TSTP Solution File: SEU107+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU107+1 : TPTP v8.1.2. Released v3.2.0.
% 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 16:40:13 EDT 2023
% Result : Theorem 89.78s 90.01s
% Output : Proof 89.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU107+1 : TPTP v8.1.2. Released v3.2.0.
% 0.14/0.14 % Command : duper %s
% 0.16/0.35 % Computer : n010.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Wed Aug 23 18:03:51 EDT 2023
% 0.16/0.35 % CPUTime :
% 89.78/90.01 SZS status Theorem for theBenchmark.p
% 89.78/90.01 SZS output start Proof for theBenchmark.p
% 89.78/90.01 Clause #5 (by assumption #[]): Eq
% 89.78/90.01 (∀ (A B C : Iota),
% 89.78/90.01 And (And (And (Not (empty A)) (preboolean A)) (element B A)) (element C A) → element (prebool_difference A B C) A)
% 89.78/90.01 True
% 89.78/90.01 Clause #6 (by assumption #[]): Eq (∀ (A : Iota), Exists fun B => element B A) True
% 89.78/90.01 Clause #18 (by assumption #[]): Eq
% 89.78/90.01 (∀ (A B C : Iota),
% 89.78/90.01 And (And (And (Not (empty A)) (preboolean A)) (element B A)) (element C A) →
% 89.78/90.01 Eq (prebool_difference A B C) (set_difference B C))
% 89.78/90.01 True
% 89.78/90.01 Clause #19 (by assumption #[]): Eq (∀ (A : Iota), Iota → subset A A) True
% 89.78/90.01 Clause #20 (by assumption #[]): Eq (Not (∀ (A : Iota), And (Not (empty A)) (preboolean A) → in empty_set A)) True
% 89.78/90.01 Clause #22 (by assumption #[]): Eq (∀ (A B : Iota), element A B → Or (empty B) (in A B)) True
% 89.78/90.01 Clause #23 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq (set_difference A B) empty_set) (subset A B)) True
% 89.78/90.01 Clause #48 (by clausification #[19]): ∀ (a : Iota), Eq (Iota → subset a a) True
% 89.78/90.01 Clause #49 (by clausification #[48]): ∀ (a : Iota), Iota → Eq (subset a a) True
% 89.78/90.01 Clause #55 (by clausification #[20]): Eq (∀ (A : Iota), And (Not (empty A)) (preboolean A) → in empty_set A) False
% 89.78/90.01 Clause #56 (by clausification #[55]): ∀ (a : Iota), Eq (Not (And (Not (empty (skS.0 2 a))) (preboolean (skS.0 2 a)) → in empty_set (skS.0 2 a))) True
% 89.78/90.01 Clause #57 (by clausification #[56]): ∀ (a : Iota), Eq (And (Not (empty (skS.0 2 a))) (preboolean (skS.0 2 a)) → in empty_set (skS.0 2 a)) False
% 89.78/90.01 Clause #58 (by clausification #[57]): ∀ (a : Iota), Eq (And (Not (empty (skS.0 2 a))) (preboolean (skS.0 2 a))) True
% 89.78/90.01 Clause #59 (by clausification #[57]): ∀ (a : Iota), Eq (in empty_set (skS.0 2 a)) False
% 89.78/90.01 Clause #60 (by clausification #[58]): ∀ (a : Iota), Eq (preboolean (skS.0 2 a)) True
% 89.78/90.01 Clause #61 (by clausification #[58]): ∀ (a : Iota), Eq (Not (empty (skS.0 2 a))) True
% 89.78/90.01 Clause #83 (by clausification #[5]): ∀ (a : Iota),
% 89.78/90.01 Eq
% 89.78/90.01 (∀ (B C : Iota),
% 89.78/90.01 And (And (And (Not (empty a)) (preboolean a)) (element B a)) (element C a) → element (prebool_difference a B C) a)
