%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU786^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n021.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 08:02:26 PM UTC 2025 % Result : Theorem 3.94s 4.12s % Output : Proof 3.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SEU786^2 : TPTP v9.2.0. Released v3.7.0. % 0.10/0.13 % Command : duper %s % 0.13/0.34 % Computer : n021.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 : Fri Oct 3 06:05:23 EDT 2025 % 0.13/0.34 % CPUTime : % 3.94/4.12 SZS status Theorem for theBenchmark.p % 3.94/4.12 SZS output start Proof for theBenchmark.p % 3.94/4.12 Clause #0 (by assumption #[]): Eq (Eq binunionE (∀ (A B Xx : Iota), in Xx (binunion A B) → Or (in Xx A) (in Xx B))) True % 3.94/4.12 Clause #1 (by assumption #[]): Eq % 3.94/4.12 (Not % 3.94/4.12 (binunionE → % 3.94/4.12 ∀ (A R : Iota), % 3.94/4.12 breln1 A R → % 3.94/4.12 ∀ (S : Iota), % 3.94/4.12 breln1 A S → % 3.94/4.12 ∀ (Xx : Iota), % 3.94/4.12 in Xx A → % 3.94/4.12 ∀ (Xy : Iota), % 3.94/4.12 in Xy A → in (kpair Xx Xy) (binunion R S) → Or (in (kpair Xx Xy) R) (in (kpair Xx Xy) S))) % 3.94/4.12 True % 3.94/4.12 Clause #2 (by clausification #[0]): Eq binunionE (∀ (A B Xx : Iota), in Xx (binunion A B) → Or (in Xx A) (in Xx B)) % 3.94/4.12 Clause #19 (by clausification #[1]): Eq % 3.94/4.12 (binunionE → % 3.94/4.12 ∀ (A R : Iota), % 3.94/4.12 breln1 A R → % 3.94/4.12 ∀ (S : Iota), % 3.94/4.12 breln1 A S → % 3.94/4.12 ∀ (Xx : Iota), % 3.94/4.12 in Xx A → % 3.94/4.12 ∀ (Xy : Iota), in Xy A → in (kpair Xx Xy) (binunion R S) → Or (in (kpair Xx Xy) R) (in (kpair Xx Xy) S)) % 3.94/4.12 False % 3.94/4.12 Clause #20 (by clausification #[19]): Eq binunionE True % 3.94/4.12 Clause #21 (by clausification #[19]): Eq % 3.94/4.12 (∀ (A R : Iota), % 3.94/4.12 breln1 A R → % 3.94/4.12 ∀ (S : Iota), % 3.94/4.12 breln1 A S → % 3.94/4.12 ∀ (Xx : Iota), % 3.94/4.12 in Xx A → % 3.94/4.12 ∀ (Xy : Iota), in Xy A → in (kpair Xx Xy) (binunion R S) → Or (in (kpair Xx Xy) R) (in (kpair Xx Xy) S)) % 3.94/4.12 False % 3.94/4.12 Clause #22 (by backward demodulation #[20, 2]): Eq True (∀ (A B Xx : Iota), in Xx (binunion A B) → Or (in Xx A) (in Xx B)) % 3.94/4.12 Clause #28 (by clausification #[22]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (binunion a B) → Or (in Xx a) (in Xx B)) True % 3.94/4.12 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (binunion a a_1) → Or (in Xx a) (in Xx a_1)) True % 3.94/4.12 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Eq (in a (binunion a_1 a_2) → Or (in a a_1) (in a a_2)) True % 3.94/4.12 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (binunion a_1 a_2)) False) (Eq (Or (in a a_1) (in a a_2)) True) % 3.94/4.12 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (binunion a_1 a_2)) False) (Or (Eq (in a a_1) True) (Eq (in a a_2) True)) % 3.94/4.12 Clause #34 (by clausification #[21]): ∀ (a : Iota), % 3.94/4.12 Eq % 3.94/4.12 (Not % 3.94/4.12 (∀ (R : Iota), % 3.94/4.12 breln1 (skS.0 3 a) R → % 3.94/4.12 ∀ (S : Iota), % 3.94/4.12 breln1 (skS.0 3 a) S → % 3.94/4.12 ∀ (Xx : Iota), % 3.94/4.12 in Xx (skS.0 3 a) → % 3.94/4.12 ∀ (Xy : Iota), % 3.94/4.12 in Xy (skS.0 3 a) → in (kpair Xx Xy) (binunion R S) → Or (in (kpair Xx Xy) R) (in (kpair Xx Xy) S))) % 3.94/4.12 True % 3.94/4.12 Clause #35 (by clausification #[34]): ∀ (a : Iota), % 3.94/4.12 Eq % 3.94/4.12 (∀ (R : Iota), % 3.94/4.12 breln1 (skS.0 3 a) R → % 3.94/4.12 ∀ (S : Iota), % 3.94/4.12 breln1 (skS.0 3 a) S → % 3.94/4.12 ∀ (Xx : Iota), % 3.94/4.12 in Xx (skS.0 3 a) → % 3.94/4.12 ∀ (Xy : Iota), % 3.94/4.12 in Xy (skS.0 3 a) → in (kpair Xx Xy) (binunion R S) → Or (in (kpair Xx Xy) R) (in (kpair Xx Xy) S)) % 3.94/4.12 False % 3.94/4.12 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), % 3.94/4.12 Eq % 3.94/4.12 (Not % 3.94/4.12 (breln1 (skS.0 3 a) (skS.0 4 a a_1) → % 3.94/4.12 ∀ (S : Iota), % 3.94/4.12 breln1 (skS.0 3 a) S → % 3.94/4.12 ∀ (Xx : Iota), % 3.94/4.12 in Xx (skS.0 3 a) → % 3.94/4.12 ∀ (Xy : Iota), % 3.94/4.12 in Xy (skS.0 3 a) → % 3.94/4.12 in (kpair Xx Xy) (binunion (skS.0 4 a a_1) S) → % 3.94/4.12 Or (in (kpair Xx Xy) (skS.0 4 a a_1)) (in (kpair Xx Xy) S))) % 3.94/4.12 True % 3.94/4.12 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), % 3.94/4.12 Eq % 3.94/4.12 (breln1 (skS.0 3 a) (skS.0 4 a a_1) → % 3.94/4.12 ∀ (S : Iota), % 3.94/4.12 breln1 (skS.0 3 a) S → % 3.94/4.12 ∀ (Xx : Iota), % 3.94/4.12 in Xx (skS.0 3 a) → % 3.94/4.12 ∀ (Xy : Iota), % 3.94/4.12 in Xy (skS.0 3 a) → % 3.94/4.12 in (kpair Xx Xy) (binunion (skS.0 4 a a_1) S) → % 3.94/4.12 Or (in (kpair Xx Xy) (skS.0 4 a a_1)) (in (kpair Xx Xy) S)) % 3.94/4.12 False % 3.94/4.12 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota), % 3.94/4.12 Eq % 3.94/4.12 (∀ (S : Iota), % 3.94/4.12 breln1 (skS.0 3 a) S → % 3.94/4.12 ∀ (Xx : Iota), % 3.96/4.14 in Xx (skS.0 3 a) → % 3.96/4.14 ∀ (Xy : Iota), % 3.96/4.14 in Xy (skS.0 3 a) → % 3.96/4.14 in (kpair Xx Xy) (binunion (skS.0 4 a a_1) S) → % 3.96/4.14 Or (in (kpair Xx Xy) (skS.0 4 a a_1)) (in (kpair Xx Xy) S)) % 3.96/4.14 False % 3.96/4.14 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), % 3.96/4.14 Eq % 3.96/4.14 (Not % 3.96/4.14 (breln1 (skS.0 3 a) (skS.0 5 a a_1 a_2) → % 3.96/4.14 ∀ (Xx : Iota), % 3.96/4.14 in Xx (skS.0 3 a) → % 3.96/4.14 ∀ (Xy : Iota), % 3.96/4.14 in Xy (skS.0 3 a) → % 3.96/4.14 in (kpair Xx Xy) (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)) → % 3.96/4.14 Or (in (kpair Xx Xy) (skS.0 4 a a_1)) (in (kpair Xx Xy) (skS.0 5 a a_1 a_2)))) % 3.96/4.14 True % 3.96/4.14 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 3.96/4.14 Eq % 3.96/4.14 (breln1 (skS.0 3 a) (skS.0 5 a a_1 a_2) → % 3.96/4.14 ∀ (Xx : Iota), % 3.96/4.14 in Xx (skS.0 3 a) → % 3.96/4.14 ∀ (Xy : Iota), % 3.96/4.14 in Xy (skS.0 3 a) → % 3.96/4.14 in (kpair Xx Xy) (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)) → % 3.96/4.14 Or (in (kpair Xx Xy) (skS.0 4 a a_1)) (in (kpair Xx Xy) (skS.0 5 a a_1 a_2))) % 3.96/4.15 False % 3.96/4.15 Clause #43 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), % 3.96/4.15 Eq % 3.96/4.15 (∀ (Xx : Iota), % 3.96/4.15 in Xx (skS.0 3 a) → % 3.96/4.15 ∀ (Xy : Iota), % 3.96/4.15 in Xy (skS.0 3 a) → % 3.96/4.15 in (kpair Xx Xy) (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)) → % 3.96/4.15 Or (in (kpair Xx Xy) (skS.0 4 a a_1)) (in (kpair Xx Xy) (skS.0 5 a a_1 a_2))) % 3.96/4.15 False % 3.96/4.15 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota), % 3.96/4.15 Eq % 3.96/4.15 (Not % 3.96/4.15 (in (skS.0 6 a a_1 a_2 a_3) (skS.0 3 a) → % 3.96/4.15 ∀ (Xy : Iota), % 3.96/4.15 in Xy (skS.0 3 a) → % 3.96/4.15 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)) → % 3.96/4.15 Or (in (kpair (skS.0 6 a a_1 a_2 a_3) Xy) (skS.0 4 a a_1)) % 3.96/4.15 (in (kpair (skS.0 6 a a_1 a_2 a_3) Xy) (skS.0 5 a a_1 a_2)))) % 3.96/4.15 True % 3.96/4.15 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota), % 3.96/4.15 Eq % 3.96/4.15 (in (skS.0 6 a a_1 a_2 a_3) (skS.0 3 a) → % 3.96/4.15 ∀ (Xy : Iota), % 3.96/4.15 in Xy (skS.0 3 a) → % 3.96/4.15 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)) → % 