TSTP Solution File: SET793+4 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET793+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n004.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 14:47:37 EDT 2023
% Result : Theorem 285.34s 285.56s
% Output : Proof 285.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET793+4 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 10:08:07 EDT 2023
% 0.14/0.35 % CPUTime :
% 285.34/285.56 SZS status Theorem for theBenchmark.p
% 285.34/285.56 SZS output start Proof for theBenchmark.p
% 285.34/285.56 Clause #0 (by assumption #[]): Eq
% 285.34/285.56 (∀ (R E : Iota),
% 285.34/285.56 Iff (order R E)
% 285.34/285.56 (And
% 285.34/285.56 (And (∀ (X : Iota), member X E → apply R X X)
% 285.34/285.56 (∀ (X Y : Iota), And (member X E) (member Y E) → And (apply R X Y) (apply R Y X) → Eq X Y))
% 285.34/285.56 (∀ (X Y Z : Iota),
% 285.34/285.56 And (And (member X E) (member Y E)) (member Z E) → And (apply R X Y) (apply R Y Z) → apply R X Z)))
% 285.34/285.56 True
% 285.34/285.56 Clause #1 (by assumption #[]): Eq
% 285.34/285.56 (∀ (R E : Iota),
% 285.34/285.56 Iff (total_order R E)
% 285.34/285.56 (And (order R E) (∀ (X Y : Iota), And (member X E) (member Y E) → Or (apply R X Y) (apply R Y X))))
% 285.34/285.56 True
% 285.34/285.56 Clause #2 (by assumption #[]): Eq (∀ (R E M : Iota), Iff (upper_bound M R E) (∀ (X : Iota), member X E → apply R X M)) True
% 285.34/285.56 Clause #4 (by assumption #[]): Eq (∀ (R E M : Iota), Iff (greatest M R E) (And (member M E) (∀ (X : Iota), member X E → apply R X M))) True
% 285.34/285.56 Clause #6 (by assumption #[]): Eq (∀ (R E M : Iota), Iff (max M R E) (And (member M E) (∀ (X : Iota), And (member X E) (apply R M X) → Eq M X))) True
% 285.34/285.56 Clause #10 (by assumption #[]): Eq (Not (∀ (R E M : Iota), And (total_order R E) (max M R E) → greatest M R E)) True
% 285.34/285.56 Clause #11 (by clausification #[10]): Eq (∀ (R E M : Iota), And (total_order R E) (max M R E) → greatest M R E) False
% 285.34/285.56 Clause #12 (by clausification #[11]): ∀ (a : Iota),
% 285.34/285.56 Eq (Not (∀ (E M : Iota), And (total_order (skS.0 0 a) E) (max M (skS.0 0 a) E) → greatest M (skS.0 0 a) E)) True
% 285.34/285.56 Clause #13 (by clausification #[12]): ∀ (a : Iota),
% 285.34/285.56 Eq (∀ (E M : Iota), And (total_order (skS.0 0 a) E) (max M (skS.0 0 a) E) → greatest M (skS.0 0 a) E) False
% 285.34/285.56 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota),
% 285.34/285.56 Eq
% 285.34/285.56 (Not
% 285.34/285.56 (∀ (M : Iota),
% 285.34/285.56 And (total_order (skS.0 0 a) (skS.0 1 a a_1)) (max M (skS.0 0 a) (skS.0 1 a a_1)) →
% 285.34/285.56 greatest M (skS.0 0 a) (skS.0 1 a a_1)))
% 285.34/285.56 True
% 285.34/285.56 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota),
% 285.34/285.56 Eq
% 285.34/285.56 (∀ (M : Iota),
% 285.34/285.56 And (total_order (skS.0 0 a) (skS.0 1 a a_1)) (max M (skS.0 0 a) (skS.0 1 a a_1)) →
% 285.34/285.56 greatest M (skS.0 0 a) (skS.0 1 a a_1))
% 285.34/285.56 False
% 285.34/285.56 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 : Iota),
% 285.34/285.56 Eq
% 285.34/285.56 (Not
% 285.34/285.56 (And (total_order (skS.0 0 a) (skS.0 1 a a_1)) (max (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 1 a a_1)) →
% 285.34/285.56 greatest (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 1 a a_1)))
