TSTP Solution File: SEV200^5 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEV200^5 : 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 : Thu Aug 31 19:24:28 EDT 2023
% Result : Theorem 4.08s 4.26s
% Output : Proof 4.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV200^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : duper %s
% 0.14/0.33 % Computer : n011.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Thu Aug 24 02:30:52 EDT 2023
% 0.14/0.33 % CPUTime :
% 4.08/4.26 SZS status Theorem for theBenchmark.p
% 4.08/4.26 SZS output start Proof for theBenchmark.p
% 4.08/4.26 Clause #0 (by assumption #[]): Eq
% 4.08/4.26 (Not
% 4.08/4.26 (And
% 4.08/4.26 (And (∀ (Xx0 Xy : a), Ne (cP Xx0 Xy) cZ)
% 4.08/4.26 (∀ (Xx0 Xy Xu Xv : a), Eq (cP Xx0 Xu) (cP Xy Xv) → And (Eq Xx0 Xy) (Eq Xu Xv)))
% 4.08/4.26 (∀ (X : a → Prop), And (X cZ) (∀ (Xx0 Xy : a), And (X Xx0) (X Xy) → X (cP Xx0 Xy)) → ∀ (Xx0 : a), X Xx0) →
% 4.08/4.26 ∀ (R : a → a → a → Prop),
% 4.08/4.26 And True
% 4.08/4.26 (∀ (Xa Xb Xc : a),
% 4.08/4.26 Or (Or (And (Eq Xa cZ) (Eq Xb Xc)) (And (Eq Xb cZ) (Eq Xa Xc)))
% 4.08/4.26 (Exists fun Xx1 =>
% 4.08/4.26 Exists fun Xx2 =>
% 4.08/4.26 Exists fun Xy1 =>
% 4.08/4.26 Exists fun Xy2 =>
% 4.08/4.26 Exists fun Xz1 =>
% 4.08/4.26 Exists fun Xz2 =>
% 4.08/4.26 And
% 4.08/4.26 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2)))
% 4.08/4.26 (R Xx1 Xy1 Xz1))
% 4.08/4.26 (R Xx2 Xy2 Xz2)) →
% 4.08/4.26 R Xa Xb Xc) →
% 4.08/4.26 R cZ x x))
% 4.08/4.26 True
% 4.08/4.26 Clause #1 (by clausification #[0]): Eq
% 4.08/4.26 (And
% 4.08/4.26 (And (∀ (Xx0 Xy : a), Ne (cP Xx0 Xy) cZ)
% 4.08/4.26 (∀ (Xx0 Xy Xu Xv : a), Eq (cP Xx0 Xu) (cP Xy Xv) → And (Eq Xx0 Xy) (Eq Xu Xv)))
% 4.08/4.26 (∀ (X : a → Prop), And (X cZ) (∀ (Xx0 Xy : a), And (X Xx0) (X Xy) → X (cP Xx0 Xy)) → ∀ (Xx0 : a), X Xx0) →
% 4.08/4.26 ∀ (R : a → a → a → Prop),
% 4.08/4.26 And True
% 4.08/4.26 (∀ (Xa Xb Xc : a),
% 4.08/4.26 Or (Or (And (Eq Xa cZ) (Eq Xb Xc)) (And (Eq Xb cZ) (Eq Xa Xc)))
% 4.08/4.26 (Exists fun Xx1 =>
% 4.08/4.26 Exists fun Xx2 =>
% 4.08/4.26 Exists fun Xy1 =>
% 4.08/4.26 Exists fun Xy2 =>
% 4.08/4.26 Exists fun Xz1 =>
% 4.08/4.26 Exists fun Xz2 =>
% 4.08/4.26 And
% 4.08/4.26 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2)))
% 4.08/4.26 (R Xx1 Xy1 Xz1))
% 4.08/4.26 (R Xx2 Xy2 Xz2)) →
% 4.08/4.26 R Xa Xb Xc) →
% 4.08/4.26 R cZ x x)
% 4.08/4.26 False
% 4.08/4.26 Clause #3 (by clausification #[1]): Eq
