%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV409^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n002.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 08:03:09 PM UTC 2025 % Result : Theorem 5.54s 5.76s % Output : Proof 5.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEV409^5 : TPTP v9.2.0. Released v4.0.0. % 0.03/0.13 % Command : duper %s % 0.12/0.33 % Computer : n002.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Oct 3 01:38:23 EDT 2025 % 0.12/0.34 % CPUTime : % 5.54/5.76 SZS status Theorem for theBenchmark.p % 5.54/5.76 SZS output start Proof for theBenchmark.p % 5.54/5.76 Clause #0 (by assumption #[]): Eq (Not (Exists fun R => ∀ (X Y : Iota → Prop), And (R X Y) (R Y X) → ∀ (Xx : Iota), Iff (X Xx) (Y Xx))) True % 5.54/5.76 Clause #1 (by clausification #[0]): Eq (Exists fun R => ∀ (X Y : Iota → Prop), And (R X Y) (R Y X) → ∀ (Xx : Iota), Iff (X Xx) (Y Xx)) False % 5.54/5.76 Clause #2 (by clausification #[1]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop), % 5.54/5.76 Eq (∀ (X Y : Iota → Prop), And (a X Y) (a Y X) → ∀ (Xx : Iota), Iff (X Xx) (Y Xx)) False % 5.54/5.76 Clause #3 (by clausification #[2]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop) (a_1 : Iota → Prop), % 5.54/5.76 Eq % 5.54/5.76 (Not % 5.54/5.76 (∀ (Y : Iota → Prop), % 5.54/5.76 And (a (skS.0 0 a a_1) Y) (a Y (skS.0 0 a a_1)) → ∀ (Xx : Iota), Iff (skS.0 0 a a_1 Xx) (Y Xx))) % 5.54/5.76 True % 5.54/5.76 Clause #4 (by clausification #[3]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop) (a_1 : Iota → Prop), % 5.54/5.76 Eq % 5.54/5.76 (∀ (Y : Iota → Prop), % 5.54/5.76 And (a (skS.0 0 a a_1) Y) (a Y (skS.0 0 a a_1)) → ∀ (Xx : Iota), Iff (skS.0 0 a a_1 Xx) (Y Xx)) % 5.54/5.76 False % 5.54/5.76 Clause #5 (by clausification #[4]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop) (a_1 a_2 : Iota → Prop), % 5.54/5.76 Eq % 5.54/5.76 (Not % 5.54/5.76 (And (a (skS.0 0 a a_1) (skS.0 1 a a_1 a_2)) (a (skS.0 1 a a_1 a_2) (skS.0 0 a a_1)) → % 5.54/5.76 ∀ (Xx : Iota), Iff (skS.0 0 a a_1 Xx) (skS.0 1 a a_1 a_2 Xx))) % 5.54/5.76 True % 5.54/5.76 Clause #6 (by clausification #[5]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop) (a_1 a_2 : Iota → Prop), % 5.54/5.76 Eq % 5.54/5.76 (And (a (skS.0 0 a a_1) (skS.0 1 a a_1 a_2)) (a (skS.0 1 a a_1 a_2) (skS.0 0 a a_1)) → % 5.54/5.76 ∀ (Xx : Iota), Iff (skS.0 0 a a_1 Xx) (skS.0 1 a a_1 a_2 Xx)) % 5.54/5.76 False % 5.54/5.76 Clause #7 (by clausification #[6]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop) (a_1 a_2 : Iota → Prop), % 5.54/5.76 Eq (And (a (skS.0 0 a a_1) (skS.0 1 a a_1 a_2)) (a (skS.0 1 a a_1 a_2) (skS.0 0 a a_1))) True % 5.54/5.76 Clause #8 (by clausification #[6]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop) (a_1 a_2 : Iota → Prop), % 5.54/5.76 Eq (∀ (Xx : Iota), Iff (skS.0 0 a a_1 Xx) (skS.0 1 a a_1 a_2 Xx)) False % 5.54/5.76 Clause #9 (by clausification #[7]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop) (a_1 a_2 : Iota → Prop), Eq (a (skS.0 1 a a_1 a_2) (skS.0 0 a a_1)) True % 5.54/5.76 Clause #99 (by clausification #[8]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop) (a_1 a_2 : Iota → Prop) (a_3 : Iota), % 5.54/5.76 Eq (Not (Iff (skS.0 0 a a_1 (skS.0 2 a a_1 a_2 a_3)) (skS.0 1 a a_1 a_2 (skS.0 2 a a_1 a_2 a_3)))) True % 5.54/5.76 Clause #100 (by clausification #[99]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop) (a_1 a_2 : Iota → Prop) (a_3 : Iota), % 5.54/5.76 Eq (Iff (skS.0 0 a a_1 (skS.0 2 a a_1 a_2 a_3)) (skS.0 1 a a_1 a_2 (skS.0 2 a a_1 a_2 a_3))) False % 5.54/5.76 Clause #101 (by clausification #[100]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop) (a_1 a_2 : Iota → Prop) (a_3 : Iota), % 5.54/5.76 Or (Eq (skS.0 0 a a_1 (skS.0 2 a a_1 a_2 a_3)) False) (Eq (skS.0 1 a a_1 a_2 (skS.0 2 a a_1 a_2 a_3)) False) % 5.54/5.76 Clause #103 (by fluidSup #[101, 9]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop) (a_1 a_2 : Iota → Prop) (a_3 : Iota) (a_4 : Prop), % 5.54/5.76 Or (Eq (skS.0 1 a a_1 a_2 (skS.0 2 a a_1 a_2 a_3)) False) (Eq ((fun _ => a_4) False) True) % 5.54/5.76 Clause #367 (by betaEtaReduce #[103]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop) (a_1 a_2 : Iota → Prop) (a_3 : Iota) (a_4 : Prop), % 5.54/5.76 Or (Eq (skS.0 1 a a_1 a_2 (skS.0 2 a a_1 a_2 a_3)) False) (Eq a_4 True) % 5.54/5.76 Clause #374 (by fluidSup #[367, 9]): ∀ (a a_1 : Prop), Or (Eq a True) (Eq ((fun _ => a_1) False) True) % 5.54/5.76 Clause #377 (by betaEtaReduce #[374]): ∀ (a a_1 : Prop), Or (Eq a True) (Eq a_1 True) % 5.54/5.76 Clause #384 (by falseElim #[377]): ∀ (a : Prop), Eq a True % 5.54/5.76 Clause #429 (by falseElim #[384]): False % 5.54/5.76 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------