% 285.34/285.56 True
% 285.34/285.56 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 : Iota),
% 285.34/285.56 Eq
% 285.34/285.56 (And (total_order (skS.0 0 a) (skS.0 1 a a_1)) (max (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 1 a a_1)) →
% 285.34/285.56 greatest (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 1 a a_1))
% 285.34/285.56 False
% 285.34/285.56 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : Iota),
% 285.34/285.56 Eq (And (total_order (skS.0 0 a) (skS.0 1 a a_1)) (max (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 1 a a_1))) True
% 285.34/285.56 Clause #19 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), Eq (greatest (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 1 a a_1)) False
% 285.34/285.56 Clause #20 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), Eq (max (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 1 a a_1)) True
% 285.34/285.56 Clause #21 (by clausification #[18]): ∀ (a a_1 : Iota), Eq (total_order (skS.0 0 a) (skS.0 1 a a_1)) True
% 285.34/285.56 Clause #33 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (E M : Iota), Iff (upper_bound M a E) (∀ (X : Iota), member X E → apply a X M)) True
% 285.34/285.56 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Eq (∀ (M : Iota), Iff (upper_bound M a a_1) (∀ (X : Iota), member X a_1 → apply a X M)) True
% 285.34/285.56 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), Eq (Iff (upper_bound a a_1 a_2) (∀ (X : Iota), member X a_2 → apply a_1 X a)) True
% 285.34/285.56 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), Or (Eq (upper_bound a a_1 a_2) True) (Eq (∀ (X : Iota), member X a_2 → apply a_1 X a) False)
% 285.34/285.56 Clause #37 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), Or (Eq (upper_bound a a_1 a_2) False) (Eq (∀ (X : Iota), member X a_2 → apply a_1 X a) True)
% 285.34/285.56 Clause #38 (by clausification #[36]): ∀ (a a_1 a_2 a_3 : Iota),
% 285.34/285.56 Or (Eq (upper_bound a a_1 a_2) True)
% 285.43/285.59 (Eq (Not (member (skS.0 4 a_2 a_1 a a_3) a_2 → apply a_1 (skS.0 4 a_2 a_1 a a_3) a)) True)
% 285.43/285.59 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 a_3 : Iota),
% 285.43/285.59 Or (Eq (upper_bound a a_1 a_2) True)
% 285.43/285.59 (Eq (member (skS.0 4 a_2 a_1 a a_3) a_2 → apply a_1 (skS.0 4 a_2 a_1 a a_3) a) False)
% 285.43/285.59 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (upper_bound a a_1 a_2) True) (Eq (member (skS.0 4 a_2 a_1 a a_3) a_2) True)
% 285.43/285.59 Clause #41 (by clausification #[39]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (upper_bound a a_1 a_2) True) (Eq (apply a_1 (skS.0 4 a_2 a_1 a a_3) a) False)
% 285.43/285.59 Clause #42 (by clausification #[37]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (upper_bound a a_1 a_2) False) (Eq (member a_3 a_2 → apply a_1 a_3 a) True)
% 285.43/285.59 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota),
% 285.43/285.59 Or (Eq (upper_bound a a_1 a_2) False) (Or (Eq (member a_3 a_2) False) (Eq (apply a_1 a_3 a) True))
% 285.43/285.59 Clause #44 (by clausification #[0]): ∀ (a : Iota),
% 285.43/285.59 Eq
% 285.43/285.59 (∀ (E : Iota),
% 285.43/285.59 Iff (order a E)
% 285.43/285.59 (And
% 285.43/285.59 (And (∀ (X : Iota), member X E → apply a X X)
