TSTP Solution File: SEV194^5 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEV194^5 : TPTP v8.1.2. Released v4.0.0.
% 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 : Thu Aug 31 19:24:27 EDT 2023
% Result : Theorem 3.42s 3.69s
% Output : Proof 3.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV194^5 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % Command : duper %s
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 24 03:42:32 EDT 2023
% 0.14/0.36 % CPUTime :
% 3.42/3.69 SZS status Theorem for theBenchmark.p
% 3.42/3.69 SZS output start Proof for theBenchmark.p
% 3.42/3.69 Clause #0 (by assumption #[]): Eq
% 3.42/3.69 (Not
% 3.42/3.69 (∀ (R : a → a → a → Prop),
% 3.42/3.69 And True
% 3.42/3.69 (∀ (Xa Xb Xc : a),
% 3.42/3.69 Or (Or (And (Eq Xa c0) (Eq Xb Xc)) (And (Eq Xb c0) (Eq Xa Xc)))
% 3.42/3.69 (Exists fun Xx1 =>
% 3.42/3.69 Exists fun Xx2 =>
% 3.42/3.69 Exists fun Xy1 =>
% 3.42/3.69 Exists fun Xy2 =>
% 3.42/3.69 Exists fun Xz1 =>
% 3.42/3.69 Exists fun Xz2 =>
% 3.42/3.69 And
% 3.42/3.69 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2)))
% 3.42/3.69 (R Xx1 Xy1 Xz1))
% 3.42/3.69 (R Xx2 Xy2 Xz2)) →
% 3.42/3.69 R Xa Xb Xc) →
% 3.42/3.69 R c0 x x))
% 3.42/3.69 True
% 3.42/3.69 Clause #1 (by clausification #[0]): Eq
% 3.42/3.69 (∀ (R : a → a → a → Prop),
% 3.42/3.69 And True
% 3.42/3.69 (∀ (Xa Xb Xc : a),
% 3.42/3.69 Or (Or (And (Eq Xa c0) (Eq Xb Xc)) (And (Eq Xb c0) (Eq Xa Xc)))
% 3.42/3.69 (Exists fun Xx1 =>
% 3.42/3.69 Exists fun Xx2 =>
% 3.42/3.69 Exists fun Xy1 =>
% 3.42/3.69 Exists fun Xy2 =>
% 3.42/3.69 Exists fun Xz1 =>
% 3.42/3.69 Exists fun Xz2 =>
% 3.42/3.69 And
% 3.42/3.69 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2)))
% 3.42/3.69 (R Xx1 Xy1 Xz1))
% 3.42/3.69 (R Xx2 Xy2 Xz2)) →
% 3.42/3.69 R Xa Xb Xc) →
% 3.42/3.69 R c0 x x)
% 3.42/3.69 False
% 3.42/3.69 Clause #2 (by clausification #[1]): ∀ (a_1 : a → a → a → Prop),
% 3.42/3.69 Eq
% 3.42/3.69 (Not
% 3.42/3.69 (And True
% 3.42/3.69 (∀ (Xa Xb Xc : a),
% 3.42/3.69 Or (Or (And (Eq Xa c0) (Eq Xb Xc)) (And (Eq Xb c0) (Eq Xa Xc)))
% 3.42/3.69 (Exists fun Xx1 =>
% 3.42/3.69 Exists fun Xx2 =>
% 3.42/3.69 Exists fun Xy1 =>
% 3.42/3.69 Exists fun Xy2 =>
% 3.42/3.69 Exists fun Xz1 =>
% 3.42/3.69 Exists fun Xz2 =>
% 3.42/3.69 And
% 3.42/3.69 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2)))
% 3.42/3.69 (skS.0 0 a_1 Xx1 Xy1 Xz1))
% 3.42/3.69 (skS.0 0 a_1 Xx2 Xy2 Xz2)) →
% 3.42/3.69 skS.0 0 a_1 Xa Xb Xc) →
% 3.42/3.69 skS.0 0 a_1 c0 x x))
% 3.42/3.69 True
% 3.42/3.69 Clause #3 (by clausification #[2]): ∀ (a_1 : a → a → a → Prop),
% 3.42/3.69 Eq
% 3.42/3.69 (And True
% 3.42/3.69 (∀ (Xa Xb Xc : a),
% 3.42/3.69 Or (Or (And (Eq Xa c0) (Eq Xb Xc)) (And (Eq Xb c0) (Eq Xa Xc)))
% 3.42/3.69 (Exists fun Xx1 =>
% 3.42/3.69 Exists fun Xx2 =>
% 3.42/3.69 Exists fun Xy1 =>
% 3.42/3.69 Exists fun Xy2 =>
% 3.42/3.69 Exists fun Xz1 =>
% 3.42/3.69 Exists fun Xz2 =>
