TSTP Solution File: SEV196^5 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEV196^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n010.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 3.80s 4.07s
% Output : Proof 3.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV196^5 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : duper %s
% 0.14/0.33 % Computer : n010.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 02:49:21 EDT 2023
% 0.14/0.34 % CPUTime :
% 3.80/4.07 SZS status Theorem for theBenchmark.p
% 3.80/4.07 SZS output start Proof for theBenchmark.p
% 3.80/4.07 Clause #0 (by assumption #[]): Eq
% 3.80/4.07 (Not
% 3.80/4.07 (∀ (R : a → a → a → Prop),
% 3.80/4.07 And True
% 3.80/4.07 (∀ (Xa Xb Xc : a),
% 3.80/4.07 Or (Or (And (Eq Xa c0) (Eq Xb Xc)) (And (Eq Xb c0) (Eq Xa Xc)))
% 3.80/4.07 (Exists fun Xx1 =>
% 3.80/4.07 Exists fun Xx2 =>
% 3.80/4.07 Exists fun Xy1 =>
% 3.80/4.07 Exists fun Xy2 =>
% 3.80/4.07 Exists fun Xz1 =>
% 3.80/4.07 Exists fun Xz2 =>
% 3.80/4.07 And
% 3.80/4.07 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2)))
% 3.80/4.07 (R Xx1 Xy1 Xz1))
% 3.80/4.07 (R Xx2 Xy2 Xz2)) →
% 3.80/4.07 R Xa Xb Xc) →
% 3.80/4.07 R (cP x c0) (cP c0 y) (cP x y)))
% 3.80/4.07 True
% 3.80/4.07 Clause #1 (by clausification #[0]): Eq
% 3.80/4.07 (∀ (R : a → a → a → Prop),
% 3.80/4.07 And True
% 3.80/4.07 (∀ (Xa Xb Xc : a),
% 3.80/4.07 Or (Or (And (Eq Xa c0) (Eq Xb Xc)) (And (Eq Xb c0) (Eq Xa Xc)))
% 3.80/4.07 (Exists fun Xx1 =>
% 3.80/4.07 Exists fun Xx2 =>
% 3.80/4.07 Exists fun Xy1 =>
% 3.80/4.07 Exists fun Xy2 =>
% 3.80/4.07 Exists fun Xz1 =>
% 3.80/4.07 Exists fun Xz2 =>
% 3.80/4.07 And
% 3.80/4.07 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2)))
% 3.80/4.07 (R Xx1 Xy1 Xz1))
% 3.80/4.07 (R Xx2 Xy2 Xz2)) →
% 3.80/4.07 R Xa Xb Xc) →
% 3.80/4.07 R (cP x c0) (cP c0 y) (cP x y))
% 3.80/4.07 False
% 3.80/4.07 Clause #2 (by clausification #[1]): ∀ (a_1 : a → a → a → Prop),
% 3.80/4.07 Eq
% 3.80/4.07 (Not
% 3.80/4.07 (And True
% 3.80/4.07 (∀ (Xa Xb Xc : a),
% 3.80/4.07 Or (Or (And (Eq Xa c0) (Eq Xb Xc)) (And (Eq Xb c0) (Eq Xa Xc)))
% 3.80/4.07 (Exists fun Xx1 =>
% 3.80/4.07 Exists fun Xx2 =>
% 3.80/4.07 Exists fun Xy1 =>
% 3.80/4.07 Exists fun Xy2 =>
% 3.80/4.07 Exists fun Xz1 =>
% 3.80/4.07 Exists fun Xz2 =>
% 3.80/4.07 And
% 3.80/4.07 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2)))
% 3.80/4.07 (skS.0 0 a_1 Xx1 Xy1 Xz1))
% 3.80/4.07 (skS.0 0 a_1 Xx2 Xy2 Xz2)) →
% 3.80/4.07 skS.0 0 a_1 Xa Xb Xc) →
% 3.80/4.07 skS.0 0 a_1 (cP x c0) (cP c0 y) (cP x y)))
% 3.80/4.07 True
% 3.80/4.07 Clause #3 (by clausification #[2]): ∀ (a_1 : a → a → a → Prop),
% 3.80/4.07 Eq
% 3.80/4.07 (And True
% 3.80/4.07 (∀ (Xa Xb Xc : a),
% 3.80/4.07 Or (Or (And (Eq Xa c0) (Eq Xb Xc)) (And (Eq Xb c0) (Eq Xa Xc)))
% 3.80/4.07 (Exists fun Xx1 =>
% 3.80/4.07 Exists fun Xx2 =>
% 3.80/4.07 Exists fun Xy1 =>
% 3.80/4.07 Exists fun Xy2 =>
% 3.80/4.07 Exists fun Xz1 =>
