TSTP Solution File: SET804+4 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET804+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n024.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 14:47:39 EDT 2023
% Result : Theorem 10.23s 10.41s
% Output : Proof 10.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET804+4 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.15 % Command : duper %s
% 0.14/0.36 % Computer : n024.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 : Sat Aug 26 12:19:09 EDT 2023
% 0.14/0.36 % CPUTime :
% 10.23/10.41 SZS status Theorem for theBenchmark.p
% 10.23/10.41 SZS output start Proof for theBenchmark.p
% 10.23/10.41 Clause #5 (by assumption #[]): Eq (∀ (R E M : Iota), Iff (least M R E) (And (member M E) (∀ (X : Iota), member X E → apply R M X))) True
% 10.23/10.41 Clause #7 (by assumption #[]): Eq (∀ (R E M : Iota), Iff (min M R E) (And (member M E) (∀ (X : Iota), And (member X E) (apply R X M) → Eq M X))) True
% 10.23/10.41 Clause #10 (by assumption #[]): Eq
% 10.23/10.41 (Not
% 10.23/10.41 (∀ (R E : Iota),
% 10.23/10.41 order R E → ∀ (M1 M2 : Iota), And (And (min M1 R E) (min M2 R E)) (Ne M1 M2) → Not (Exists fun M => least M R E)))
% 10.23/10.41 True
% 10.23/10.41 Clause #33 (by clausification #[10]): Eq
% 10.23/10.41 (∀ (R E : Iota),
% 10.23/10.41 order R E → ∀ (M1 M2 : Iota), And (And (min M1 R E) (min M2 R E)) (Ne M1 M2) → Not (Exists fun M => least M R E))
% 10.23/10.41 False
% 10.23/10.41 Clause #34 (by clausification #[33]): ∀ (a : Iota),
% 10.23/10.41 Eq
% 10.23/10.41 (Not
% 10.23/10.41 (∀ (E : Iota),
% 10.23/10.41 order (skS.0 2 a) E →
% 10.23/10.41 ∀ (M1 M2 : Iota),
% 10.23/10.41 And (And (min M1 (skS.0 2 a) E) (min M2 (skS.0 2 a) E)) (Ne M1 M2) →
% 10.23/10.41 Not (Exists fun M => least M (skS.0 2 a) E)))
% 10.23/10.41 True
% 10.23/10.41 Clause #35 (by clausification #[34]): ∀ (a : Iota),
% 10.23/10.41 Eq
% 10.23/10.41 (∀ (E : Iota),
% 10.23/10.41 order (skS.0 2 a) E →
% 10.23/10.41 ∀ (M1 M2 : Iota),
% 10.23/10.41 And (And (min M1 (skS.0 2 a) E) (min M2 (skS.0 2 a) E)) (Ne M1 M2) →
% 10.23/10.41 Not (Exists fun M => least M (skS.0 2 a) E))
% 10.23/10.41 False
% 10.23/10.41 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota),
% 10.23/10.41 Eq
% 10.23/10.41 (Not
% 10.23/10.41 (order (skS.0 2 a) (skS.0 3 a a_1) →
% 10.23/10.41 ∀ (M1 M2 : Iota),
% 10.23/10.41 And (And (min M1 (skS.0 2 a) (skS.0 3 a a_1)) (min M2 (skS.0 2 a) (skS.0 3 a a_1))) (Ne M1 M2) →
% 10.23/10.41 Not (Exists fun M => least M (skS.0 2 a) (skS.0 3 a a_1))))
% 10.23/10.41 True
% 10.23/10.41 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota),
% 10.23/10.41 Eq
% 10.23/10.41 (order (skS.0 2 a) (skS.0 3 a a_1) →
% 10.23/10.41 ∀ (M1 M2 : Iota),
% 10.23/10.41 And (And (min M1 (skS.0 2 a) (skS.0 3 a a_1)) (min M2 (skS.0 2 a) (skS.0 3 a a_1))) (Ne M1 M2) →
% 10.23/10.41 Not (Exists fun M => least M (skS.0 2 a) (skS.0 3 a a_1)))
% 10.23/10.41 False
% 10.23/10.41 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota),
