%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN992^1 : TPTP v9.2.0. Bugfixed v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n004.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 08:08:23 PM UTC 2025 % Result : Theorem 5.86s 6.05s % Output : Proof 5.86s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SYN992^1 : TPTP v9.2.0. Bugfixed v4.0.0. % 0.12/0.13 % Command : duper %s % 0.13/0.34 % Computer : n004.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 : Thu Oct 2 15:11:23 EDT 2025 % 0.13/0.34 % CPUTime : % 5.86/6.05 SZS status Theorem for theBenchmark.p % 5.86/6.05 SZS output start Proof for theBenchmark.p % 5.86/6.05 Clause #0 (by assumption #[]): Eq (Eq refl fun R => ∀ (X : Iota), R X X) True % 5.86/6.05 Clause #1 (by assumption #[]): Eq (Not (Exists fun R => refl R)) True % 5.86/6.05 Clause #2 (by betaEtaReduce #[1]): Eq (Not (Exists refl)) True % 5.86/6.05 Clause #3 (by clausification #[2]): Eq (Exists refl) False % 5.86/6.05 Clause #4 (by clausification #[3]): ∀ (a : Iota → Iota → Prop), Eq (refl a) False % 5.86/6.05 Clause #5 (by clausification #[0]): Eq refl fun R => ∀ (X : Iota), R X X % 5.86/6.05 Clause #6 (by argument congruence #[5]): ∀ (a : Iota → Iota → Prop), Eq (refl a) ((fun R => ∀ (X : Iota), R X X) a) % 5.86/6.05 Clause #7 (by betaEtaReduce #[6]): ∀ (a : Iota → Iota → Prop), Eq (refl a) (∀ (X : Iota), a X X) % 5.86/6.05 Clause #8 (by forward demodulation #[7, 4]): ∀ (a : Iota → Iota → Prop), Eq False (∀ (X : Iota), a X X) % 5.86/6.05 Clause #9 (by clausification #[8]): ∀ (a : Iota → Iota → Prop) (a_1 : Iota), Eq (Not (a (skS.0 0 a a_1) (skS.0 0 a a_1))) True % 5.86/6.05 Clause #10 (by clausification #[9]): ∀ (a : Iota → Iota → Prop) (a_1 : Iota), Eq (a (skS.0 0 a a_1) (skS.0 0 a a_1)) False % 5.86/6.05 Clause #13 (by existsHoist #[10]): ∀ (a : Iota → Iota → Sort _abstMVar.0) (a_1 : (x x_1 : Iota) → a x x_1 → Prop) (a_2 : Iota) % 5.86/6.05 (a_3 : a (skS.0 0 (fun x x_1 => Exists (a_1 x x_1)) a_2) (skS.0 0 (fun x x_1 => Exists (a_1 x x_1)) a_2)), % 5.86/6.05 Or (Eq True False) % 5.86/6.05 (Eq % 5.86/6.05 ((fun x => a_1 (skS.0 0 (fun x x_1 => Exists (a_1 x x_1)) a_2) (skS.0 0 (fun x x_1 => Exists (a_1 x x_1)) a_2) x) % 5.86/6.05 a_3) % 5.86/6.05 False) % 5.86/6.05 Clause #117 (by betaEtaReduce #[13]): ∀ (a : Iota → Iota → Sort _abstMVar.0) (a_1 : (x x_1 : Iota) → a x x_1 → Prop) (a_2 : Iota) % 5.86/6.05 (a_3 : a (skS.0 0 (fun x x_1 => Exists (a_1 x x_1)) a_2) (skS.0 0 (fun x x_1 => Exists (a_1 x x_1)) a_2)), % 5.86/6.05 Or (Eq True False) % 5.86/6.05 (Eq (a_1 (skS.0 0 (fun x x_1 => Exists (a_1 x x_1)) a_2) (skS.0 0 (fun x x_1 => Exists (a_1 x x_1)) a_2) a_3) False) % 5.86/6.05 Clause #118 (by clausification #[117]): ∀ (a : Iota → Iota → Sort _abstMVar.0) (a_1 : (x x_1 : Iota) → a x x_1 → Prop) (a_2 : Iota) % 5.86/6.05 (a_3 : a (skS.0 0 (fun x x_1 => Exists (a_1 x x_1)) a_2) (skS.0 0 (fun x x_1 => Exists (a_1 x x_1)) a_2)), % 5.86/6.05 Eq (a_1 (skS.0 0 (fun x x_1 => Exists (a_1 x x_1)) a_2) (skS.0 0 (fun x x_1 => Exists (a_1 x x_1)) a_2) a_3) False % 5.86/6.05 Clause #146 (by fluidLoobHoist #[118]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (a True) False) (Eq a_1 False) % 5.86/6.05 Clause #161 (by fluidLoobHoist #[146]): ∀ (a : Prop) (a_1 : Prop → Prop), Or (Eq a False) (Or (Eq True False) (Eq (a_1 True) False)) % 5.86/6.05 Clause #163 (by clausification #[161]): ∀ (a : Prop) (a_1 : Prop → Prop), Or (Eq a False) (Eq (a_1 True) False) % 5.86/6.05 Clause #164 (by falseElim #[163]): ∀ (a : Prop → Prop), Eq (a True) False % 5.86/6.05 Clause #177 (by neHoist #[164]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (_ : Prop) → a _), Or (Eq True False) (Eq (a_1 True) (a_2 True)) % 5.86/6.05 Clause #182 (by clausification #[177]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (_ : Prop) → a _), Eq (a_1 True) (a_2 True) % 5.86/6.05 Clause #183 (by superposition #[182, 4]): ∀ (a : (_ : Prop) → (fun _ => Prop) _), Eq (a True) False % 5.86/6.05 Clause #212 (by fluidSup #[183, 182]): ∀ (a : (_ : Prop) → (fun _ => Prop) _), Eq (a True) ((fun _ => True) False) % 5.86/6.05 Clause #215 (by betaEtaReduce #[212]): ∀ (a : (_ : Prop) → (fun _ => Prop) _), Eq (a True) True % 5.86/6.05 Clause #216 (by superposition #[215, 4]): Eq True False % 5.86/6.05 Clause #251 (by clausification #[216]): False % 5.86/6.05 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------