%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU802^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n012.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 4.97s 5.14s % Output : Proof 4.97s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SEU802^2 : TPTP v9.2.0. Released v3.7.0. % 0.08/0.13 % Command : duper %s % 0.12/0.35 % Computer : n012.cluster.edu % 0.12/0.35 % Model : x86_64 x86_64 % 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.35 % Memory : 8042.1875MB % 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.35 % CPULimit : 300 % 0.12/0.35 % WCLimit : 300 % 0.12/0.35 % DateTime : Fri Oct 3 05:10:53 EDT 2025 % 0.12/0.35 % CPUTime : % 4.97/5.14 SZS status Theorem for theBenchmark.p % 4.97/5.14 SZS output start Proof for theBenchmark.p % 4.97/5.14 Clause #0 (by assumption #[]): Eq (Eq dsetconstrER (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A fun Xy => Xphi Xy) → Xphi Xx)) % 4.97/5.14 True % 4.97/5.14 Clause #2 (by assumption #[]): Eq (Eq surjFuncSet fun A B => dsetconstr (funcSet A B) fun Xf => surjective A B Xf) True % 4.97/5.14 Clause #3 (by assumption #[]): Eq (Not (dsetconstrER → ∀ (Xx Xy Xf : Iota), in Xf (surjFuncSet Xx Xy) → surjective Xx Xy Xf)) True % 4.97/5.14 Clause #4 (by betaEtaReduce #[0]): Eq (Eq dsetconstrER (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → Xphi Xx)) True % 4.97/5.14 Clause #5 (by clausification #[4]): Eq dsetconstrER (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → Xphi Xx) % 4.97/5.14 Clause #21 (by clausification #[3]): Eq (dsetconstrER → ∀ (Xx Xy Xf : Iota), in Xf (surjFuncSet Xx Xy) → surjective Xx Xy Xf) False % 4.97/5.14 Clause #22 (by clausification #[21]): Eq dsetconstrER True % 4.97/5.14 Clause #23 (by clausification #[21]): Eq (∀ (Xx Xy Xf : Iota), in Xf (surjFuncSet Xx Xy) → surjective Xx Xy Xf) False % 4.97/5.14 Clause #24 (by backward demodulation #[22, 5]): Eq True (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → Xphi Xx) % 4.97/5.14 Clause #31 (by clausification #[24]): ∀ (a : Iota), Eq (∀ (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr a Xphi) → Xphi Xx) True % 4.97/5.14 Clause #32 (by clausification #[31]): ∀ (a : Iota) (a_1 : Iota → Prop), Eq (∀ (Xx : Iota), in Xx (dsetconstr a a_1) → a_1 Xx) True % 4.97/5.14 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Eq (in a (dsetconstr a_1 a_2) → a_2 a) True % 4.97/5.14 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Or (Eq (in a (dsetconstr a_1 a_2)) False) (Eq (a_2 a) True) % 4.97/5.14 Clause #37 (by clausification #[23]): ∀ (a : Iota), Eq (Not (∀ (Xy Xf : Iota), in Xf (surjFuncSet (skS.0 3 a) Xy) → surjective (skS.0 3 a) Xy Xf)) True % 4.97/5.14 Clause #38 (by clausification #[37]): ∀ (a : Iota), Eq (∀ (Xy Xf : Iota), in Xf (surjFuncSet (skS.0 3 a) Xy) → surjective (skS.0 3 a) Xy Xf) False % 4.97/5.14 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), % 4.97/5.14 Eq (Not (∀ (Xf : Iota), in Xf (surjFuncSet (skS.0 3 a) (skS.0 4 a a_1)) → surjective (skS.0 3 a) (skS.0 4 a a_1) Xf)) % 4.97/5.14 True % 4.97/5.14 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), % 4.97/5.14 Eq (∀ (Xf : Iota), in Xf (surjFuncSet (skS.0 3 a) (skS.0 4 a a_1)) → surjective (skS.0 3 a) (skS.0 4 a a_1) Xf) False % 4.97/5.14 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 4.97/5.14 Eq % 4.97/5.14 (Not % 4.97/5.14 (in (skS.0 5 a a_1 a_2) (surjFuncSet (skS.0 3 a) (skS.0 4 a a_1)) → % 4.97/5.14 surjective (skS.0 3 a) (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))) % 4.97/5.14 True % 4.97/5.14 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), % 4.97/5.14 Eq % 4.97/5.14 (in (skS.0 5 a a_1 a_2) (surjFuncSet (skS.0 3 a) (skS.0 4 a a_1)) → % 4.97/5.14 surjective (skS.0 3 a) (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)) % 4.97/5.14 False % 4.97/5.14 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 5 a a_1 a_2) (surjFuncSet (skS.0 3 a) (skS.0 4 a a_1))) True % 4.97/5.14 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), Eq (surjective (skS.0 3 a) (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)) False % 4.97/5.14 Clause #51 (by betaEtaReduce #[2]): Eq (Eq surjFuncSet fun A B => dsetconstr (funcSet A B) (surjective A B)) True % 4.97/5.14 Clause #52 (by clausification #[51]): Eq surjFuncSet fun A B => dsetconstr (funcSet A B) (surjective A B) % 4.97/5.14 Clause #53 (by argument congruence #[52]): ∀ (a : Iota), Eq (surjFuncSet a) ((fun A B => dsetconstr (funcSet A B) (surjective A B)) a) % 4.97/5.14 Clause #59 (by betaEtaReduce #[53]): ∀ (a : Iota), Eq (surjFuncSet a) fun B => dsetconstr (funcSet a B) (surjective a B) % 4.97/5.14 Clause #60 (by argument congruence #[59]): ∀ (a a_1 : Iota), Eq (surjFuncSet a a_1) ((fun B => dsetconstr (funcSet a B) (surjective a B)) a_1) % 4.97/5.14 Clause #67 (by betaEtaReduce #[60]): ∀ (a a_1 : Iota), Eq (surjFuncSet a a_1) (dsetconstr (funcSet a a_1) (surjective a a_1)) % 4.97/5.14 Clause #68 (by superposition #[67, 34]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (surjFuncSet a_1 a_2)) False) (Eq (surjective a_1 a_2 a) True) % 4.97/5.16 Clause #72 (by superposition #[68, 43]): ∀ (a a_1 a_2 : Iota), Or (Eq (surjective (skS.0 3 a) (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)) True) (Eq False True) % 4.97/5.16 Clause #282 (by clausification #[72]): ∀ (a a_1 a_2 : Iota), Eq (surjective (skS.0 3 a) (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)) True % 4.97/5.16 Clause #283 (by superposition #[282, 44]): Eq True False % 4.97/5.16 Clause #293 (by clausification #[283]): False % 4.97/5.16 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------