0.12/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.12/0.13	% Command    : duper %s
0.13/0.34	% Computer : n008.cluster.edu
0.13/0.34	% Model    : x86_64 x86_64
0.13/0.34	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory   : 8042.1875MB
0.13/0.34	% OS       : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit   : 1440
0.13/0.34	% WCLimit    : 180
0.13/0.34	% DateTime   : Mon Jul  3 03:45:19 EDT 2023
0.13/0.34	% CPUTime    : 
7.85/8.07	SZS status Theorem for theBenchmark.p
7.85/8.07	SZS output start Proof for theBenchmark.p
7.85/8.07	Clause #0 (by assumption #[]): Eq
7.85/8.07	  (Not
7.85/8.07	    (And
7.85/8.07	        (And
7.85/8.07	          (And (∀ (Xx Xy Xz : Iota), And (cP Xx Xy) (cP Xy Xz) → cP Xx Xz)
7.85/8.07	            (∀ (Xx Xy Xz : Iota), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz))
7.85/8.07	          (∀ (Xx Xy : Iota), cQ Xx Xy → cQ Xy Xx))
7.85/8.07	        (∀ (Xx Xy : Iota), Or (cQ Xx Xy) (cP Xx Xy)) →
7.85/8.07	      Or (∀ (Xx Xy : Iota), cQ Xx Xy) (∀ (Xx Xy : Iota), cP Xx Xy)))
7.85/8.07	  True
7.85/8.07	Clause #1 (by clausification #[0]): Eq
7.85/8.07	  (And
7.85/8.07	      (And
7.85/8.07	        (And (∀ (Xx Xy Xz : Iota), And (cP Xx Xy) (cP Xy Xz) → cP Xx Xz)
7.85/8.07	          (∀ (Xx Xy Xz : Iota), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz))
7.85/8.07	        (∀ (Xx Xy : Iota), cQ Xx Xy → cQ Xy Xx))
7.85/8.07	      (∀ (Xx Xy : Iota), Or (cQ Xx Xy) (cP Xx Xy)) →
7.85/8.07	    Or (∀ (Xx Xy : Iota), cQ Xx Xy) (∀ (Xx Xy : Iota), cP Xx Xy))
7.85/8.07	  False
7.85/8.07	Clause #2 (by clausification #[1]): Eq
7.85/8.07	  (And
7.85/8.07	    (And
7.85/8.07	      (And (∀ (Xx Xy Xz : Iota), And (cP Xx Xy) (cP Xy Xz) → cP Xx Xz)
7.85/8.07	        (∀ (Xx Xy Xz : Iota), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz))
7.85/8.07	      (∀ (Xx Xy : Iota), cQ Xx Xy → cQ Xy Xx))
7.85/8.07	    (∀ (Xx Xy : Iota), Or (cQ Xx Xy) (cP Xx Xy)))
7.85/8.07	  True
7.85/8.07	Clause #3 (by clausification #[1]): Eq (Or (∀ (Xx Xy : Iota), cQ Xx Xy) (∀ (Xx Xy : Iota), cP Xx Xy)) False
7.85/8.07	Clause #4 (by clausification #[2]): Eq (∀ (Xx Xy : Iota), Or (cQ Xx Xy) (cP Xx Xy)) True
7.85/8.07	Clause #5 (by clausification #[2]): Eq
7.85/8.07	  (And
7.85/8.07	    (And (∀ (Xx Xy Xz : Iota), And (cP Xx Xy) (cP Xy Xz) → cP Xx Xz)
7.85/8.07	      (∀ (Xx Xy Xz : Iota), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz))
7.85/8.07	    (∀ (Xx Xy : Iota), cQ Xx Xy → cQ Xy Xx))
7.85/8.07	  True
7.85/8.07	Clause #6 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (Xy : Iota), Or (cQ a Xy) (cP a Xy)) True
7.85/8.07	Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (Or (cQ a a_1) (cP a a_1)) True
7.85/8.07	Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (cQ a a_1) True) (Eq (cP a a_1) True)
7.85/8.07	Clause #9 (by clausification #[3]): Eq (∀ (Xx Xy : Iota), cP Xx Xy) False
7.85/8.07	Clause #10 (by clausification #[3]): Eq (∀ (Xx Xy : Iota), cQ Xx Xy) False
7.85/8.07	Clause #11 (by clausification #[9]): ∀ (a : Iota), Eq (Not (∀ (Xy : Iota), cP (skS.0 0 a) Xy)) True
7.85/8.07	Clause #12 (by clausification #[11]): ∀ (a : Iota), Eq (∀ (Xy : Iota), cP (skS.0 0 a) Xy) False
7.85/8.07	Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Eq (Not (cP (skS.0 0 a) (skS.0 1 a a_1))) True
