%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU783^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n027.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 : Fri Oct 3 08:02:25 PM UTC 2025 % Result : Theorem 4.64s 4.80s % Output : Proof 4.64s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU783^2 : TPTP v9.2.0. Released v3.7.0. % 0.11/0.14 % Command : duper %s % 0.14/0.35 % Computer : n027.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 : Fri Oct 3 04:55:23 EDT 2025 % 0.14/0.35 % CPUTime : % 4.64/4.80 SZS status Theorem for theBenchmark.p % 4.64/4.80 SZS output start Proof for theBenchmark.p % 4.64/4.80 Clause #0 (by assumption #[]): Eq (Eq binunionIL (∀ (A B Xx : Iota), in Xx A → in Xx (binunion A B))) True % 4.64/4.80 Clause #1 (by assumption #[]): Eq % 4.64/4.80 (Not % 4.64/4.80 (binunionIL → % 4.64/4.80 ∀ (A R : Iota), % 4.64/4.80 breln1 A R → % 4.64/4.80 ∀ (S : Iota), % 4.64/4.80 breln1 A S → % 4.64/4.80 ∀ (Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy A → in (kpair Xx Xy) R → in (kpair Xx Xy) (binunion R S))) % 4.64/4.80 True % 4.64/4.80 Clause #2 (by clausification #[0]): Eq binunionIL (∀ (A B Xx : Iota), in Xx A → in Xx (binunion A B)) % 4.64/4.80 Clause #18 (by clausification #[1]): Eq % 4.64/4.80 (binunionIL → % 4.64/4.80 ∀ (A R : Iota), % 4.64/4.80 breln1 A R → % 4.64/4.80 ∀ (S : Iota), % 4.64/4.80 breln1 A S → % 4.64/4.80 ∀ (Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy A → in (kpair Xx Xy) R → in (kpair Xx Xy) (binunion R S)) % 4.64/4.80 False % 4.64/4.80 Clause #19 (by clausification #[18]): Eq binunionIL True % 4.64/4.80 Clause #20 (by clausification #[18]): Eq % 4.64/4.80 (∀ (A R : Iota), % 4.64/4.80 breln1 A R → % 4.64/4.80 ∀ (S : Iota), % 4.64/4.80 breln1 A S → % 4.64/4.80 ∀ (Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy A → in (kpair Xx Xy) R → in (kpair Xx Xy) (binunion R S)) % 4.64/4.80 False % 4.64/4.80 Clause #21 (by backward demodulation #[19, 2]): Eq True (∀ (A B Xx : Iota), in Xx A → in Xx (binunion A B)) % 4.64/4.80 Clause #25 (by clausification #[21]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx a → in Xx (binunion a B)) True % 4.64/4.80 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx a → in Xx (binunion a a_1)) True % 4.64/4.80 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Eq (in a a_1 → in a (binunion a_1 a_2)) True % 4.64/4.80 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) % 4.64/4.80 Clause #29 (by clausification #[20]): ∀ (a : Iota), % 4.64/4.80 Eq % 4.64/4.80 (Not % 4.64/4.80 (∀ (R : Iota), % 4.64/4.80 breln1 (skS.0 3 a) R → % 4.64/4.80 ∀ (S : Iota), % 4.64/4.80 breln1 (skS.0 3 a) S → % 4.64/4.80 ∀ (Xx : Iota), % 4.64/4.80 in Xx (skS.0 3 a) → % 4.64/4.80 ∀ (Xy : Iota), in Xy (skS.0 3 a) → in (kpair Xx Xy) R → in (kpair Xx Xy) (binunion R S))) % 4.64/4.80 True % 4.64/4.80 Clause #30 (by clausification #[29]): ∀ (a : Iota), % 4.64/4.80 Eq % 4.64/4.80 (∀ (R : Iota), % 4.64/4.80 breln1 (skS.0 3 a) R → % 4.64/4.80 ∀ (S : Iota), % 4.64/4.80 breln1 (skS.0 3 a) S → % 4.64/4.80 ∀ (Xx : Iota), % 4.64/4.80 in Xx (skS.0 3 a) → % 4.64/4.80 ∀ (Xy : Iota), in Xy (skS.0 3 a) → in (kpair Xx Xy) R → in (kpair Xx Xy) (binunion R S)) % 4.64/4.80 False % 4.64/4.80 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), % 4.64/4.80 Eq % 4.64/4.80 (Not % 4.64/4.80 (breln1 (skS.0 3 a) (skS.0 4 a a_1) → % 4.64/4.80 ∀ (S : Iota), % 4.64/4.80 breln1 (skS.0 3 a) S → % 4.64/4.80 ∀ (Xx : Iota), % 4.64/4.80 in Xx (skS.0 3 a) → % 4.64/4.80 ∀ (Xy : Iota), % 4.64/4.80 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))) % 4.64/4.80 True % 4.64/4.80 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), % 4.64/4.80 Eq % 4.64/4.80 (breln1 (skS.0 3 a) (skS.0 4 a a_1) → % 4.64/4.80 ∀ (S : Iota), % 4.64/4.80 breln1 (skS.0 3 a) S → % 4.64/4.80 ∀ (Xx : Iota), % 4.64/4.80 in Xx (skS.0 3 a) → % 4.64/4.80 ∀ (Xy : Iota), % 4.64/4.80 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)) % 4.64/4.80 False % 4.64/4.80 Clause #34 (by clausification #[32]): ∀ (a a_1 : Iota), % 4.64/4.80 Eq % 4.64/4.80 (∀ (S : Iota), % 