% 3.80/4.07 Exists fun Xz2 =>
% 3.80/4.07 And
% 3.80/4.07 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2)))
% 3.80/4.07 (skS.0 0 a_1 Xx1 Xy1 Xz1))
% 3.80/4.07 (skS.0 0 a_1 Xx2 Xy2 Xz2)) →
% 3.80/4.07 skS.0 0 a_1 Xa Xb Xc) →
% 3.80/4.07 skS.0 0 a_1 (cP x c0) (cP c0 y) (cP x y))
% 3.80/4.07 False
% 3.80/4.07 Clause #4 (by clausification #[3]): ∀ (a_1 : a → a → a → Prop),
% 3.80/4.07 Eq
% 3.80/4.07 (And True
% 3.80/4.07 (∀ (Xa Xb Xc : a),
% 3.80/4.07 Or (Or (And (Eq Xa c0) (Eq Xb Xc)) (And (Eq Xb c0) (Eq Xa Xc)))
% 3.80/4.07 (Exists fun Xx1 =>
% 3.80/4.07 Exists fun Xx2 =>
% 3.80/4.07 Exists fun Xy1 =>
% 3.80/4.07 Exists fun Xy2 =>
% 3.80/4.07 Exists fun Xz1 =>
% 3.80/4.07 Exists fun Xz2 =>
% 3.80/4.07 And
% 3.80/4.07 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2)))
% 3.80/4.07 (skS.0 0 a_1 Xx1 Xy1 Xz1))
% 3.80/4.07 (skS.0 0 a_1 Xx2 Xy2 Xz2)) →
% 3.80/4.07 skS.0 0 a_1 Xa Xb Xc))
% 3.80/4.07 True
% 3.80/4.07 Clause #5 (by clausification #[3]): ∀ (a_1 : a → a → a → Prop), Eq (skS.0 0 a_1 (cP x c0) (cP c0 y) (cP x y)) False
% 3.80/4.07 Clause #6 (by clausification #[4]): ∀ (a_1 : a → a → a → Prop),
% 3.80/4.07 Eq
% 3.80/4.07 (∀ (Xa Xb Xc : a),
% 3.80/4.07 Or (Or (And (Eq Xa c0) (Eq Xb Xc)) (And (Eq Xb c0) (Eq Xa Xc)))
% 3.80/4.09 (Exists fun Xx1 =>
% 3.80/4.09 Exists fun Xx2 =>
% 3.80/4.09 Exists fun Xy1 =>
% 3.80/4.09 Exists fun Xy2 =>
% 3.80/4.09 Exists fun Xz1 =>
% 3.80/4.09 Exists fun Xz2 =>
% 3.80/4.09 And
% 3.80/4.09 (And (And (And (Eq Xa (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2)))
% 3.80/4.09 (skS.0 0 a_1 Xx1 Xy1 Xz1))
% 3.80/4.09 (skS.0 0 a_1 Xx2 Xy2 Xz2)) →
% 3.80/4.09 skS.0 0 a_1 Xa Xb Xc)
% 3.80/4.09 True
% 3.80/4.09 Clause #8 (by clausification #[6]): ∀ (a_1 : a) (a_2 : a → a → a → Prop),
% 3.80/4.09 Eq
% 3.80/4.09 (∀ (Xb Xc : a),
% 3.80/4.09 Or (Or (And (Eq a_1 c0) (Eq Xb Xc)) (And (Eq Xb c0) (Eq a_1 Xc)))
% 3.80/4.09 (Exists fun Xx1 =>
% 3.80/4.09 Exists fun Xx2 =>
% 3.80/4.09 Exists fun Xy1 =>
% 3.80/4.09 Exists fun Xy2 =>
% 3.80/4.09 Exists fun Xz1 =>
% 3.80/4.09 Exists fun Xz2 =>
% 3.80/4.09 And
% 3.80/4.09 (And (And (And (Eq a_1 (cP Xx1 Xx2)) (Eq Xb (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2)))
% 3.80/4.09 (skS.0 0 a_2 Xx1 Xy1 Xz1))
% 3.80/4.09 (skS.0 0 a_2 Xx2 Xy2 Xz2)) →
% 3.80/4.09 skS.0 0 a_2 a_1 Xb Xc)
% 3.80/4.09 True
% 3.80/4.09 Clause #9 (by clausification #[8]): ∀ (a_1 a_2 : a) (a_3 : a → a → a → Prop),
% 3.80/4.09 Eq
% 3.80/4.09 (∀ (Xc : a),
% 3.80/4.09 Or (Or (And (Eq a_1 c0) (Eq a_2 Xc)) (And (Eq a_2 c0) (Eq a_1 Xc)))
% 3.80/4.09 (Exists fun Xx1 =>
% 3.80/4.09 Exists fun Xx2 =>
% 3.80/4.09 Exists fun Xy1 =>
% 3.80/4.09 Exists fun Xy2 =>
% 3.80/4.09 Exists fun Xz1 =>
% 3.80/4.09 Exists fun Xz2 =>
% 3.80/4.09 And
% 3.80/4.09 (And (And (And (Eq a_1 (cP Xx1 Xx2)) (Eq a_2 (cP Xy1 Xy2))) (Eq Xc (cP Xz1 Xz2)))
% 3.80/4.09 (skS.0 0 a_3 Xx1 Xy1 Xz1))
% 3.80/4.09 (skS.0 0 a_3 Xx2 Xy2 Xz2)) →
% 3.80/4.09 skS.0 0 a_3 a_1 a_2 Xc)