% 4.08/4.26 (∀ (R : a → a → a → Prop),
% 4.08/4.26 And True
% 4.08/4.26 (∀ (Xa Xb Xc : a),
% 4.08/4.26 Or (Or (And (Eq Xa cZ) (Eq Xb Xc)) (And (Eq Xb cZ) (Eq Xa Xc)))
% 4.08/4.26 (Exists fun Xx1 =>
% 4.08/4.26 Exists fun Xx2 =>
% 4.08/4.26 Exists fun Xy1 =>
% 4.08/4.26 Exists fun Xy2 =>
% 4.08/4.26 Exists fun Xz1 =>
% 4.08/4.26 Exists fun Xz2 =>
% 4.08/4.26 And
% 4.08/4.26 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2)))
% 4.08/4.26 (R Xx1 Xy1 Xz1))
% 4.08/4.26 (R Xx2 Xy2 Xz2)) →
% 4.08/4.26 R Xa Xb Xc) →
% 4.08/4.26 R cZ x x)
% 4.08/4.26 False
% 4.08/4.26 Clause #26 (by clausification #[3]): ∀ (a_1 : a → a → a → Prop),
% 4.08/4.26 Eq
% 4.08/4.26 (Not
% 4.08/4.26 (And True
% 4.08/4.26 (∀ (Xa Xb Xc : a),
% 4.08/4.26 Or (Or (And (Eq Xa cZ) (Eq Xb Xc)) (And (Eq Xb cZ) (Eq Xa Xc)))
% 4.08/4.26 (Exists fun Xx1 =>
% 4.08/4.26 Exists fun Xx2 =>
% 4.08/4.26 Exists fun Xy1 =>
% 4.08/4.26 Exists fun Xy2 =>
% 4.08/4.26 Exists fun Xz1 =>
% 4.08/4.26 Exists fun Xz2 =>
% 4.08/4.26 And
% 4.08/4.26 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2)))
% 4.08/4.26 (skS.0 2 a_1 Xx1 Xy1 Xz1))
% 4.08/4.26 (skS.0 2 a_1 Xx2 Xy2 Xz2)) →
% 4.08/4.26 skS.0 2 a_1 Xa Xb Xc) →
% 4.08/4.26 skS.0 2 a_1 cZ x x))
% 4.08/4.26 True
% 4.08/4.26 Clause #27 (by clausification #[26]): ∀ (a_1 : a → a → a → Prop),
% 4.08/4.26 Eq
% 4.08/4.26 (And True
% 4.08/4.26 (∀ (Xa Xb Xc : a),
% 4.08/4.26 Or (Or (And (Eq Xa cZ) (Eq Xb Xc)) (And (Eq Xb cZ) (Eq Xa Xc)))
% 4.08/4.26 (Exists fun Xx1 =>
% 4.08/4.26 Exists fun Xx2 =>
% 4.08/4.26 Exists fun Xy1 =>
% 4.08/4.26 Exists fun Xy2 =>
% 4.08/4.26 Exists fun Xz1 =>
% 4.08/4.26 Exists fun Xz2 =>
% 4.08/4.26 And
% 4.08/4.26 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2)))
% 4.08/4.28 (skS.0 2 a_1 Xx1 Xy1 Xz1))
% 4.08/4.28 (skS.0 2 a_1 Xx2 Xy2 Xz2)) →
% 4.08/4.28 skS.0 2 a_1 Xa Xb Xc) →
% 4.08/4.28 skS.0 2 a_1 cZ x x)
% 4.08/4.28 False
% 4.08/4.28 Clause #28 (by clausification #[27]): ∀ (a_1 : a → a → a → Prop),
% 4.08/4.28 Eq
% 4.08/4.28 (And True
% 4.08/4.28 (∀ (Xa Xb Xc : a),
% 4.08/4.28 Or (Or (And (Eq Xa cZ) (Eq Xb Xc)) (And (Eq Xb cZ) (Eq Xa Xc)))
% 4.08/4.28 (Exists fun Xx1 =>
% 4.08/4.28 Exists fun Xx2 =>
% 4.08/4.28 Exists fun Xy1 =>
% 4.08/4.28 Exists fun Xy2 =>
% 4.08/4.28 Exists fun Xz1 =>
% 4.08/4.28 Exists fun Xz2 =>
% 4.08/4.28 And
% 4.08/4.28 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2)))
% 4.08/4.28 (skS.0 2 a_1 Xx1 Xy1 Xz1))
% 4.08/4.28 (skS.0 2 a_1 Xx2 Xy2 Xz2)) →