% 3.42/3.69 And
% 3.42/3.69 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2)))
% 3.42/3.69 (skS.0 0 a_1 Xx1 Xy1 Xz1))
% 3.42/3.69 (skS.0 0 a_1 Xx2 Xy2 Xz2)) →
% 3.42/3.69 skS.0 0 a_1 Xa Xb Xc) →
% 3.42/3.69 skS.0 0 a_1 c0 x x)
% 3.42/3.69 False
% 3.42/3.69 Clause #4 (by clausification #[3]): ∀ (a_1 : a → a → a → Prop),
% 3.42/3.69 Eq
% 3.42/3.69 (And True
% 3.42/3.69 (∀ (Xa Xb Xc : a),
% 3.42/3.69 Or (Or (And (Eq Xa c0) (Eq Xb Xc)) (And (Eq Xb c0) (Eq Xa Xc)))
% 3.42/3.69 (Exists fun Xx1 =>
% 3.42/3.69 Exists fun Xx2 =>
% 3.42/3.69 Exists fun Xy1 =>
% 3.42/3.69 Exists fun Xy2 =>
% 3.42/3.69 Exists fun Xz1 =>
% 3.42/3.69 Exists fun Xz2 =>
% 3.42/3.69 And
% 3.42/3.69 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2)))
% 3.42/3.69 (skS.0 0 a_1 Xx1 Xy1 Xz1))
% 3.42/3.69 (skS.0 0 a_1 Xx2 Xy2 Xz2)) →
% 3.42/3.69 skS.0 0 a_1 Xa Xb Xc))
% 3.42/3.69 True
% 3.42/3.69 Clause #5 (by clausification #[3]): ∀ (a_1 : a → a → a → Prop), Eq (skS.0 0 a_1 c0 x x) False
% 3.42/3.69 Clause #6 (by clausification #[4]): ∀ (a_1 : a → a → a → Prop),
% 3.42/3.69 Eq
% 3.42/3.69 (∀ (Xa Xb Xc : a),
% 3.42/3.69 Or (Or (And (Eq Xa c0) (Eq Xb Xc)) (And (Eq Xb c0) (Eq Xa Xc)))
% 3.42/3.69 (Exists fun Xx1 =>
% 3.42/3.69 Exists fun Xx2 =>
% 3.42/3.69 Exists fun Xy1 =>
% 3.42/3.71 Exists fun Xy2 =>
% 3.42/3.71 Exists fun Xz1 =>
% 3.42/3.71 Exists fun Xz2 =>
% 3.42/3.71 And
% 3.42/3.71 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2)))
% 3.42/3.71 (skS.0 0 a_1 Xx1 Xy1 Xz1))
% 3.42/3.71 (skS.0 0 a_1 Xx2 Xy2 Xz2)) →
% 3.42/3.71 skS.0 0 a_1 Xa Xb Xc)
% 3.42/3.71 True
% 3.42/3.71 Clause #8 (by clausification #[6]): ∀ (a_1 : a) (a_2 : a → a → a → Prop),
% 3.42/3.71 Eq
% 3.42/3.71 (∀ (Xb Xc : a),
% 3.42/3.71 Or (Or (And (Eq a_1 c0) (Eq Xb Xc)) (And (Eq Xb c0) (Eq a_1 Xc)))
% 3.42/3.71 (Exists fun Xx1 =>
% 3.42/3.71 Exists fun Xx2 =>
% 3.42/3.71 Exists fun Xy1 =>
% 3.42/3.71 Exists fun Xy2 =>
% 3.42/3.71 Exists fun Xz1 =>
% 3.42/3.71 Exists fun Xz2 =>
% 3.42/3.71 And
% 3.42/3.71 (And (And (And (Eq a_1 (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2)))
% 3.42/3.71 (skS.0 0 a_2 Xx1 Xy1 Xz1))
% 3.42/3.71 (skS.0 0 a_2 Xx2 Xy2 Xz2)) →
% 3.42/3.71 skS.0 0 a_2 a_1 Xb Xc)
% 3.42/3.71 True
% 3.42/3.71 Clause #9 (by clausification #[8]): ∀ (a_1 a_2 : a) (a_3 : a → a → a → Prop),
% 3.42/3.71 Eq
% 3.42/3.71 (∀ (Xc : a),
% 3.42/3.71 Or (Or (And (Eq a_1 c0) (Eq a_2 Xc)) (And (Eq a_2 c0) (Eq a_1 Xc)))
% 3.42/3.71 (Exists fun Xx1 =>
% 3.42/3.71 Exists fun Xx2 =>
% 3.42/3.71 Exists fun Xy1 =>
% 3.42/3.71 Exists fun Xy2 =>
% 3.42/3.71 Exists fun Xz1 =>
% 3.42/3.71 Exists fun Xz2 =>
% 3.42/3.71 And
% 3.42/3.71 (And (And (And (Eq a_1 (cP Xx1 Xx2)) (Eq a_2 (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2)))
% 3.42/3.71 (skS.0 0 a_3 Xx1 Xy1 Xz1))
% 3.42/3.71 (skS.0 0 a_3 Xx2 Xy2 Xz2)) →
% 3.42/3.71 skS.0 0 a_3 a_1 a_2 Xc)
% 3.42/3.71 True