% 285.43/285.59 (∀ (X Y : Iota), And (member X E) (member Y E) → And (apply a X Y) (apply a Y X) → Eq X Y))
% 285.43/285.59 (∀ (X Y Z : Iota),
% 285.43/285.59 And (And (member X E) (member Y E)) (member Z E) → And (apply a X Y) (apply a Y Z) → apply a X Z)))
% 285.43/285.59 True
% 285.43/285.59 Clause #45 (by clausification #[44]): ∀ (a a_1 : Iota),
% 285.43/285.59 Eq
% 285.43/285.59 (Iff (order a a_1)
% 285.43/285.59 (And
% 285.43/285.59 (And (∀ (X : Iota), member X a_1 → apply a X X)
% 285.43/285.59 (∀ (X Y : Iota), And (member X a_1) (member Y a_1) → And (apply a X Y) (apply a Y X) → Eq X Y))
% 285.43/285.59 (∀ (X Y Z : Iota),
% 285.43/285.59 And (And (member X a_1) (member Y a_1)) (member Z a_1) → And (apply a X Y) (apply a Y Z) → apply a X Z)))
% 285.43/285.59 True
% 285.43/285.59 Clause #47 (by clausification #[45]): ∀ (a a_1 : Iota),
% 285.43/285.59 Or (Eq (order a a_1) False)
% 285.43/285.59 (Eq
% 285.43/285.59 (And
% 285.43/285.59 (And (∀ (X : Iota), member X a_1 → apply a X X)
% 285.43/285.59 (∀ (X Y : Iota), And (member X a_1) (member Y a_1) → And (apply a X Y) (apply a Y X) → Eq X Y))
% 285.43/285.59 (∀ (X Y Z : Iota),
% 285.43/285.59 And (And (member X a_1) (member Y a_1)) (member Z a_1) → And (apply a X Y) (apply a Y Z) → apply a X Z))
% 285.43/285.59 True)
% 285.43/285.59 Clause #95 (by clausification #[6]): ∀ (a : Iota),
% 285.43/285.59 Eq (∀ (E M : Iota), Iff (max M a E) (And (member M E) (∀ (X : Iota), And (member X E) (apply a M X) → Eq M X))) True
% 285.43/285.59 Clause #96 (by clausification #[95]): ∀ (a a_1 : Iota),
% 285.43/285.59 Eq (∀ (M : Iota), Iff (max M a a_1) (And (member M a_1) (∀ (X : Iota), And (member X a_1) (apply a M X) → Eq M X)))
% 285.43/285.59 True
% 285.43/285.59 Clause #97 (by clausification #[96]): ∀ (a a_1 a_2 : Iota),
% 285.43/285.59 Eq (Iff (max a a_1 a_2) (And (member a a_2) (∀ (X : Iota), And (member X a_2) (apply a_1 a X) → Eq a X))) True
% 285.43/285.59 Clause #99 (by clausification #[97]): ∀ (a a_1 a_2 : Iota),
% 285.43/285.59 Or (Eq (max a a_1 a_2) False)
% 285.43/285.59 (Eq (And (member a a_2) (∀ (X : Iota), And (member X a_2) (apply a_1 a X) → Eq a X)) True)
% 285.43/285.59 Clause #112 (by clausification #[1]): ∀ (a : Iota),
% 285.43/285.59 Eq
% 285.43/285.59 (∀ (E : Iota),
% 285.43/285.59 Iff (total_order a E)
% 285.43/285.59 (And (order a E) (∀ (X Y : Iota), And (member X E) (member Y E) → Or (apply a X Y) (apply a Y X))))
% 285.43/285.59 True
% 285.43/285.59 Clause #113 (by clausification #[112]): ∀ (a a_1 : Iota),
% 285.43/285.59 Eq
% 285.43/285.59 (Iff (total_order a a_1)
% 285.43/285.59 (And (order a a_1) (∀ (X Y : Iota), And (member X a_1) (member Y a_1) → Or (apply a X Y) (apply a Y X))))
% 285.43/285.59 True
% 285.43/285.59 Clause #115 (by clausification #[113]): ∀ (a a_1 : Iota),
% 285.43/285.59 Or (Eq (total_order a a_1) False)
% 285.43/285.59 (Eq (And (order a a_1) (∀ (X Y : Iota), And (member X a_1) (member Y a_1) → Or (apply a X Y) (apply a Y X))) True)
% 285.43/285.59 Clause #125 (by clausification #[99]): ∀ (a a_1 a_2 : Iota),
% 285.43/285.59 Or (Eq (max a a_1 a_2) False) (Eq (∀ (X : Iota), And (member X a_2) (apply a_1 a X) → Eq a X) True)
% 285.43/285.59 Clause #126 (by clausification #[99]): ∀ (a a_1 a_2 : Iota), Or (Eq (max a a_1 a_2) False) (Eq (member a a_2) True)
