%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU799^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n020.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 3.65s 3.86s % Output : Proof 3.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU799^2 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n020.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 06:02:23 EDT 2025 % 0.13/0.34 % CPUTime : % 3.65/3.86 SZS status Theorem for theBenchmark.p % 3.65/3.86 SZS output start Proof for theBenchmark.p % 3.65/3.86 Clause #0 (by assumption #[]): Eq (Eq dsetconstrEL (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A fun Xy => Xphi Xy) → in Xx A)) % 3.65/3.86 True % 3.65/3.86 Clause #1 (by assumption #[]): Eq (Eq injFuncSet fun A B => dsetconstr (funcSet A B) fun Xf => injective A B Xf) True % 3.65/3.86 Clause #2 (by assumption #[]): Eq (Not (dsetconstrEL → ∀ (A B Xf : Iota), in Xf (injFuncSet A B) → in Xf (funcSet A B))) True % 3.65/3.86 Clause #3 (by betaEtaReduce #[0]): Eq (Eq dsetconstrEL (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → in Xx A)) True % 3.65/3.86 Clause #4 (by clausification #[3]): Eq dsetconstrEL (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → in Xx A) % 3.65/3.86 Clause #20 (by clausification #[2]): Eq (dsetconstrEL → ∀ (A B Xf : Iota), in Xf (injFuncSet A B) → in Xf (funcSet A B)) False % 3.65/3.86 Clause #21 (by clausification #[20]): Eq dsetconstrEL True % 3.65/3.86 Clause #22 (by clausification #[20]): Eq (∀ (A B Xf : Iota), in Xf (injFuncSet A B) → in Xf (funcSet A B)) False % 3.65/3.86 Clause #23 (by backward demodulation #[21, 4]): Eq True (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → in Xx A) % 3.65/3.86 Clause #26 (by betaEtaReduce #[1]): Eq (Eq injFuncSet fun A B => dsetconstr (funcSet A B) (injective A B)) True % 3.65/3.86 Clause #27 (by clausification #[26]): Eq injFuncSet fun A B => dsetconstr (funcSet A B) (injective A B) % 3.65/3.86 Clause #28 (by argument congruence #[27]): ∀ (a : Iota), Eq (injFuncSet a) ((fun A B => dsetconstr (funcSet A B) (injective A B)) a) % 3.65/3.86 Clause #30 (by clausification #[23]): ∀ (a : Iota), Eq (∀ (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr a Xphi) → in Xx a) True % 3.65/3.86 Clause #31 (by clausification #[30]): ∀ (a : Iota) (a_1 : Iota → Prop), Eq (∀ (Xx : Iota), in Xx (dsetconstr a a_1) → in Xx a) True % 3.65/3.86 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Eq (in a (dsetconstr a_1 a_2) → in a a_1) True % 3.65/3.86 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Or (Eq (in a (dsetconstr a_1 a_2)) False) (Eq (in a a_1) True) % 3.65/3.86 Clause #34 (by clausification #[22]): ∀ (a : Iota), Eq (Not (∀ (B Xf : Iota), in Xf (injFuncSet (skS.0 3 a) B) → in Xf (funcSet (skS.0 3 a) B))) True % 3.65/3.86 Clause #35 (by clausification #[34]): ∀ (a : Iota), Eq (∀ (B Xf : Iota), in Xf (injFuncSet (skS.0 3 a) B) → in Xf (funcSet (skS.0 3 a) B)) False % 3.65/3.86 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), % 3.65/3.86 Eq (Not (∀ (Xf : Iota), in Xf (injFuncSet (skS.0 3 a) (skS.0 4 a a_1)) → in Xf (funcSet (skS.0 3 a) (skS.0 4 a a_1)))) % 3.65/3.86 True % 3.65/3.86 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), % 3.65/3.86 Eq (∀ (Xf : Iota), in Xf (injFuncSet (skS.0 3 a) (skS.0 4 a a_1)) → in Xf (funcSet (skS.0 3 a) (skS.0 4 a a_1))) False % 3.65/3.86 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), % 3.65/3.86 Eq % 3.65/3.86 (Not % 3.65/3.86 (in (skS.0 5 a a_1 a_2) (injFuncSet (skS.0 3 a) (skS.0 4 a a_1)) → % 3.65/3.86 in (skS.0 5 a a_1 a_2) (funcSet (skS.0 3 a) (skS.0 4 a a_1)))) % 3.65/3.86 True % 3.65/3.86 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), % 3.65/3.86 Eq % 3.65/3.86 (in (skS.0 5 a a_1 a_2) (injFuncSet (skS.0 3 a) (skS.0 4 a a_1)) → % 3.65/3.86 in (skS.0 5 a a_1 a_2) (funcSet (skS.0 3 a) (skS.0 4 a a_1))) % 3.65/3.86 False % 3.65/3.86 Clause #40 (by clausification #[39]): ∀ (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 % 3.65/3.86 Clause #41 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 5 a a_1 a_2) (funcSet (skS.0 3 a) (skS.0 4 a a_1))) False % 3.65/3.86 Clause #42 (by betaEtaReduce #[28]): ∀ (a : Iota), Eq (injFuncSet a) fun B => dsetconstr (funcSet a B) (injective a B) % 3.65/3.86 Clause #43 (by argument congruence #[42]): ∀ (a a_1 : Iota), Eq (injFuncSet a a_1) ((fun B => dsetconstr (funcSet a B) (injective a B)) a_1) % 3.65/3.86 Clause #46 (by betaEtaReduce #[43]): ∀ (a a_1 : Iota), Eq (injFuncSet a a_1) (dsetconstr (funcSet a a_1) (injective a a_1)) % 3.65/3.86 Clause #47 (by superposition #[46, 33]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (injFuncSet a_1 a_2)) False) (Eq (in a (funcSet a_1 a_2)) True) % 3.65/3.86 Clause #49 (by superposition #[47, 40]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 5 a a_1 a_2) (funcSet (skS.0 3 a) (skS.0 4 a a_1))) True) (Eq False True) % 3.65/3.86 Clause #67 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 5 a a_1 a_2) (funcSet (skS.0 3 a) (skS.0 4 a a_1))) True % 3.65/3.86 Clause #68 (by superposition #[67, 41]): Eq True False % 3.65/3.86 Clause #72 (by clausification #[68]): False % 3.65/3.86 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------