TSTP Solution File: SYN063+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYN063+1 : TPTP v8.1.2. Released v2.0.0.
% 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 : Fri Sep 1 02:10:24 EDT 2023
% Result : Theorem 3.80s 4.01s
% Output : Proof 3.86s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYN063+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n013.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 20:28:02 EDT 2023
% 0.14/0.35 % CPUTime :
% 3.80/4.01 SZS status Theorem for theBenchmark.p
% 3.80/4.01 SZS output start Proof for theBenchmark.p
% 3.80/4.01 Clause #0 (by assumption #[]): Eq
% 3.80/4.01 (Not
% 3.80/4.01 (Iff (∀ (X : Iota), And (big_p a) (big_p X → big_p b) → big_p c)
% 3.80/4.01 (∀ (X1 : Iota),
% 3.80/4.01 And (Or (Or (Not (big_p a)) (big_p X1)) (big_p c)) (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c)))))
% 3.80/4.01 True
% 3.80/4.01 Clause #1 (by clausification #[0]): Eq
% 3.80/4.01 (Iff (∀ (X : Iota), And (big_p a) (big_p X → big_p b) → big_p c)
% 3.80/4.01 (∀ (X1 : Iota),
% 3.80/4.01 And (Or (Or (Not (big_p a)) (big_p X1)) (big_p c)) (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c))))
% 3.80/4.01 False
% 3.80/4.01 Clause #2 (by clausification #[1]): Or (Eq (∀ (X : Iota), And (big_p a) (big_p X → big_p b) → big_p c) False)
% 3.80/4.01 (Eq
% 3.80/4.01 (∀ (X1 : Iota),
% 3.80/4.01 And (Or (Or (Not (big_p a)) (big_p X1)) (big_p c)) (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c)))
% 3.80/4.01 False)
% 3.80/4.01 Clause #3 (by clausification #[1]): Or (Eq (∀ (X : Iota), And (big_p a) (big_p X → big_p b) → big_p c) True)
% 3.80/4.01 (Eq
% 3.80/4.01 (∀ (X1 : Iota),
% 3.80/4.01 And (Or (Or (Not (big_p a)) (big_p X1)) (big_p c)) (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c)))
% 3.80/4.01 True)
% 3.80/4.01 Clause #4 (by clausification #[2]): ∀ (a_1 : Iota),
% 3.80/4.01 Or
% 3.80/4.01 (Eq
% 3.80/4.01 (∀ (X1 : Iota),
% 3.80/4.01 And (Or (Or (Not (big_p a)) (big_p X1)) (big_p c)) (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c)))
% 3.80/4.01 False)
% 3.80/4.01 (Eq (Not (And (big_p a) (big_p (skS.0 0 a_1) → big_p b) → big_p c)) True)
% 3.80/4.01 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : Iota),
% 3.80/4.01 Or (Eq (Not (And (big_p a) (big_p (skS.0 0 a_1) → big_p b) → big_p c)) True)
% 3.80/4.01 (Eq
% 3.80/4.01 (Not
% 3.80/4.01 (And (Or (Or (Not (big_p a)) (big_p (skS.0 1 a_2))) (big_p c))
% 3.80/4.01 (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c))))
% 3.80/4.01 True)
% 3.80/4.01 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 : Iota),
% 3.80/4.01 Or
% 3.80/4.01 (Eq
% 3.80/4.01 (Not
% 3.80/4.01 (And (Or (Or (Not (big_p a)) (big_p (skS.0 1 a_1))) (big_p c))
% 3.80/4.01 (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c))))
% 3.80/4.01 True)
% 3.80/4.01 (Eq (And (big_p a) (big_p (skS.0 0 a_2) → big_p b) → big_p c) False)
% 3.80/4.01 Clause #7 (by clausification #[6]): ∀ (a_1 a_2 : Iota),
% 3.80/4.01 Or (Eq (And (big_p a) (big_p (skS.0 0 a_1) → big_p b) → big_p c) False)
% 3.80/4.01 (Eq
% 3.80/4.01 (And (Or (Or (Not (big_p a)) (big_p (skS.0 1 a_2))) (big_p c))
% 3.80/4.01 (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c)))
% 3.80/4.01 False)
