%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU603^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n014.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 08:02:01 PM UTC 2025 % Result : Theorem 7.85s 8.02s % Output : Proof 7.88s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU603^2 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n014.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 06:42:38 EDT 2025 % 0.13/0.34 % CPUTime : % 7.85/8.02 SZS status Theorem for theBenchmark.p % 7.85/8.02 SZS output start Proof for theBenchmark.p % 7.85/8.02 Clause #0 (by assumption #[]): Eq (Eq dsetconstrER (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A fun Xy => Xphi Xy) → Xphi Xx)) % 7.85/8.02 True % 7.85/8.02 Clause #1 (by assumption #[]): Eq (Eq setminus fun A B => dsetconstr A fun Xx => Not (in Xx B)) True % 7.85/8.02 Clause #2 (by assumption #[]): Eq (Not (dsetconstrER → ∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B))) True % 7.85/8.02 Clause #3 (by betaEtaReduce #[0]): Eq (Eq dsetconstrER (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → Xphi Xx)) True % 7.85/8.02 Clause #4 (by clausification #[3]): Eq dsetconstrER (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → Xphi Xx) % 7.85/8.02 Clause #20 (by clausification #[2]): Eq (dsetconstrER → ∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B)) False % 7.85/8.02 Clause #21 (by clausification #[20]): Eq dsetconstrER True % 7.85/8.02 Clause #22 (by clausification #[20]): Eq (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B)) False % 7.85/8.02 Clause #23 (by backward demodulation #[21, 4]): Eq True (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → Xphi Xx) % 7.85/8.02 Clause #26 (by clausification #[1]): Eq setminus fun A B => dsetconstr A fun Xx => Not (in Xx B) % 7.85/8.02 Clause #27 (by argument congruence #[26]): ∀ (a : Iota), Eq (setminus a) ((fun A B => dsetconstr A fun Xx => Not (in Xx B)) a) % 7.85/8.02 Clause #29 (by clausification #[23]): ∀ (a : Iota), Eq (∀ (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr a Xphi) → Xphi Xx) True % 7.85/8.02 Clause #30 (by clausification #[29]): ∀ (a : Iota) (a_1 : Iota → Prop), Eq (∀ (Xx : Iota), in Xx (dsetconstr a a_1) → a_1 Xx) True % 7.85/8.02 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Eq (in a (dsetconstr a_1 a_2) → a_2 a) True % 7.85/8.02 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Or (Eq (in a (dsetconstr a_1 a_2)) False) (Eq (a_2 a) True) % 7.85/8.02 Clause #35 (by clausification #[22]): ∀ (a : Iota), Eq (Not (∀ (B Xx : Iota), in Xx (setminus (skS.0 3 a) B) → Not (in Xx B))) True % 7.85/8.02 Clause #36 (by clausification #[35]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (setminus (skS.0 3 a) B) → Not (in Xx B)) False % 7.85/8.02 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), % 7.85/8.02 Eq (Not (∀ (Xx : Iota), in Xx (setminus (skS.0 3 a) (skS.0 4 a a_1)) → Not (in Xx (skS.0 4 a a_1)))) True % 7.85/8.02 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (setminus (skS.0 3 a) (skS.0 4 a a_1)) → Not (in Xx (skS.0 4 a a_1))) False % 7.85/8.02 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), % 7.85/8.02 Eq % 7.85/8.02 (Not (in (skS.0 5 a a_1 a_2) (setminus (skS.0 3 a) (skS.0 4 a a_1)) → Not (in (skS.0 5 a a_1 a_2) (skS.0 4 a a_1)))) % 7.85/8.02 True % 7.85/8.02 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), % 7.85/8.02 Eq (in (skS.0 5 a a_1 a_2) (setminus (skS.0 3 a) (skS.0 4 a a_1)) → Not (in (skS.0 5 a a_1 a_2) (skS.0 4 a a_1))) % 7.85/8.02 False % 7.85/8.02 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 5 a a_1 a_2) (setminus (skS.0 3 a) (skS.0 4 a a_1))) True % 7.85/8.02 Clause #42 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), Eq (Not (in (skS.0 5 a a_1 a_2) (skS.0 4 a a_1))) False % 7.85/8.02 Clause #49 (by betaEtaReduce #[27]): ∀ (a : Iota), Eq (setminus a) fun B => dsetconstr a fun Xx => Not (in Xx B) % 7.85/8.02 Clause #50 (by argument congruence #[49]): ∀ (a a_1 : Iota), Eq (setminus a a_1) ((fun B => dsetconstr a fun Xx => Not (in Xx B)) a_1) % 7.85/8.02 Clause #58 (by betaEtaReduce #[50]): ∀ (a a_1 : Iota), Eq (setminus a a_1) (dsetconstr a fun Xx => Not (in Xx a_1)) % 7.85/8.02 Clause #60 (by superposition #[58, 32]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setminus a_1 a_2)) False) (Eq (Not (in a a_2)) True) % 7.85/8.02 Clause #72 (by clausification #[60]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setminus a_1 a_2)) False) (Eq (in a a_2) False) % 7.85/8.02 Clause #73 (by superposition #[72, 41]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 5 a a_1 a_2) (skS.0 4 a a_1)) False) (Eq False True) % 7.85/8.02 Clause #152 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 5 a a_1 a_2) (skS.0 4 a a_1)) True % 7.85/8.02 Clause #976 (by clausification #[73]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 5 a a_1 a_2) (skS.0 4 a a_1)) False % 7.88/8.06 Clause #977 (by superposition #[976, 152]): Eq False True % 7.88/8.06 Clause #978 (by clausification #[977]): False % 7.88/8.06 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------