TSTP Solution File: SYN726+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYN726+1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n003.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 02:12:45 EDT 2023
% Result : Theorem 7.48s 7.83s
% Output : Proof 7.70s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN726+1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.14 % Command : duper %s
% 0.17/0.35 % Computer : n003.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Sat Aug 26 20:36:54 EDT 2023
% 0.17/0.35 % CPUTime :
% 7.48/7.83 SZS status Theorem for theBenchmark.p
% 7.48/7.83 SZS output start Proof for theBenchmark.p
% 7.48/7.83 Clause #0 (by assumption #[]): Eq
% 7.48/7.83 (Not
% 7.48/7.83 (Or
% 7.48/7.83 (And
% 7.48/7.83 (And (And (∀ (X Y Z : Iota), And (p X Y) (p Y Z) → p X Z) (∀ (X Y Z : Iota), And (q X Y) (q Y Z) → q X Z))
% 7.48/7.83 (∀ (X Y : Iota), q X Y → q Y X))
% 7.48/7.83 (∀ (X Y : Iota), Or (p X Y) (q X Y)) →
% 7.48/7.83 ∀ (X Y : Iota), p X Y)
% 7.48/7.83 (∀ (X Y : Iota), q X Y)))
% 7.48/7.83 True
% 7.48/7.83 Clause #1 (by clausification #[0]): Eq
% 7.48/7.83 (Or
% 7.48/7.83 (And
% 7.48/7.83 (And (And (∀ (X Y Z : Iota), And (p X Y) (p Y Z) → p X Z) (∀ (X Y Z : Iota), And (q X Y) (q Y Z) → q X Z))
% 7.48/7.83 (∀ (X Y : Iota), q X Y → q Y X))
% 7.48/7.83 (∀ (X Y : Iota), Or (p X Y) (q X Y)) →
% 7.48/7.83 ∀ (X Y : Iota), p X Y)
% 7.48/7.83 (∀ (X Y : Iota), q X Y))
% 7.48/7.83 False
% 7.48/7.83 Clause #2 (by clausification #[1]): Eq (∀ (X Y : Iota), q X Y) False
% 7.48/7.83 Clause #3 (by clausification #[1]): Eq
% 7.48/7.83 (And
% 7.48/7.83 (And (And (∀ (X Y Z : Iota), And (p X Y) (p Y Z) → p X Z) (∀ (X Y Z : Iota), And (q X Y) (q Y Z) → q X Z))
% 7.48/7.83 (∀ (X Y : Iota), q X Y → q Y X))
% 7.48/7.83 (∀ (X Y : Iota), Or (p X Y) (q X Y)) →
% 7.48/7.83 ∀ (X Y : Iota), p X Y)
% 7.48/7.83 False
% 7.48/7.83 Clause #4 (by clausification #[2]): ∀ (a : Iota), Eq (Not (∀ (Y : Iota), q (skS.0 0 a) Y)) True
% 7.48/7.83 Clause #5 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (Y : Iota), q (skS.0 0 a) Y) False
% 7.48/7.83 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), Eq (Not (q (skS.0 0 a) (skS.0 1 a a_1))) True
% 7.48/7.83 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (q (skS.0 0 a) (skS.0 1 a a_1)) False
% 7.48/7.83 Clause #8 (by clausification #[3]): Eq
% 7.48/7.83 (And
% 7.48/7.83 (And (And (∀ (X Y Z : Iota), And (p X Y) (p Y Z) → p X Z) (∀ (X Y Z : Iota), And (q X Y) (q Y Z) → q X Z))
% 7.48/7.83 (∀ (X Y : Iota), q X Y → q Y X))
% 7.48/7.83 (∀ (X Y : Iota), Or (p X Y) (q X Y)))
% 7.48/7.83 True
% 7.48/7.83 Clause #9 (by clausification #[3]): Eq (∀ (X Y : Iota), p X Y) False
% 7.48/7.83 Clause #10 (by clausification #[8]): Eq (∀ (X Y : Iota), Or (p X Y) (q X Y)) True
% 7.48/7.83 Clause #11 (by clausification #[8]): Eq
% 7.48/7.83 (And (And (∀ (X Y Z : Iota), And (p X Y) (p Y Z) → p X Z) (∀ (X Y Z : Iota), And (q X Y) (q Y Z) → q X Z))
% 7.48/7.83 (∀ (X Y : Iota), q X Y → q Y X))
% 7.48/7.83 True
% 7.48/7.83 Clause #12 (by clausification #[10]): ∀ (a : Iota), Eq (∀ (Y : Iota), Or (p a Y) (q a Y)) True