% 3.80/4.01 Clause #8 (by clausification #[7]): ∀ (a_1 a_2 : Iota),
% 3.80/4.01 Or
% 3.80/4.01 (Eq
% 3.80/4.01 (And (Or (Or (Not (big_p a)) (big_p (skS.0 1 a_1))) (big_p c))
% 3.80/4.01 (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c)))
% 3.80/4.01 False)
% 3.80/4.01 (Eq (And (big_p a) (big_p (skS.0 0 a_2) → big_p b)) True)
% 3.80/4.01 Clause #9 (by clausification #[7]): ∀ (a_1 : Iota),
% 3.80/4.01 Or
% 3.80/4.01 (Eq
% 3.80/4.01 (And (Or (Or (Not (big_p a)) (big_p (skS.0 1 a_1))) (big_p c))
% 3.80/4.01 (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c)))
% 3.80/4.01 False)
% 3.80/4.01 (Eq (big_p c) False)
% 3.80/4.01 Clause #10 (by clausification #[8]): ∀ (a_1 a_2 : Iota),
% 3.80/4.01 Or (Eq (And (big_p a) (big_p (skS.0 0 a_1) → big_p b)) True)
% 3.80/4.01 (Or (Eq (Or (Or (Not (big_p a)) (big_p (skS.0 1 a_2))) (big_p c)) False)
% 3.80/4.01 (Eq (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c)) False))
% 3.80/4.01 Clause #12 (by clausification #[10]): ∀ (a_1 : Iota),
% 3.80/4.01 Or (Eq (Or (Or (Not (big_p a)) (big_p (skS.0 1 a_1))) (big_p c)) False)
% 3.80/4.01 (Or (Eq (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c)) False) (Eq (big_p a) True))
% 3.80/4.01 Clause #35 (by clausification #[3]): ∀ (a_1 : Iota),
% 3.80/4.01 Or
% 3.80/4.01 (Eq
% 3.80/4.01 (∀ (X1 : Iota),
% 3.80/4.01 And (Or (Or (Not (big_p a)) (big_p X1)) (big_p c)) (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c)))
% 3.80/4.01 True)
% 3.80/4.01 (Eq (And (big_p a) (big_p a_1 → big_p b) → big_p c) True)
% 3.80/4.01 Clause #36 (by clausification #[35]): ∀ (a_1 a_2 : Iota),
% 3.80/4.01 Or (Eq (And (big_p a) (big_p a_1 → big_p b) → big_p c) True)
% 3.80/4.01 (Eq (And (Or (Or (Not (big_p a)) (big_p a_2)) (big_p c)) (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c))) True)
% 3.80/4.01 Clause #37 (by clausification #[36]): ∀ (a_1 a_2 : Iota),
% 3.80/4.01 Or (Eq (And (Or (Or (Not (big_p a)) (big_p a_1)) (big_p c)) (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c))) True)
% 3.80/4.01 (Or (Eq (And (big_p a) (big_p a_2 → big_p b)) False) (Eq (big_p c) True))
% 3.86/4.03 Clause #39 (by clausification #[37]): ∀ (a_1 a_2 : Iota),
% 3.86/4.03 Or (Eq (And (big_p a) (big_p a_1 → big_p b)) False)
% 3.86/4.03 (Or (Eq (big_p c) True) (Eq (Or (Or (Not (big_p a)) (big_p a_2)) (big_p c)) True))
% 3.86/4.03 Clause #52 (by clausification #[39]): ∀ (a_1 a_2 : Iota),
% 3.86/4.03 Or (Eq (big_p c) True)
% 3.86/4.03 (Or (Eq (Or (Or (Not (big_p a)) (big_p a_1)) (big_p c)) True)
% 3.86/4.03 (Or (Eq (big_p a) False) (Eq (big_p a_2 → big_p b) False)))
% 3.86/4.03 Clause #53 (by clausification #[52]): ∀ (a_1 a_2 : Iota),
% 3.86/4.03 Or (Eq (big_p c) True)
% 3.86/4.03 (Or (Eq (big_p a) False)
% 3.86/4.03 (Or (Eq (big_p a_1 → big_p b) False) (Or (Eq (Or (Not (big_p a)) (big_p a_2)) True) (Eq (big_p c) True))))
% 3.86/4.03 Clause #54 (by clausification #[53]): ∀ (a_1 a_2 : Iota),
% 3.86/4.03 Or (Eq (big_p c) True)
% 3.86/4.03 (Or (Eq (big_p a) False)
% 3.86/4.03 (Or (Eq (Or (Not (big_p a)) (big_p a_1)) True) (Or (Eq (big_p c) True) (Eq (big_p a_2) True))))
% 3.86/4.03 Clause #56 (by clausification #[54]): ∀ (a_1 a_2 : Iota),
% 3.86/4.03 Or (Eq (big_p c) True)
% 3.86/4.03 (Or (Eq (big_p a) False)
