%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV135^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n007.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 08:02:52 PM UTC 2025 % Result : Theorem 3.73s 3.88s % Output : Proof 3.73s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.14 % Problem : SEV135^5 : TPTP v9.2.0. Released v4.0.0. % 0.13/0.15 % Command : duper %s % 0.15/0.36 % Computer : n007.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 300 % 0.15/0.36 % DateTime : Fri Oct 3 01:37:23 EDT 2025 % 0.15/0.36 % CPUTime : % 3.73/3.88 SZS status Theorem for theBenchmark.p % 3.73/3.88 SZS output start Proof for theBenchmark.p % 3.73/3.88 Clause #0 (by assumption #[]): Eq % 3.73/3.88 (Not % 3.73/3.88 (∀ (Xr : a → a → Prop) (Xx Xy : a), % 3.73/3.88 Xr Xx Xy → % 3.73/3.88 ∀ (Xq : a → Prop), And (∀ (Xw : a), Xr Xx Xw → Xq Xw) (∀ (Xu Xv : a), And (Xq Xu) (Xr Xu Xv) → Xq Xv) → Xq Xy)) % 3.73/3.88 True % 3.73/3.88 Clause #1 (by clausification #[0]): Eq % 3.73/3.88 (∀ (Xr : a → a → Prop) (Xx Xy : a), % 3.73/3.88 Xr Xx Xy → % 3.73/3.88 ∀ (Xq : a → Prop), And (∀ (Xw : a), Xr Xx Xw → Xq Xw) (∀ (Xu Xv : a), And (Xq Xu) (Xr Xu Xv) → Xq Xv) → Xq Xy) % 3.73/3.88 False % 3.73/3.88 Clause #2 (by clausification #[1]): ∀ (a_1 : a → a → Prop), % 3.73/3.88 Eq % 3.73/3.88 (Not % 3.73/3.88 (∀ (Xx Xy : a), % 3.73/3.88 skS.0 0 a_1 Xx Xy → % 3.73/3.88 ∀ (Xq : a → Prop), % 3.73/3.88 And (∀ (Xw : a), skS.0 0 a_1 Xx Xw → Xq Xw) (∀ (Xu Xv : a), And (Xq Xu) (skS.0 0 a_1 Xu Xv) → Xq Xv) → % 3.73/3.88 Xq Xy)) % 3.73/3.88 True % 3.73/3.88 Clause #3 (by clausification #[2]): ∀ (a_1 : a → a → Prop), % 3.73/3.88 Eq % 3.73/3.88 (∀ (Xx Xy : a), % 3.73/3.88 skS.0 0 a_1 Xx Xy → % 3.73/3.88 ∀ (Xq : a → Prop), % 3.73/3.88 And (∀ (Xw : a), skS.0 0 a_1 Xx Xw → Xq Xw) (∀ (Xu Xv : a), And (Xq Xu) (skS.0 0 a_1 Xu Xv) → Xq Xv) → Xq Xy) % 3.73/3.88 False % 3.73/3.88 Clause #4 (by clausification #[3]): ∀ (a_1 : a → a → Prop) (a_2 : a), % 3.73/3.88 Eq % 3.73/3.88 (Not % 3.73/3.88 (∀ (Xy : a), % 3.73/3.88 skS.0 0 a_1 (skS.0 1 a_1 a_2) Xy → % 3.73/3.88 ∀ (Xq : a → Prop), % 3.73/3.88 And (∀ (Xw : a), skS.0 0 a_1 (skS.0 1 a_1 a_2) Xw → Xq Xw) % 3.73/3.88 (∀ (Xu Xv : a), And (Xq Xu) (skS.0 0 a_1 Xu Xv) → Xq Xv) → % 3.73/3.88 Xq Xy)) % 3.73/3.88 True % 3.73/3.88 Clause #5 (by clausification #[4]): ∀ (a_1 : a → a → Prop) (a_2 : a), % 3.73/3.88 Eq % 3.73/3.88 (∀ (Xy : a), % 3.73/3.88 skS.0 0 a_1 (skS.0 1 a_1 a_2) Xy → % 3.73/3.88 ∀ (Xq : a → Prop), % 3.73/3.88 And (∀ (Xw : a), skS.0 0 a_1 (skS.0 1 a_1 a_2) Xw → Xq Xw) % 3.73/3.88 (∀ (Xu Xv : a), And (Xq Xu) (skS.0 0 a_1 Xu Xv) → Xq Xv) → % 3.73/3.88 Xq Xy) % 3.73/3.88 False % 3.73/3.88 Clause #6 (by clausification #[5]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), % 3.73/3.88 Eq % 3.73/3.88 (Not % 3.73/3.88 (skS.0 0 a_1 (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_2 a_3) → % 3.73/3.88 ∀ (Xq : a → Prop), % 3.73/3.88 And (∀ (Xw : a), skS.0 0 a_1 (skS.0 1 a_1 a_2) Xw → Xq Xw) % 3.73/3.88 (∀ (Xu Xv : a), And (Xq Xu) (skS.0 0 a_1 Xu Xv) → Xq Xv) → % 3.73/3.88 Xq (skS.0 2 a_1 a_2 a_3))) % 3.73/3.88 True % 3.73/3.88 Clause #7 (by clausification #[6]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), % 3.73/3.88 Eq % 3.73/3.88 (skS.0 0 a_1 (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_2 a_3) → % 3.73/3.88 ∀ (Xq : a → Prop), % 3.73/3.88 And (∀ (Xw : a), skS.0 0 a_1 (skS.0 1 a_1 a_2) Xw → Xq Xw) % 3.73/3.88 (∀ (Xu Xv : a), And (Xq Xu) (skS.0 0 a_1 Xu Xv) → Xq Xv) → % 3.73/3.88 Xq (skS.0 2 a_1 a_2 a_3)) % 3.73/3.88 False % 3.73/3.88 Clause #8 (by clausification #[7]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_2 a_3)) True % 3.73/3.88 Clause #9 (by clausification #[7]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), % 3.73/3.88 Eq % 3.73/3.88 (∀ (Xq : a → Prop), % 3.73/3.88 And (∀ (Xw : a), skS.0 0 a_1 (skS.0 1 a_1 a_2) Xw → Xq Xw) % 3.73/3.88 (∀ (Xu Xv : a), And (Xq Xu) (skS.0 0 a_1 Xu Xv) → Xq Xv) → % 3.73/3.88 Xq (skS.0 2 a_1 a_2 a_3)) % 3.73/3.88 False % 3.73/3.88 Clause #10 (by clausification #[9]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop), % 3.73/3.88 Eq % 3.73/3.88 (Not % 3.73/3.88 (And (∀ (Xw : a), skS.0 0 a_1 (skS.0 1 a_1 a_2) Xw → skS.0 3 a_1 a_2 a_3 a_4 Xw) % 3.73/3.88 (∀ (Xu Xv : a), And (skS.0 3 a_1 a_2 a_3 a_4 Xu) (skS.0 0 a_1 Xu Xv) → skS.0 3 a_1 a_2 a_3 a_4 Xv) → % 3.73/3.88 skS.0 3 a_1 a_2 a_3 a_4 (skS.0 2 a_1 a_2 a_3))) % 3.73/3.88 True % 3.73/3.88 Clause #11 (by clausification #[10]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop), % 3.73/3.88 Eq % 3.73/3.88 (And (∀ (Xw : a), skS.0 0 a_1 (skS.0 1 a_1 a_2) Xw → skS.0 3 a_1 a_2 a_3 a_4 Xw) % 3.73/3.88 (∀ (Xu Xv : a), And (skS.0 3 a_1 a_2 a_3 a_4 Xu) (skS.0 0 a_1 Xu Xv) → skS.0 3 a_1 a_2 a_3 a_4 Xv) → % 3.73/3.88 skS.0 3 a_1 a_2 a_3 a_4 (skS.0 2 a_1 a_2 a_3)) % 3.73/3.88 False % 3.73/3.88 Clause #12 (by clausification #[11]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop), % 3.73/3.88 Eq % 3.73/3.88 (And (∀ (Xw : a), skS.0 0 a_1 (skS.0 1 a_1 a_2) Xw → skS.0 3 a_1 a_2 a_3 a_4 Xw) % 3.73/3.88 (∀ (Xu Xv : a), And (skS.0 3 a_1 a_2 a_3 a_4 Xu) (skS.0 0 a_1 Xu Xv) → skS.0 3 a_1 a_2 a_3 a_4 Xv)) % 3.73/3.89 True % 3.73/3.89 Clause #13 (by clausification #[11]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop), Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 2 a_1 a_2 a_3)) False % 3.73/3.89 Clause #15 (by clausification #[12]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop), % 3.73/3.89 Eq (∀ (Xw : a), skS.0 0 a_1 (skS.0 1 a_1 a_2) Xw → skS.0 3 a_1 a_2 a_3 a_4 Xw) True % 3.73/3.89 Clause #20 (by clausification #[15]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a) (a_5 : a → Prop), % 3.73/3.89 Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2) a_3 → skS.0 3 a_1 a_2 a_4 a_5 a_3) True % 3.73/3.89 Clause #21 (by clausification #[20]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a) (a_5 : a → Prop), % 3.73/3.89 Or (Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2) a_3) False) (Eq (skS.0 3 a_1 a_2 a_4 a_5 a_3) True) % 3.73/3.89 Clause #22 (by superposition #[21, 8]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop) (a_5 : a), % 3.73/3.89 Or (Eq (skS.0 3 (fun x x_1 => a_1 x x_1) a_2 a_3 a_4 (skS.0 2 a_1 a_2 a_5)) True) (Eq False True) % 3.73/3.89 Clause #23 (by betaEtaReduce #[22]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop) (a_5 : a), % 3.73/3.89 Or (Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 2 a_1 a_2 a_5)) True) (Eq False True) % 3.73/3.89 Clause #24 (by clausification #[23]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop) (a_5 : a), Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 2 a_1 a_2 a_5)) True % 3.73/3.89 Clause #25 (by superposition #[24, 13]): Eq True False % 3.73/3.89 Clause #27 (by clausification #[25]): False % 3.73/3.89 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------