%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU581^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n016.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 08:01:58 PM UTC 2025 % Result : Theorem 3.59s 3.77s % Output : Proof 3.59s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU581^2 : TPTP v9.2.0. Released v3.7.0. % 0.03/0.14 % Command : duper %s % 0.13/0.35 % Computer : n016.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Oct 3 04:50:53 EDT 2025 % 0.13/0.35 % CPUTime : % 3.59/3.77 SZS status Theorem for theBenchmark.p % 3.59/3.77 SZS output start Proof for theBenchmark.p % 3.59/3.77 Clause #0 (by assumption #[]): Eq (Eq powersetE1 (∀ (A B : Iota), in B (powerset A) → subset B A)) True % 3.59/3.77 Clause #1 (by assumption #[]): Eq (Eq sepInPowerset (∀ (A : Iota) (Xphi : Iota → Prop), in (dsetconstr A fun Xx => Xphi Xx) (powerset A))) True % 3.59/3.77 Clause #2 (by assumption #[]): Eq (Not (powersetE1 → sepInPowerset → ∀ (A : Iota) (Xphi : Iota → Prop), subset (dsetconstr A fun Xx => Xphi Xx) A)) % 3.59/3.77 True % 3.59/3.77 Clause #3 (by clausification #[0]): Eq powersetE1 (∀ (A B : Iota), in B (powerset A) → subset B A) % 3.59/3.77 Clause #16 (by betaEtaReduce #[2]): Eq (Not (powersetE1 → sepInPowerset → ∀ (A : Iota) (Xphi : Iota → Prop), subset (dsetconstr A Xphi) A)) True % 3.59/3.77 Clause #17 (by clausification #[16]): Eq (powersetE1 → sepInPowerset → ∀ (A : Iota) (Xphi : Iota → Prop), subset (dsetconstr A Xphi) A) False % 3.59/3.77 Clause #18 (by clausification #[17]): Eq powersetE1 True % 3.59/3.77 Clause #19 (by clausification #[17]): Eq (sepInPowerset → ∀ (A : Iota) (Xphi : Iota → Prop), subset (dsetconstr A Xphi) A) False % 3.59/3.77 Clause #20 (by backward demodulation #[18, 3]): Eq True (∀ (A B : Iota), in B (powerset A) → subset B A) % 3.59/3.77 Clause #23 (by betaEtaReduce #[1]): Eq (Eq sepInPowerset (∀ (A : Iota) (Xphi : Iota → Prop), in (dsetconstr A Xphi) (powerset A))) True % 3.59/3.77 Clause #24 (by clausification #[23]): Eq sepInPowerset (∀ (A : Iota) (Xphi : Iota → Prop), in (dsetconstr A Xphi) (powerset A)) % 3.59/3.77 Clause #28 (by clausification #[20]): ∀ (a : Iota), Eq (∀ (B : Iota), in B (powerset a) → subset B a) True % 3.59/3.77 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (in a (powerset a_1) → subset a a_1) True % 3.59/3.77 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Or (Eq (in a (powerset a_1)) False) (Eq (subset a a_1) True) % 3.59/3.77 Clause #31 (by clausification #[19]): Eq sepInPowerset True % 3.59/3.77 Clause #32 (by clausification #[19]): Eq (∀ (A : Iota) (Xphi : Iota → Prop), subset (dsetconstr A Xphi) A) False % 3.59/3.77 Clause #33 (by backward demodulation #[31, 24]): Eq True (∀ (A : Iota) (Xphi : Iota → Prop), in (dsetconstr A Xphi) (powerset A)) % 3.59/3.77 Clause #34 (by clausification #[32]): ∀ (a : Iota), Eq (Not (∀ (Xphi : Iota → Prop), subset (dsetconstr (skS.0 2 a) Xphi) (skS.0 2 a))) True % 3.59/3.77 Clause #35 (by clausification #[34]): ∀ (a : Iota), Eq (∀ (Xphi : Iota → Prop), subset (dsetconstr (skS.0 2 a) Xphi) (skS.0 2 a)) False % 3.59/3.77 Clause #36 (by clausification #[35]): ∀ (a : Iota) (a_1 : Iota → Prop), Eq (Not (subset (dsetconstr (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 2 a))) True % 3.59/3.77 Clause #37 (by clausification #[36]): ∀ (a : Iota) (a_1 : Iota → Prop), Eq (subset (dsetconstr (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 2 a)) False % 3.59/3.77 Clause #38 (by clausification #[33]): ∀ (a : Iota), Eq (∀ (Xphi : Iota → Prop), in (dsetconstr a Xphi) (powerset a)) True % 3.59/3.77 Clause #39 (by clausification #[38]): ∀ (a : Iota) (a_1 : Iota → Prop), Eq (in (dsetconstr a a_1) (powerset a)) True % 3.59/3.77 Clause #40 (by superposition #[39, 30]): ∀ (a : Iota) (a_1 : Iota → Prop), Or (Eq True False) (Eq (subset (dsetconstr a a_1) a) True) % 3.59/3.77 Clause #41 (by clausification #[40]): ∀ (a : Iota) (a_1 : Iota → Prop), Eq (subset (dsetconstr a a_1) a) True % 3.59/3.77 Clause #42 (by superposition #[41, 37]): Eq True False % 3.59/3.77 Clause #44 (by clausification #[42]): False % 3.59/3.77 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------