3.96/4.15 Or (in (kpair (skS.0 6 a a_1 a_2 a_3) Xy) (skS.0 4 a a_1)) % 3.96/4.15 (in (kpair (skS.0 6 a a_1 a_2 a_3) Xy) (skS.0 5 a a_1 a_2))) % 3.96/4.15 False % 3.96/4.15 Clause #47 (by clausification #[45]): ∀ (a a_1 a_2 a_3 : Iota), % 3.96/4.15 Eq % 3.96/4.15 (∀ (Xy : Iota), % 3.96/4.15 in Xy (skS.0 3 a) → % 3.96/4.15 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)) → % 3.96/4.15 Or (in (kpair (skS.0 6 a a_1 a_2 a_3) Xy) (skS.0 4 a a_1)) % 3.96/4.15 (in (kpair (skS.0 6 a a_1 a_2 a_3) Xy) (skS.0 5 a a_1 a_2))) % 3.96/4.15 False % 3.96/4.15 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 3.96/4.15 Eq % 3.96/4.15 (Not % 3.96/4.15 (in (skS.0 7 a a_1 a_2 a_3 a_4) (skS.0 3 a) → % 3.96/4.15 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)) → % 3.96/4.15 Or (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)) % 3.96/4.15 (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 5 a a_1 a_2)))) % 3.96/4.15 True % 3.96/4.15 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 3.96/4.15 Eq % 3.96/4.15 (in (skS.0 7 a a_1 a_2 a_3 a_4) (skS.0 3 a) → % 3.96/4.15 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)) → % 3.96/4.15 Or (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)) % 3.96/4.15 (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 5 a a_1 a_2))) % 3.96/4.15 False % 3.96/4.15 Clause #51 (by clausification #[49]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 3.96/4.15 Eq % 3.96/4.15 (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)) → % 3.96/4.15 Or (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)) % 3.96/4.15 (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 5 a a_1 a_2))) % 3.96/4.15 False % 3.96/4.15 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 3.96/4.15 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))) % 3.96/4.16 True % 3.96/4.16 Clause #53 (by clausification #[51]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 3.96/4.16 Eq % 3.96/4.16 (Or (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)) % 3.96/4.16 (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 5 a a_1 a_2))) % 3.96/4.16 False % 3.96/4.16 Clause #54 (by superposition #[52, 32]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 3.96/4.16 Or (Eq True False) % 3.96/4.16 (Or (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) % 3.96/4.16 (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 5 a a_1 a_2)) True)) % 3.96/4.16 Clause #55 (by clausification #[53]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 3.96/4.16 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 5 a a_1 a_2)) False % 3.96/4.16 Clause #56 (by clausification #[53]): ∀ (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)) False % 3.96/4.16 Clause #57 (by clausification #[54]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 3.96/4.16 Or (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) % 3.96/4.16 (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 5 a a_1 a_2)) True) % 3.96/4.16 Clause #58 (by forward demodulation #[57, 56]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 3.96/4.16 Or (Eq False True) (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 5 a a_1 a_2)) True) % 3.96/4.16 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 3.96/4.16 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 5 a a_1 a_2)) True % 3.96/4.16 Clause #60 (by superposition #[59, 55]): Eq True False % 3.96/4.16 Clause #61 (by clausification #[60]): False % 3.96/4.16 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------