4.64/4.80 breln1 (skS.0 3 a) S → % 4.64/4.80 ∀ (Xx : Iota), % 4.64/4.80 in Xx (skS.0 3 a) → % 4.64/4.80 ∀ (Xy : Iota), % 4.64/4.80 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)) % 4.64/4.80 False % 4.64/4.80 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), % 4.64/4.80 Eq % 4.64/4.80 (Not % 4.64/4.80 (breln1 (skS.0 3 a) (skS.0 5 a a_1 a_2) → % 4.64/4.80 ∀ (Xx : Iota), % 4.64/4.80 in Xx (skS.0 3 a) → % 4.64/4.80 ∀ (Xy : Iota), % 4.64/4.80 in Xy (skS.0 3 a) → % 4.64/4.80 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)))) % 4.64/4.80 True % 4.64/4.80 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), % 4.64/4.80 Eq % 4.64/4.80 (breln1 (skS.0 3 a) (skS.0 5 a a_1 a_2) → % 4.64/4.82 ∀ (Xx : Iota), % 4.64/4.82 in Xx (skS.0 3 a) → % 4.64/4.82 ∀ (Xy : Iota), % 4.64/4.82 in Xy (skS.0 3 a) → % 4.64/4.82 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))) % 4.64/4.82 False % 4.64/4.82 Clause #38 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), % 4.64/4.82 Eq % 4.64/4.82 (∀ (Xx : Iota), % 4.64/4.82 in Xx (skS.0 3 a) → % 4.64/4.82 ∀ (Xy : Iota), % 4.64/4.82 in Xy (skS.0 3 a) → % 4.64/4.82 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))) % 4.64/4.82 False % 4.64/4.82 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 a_3 : Iota), % 4.64/4.82 Eq % 4.64/4.82 (Not % 4.64/4.82 (in (skS.0 6 a a_1 a_2 a_3) (skS.0 3 a) → % 4.64/4.82 ∀ (Xy : Iota), % 4.64/4.82 in Xy (skS.0 3 a) → % 4.64/4.82 in (kpair (skS.0 6 a a_1 a_2 a_3) Xy) (skS.0 4 a a_1) → % 4.64/4.82 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)))) % 4.64/4.82 True % 4.64/4.82 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 a_3 : Iota), % 4.64/4.82 Eq % 4.64/4.82 (in (skS.0 6 a a_1 a_2 a_3) (skS.0 3 a) → % 4.64/4.82 ∀ (Xy : Iota), % 4.64/4.82 in Xy (skS.0 3 a) → % 4.64/4.82 in (kpair (skS.0 6 a a_1 a_2 a_3) Xy) (skS.0 4 a a_1) → % 4.64/4.82 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))) % 4.64/4.82 False % 4.64/4.82 Clause #42 (by clausification #[40]): ∀ (a a_1 a_2 a_3 : Iota), % 4.64/4.82 Eq % 4.64/4.82 (∀ (Xy : Iota), % 4.64/4.82 in Xy (skS.0 3 a) → % 4.64/4.82 in (kpair (skS.0 6 a a_1 a_2 a_3) Xy) (skS.0 4 a a_1) → % 4.64/4.82 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))) % 4.64/4.82 False % 4.64/4.82 Clause #54 (by clausification #[42]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.64/4.82 Eq % 4.64/4.82 (Not % 4.64/4.82 (in (skS.0 7 a a_1 a_2 a_3 a_4) (skS.0 3 a) → % 4.64/4.82 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) → % 4.64/4.82 in (kpair (skS.0 6 a a_1 a_2 a_3) (skS.0 7 a a_1 a_2 a_3 a_4)) % 4.64/4.82 (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)))) % 4.64/4.82 True % 4.64/4.82 Clause #55 (by clausification #[54]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.64/4.82 Eq % 4.64/4.82 (in (skS.0 7 a a_1 a_2 a_3 a_4) (skS.0 3 a) → % 4.64/4.82 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) → % 4.64/4.82 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))) % 4.64/4.82 False % 4.64/4.82 Clause #57 (by clausification #[55]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.64/4.82 Eq % 4.64/4.82 (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) → % 4.64/4.82 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))) % 4.64/4.82 False % 4.64/4.82 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 % 4.64/4.82 Clause #70 (by clausification #[57]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.64/4.82 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))) % 4.64/4.82 False % 4.64/4.82 Clause #71 (by superposition #[69, 28]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.64/4.82 Or (Eq True False) % 4.64/4.82 (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) % 4.64/4.82 Clause #86 (by clausification #[71]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.64/4.82 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 % 4.64/4.82 Clause #87 (by superposition #[86, 70]): Eq True False % 4.64/4.82 Clause #89 (by clausification #[87]): False % 4.64/4.82 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------