TSTP Solution File: NUM393+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : NUM393+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n019.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 10:55:28 EDT 2023
% Result : Theorem 8.05s 8.34s
% Output : Proof 8.05s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM393+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : duper %s
% 0.15/0.36 % Computer : n019.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Aug 25 10:54:43 EDT 2023
% 0.15/0.36 % CPUTime :
% 8.05/8.34 SZS status Theorem for theBenchmark.p
% 8.05/8.34 SZS output start Proof for theBenchmark.p
% 8.05/8.34 Clause #6 (by assumption #[]): Eq (∀ (A B : Iota), And (ordinal A) (ordinal B) → Or (ordinal_subset A B) (ordinal_subset B A)) True
% 8.05/8.34 Clause #7 (by assumption #[]): Eq (∀ (A B : Iota), Iff (inclusion_comparable A B) (Or (subset A B) (subset B A))) True
% 8.05/8.34 Clause #23 (by assumption #[]): Eq (∀ (A B : Iota), And (ordinal A) (ordinal B) → Iff (ordinal_subset A B) (subset A B)) True
% 8.05/8.34 Clause #27 (by assumption #[]): Eq (∀ (A B : Iota), inclusion_comparable A B → inclusion_comparable B A) True
% 8.05/8.34 Clause #29 (by assumption #[]): Eq (Not (∀ (A : Iota), ordinal A → ∀ (B : Iota), ordinal B → inclusion_comparable A B)) True
% 8.05/8.34 Clause #82 (by clausification #[27]): ∀ (a : Iota), Eq (∀ (B : Iota), inclusion_comparable a B → inclusion_comparable B a) True
% 8.05/8.34 Clause #83 (by clausification #[82]): ∀ (a a_1 : Iota), Eq (inclusion_comparable a a_1 → inclusion_comparable a_1 a) True
% 8.05/8.34 Clause #84 (by clausification #[83]): ∀ (a a_1 : Iota), Or (Eq (inclusion_comparable a a_1) False) (Eq (inclusion_comparable a_1 a) True)
% 8.05/8.34 Clause #98 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (B : Iota), And (ordinal a) (ordinal B) → Or (ordinal_subset a B) (ordinal_subset B a)) True
% 8.05/8.34 Clause #99 (by clausification #[98]): ∀ (a a_1 : Iota), Eq (And (ordinal a) (ordinal a_1) → Or (ordinal_subset a a_1) (ordinal_subset a_1 a)) True
% 8.05/8.34 Clause #100 (by clausification #[99]): ∀ (a a_1 : Iota),
% 8.05/8.34 Or (Eq (And (ordinal a) (ordinal a_1)) False) (Eq (Or (ordinal_subset a a_1) (ordinal_subset a_1 a)) True)
% 8.05/8.34 Clause #101 (by clausification #[100]): ∀ (a a_1 : Iota),
% 8.05/8.34 Or (Eq (Or (ordinal_subset a a_1) (ordinal_subset a_1 a)) True) (Or (Eq (ordinal a) False) (Eq (ordinal a_1) False))
% 8.05/8.34 Clause #102 (by clausification #[101]): ∀ (a a_1 : Iota),
% 8.05/8.34 Or (Eq (ordinal a) False)
% 8.05/8.34 (Or (Eq (ordinal a_1) False) (Or (Eq (ordinal_subset a a_1) True) (Eq (ordinal_subset a_1 a) True)))
% 8.05/8.34 Clause #112 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (inclusion_comparable a B) (Or (subset a B) (subset B a))) True
% 8.05/8.34 Clause #113 (by clausification #[112]): ∀ (a a_1 : Iota), Eq (Iff (inclusion_comparable a a_1) (Or (subset a a_1) (subset a_1 a))) True
% 8.05/8.34 Clause #114 (by clausification #[113]): ∀ (a a_1 : Iota), Or (Eq (inclusion_comparable a a_1) True) (Eq (Or (subset a a_1) (subset a_1 a)) False)
% 8.05/8.34 Clause #117 (by clausification #[114]): ∀ (a a_1 : Iota), Or (Eq (inclusion_comparable a a_1) True) (Eq (subset a a_1) False)
% 8.05/8.34 Clause #121 (by clausification #[29]): Eq (∀ (A : Iota), ordinal A → ∀ (B : Iota), ordinal B → inclusion_comparable A B) False