% 7.48/7.83 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Eq (Or (p a a_1) (q a a_1)) True
% 7.48/7.83 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (p a a_1) True) (Eq (q a a_1) True)
% 7.48/7.83 Clause #15 (by clausification #[9]): ∀ (a : Iota), Eq (Not (∀ (Y : Iota), p (skS.0 2 a) Y)) True
% 7.48/7.83 Clause #16 (by clausification #[15]): ∀ (a : Iota), Eq (∀ (Y : Iota), p (skS.0 2 a) Y) False
% 7.48/7.83 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (Not (p (skS.0 2 a) (skS.0 3 a a_1))) True
% 7.48/7.83 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (p (skS.0 2 a) (skS.0 3 a a_1)) False
% 7.48/7.83 Clause #19 (by superposition #[18, 14]): ∀ (a a_1 : Iota), Or (Eq False True) (Eq (q (skS.0 2 a) (skS.0 3 a a_1)) True)
% 7.48/7.83 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (q (skS.0 2 a) (skS.0 3 a a_1)) True
% 7.48/7.83 Clause #21 (by clausification #[11]): Eq (∀ (X Y : Iota), q X Y → q Y X) True
% 7.48/7.83 Clause #22 (by clausification #[11]): Eq (And (∀ (X Y Z : Iota), And (p X Y) (p Y Z) → p X Z) (∀ (X Y Z : Iota), And (q X Y) (q Y Z) → q X Z)) True
% 7.48/7.83 Clause #23 (by clausification #[21]): ∀ (a : Iota), Eq (∀ (Y : Iota), q a Y → q Y a) True
% 7.48/7.83 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (q a a_1 → q a_1 a) True
% 7.48/7.83 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (q a a_1) False) (Eq (q a_1 a) True)
% 7.48/7.83 Clause #27 (by clausification #[22]): Eq (∀ (X Y Z : Iota), And (q X Y) (q Y Z) → q X Z) True
% 7.48/7.83 Clause #28 (by clausification #[22]): Eq (∀ (X Y Z : Iota), And (p X Y) (p Y Z) → p X Z) True
% 7.48/7.83 Clause #29 (by clausification #[27]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), And (q a Y) (q Y Z) → q a Z) True
% 7.48/7.83 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), And (q a a_1) (q a_1 Z) → q a Z) True
% 7.48/7.83 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), Eq (And (q a a_1) (q a_1 a_2) → q a a_2) True
% 7.70/7.87 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (q a a_1) (q a_1 a_2)) False) (Eq (q a a_2) True)
% 7.70/7.87 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Or (Eq (q a a_1) True) (Or (Eq (q a a_2) False) (Eq (q a_2 a_1) False))
% 7.70/7.87 Clause #34 (by superposition #[33, 20]): ∀ (a a_1 a_2 : Iota), Or (Eq (q (skS.0 2 a) a_1) True) (Or (Eq (q (skS.0 3 a a_2) a_1) False) (Eq False True))
% 7.70/7.87 Clause #35 (by clausification #[28]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), And (p a Y) (p Y Z) → p a Z) True
% 7.70/7.87 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), And (p a a_1) (p a_1 Z) → p a Z) True
% 7.70/7.87 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Eq (And (p a a_1) (p a_1 a_2) → p a a_2) True
% 7.70/7.87 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (p a a_1) (p a_1 a_2)) False) (Eq (p a a_2) True)
% 7.70/7.87 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), Or (Eq (p a a_1) True) (Or (Eq (p a a_2) False) (Eq (p a_2 a_1) False))
% 7.70/7.87 Clause #40 (by superposition #[39, 14]): ∀ (a a_1 a_2 : Iota), Or (Eq (p a a_1) True) (Or (Eq (p a_2 a_1) False) (Or (Eq False True) (Eq (q a a_2) True)))