% 10.23/10.41 Eq
% 10.23/10.41 (∀ (M1 M2 : Iota),
% 10.23/10.41 And (And (min M1 (skS.0 2 a) (skS.0 3 a a_1)) (min M2 (skS.0 2 a) (skS.0 3 a a_1))) (Ne M1 M2) →
% 10.23/10.41 Not (Exists fun M => least M (skS.0 2 a) (skS.0 3 a a_1)))
% 10.23/10.41 False
% 10.23/10.41 Clause #68 (by clausification #[7]): ∀ (a : Iota),
% 10.23/10.41 Eq (∀ (E M : Iota), Iff (min M a E) (And (member M E) (∀ (X : Iota), And (member X E) (apply a X M) → Eq M X))) True
% 10.23/10.41 Clause #69 (by clausification #[68]): ∀ (a a_1 : Iota),
% 10.23/10.41 Eq (∀ (M : Iota), Iff (min M a a_1) (And (member M a_1) (∀ (X : Iota), And (member X a_1) (apply a X M) → Eq M X)))
% 10.23/10.41 True
% 10.23/10.41 Clause #70 (by clausification #[69]): ∀ (a a_1 a_2 : Iota),
% 10.23/10.41 Eq (Iff (min a a_1 a_2) (And (member a a_2) (∀ (X : Iota), And (member X a_2) (apply a_1 X a) → Eq a X))) True
% 10.23/10.41 Clause #72 (by clausification #[70]): ∀ (a a_1 a_2 : Iota),
% 10.23/10.41 Or (Eq (min a a_1 a_2) False)
% 10.23/10.41 (Eq (And (member a a_2) (∀ (X : Iota), And (member X a_2) (apply a_1 X a) → Eq a X)) True)
% 10.23/10.41 Clause #85 (by clausification #[72]): ∀ (a a_1 a_2 : Iota),
% 10.23/10.41 Or (Eq (min a a_1 a_2) False) (Eq (∀ (X : Iota), And (member X a_2) (apply a_1 X a) → Eq a X) True)
% 10.23/10.41 Clause #86 (by clausification #[72]): ∀ (a a_1 a_2 : Iota), Or (Eq (min a a_1 a_2) False) (Eq (member a a_2) True)
% 10.23/10.41 Clause #87 (by clausification #[85]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (min a a_1 a_2) False) (Eq (And (member a_3 a_2) (apply a_1 a_3 a) → Eq a a_3) True)
% 10.23/10.41 Clause #88 (by clausification #[87]): ∀ (a a_1 a_2 a_3 : Iota),
% 10.23/10.41 Or (Eq (min a a_1 a_2) False) (Or (Eq (And (member a_3 a_2) (apply a_1 a_3 a)) False) (Eq (Eq a a_3) True))
% 10.23/10.41 Clause #89 (by clausification #[88]): ∀ (a a_1 a_2 a_3 : Iota),
% 10.23/10.41 Or (Eq (min 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_3 a) False)))
% 10.23/10.41 Clause #90 (by clausification #[89]): ∀ (a a_1 a_2 a_3 : Iota),
% 10.23/10.41 Or (Eq (min a a_1 a_2) False) (Or (Eq (member a_3 a_2) False) (Or (Eq (apply a_1 a_3 a) False) (Eq a a_3)))
% 10.23/10.41 Clause #128 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (E M : Iota), Iff (least M a E) (And (member M E) (∀ (X : Iota), member X E → apply a M X))) True
% 10.23/10.43 Clause #129 (by clausification #[128]): ∀ (a a_1 : Iota),
% 10.23/10.43 Eq (∀ (M : Iota), Iff (least M a a_1) (And (member M a_1) (∀ (X : Iota), member X a_1 → apply a M X))) True
% 10.23/10.43 Clause #130 (by clausification #[129]): ∀ (a a_1 a_2 : Iota), Eq (Iff (least a a_1 a_2) (And (member a a_2) (∀ (X : Iota), member X a_2 → apply a_1 a X))) True
% 10.23/10.43 Clause #132 (by clausification #[130]): ∀ (a a_1 a_2 : Iota),
% 10.23/10.43 Or (Eq (least a a_1 a_2) False) (Eq (And (member a a_2) (∀ (X : Iota), member X a_2 → apply a_1 a X)) True)