7.85/8.07	Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Eq (cP (skS.0 0 a) (skS.0 1 a a_1)) False
7.85/8.07	Clause #15 (by superposition #[14, 8]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq False True)
7.85/8.07	Clause #16 (by clausification #[10]): ∀ (a : Iota), Eq (Not (∀ (Xy : Iota), cQ (skS.0 2 a) Xy)) True
7.85/8.07	Clause #17 (by clausification #[16]): ∀ (a : Iota), Eq (∀ (Xy : Iota), cQ (skS.0 2 a) Xy) False
7.85/8.07	Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (Not (cQ (skS.0 2 a) (skS.0 3 a a_1))) True
7.85/8.07	Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Eq (cQ (skS.0 2 a) (skS.0 3 a a_1)) False
7.85/8.07	Clause #20 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (cQ (skS.0 0 a) (skS.0 1 a a_1)) True
7.85/8.07	Clause #21 (by clausification #[5]): Eq (∀ (Xx Xy : Iota), cQ Xx Xy → cQ Xy Xx) True
7.85/8.07	Clause #22 (by clausification #[5]): Eq
7.85/8.07	  (And (∀ (Xx Xy Xz : Iota), And (cP Xx Xy) (cP Xy Xz) → cP Xx Xz)
7.85/8.07	    (∀ (Xx Xy Xz : Iota), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz))
7.85/8.07	  True
7.85/8.07	Clause #23 (by clausification #[21]): ∀ (a : Iota), Eq (∀ (Xy : Iota), cQ a Xy → cQ Xy a) True
7.85/8.07	Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (cQ a a_1 → cQ a_1 a) True
7.85/8.07	Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (cQ a a_1) False) (Eq (cQ a_1 a) True)
7.85/8.07	Clause #27 (by clausification #[22]): Eq (∀ (Xx Xy Xz : Iota), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz) True
7.85/8.07	Clause #28 (by clausification #[22]): Eq (∀ (Xx Xy Xz : Iota), And (cP Xx Xy) (cP Xy Xz) → cP Xx Xz) True
7.85/8.07	Clause #29 (by clausification #[27]): ∀ (a : Iota), Eq (∀ (Xy Xz : Iota), And (cQ a Xy) (cQ Xy Xz) → cQ a Xz) True
7.85/8.07	Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Eq (∀ (Xz : Iota), And (cQ a a_1) (cQ a_1 Xz) → cQ a Xz) True
7.85/8.09	Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), Eq (And (cQ a a_1) (cQ a_1 a_2) → cQ a a_2) True
7.85/8.09	Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (cQ a a_1) (cQ a_1 a_2)) False) (Eq (cQ a a_2) True)
7.85/8.09	Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Or (Eq (cQ a a_1) True) (Or (Eq (cQ a a_2) False) (Eq (cQ a_2 a_1) False))
7.85/8.09	Clause #34 (by superposition #[33, 20]): ∀ (a a_1 a_2 : Iota), Or (Eq (cQ (skS.0 0 a) a_1) True) (Or (Eq (cQ (skS.0 1 a a_2) a_1) False) (Eq False True))
7.85/8.09	Clause #35 (by clausification #[28]): ∀ (a : Iota), Eq (∀ (Xy Xz : Iota), And (cP a Xy) (cP Xy Xz) → cP a Xz) True
7.85/8.09	Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Eq (∀ (Xz : Iota), And (cP a a_1) (cP a_1 Xz) → cP a Xz) True
7.85/8.09	Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Eq (And (cP a a_1) (cP a_1 a_2) → cP a a_2) True
7.85/8.09	Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (cP a a_1) (cP a_1 a_2)) False) (Eq (cP a a_2) True)
7.85/8.09	Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a a_1) True) (Or (Eq (cP a a_2) False) (Eq (cP a_2 a_1) False))
7.85/8.09	Clause #40 (by superposition #[39, 8]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a a_1) True) (Or (Eq (cP a_2 a_1) False) (Or (Eq (cQ a a_2) True) (Eq False True)))