% 285.43/285.59 Clause #127 (by clausification #[125]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (max a a_1 a_2) False) (Eq (And (member a_3 a_2) (apply a_1 a a_3) → Eq a a_3) True)
% 285.43/285.59 Clause #128 (by clausification #[127]): ∀ (a a_1 a_2 a_3 : Iota),
% 285.46/285.61 Or (Eq (max a a_1 a_2) False) (Or (Eq (And (member a_3 a_2) (apply a_1 a a_3)) False) (Eq (Eq a a_3) True))
% 285.46/285.61 Clause #129 (by clausification #[128]): ∀ (a a_1 a_2 a_3 : Iota),
% 285.46/285.61 Or (Eq (max a a_1 a_2) False) (Or (Eq (Eq a a_3) True) (Or (Eq (member a_3 a_2) False) (Eq (apply a_1 a a_3) False)))
% 285.46/285.61 Clause #130 (by clausification #[129]): ∀ (a a_1 a_2 a_3 : Iota),
% 285.46/285.61 Or (Eq (max a a_1 a_2) False) (Or (Eq (member a_3 a_2) False) (Or (Eq (apply a_1 a a_3) False) (Eq a a_3)))
% 285.46/285.61 Clause #131 (by superposition #[130, 20]): ∀ (a a_1 a_2 a_3 : Iota),
% 285.46/285.61 Or (Eq (member a (skS.0 1 a_1 a_2)) False)
% 285.46/285.61 (Or (Eq (apply (skS.0 0 a_1) (skS.0 2 a_1 a_2 a_3) a) False) (Or (Eq (skS.0 2 a_1 a_2 a_3) a) (Eq False True)))
% 285.46/285.61 Clause #132 (by superposition #[126, 20]): ∀ (a a_1 a_2 : Iota), Or (Eq (member (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True) (Eq False True)
% 285.46/285.61 Clause #152 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (E M : Iota), Iff (greatest M a E) (And (member M E) (∀ (X : Iota), member X E → apply a X M))) True
% 285.46/285.61 Clause #153 (by clausification #[152]): ∀ (a a_1 : Iota),
% 285.46/285.61 Eq (∀ (M : Iota), Iff (greatest M a a_1) (And (member M a_1) (∀ (X : Iota), member X a_1 → apply a X M))) True
% 285.46/285.61 Clause #154 (by clausification #[153]): ∀ (a a_1 a_2 : Iota),
% 285.46/285.61 Eq (Iff (greatest a a_1 a_2) (And (member a a_2) (∀ (X : Iota), member X a_2 → apply a_1 X a))) True
% 285.46/285.61 Clause #155 (by clausification #[154]): ∀ (a a_1 a_2 : Iota),
% 285.46/285.61 Or (Eq (greatest a a_1 a_2) True) (Eq (And (member a a_2) (∀ (X : Iota), member X a_2 → apply a_1 X a)) False)
% 285.46/285.61 Clause #157 (by clausification #[155]): ∀ (a a_1 a_2 : Iota),
% 285.46/285.61 Or (Eq (greatest a a_1 a_2) True)
% 285.46/285.61 (Or (Eq (member a a_2) False) (Eq (∀ (X : Iota), member X a_2 → apply a_1 X a) False))
% 285.46/285.61 Clause #158 (by clausification #[157]): ∀ (a a_1 a_2 a_3 : Iota),
% 285.46/285.61 Or (Eq (greatest a a_1 a_2) True)
% 285.46/285.61 (Or (Eq (member a a_2) False)
% 285.46/285.61 (Eq (Not (member (skS.0 16 a_2 a_1 a a_3) a_2 → apply a_1 (skS.0 16 a_2 a_1 a a_3) a)) True))
% 285.46/285.61 Clause #159 (by clausification #[158]): ∀ (a a_1 a_2 a_3 : Iota),
% 285.46/285.61 Or (Eq (greatest a a_1 a_2) True)
% 285.46/285.61 (Or (Eq (member a a_2) False)
% 285.46/285.61 (Eq (member (skS.0 16 a_2 a_1 a a_3) a_2 → apply a_1 (skS.0 16 a_2 a_1 a a_3) a) False))
% 285.46/285.61 Clause #160 (by clausification #[159]): ∀ (a a_1 a_2 a_3 : Iota),
% 285.46/285.61 Or (Eq (greatest a a_1 a_2) True) (Or (Eq (member a a_2) False) (Eq (member (skS.0 16 a_2 a_1 a a_3) a_2) True))
% 285.46/285.61 Clause #161 (by clausification #[159]): ∀ (a a_1 a_2 a_3 : Iota),
% 285.46/285.61 Or (Eq (greatest a a_1 a_2) True) (Or (Eq (member a a_2) False) (Eq (apply a_1 (skS.0 16 a_2 a_1 a a_3) a) False))
% 285.46/285.61 Clause #171 (by clausification #[115]): ∀ (a a_1 : Iota),
% 285.46/285.61 Or (Eq (total_order a a_1) False)