% 3.80/4.09 True
% 3.80/4.09 Clause #10 (by clausification #[9]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → a → a → Prop),
% 3.80/4.09 Eq
% 3.80/4.09 (Or (Or (And (Eq a_1 c0) (Eq a_2 a_3)) (And (Eq a_2 c0) (Eq a_1 a_3)))
% 3.80/4.09 (Exists fun Xx1 =>
% 3.80/4.09 Exists fun Xx2 =>
% 3.80/4.09 Exists fun Xy1 =>
% 3.80/4.09 Exists fun Xy2 =>
% 3.80/4.09 Exists fun Xz1 =>
% 3.80/4.09 Exists fun Xz2 =>
% 3.80/4.09 And
% 3.80/4.09 (And (And (And (Eq a_1 (cP Xx1 Xx2)) (Eq a_2 (cP Xy1 Xy2))) (Eq a_3 (cP Xz1 Xz2)))
% 3.80/4.09 (skS.0 0 a_4 Xx1 Xy1 Xz1))
% 3.80/4.09 (skS.0 0 a_4 Xx2 Xy2 Xz2)) →
% 3.80/4.09 skS.0 0 a_4 a_1 a_2 a_3)
% 3.80/4.09 True
% 3.80/4.09 Clause #11 (by clausification #[10]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → a → a → Prop),
% 3.80/4.09 Or
% 3.80/4.09 (Eq
% 3.80/4.09 (Or (Or (And (Eq a_1 c0) (Eq a_2 a_3)) (And (Eq a_2 c0) (Eq a_1 a_3)))
% 3.80/4.09 (Exists fun Xx1 =>
% 3.80/4.09 Exists fun Xx2 =>
% 3.80/4.09 Exists fun Xy1 =>
% 3.80/4.09 Exists fun Xy2 =>
% 3.80/4.09 Exists fun Xz1 =>
% 3.80/4.09 Exists fun Xz2 =>
% 3.80/4.09 And
% 3.80/4.09 (And (And (And (Eq a_1 (cP Xx1 Xx2)) (Eq a_2 (cP Xy1 Xy2))) (Eq a_3 (cP Xz1 Xz2)))
% 3.80/4.09 (skS.0 0 a_4 Xx1 Xy1 Xz1))
% 3.80/4.09 (skS.0 0 a_4 Xx2 Xy2 Xz2)))
% 3.80/4.09 False)
% 3.80/4.09 (Eq (skS.0 0 a_4 a_1 a_2 a_3) True)
% 3.80/4.09 Clause #12 (by clausification #[11]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a),
% 3.80/4.09 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True)
% 3.80/4.09 (Eq
% 3.80/4.09 (Exists fun Xx1 =>
% 3.80/4.09 Exists fun Xx2 =>
% 3.80/4.09 Exists fun Xy1 =>
% 3.80/4.09 Exists fun Xy2 =>
% 3.80/4.09 Exists fun Xz1 =>
% 3.80/4.09 Exists fun Xz2 =>
% 3.80/4.09 And
% 3.80/4.09 (And (And (And (Eq a_2 (cP Xx1 Xx2)) (Eq a_3 (cP Xy1 Xy2))) (Eq a_4 (cP Xz1 Xz2)))
% 3.80/4.09 (skS.0 0 a_1 Xx1 Xy1 Xz1))
% 3.80/4.09 (skS.0 0 a_1 Xx2 Xy2 Xz2))
% 3.80/4.09 False)
% 3.80/4.09 Clause #13 (by clausification #[11]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a),
% 3.80/4.09 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)
% 3.80/4.09 Clause #14 (by clausification #[12]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 : a),
% 3.80/4.09 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True)
% 3.80/4.09 (Eq
% 3.80/4.09 (Exists fun Xx2 =>
% 3.80/4.09 Exists fun Xy1 =>
% 3.80/4.09 Exists fun Xy2 =>
% 3.80/4.09 Exists fun Xz1 =>
% 3.80/4.11 Exists fun Xz2 =>
% 3.80/4.11 And
% 3.80/4.11 (And (And (And (Eq a_2 (cP a_5 Xx2)) (Eq a_3 (cP Xy1 Xy2))) (Eq a_4 (cP Xz1 Xz2)))
% 3.80/4.11 (skS.0 0 a_1 a_5 Xy1 Xz1))
% 3.80/4.11 (skS.0 0 a_1 Xx2 Xy2 Xz2))
% 3.80/4.11 False)
% 3.80/4.11 Clause #15 (by clausification #[14]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 a_6 : a),
% 3.80/4.11 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True)
% 3.80/4.11 (Eq
% 3.80/4.11 (Exists fun Xy1 =>
% 3.80/4.11 Exists fun Xy2 =>
% 3.80/4.11 Exists fun Xz1 =>
