TSTP Solution File: SET929+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET929+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n003.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 14:48:06 EDT 2023
% Result : Theorem 4.38s 4.59s
% Output : Proof 4.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET929+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 09:25:24 EDT 2023
% 0.13/0.34 % CPUTime :
% 4.38/4.59 SZS status Theorem for theBenchmark.p
% 4.38/4.59 SZS output start Proof for theBenchmark.p
% 4.38/4.59 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Eq (unordered_pair A B) (unordered_pair B A)) True
% 4.38/4.59 Clause #6 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq (set_difference A B) empty_set) (subset A B)) True
% 4.38/4.59 Clause #7 (by assumption #[]): Eq (∀ (A B C : Iota), Iff (subset (unordered_pair A B) C) (And (in A C) (in B C))) True
% 4.38/4.59 Clause #8 (by assumption #[]): Eq (Not (∀ (A B C : Iota), Iff (Eq (set_difference (unordered_pair A B) C) empty_set) (And (in A C) (in B C)))) True
% 4.38/4.59 Clause #19 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (unordered_pair a B) (unordered_pair B a)) True
% 4.38/4.59 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (Eq (unordered_pair a a_1) (unordered_pair a_1 a)) True
% 4.38/4.59 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (unordered_pair a a_1) (unordered_pair a_1 a)
% 4.38/4.59 Clause #22 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq (set_difference a B) empty_set) (subset a B)) True
% 4.38/4.59 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Eq (Iff (Eq (set_difference a a_1) empty_set) (subset a a_1)) True
% 4.38/4.59 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (Eq (set_difference a a_1) empty_set) True) (Eq (subset a a_1) False)
% 4.38/4.59 Clause #25 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (Eq (set_difference a a_1) empty_set) False) (Eq (subset a a_1) True)
% 4.38/4.59 Clause #26 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (set_difference a a_1) empty_set)
% 4.38/4.59 Clause #29 (by clausification #[25]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Ne (set_difference a a_1) empty_set)
% 4.38/4.59 Clause #32 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (B C : Iota), Iff (subset (unordered_pair a B) C) (And (in a C) (in B C))) True
% 4.38/4.59 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), Iff (subset (unordered_pair a a_1) C) (And (in a C) (in a_1 C))) True
% 4.38/4.59 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), Eq (Iff (subset (unordered_pair a a_1) a_2) (And (in a a_2) (in a_1 a_2))) True
% 4.38/4.59 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset (unordered_pair a a_1) a_2) True) (Eq (And (in a a_2) (in a_1 a_2)) False)
% 4.38/4.59 Clause #36 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset (unordered_pair a a_1) a_2) False) (Eq (And (in a a_2) (in a_1 a_2)) True)
% 4.38/4.59 Clause #37 (by clausification #[35]): ∀ (a a_1 a_2 : Iota),
% 4.38/4.59 Or (Eq (subset (unordered_pair a a_1) a_2) True) (Or (Eq (in a a_2) False) (Eq (in a_1 a_2) False))
% 4.38/4.59 Clause #38 (by clausification #[8]): Eq (∀ (A B C : Iota), Iff (Eq (set_difference (unordered_pair A B) C) empty_set) (And (in A C) (in B C))) False
% 4.38/4.59 Clause #39 (by clausification #[38]): ∀ (a : Iota),
% 4.38/4.59 Eq
% 4.38/4.59 (Not
% 4.38/4.59 (∀ (B C : Iota),
% 4.38/4.59 Iff (Eq (set_difference (unordered_pair (skS.0 2 a) B) C) empty_set) (And (in (skS.0 2 a) C) (in B C))))
% 4.38/4.59 True
% 4.38/4.59 Clause #40 (by clausification #[39]): ∀ (a : Iota),
% 4.38/4.59 Eq
% 4.38/4.59 (∀ (B C : Iota),
% 4.38/4.59 Iff (Eq (set_difference (unordered_pair (skS.0 2 a) B) C) empty_set) (And (in (skS.0 2 a) C) (in B C)))
% 4.38/4.59 False
% 4.38/4.59 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota),
% 4.38/4.59 Eq
% 4.38/4.59 (Not
% 4.38/4.59 (∀ (C : Iota),
% 4.38/4.59 Iff (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) C) empty_set)
% 4.38/4.59 (And (in (skS.0 2 a) C) (in (skS.0 3 a a_1) C))))
% 4.38/4.59 True
% 4.38/4.59 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota),
% 4.38/4.59 Eq
% 4.38/4.59 (∀ (C : Iota),
% 4.38/4.59 Iff (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) C) empty_set)
% 4.38/4.59 (And (in (skS.0 2 a) C) (in (skS.0 3 a a_1) C)))
% 4.38/4.59 False
% 4.38/4.59 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 : Iota),
% 4.38/4.59 Eq
% 4.38/4.59 (Not
% 4.38/4.59 (Iff (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) empty_set)
% 4.38/4.59 (And (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))))
% 4.38/4.59 True
% 4.38/4.59 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 : Iota),
% 4.38/4.59 Eq
% 4.38/4.59 (Iff (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) empty_set)
% 4.45/4.62 (And (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))))
% 4.45/4.62 False
% 4.45/4.62 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 : Iota),
% 4.45/4.62 Or (Eq (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) empty_set) False)
% 4.45/4.62 (Eq (And (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) False)
% 4.45/4.62 Clause #46 (by clausification #[44]): ∀ (a a_1 a_2 : Iota),
% 4.45/4.62 Or (Eq (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) empty_set) True)
% 4.45/4.62 (Eq (And (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) True)
% 4.45/4.62 Clause #47 (by clausification #[45]): ∀ (a a_1 a_2 : Iota),
% 4.45/4.62 Or (Eq (And (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) False)
% 4.45/4.62 (Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) empty_set)
