%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU800^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n024.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 08:02:28 PM UTC 2025 % Result : Theorem 4.51s 4.68s % Output : Proof 4.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SEU800^2 : TPTP v9.2.0. Released v3.7.0. % 0.08/0.13 % Command : duper %s % 0.14/0.34 % Computer : n024.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Oct 3 06:20:38 EDT 2025 % 0.14/0.34 % CPUTime : % 4.51/4.68 SZS status Theorem for theBenchmark.p % 4.51/4.68 SZS output start Proof for theBenchmark.p % 4.51/4.68 Clause #0 (by assumption #[]): Eq (Eq dsetconstrER (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A fun Xy => Xphi Xy) → Xphi Xx)) % 4.51/4.68 True % 4.51/4.68 Clause #1 (by assumption #[]): Eq (Eq injFuncSet fun A B => dsetconstr (funcSet A B) fun Xf => injective A B Xf) True % 4.51/4.68 Clause #2 (by assumption #[]): Eq (Not (dsetconstrER → ∀ (Xx Xy Xf : Iota), in Xf (injFuncSet Xx Xy) → injective Xx Xy Xf)) True % 4.51/4.68 Clause #3 (by betaEtaReduce #[0]): Eq (Eq dsetconstrER (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → Xphi Xx)) True % 4.51/4.68 Clause #4 (by clausification #[3]): Eq dsetconstrER (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → Xphi Xx) % 4.51/4.68 Clause #20 (by clausification #[2]): Eq (dsetconstrER → ∀ (Xx Xy Xf : Iota), in Xf (injFuncSet Xx Xy) → injective Xx Xy Xf) False % 4.51/4.68 Clause #21 (by clausification #[20]): Eq dsetconstrER True % 4.51/4.68 Clause #22 (by clausification #[20]): Eq (∀ (Xx Xy Xf : Iota), in Xf (injFuncSet Xx Xy) → injective Xx Xy Xf) False % 4.51/4.68 Clause #23 (by backward demodulation #[21, 4]): Eq True (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → Xphi Xx) % 4.51/4.68 Clause #26 (by betaEtaReduce #[1]): Eq (Eq injFuncSet fun A B => dsetconstr (funcSet A B) (injective A B)) True % 4.51/4.68 Clause #27 (by clausification #[26]): Eq injFuncSet fun A B => dsetconstr (funcSet A B) (injective A B) % 4.51/4.68 Clause #28 (by argument congruence #[27]): ∀ (a : Iota), Eq (injFuncSet a) ((fun A B => dsetconstr (funcSet A B) (injective A B)) a) % 4.51/4.68 Clause #30 (by clausification #[23]): ∀ (a : Iota), Eq (∀ (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr a Xphi) → Xphi Xx) True % 4.51/4.68 Clause #31 (by clausification #[30]): ∀ (a : Iota) (a_1 : Iota → Prop), Eq (∀ (Xx : Iota), in Xx (dsetconstr a a_1) → a_1 Xx) True % 4.51/4.68 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Eq (in a (dsetconstr a_1 a_2) → a_2 a) True % 4.51/4.68 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Or (Eq (in a (dsetconstr a_1 a_2)) False) (Eq (a_2 a) True) % 4.51/4.68 Clause #36 (by clausification #[22]): ∀ (a : Iota), Eq (Not (∀ (Xy Xf : Iota), in Xf (injFuncSet (skS.0 3 a) Xy) → injective (skS.0 3 a) Xy Xf)) True % 4.51/4.68 Clause #37 (by clausification #[36]): ∀ (a : Iota), Eq (∀ (Xy Xf : Iota), in Xf (injFuncSet (skS.0 3 a) Xy) → injective (skS.0 3 a) Xy Xf) False % 4.51/4.68 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), % 4.51/4.68 Eq (Not (∀ (Xf : Iota), in Xf (injFuncSet (skS.0 3 a) (skS.0 4 a a_1)) → injective (skS.0 3 a) (skS.0 4 a a_1) Xf)) % 4.51/4.68 True % 4.51/4.68 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), % 4.51/4.68 Eq (∀ (Xf : Iota), in Xf (injFuncSet (skS.0 3 a) (skS.0 4 a a_1)) → injective (skS.0 3 a) (skS.0 4 a a_1) Xf) False % 4.51/4.68 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), % 4.51/4.68 Eq % 4.51/4.68 (Not % 4.51/4.68 (in (skS.0 5 a a_1 a_2) (injFuncSet (skS.0 3 a) (skS.0 4 a a_1)) → % 4.51/4.68 injective (skS.0 3 a) (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))) % 4.51/4.68 True % 4.51/4.68 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 4.51/4.68 Eq % 4.51/4.68 (in (skS.0 5 a a_1 a_2) (injFuncSet (skS.0 3 a) (skS.0 4 a a_1)) → % 4.51/4.68 injective (skS.0 3 a) (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)) % 4.51/4.68 False % 4.51/4.68 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 5 a a_1 a_2) (injFuncSet (skS.0 3 a) (skS.0 4 a a_1))) True % 4.51/4.68 Clause #43 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), Eq (injective (skS.0 3 a) (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)) False % 4.51/4.68 Clause #50 (by betaEtaReduce #[28]): ∀ (a : Iota), Eq (injFuncSet a) fun B => dsetconstr (funcSet a B) (injective a B) % 4.51/4.68 Clause #51 (by argument congruence #[50]): ∀ (a a_1 : Iota), Eq (injFuncSet a a_1) ((fun B => dsetconstr (funcSet a B) (injective a B)) a_1) % 4.51/4.68 Clause #60 (by betaEtaReduce #[51]): ∀ (a a_1 : Iota), Eq (injFuncSet a a_1) (dsetconstr (funcSet a a_1) (injective a a_1)) % 4.51/4.68 Clause #61 (by superposition #[60, 33]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (injFuncSet a_1 a_2)) False) (Eq (injective a_1 a_2 a) True) % 4.51/4.68 Clause #65 (by superposition #[61, 42]): ∀ (a a_1 a_2 : Iota), Or (Eq (injective (skS.0 3 a) (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)) True) (Eq False True) % 4.51/4.69 Clause #168 (by clausification #[65]): ∀ (a a_1 a_2 : Iota), Eq (injective (skS.0 3 a) (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)) True % 4.51/4.69 Clause #169 (by superposition #[168, 43]): Eq True False % 4.51/4.69 Clause #178 (by clausification #[169]): False % 4.51/4.69 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------