% 3.80/4.11 Exists fun Xz2 =>
% 3.80/4.11 And
% 3.80/4.11 (And (And (And (Eq a_2 (cP a_5 a_6)) (Eq a_3 (cP Xy1 Xy2))) (Eq a_4 (cP Xz1 Xz2)))
% 3.80/4.11 (skS.0 0 a_1 a_5 Xy1 Xz1))
% 3.80/4.11 (skS.0 0 a_1 a_6 Xy2 Xz2))
% 3.80/4.11 False)
% 3.80/4.11 Clause #16 (by clausification #[15]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 a_6 a_7 : a),
% 3.80/4.11 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True)
% 3.80/4.11 (Eq
% 3.80/4.11 (Exists fun Xy2 =>
% 3.80/4.11 Exists fun Xz1 =>
% 3.80/4.11 Exists fun Xz2 =>
% 3.80/4.11 And
% 3.80/4.11 (And (And (And (Eq a_2 (cP a_5 a_6)) (Eq a_3 (cP a_7 Xy2))) (Eq a_4 (cP Xz1 Xz2)))
% 3.80/4.11 (skS.0 0 a_1 a_5 a_7 Xz1))
% 3.80/4.11 (skS.0 0 a_1 a_6 Xy2 Xz2))
% 3.80/4.11 False)
% 3.80/4.11 Clause #17 (by clausification #[16]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 a_6 a_7 a_8 : a),
% 3.80/4.11 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True)
% 3.80/4.11 (Eq
% 3.80/4.11 (Exists fun Xz1 =>
% 3.80/4.11 Exists fun Xz2 =>
% 3.80/4.11 And
% 3.80/4.11 (And (And (And (Eq a_2 (cP a_5 a_6)) (Eq a_3 (cP a_7 a_8))) (Eq a_4 (cP Xz1 Xz2)))
% 3.80/4.11 (skS.0 0 a_1 a_5 a_7 Xz1))
% 3.80/4.11 (skS.0 0 a_1 a_6 a_8 Xz2))
% 3.80/4.11 False)
% 3.80/4.11 Clause #18 (by clausification #[17]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 : a),
% 3.80/4.11 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True)
% 3.80/4.11 (Eq
% 3.80/4.11 (Exists fun Xz2 =>
% 3.80/4.11 And
% 3.80/4.11 (And (And (And (Eq a_2 (cP a_5 a_6)) (Eq a_3 (cP a_7 a_8))) (Eq a_4 (cP a_9 Xz2))) (skS.0 0 a_1 a_5 a_7 a_9))
% 3.80/4.11 (skS.0 0 a_1 a_6 a_8 Xz2))
% 3.80/4.11 False)
% 3.80/4.11 Clause #19 (by clausification #[18]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : a),
% 3.80/4.11 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True)
% 3.80/4.11 (Eq
% 3.80/4.11 (And
% 3.80/4.11 (And (And (And (Eq a_2 (cP a_5 a_6)) (Eq a_3 (cP a_7 a_8))) (Eq a_4 (cP a_9 a_10))) (skS.0 0 a_1 a_5 a_7 a_9))
% 3.80/4.11 (skS.0 0 a_1 a_6 a_8 a_10))
% 3.80/4.11 False)
% 3.80/4.11 Clause #20 (by clausification #[19]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : a),
% 3.80/4.11 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True)
% 3.80/4.11 (Or
% 3.80/4.11 (Eq (And (And (And (Eq a_2 (cP a_5 a_6)) (Eq a_3 (cP a_7 a_8))) (Eq a_4 (cP a_9 a_10))) (skS.0 0 a_1 a_5 a_7 a_9))
% 3.80/4.11 False)
% 3.80/4.11 (Eq (skS.0 0 a_1 a_6 a_8 a_10) False))
% 3.80/4.11 Clause #21 (by clausification #[20]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : a),
% 3.80/4.11 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True)
% 3.80/4.11 (Or (Eq (skS.0 0 a_1 a_5 a_6 a_7) False)
% 3.80/4.11 (Or (Eq (And (And (Eq a_2 (cP a_8 a_5)) (Eq a_3 (cP a_9 a_6))) (Eq a_4 (cP a_10 a_7))) False)
% 3.80/4.11 (Eq (skS.0 0 a_1 a_8 a_9 a_10) False)))
% 3.80/4.11 Clause #22 (by clausification #[21]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : a),