% 10.23/10.43 Clause #143 (by clausification #[132]): ∀ (a a_1 a_2 : Iota), Or (Eq (least a a_1 a_2) False) (Eq (∀ (X : Iota), member X a_2 → apply a_1 a X) True)
% 10.23/10.43 Clause #144 (by clausification #[132]): ∀ (a a_1 a_2 : Iota), Or (Eq (least a a_1 a_2) False) (Eq (member a a_2) True)
% 10.23/10.43 Clause #145 (by clausification #[143]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (least a a_1 a_2) False) (Eq (member a_3 a_2 → apply a_1 a a_3) True)
% 10.23/10.43 Clause #146 (by clausification #[145]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (least a a_1 a_2) False) (Or (Eq (member a_3 a_2) False) (Eq (apply a_1 a a_3) True))
% 10.23/10.43 Clause #219 (by clausification #[39]): ∀ (a a_1 a_2 : Iota),
% 10.23/10.43 Eq
% 10.23/10.43 (Not
% 10.23/10.43 (∀ (M2 : Iota),
% 10.23/10.43 And (And (min (skS.0 18 a a_1 a_2) (skS.0 2 a) (skS.0 3 a a_1)) (min M2 (skS.0 2 a) (skS.0 3 a a_1)))
% 10.23/10.43 (Ne (skS.0 18 a a_1 a_2) M2) →
% 10.23/10.43 Not (Exists fun M => least M (skS.0 2 a) (skS.0 3 a a_1))))
% 10.23/10.43 True
% 10.23/10.43 Clause #220 (by clausification #[219]): ∀ (a a_1 a_2 : Iota),
% 10.23/10.43 Eq
% 10.23/10.43 (∀ (M2 : Iota),
% 10.23/10.43 And (And (min (skS.0 18 a a_1 a_2) (skS.0 2 a) (skS.0 3 a a_1)) (min M2 (skS.0 2 a) (skS.0 3 a a_1)))
% 10.23/10.43 (Ne (skS.0 18 a a_1 a_2) M2) →
% 10.23/10.43 Not (Exists fun M => least M (skS.0 2 a) (skS.0 3 a a_1)))
% 10.23/10.43 False
% 10.23/10.43 Clause #221 (by clausification #[220]): ∀ (a a_1 a_2 a_3 : Iota),
% 10.23/10.43 Eq
% 10.23/10.43 (Not
% 10.23/10.43 (And
% 10.23/10.43 (And (min (skS.0 18 a a_1 a_2) (skS.0 2 a) (skS.0 3 a a_1))
% 10.23/10.43 (min (skS.0 19 a a_1 a_2 a_3) (skS.0 2 a) (skS.0 3 a a_1)))
% 10.23/10.43 (Ne (skS.0 18 a a_1 a_2) (skS.0 19 a a_1 a_2 a_3)) →
% 10.23/10.43 Not (Exists fun M => least M (skS.0 2 a) (skS.0 3 a a_1))))
% 10.23/10.43 True
% 10.23/10.43 Clause #222 (by clausification #[221]): ∀ (a a_1 a_2 a_3 : Iota),
% 10.23/10.43 Eq
% 10.23/10.43 (And
% 10.23/10.43 (And (min (skS.0 18 a a_1 a_2) (skS.0 2 a) (skS.0 3 a a_1))
% 10.23/10.43 (min (skS.0 19 a a_1 a_2 a_3) (skS.0 2 a) (skS.0 3 a a_1)))
% 10.23/10.43 (Ne (skS.0 18 a a_1 a_2) (skS.0 19 a a_1 a_2 a_3)) →
% 10.23/10.43 Not (Exists fun M => least M (skS.0 2 a) (skS.0 3 a a_1)))
% 10.23/10.43 False
% 10.23/10.43 Clause #223 (by clausification #[222]): ∀ (a a_1 a_2 a_3 : Iota),
% 10.23/10.43 Eq
% 10.23/10.43 (And
% 10.23/10.43 (And (min (skS.0 18 a a_1 a_2) (skS.0 2 a) (skS.0 3 a a_1))
% 10.23/10.43 (min (skS.0 19 a a_1 a_2 a_3) (skS.0 2 a) (skS.0 3 a a_1)))
% 10.23/10.43 (Ne (skS.0 18 a a_1 a_2) (skS.0 19 a a_1 a_2 a_3)))
% 10.23/10.43 True
% 10.23/10.43 Clause #224 (by clausification #[222]): ∀ (a a_1 : Iota), Eq (Not (Exists fun M => least M (skS.0 2 a) (skS.0 3 a a_1))) False
% 10.23/10.43 Clause #225 (by clausification #[223]): ∀ (a a_1 a_2 a_3 : Iota), Eq (Ne (skS.0 18 a a_1 a_2) (skS.0 19 a a_1 a_2 a_3)) True
% 10.23/10.43 Clause #226 (by clausification #[223]): ∀ (a a_1 a_2 a_3 : Iota),
% 10.23/10.43 Eq
% 10.23/10.43 (And (min (skS.0 18 a a_1 a_2) (skS.0 2 a) (skS.0 3 a a_1))