% 3.42/3.71 Clause #10 (by clausification #[9]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → a → a → Prop),
% 3.42/3.71 Eq
% 3.42/3.71 (Or (Or (And (Eq a_1 c0) (Eq a_2 a_3)) (And (Eq a_2 c0) (Eq a_1 a_3)))
% 3.42/3.71 (Exists fun Xx1 =>
% 3.42/3.71 Exists fun Xx2 =>
% 3.42/3.71 Exists fun Xy1 =>
% 3.42/3.71 Exists fun Xy2 =>
% 3.42/3.71 Exists fun Xz1 =>
% 3.42/3.71 Exists fun Xz2 =>
% 3.42/3.71 And
% 3.42/3.71 (And (And (And (Eq a_1 (cP Xx1 Xx2)) (Eq a_2 (cP Xy1 Xy2))) (Eq a_3 (cP Xz1 Xz2)))
% 3.42/3.71 (skS.0 0 a_4 Xx1 Xy1 Xz1))
% 3.42/3.71 (skS.0 0 a_4 Xx2 Xy2 Xz2)) →
% 3.42/3.71 skS.0 0 a_4 a_1 a_2 a_3)
% 3.42/3.71 True
% 3.42/3.71 Clause #11 (by clausification #[10]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → a → a → Prop),
% 3.42/3.71 Or
% 3.42/3.71 (Eq
% 3.42/3.71 (Or (Or (And (Eq a_1 c0) (Eq a_2 a_3)) (And (Eq a_2 c0) (Eq a_1 a_3)))
% 3.42/3.71 (Exists fun Xx1 =>
% 3.42/3.71 Exists fun Xx2 =>
% 3.42/3.71 Exists fun Xy1 =>
% 3.42/3.71 Exists fun Xy2 =>
% 3.42/3.71 Exists fun Xz1 =>
% 3.42/3.71 Exists fun Xz2 =>
% 3.42/3.71 And
% 3.42/3.71 (And (And (And (Eq a_1 (cP Xx1 Xx2)) (Eq a_2 (cP Xy1 Xy2))) (Eq a_3 (cP Xz1 Xz2)))
% 3.42/3.71 (skS.0 0 a_4 Xx1 Xy1 Xz1))
% 3.42/3.71 (skS.0 0 a_4 Xx2 Xy2 Xz2)))
% 3.42/3.71 False)
% 3.42/3.71 (Eq (skS.0 0 a_4 a_1 a_2 a_3) True)
% 3.42/3.71 Clause #13 (by clausification #[11]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a),
% 3.42/3.71 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True) (Eq (Or (And (Eq a_2 c0) (Eq a_3 a_4)) (And (Eq a_3 c0) (Eq a_2 a_4))) False)
% 3.42/3.71 Clause #31 (by clausification #[13]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a),
% 3.42/3.71 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True) (Eq (And (Eq a_2 c0) (Eq a_3 a_4)) False)
% 3.42/3.71 Clause #38 (by clausification #[31]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a),
% 3.42/3.71 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True) (Or (Eq (Eq a_2 c0) False) (Eq (Eq a_3 a_4) False))
% 3.42/3.71 Clause #39 (by clausification #[38]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a),
% 3.42/3.71 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True) (Or (Eq (Eq a_3 a_4) False) (Ne a_2 c0))
% 3.42/3.71 Clause #40 (by clausification #[39]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a), Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True) (Or (Ne a_2 c0) (Ne a_3 a_4))
% 3.42/3.71 Clause #41 (by destructive equality resolution #[40]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 : a), Or (Eq (skS.0 0 a_1 c0 a_2 a_3) True) (Ne a_2 a_3)
% 3.42/3.71 Clause #42 (by destructive equality resolution #[41]): ∀ (a_1 : a → a → a → Prop) (a_2 : a), Eq (skS.0 0 a_1 c0 a_2 a_2) True
% 3.42/3.71 Clause #43 (by superposition #[42, 5]): Eq True False
% 3.42/3.71 Clause #48 (by clausification #[43]): False
% 3.42/3.71 SZS output end Proof for theBenchmark.p
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