% 8.05/8.34 Clause #122 (by clausification #[121]): ∀ (a : Iota), Eq (Not (ordinal (skS.0 5 a) → ∀ (B : Iota), ordinal B → inclusion_comparable (skS.0 5 a) B)) True
% 8.05/8.34 Clause #123 (by clausification #[122]): ∀ (a : Iota), Eq (ordinal (skS.0 5 a) → ∀ (B : Iota), ordinal B → inclusion_comparable (skS.0 5 a) B) False
% 8.05/8.34 Clause #124 (by clausification #[123]): ∀ (a : Iota), Eq (ordinal (skS.0 5 a)) True
% 8.05/8.34 Clause #125 (by clausification #[123]): ∀ (a : Iota), Eq (∀ (B : Iota), ordinal B → inclusion_comparable (skS.0 5 a) B) False
% 8.05/8.34 Clause #129 (by superposition #[124, 102]): ∀ (a a_1 : Iota),
% 8.05/8.34 Or (Eq True False)
% 8.05/8.34 (Or (Eq (ordinal a) False)
% 8.05/8.34 (Or (Eq (ordinal_subset (skS.0 5 a_1) a) True) (Eq (ordinal_subset a (skS.0 5 a_1)) True)))
% 8.05/8.34 Clause #170 (by clausification #[125]): ∀ (a a_1 : Iota), Eq (Not (ordinal (skS.0 11 a a_1) → inclusion_comparable (skS.0 5 a) (skS.0 11 a a_1))) True
% 8.05/8.34 Clause #171 (by clausification #[170]): ∀ (a a_1 : Iota), Eq (ordinal (skS.0 11 a a_1) → inclusion_comparable (skS.0 5 a) (skS.0 11 a a_1)) False
% 8.05/8.34 Clause #172 (by clausification #[171]): ∀ (a a_1 : Iota), Eq (ordinal (skS.0 11 a a_1)) True
% 8.05/8.34 Clause #173 (by clausification #[171]): ∀ (a a_1 : Iota), Eq (inclusion_comparable (skS.0 5 a) (skS.0 11 a a_1)) False
% 8.05/8.34 Clause #178 (by clausification #[23]): ∀ (a : Iota), Eq (∀ (B : Iota), And (ordinal a) (ordinal B) → Iff (ordinal_subset a B) (subset a B)) True
% 8.05/8.34 Clause #179 (by clausification #[178]): ∀ (a a_1 : Iota), Eq (And (ordinal a) (ordinal a_1) → Iff (ordinal_subset a a_1) (subset a a_1)) True
% 8.05/8.36 Clause #180 (by clausification #[179]): ∀ (a a_1 : Iota), Or (Eq (And (ordinal a) (ordinal a_1)) False) (Eq (Iff (ordinal_subset a a_1) (subset a a_1)) True)
% 8.05/8.36 Clause #181 (by clausification #[180]): ∀ (a a_1 : Iota),
% 8.05/8.36 Or (Eq (Iff (ordinal_subset a a_1) (subset a a_1)) True) (Or (Eq (ordinal a) False) (Eq (ordinal a_1) False))
% 8.05/8.36 Clause #183 (by clausification #[181]): ∀ (a a_1 : Iota),
% 8.05/8.36 Or (Eq (ordinal a) False)
% 8.05/8.36 (Or (Eq (ordinal a_1) False) (Or (Eq (ordinal_subset a a_1) False) (Eq (subset a a_1) True)))
% 8.05/8.36 Clause #254 (by superposition #[183, 124]): ∀ (a a_1 : Iota),
% 8.05/8.36 Or (Eq (ordinal a) False)
% 8.05/8.36 (Or (Eq (ordinal_subset (skS.0 5 a_1) a) False) (Or (Eq (subset (skS.0 5 a_1) a) True) (Eq False True)))
% 8.05/8.36 Clause #256 (by superposition #[183, 172]): ∀ (a a_1 a_2 : Iota),
% 8.05/8.36 Or (Eq (ordinal a) False)
% 8.05/8.36 (Or (Eq (ordinal_subset (skS.0 11 a_1 a_2) a) False) (Or (Eq (subset (skS.0 11 a_1 a_2) a) True) (Eq False True)))
% 8.05/8.36 Clause #269 (by clausification #[129]): ∀ (a a_1 : Iota),
% 8.05/8.36 Or (Eq (ordinal a) False) (Or (Eq (ordinal_subset (skS.0 5 a_1) a) True) (Eq (ordinal_subset a (skS.0 5 a_1)) True))
% 8.05/8.36 Clause #272 (by superposition #[269, 172]): ∀ (a a_1 a_2 : Iota),
% 8.05/8.36 Or (Eq (ordinal_subset (skS.0 5 a) (skS.0 11 a_1 a_2)) True)
% 8.05/8.36 (Or (Eq (ordinal_subset (skS.0 11 a_1 a_2) (skS.0 5 a)) True) (Eq False True))
% 8.05/8.36 Clause #349 (by clausification #[254]): ∀ (a a_1 : Iota),
% 8.05/8.36 Or (Eq (ordinal a) False) (Or (Eq (ordinal_subset (skS.0 5 a_1) a) False) (Eq (subset (skS.0 5 a_1) a) True))
% 8.05/8.36 Clause #352 (by superposition #[349, 172]): ∀ (a a_1 a_2 : Iota),
% 8.05/8.36 Or (Eq (ordinal_subset (skS.0 5 a) (skS.0 11 a_1 a_2)) False)
