%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN949+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n020.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 08:08:17 PM UTC 2025 % Result : Theorem 3.37s 3.60s % Output : Proof 3.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SYN949+1 : TPTP v9.2.0. Released v3.1.0. % 0.03/0.13 % Command : duper %s % 0.12/0.34 % Computer : n020.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % 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 : Thu Oct 2 15:22:08 EDT 2025 % 0.12/0.34 % CPUTime : % 3.37/3.60 SZS status Theorem for theBenchmark.p % 3.37/3.60 SZS output start Proof for theBenchmark.p % 3.37/3.60 Clause #0 (by assumption #[]): Eq % 3.37/3.60 (Not % 3.37/3.60 (∀ (A B C : Iota), % 3.37/3.60 And (And (And (And (s A) (s B)) (r B C)) (∀ (X : Iota), s X → p X)) (∀ (X Y : Iota), r X Y → q X Y) → % 3.37/3.60 Exists fun X => Exists fun Y => And (p X) (q X Y))) % 3.37/3.60 True % 3.37/3.60 Clause #1 (by clausification #[0]): Eq % 3.37/3.60 (∀ (A B C : Iota), % 3.37/3.60 And (And (And (And (s A) (s B)) (r B C)) (∀ (X : Iota), s X → p X)) (∀ (X Y : Iota), r X Y → q X Y) → % 3.37/3.60 Exists fun X => Exists fun Y => And (p X) (q X Y)) % 3.37/3.60 False % 3.37/3.60 Clause #2 (by clausification #[1]): ∀ (a : Iota), % 3.37/3.60 Eq % 3.37/3.60 (Not % 3.37/3.60 (∀ (B C : Iota), % 3.37/3.60 And (And (And (And (s (skS.0 0 a)) (s B)) (r B C)) (∀ (X : Iota), s X → p X)) (∀ (X Y : Iota), r X Y → q X Y) → % 3.37/3.60 Exists fun X => Exists fun Y => And (p X) (q X Y))) % 3.37/3.60 True % 3.37/3.60 Clause #3 (by clausification #[2]): ∀ (a : Iota), % 3.37/3.60 Eq % 3.37/3.60 (∀ (B C : Iota), % 3.37/3.60 And (And (And (And (s (skS.0 0 a)) (s B)) (r B C)) (∀ (X : Iota), s X → p X)) (∀ (X Y : Iota), r X Y → q X Y) → % 3.37/3.60 Exists fun X => Exists fun Y => And (p X) (q X Y)) % 3.37/3.60 False % 3.37/3.60 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota), % 3.37/3.60 Eq % 3.37/3.60 (Not % 3.37/3.60 (∀ (C : Iota), % 3.37/3.60 And (And (And (And (s (skS.0 0 a)) (s (skS.0 1 a a_1))) (r (skS.0 1 a a_1) C)) (∀ (X : Iota), s X → p X)) % 3.37/3.60 (∀ (X Y : Iota), r X Y → q X Y) → % 3.37/3.60 Exists fun X => Exists fun Y => And (p X) (q X Y))) % 3.37/3.60 True % 3.37/3.60 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), % 3.37/3.60 Eq % 3.37/3.60 (∀ (C : Iota), % 3.37/3.60 And (And (And (And (s (skS.0 0 a)) (s (skS.0 1 a a_1))) (r (skS.0 1 a a_1) C)) (∀ (X : Iota), s X → p X)) % 3.37/3.60 (∀ (X Y : Iota), r X Y → q X Y) → % 3.37/3.60 Exists fun X => Exists fun Y => And (p X) (q X Y)) % 3.37/3.60 False % 3.37/3.60 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Iota), % 3.37/3.60 Eq % 3.37/3.60 (Not % 3.37/3.60 (And % 3.37/3.60 (And (And (And (s (skS.0 0 a)) (s (skS.0 1 a a_1))) (r (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 3.37/3.60 (∀ (X : Iota), s X → p X)) % 3.37/3.60 (∀ (X Y : Iota), r X Y → q X Y) → % 3.37/3.60 Exists fun X => Exists fun Y => And (p X) (q X Y))) % 3.37/3.60 True % 3.37/3.60 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 : Iota), % 3.37/3.60 Eq % 3.37/3.60 (And % 3.37/3.60 (And (And (And (s (skS.0 0 a)) (s (skS.0 1 a a_1))) (r (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 3.37/3.60 (∀ (X : Iota), s X → p X)) % 3.37/3.60 (∀ (X Y : Iota), r X Y → q X Y) → % 3.37/3.60 Exists fun X => Exists fun Y => And (p X) (q X Y)) % 3.37/3.60 False % 3.37/3.60 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), % 3.37/3.60 Eq % 3.37/3.60 (And % 3.37/3.60 (And (And (And (s (skS.0 0 a)) (s (skS.0 1 a a_1))) (r (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 3.37/3.60 (∀ (X : Iota), s X → p X)) % 3.37/3.60 (∀ (X Y : Iota), r X Y → q X Y)) % 3.37/3.60 True % 3.37/3.60 Clause #9 (by clausification #[7]): Eq (Exists fun X => Exists fun Y => And (p X) (q X Y)) False % 3.37/3.60 Clause #10 (by clausification #[8]): Eq (∀ (X Y : Iota), r X Y → q X Y) True % 3.37/3.60 Clause #11 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), % 3.37/3.60 Eq % 3.37/3.60 (And (And (And (s (skS.0 0 a)) (s (skS.0 1 a a_1))) (r (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 3.37/3.60 (∀ (X : Iota), s X → p X)) % 3.37/3.60 True % 3.37/3.60 Clause #12 (by clausification #[10]): ∀ (a : Iota), Eq (∀ (Y : Iota), r a Y → q a Y) True % 3.37/3.60 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Eq (r a a_1 → q a a_1) True % 3.37/3.60 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (r a a_1) False) (Eq (q a a_1) True) % 3.37/3.60 Clause #15 (by clausification #[9]): ∀ (a : Iota), Eq (Exists fun Y => And (p a) (q a Y)) False % 3.37/3.60 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (And (p a) (q a a_1)) False % 3.37/3.60 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (p a) False) (Eq (q a a_1) False) % 3.37/3.60 Clause #18 (by clausification #[11]): Eq (∀ (X : Iota), s X → p X) True % 3.37/3.60 Clause #19 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Eq (And (And (s (skS.0 0 a)) (s (skS.0 1 a a_1))) (r (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) True % 3.37/3.60 Clause #20 (by clausification #[18]): ∀ (a : Iota), Eq (s a → p a) True % 3.37/3.60 Clause #21 (by clausification #[20]): ∀ (a : Iota), Or (Eq (s a) False) (Eq (p a) True) % 3.37/3.61 Clause #22 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), Eq (r (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) True % 3.37/3.61 Clause #23 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (And (s (skS.0 0 a)) (s (skS.0 1 a a_1))) True % 3.37/3.61 Clause #24 (by superposition #[22, 14]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (q (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) True) % 3.37/3.61 Clause #25 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (s (skS.0 1 a a_1)) True % 3.37/3.61 Clause #27 (by superposition #[25, 21]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (p (skS.0 1 a a_1)) True) % 3.37/3.61 Clause #28 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), Eq (q (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) True % 3.37/3.61 Clause #33 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (p (skS.0 1 a a_1)) True % 3.37/3.61 Clause #34 (by superposition #[33, 17]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (q (skS.0 1 a a_1) a_2) False) % 3.37/3.61 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), Eq (q (skS.0 1 a a_1) a_2) False % 3.37/3.61 Clause #36 (by superposition #[35, 28]): Eq False True % 3.37/3.61 Clause #37 (by clausification #[36]): False % 3.37/3.61 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------