% 285.46/285.61 (Eq (∀ (X Y : Iota), And (member X a_1) (member Y a_1) → Or (apply a X Y) (apply a Y X)) True)
% 285.46/285.61 Clause #172 (by clausification #[115]): ∀ (a a_1 : Iota), Or (Eq (total_order a a_1) False) (Eq (order a a_1) True)
% 285.46/285.61 Clause #173 (by clausification #[171]): ∀ (a a_1 a_2 : Iota),
% 285.46/285.61 Or (Eq (total_order a a_1) False)
% 285.46/285.61 (Eq (∀ (Y : Iota), And (member a_2 a_1) (member Y a_1) → Or (apply a a_2 Y) (apply a Y a_2)) True)
% 285.46/285.62 Clause #174 (by clausification #[173]): ∀ (a a_1 a_2 a_3 : Iota),
% 285.46/285.62 Or (Eq (total_order a a_1) False)
% 285.46/285.62 (Eq (And (member a_2 a_1) (member a_3 a_1) → Or (apply a a_2 a_3) (apply a a_3 a_2)) True)
% 285.46/285.62 Clause #175 (by clausification #[174]): ∀ (a a_1 a_2 a_3 : Iota),
% 285.46/285.62 Or (Eq (total_order a a_1) False)
% 285.46/285.62 (Or (Eq (And (member a_2 a_1) (member a_3 a_1)) False) (Eq (Or (apply a a_2 a_3) (apply a a_3 a_2)) True))
% 285.46/285.62 Clause #176 (by clausification #[175]): ∀ (a a_1 a_2 a_3 : Iota),
% 285.46/285.62 Or (Eq (total_order a a_1) False)
% 285.46/285.62 (Or (Eq (Or (apply a a_2 a_3) (apply a a_3 a_2)) True) (Or (Eq (member a_2 a_1) False) (Eq (member a_3 a_1) False)))
% 285.46/285.62 Clause #177 (by clausification #[176]): ∀ (a a_1 a_2 a_3 : Iota),
% 285.46/285.62 Or (Eq (total_order a a_1) False)
% 285.46/285.62 (Or (Eq (member a_2 a_1) False)
% 285.46/285.62 (Or (Eq (member a_3 a_1) False) (Or (Eq (apply a a_2 a_3) True) (Eq (apply a a_3 a_2) True))))
% 285.46/285.62 Clause #178 (by superposition #[177, 21]): ∀ (a a_1 a_2 a_3 : Iota),
% 285.46/285.64 Or (Eq (member a (skS.0 1 a_1 a_2)) False)
% 285.46/285.64 (Or (Eq (member a_3 (skS.0 1 a_1 a_2)) False)
% 285.46/285.64 (Or (Eq (apply (skS.0 0 a_1) a a_3) True) (Or (Eq (apply (skS.0 0 a_1) a_3 a) True) (Eq False True))))
% 285.46/285.64 Clause #179 (by superposition #[172, 21]): ∀ (a a_1 : Iota), Or (Eq (order (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq False True)
% 285.46/285.64 Clause #180 (by clausification #[179]): ∀ (a a_1 : Iota), Eq (order (skS.0 0 a) (skS.0 1 a a_1)) True
% 285.46/285.64 Clause #202 (by clausification #[132]): ∀ (a a_1 a_2 : Iota), Eq (member (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True
% 285.46/285.64 Clause #206 (by superposition #[202, 160]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 285.46/285.64 Or (Eq (greatest (skS.0 2 a a_1 a_2) a_3 (skS.0 1 a a_1)) True)
% 285.46/285.64 (Or (Eq True False) (Eq (member (skS.0 16 (skS.0 1 a a_1) a_3 (skS.0 2 a a_1 a_2) a_4) (skS.0 1 a a_1)) True))
% 285.46/285.64 Clause #266 (by superposition #[161, 202]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 285.46/285.64 Or (Eq (greatest (skS.0 2 a a_1 a_2) a_3 (skS.0 1 a a_1)) True)
% 285.46/285.64 (Or (Eq True False)
% 285.46/285.64 (Eq (apply a_3 (skS.0 16 (skS.0 1 a a_1) a_3 (skS.0 2 a a_1 a_2) a_4) (skS.0 2 a a_1 a_2)) False))
% 285.46/285.64 Clause #274 (by clausification #[47]): ∀ (a a_1 : Iota),
% 285.46/285.64 Or (Eq (order a a_1) False)
% 285.46/285.64 (Eq
% 285.46/285.64 (And (∀ (X : Iota), member X a_1 → apply a X X)
% 285.46/285.64 (∀ (X Y : Iota), And (member X a_1) (member Y a_1) → And (apply a X Y) (apply a Y X) → Eq X Y))
% 285.46/285.64 True)
