ zero) a_1) True)
% 3.90/4.19 Clause #12 (by superposition #[11, 3]): ∀ (a : Iota), Or (Eq (r a (succ zero) (succ (succ a))) True) (Eq False True)
% 3.90/4.19 Clause #13 (by clausification #[12]): ∀ (a : Iota), Eq (r a (succ zero) (succ (succ a))) True
% 3.90/4.19 Clause #14 (by superposition #[13, 9]): ∀ (a a_1 : Iota),
% 3.90/4.19 Or (Eq True False) (Or (Eq (r (succ (succ a)) (succ zero) a_1) False) (Eq (r a (succ (succ zero)) a_1) True))
% 3.90/4.19 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (r (succ (succ a)) (succ zero) a_1) False) (Eq (r a (succ (succ zero)) a_1) True)
% 3.90/4.19 Clause #16 (by superposition #[15, 13]): ∀ (a : Iota), Or (Eq (r a (succ (succ zero)) (succ (succ (succ (succ a))))) True) (Eq False True)
% 3.90/4.19 Clause #17 (by clausification #[2]): Eq
% 3.90/4.19 (Exists fun Z3 =>
% 3.90/4.19 Exists fun Z2 =>
% 3.90/4.19 Exists fun Z1 => Exists fun Z0 => And (And (And (r zero zero Z3) (r zero Z3 Z2)) (r zero Z2 Z1)) (r zero Z1 Z0))
% 3.90/4.19 False
% 3.90/4.19 Clause #18 (by clausification #[17]): ∀ (a : Iota),
% 3.90/4.19 Eq
% 3.90/4.19 (Exists fun Z2 =>
% 3.90/4.19 Exists fun Z1 => Exists fun Z0 => And (And (And (r zero zero a) (r zero a Z2)) (r zero Z2 Z1)) (r zero Z1 Z0))
% 3.90/4.19 False
% 3.90/4.19 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota),
% 3.90/4.19 Eq (Exists fun Z1 => Exists fun Z0 => And (And (And (r zero zero a) (r zero a a_1)) (r zero a_1 Z1)) (r zero Z1 Z0))
% 3.90/4.19 False
% 3.90/4.19 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota),
% 3.90/4.19 Eq (Exists fun Z0 => And (And (And (r zero zero a) (r zero a a_1)) (r zero a_1 a_2)) (r zero a_2 Z0)) False
% 3.90/4.19 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 a_3 : Iota), Eq (And (And (And (r zero zero a) (r zero a a_1)) (r zero a_1 a_2)) (r zero a_2 a_3)) False
% 3.90/4.19 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.90/4.19 Or (Eq (And (And (r zero zero a) (r zero a a_1)) (r zero a_1 a_2)) False) (Eq (r zero a_2 a_3) False)
% 3.90/4.19 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.90/4.19 Or (Eq (r zero a a_1) False) (Or (Eq (And (r zero zero a_2) (r zero a_2 a_3)) False) (Eq (r zero a_3 a) False))
% 3.90/4.19 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.90/4.19 Or (Eq (r zero a a_1) False)
% 3.90/4.19 (Or (Eq (r zero a_2 a) False) (Or (Eq (r zero zero a_3) False) (Eq (r zero a_3 a_2) False)))
% 3.90/4.19 Clause #27 (by clausification #[16]): ∀ (a : Iota), Eq (r a (succ (succ zero)) (succ (succ (succ (succ a))))) True
% 3.90/4.19 Clause #28 (by superposition #[27, 9]): ∀ (a a_1 : Iota),
% 3.90/4.19 Or (Eq True False)
% 3.90/4.19 (Or (Eq (r (succ (succ (succ (succ a)))) (succ (succ zero)) a_1) False)
% 3.90/4.19 (Eq (r a (succ (succ (succ zero))) a_1) True))
% 3.90/4.21 Clause #36 (by clausification #[28]): ∀ (a a_1 : Iota),