% 4.45/4.62 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 : Iota),
% 4.45/4.62 Or (Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) empty_set)
% 4.45/4.62 (Or (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) False) (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) False))
% 4.45/4.62 Clause #49 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset (unordered_pair a a_1) a_2) False) (Eq (in a_1 a_2) True)
% 4.45/4.62 Clause #50 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset (unordered_pair a a_1) a_2) False) (Eq (in a a_2) True)
% 4.45/4.62 Clause #60 (by clausification #[46]): ∀ (a a_1 a_2 : Iota),
% 4.45/4.62 Or (Eq (And (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) True)
% 4.45/4.62 (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) empty_set)
% 4.45/4.62 Clause #61 (by clausification #[60]): ∀ (a a_1 a_2 : Iota),
% 4.45/4.62 Or (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) empty_set)
% 4.45/4.62 (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) True)
% 4.45/4.62 Clause #62 (by clausification #[60]): ∀ (a a_1 a_2 : Iota),
% 4.45/4.62 Or (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) empty_set)
% 4.45/4.62 (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True)
% 4.45/4.62 Clause #64 (by superposition #[61, 29]): ∀ (a a_1 a_2 : Iota),
% 4.45/4.62 Or (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) True)
% 4.45/4.62 (Or (Eq (subset (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) True) (Ne empty_set empty_set))
% 4.45/4.62 Clause #82 (by superposition #[62, 29]): ∀ (a a_1 a_2 : Iota),
% 4.45/4.62 Or (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True)
% 4.45/4.62 (Or (Eq (subset (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) True) (Ne empty_set empty_set))
% 4.45/4.62 Clause #90 (by eliminate resolved literals #[64]): ∀ (a a_1 a_2 : Iota),
% 4.45/4.62 Or (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) True)
% 4.45/4.62 (Eq (subset (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) True)
% 4.45/4.62 Clause #91 (by superposition #[90, 49]): ∀ (a a_1 a_2 : Iota),
% 4.45/4.62 Or (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) True)
% 4.45/4.62 (Or (Eq True False) (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) True))
% 4.45/4.62 Clause #98 (by clausification #[91]): ∀ (a a_1 a_2 : Iota),
% 4.45/4.62 Or (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) True) (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) True)
% 4.45/4.62 Clause #99 (by eliminate duplicate literals #[98]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) True
% 4.45/4.62 Clause #100 (by backward demodulation #[99, 48]): ∀ (a a_1 a_2 : Iota),
% 4.45/4.62 Or (Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) empty_set)
% 4.45/4.62 (Or (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) False) (Eq True False))
% 4.45/4.62 Clause #104 (by superposition #[99, 37]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.45/4.62 Or (Eq (subset (unordered_pair (skS.0 3 a a_1) a_2) (skS.0 4 a a_1 a_3)) True)
% 4.45/4.62 (Or (Eq True False) (Eq (in a_2 (skS.0 4 a a_1 a_3)) False))
% 4.45/4.62 Clause #106 (by clausification #[104]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.45/4.62 Or (Eq (subset (unordered_pair (skS.0 3 a a_1) a_2) (skS.0 4 a a_1 a_3)) True) (Eq (in a_2 (skS.0 4 a a_1 a_3)) False)
% 4.45/4.62 Clause #113 (by eliminate resolved literals #[82]): ∀ (a a_1 a_2 : Iota),
% 4.45/4.62 Or (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True)
% 4.45/4.63 (Eq (subset (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) True)
% 4.45/4.63 Clause #115 (by superposition #[113, 50]): ∀ (a a_1 a_2 : Iota),
% 4.45/4.63 Or (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True) (Or (Eq True False) (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True))
% 4.45/4.63 Clause #117 (by clausification #[115]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True) (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True)
% 4.45/4.63 Clause #118 (by eliminate duplicate literals #[117]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True
% 4.45/4.63 Clause #119 (by superposition #[118, 106]): ∀ (a a_1 a_2 : Iota),
% 4.45/4.63 Or (Eq (subset (unordered_pair (skS.0 3 a a_1) (skS.0 2 a)) (skS.0 4 a a_1 a_2)) True) (Eq True False)
% 4.45/4.63 Clause #123 (by clausification #[119]): ∀ (a a_1 a_2 : Iota), Eq (subset (unordered_pair (skS.0 3 a a_1) (skS.0 2 a)) (skS.0 4 a a_1 a_2)) True
% 4.45/4.63 Clause #124 (by forward demodulation #[123, 21]): ∀ (a a_1 a_2 : Iota), Eq (subset (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) True
% 4.45/4.63 Clause #126 (by superposition #[124, 26]): ∀ (a a_1 a_2 : Iota),
% 4.45/4.63 Or (Eq True False) (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) empty_set)
% 4.45/4.63 Clause #129 (by clausification #[126]): ∀ (a a_1 a_2 : Iota), Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) empty_set
% 4.45/4.63 Clause #143 (by clausification #[100]): ∀ (a a_1 a_2 : Iota),
% 4.45/4.63 Or (Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) empty_set)
% 4.45/4.63 (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) False)
% 4.45/4.63 Clause #144 (by forward demodulation #[143, 129]): ∀ (a a_1 a_2 : Iota), Or (Ne empty_set empty_set) (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) False)
% 4.45/4.63 Clause #145 (by eliminate resolved literals #[144]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) False
% 4.45/4.63 Clause #146 (by superposition #[145, 118]): Eq False True
% 4.45/4.63 Clause #147 (by clausification #[146]): False
% 4.45/4.63 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------