%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET594^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n019.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 08:00:12 PM UTC 2025 % Result : Theorem 3.64s 3.80s % Output : Proof 3.66s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : SET594^5 : TPTP v9.2.0. Released v4.0.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n019.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 13:46:23 EDT 2025 % 0.13/0.34 % CPUTime : % 3.64/3.80 SZS status Theorem for theBenchmark.p % 3.64/3.80 SZS output start Proof for theBenchmark.p % 3.64/3.80 Clause #0 (by assumption #[]): Eq % 3.64/3.80 (Not % 3.64/3.80 (∀ (X Y Z : a → Prop), % 3.64/3.80 Eq (fun Xz => Or (And (X Xz) (Y Xz)) (And (X Xz) (Z Xz))) X → ∀ (Xx : a), X Xx → Or (Y Xx) (Z Xx))) % 3.64/3.80 True % 3.64/3.80 Clause #1 (by clausification #[0]): Eq % 3.64/3.80 (∀ (X Y Z : a → Prop), % 3.64/3.80 Eq (fun Xz => Or (And (X Xz) (Y Xz)) (And (X Xz) (Z Xz))) X → ∀ (Xx : a), X Xx → Or (Y Xx) (Z Xx)) % 3.64/3.80 False % 3.64/3.80 Clause #2 (by clausification #[1]): ∀ (a_1 : a → Prop), % 3.64/3.80 Eq % 3.64/3.80 (Not % 3.64/3.80 (∀ (Y Z : a → Prop), % 3.64/3.80 Eq (fun Xz => Or (And (skS.0 0 a_1 Xz) (Y Xz)) (And (skS.0 0 a_1 Xz) (Z Xz))) (skS.0 0 a_1) → % 3.64/3.80 ∀ (Xx : a), skS.0 0 a_1 Xx → Or (Y Xx) (Z Xx))) % 3.64/3.80 True % 3.64/3.80 Clause #3 (by clausification #[2]): ∀ (a_1 : a → Prop), % 3.64/3.80 Eq % 3.64/3.80 (∀ (Y Z : a → Prop), % 3.64/3.80 Eq (fun Xz => Or (And (skS.0 0 a_1 Xz) (Y Xz)) (And (skS.0 0 a_1 Xz) (Z Xz))) (skS.0 0 a_1) → % 3.64/3.80 ∀ (Xx : a), skS.0 0 a_1 Xx → Or (Y Xx) (Z Xx)) % 3.64/3.80 False % 3.64/3.80 Clause #4 (by clausification #[3]): ∀ (a_1 a_2 : a → Prop), % 3.64/3.80 Eq % 3.64/3.80 (Not % 3.64/3.80 (∀ (Z : a → Prop), % 3.64/3.80 Eq (fun Xz => Or (And (skS.0 0 a_1 Xz) (skS.0 1 a_1 a_2 Xz)) (And (skS.0 0 a_1 Xz) (Z Xz))) (skS.0 0 a_1) → % 3.64/3.80 ∀ (Xx : a), skS.0 0 a_1 Xx → Or (skS.0 1 a_1 a_2 Xx) (Z Xx))) % 3.64/3.80 True % 3.64/3.80 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : a → Prop), % 3.64/3.80 Eq % 3.64/3.80 (∀ (Z : a → Prop), % 3.64/3.80 Eq (fun Xz => Or (And (skS.0 0 a_1 Xz) (skS.0 1 a_1 a_2 Xz)) (And (skS.0 0 a_1 Xz) (Z Xz))) (skS.0 0 a_1) → % 3.64/3.80 ∀ (Xx : a), skS.0 0 a_1 Xx → Or (skS.0 1 a_1 a_2 Xx) (Z Xx)) % 3.64/3.80 False % 3.64/3.80 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 a_3 : a → Prop), % 3.64/3.80 Eq % 3.64/3.80 (Not % 3.64/3.80 (Eq (fun Xz => Or (And (skS.0 0 a_1 Xz) (skS.0 1 a_1 a_2 Xz)) (And (skS.0 0 a_1 Xz) (skS.0 2 a_1 a_2 a_3 Xz))) % 3.64/3.80 (skS.0 0 a_1) → % 3.64/3.80 ∀ (Xx : a), skS.0 0 a_1 Xx → Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx))) % 3.64/3.80 True % 3.64/3.80 Clause #7 (by clausification #[6]): ∀ (a_1 a_2 a_3 : a → Prop), % 3.64/3.80 Eq % 3.64/3.80 (Eq (fun Xz => Or (And (skS.0 0 a_1 Xz) (skS.0 1 a_1 a_2 Xz)) (And (skS.0 0 a_1 Xz) (skS.0 2 a_1 a_2 a_3 Xz))) % 3.64/3.80 (skS.0 0 a_1) → % 3.64/3.80 ∀ (Xx : a), skS.0 0 a_1 Xx → Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) % 3.64/3.80 False % 3.64/3.80 Clause #8 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop), % 3.64/3.80 Eq % 3.64/3.80 (Eq (fun Xz => Or (And (skS.0 0 a_1 Xz) (skS.0 1 a_1 a_2 Xz)) (And (skS.0 0 a_1 Xz) (skS.0 2 a_1 a_2 a_3 Xz))) % 3.64/3.80 (skS.0 0 a_1)) % 3.64/3.80 True % 3.64/3.80 Clause #9 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop), Eq (∀ (Xx : a), skS.0 0 a_1 Xx → Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) False % 3.64/3.80 Clause #10 (by clausification #[8]): ∀ (a_1 a_2 a_3 : a → Prop), % 3.64/3.80 Eq (fun Xz => Or (And (skS.0 0 a_1 Xz) (skS.0 1 a_1 a_2 Xz)) (And (skS.0 0 a_1 Xz) (skS.0 2 a_1 a_2 a_3 Xz))) % 3.64/3.80 (skS.0 0 a_1) % 3.64/3.80 Clause #11 (by argument congruence #[10]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.64/3.80 Eq ((fun Xz => Or (And (skS.0 0 a_1 Xz) (skS.0 1 a_1 a_2 Xz)) (And (skS.0 0 a_1 Xz) (skS.0 2 a_1 a_2 a_3 Xz))) a_4) % 3.64/3.80 (skS.0 0 a_1 a_4) % 3.64/3.80 Clause #12 (by clausification #[9]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.64/3.80 Eq % 3.64/3.80 (Not % 3.64/3.80 (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4) → % 3.64/3.80 Or (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)))) % 3.64/3.80 True % 3.64/3.80 Clause #13 (by clausification #[12]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.64/3.80 Eq % 3.64/3.80 (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4) → % 3.64/3.80 Or (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4))) % 3.64/3.80 False % 3.64/3.80 Clause #14 (by clausification #[13]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True % 3.64/3.80 Clause #15 (by clausification #[13]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.64/3.80 Eq (Or (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4))) False % 3.64/3.80 Clause #16 (by clausification #[15]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) False % 3.64/3.80 Clause #17 (by clausification #[15]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) False % 3.66/3.82 Clause #18 (by betaEtaReduce #[11]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop), % 3.66/3.82 Eq (Or (And (skS.0 0 a_1 a_2) (skS.0 1 a_1 a_3 a_2)) (And (skS.0 0 a_1 a_2) (skS.0 2 a_1 a_3 a_4 a_2))) % 3.66/3.82 (skS.0 0 a_1 a_2) % 3.66/3.82 Clause #20 (by identity boolHoist #[18]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop), % 3.66/3.82 Or (Eq (Or (And (skS.0 0 a_1 a_2) (skS.0 1 a_1 a_3 a_2)) False) (skS.0 0 a_1 a_2)) % 3.66/3.82 (Eq (And (skS.0 0 a_1 a_2) (skS.0 2 a_1 a_3 a_4 a_2)) True) % 3.66/3.82 Clause #23 (by clausification #[20]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop), % 3.66/3.82 Or (Eq (Or (And (skS.0 0 a_1 a_2) (skS.0 1 a_1 a_3 a_2)) False) (skS.0 0 a_1 a_2)) (Eq (skS.0 2 a_1 a_3 a_4 a_2) True) % 3.66/3.82 Clause #25 (by bool simp #[23]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop), % 3.66/3.82 Or (Eq (And (skS.0 0 a_1 a_2) (skS.0 1 a_1 a_3 a_2)) (skS.0 0 a_1 a_2)) (Eq (skS.0 2 a_1 a_3 a_4 a_2) True) % 3.66/3.82 Clause #27 (by identity boolHoist #[25]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.66/3.82 Or (Eq (skS.0 2 a_1 a_2 a_3 a_4) True) % 3.66/3.82 (Or (Eq (And (skS.0 0 a_1 a_4) False) (skS.0 0 a_1 a_4)) (Eq (skS.0 1 a_1 a_2 a_4) True)) % 3.66/3.82 Clause #34 (by bool simp #[27]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.66/3.82 Or (Eq (skS.0 2 a_1 a_2 a_3 a_4) True) (Or (Eq False (skS.0 0 a_1 a_4)) (Eq (skS.0 1 a_1 a_2 a_4) True)) % 3.66/3.82 Clause #37 (by superposition #[34, 14]): ∀ (a_1 a_2 a_3 a_4 a_5 : a → Prop) (a_6 : a), % 3.66/3.82 Or (Eq (skS.0 2 (fun x => a_1 x) a_2 a_3 (skS.0 3 a_1 a_4 a_5 a_6)) True) % 3.66/3.82 (Or (Eq (skS.0 1 (fun x => a_1 x) a_2 (skS.0 3 a_1 a_4 a_5 a_6)) True) (Eq False True)) % 3.66/3.82 Clause #39 (by betaEtaReduce #[37]): ∀ (a_1 a_2 a_3 a_4 a_5 : a → Prop) (a_6 : a), % 3.66/3.82 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_4 a_5 a_6)) True) % 3.66/3.82 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_4 a_5 a_6)) True) (Eq False True)) % 3.66/3.82 Clause #40 (by clausification #[39]): ∀ (a_1 a_2 a_3 a_4 a_5 : a → Prop) (a_6 : a), % 3.66/3.82 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_4 a_5 a_6)) True) (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_4 a_5 a_6)) True) % 3.66/3.82 Clause #41 (by superposition #[40, 16]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.66/3.82 Or % 3.66/3.82 (Eq (skS.0 1 (fun x => a_1 x) (fun x => a_2 x) (skS.0 3 (fun x => a_1 x) (fun x => a_2 x) (fun x => a_3 x) a_4)) % 3.66/3.82 True) % 3.66/3.82 (Eq True False) % 3.66/3.82 Clause #42 (by betaEtaReduce #[41]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq True False) % 3.66/3.82 Clause #43 (by clausification #[42]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True % 3.66/3.82 Clause #44 (by superposition #[43, 17]): Eq True False % 3.66/3.82 Clause #45 (by clausification #[44]): False % 3.66/3.82 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------