% 3.80/4.11 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True)
% 3.80/4.11 (Or (Eq (skS.0 0 a_1 a_5 a_6 a_7) False)
% 3.80/4.11 (Or (Eq (skS.0 0 a_1 a_8 a_9 a_10) False)
% 3.80/4.11 (Or (Eq (And (Eq a_2 (cP a_8 a_5)) (Eq a_3 (cP a_9 a_6))) False) (Eq (Eq a_4 (cP a_10 a_7)) False))))
% 3.80/4.11 Clause #23 (by clausification #[22]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : a),
% 3.80/4.11 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True)
% 3.80/4.11 (Or (Eq (skS.0 0 a_1 a_5 a_6 a_7) False)
% 3.80/4.11 (Or (Eq (skS.0 0 a_1 a_8 a_9 a_10) False)
% 3.80/4.11 (Or (Eq (Eq a_4 (cP a_10 a_7)) False) (Or (Eq (Eq a_2 (cP a_8 a_5)) False) (Eq (Eq a_3 (cP a_9 a_6)) False)))))
% 3.80/4.11 Clause #24 (by clausification #[23]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : a),
% 3.80/4.11 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True)
% 3.80/4.11 (Or (Eq (skS.0 0 a_1 a_5 a_6 a_7) False)
% 3.80/4.11 (Or (Eq (skS.0 0 a_1 a_8 a_9 a_10) False)
% 3.80/4.11 (Or (Eq (Eq a_2 (cP a_8 a_5)) False) (Or (Eq (Eq a_3 (cP a_9 a_6)) False) (Ne a_4 (cP a_10 a_7))))))
% 3.95/4.14 Clause #25 (by clausification #[24]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : a),
% 3.95/4.14 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True)
% 3.95/4.14 (Or (Eq (skS.0 0 a_1 a_5 a_6 a_7) False)
% 3.95/4.14 (Or (Eq (skS.0 0 a_1 a_8 a_9 a_10) False)
% 3.95/4.14 (Or (Eq (Eq a_3 (cP a_9 a_6)) False) (Or (Ne a_4 (cP a_10 a_7)) (Ne a_2 (cP a_8 a_5))))))
% 3.95/4.14 Clause #26 (by clausification #[25]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : a),
% 3.95/4.14 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True)
% 3.95/4.14 (Or (Eq (skS.0 0 a_1 a_5 a_6 a_7) False)
% 3.95/4.14 (Or (Eq (skS.0 0 a_1 a_8 a_9 a_10) False)
% 3.95/4.14 (Or (Ne a_4 (cP a_10 a_7)) (Or (Ne a_2 (cP a_8 a_5)) (Ne a_3 (cP a_9 a_6))))))
% 3.95/4.14 Clause #27 (by destructive equality resolution #[26]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 : a),
% 3.95/4.14 Or (Eq (skS.0 0 a_1 a_2 a_3 (cP a_4 a_5)) True)
% 3.95/4.14 (Or (Eq (skS.0 0 a_1 a_6 a_7 a_5) False)
% 3.95/4.14 (Or (Eq (skS.0 0 a_1 a_8 a_9 a_4) False) (Or (Ne a_2 (cP a_8 a_6)) (Ne a_3 (cP a_9 a_7)))))
% 3.95/4.14 Clause #28 (by destructive equality resolution #[27]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 a_6 a_7 a_8 : a),
% 3.95/4.14 Or (Eq (skS.0 0 a_1 (cP a_2 a_3) a_4 (cP a_5 a_6)) True)
% 3.95/4.14 (Or (Eq (skS.0 0 a_1 a_3 a_7 a_6) False) (Or (Eq (skS.0 0 a_1 a_2 a_8 a_5) False) (Ne a_4 (cP a_8 a_7))))
% 3.95/4.14 Clause #29 (by destructive equality resolution #[28]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 a_6 a_7 : a),
% 3.95/4.14 Or (Eq (skS.0 0 a_1 (cP a_2 a_3) (cP a_4 a_5) (cP a_6 a_7)) True)
% 3.95/4.14 (Or (Eq (skS.0 0 a_1 a_3 a_5 a_7) False) (Eq (skS.0 0 a_1 a_2 a_4 a_6) False))
% 3.95/4.14 Clause #30 (by clausification #[13]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a),
