%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU675^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n015.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 08:02:11 PM UTC 2025 % Result : Theorem 28.44s 28.62s % Output : Proof 28.70s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU675^2 : TPTP v9.2.0. Released v3.7.0. % 0.03/0.14 % Command : duper %s % 0.14/0.35 % Computer : n015.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Fri Oct 3 04:33:08 EDT 2025 % 0.14/0.35 % CPUTime : % 28.44/28.62 SZS status Theorem for theBenchmark.p % 28.44/28.62 SZS output start Proof for theBenchmark.p % 28.44/28.62 Clause #0 (by assumption #[]): Eq (Eq dsetconstrER (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A fun Xy => Xphi Xy) → Xphi Xx)) % 28.44/28.62 True % 28.44/28.62 Clause #5 (by assumption #[]): Eq (Eq funcSet fun A B => dsetconstr (powerset (cartprod A B)) fun Xf => func A B Xf) True % 28.44/28.62 Clause #6 (by assumption #[]): Eq (Not (dsetconstrER → ∀ (A B Xf : Iota), in Xf (funcSet A B) → func A B Xf)) True % 28.44/28.62 Clause #7 (by betaEtaReduce #[0]): Eq (Eq dsetconstrER (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → Xphi Xx)) True % 28.44/28.62 Clause #8 (by clausification #[7]): Eq dsetconstrER (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → Xphi Xx) % 28.44/28.62 Clause #24 (by clausification #[6]): Eq (dsetconstrER → ∀ (A B Xf : Iota), in Xf (funcSet A B) → func A B Xf) False % 28.44/28.62 Clause #25 (by clausification #[24]): Eq dsetconstrER True % 28.44/28.62 Clause #26 (by clausification #[24]): Eq (∀ (A B Xf : Iota), in Xf (funcSet A B) → func A B Xf) False % 28.44/28.62 Clause #27 (by backward demodulation #[25, 8]): Eq True (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → Xphi Xx) % 28.44/28.62 Clause #32 (by clausification #[27]): ∀ (a : Iota), Eq (∀ (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr a Xphi) → Xphi Xx) True % 28.44/28.62 Clause #33 (by clausification #[32]): ∀ (a : Iota) (a_1 : Iota → Prop), Eq (∀ (Xx : Iota), in Xx (dsetconstr a a_1) → a_1 Xx) True % 28.44/28.62 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Eq (in a (dsetconstr a_1 a_2) → a_2 a) True % 28.44/28.62 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Or (Eq (in a (dsetconstr a_1 a_2)) False) (Eq (a_2 a) True) % 28.44/28.62 Clause #38 (by clausification #[26]): ∀ (a : Iota), Eq (Not (∀ (B Xf : Iota), in Xf (funcSet (skS.0 3 a) B) → func (skS.0 3 a) B Xf)) True % 28.44/28.62 Clause #39 (by clausification #[38]): ∀ (a : Iota), Eq (∀ (B Xf : Iota), in Xf (funcSet (skS.0 3 a) B) → func (skS.0 3 a) B Xf) False % 28.44/28.62 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), % 28.44/28.62 Eq (Not (∀ (Xf : Iota), in Xf (funcSet (skS.0 3 a) (skS.0 4 a a_1)) → func (skS.0 3 a) (skS.0 4 a a_1) Xf)) True % 28.44/28.62 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), % 28.44/28.62 Eq (∀ (Xf : Iota), in Xf (funcSet (skS.0 3 a) (skS.0 4 a a_1)) → func (skS.0 3 a) (skS.0 4 a a_1) Xf) False % 28.44/28.62 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), % 28.44/28.62 Eq % 28.44/28.62 (Not % 28.44/28.62 (in (skS.0 5 a a_1 a_2) (funcSet (skS.0 3 a) (skS.0 4 a a_1)) → % 28.44/28.62 func (skS.0 3 a) (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))) % 28.44/28.62 True % 28.44/28.62 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), % 28.44/28.62 Eq % 28.44/28.62 (in (skS.0 5 a a_1 a_2) (funcSet (skS.0 3 a) (skS.0 4 a a_1)) → % 28.44/28.62 func (skS.0 3 a) (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)) % 28.44/28.62 False % 28.44/28.62 Clause #44 (by clausification #[43]): ∀ (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 % 28.44/28.62 Clause #45 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), Eq (func (skS.0 3 a) (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)) False % 28.44/28.62 Clause #162 (by betaEtaReduce #[5]): Eq (Eq funcSet fun A B => dsetconstr (powerset (cartprod A B)) (func A B)) True % 28.44/28.62 Clause #163 (by clausification #[162]): Eq funcSet fun A B => dsetconstr (powerset (cartprod A B)) (func A B) % 28.44/28.62 Clause #164 (by argument congruence #[163]): ∀ (a : Iota), Eq (funcSet a) ((fun A B => dsetconstr (powerset (cartprod A B)) (func A B)) a) % 28.44/28.62 Clause #170 (by betaEtaReduce #[164]): ∀ (a : Iota), Eq (funcSet a) fun B => dsetconstr (powerset (cartprod a B)) (func a B) % 28.44/28.62 Clause #171 (by argument congruence #[170]): ∀ (a a_1 : Iota), Eq (funcSet a a_1) ((fun B => dsetconstr (powerset (cartprod a B)) (func a B)) a_1) % 28.44/28.62 Clause #181 (by betaEtaReduce #[171]): ∀ (a a_1 : Iota), Eq (funcSet a a_1) (dsetconstr (powerset (cartprod a a_1)) (func a a_1)) % 28.44/28.62 Clause #182 (by superposition #[181, 35]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (funcSet a_1 a_2)) False) (Eq (func a_1 a_2 a) True) % 28.44/28.62 Clause #190 (by superposition #[182, 44]): ∀ (a a_1 a_2 : Iota), Or (Eq (func (skS.0 3 a) (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)) True) (Eq False True) % 28.70/28.91 Clause #7063 (by clausification #[190]): ∀ (a a_1 a_2 : Iota), Eq (func (skS.0 3 a) (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)) True % 28.70/28.91 Clause #7064 (by superposition #[7063, 45]): Eq True False % 28.70/28.91 Clause #7094 (by clausification #[7064]): False % 28.70/28.91 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------