TSTP Solution File: SEU783^2 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU783^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n017.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 16:43:52 EDT 2023
% Result : Theorem 4.64s 4.79s
% Output : Proof 4.64s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU783^2 : TPTP v8.1.2. Released v3.7.0.
% 0.13/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n017.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 : Wed Aug 23 16:32:38 EDT 2023
% 0.14/0.35 % CPUTime :
% 4.64/4.79 SZS status Theorem for theBenchmark.p
% 4.64/4.79 SZS output start Proof for theBenchmark.p
% 4.64/4.79 Clause #0 (by assumption #[]): Eq (Eq binunionIL (∀ (A B Xx : Iota), in Xx A → in Xx (binunion A B))) True
% 4.64/4.79 Clause #1 (by assumption #[]): Eq
% 4.64/4.79 (Not
% 4.64/4.79 (binunionIL →
% 4.64/4.79 ∀ (A R : Iota),
% 4.64/4.79 breln1 A R →
% 4.64/4.79 ∀ (S : Iota),
% 4.64/4.79 breln1 A S →
% 4.64/4.79 ∀ (Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy A → in (kpair Xx Xy) R → in (kpair Xx Xy) (binunion R S)))
% 4.64/4.79 True
% 4.64/4.79 Clause #2 (by clausification #[0]): Eq binunionIL (∀ (A B Xx : Iota), in Xx A → in Xx (binunion A B))
% 4.64/4.79 Clause #18 (by clausification #[1]): Eq
% 4.64/4.79 (binunionIL →
% 4.64/4.79 ∀ (A R : Iota),
% 4.64/4.79 breln1 A R →
% 4.64/4.79 ∀ (S : Iota),
% 4.64/4.79 breln1 A S →
% 4.64/4.79 ∀ (Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy A → in (kpair Xx Xy) R → in (kpair Xx Xy) (binunion R S))
% 4.64/4.79 False
% 4.64/4.79 Clause #19 (by clausification #[18]): Eq binunionIL True
% 4.64/4.79 Clause #20 (by clausification #[18]): Eq
% 4.64/4.79 (∀ (A R : Iota),
% 4.64/4.79 breln1 A R →
% 4.64/4.79 ∀ (S : Iota),
% 4.64/4.79 breln1 A S →
% 4.64/4.79 ∀ (Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy A → in (kpair Xx Xy) R → in (kpair Xx Xy) (binunion R S))
% 4.64/4.79 False
% 4.64/4.79 Clause #21 (by backward demodulation #[19, 2]): Eq True (∀ (A B Xx : Iota), in Xx A → in Xx (binunion A B))
% 4.64/4.79 Clause #25 (by clausification #[21]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx a → in Xx (binunion a B)) True
% 4.64/4.79 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx a → in Xx (binunion a a_1)) True
% 4.64/4.79 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Eq (in a a_1 → in a (binunion a_1 a_2)) True
% 4.64/4.79 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Eq (in a (binunion a_1 a_2)) True)
% 4.64/4.79 Clause #29 (by clausification #[20]): ∀ (a : Iota),
% 4.64/4.79 Eq
% 4.64/4.79 (Not
% 4.64/4.79 (∀ (R : Iota),
% 4.64/4.79 breln1 (skS.0 3 a) R →
% 4.64/4.79 ∀ (S : Iota),
% 4.64/4.79 breln1 (skS.0 3 a) S →
% 4.64/4.79 ∀ (Xx : Iota),
% 4.64/4.79 in Xx (skS.0 3 a) →
% 4.64/4.79 ∀ (Xy : Iota), in Xy (skS.0 3 a) → in (kpair Xx Xy) R → in (kpair Xx Xy) (binunion R S)))
% 4.64/4.79 True
% 4.64/4.79 Clause #30 (by clausification #[29]): ∀ (a : Iota),
% 4.64/4.79 Eq
% 4.64/4.79 (∀ (R : Iota),
% 4.64/4.79 breln1 (skS.0 3 a) R →
% 4.64/4.79 ∀ (S : Iota),
