0.06/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.06/0.12	% Command    : duper %s
0.12/0.33	% Computer : n005.cluster.edu
0.12/0.33	% Model    : x86_64 x86_64
0.12/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory   : 8042.1875MB
0.12/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit   : 1440
0.12/0.33	% WCLimit    : 180
0.12/0.33	% DateTime   : Mon Jul  3 04:05:30 EDT 2023
0.12/0.34	% CPUTime    : 
10.97/11.21	SZS status Theorem for theBenchmark.p
10.97/11.21	SZS output start Proof for theBenchmark.p
10.97/11.21	Clause #0 (by assumption #[]): Eq
10.97/11.21	  (Not
10.97/11.21	    (And
10.97/11.21	        (And (And (∀ (Xy Xz : Iota), cEQ (f Xy) (f Xz) → cEQ Xy Xz) (cP a))
10.97/11.21	          (∀ (Xx Xy : Iota), And (cP Xx) (cEQ Xx Xy) → cP Xy))
10.97/11.21	        (∀ (Xx : Iota), cEQ Xx Xx) →
10.97/11.21	      Exists fun A => And (Exists fun Xz => A Xz) (∀ (Xx : Iota), A (f Xx) → cP Xx)))
10.97/11.21	  True
10.97/11.21	Clause #1 (by betaEtaReduce #[0]): Eq
10.97/11.21	  (Not
10.97/11.21	    (And
10.97/11.21	        (And (And (∀ (Xy Xz : Iota), cEQ (f Xy) (f Xz) → cEQ Xy Xz) (cP a))
10.97/11.21	          (∀ (Xx Xy : Iota), And (cP Xx) (cEQ Xx Xy) → cP Xy))
10.97/11.21	        (∀ (Xx : Iota), cEQ Xx Xx) →
10.97/11.21	      Exists fun A => And (Exists A) (∀ (Xx : Iota), A (f Xx) → cP Xx)))
10.97/11.21	  True
10.97/11.21	Clause #2 (by clausification #[1]): Eq
10.97/11.21	  (And
10.97/11.21	      (And (And (∀ (Xy Xz : Iota), cEQ (f Xy) (f Xz) → cEQ Xy Xz) (cP a))
10.97/11.21	        (∀ (Xx Xy : Iota), And (cP Xx) (cEQ Xx Xy) → cP Xy))
10.97/11.21	      (∀ (Xx : Iota), cEQ Xx Xx) →
10.97/11.21	    Exists fun A => And (Exists A) (∀ (Xx : Iota), A (f Xx) → cP Xx))
10.97/11.21	  False
10.97/11.21	Clause #3 (by clausification #[2]): Eq
10.97/11.21	  (And
10.97/11.21	    (And (And (∀ (Xy Xz : Iota), cEQ (f Xy) (f Xz) → cEQ Xy Xz) (cP a))
10.97/11.21	      (∀ (Xx Xy : Iota), And (cP Xx) (cEQ Xx Xy) → cP Xy))
10.97/11.21	    (∀ (Xx : Iota), cEQ Xx Xx))
10.97/11.21	  True
10.97/11.21	Clause #4 (by clausification #[2]): Eq (Exists fun A => And (Exists A) (∀ (Xx : Iota), A (f Xx) → cP Xx)) False
10.97/11.21	Clause #5 (by clausification #[3]): Eq (∀ (Xx : Iota), cEQ Xx Xx) True
10.97/11.21	Clause #6 (by clausification #[3]): Eq
10.97/11.21	  (And (And (∀ (Xy Xz : Iota), cEQ (f Xy) (f Xz) → cEQ Xy Xz) (cP a))
10.97/11.21	    (∀ (Xx Xy : Iota), And (cP Xx) (cEQ Xx Xy) → cP Xy))
10.97/11.21	  True
10.97/11.21	Clause #7 (by clausification #[5]): ∀ (a : Iota), Eq (cEQ a a) True
10.97/11.21	Clause #8 (by clausification #[4]): ∀ (a : Iota → Prop), Eq (And (Exists a) (∀ (Xx : Iota), a (f Xx) → cP Xx)) False
10.97/11.21	Clause #9 (by clausification #[8]): ∀ (a : Iota → Prop), Or (Eq (Exists a) False) (Eq (∀ (Xx : Iota), a (f Xx) → cP Xx) False)
10.97/11.21	Clause #10 (by clausification #[9]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (∀ (Xx : Iota), a (f Xx) → cP Xx) False) (Eq (a a_1) False)
10.97/11.21	Clause #11 (by clausification #[10]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (a a_1) False) (Eq (Not (a (f (skS.0 0 a a_2)) → cP (skS.0 0 a a_2))) True)
10.97/11.21	Clause #12 (by clausification #[11]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (a a_1) False) (Eq (a (f (skS.0 0 a a_2)) → cP (skS.0 0 a a_2)) False)