% 10.23/10.43 (min (skS.0 19 a a_1 a_2 a_3) (skS.0 2 a) (skS.0 3 a a_1)))
% 10.23/10.43 True
% 10.23/10.43 Clause #227 (by clausification #[225]): ∀ (a a_1 a_2 a_3 : Iota), Ne (skS.0 18 a a_1 a_2) (skS.0 19 a a_1 a_2 a_3)
% 10.23/10.43 Clause #228 (by clausification #[224]): ∀ (a a_1 : Iota), Eq (Exists fun M => least M (skS.0 2 a) (skS.0 3 a a_1)) True
% 10.23/10.43 Clause #229 (by clausification #[228]): ∀ (a a_1 a_2 : Iota), Eq (least (skS.0 20 a a_1 a_2) (skS.0 2 a) (skS.0 3 a a_1)) True
% 10.23/10.43 Clause #230 (by superposition #[229, 146]): ∀ (a a_1 a_2 a_3 : Iota),
% 10.23/10.43 Or (Eq True False)
% 10.23/10.43 (Or (Eq (member a (skS.0 3 a_1 a_2)) False) (Eq (apply (skS.0 2 a_1) (skS.0 20 a_1 a_2 a_3) a) True))
% 10.23/10.43 Clause #231 (by superposition #[229, 144]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (member (skS.0 20 a a_1 a_2) (skS.0 3 a a_1)) True)
% 10.23/10.43 Clause #232 (by clausification #[231]): ∀ (a a_1 a_2 : Iota), Eq (member (skS.0 20 a a_1 a_2) (skS.0 3 a a_1)) True
% 10.23/10.46 Clause #364 (by clausification #[230]): ∀ (a a_1 a_2 a_3 : Iota),
% 10.23/10.46 Or (Eq (member a (skS.0 3 a_1 a_2)) False) (Eq (apply (skS.0 2 a_1) (skS.0 20 a_1 a_2 a_3) a) True)
% 10.23/10.46 Clause #838 (by clausification #[226]): ∀ (a a_1 a_2 a_3 : Iota), Eq (min (skS.0 19 a a_1 a_2 a_3) (skS.0 2 a) (skS.0 3 a a_1)) True
% 10.23/10.46 Clause #839 (by clausification #[226]): ∀ (a a_1 a_2 : Iota), Eq (min (skS.0 18 a a_1 a_2) (skS.0 2 a) (skS.0 3 a a_1)) True
% 10.23/10.46 Clause #840 (by superposition #[838, 90]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 10.23/10.46 Or (Eq True False)
% 10.23/10.46 (Or (Eq (member a (skS.0 3 a_1 a_2)) False)
% 10.23/10.46 (Or (Eq (apply (skS.0 2 a_1) a (skS.0 19 a_1 a_2 a_3 a_4)) False) (Eq (skS.0 19 a_1 a_2 a_3 a_4) a)))
% 10.23/10.46 Clause #841 (by superposition #[838, 86]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq True False) (Eq (member (skS.0 19 a a_1 a_2 a_3) (skS.0 3 a a_1)) True)
% 10.23/10.46 Clause #842 (by clausification #[841]): ∀ (a a_1 a_2 a_3 : Iota), Eq (member (skS.0 19 a a_1 a_2 a_3) (skS.0 3 a a_1)) True
% 10.23/10.46 Clause #844 (by superposition #[842, 364]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 10.23/10.46 Or (Eq True False) (Eq (apply (skS.0 2 a) (skS.0 20 a a_1 a_2) (skS.0 19 a a_1 a_3 a_4)) True)
% 10.23/10.46 Clause #862 (by superposition #[839, 90]): ∀ (a a_1 a_2 a_3 : Iota),
% 10.23/10.46 Or (Eq True False)
% 10.23/10.46 (Or (Eq (member a (skS.0 3 a_1 a_2)) False)
% 10.23/10.46 (Or (Eq (apply (skS.0 2 a_1) a (skS.0 18 a_1 a_2 a_3)) False) (Eq (skS.0 18 a_1 a_2 a_3) a)))
% 10.23/10.46 Clause #863 (by superposition #[839, 86]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (member (skS.0 18 a a_1 a_2) (skS.0 3 a a_1)) True)
% 10.23/10.46 Clause #864 (by clausification #[863]): ∀ (a a_1 a_2 : Iota), Eq (member (skS.0 18 a a_1 a_2) (skS.0 3 a a_1)) True