% 285.46/285.64 Clause #285 (by clausification #[274]): ∀ (a a_1 : Iota), Or (Eq (order a a_1) False) (Eq (∀ (X : Iota), member X a_1 → apply a X X) True)
% 285.46/285.64 Clause #294 (by clausification #[285]): ∀ (a a_1 a_2 : Iota), Or (Eq (order a a_1) False) (Eq (member a_2 a_1 → apply a a_2 a_2) True)
% 285.46/285.64 Clause #295 (by clausification #[294]): ∀ (a a_1 a_2 : Iota), Or (Eq (order a a_1) False) (Or (Eq (member a_2 a_1) False) (Eq (apply a a_2 a_2) True))
% 285.46/285.64 Clause #296 (by superposition #[295, 180]): ∀ (a a_1 a_2 : Iota),
% 285.46/285.64 Or (Eq (member a (skS.0 1 a_1 a_2)) False) (Or (Eq (apply (skS.0 0 a_1) a a) True) (Eq False True))
% 285.46/285.64 Clause #297 (by clausification #[296]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (skS.0 1 a_1 a_2)) False) (Eq (apply (skS.0 0 a_1) a a) True)
% 285.46/285.64 Clause #298 (by superposition #[297, 202]): ∀ (a a_1 a_2 : Iota), Or (Eq (apply (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 2 a a_1 a_2)) True) (Eq False True)
% 285.46/285.64 Clause #311 (by clausification #[298]): ∀ (a a_1 a_2 : Iota), Eq (apply (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 2 a a_1 a_2)) True
% 285.46/285.64 Clause #349 (by clausification #[131]): ∀ (a a_1 a_2 a_3 : Iota),
% 285.46/285.64 Or (Eq (member a (skS.0 1 a_1 a_2)) False)
% 285.46/285.64 (Or (Eq (apply (skS.0 0 a_1) (skS.0 2 a_1 a_2 a_3) a) False) (Eq (skS.0 2 a_1 a_2 a_3) a))
% 285.46/285.64 Clause #352 (by superposition #[349, 40]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 285.46/285.64 Or (Eq (apply (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 4 (skS.0 1 a a_1) a_3 a_4 a_5)) False)
% 285.46/285.64 (Or (Eq (skS.0 2 a a_1 a_2) (skS.0 4 (skS.0 1 a a_1) a_3 a_4 a_5))
% 285.46/285.64 (Or (Eq (upper_bound a_4 a_3 (skS.0 1 a a_1)) True) (Eq False True)))
% 285.46/285.64 Clause #401 (by clausification #[178]): ∀ (a a_1 a_2 a_3 : Iota),
% 285.46/285.64 Or (Eq (member a (skS.0 1 a_1 a_2)) False)
% 285.46/285.64 (Or (Eq (member a_3 (skS.0 1 a_1 a_2)) False)
% 285.46/285.64 (Or (Eq (apply (skS.0 0 a_1) a a_3) True) (Eq (apply (skS.0 0 a_1) a_3 a) True)))
% 285.46/285.64 Clause #402 (by superposition #[401, 202]): ∀ (a a_1 a_2 a_3 : Iota),
% 285.46/285.64 Or (Eq (member a (skS.0 1 a_1 a_2)) False)
% 285.46/285.64 (Or (Eq (apply (skS.0 0 a_1) (skS.0 2 a_1 a_2 a_3) a) True)
% 285.46/285.64 (Or (Eq (apply (skS.0 0 a_1) a (skS.0 2 a_1 a_2 a_3)) True) (Eq False True)))
% 285.46/285.64 Clause #700 (by clausification #[402]): ∀ (a a_1 a_2 a_3 : Iota),
% 285.46/285.64 Or (Eq (member a (skS.0 1 a_1 a_2)) False)
% 285.46/285.64 (Or (Eq (apply (skS.0 0 a_1) (skS.0 2 a_1 a_2 a_3) a) True) (Eq (apply (skS.0 0 a_1) a (skS.0 2 a_1 a_2 a_3)) True))
% 285.46/285.64 Clause #703 (by superposition #[700, 40]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 285.46/285.64 Or (Eq (apply (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 4 (skS.0 1 a a_1) a_3 a_4 a_5)) True)
% 285.46/285.64 (Or (Eq (apply (skS.0 0 a) (skS.0 4 (skS.0 1 a a_1) a_3 a_4 a_5) (skS.0 2 a a_1 a_2)) True)
% 285.46/285.64 (Or (Eq (upper_bound a_4 a_3 (skS.0 1 a a_1)) True) (Eq False True)))
% 285.46/285.64 Clause #1308 (by clausification #[206]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 285.46/285.67 Or (Eq (greatest (skS.0 2 a a_1 a_2) a_3 (skS.0 1 a a_1)) True)
