%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU504^2 : 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 08:01:46 PM UTC 2025 % Result : Theorem 3.86s 4.07s % Output : Proof 3.86s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SEU504^2 : TPTP v9.2.0. Released v3.7.0. % 0.06/0.13 % Command : duper %s % 0.13/0.34 % Computer : n012.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 05:54:08 EDT 2025 % 0.13/0.34 % CPUTime : % 3.86/4.07 SZS status Theorem for theBenchmark.p % 3.86/4.07 SZS output start Proof for theBenchmark.p % 3.86/4.07 Clause #1 (by assumption #[]): Eq % 3.86/4.07 (Eq exuE1 % 3.86/4.07 (∀ (Xphi : Iota → Prop), % 3.86/4.07 (exu fun Xx => Xphi Xx) → Exists fun Xx => And (Xphi Xx) (∀ (Xy : Iota), Xphi Xy → Eq Xx Xy))) % 3.86/4.07 True % 3.86/4.07 Clause #2 (by assumption #[]): Eq (Not (exuE1 → ∀ (Xphi : Iota → Prop), (exu fun Xx => Xphi Xx) → Exists fun Xx => Xphi Xx)) True % 3.86/4.07 Clause #3 (by betaEtaReduce #[2]): Eq (Not (exuE1 → ∀ (Xphi : Iota → Prop), exu Xphi → Exists Xphi)) True % 3.86/4.07 Clause #4 (by clausification #[3]): Eq (exuE1 → ∀ (Xphi : Iota → Prop), exu Xphi → Exists Xphi) False % 3.86/4.07 Clause #5 (by clausification #[4]): Eq exuE1 True % 3.86/4.07 Clause #6 (by clausification #[4]): Eq (∀ (Xphi : Iota → Prop), exu Xphi → Exists Xphi) False % 3.86/4.07 Clause #7 (by clausification #[6]): ∀ (a : Iota → Prop), Eq (Not (exu (skS.0 0 a) → Exists (skS.0 0 a))) True % 3.86/4.07 Clause #8 (by clausification #[7]): ∀ (a : Iota → Prop), Eq (exu (skS.0 0 a) → Exists (skS.0 0 a)) False % 3.86/4.07 Clause #9 (by clausification #[8]): ∀ (a : Iota → Prop), Eq (exu (skS.0 0 a)) True % 3.86/4.07 Clause #10 (by clausification #[8]): ∀ (a : Iota → Prop), Eq (Exists (skS.0 0 a)) False % 3.86/4.07 Clause #11 (by clausification #[10]): ∀ (a : Iota → Prop) (a_1 : Iota), Eq (skS.0 0 a a_1) False % 3.86/4.07 Clause #12 (by betaEtaReduce #[1]): Eq (Eq exuE1 (∀ (Xphi : Iota → Prop), exu Xphi → Exists fun Xx => And (Xphi Xx) (∀ (Xy : Iota), Xphi Xy → Eq Xx Xy))) % 3.86/4.07 True % 3.86/4.07 Clause #13 (by clausification #[12]): Eq exuE1 (∀ (Xphi : Iota → Prop), exu Xphi → Exists fun Xx => And (Xphi Xx) (∀ (Xy : Iota), Xphi Xy → Eq Xx Xy)) % 3.86/4.07 Clause #14 (by forward demodulation #[13, 5]): Eq True (∀ (Xphi : Iota → Prop), exu Xphi → Exists fun Xx => And (Xphi Xx) (∀ (Xy : Iota), Xphi Xy → Eq Xx Xy)) % 3.86/4.07 Clause #15 (by clausification #[14]): ∀ (a : Iota → Prop), Eq (exu a → Exists fun Xx => And (a Xx) (∀ (Xy : Iota), a Xy → Eq Xx Xy)) True % 3.86/4.07 Clause #16 (by clausification #[15]): ∀ (a : Iota → Prop), Or (Eq (exu a) False) (Eq (Exists fun Xx => And (a Xx) (∀ (Xy : Iota), a Xy → Eq Xx Xy)) True) % 3.86/4.07 Clause #17 (by clausification #[16]): ∀ (a : Iota → Prop) (a_1 : Iota), % 3.86/4.07 Or (Eq (exu a) False) (Eq (And (a (skS.0 1 a a_1)) (∀ (Xy : Iota), a Xy → Eq (skS.0 1 a a_1) Xy)) True) % 3.86/4.07 Clause #19 (by clausification #[17]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (exu a) False) (Eq (a (skS.0 1 a a_1)) True) % 3.86/4.07 Clause #24 (by superposition #[19, 9]): ∀ (a : Iota → Prop) (a_1 : Iota), % 3.86/4.07 Or (Eq ((fun x => skS.0 0 a x) (skS.0 1 (fun x => skS.0 0 a x) a_1)) True) (Eq False True) % 3.86/4.07 Clause #139 (by betaEtaReduce #[24]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (skS.0 0 a (skS.0 1 (skS.0 0 a) a_1)) True) (Eq False True) % 3.86/4.07 Clause #140 (by clausification #[139]): ∀ (a : Iota → Prop) (a_1 : Iota), Eq (skS.0 0 a (skS.0 1 (skS.0 0 a) a_1)) True % 3.86/4.07 Clause #141 (by superposition #[140, 11]): Eq True False % 3.86/4.07 Clause #151 (by clausification #[141]): False % 3.86/4.07 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------