10.97/11.21	Clause #13 (by clausification #[12]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (a a_1) False) (Eq (a (f (skS.0 0 a a_2))) True)
10.97/11.21	Clause #14 (by clausification #[12]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (a a_1) False) (Eq (cP (skS.0 0 a a_2)) False)
10.97/11.21	Clause #32 (by fluidLoobHoist #[14]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (cP (skS.0 0 a a_1)) False) (Or (Eq True False) (Eq (a a_2) False))
10.97/11.21	Clause #42 (by clausification #[32]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), Or (Eq (cP (skS.0 0 a a_1)) False) (Eq (a a_2) False)
10.97/11.21	Clause #51 (by clausification #[6]): Eq (∀ (Xx Xy : Iota), And (cP Xx) (cEQ Xx Xy) → cP Xy) True
10.97/11.21	Clause #52 (by clausification #[6]): Eq (And (∀ (Xy Xz : Iota), cEQ (f Xy) (f Xz) → cEQ Xy Xz) (cP a)) True
10.97/11.21	Clause #53 (by clausification #[51]): ∀ (a : Iota), Eq (∀ (Xy : Iota), And (cP a) (cEQ a Xy) → cP Xy) True
10.97/11.21	Clause #54 (by clausification #[53]): ∀ (a a_1 : Iota), Eq (And (cP a) (cEQ a a_1) → cP a_1) True
10.97/11.21	Clause #55 (by clausification #[54]): ∀ (a a_1 : Iota), Or (Eq (And (cP a) (cEQ a a_1)) False) (Eq (cP a_1) True)
10.97/11.21	Clause #56 (by clausification #[55]): ∀ (a a_1 : Iota), Or (Eq (cP a) True) (Or (Eq (cP a_1) False) (Eq (cEQ a_1 a) False))
10.97/11.21	Clause #62 (by clausification #[52]): Eq (cP a) True
10.97/11.21	Clause #63 (by clausification #[52]): Eq (∀ (Xy Xz : Iota), cEQ (f Xy) (f Xz) → cEQ Xy Xz) True
10.97/11.21	Clause #64 (by superposition #[62, 56]): ∀ (a_1 : Iota), Or (Eq (cP a_1) True) (Or (Eq True False) (Eq (cEQ a a_1) False))
10.97/11.21	Clause #71 (by clausification #[63]): ∀ (a : Iota), Eq (∀ (Xz : Iota), cEQ (f a) (f Xz) → cEQ a Xz) True
10.97/11.21	Clause #72 (by clausification #[71]): ∀ (a a_1 : Iota), Eq (cEQ (f a) (f a_1) → cEQ a a_1) True
11.12/11.30	Clause #73 (by clausification #[72]): ∀ (a a_1 : Iota), Or (Eq (cEQ (f a) (f a_1)) False) (Eq (cEQ a a_1) True)
11.12/11.30	Clause #83 (by clausification #[64]): ∀ (a_1 : Iota), Or (Eq (cP a_1) True) (Eq (cEQ a a_1) False)
11.12/11.30	Clause #1073 (by superposition #[13, 7]): ∀ (a a_1 : Iota), Or (Eq ((fun x => cEQ a x) (f (skS.0 0 (fun x => cEQ a x) a_1))) True) (Eq False True)
11.12/11.30	Clause #1074 (by betaEtaReduce #[1073]): ∀ (a a_1 : Iota), Or (Eq (cEQ a (f (skS.0 0 (cEQ a) a_1))) True) (Eq False True)
11.12/11.30	Clause #1075 (by clausification #[1074]): ∀ (a a_1 : Iota), Eq (cEQ a (f (skS.0 0 (cEQ a) a_1))) True
11.12/11.30	Clause #1076 (by superposition #[1075, 73]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (cEQ a (skS.0 0 (cEQ (f a)) a_1)) True)
11.12/11.30	Clause #1108 (by clausification #[1076]): ∀ (a a_1 : Iota), Eq (cEQ a (skS.0 0 (cEQ (f a)) a_1)) True
11.12/11.30	Clause #1109 (by superposition #[1108, 83]): ∀ (a_1 : Iota), Or (Eq (cP (skS.0 0 (cEQ (f a)) a_1)) True) (Eq True False)
11.12/11.30	Clause #1125 (by clausification #[1109]): ∀ (a_1 : Iota), Eq (cP (skS.0 0 (cEQ (f a)) a_1)) True
11.12/11.30	Clause #1126 (by superposition #[1125, 42]): ∀ (a_1 : Iota), Or (Eq True False) (Eq (cEQ (f a) a_1) False)
11.12/11.30	Clause #1140 (by clausification #[1126]): ∀ (a_1 : Iota), Eq (cEQ (f a) a_1) False
11.12/11.30	Clause #1141 (by superposition #[1140, 1075]): Eq False True
11.12/11.30	Clause #1157 (by clausification #[1141]): False
11.12/11.30	SZS output end Proof for theBenchmark.p
11.12/11.31	EOF