% 89.78/90.01 True
% 89.78/90.01 Clause #84 (by clausification #[83]): ∀ (a a_1 : Iota),
% 89.78/90.01 Eq
% 89.78/90.01 (∀ (C : Iota),
% 89.78/90.01 And (And (And (Not (empty a)) (preboolean a)) (element a_1 a)) (element C a) →
% 89.78/90.01 element (prebool_difference a a_1 C) a)
% 89.78/90.01 True
% 89.78/90.01 Clause #85 (by clausification #[84]): ∀ (a a_1 a_2 : Iota),
% 89.78/90.01 Eq
% 89.78/90.01 (And (And (And (Not (empty a)) (preboolean a)) (element a_1 a)) (element a_2 a) →
% 89.78/90.01 element (prebool_difference a a_1 a_2) a)
% 89.78/90.01 True
% 89.78/90.01 Clause #86 (by clausification #[85]): ∀ (a a_1 a_2 : Iota),
% 89.78/90.01 Or (Eq (And (And (And (Not (empty a)) (preboolean a)) (element a_1 a)) (element a_2 a)) False)
% 89.78/90.01 (Eq (element (prebool_difference a a_1 a_2) a) True)
% 89.78/90.01 Clause #87 (by clausification #[86]): ∀ (a a_1 a_2 : Iota),
% 89.78/90.01 Or (Eq (element (prebool_difference a a_1 a_2) a) True)
% 89.78/90.01 (Or (Eq (And (And (Not (empty a)) (preboolean a)) (element a_1 a)) False) (Eq (element a_2 a) False))
% 89.78/90.01 Clause #88 (by clausification #[87]): ∀ (a a_1 a_2 : Iota),
% 89.78/90.01 Or (Eq (element (prebool_difference a a_1 a_2) a) True)
% 89.78/90.01 (Or (Eq (element a_2 a) False) (Or (Eq (And (Not (empty a)) (preboolean a)) False) (Eq (element a_1 a) False)))
% 89.78/90.01 Clause #89 (by clausification #[88]): ∀ (a a_1 a_2 : Iota),
% 89.78/90.01 Or (Eq (element (prebool_difference a a_1 a_2) a) True)
% 89.78/90.01 (Or (Eq (element a_2 a) False)
% 89.78/90.01 (Or (Eq (element a_1 a) False) (Or (Eq (Not (empty a)) False) (Eq (preboolean a) False))))
% 89.78/90.01 Clause #90 (by clausification #[89]): ∀ (a a_1 a_2 : Iota),
% 89.78/90.01 Or (Eq (element (prebool_difference a a_1 a_2) a) True)
% 89.78/90.01 (Or (Eq (element a_2 a) False) (Or (Eq (element a_1 a) False) (Or (Eq (preboolean a) False) (Eq (empty a) True))))
% 89.78/90.01 Clause #94 (by clausification #[6]): ∀ (a : Iota), Eq (Exists fun B => element B a) True
% 89.78/90.01 Clause #95 (by clausification #[94]): ∀ (a a_1 : Iota), Eq (element (skS.0 3 a a_1) a) True
% 89.78/90.01 Clause #96 (by superposition #[95, 90]): ∀ (a a_1 a_2 : Iota),
% 89.78/90.01 Or (Eq (element (prebool_difference a a_1 (skS.0 3 a a_2)) a) True)
% 89.78/90.01 (Or (Eq True False) (Or (Eq (element a_1 a) False) (Or (Eq (preboolean a) False) (Eq (empty a) True))))
% 89.88/90.03 Clause #111 (by clausification #[61]): ∀ (a : Iota), Eq (empty (skS.0 2 a)) False
% 89.88/90.03 Clause #137 (by clausification #[22]): ∀ (a : Iota), Eq (∀ (B : Iota), element a B → Or (empty B) (in a B)) True
% 89.88/90.03 Clause #138 (by clausification #[137]): ∀ (a a_1 : Iota), Eq (element a a_1 → Or (empty a_1) (in a a_1)) True
% 89.88/90.03 Clause #139 (by clausification #[138]): ∀ (a a_1 : Iota), Or (Eq (element a a_1) False) (Eq (Or (empty a_1) (in a a_1)) True)