% 4.64/4.79 breln1 (skS.0 3 a) S →
% 4.64/4.79 ∀ (Xx : Iota),
% 4.64/4.79 in Xx (skS.0 3 a) →
% 4.64/4.79 ∀ (Xy : Iota), in Xy (skS.0 3 a) → in (kpair Xx Xy) R → in (kpair Xx Xy) (binunion R S))
% 4.64/4.79 False
% 4.64/4.79 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota),
% 4.64/4.79 Eq
% 4.64/4.79 (Not
% 4.64/4.79 (breln1 (skS.0 3 a) (skS.0 4 a a_1) →
% 4.64/4.79 ∀ (S : Iota),
% 4.64/4.79 breln1 (skS.0 3 a) S →
% 4.64/4.79 ∀ (Xx : Iota),
% 4.64/4.79 in Xx (skS.0 3 a) →
% 4.64/4.79 ∀ (Xy : Iota),
% 4.64/4.79 in Xy (skS.0 3 a) → in (kpair Xx Xy) (skS.0 4 a a_1) → in (kpair Xx Xy) (binunion (skS.0 4 a a_1) S)))
% 4.64/4.79 True
% 4.64/4.79 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota),
% 4.64/4.79 Eq
% 4.64/4.79 (breln1 (skS.0 3 a) (skS.0 4 a a_1) →
% 4.64/4.79 ∀ (S : Iota),
% 4.64/4.79 breln1 (skS.0 3 a) S →
% 4.64/4.79 ∀ (Xx : Iota),
% 4.64/4.79 in Xx (skS.0 3 a) →
% 4.64/4.79 ∀ (Xy : Iota),
% 4.64/4.79 in Xy (skS.0 3 a) → in (kpair Xx Xy) (skS.0 4 a a_1) → in (kpair Xx Xy) (binunion (skS.0 4 a a_1) S))
% 4.64/4.79 False
% 4.64/4.79 Clause #34 (by clausification #[32]): ∀ (a a_1 : Iota),
% 4.64/4.79 Eq
% 4.64/4.79 (∀ (S : Iota),
% 4.64/4.79 breln1 (skS.0 3 a) S →
% 4.64/4.79 ∀ (Xx : Iota),
% 4.64/4.79 in Xx (skS.0 3 a) →
% 4.64/4.79 ∀ (Xy : Iota),
% 4.64/4.79 in Xy (skS.0 3 a) → in (kpair Xx Xy) (skS.0 4 a a_1) → in (kpair Xx Xy) (binunion (skS.0 4 a a_1) S))
% 4.64/4.79 False
% 4.64/4.79 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota),
% 4.64/4.79 Eq
% 4.64/4.79 (Not
% 4.64/4.79 (breln1 (skS.0 3 a) (skS.0 5 a a_1 a_2) →
% 4.64/4.79 ∀ (Xx : Iota),
% 4.64/4.79 in Xx (skS.0 3 a) →
% 4.64/4.79 ∀ (Xy : Iota),
% 4.64/4.79 in Xy (skS.0 3 a) →
% 4.64/4.79 in (kpair Xx Xy) (skS.0 4 a a_1) → in (kpair Xx Xy) (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))))
% 4.64/4.79 True
% 4.64/4.79 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 : Iota),
% 4.64/4.79 Eq
% 4.64/4.79 (breln1 (skS.0 3 a) (skS.0 5 a a_1 a_2) →
% 4.64/4.81 ∀ (Xx : Iota),
% 4.64/4.81 in Xx (skS.0 3 a) →
% 4.64/4.81 ∀ (Xy : Iota),
% 4.64/4.81 in Xy (skS.0 3 a) →
% 4.64/4.81 in (kpair Xx Xy) (skS.0 4 a a_1) → in (kpair Xx Xy) (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)))
% 4.64/4.81 False
% 4.64/4.81 Clause #38 (by clausification #[36]): ∀ (a a_1 a_2 : Iota),
% 4.64/4.81 Eq
% 4.64/4.81 (∀ (Xx : Iota),
% 4.64/4.81 in Xx (skS.0 3 a) →
% 4.64/4.81 ∀ (Xy : Iota),
% 4.64/4.81 in Xy (skS.0 3 a) →
% 4.64/4.81 in (kpair Xx Xy) (skS.0 4 a a_1) → in (kpair Xx Xy) (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)))
% 4.64/4.81 False
% 4.64/4.81 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.64/4.81 Eq
% 4.64/4.81 (Not
% 4.64/4.81 (in (skS.0 6 a a_1 a_2 a_3) (skS.0 3 a) →
% 4.64/4.81 ∀ (Xy : Iota),
% 4.64/4.81 in Xy (skS.0 3 a) →
% 4.64/4.81 in (kpair (skS.0 6 a a_1 a_2 a_3) Xy) (skS.0 4 a a_1) →
% 4.64/4.81 in (kpair (skS.0 6 a a_1 a_2 a_3) Xy) (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))))
% 4.64/4.81 True
% 4.64/4.81 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.64/4.81 Eq