% 8.05/8.36 (Or (Eq (subset (skS.0 5 a) (skS.0 11 a_1 a_2)) True) (Eq False True))
% 8.05/8.36 Clause #372 (by clausification #[256]): ∀ (a a_1 a_2 : Iota),
% 8.05/8.36 Or (Eq (ordinal a) False)
% 8.05/8.36 (Or (Eq (ordinal_subset (skS.0 11 a_1 a_2) a) False) (Eq (subset (skS.0 11 a_1 a_2) a) True))
% 8.05/8.36 Clause #373 (by superposition #[372, 124]): ∀ (a a_1 a_2 : Iota),
% 8.05/8.36 Or (Eq (ordinal_subset (skS.0 11 a a_1) (skS.0 5 a_2)) False)
% 8.05/8.36 (Or (Eq (subset (skS.0 11 a a_1) (skS.0 5 a_2)) True) (Eq False True))
% 8.05/8.36 Clause #400 (by clausification #[272]): ∀ (a a_1 a_2 : Iota),
% 8.05/8.36 Or (Eq (ordinal_subset (skS.0 5 a) (skS.0 11 a_1 a_2)) True) (Eq (ordinal_subset (skS.0 11 a_1 a_2) (skS.0 5 a)) True)
% 8.05/8.36 Clause #514 (by clausification #[352]): ∀ (a a_1 a_2 : Iota),
% 8.05/8.36 Or (Eq (ordinal_subset (skS.0 5 a) (skS.0 11 a_1 a_2)) False) (Eq (subset (skS.0 5 a) (skS.0 11 a_1 a_2)) True)
% 8.05/8.36 Clause #563 (by clausification #[373]): ∀ (a a_1 a_2 : Iota),
% 8.05/8.36 Or (Eq (ordinal_subset (skS.0 11 a a_1) (skS.0 5 a_2)) False) (Eq (subset (skS.0 11 a a_1) (skS.0 5 a_2)) True)
% 8.05/8.36 Clause #564 (by superposition #[563, 400]): ∀ (a a_1 a_2 : Iota),
% 8.05/8.36 Or (Eq (subset (skS.0 11 a a_1) (skS.0 5 a_2)) True)
% 8.05/8.36 (Or (Eq (ordinal_subset (skS.0 5 a_2) (skS.0 11 a a_1)) True) (Eq False True))
% 8.05/8.36 Clause #565 (by clausification #[564]): ∀ (a a_1 a_2 : Iota),
% 8.05/8.36 Or (Eq (subset (skS.0 11 a a_1) (skS.0 5 a_2)) True) (Eq (ordinal_subset (skS.0 5 a_2) (skS.0 11 a a_1)) True)
% 8.05/8.36 Clause #566 (by superposition #[565, 514]): ∀ (a a_1 a_2 : Iota),
% 8.05/8.36 Or (Eq (subset (skS.0 11 a a_1) (skS.0 5 a_2)) True)
% 8.05/8.36 (Or (Eq True False) (Eq (subset (skS.0 5 a_2) (skS.0 11 a a_1)) True))
% 8.05/8.36 Clause #567 (by clausification #[566]): ∀ (a a_1 a_2 : Iota),
% 8.05/8.36 Or (Eq (subset (skS.0 11 a a_1) (skS.0 5 a_2)) True) (Eq (subset (skS.0 5 a_2) (skS.0 11 a a_1)) True)
% 8.05/8.36 Clause #574 (by superposition #[567, 117]): ∀ (a a_1 a_2 : Iota),
% 8.05/8.36 Or (Eq (subset (skS.0 11 a a_1) (skS.0 5 a_2)) True)
% 8.05/8.36 (Or (Eq (inclusion_comparable (skS.0 5 a_2) (skS.0 11 a a_1)) True) (Eq True False))
% 8.05/8.36 Clause #576 (by clausification #[574]): ∀ (a a_1 a_2 : Iota),
% 8.05/8.36 Or (Eq (subset (skS.0 11 a a_1) (skS.0 5 a_2)) True) (Eq (inclusion_comparable (skS.0 5 a_2) (skS.0 11 a a_1)) True)
% 8.05/8.36 Clause #577 (by superposition #[576, 173]): ∀ (a a_1 : Iota), Or (Eq (subset (skS.0 11 a a_1) (skS.0 5 a)) True) (Eq True False)
% 8.05/8.36 Clause #580 (by clausification #[577]): ∀ (a a_1 : Iota), Eq (subset (skS.0 11 a a_1) (skS.0 5 a)) True
% 8.05/8.37 Clause #583 (by superposition #[580, 117]): ∀ (a a_1 : Iota), Or (Eq (inclusion_comparable (skS.0 11 a a_1) (skS.0 5 a)) True) (Eq True False)
% 8.05/8.37 Clause #585 (by clausification #[583]): ∀ (a a_1 : Iota), Eq (inclusion_comparable (skS.0 11 a a_1) (skS.0 5 a)) True
% 8.05/8.37 Clause #586 (by superposition #[585, 84]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (inclusion_comparable (skS.0 5 a) (skS.0 11 a a_1)) True)
% 8.05/8.37 Clause #592 (by clausification #[586]): ∀ (a a_1 : Iota), Eq (inclusion_comparable (skS.0 5 a) (skS.0 11 a a_1)) True
% 8.05/8.37 Clause #593 (by superposition #[592, 173]): Eq True False
% 8.05/8.37 Clause #596 (by clausification #[593]): False
% 8.05/8.37 SZS output end Proof for theBenchmark.p
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