%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU500^2 : 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 08:01:45 PM UTC 2025 % Result : Theorem 15.34s 15.54s % Output : Proof 15.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SEU500^2 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.14 % Command : duper %s % 0.13/0.35 % Computer : n027.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 06:26:38 EDT 2025 % 0.13/0.35 % CPUTime : % 15.34/15.54 SZS status Theorem for theBenchmark.p % 15.34/15.54 SZS output start Proof for theBenchmark.p % 15.34/15.54 Clause #0 (by assumption #[]): Eq (Eq dsetconstrER (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A fun Xy => Xphi Xy) → Xphi Xx)) % 15.34/15.54 True % 15.34/15.54 Clause #1 (by assumption #[]): Eq (Eq prop2set fun Xphi => dsetconstr (powerset emptyset) fun Xx => Xphi) True % 15.34/15.54 Clause #2 (by assumption #[]): Eq (Not (dsetconstrER → ∀ (Xphi : Prop) (Xx : Iota), in Xx (prop2set Xphi) → Xphi)) True % 15.34/15.54 Clause #3 (by clausification #[2]): Eq (dsetconstrER → ∀ (Xphi : Prop) (Xx : Iota), in Xx (prop2set Xphi) → Xphi) False % 15.34/15.54 Clause #4 (by clausification #[3]): Eq dsetconstrER True % 15.34/15.54 Clause #5 (by clausification #[3]): Eq (∀ (Xphi : Prop) (Xx : Iota), in Xx (prop2set Xphi) → Xphi) False % 15.34/15.54 Clause #6 (by clausification #[5]): ∀ (a : Prop), Eq (Not (∀ (Xx : Iota), in Xx (prop2set (skS.0 0 a)) → skS.0 0 a)) True % 15.34/15.54 Clause #7 (by clausification #[6]): ∀ (a : Prop), Eq (∀ (Xx : Iota), in Xx (prop2set (skS.0 0 a)) → skS.0 0 a) False % 15.34/15.54 Clause #8 (by clausification #[7]): ∀ (a : Prop) (a_1 : Iota), Eq (Not (in (skS.0 1 a a_1) (prop2set (skS.0 0 a)) → skS.0 0 a)) True % 15.34/15.54 Clause #9 (by clausification #[8]): ∀ (a : Prop) (a_1 : Iota), Eq (in (skS.0 1 a a_1) (prop2set (skS.0 0 a)) → skS.0 0 a) False % 15.34/15.54 Clause #10 (by clausification #[9]): ∀ (a : Prop) (a_1 : Iota), Eq (in (skS.0 1 a a_1) (prop2set (skS.0 0 a))) True % 15.34/15.54 Clause #11 (by clausification #[9]): ∀ (a : Prop), Eq (skS.0 0 a) False % 15.34/15.54 Clause #13 (by identity boolHoist #[10]): ∀ (a : Prop) (a_1 : Iota), Or (Eq (in (skS.0 1 a a_1) (prop2set False)) True) (Eq (skS.0 0 a) True) % 15.34/15.54 Clause #21 (by identity loobHoist #[11]): ∀ (a : Prop), Or (Eq (skS.0 0 True) False) (Eq a False) % 15.34/15.54 Clause #23 (by betaEtaReduce #[0]): Eq (Eq dsetconstrER (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → Xphi Xx)) True % 15.34/15.54 Clause #24 (by clausification #[23]): Eq dsetconstrER (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → Xphi Xx) % 15.34/15.54 Clause #25 (by forward demodulation #[24, 4]): Eq True (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → Xphi Xx) % 15.34/15.54 Clause #26 (by clausification #[25]): ∀ (a : Iota), Eq (∀ (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr a Xphi) → Xphi Xx) True % 15.34/15.54 Clause #27 (by clausification #[26]): ∀ (a : Iota) (a_1 : Iota → Prop), Eq (∀ (Xx : Iota), in Xx (dsetconstr a a_1) → a_1 