%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU584^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n026.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 08:01:58 PM UTC 2025 % Result : Theorem 4.13s 4.31s % Output : Proof 4.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SEU584^2 : TPTP v9.2.0. Released v3.7.0. % 0.06/0.13 % Command : duper %s % 0.13/0.35 % Computer : n026.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Oct 3 05:43:53 EDT 2025 % 0.13/0.35 % CPUTime : % 4.13/4.31 SZS status Theorem for theBenchmark.p % 4.13/4.31 SZS output start Proof for theBenchmark.p % 4.13/4.31 Clause #0 (by assumption #[]): Eq (Eq setunionI (∀ (A Xx B : Iota), in Xx B → in B A → in Xx (setunion A))) True % 4.13/4.31 Clause #1 (by assumption #[]): Eq (Eq binunion fun Xx Xy => setunion (setadjoin Xx (setadjoin Xy emptyset))) True % 4.13/4.31 Clause #2 (by assumption #[]): Eq (Eq upairset2IR (∀ (Xx Xy : Iota), in Xy (setadjoin Xx (setadjoin Xy emptyset)))) True % 4.13/4.31 Clause #3 (by assumption #[]): Eq (Not (setunionI → upairset2IR → ∀ (A B Xx : Iota), in Xx B → in Xx (binunion A B))) True % 4.13/4.31 Clause #4 (by clausification #[3]): Eq (setunionI → upairset2IR → ∀ (A B Xx : Iota), in Xx B → in Xx (binunion A B)) False % 4.13/4.31 Clause #5 (by clausification #[4]): Eq setunionI True % 4.13/4.31 Clause #6 (by clausification #[4]): Eq (upairset2IR → ∀ (A B Xx : Iota), in Xx B → in Xx (binunion A B)) False % 4.13/4.31 Clause #7 (by clausification #[6]): Eq upairset2IR True % 4.13/4.31 Clause #8 (by clausification #[6]): Eq (∀ (A B Xx : Iota), in Xx B → in Xx (binunion A B)) False % 4.13/4.31 Clause #9 (by clausification #[8]): ∀ (a : Iota), Eq (Not (∀ (B Xx : Iota), in Xx B → in Xx (binunion (skS.0 0 a) B))) True % 4.13/4.31 Clause #10 (by clausification #[9]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx B → in Xx (binunion (skS.0 0 a) B)) False % 4.13/4.31 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (Not (∀ (Xx : Iota), in Xx (skS.0 1 a a_1) → in Xx (binunion (skS.0 0 a) (skS.0 1 a a_1)))) True % 4.13/4.31 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (skS.0 1 a a_1) → in Xx (binunion (skS.0 0 a) (skS.0 1 a a_1))) False % 4.13/4.31 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), % 4.13/4.31 Eq (Not (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1) → in (skS.0 2 a a_1 a_2) (binunion (skS.0 0 a) (skS.0 1 a a_1)))) True % 4.13/4.31 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 : Iota), % 4.13/4.31 Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1) → in (skS.0 2 a a_1 a_2) (binunion (skS.0 0 a) (skS.0 1 a a_1))) False % 4.13/4.31 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True % 4.13/4.31 Clause #16 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (binunion (skS.0 0 a) (skS.0 1 a a_1))) False % 4.13/4.31 Clause #17 (by clausification #[0]): Eq setunionI (∀ (A Xx B : Iota), in Xx B → in B A → in Xx (setunion A)) % 4.13/4.31 Clause #18 (by forward demodulation #[17, 5]): Eq True (∀ (A Xx B : Iota), in Xx B → in B A → in Xx (setunion A)) % 4.13/4.31 Clause #19 (by clausification #[18]): ∀ (a : Iota), Eq (∀ (Xx B : Iota), in Xx B → in B a → in Xx (setunion a)) True % 4.13/4.31 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (∀ (B : Iota), in a B → in B a_1 → in a (setunion a_1)) True % 4.13/4.31 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), Eq (in a a_1 → in a_1 a_2 → in a (setunion a_2)) True % 4.13/4.31 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Eq (in a_1 a_2 → in a (setunion a_2)) True) % 4.13/4.31 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Or (Eq (in a_1 a_2) False) (Eq (in a (setunion a_2)) True)) % 4.13/4.31 Clause #24 (by superposition #[23, 15]): ∀ (a a_1 a_2 a_3 : Iota), % 4.13/4.31 Or (Eq (in (skS.0 1 a a_1) a_2) False) (Or (Eq (in (skS.0 2 a a_1 a_3) (setunion a_2)) True) (Eq False True)) % 4.13/4.31 Clause #25 (by clausification #[2]): Eq upairset2IR (∀ (Xx Xy : Iota), in Xy (setadjoin Xx (setadjoin Xy emptyset))) % 4.13/4.31 Clause #26 (by forward demodulation #[25, 7]): Eq True (∀ (Xx Xy : Iota), in Xy (setadjoin Xx (setadjoin Xy emptyset))) % 4.13/4.31 Clause #27 (by clausification #[26]): ∀ (a : Iota), Eq (∀ (Xy : Iota), in Xy (setadjoin a (setadjoin Xy emptyset))) True % 4.13/4.31 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (in a (setadjoin a_1 (setadjoin a emptyset))) True % 4.13/4.31 Clause #30 (by clausification #[1]): Eq binunion fun Xx Xy => setunion (setadjoin Xx (setadjoin Xy emptyset)) % 4.13/4.31 Clause #31 (by argument congruence #[30]): ∀ (a : Iota), Eq (binunion a) ((fun Xx Xy => setunion (setadjoin Xx (setadjoin Xy emptyset))) a) % 4.13/4.31 Clause #33 (by betaEtaReduce #[31]): ∀ (a : Iota), Eq (binunion a) fun Xy => setunion (setadjoin a (setadjoin Xy emptyset)) % 4.17/4.32 Clause #34 (by argument congruence #[33]): ∀ (a a_1 : Iota), Eq (binunion a a_1) ((fun Xy => setunion (setadjoin a (setadjoin Xy emptyset))) a_1) % 4.17/4.32 Clause #40 (by betaEtaReduce #[34]): ∀ (a a_1 : Iota), Eq (binunion a a_1) (setunion (setadjoin a (setadjoin a_1 emptyset))) % 4.17/4.32 Clause #55 (by clausification #[24]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in (skS.0 1 a a_1) a_2) False) (Eq (in (skS.0 2 a a_1 a_3) (setunion a_2)) True) % 4.17/4.32 Clause #56 (by superposition #[55, 28]): ∀ (a a_1 a_2 a_3 : Iota), % 4.17/4.32 Or (Eq (in (skS.0 2 a a_1 a_2) (setunion (setadjoin a_3 (setadjoin (skS.0 1 a a_1) emptyset)))) True) (Eq False True) % 4.17/4.32 Clause #194 (by clausification #[56]): ∀ (a a_1 a_2 a_3 : Iota), % 4.17/4.32 Eq (in (skS.0 2 a a_1 a_2) (setunion (setadjoin a_3 (setadjoin (skS.0 1 a a_1) emptyset)))) True % 4.17/4.32 Clause #195 (by forward demodulation #[194, 40]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 2 a a_1 a_2) (binunion a_3 (skS.0 1 a a_1))) True % 4.17/4.32 Clause #196 (by superposition #[195, 16]): Eq True False % 4.17/4.32 Clause #202 (by clausification #[196]): False % 4.17/4.32 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------