% 89.88/90.03 Clause #140 (by clausification #[139]): ∀ (a a_1 : Iota), Or (Eq (element a a_1) False) (Or (Eq (empty a_1) True) (Eq (in a a_1) True))
% 89.88/90.03 Clause #198 (by clausification #[18]): ∀ (a : Iota),
% 89.88/90.03 Eq
% 89.88/90.03 (∀ (B C : Iota),
% 89.88/90.03 And (And (And (Not (empty a)) (preboolean a)) (element B a)) (element C a) →
% 89.88/90.03 Eq (prebool_difference a B C) (set_difference B C))
% 89.88/90.03 True
% 89.88/90.03 Clause #199 (by clausification #[198]): ∀ (a a_1 : Iota),
% 89.88/90.03 Eq
% 89.88/90.03 (∀ (C : Iota),
% 89.88/90.03 And (And (And (Not (empty a)) (preboolean a)) (element a_1 a)) (element C a) →
% 89.88/90.03 Eq (prebool_difference a a_1 C) (set_difference a_1 C))
% 89.88/90.03 True
% 89.88/90.03 Clause #200 (by clausification #[199]): ∀ (a a_1 a_2 : Iota),
% 89.88/90.03 Eq
% 89.88/90.03 (And (And (And (Not (empty a)) (preboolean a)) (element a_1 a)) (element a_2 a) →
% 89.88/90.03 Eq (prebool_difference a a_1 a_2) (set_difference a_1 a_2))
% 89.88/90.03 True
% 89.88/90.03 Clause #201 (by clausification #[200]): ∀ (a a_1 a_2 : Iota),
% 89.88/90.03 Or (Eq (And (And (And (Not (empty a)) (preboolean a)) (element a_1 a)) (element a_2 a)) False)
% 89.88/90.03 (Eq (Eq (prebool_difference a a_1 a_2) (set_difference a_1 a_2)) True)
% 89.88/90.03 Clause #202 (by clausification #[201]): ∀ (a a_1 a_2 : Iota),
% 89.88/90.03 Or (Eq (Eq (prebool_difference a a_1 a_2) (set_difference a_1 a_2)) True)
% 89.88/90.03 (Or (Eq (And (And (Not (empty a)) (preboolean a)) (element a_1 a)) False) (Eq (element a_2 a) False))
% 89.88/90.03 Clause #203 (by clausification #[202]): ∀ (a a_1 a_2 : Iota),
% 89.88/90.03 Or (Eq (And (And (Not (empty a)) (preboolean a)) (element a_1 a)) False)
% 89.88/90.03 (Or (Eq (element a_2 a) False) (Eq (prebool_difference a a_1 a_2) (set_difference a_1 a_2)))
% 89.88/90.03 Clause #204 (by clausification #[203]): ∀ (a a_1 a_2 : Iota),
% 89.88/90.03 Or (Eq (element a a_1) False)
% 89.88/90.03 (Or (Eq (prebool_difference a_1 a_2 a) (set_difference a_2 a))
% 89.88/90.03 (Or (Eq (And (Not (empty a_1)) (preboolean a_1)) False) (Eq (element a_2 a_1) False)))
% 89.88/90.03 Clause #205 (by clausification #[204]): ∀ (a a_1 a_2 : Iota),
% 89.88/90.03 Or (Eq (element a a_1) False)
% 89.88/90.03 (Or (Eq (prebool_difference a_1 a_2 a) (set_difference a_2 a))
% 89.88/90.03 (Or (Eq (element a_2 a_1) False) (Or (Eq (Not (empty a_1)) False) (Eq (preboolean a_1) False))))
% 89.88/90.03 Clause #206 (by clausification #[205]): ∀ (a a_1 a_2 : Iota),
% 89.88/90.03 Or (Eq (element a a_1) False)
% 89.88/90.03 (Or (Eq (prebool_difference a_1 a_2 a) (set_difference a_2 a))
% 89.88/90.03 (Or (Eq (element a_2 a_1) False) (Or (Eq (preboolean a_1) False) (Eq (empty a_1) True))))
% 89.88/90.03 Clause #209 (by superposition #[206, 95]): ∀ (a a_1 a_2 : Iota),
% 89.88/90.03 Or (Eq (prebool_difference a a_1 (skS.0 3 a a_2)) (set_difference a_1 (skS.0 3 a a_2)))