% 10.23/10.46 Clause #866 (by superposition #[864, 364]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq True False) (Eq (apply (skS.0 2 a) (skS.0 20 a a_1 a_2) (skS.0 18 a a_1 a_3)) True)
% 10.23/10.46 Clause #886 (by clausification #[866]): ∀ (a a_1 a_2 a_3 : Iota), Eq (apply (skS.0 2 a) (skS.0 20 a a_1 a_2) (skS.0 18 a a_1 a_3)) True
% 10.23/10.46 Clause #887 (by clausification #[844]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (apply (skS.0 2 a) (skS.0 20 a a_1 a_2) (skS.0 19 a a_1 a_3 a_4)) True
% 10.23/10.46 Clause #889 (by clausification #[862]): ∀ (a a_1 a_2 a_3 : Iota),
% 10.23/10.46 Or (Eq (member a (skS.0 3 a_1 a_2)) False)
% 10.23/10.46 (Or (Eq (apply (skS.0 2 a_1) a (skS.0 18 a_1 a_2 a_3)) False) (Eq (skS.0 18 a_1 a_2 a_3) a))
% 10.23/10.46 Clause #890 (by superposition #[889, 232]): ∀ (a a_1 a_2 a_3 : Iota),
% 10.23/10.46 Or (Eq (apply (skS.0 2 a) (skS.0 20 a a_1 a_2) (skS.0 18 a a_1 a_3)) False)
% 10.23/10.46 (Or (Eq (skS.0 18 a a_1 a_3) (skS.0 20 a a_1 a_2)) (Eq False True))
% 10.23/10.46 Clause #921 (by clausification #[840]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 10.23/10.46 Or (Eq (member a (skS.0 3 a_1 a_2)) False)
% 10.23/10.46 (Or (Eq (apply (skS.0 2 a_1) a (skS.0 19 a_1 a_2 a_3 a_4)) False) (Eq (skS.0 19 a_1 a_2 a_3 a_4) a))
% 10.23/10.46 Clause #926 (by superposition #[921, 864]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 10.23/10.46 Or (Eq (apply (skS.0 2 a) (skS.0 18 a a_1 a_2) (skS.0 19 a a_1 a_3 a_4)) False)
% 10.23/10.46 (Or (Eq (skS.0 19 a a_1 a_3 a_4) (skS.0 18 a a_1 a_2)) (Eq False True))
% 10.23/10.46 Clause #999 (by clausification #[890]): ∀ (a a_1 a_2 a_3 : Iota),
% 10.23/10.46 Or (Eq (apply (skS.0 2 a) (skS.0 20 a a_1 a_2) (skS.0 18 a a_1 a_3)) False)
% 10.23/10.46 (Eq (skS.0 18 a a_1 a_3) (skS.0 20 a a_1 a_2))
% 10.23/10.46 Clause #1000 (by superposition #[999, 886]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (skS.0 18 a a_1 a_2) (skS.0 20 a a_1 a_3)) (Eq False True)
% 10.23/10.46 Clause #1001 (by clausification #[1000]): ∀ (a a_1 a_2 a_3 : Iota), Eq (skS.0 18 a a_1 a_2) (skS.0 20 a a_1 a_3)
% 10.23/10.46 Clause #1010 (by superposition #[1001, 887]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (apply (skS.0 2 a) (skS.0 18 a a_1 a_2) (skS.0 19 a a_1 a_3 a_4)) True
% 10.23/10.46 Clause #1232 (by clausification #[926]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 10.23/10.46 Or (Eq (apply (skS.0 2 a) (skS.0 18 a a_1 a_2) (skS.0 19 a a_1 a_3 a_4)) False)
% 10.23/10.46 (Eq (skS.0 19 a a_1 a_3 a_4) (skS.0 18 a a_1 a_2))
% 10.23/10.46 Clause #1233 (by superposition #[1232, 1010]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq (skS.0 19 a a_1 a_2 a_3) (skS.0 18 a a_1 a_4)) (Eq False True)
% 10.23/10.46 Clause #1235 (by clausification #[1233]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (skS.0 19 a a_1 a_2 a_3) (skS.0 18 a a_1 a_4)
% 10.23/10.47 Clause #1236 (by backward contextual literal cutting #[1235, 227]): False
% 10.23/10.47 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------