Xx) True % 15.34/15.54 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Eq (in a (dsetconstr a_1 a_2) → a_2 a) True % 15.34/15.54 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Or (Eq (in a (dsetconstr a_1 a_2)) False) (Eq (a_2 a) True) % 15.34/15.54 Clause #31 (by clausification #[1]): Eq prop2set fun Xphi => dsetconstr (powerset emptyset) fun Xx => Xphi % 15.34/15.54 Clause #32 (by argument congruence #[31]): ∀ (a : Prop), Eq (prop2set a) ((fun Xphi => dsetconstr (powerset emptyset) fun Xx => Xphi) a) % 15.34/15.54 Clause #34 (by betaEtaReduce #[32]): ∀ (a : Prop), Eq (prop2set a) (dsetconstr (powerset emptyset) fun Xx => a) % 15.34/15.54 Clause #36 (by identity boolHoist #[34]): ∀ (a : Prop), Or (Eq (prop2set False) (dsetconstr (powerset emptyset) fun Xx => a)) (Eq a True) % 15.34/15.54 Clause #63 (by fluidBoolHoist #[36]): ∀ (a : Prop), Or (Eq a True) (Or (Eq (prop2set False) (dsetconstr (powerset emptyset) fun Xx => False)) (Eq a True)) % 15.34/15.54 Clause #69 (by identity loobHoist #[13]): ∀ (a : Prop) (a_1 : Iota), Or (Eq (skS.0 0 a) True) (Or (Eq (in (skS.0 1 True a_1) (prop2set False)) True) (Eq a False)) % 15.34/15.54 Clause #71 (by identity loobHoist #[69]): ∀ (a : Iota) (a_1 : Prop), % 15.34/15.54 Or (Eq (in (skS.0 1 True a) (prop2set False)) True) (Or (Eq a_1 False) (Or (Eq (skS.0 0 True) True) (Eq a_1 False))) % 15.34/15.54 Clause #73 (by eliminate duplicate literals #[71]): ∀ (a : Iota) (a_1 : Prop), % 15.34/15.54 Or (Eq (in (skS.0 1 True a) (prop2set False)) True) (Or (Eq a_1 False) (Eq (skS.0 0 True) True)) % 15.34/15.54 Clause #75 (by falseElim #[73]): ∀ (a : Iota), Or (Eq (in (skS.0 1 True a) (prop2set False)) True) (Eq (skS.0 0 True) True) % 15.34/15.54 Clause #122 (by eliminate duplicate literals #[63]): ∀ (a : Prop), Or (Eq a True) (Eq (prop2set False) (dsetconstr (powerset emptyset) fun Xx => False)) % 15.48/15.69 Clause #123 (by superposition #[122, 21]): ∀ (a : Prop), % 15.48/15.69 Or (Eq (prop2set False) (dsetconstr (powerset emptyset) fun Xx => False)) (Or (Eq True False) (Eq a False)) % 15.48/15.69 Clause #148 (by clausification #[123]): ∀ (a : Prop), Or (Eq (prop2set False) (dsetconstr (powerset emptyset) fun Xx => False)) (Eq a False) % 15.48/15.69 Clause #150 (by falseElim #[148]): Eq (prop2set False) (dsetconstr (powerset emptyset) fun Xx => False) % 15.48/15.69 Clause #153 (by superposition #[150, 29]): ∀ (a : Iota), Or (Eq (in a (prop2set False)) False) (Eq False True) % 15.48/15.69 Clause #164 (by clausification #[153]): ∀ (a : Iota), Eq (in a (prop2set False)) False % 15.48/15.69 Clause #2232 (by superposition #[75, 164]): Or (Eq False True) (Eq (skS.0 0 True) True) % 15.48/15.69 Clause #2275 (by clausification #[2232]): Eq (skS.0 0 True) True % 15.48/15.69 Clause #2278 (by superposition #[2275, 21]): ∀ (a : Prop), Or (Eq True False) (Eq a False) % 15.48/15.69 Clause #2309 (by clausification #[2278]): ∀ (a : Prop), Eq a False % 15.48/15.69 Clause #2311 (by falseElim #[2309]): False % 15.48/15.69 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------