% 285.46/285.67 (Eq (member (skS.0 16 (skS.0 1 a a_1) a_3 (skS.0 2 a a_1 a_2) a_4) (skS.0 1 a a_1)) True)
% 285.46/285.67 Clause #1403 (by clausification #[266]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 285.46/285.67 Or (Eq (greatest (skS.0 2 a a_1 a_2) a_3 (skS.0 1 a a_1)) True)
% 285.46/285.67 (Eq (apply a_3 (skS.0 16 (skS.0 1 a a_1) a_3 (skS.0 2 a a_1 a_2) a_4) (skS.0 2 a a_1 a_2)) False)
% 285.46/285.67 Clause #7133 (by clausification #[352]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 285.46/285.67 Or (Eq (apply (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 4 (skS.0 1 a a_1) a_3 a_4 a_5)) False)
% 285.46/285.67 (Or (Eq (skS.0 2 a a_1 a_2) (skS.0 4 (skS.0 1 a a_1) a_3 a_4 a_5)) (Eq (upper_bound a_4 a_3 (skS.0 1 a a_1)) True))
% 285.46/285.67 Clause #13845 (by clausification #[703]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 285.46/285.67 Or (Eq (apply (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 4 (skS.0 1 a a_1) a_3 a_4 a_5)) True)
% 285.46/285.67 (Or (Eq (apply (skS.0 0 a) (skS.0 4 (skS.0 1 a a_1) a_3 a_4 a_5) (skS.0 2 a a_1 a_2)) True)
% 285.46/285.67 (Eq (upper_bound a_4 a_3 (skS.0 1 a a_1)) True))
% 285.46/285.67 Clause #13846 (by superposition #[13845, 7133]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 285.46/285.67 Or (Eq (apply (skS.0 0 a) (skS.0 4 (skS.0 1 a a_1) a_2 a_3 a_4) (skS.0 2 a a_1 a_5)) True)
% 285.46/285.67 (Or (Eq (upper_bound a_3 a_2 (skS.0 1 a a_1)) True)
% 285.46/285.67 (Or (Eq True False)
% 285.46/285.67 (Or (Eq (skS.0 2 a a_1 a_5) (skS.0 4 (skS.0 1 a a_1) a_2 a_3 a_4))
% 285.46/285.67 (Eq (upper_bound a_3 a_2 (skS.0 1 a a_1)) True))))
% 285.46/285.67 Clause #15511 (by clausification #[13846]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 285.46/285.67 Or (Eq (apply (skS.0 0 a) (skS.0 4 (skS.0 1 a a_1) a_2 a_3 a_4) (skS.0 2 a a_1 a_5)) True)
% 285.46/285.67 (Or (Eq (upper_bound a_3 a_2 (skS.0 1 a a_1)) True)
% 285.46/285.67 (Or (Eq (skS.0 2 a a_1 a_5) (skS.0 4 (skS.0 1 a a_1) a_2 a_3 a_4))
% 285.46/285.67 (Eq (upper_bound a_3 a_2 (skS.0 1 a a_1)) True)))
% 285.46/285.67 Clause #15512 (by eliminate duplicate literals #[15511]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 285.46/285.67 Or (Eq (apply (skS.0 0 a) (skS.0 4 (skS.0 1 a a_1) a_2 a_3 a_4) (skS.0 2 a a_1 a_5)) True)
% 285.46/285.67 (Or (Eq (upper_bound a_3 a_2 (skS.0 1 a a_1)) True) (Eq (skS.0 2 a a_1 a_5) (skS.0 4 (skS.0 1 a a_1) a_2 a_3 a_4)))
% 285.46/285.67 Clause #15513 (by superposition #[15512, 41]): ∀ (a a_1 a_2 a_3 : Iota),
% 285.46/285.67 Or (Eq (upper_bound (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 1 a a_1)) True)
% 285.46/285.67 (Or (Eq (skS.0 2 a a_1 a_2) (skS.0 4 (skS.0 1 a a_1) (skS.0 0 a) (skS.0 2 a a_1 a_2) a_3))
% 285.46/285.67 (Or (Eq (upper_bound (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq True False)))
% 285.46/285.67 Clause #31823 (by clausification #[15513]): ∀ (a a_1 a_2 a_3 : Iota),
% 285.46/285.67 Or (Eq (upper_bound (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 1 a a_1)) True)
% 285.46/285.67 (Or (Eq (skS.0 2 a a_1 a_2) (skS.0 4 (skS.0 1 a a_1) (skS.0 0 a) (skS.0 2 a a_1 a_2) a_3))
% 285.46/285.67 (Eq (upper_bound (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 1 a a_1)) True))
% 285.46/285.67 Clause #31824 (by eliminate duplicate literals #[31823]): ∀ (a a_1 a_2 a_3 : Iota),