% 89.88/90.03 (Or (Eq (element a_1 a) False) (Or (Eq (preboolean a) False) (Or (Eq (empty a) True) (Eq False True))))
% 89.88/90.03 Clause #219 (by clausification #[23]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq (set_difference a B) empty_set) (subset a B)) True
% 89.88/90.03 Clause #220 (by clausification #[219]): ∀ (a a_1 : Iota), Eq (Iff (Eq (set_difference a a_1) empty_set) (subset a a_1)) True
% 89.88/90.03 Clause #221 (by clausification #[220]): ∀ (a a_1 : Iota), Or (Eq (Eq (set_difference a a_1) empty_set) True) (Eq (subset a a_1) False)
% 89.88/90.03 Clause #223 (by clausification #[221]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (set_difference a a_1) empty_set)
% 89.88/90.03 Clause #225 (by superposition #[223, 49]): ∀ (a : Iota), Or (Eq (set_difference a a) empty_set) (Eq False True)
% 89.88/90.03 Clause #226 (by clausification #[225]): ∀ (a : Iota), Eq (set_difference a a) empty_set
% 89.88/90.03 Clause #252 (by clausification #[96]): ∀ (a a_1 a_2 : Iota),
% 89.88/90.03 Or (Eq (element (prebool_difference a a_1 (skS.0 3 a a_2)) a) True)
% 89.88/90.03 (Or (Eq (element a_1 a) False) (Or (Eq (preboolean a) False) (Eq (empty a) True)))
% 89.88/90.08 Clause #255 (by superposition #[252, 95]): ∀ (a a_1 a_2 : Iota),
% 89.88/90.08 Or (Eq (element (prebool_difference a (skS.0 3 a a_1) (skS.0 3 a a_2)) a) True)
% 89.88/90.08 (Or (Eq (preboolean a) False) (Or (Eq (empty a) True) (Eq False True)))
% 89.88/90.08 Clause #434 (by clausification #[209]): ∀ (a a_1 a_2 : Iota),
% 89.88/90.08 Or (Eq (prebool_difference a a_1 (skS.0 3 a a_2)) (set_difference a_1 (skS.0 3 a a_2)))
% 89.88/90.08 (Or (Eq (element a_1 a) False) (Or (Eq (preboolean a) False) (Eq (empty a) True)))
% 89.88/90.08 Clause #439 (by superposition #[434, 95]): ∀ (a a_1 a_2 : Iota),
% 89.88/90.08 Or (Eq (prebool_difference a (skS.0 3 a a_1) (skS.0 3 a a_2)) (set_difference (skS.0 3 a a_1) (skS.0 3 a a_2)))
% 89.88/90.08 (Or (Eq (preboolean a) False) (Or (Eq (empty a) True) (Eq False True)))
% 89.88/90.08 Clause #484 (by clausification #[255]): ∀ (a a_1 a_2 : Iota),
% 89.88/90.08 Or (Eq (element (prebool_difference a (skS.0 3 a a_1) (skS.0 3 a a_2)) a) True)
% 89.88/90.08 (Or (Eq (preboolean a) False) (Eq (empty a) True))
% 89.88/90.08 Clause #485 (by superposition #[484, 60]): ∀ (a a_1 a_2 : Iota),
% 89.88/90.08 Or
% 89.88/90.08 (Eq (element (prebool_difference (skS.0 2 a) (skS.0 3 (skS.0 2 a) a_1) (skS.0 3 (skS.0 2 a) a_2)) (skS.0 2 a)) True)
% 89.88/90.08 (Or (Eq (empty (skS.0 2 a)) True) (Eq False True))
% 89.88/90.08 Clause #932 (by clausification #[439]): ∀ (a a_1 a_2 : Iota),
% 89.88/90.08 Or (Eq (prebool_difference a (skS.0 3 a a_1) (skS.0 3 a a_2)) (set_difference (skS.0 3 a a_1) (skS.0 3 a a_2)))
% 89.88/90.08 (Or (Eq (preboolean a) False) (Eq (empty a) True))
% 89.88/90.08 Clause #933 (by superposition #[932, 60]): ∀ (a a_1 a_2 : Iota),
% 89.88/90.08 Or