% 4.08/4.28 skS.0 2 a_1 Xa Xb Xc))
% 4.08/4.28 True
% 4.08/4.28 Clause #29 (by clausification #[27]): ∀ (a_1 : a → a → a → Prop), Eq (skS.0 2 a_1 cZ x x) False
% 4.08/4.28 Clause #30 (by clausification #[28]): ∀ (a_1 : a → a → a → Prop),
% 4.08/4.28 Eq
% 4.08/4.28 (∀ (Xa Xb Xc : a),
% 4.08/4.28 Or (Or (And (Eq Xa cZ) (Eq Xb Xc)) (And (Eq Xb cZ) (Eq Xa Xc)))
% 4.08/4.28 (Exists fun Xx1 =>
% 4.08/4.28 Exists fun Xx2 =>
% 4.08/4.28 Exists fun Xy1 =>
% 4.08/4.28 Exists fun Xy2 =>
% 4.08/4.28 Exists fun Xz1 =>
% 4.08/4.28 Exists fun Xz2 =>
% 4.08/4.28 And
% 4.08/4.28 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2)))
% 4.08/4.28 (skS.0 2 a_1 Xx1 Xy1 Xz1))
% 4.08/4.28 (skS.0 2 a_1 Xx2 Xy2 Xz2)) →
% 4.08/4.28 skS.0 2 a_1 Xa Xb Xc)
% 4.08/4.28 True
% 4.08/4.28 Clause #32 (by clausification #[30]): ∀ (a_1 : a) (a_2 : a → a → a → Prop),
% 4.08/4.28 Eq
% 4.08/4.28 (∀ (Xb Xc : a),
% 4.08/4.28 Or (Or (And (Eq a_1 cZ) (Eq Xb Xc)) (And (Eq Xb cZ) (Eq a_1 Xc)))
% 4.08/4.28 (Exists fun Xx1 =>
% 4.08/4.28 Exists fun Xx2 =>
% 4.08/4.28 Exists fun Xy1 =>
% 4.08/4.28 Exists fun Xy2 =>
% 4.08/4.28 Exists fun Xz1 =>
% 4.08/4.28 Exists fun Xz2 =>
% 4.08/4.28 And
% 4.08/4.28 (And (And (And (Eq a_1 (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2)))
% 4.08/4.28 (skS.0 2 a_2 Xx1 Xy1 Xz1))
% 4.08/4.28 (skS.0 2 a_2 Xx2 Xy2 Xz2)) →
% 4.08/4.28 skS.0 2 a_2 a_1 Xb Xc)
% 4.08/4.28 True
% 4.08/4.28 Clause #33 (by clausification #[32]): ∀ (a_1 a_2 : a) (a_3 : a → a → a → Prop),
% 4.08/4.28 Eq
% 4.08/4.28 (∀ (Xc : a),
% 4.08/4.28 Or (Or (And (Eq a_1 cZ) (Eq a_2 Xc)) (And (Eq a_2 cZ) (Eq a_1 Xc)))
% 4.08/4.28 (Exists fun Xx1 =>
% 4.08/4.28 Exists fun Xx2 =>
% 4.08/4.28 Exists fun Xy1 =>
% 4.08/4.28 Exists fun Xy2 =>
% 4.08/4.28 Exists fun Xz1 =>
% 4.08/4.28 Exists fun Xz2 =>
% 4.08/4.28 And
% 4.08/4.28 (And (And (And (Eq a_1 (cP Xx1 Xx2)) (Eq a_2 (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2)))
% 4.08/4.28 (skS.0 2 a_3 Xx1 Xy1 Xz1))
% 4.08/4.28 (skS.0 2 a_3 Xx2 Xy2 Xz2)) →
% 4.08/4.28 skS.0 2 a_3 a_1 a_2 Xc)
% 4.08/4.28 True
% 4.08/4.28 Clause #34 (by clausification #[33]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → a → a → Prop),
% 4.08/4.28 Eq
% 4.08/4.28 (Or (Or (And (Eq a_1 cZ) (Eq a_2 a_3)) (And (Eq a_2 cZ) (Eq a_1 a_3)))
% 4.08/4.28 (Exists fun Xx1 =>
% 4.08/4.28 Exists fun Xx2 =>
% 4.08/4.28 Exists fun Xy1 =>
% 4.08/4.28 Exists fun Xy2 =>
% 4.08/4.28 Exists fun Xz1 =>
% 4.08/4.28 Exists fun Xz2 =>
% 4.08/4.28 And