% 4.64/4.81 (in (skS.0 6 a a_1 a_2 a_3) (skS.0 3 a) →
% 4.64/4.81 ∀ (Xy : Iota),
% 4.64/4.81 in Xy (skS.0 3 a) →
% 4.64/4.81 in (kpair (skS.0 6 a a_1 a_2 a_3) Xy) (skS.0 4 a a_1) →
% 4.64/4.81 in (kpair (skS.0 6 a a_1 a_2 a_3) Xy) (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)))
% 4.64/4.81 False
% 4.64/4.81 Clause #42 (by clausification #[40]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.64/4.81 Eq
% 4.64/4.81 (∀ (Xy : Iota),
% 4.64/4.81 in Xy (skS.0 3 a) →
% 4.64/4.81 in (kpair (skS.0 6 a a_1 a_2 a_3) Xy) (skS.0 4 a a_1) →
% 4.64/4.81 in (kpair (skS.0 6 a a_1 a_2 a_3) Xy) (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)))
% 4.64/4.81 False
% 4.64/4.81 Clause #54 (by clausification #[42]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.64/4.81 Eq
% 4.64/4.81 (Not
% 4.64/4.81 (in (skS.0 7 a a_1 a_2 a_3 a_4) (skS.0 3 a) →
% 4.64/4.81 in (kpair (skS.0 6 a a_1 a_2 a_3) (skS.0 7 a a_1 a_2 a_3 a_4)) (skS.0 4 a a_1) →
% 4.64/4.81 in (kpair (skS.0 6 a a_1 a_2 a_3) (skS.0 7 a a_1 a_2 a_3 a_4))
% 4.64/4.81 (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))))
% 4.64/4.81 True
% 4.64/4.81 Clause #55 (by clausification #[54]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.64/4.81 Eq
% 4.64/4.81 (in (skS.0 7 a a_1 a_2 a_3 a_4) (skS.0 3 a) →
% 4.64/4.81 in (kpair (skS.0 6 a a_1 a_2 a_3) (skS.0 7 a a_1 a_2 a_3 a_4)) (skS.0 4 a a_1) →
% 4.64/4.81 in (kpair (skS.0 6 a a_1 a_2 a_3) (skS.0 7 a a_1 a_2 a_3 a_4)) (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)))
% 4.64/4.81 False
% 4.64/4.81 Clause #57 (by clausification #[55]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.64/4.81 Eq
% 4.64/4.81 (in (kpair (skS.0 6 a a_1 a_2 a_3) (skS.0 7 a a_1 a_2 a_3 a_4)) (skS.0 4 a a_1) →
% 4.64/4.81 in (kpair (skS.0 6 a a_1 a_2 a_3) (skS.0 7 a a_1 a_2 a_3 a_4)) (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)))
% 4.64/4.81 False
% 4.64/4.81 Clause #69 (by clausification #[57]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (in (kpair (skS.0 6 a a_1 a_2 a_3) (skS.0 7 a a_1 a_2 a_3 a_4)) (skS.0 4 a a_1)) True
% 4.64/4.81 Clause #70 (by clausification #[57]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.64/4.81 Eq (in (kpair (skS.0 6 a a_1 a_2 a_3) (skS.0 7 a a_1 a_2 a_3 a_4)) (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)))
% 4.64/4.81 False
% 4.64/4.81 Clause #71 (by superposition #[69, 28]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 4.64/4.81 Or (Eq True False)
% 4.64/4.81 (Eq (in (kpair (skS.0 6 a a_1 a_2 a_3) (skS.0 7 a a_1 a_2 a_3 a_4)) (binunion (skS.0 4 a a_1) a_5)) True)
% 4.64/4.81 Clause #86 (by clausification #[71]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 4.64/4.81 Eq (in (kpair (skS.0 6 a a_1 a_2 a_3) (skS.0 7 a a_1 a_2 a_3 a_4)) (binunion (skS.0 4 a a_1) a_5)) True
% 4.64/4.81 Clause #87 (by superposition #[86, 70]): Eq True False
% 4.64/4.81 Clause #89 (by clausification #[87]): False
% 4.64/4.81 SZS output end Proof for theBenchmark.p
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