% 285.46/285.67 Or (Eq (upper_bound (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 1 a a_1)) True)
% 285.46/285.67 (Eq (skS.0 2 a a_1 a_2) (skS.0 4 (skS.0 1 a a_1) (skS.0 0 a) (skS.0 2 a a_1 a_2) a_3))
% 285.46/285.67 Clause #31826 (by superposition #[31824, 41]): ∀ (a a_1 a_2 : Iota),
% 285.46/285.67 Or (Eq (upper_bound (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 1 a a_1)) True)
% 285.46/285.67 (Or (Eq (upper_bound (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 1 a a_1)) True)
% 285.46/285.67 (Eq (apply (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 2 a a_1 a_2)) False))
% 285.46/285.67 Clause #31880 (by eliminate duplicate literals #[31826]): ∀ (a a_1 a_2 : Iota),
% 285.46/285.67 Or (Eq (upper_bound (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 1 a a_1)) True)
% 285.46/285.67 (Eq (apply (skS.0 0 a) (skS.0 2 a a_1 a_2) (skS.0 2 a a_1 a_2)) False)
% 285.46/285.67 Clause #31881 (by superposition #[31880, 311]): ∀ (a a_1 a_2 : Iota), Or (Eq (upper_bound (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq False True)
% 285.46/285.67 Clause #31885 (by clausification #[31881]): ∀ (a a_1 a_2 : Iota), Eq (upper_bound (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 1 a a_1)) True
% 285.46/285.67 Clause #31891 (by superposition #[31885, 43]): ∀ (a a_1 a_2 a_3 : Iota),
% 285.46/285.67 Or (Eq True False)
% 285.46/285.67 (Or (Eq (member a (skS.0 1 a_1 a_2)) False) (Eq (apply (skS.0 0 a_1) a (skS.0 2 a_1 a_2 a_3)) True))
% 285.46/285.67 Clause #31892 (by clausification #[31891]): ∀ (a a_1 a_2 a_3 : Iota),
% 285.96/286.16 Or (Eq (member a (skS.0 1 a_1 a_2)) False) (Eq (apply (skS.0 0 a_1) a (skS.0 2 a_1 a_2 a_3)) True)
% 285.96/286.16 Clause #31896 (by superposition #[31892, 1308]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 285.96/286.16 Or (Eq (apply (skS.0 0 a) (skS.0 16 (skS.0 1 a a_1) a_2 (skS.0 2 a a_1 a_3) a_4) (skS.0 2 a a_1 a_5)) True)
% 285.96/286.16 (Or (Eq (greatest (skS.0 2 a a_1 a_3) a_2 (skS.0 1 a a_1)) True) (Eq False True))
% 285.96/286.16 Clause #32674 (by clausification #[31896]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 285.96/286.16 Or (Eq (apply (skS.0 0 a) (skS.0 16 (skS.0 1 a a_1) a_2 (skS.0 2 a a_1 a_3) a_4) (skS.0 2 a a_1 a_5)) True)
% 285.96/286.16 (Eq (greatest (skS.0 2 a a_1 a_3) a_2 (skS.0 1 a a_1)) True)
% 285.96/286.16 Clause #32675 (by superposition #[32674, 1403]): ∀ (a a_1 a_2 : Iota),
% 285.96/286.16 Or (Eq (greatest (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 1 a a_1)) True)
% 285.96/286.16 (Or (Eq (greatest (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq True False))
% 285.96/286.16 Clause #32676 (by clausification #[32675]): ∀ (a a_1 a_2 : Iota),
% 285.96/286.16 Or (Eq (greatest (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 1 a a_1)) True)
% 285.96/286.16 (Eq (greatest (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 1 a a_1)) True)
% 285.96/286.16 Clause #32677 (by eliminate duplicate literals #[32676]): ∀ (a a_1 a_2 : Iota), Eq (greatest (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 1 a a_1)) True
% 285.96/286.16 Clause #32678 (by superposition #[32677, 19]): Eq True False
% 285.96/286.16 Clause #32680 (by clausification #[32678]): False
% 285.96/286.16 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------