% 4.08/4.28 (And (And (And (Eq a_1 (cP Xx1 Xx2)) (Eq a_2 (cP Xy1 Xy2))) (Eq a_3 (cP Xz1 Xz2)))
% 4.08/4.28 (skS.0 2 a_4 Xx1 Xy1 Xz1))
% 4.08/4.28 (skS.0 2 a_4 Xx2 Xy2 Xz2)) →
% 4.08/4.28 skS.0 2 a_4 a_1 a_2 a_3)
% 4.08/4.28 True
% 4.08/4.28 Clause #35 (by clausification #[34]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → a → a → Prop),
% 4.08/4.28 Or
% 4.08/4.28 (Eq
% 4.08/4.28 (Or (Or (And (Eq a_1 cZ) (Eq a_2 a_3)) (And (Eq a_2 cZ) (Eq a_1 a_3)))
% 4.08/4.28 (Exists fun Xx1 =>
% 4.08/4.28 Exists fun Xx2 =>
% 4.08/4.28 Exists fun Xy1 =>
% 4.08/4.28 Exists fun Xy2 =>
% 4.08/4.28 Exists fun Xz1 =>
% 4.08/4.28 Exists fun Xz2 =>
% 4.08/4.28 And
% 4.08/4.28 (And (And (And (Eq a_1 (cP Xx1 Xx2)) (Eq a_2 (cP Xy1 Xy2))) (Eq a_3 (cP Xz1 Xz2)))
% 4.14/4.29 (skS.0 2 a_4 Xx1 Xy1 Xz1))
% 4.14/4.29 (skS.0 2 a_4 Xx2 Xy2 Xz2)))
% 4.14/4.29 False)
% 4.14/4.29 (Eq (skS.0 2 a_4 a_1 a_2 a_3) True)
% 4.14/4.29 Clause #37 (by clausification #[35]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a),
% 4.14/4.29 Or (Eq (skS.0 2 a_1 a_2 a_3 a_4) True) (Eq (Or (And (Eq a_2 cZ) (Eq a_3 a_4)) (And (Eq a_3 cZ) (Eq a_2 a_4))) False)
% 4.14/4.29 Clause #189 (by clausification #[37]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a),
% 4.14/4.29 Or (Eq (skS.0 2 a_1 a_2 a_3 a_4) True) (Eq (And (Eq a_2 cZ) (Eq a_3 a_4)) False)
% 4.14/4.29 Clause #217 (by clausification #[189]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a),
% 4.14/4.29 Or (Eq (skS.0 2 a_1 a_2 a_3 a_4) True) (Or (Eq (Eq a_2 cZ) False) (Eq (Eq a_3 a_4) False))
% 4.14/4.29 Clause #218 (by clausification #[217]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a),
% 4.14/4.29 Or (Eq (skS.0 2 a_1 a_2 a_3 a_4) True) (Or (Eq (Eq a_3 a_4) False) (Ne a_2 cZ))
% 4.14/4.29 Clause #219 (by clausification #[218]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a), Or (Eq (skS.0 2 a_1 a_2 a_3 a_4) True) (Or (Ne a_2 cZ) (Ne a_3 a_4))
% 4.14/4.29 Clause #220 (by destructive equality resolution #[219]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 : a), Or (Eq (skS.0 2 a_1 cZ a_2 a_3) True) (Ne a_2 a_3)
% 4.14/4.29 Clause #221 (by destructive equality resolution #[220]): ∀ (a_1 : a → a → a → Prop) (a_2 : a), Eq (skS.0 2 a_1 cZ a_2 a_2) True
% 4.14/4.29 Clause #222 (by superposition #[221, 29]): Eq True False
% 4.14/4.29 Clause #230 (by clausification #[222]): False
% 4.14/4.29 SZS output end Proof for theBenchmark.p
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