% 89.88/90.08 (Eq (prebool_difference (skS.0 2 a) (skS.0 3 (skS.0 2 a) a_1) (skS.0 3 (skS.0 2 a) a_2))
% 89.88/90.08 (set_difference (skS.0 3 (skS.0 2 a) a_1) (skS.0 3 (skS.0 2 a) a_2)))
% 89.88/90.08 (Or (Eq (empty (skS.0 2 a)) True) (Eq False True))
% 89.88/90.08 Clause #1166 (by clausification #[485]): ∀ (a a_1 a_2 : Iota),
% 89.88/90.08 Or
% 89.88/90.08 (Eq (element (prebool_difference (skS.0 2 a) (skS.0 3 (skS.0 2 a) a_1) (skS.0 3 (skS.0 2 a) a_2)) (skS.0 2 a)) True)
% 89.88/90.08 (Eq (empty (skS.0 2 a)) True)
% 89.88/90.08 Clause #1167 (by forward demodulation #[1166, 111]): ∀ (a a_1 a_2 : Iota),
% 89.88/90.08 Or
% 89.88/90.08 (Eq (element (prebool_difference (skS.0 2 a) (skS.0 3 (skS.0 2 a) a_1) (skS.0 3 (skS.0 2 a) a_2)) (skS.0 2 a)) True)
% 89.88/90.08 (Eq False True)
% 89.88/90.08 Clause #1168 (by clausification #[1167]): ∀ (a a_1 a_2 : Iota),
% 89.88/90.08 Eq (element (prebool_difference (skS.0 2 a) (skS.0 3 (skS.0 2 a) a_1) (skS.0 3 (skS.0 2 a) a_2)) (skS.0 2 a)) True
% 89.88/90.08 Clause #2338 (by clausification #[933]): ∀ (a a_1 a_2 : Iota),
% 89.88/90.08 Or
% 89.88/90.08 (Eq (prebool_difference (skS.0 2 a) (skS.0 3 (skS.0 2 a) a_1) (skS.0 3 (skS.0 2 a) a_2))
% 89.88/90.08 (set_difference (skS.0 3 (skS.0 2 a) a_1) (skS.0 3 (skS.0 2 a) a_2)))
% 89.88/90.08 (Eq (empty (skS.0 2 a)) True)
% 89.88/90.08 Clause #2339 (by forward demodulation #[2338, 111]): ∀ (a a_1 a_2 : Iota),
% 89.88/90.08 Or
% 89.88/90.08 (Eq (prebool_difference (skS.0 2 a) (skS.0 3 (skS.0 2 a) a_1) (skS.0 3 (skS.0 2 a) a_2))
% 89.88/90.08 (set_difference (skS.0 3 (skS.0 2 a) a_1) (skS.0 3 (skS.0 2 a) a_2)))
% 89.88/90.08 (Eq False True)
% 89.88/90.08 Clause #2340 (by clausification #[2339]): ∀ (a a_1 a_2 : Iota),
% 89.88/90.08 Eq (prebool_difference (skS.0 2 a) (skS.0 3 (skS.0 2 a) a_1) (skS.0 3 (skS.0 2 a) a_2))
% 89.88/90.08 (set_difference (skS.0 3 (skS.0 2 a) a_1) (skS.0 3 (skS.0 2 a) a_2))
% 89.88/90.08 Clause #2341 (by backward demodulation #[2340, 1168]): ∀ (a a_1 a_2 : Iota), Eq (element (set_difference (skS.0 3 (skS.0 2 a) a_1) (skS.0 3 (skS.0 2 a) a_2)) (skS.0 2 a)) True
% 89.88/90.08 Clause #3301 (by superposition #[2341, 226]): ∀ (a : Iota), Eq (element empty_set (skS.0 2 a)) True
% 89.88/90.08 Clause #3303 (by superposition #[3301, 140]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (empty (skS.0 2 a)) True) (Eq (in empty_set (skS.0 2 a)) True))
% 89.88/90.08 Clause #3307 (by clausification #[3303]): ∀ (a : Iota), Or (Eq (empty (skS.0 2 a)) True) (Eq (in empty_set (skS.0 2 a)) True)
% 89.88/90.08 Clause #3308 (by forward demodulation #[3307, 111]): ∀ (a : Iota), Or (Eq False True) (Eq (in empty_set (skS.0 2 a)) True)
% 89.88/90.08 Clause #3309 (by clausification #[3308]): ∀ (a : Iota), Eq (in empty_set (skS.0 2 a)) True
% 89.88/90.08 Clause #3310 (by superposition #[3309, 59]): Eq True False
% 89.88/90.08 Clause #3316 (by clausification #[3310]): False
% 89.88/90.08 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------