%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU595^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n011.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 08:02:00 PM UTC 2025 % Result : Theorem 11.60s 11.75s % Output : Proof 11.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU595^2 : TPTP v9.2.0. Released v3.7.0. % 0.13/0.13 % Command : duper %s % 0.14/0.34 % Computer : n011.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 06:41:53 EDT 2025 % 0.14/0.34 % CPUTime : % 11.60/11.75 SZS status Theorem for theBenchmark.p % 11.60/11.75 SZS output start Proof for theBenchmark.p % 11.60/11.75 Clause #0 (by assumption #[]): Eq (Eq dsetconstrER (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A fun Xy => Xphi Xy) → Xphi Xx)) % 11.60/11.75 True % 11.60/11.75 Clause #1 (by assumption #[]): Eq (Eq binintersect fun A B => dsetconstr A fun Xx => in Xx B) True % 11.60/11.75 Clause #2 (by assumption #[]): Eq (Not (dsetconstrER → ∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx B)) True % 11.60/11.75 Clause #3 (by clausification #[2]): Eq (dsetconstrER → ∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx B) False % 11.60/11.75 Clause #4 (by clausification #[3]): Eq dsetconstrER True % 11.60/11.75 Clause #5 (by clausification #[3]): Eq (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx B) False % 11.60/11.75 Clause #6 (by clausification #[5]): ∀ (a : Iota), Eq (Not (∀ (B Xx : Iota), in Xx (binintersect (skS.0 0 a) B) → in Xx B)) True % 11.60/11.75 Clause #7 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (binintersect (skS.0 0 a) B) → in Xx B) False % 11.60/11.75 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), % 11.60/11.75 Eq (Not (∀ (Xx : Iota), in Xx (binintersect (skS.0 0 a) (skS.0 1 a a_1)) → in Xx (skS.0 1 a a_1))) True % 11.60/11.75 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (binintersect (skS.0 0 a) (skS.0 1 a a_1)) → in Xx (skS.0 1 a a_1)) False % 11.60/11.75 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 11.60/11.75 Eq (Not (in (skS.0 2 a a_1 a_2) (binintersect (skS.0 0 a) (skS.0 1 a a_1)) → in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1))) % 11.60/11.75 True % 11.60/11.75 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), % 11.60/11.75 Eq (in (skS.0 2 a a_1 a_2) (binintersect (skS.0 0 a) (skS.0 1 a a_1)) → in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) False % 11.60/11.75 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (binintersect (skS.0 0 a) (skS.0 1 a a_1))) True % 11.60/11.75 Clause #13 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) False % 11.60/11.75 Clause #14 (by betaEtaReduce #[0]): Eq (Eq dsetconstrER (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → Xphi Xx)) True % 11.60/11.75 Clause #15 (by clausification #[14]): Eq dsetconstrER (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → Xphi Xx) % 11.60/11.75 Clause #16 (by forward demodulation #[15, 4]): Eq True (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → Xphi Xx) % 11.60/11.75 Clause #17 (by clausification #[16]): ∀ (a : Iota), Eq (∀ (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr a Xphi) → Xphi Xx) True % 11.60/11.75 Clause #18 (by clausification #[17]): ∀ (a : Iota) (a_1 : Iota → Prop), Eq (∀ (Xx : Iota), in Xx (dsetconstr a a_1) → a_1 Xx) True % 11.60/11.75 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Eq (in a (dsetconstr a_1 a_2) → a_2 a) True % 11.60/11.75 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Or (Eq (in a (dsetconstr a_1 a_2)) False) (Eq (a_2 a) True) % 11.60/11.75 Clause #29 (by clausification #[1]): Eq binintersect fun A B => dsetconstr A fun Xx => in Xx B % 11.60/11.75 Clause #30 (by argument congruence #[29]): ∀ (a : Iota), Eq (binintersect a) ((fun A B => dsetconstr A fun Xx => in Xx B) a) % 11.60/11.75 Clause #35 (by betaEtaReduce #[30]): ∀ (a : Iota), Eq (binintersect a) fun B => dsetconstr a fun Xx => in Xx B % 11.60/11.75 Clause #36 (by argument congruence #[35]): ∀ (a a_1 : Iota), Eq (binintersect a a_1) ((fun B => dsetconstr a fun Xx => in Xx B) a_1) % 11.60/11.75 Clause #44 (by betaEtaReduce #[36]): ∀ (a a_1 : Iota), Eq (binintersect a a_1) (dsetconstr a fun Xx => in Xx a_1) % 11.60/11.75 Clause #46 (by superposition #[44, 20]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (binintersect a_1 a_2)) False) (Eq (in a a_2) True) % 11.60/11.75 Clause #59 (by superposition #[46, 12]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True) (Eq False True) % 11.60/11.75 Clause #1641 (by clausification #[59]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True % 11.60/11.75 Clause #1642 (by superposition #[1641, 13]): Eq True False % 11.60/11.75 Clause #1664 (by clausification #[1642]): False % 11.60/11.75 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------