% 7.70/7.87 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), Or (Eq (p a a_1) True) (Or (Eq (p a_2 a_1) False) (Eq (q a a_2) True))
% 7.70/7.87 Clause #42 (by superposition #[41, 14]): ∀ (a a_1 a_2 : Iota), Or (Eq (p a a_1) True) (Or (Eq (q a a_2) True) (Or (Eq False True) (Eq (q a_2 a_1) True)))
% 7.70/7.87 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), Or (Eq (p a a_1) True) (Or (Eq (q a a_2) True) (Eq (q a_2 a_1) True))
% 7.70/7.87 Clause #51 (by superposition #[43, 25]): ∀ (a a_1 a_2 : Iota), Or (Eq (p a a_1) True) (Or (Eq (q a a_2) True) (Or (Eq True False) (Eq (q a_1 a_2) True)))
% 7.70/7.87 Clause #53 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), Or (Eq (p a a_1) True) (Or (Eq (q a a_2) True) (Eq (q a_1 a_2) True))
% 7.70/7.87 Clause #58 (by superposition #[53, 25]): ∀ (a a_1 a_2 : Iota), Or (Eq (p a a_1) True) (Or (Eq (q a_1 a_2) True) (Or (Eq True False) (Eq (q a_2 a) True)))
% 7.70/7.87 Clause #81 (by clausification #[58]): ∀ (a a_1 a_2 : Iota), Or (Eq (p a a_1) True) (Or (Eq (q a_1 a_2) True) (Eq (q a_2 a) True))
% 7.70/7.87 Clause #82 (by superposition #[81, 18]): ∀ (a a_1 a_2 : Iota), Or (Eq (q (skS.0 3 a a_1) a_2) True) (Or (Eq (q a_2 (skS.0 2 a)) True) (Eq True False))
% 7.70/7.87 Clause #91 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), Or (Eq (q (skS.0 2 a) a_1) True) (Eq (q (skS.0 3 a a_2) a_1) False)
% 7.70/7.87 Clause #641 (by clausification #[82]): ∀ (a a_1 a_2 : Iota), Or (Eq (q (skS.0 3 a a_1) a_2) True) (Eq (q a_2 (skS.0 2 a)) True)
% 7.70/7.87 Clause #642 (by superposition #[641, 91]): ∀ (a a_1 : Iota), Or (Eq (q a (skS.0 2 a_1)) True) (Or (Eq (q (skS.0 2 a_1) a) True) (Eq True False))
% 7.70/7.87 Clause #1777 (by clausification #[642]): ∀ (a a_1 : Iota), Or (Eq (q a (skS.0 2 a_1)) True) (Eq (q (skS.0 2 a_1) a) True)
% 7.70/7.87 Clause #1780 (by superposition #[1777, 25]): ∀ (a a_1 : Iota), Or (Eq (q (skS.0 2 a) a_1) True) (Or (Eq True False) (Eq (q (skS.0 2 a) a_1) True))
% 7.70/7.87 Clause #1820 (by clausification #[1780]): ∀ (a a_1 : Iota), Or (Eq (q (skS.0 2 a) a_1) True) (Eq (q (skS.0 2 a) a_1) True)
% 7.70/7.87 Clause #1821 (by eliminate duplicate literals #[1820]): ∀ (a a_1 : Iota), Eq (q (skS.0 2 a) a_1) True
% 7.70/7.87 Clause #1826 (by superposition #[1821, 25]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (q a (skS.0 2 a_1)) True)
% 7.70/7.87 Clause #1838 (by clausification #[1826]): ∀ (a a_1 : Iota), Eq (q a (skS.0 2 a_1)) True
% 7.70/7.87 Clause #1841 (by superposition #[1838, 33]): ∀ (a a_1 a_2 : Iota), Or (Eq (q a a_1) True) (Or (Eq True False) (Eq (q (skS.0 2 a_2) a_1) False))
% 7.70/7.87 Clause #1879 (by clausification #[1841]): ∀ (a a_1 a_2 : Iota), Or (Eq (q a a_1) True) (Eq (q (skS.0 2 a_2) a_1) False)
% 7.70/7.87 Clause #1884 (by superposition #[1879, 1821]): ∀ (a a_1 : Iota), Or (Eq (q a a_1) True) (Eq False True)
% 7.70/7.87 Clause #1930 (by clausification #[1884]): ∀ (a a_1 : Iota), Eq (q a a_1) True
% 7.70/7.87 Clause #1940 (by superposition #[1930, 7]): Eq True False
% 7.70/7.87 Clause #1941 (by clausification #[1940]): False
% 7.70/7.87 SZS output end Proof for theBenchmark.p
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