7.85/8.09	Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a a_1) True) (Or (Eq (cP a_2 a_1) False) (Eq (cQ a a_2) True))
7.85/8.09	Clause #42 (by superposition #[41, 8]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a a_1) True) (Or (Eq (cQ a a_2) True) (Or (Eq (cQ a_2 a_1) True) (Eq False True)))
7.85/8.09	Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a a_1) True) (Or (Eq (cQ a a_2) True) (Eq (cQ a_2 a_1) True))
7.85/8.09	Clause #51 (by superposition #[43, 25]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a a_1) True) (Or (Eq (cQ a a_2) True) (Or (Eq True False) (Eq (cQ a_1 a_2) True)))
7.85/8.09	Clause #53 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a a_1) True) (Or (Eq (cQ a a_2) True) (Eq (cQ a_1 a_2) True))
7.85/8.09	Clause #58 (by superposition #[53, 25]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a a_1) True) (Or (Eq (cQ a_1 a_2) True) (Or (Eq True False) (Eq (cQ a_2 a) True)))
7.85/8.09	Clause #81 (by clausification #[58]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a a_1) True) (Or (Eq (cQ a_1 a_2) True) (Eq (cQ a_2 a) True))
7.85/8.09	Clause #82 (by superposition #[81, 14]): ∀ (a a_1 a_2 : Iota), Or (Eq (cQ (skS.0 1 a a_1) a_2) True) (Or (Eq (cQ a_2 (skS.0 0 a)) True) (Eq True False))
7.85/8.09	Clause #91 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), Or (Eq (cQ (skS.0 0 a) a_1) True) (Eq (cQ (skS.0 1 a a_2) a_1) False)
7.85/8.09	Clause #642 (by clausification #[82]): ∀ (a a_1 a_2 : Iota), Or (Eq (cQ (skS.0 1 a a_1) a_2) True) (Eq (cQ a_2 (skS.0 0 a)) True)
7.85/8.09	Clause #643 (by superposition #[642, 91]): ∀ (a a_1 : Iota), Or (Eq (cQ a (skS.0 0 a_1)) True) (Or (Eq (cQ (skS.0 0 a_1) a) True) (Eq True False))
7.85/8.09	Clause #1778 (by clausification #[643]): ∀ (a a_1 : Iota), Or (Eq (cQ a (skS.0 0 a_1)) True) (Eq (cQ (skS.0 0 a_1) a) True)
7.85/8.09	Clause #1781 (by superposition #[1778, 25]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 0 a) a_1) True) (Or (Eq True False) (Eq (cQ (skS.0 0 a) a_1) True))
7.85/8.09	Clause #1821 (by clausification #[1781]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 0 a) a_1) True) (Eq (cQ (skS.0 0 a) a_1) True)
7.85/8.09	Clause #1822 (by eliminate duplicate literals #[1821]): ∀ (a a_1 : Iota), Eq (cQ (skS.0 0 a) a_1) True
7.85/8.09	Clause #1827 (by superposition #[1822, 25]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (cQ a (skS.0 0 a_1)) True)
7.85/8.09	Clause #1839 (by clausification #[1827]): ∀ (a a_1 : Iota), Eq (cQ a (skS.0 0 a_1)) True
7.85/8.09	Clause #1842 (by superposition #[1839, 33]): ∀ (a a_1 a_2 : Iota), Or (Eq (cQ a a_1) True) (Or (Eq True False) (Eq (cQ (skS.0 0 a_2) a_1) False))
7.85/8.09	Clause #1880 (by clausification #[1842]): ∀ (a a_1 a_2 : Iota), Or (Eq (cQ a a_1) True) (Eq (cQ (skS.0 0 a_2) a_1) False)
7.85/8.09	Clause #1885 (by superposition #[1880, 1822]): ∀ (a a_1 : Iota), Or (Eq (cQ a a_1) True) (Eq False True)
7.85/8.09	Clause #1931 (by clausification #[1885]): ∀ (a a_1 : Iota), Eq (cQ a a_1) True
7.92/8.10	Clause #1941 (by superposition #[1931, 19]): Eq True False
7.92/8.10	Clause #1942 (by clausification #[1941]): False
7.92/8.10	SZS output end Proof for theBenchmark.p
7.92/8.11	EOF