% 3.95/4.14 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True) (Eq (And (Eq a_3 c0) (Eq a_2 a_4)) False)
% 3.95/4.14 Clause #31 (by clausification #[13]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a),
% 3.95/4.14 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)
% 3.95/4.14 Clause #32 (by clausification #[30]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a),
% 3.95/4.14 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True) (Or (Eq (Eq a_3 c0) False) (Eq (Eq a_2 a_4) False))
% 3.95/4.14 Clause #33 (by clausification #[32]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a),
% 3.95/4.14 Or (Eq (skS.0 0 a_1 a_2 a_3 a_4) True) (Or (Eq (Eq a_2 a_4) False) (Ne a_3 c0))
% 3.95/4.14 Clause #34 (by clausification #[33]): ∀ (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_3 c0) (Ne a_2 a_4))
% 3.95/4.14 Clause #35 (by destructive equality resolution #[34]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 : a), Or (Eq (skS.0 0 a_1 a_2 c0 a_3) True) (Ne a_2 a_3)
% 3.95/4.14 Clause #36 (by destructive equality resolution #[35]): ∀ (a_1 : a → a → a → Prop) (a_2 : a), Eq (skS.0 0 a_1 a_2 c0 a_2) True
% 3.95/4.14 Clause #38 (by clausification #[31]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a),
% 3.95/4.14 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))
% 3.95/4.14 Clause #39 (by clausification #[38]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 : a),
% 3.95/4.14 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))
% 3.95/4.14 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))
% 3.95/4.14 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)
% 3.95/4.14 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
% 3.95/4.14 Clause #43 (by superposition #[42, 29]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 : a),
% 3.95/4.14 Or (Eq (skS.0 0 a_1 (cP a_2 c0) (cP a_3 a_4) (cP a_5 a_4)) True)
% 3.95/4.14 (Or (Eq True False) (Eq (skS.0 0 a_1 a_2 a_3 a_5) False))
% 3.95/4.14 Clause #64 (by clausification #[43]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 a_4 a_5 : a),
% 3.95/4.14 Or (Eq (skS.0 0 a_1 (cP a_2 c0) (cP a_3 a_4) (cP a_5 a_4)) True) (Eq (skS.0 0 a_1 a_2 a_3 a_5) False)
% 3.95/4.14 Clause #70 (by superposition #[64, 36]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 : a),
% 3.95/4.14 Or (Eq (skS.0 0 (fun x x_1 x_2 => a_1 x x_1 x_2) (cP a_2 c0) (cP c0 a_3) (cP a_2 a_3)) True) (Eq False True)
% 3.95/4.14 Clause #85 (by betaEtaReduce #[70]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 : a),
% 3.95/4.14 Or (Eq (skS.0 0 a_1 (cP a_2 c0) (cP c0 a_3) (cP a_2 a_3)) True) (Eq False True)
% 3.95/4.14 Clause #86 (by clausification #[85]): ∀ (a_1 : a → a → a → Prop) (a_2 a_3 : a), Eq (skS.0 0 a_1 (cP a_2 c0) (cP c0 a_3) (cP a_2 a_3)) True
% 3.95/4.14 Clause #87 (by superposition #[86, 5]): Eq True False
% 3.95/4.14 Clause #91 (by clausification #[87]): False
% 3.95/4.14 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------