% 3.90/4.21 Or (Eq (r (succ (succ (succ (succ a)))) (succ (succ zero)) a_1) False) (Eq (r a (succ (succ (succ zero))) a_1) True)
% 3.90/4.21 Clause #37 (by superposition #[36, 27]): ∀ (a : Iota),
% 3.90/4.21 Or (Eq (r a (succ (succ (succ zero))) (succ (succ (succ (succ (succ (succ (succ (succ a))))))))) True) (Eq False True)
% 3.90/4.21 Clause #38 (by clausification #[37]): ∀ (a : Iota), Eq (r a (succ (succ (succ zero))) (succ (succ (succ (succ (succ (succ (succ (succ a))))))))) True
% 3.90/4.21 Clause #39 (by superposition #[38, 9]): ∀ (a a_1 : Iota),
% 3.90/4.21 Or (Eq True False)
% 3.90/4.21 (Or (Eq (r (succ (succ (succ (succ (succ (succ (succ (succ a)))))))) (succ (succ (succ zero))) a_1) False)
% 3.90/4.21 (Eq (r a (succ (succ (succ (succ zero)))) a_1) True))
% 3.90/4.21 Clause #47 (by clausification #[39]): ∀ (a a_1 : Iota),
% 3.90/4.21 Or (Eq (r (succ (succ (succ (succ (succ (succ (succ (succ a)))))))) (succ (succ (succ zero))) a_1) False)
% 3.90/4.21 (Eq (r a (succ (succ (succ (succ zero)))) a_1) True)
% 3.90/4.21 Clause #48 (by superposition #[47, 38]): ∀ (a : Iota),
% 3.90/4.21 Or
% 3.90/4.21 (Eq
% 3.90/4.21 (r a (succ (succ (succ (succ zero))))
% 3.90/4.21 (succ
% 3.90/4.21 (succ (succ (succ (succ (succ (succ (succ (succ (succ (succ (succ (succ (succ (succ (succ a)))))))))))))))))
% 3.90/4.21 True)
% 3.90/4.21 (Eq False True)
% 3.90/4.21 Clause #49 (by clausification #[48]): ∀ (a : Iota),
% 3.90/4.21 Eq
% 3.90/4.21 (r a (succ (succ (succ (succ zero))))
% 3.90/4.21 (succ (succ (succ (succ (succ (succ (succ (succ (succ (succ (succ (succ (succ (succ (succ (succ a)))))))))))))))))
% 3.90/4.21 True
% 3.90/4.21 Clause #51 (by superposition #[49, 24]): ∀ (a a_1 : Iota),
% 3.90/4.21 Or (Eq True False)
% 3.90/4.21 (Or (Eq (r zero a (succ (succ (succ (succ zero))))) False)
% 3.90/4.21 (Or (Eq (r zero zero a_1) False) (Eq (r zero a_1 a) False)))
% 3.90/4.21 Clause #52 (by clausification #[51]): ∀ (a a_1 : Iota),
% 3.90/4.21 Or (Eq (r zero a (succ (succ (succ (succ zero))))) False) (Or (Eq (r zero zero a_1) False) (Eq (r zero a_1 a) False))
% 3.90/4.21 Clause #53 (by superposition #[52, 27]): ∀ (a : Iota), Or (Eq (r zero zero a) False) (Or (Eq (r zero a (succ (succ zero))) False) (Eq False True))
% 3.90/4.21 Clause #54 (by clausification #[53]): ∀ (a : Iota), Or (Eq (r zero zero a) False) (Eq (r zero a (succ (succ zero))) False)
% 3.90/4.21 Clause #55 (by superposition #[54, 3]): Or (Eq (r zero (succ zero) (succ (succ zero))) False) (Eq False True)
% 3.90/4.21 Clause #56 (by clausification #[55]): Eq (r zero (succ zero) (succ (succ zero))) False
% 3.90/4.21 Clause #57 (by superposition #[56, 13]): Eq False True
% 3.90/4.21 Clause #58 (by clausification #[57]): False
% 3.90/4.21 SZS output end Proof for theBenchmark.p
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