% 3.86/4.03 (Or (Eq (big_p c) True) (Or (Eq (big_p a_1) True) (Or (Eq (Not (big_p a)) True) (Eq (big_p a_2) True)))))
% 3.86/4.03 Clause #57 (by clausification #[56]): ∀ (a_1 a_2 : Iota),
% 3.86/4.03 Or (Eq (big_p c) True)
% 3.86/4.03 (Or (Eq (big_p a) False)
% 3.86/4.03 (Or (Eq (big_p c) True) (Or (Eq (big_p a_1) True) (Or (Eq (big_p a_2) True) (Eq (big_p a) False)))))
% 3.86/4.03 Clause #58 (by eliminate duplicate literals #[57]): ∀ (a_1 a_2 : Iota), Or (Eq (big_p c) True) (Or (Eq (big_p a) False) (Or (Eq (big_p a_1) True) (Eq (big_p a_2) True)))
% 3.86/4.03 Clause #68 (by clausification #[9]): ∀ (a_1 : Iota),
% 3.86/4.03 Or (Eq (big_p c) False)
% 3.86/4.03 (Or (Eq (Or (Or (Not (big_p a)) (big_p (skS.0 1 a_1))) (big_p c)) False)
% 3.86/4.03 (Eq (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c)) False))
% 3.86/4.03 Clause #69 (by clausification #[68]): Or (Eq (big_p c) False) (Or (Eq (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c)) False) (Eq (big_p c) False))
% 3.86/4.03 Clause #71 (by clausification #[69]): Or (Eq (big_p c) False) (Or (Eq (big_p c) False) (Eq (big_p c) False))
% 3.86/4.03 Clause #73 (by eliminate duplicate literals #[71]): Eq (big_p c) False
% 3.86/4.03 Clause #76 (by backward demodulation #[73, 58]): ∀ (a_1 a_2 : Iota), Or (Eq False True) (Or (Eq (big_p a) False) (Or (Eq (big_p a_1) True) (Eq (big_p a_2) True)))
% 3.86/4.03 Clause #78 (by clausification #[76]): ∀ (a_1 a_2 : Iota), Or (Eq (big_p a) False) (Or (Eq (big_p a_1) True) (Eq (big_p a_2) True))
% 3.86/4.03 Clause #88 (by clausification #[12]): ∀ (a_1 : Iota),
% 3.86/4.03 Or (Eq (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c)) False)
% 3.86/4.03 (Or (Eq (big_p a) True) (Eq (Or (Not (big_p a)) (big_p (skS.0 1 a_1))) False))
% 3.86/4.03 Clause #101 (by clausification #[88]): ∀ (a_1 : Iota),
% 3.86/4.03 Or (Eq (big_p a) True)
% 3.86/4.03 (Or (Eq (Or (Not (big_p a)) (big_p (skS.0 1 a_1))) False) (Eq (Or (Not (big_p a)) (Not (big_p b))) False))
% 3.86/4.03 Clause #105 (by clausification #[101]): Or (Eq (big_p a) True) (Or (Eq (Or (Not (big_p a)) (Not (big_p b))) False) (Eq (Not (big_p a)) False))
% 3.86/4.03 Clause #117 (by clausification #[105]): Or (Eq (big_p a) True) (Or (Eq (Not (big_p a)) False) (Eq (Not (big_p a)) False))
% 3.86/4.03 Clause #121 (by clausification #[117]): Or (Eq (big_p a) True) (Or (Eq (Not (big_p a)) False) (Eq (big_p a) True))
% 3.86/4.03 Clause #122 (by clausification #[121]): Or (Eq (big_p a) True) (Or (Eq (big_p a) True) (Eq (big_p a) True))
% 3.86/4.03 Clause #123 (by eliminate duplicate literals #[122]): Eq (big_p a) True
% 3.86/4.03 Clause #127 (by superposition #[123, 78]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (big_p a) True) (Eq (big_p a_1) True))
% 3.86/4.03 Clause #136 (by clausification #[127]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Eq (big_p a_1) True)
% 3.86/4.03 Clause #137 (by superposition #[136, 73]): ∀ (a : Iota), Or (Eq (big_p a) True) (Eq True False)
% 3.86/4.03 Clause #141 (by clausification #[137]): ∀ (a : Iota), Eq (big_p a) True
% 3.86/4.03 Clause #142 (by superposition #[141, 73]): Eq True False
% 3.86/4.03 Clause #143 (by clausification #[142]): False
% 3.86/4.03 SZS output end Proof for theBenchmark.p
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