%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN063+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n022.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 08:07:05 PM UTC 2025 % Result : Theorem 3.52s 3.76s % Output : Proof 3.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SYN063+1 : TPTP v9.2.0. Released v2.0.0. % 0.04/0.13 % Command : duper %s % 0.13/0.34 % Computer : n022.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 : % 3.52/3.76 SZS status Theorem for theBenchmark.p % 3.52/3.76 SZS output start Proof for theBenchmark.p % 3.52/3.76 Clause #0 (by assumption #[]): Eq % 3.52/3.76 (Not % 3.52/3.76 (Iff (∀ (X : Iota), And (big_p a) (big_p X → big_p b) → big_p c) % 3.52/3.76 (∀ (X1 : Iota), % 3.52/3.76 And (Or (Or (Not (big_p a)) (big_p X1)) (big_p c)) (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c))))) % 3.52/3.76 True % 3.52/3.76 Clause #1 (by clausification #[0]): Eq % 3.52/3.76 (Iff (∀ (X : Iota), And (big_p a) (big_p X → big_p b) → big_p c) % 3.52/3.76 (∀ (X1 : Iota), % 3.52/3.76 And (Or (Or (Not (big_p a)) (big_p X1)) (big_p c)) (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c)))) % 3.52/3.76 False % 3.52/3.76 Clause #2 (by clausification #[1]): Or (Eq (∀ (X : Iota), And (big_p a) (big_p X → big_p b) → big_p c) False) % 3.52/3.76 (Eq % 3.52/3.76 (∀ (X1 : Iota), % 3.52/3.76 And (Or (Or (Not (big_p a)) (big_p X1)) (big_p c)) (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c))) % 3.52/3.76 False) % 3.52/3.76 Clause #3 (by clausification #[1]): Or (Eq (∀ (X : Iota), And (big_p a) (big_p X → big_p b) → big_p c) True) % 3.52/3.76 (Eq % 3.52/3.76 (∀ (X1 : Iota), % 3.52/3.76 And (Or (Or (Not (big_p a)) (big_p X1)) (big_p c)) (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c))) % 3.52/3.76 True) % 3.52/3.76 Clause #4 (by clausification #[2]): ∀ (a_1 : Iota), % 3.52/3.76 Or % 3.52/3.76 (Eq % 3.52/3.76 (∀ (X1 : Iota), % 3.52/3.76 And (Or (Or (Not (big_p a)) (big_p X1)) (big_p c)) (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c))) % 3.52/3.76 False) % 3.52/3.76 (Eq (Not (And (big_p a) (big_p (skS.0 0 a_1) → big_p b) → big_p c)) True) % 3.52/3.76 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : Iota), % 3.52/3.76 Or (Eq (Not (And (big_p a) (big_p (skS.0 0 a_1) → big_p b) → big_p c)) True) % 3.52/3.76 (Eq % 3.52/3.76 (Not % 3.52/3.76 (And (Or (Or (Not (big_p a)) (big_p (skS.0 1 a_2))) (big_p c)) % 3.52/3.76 (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c)))) % 3.52/3.76 True) % 3.52/3.76 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 : Iota), % 3.52/3.76 Or % 3.52/3.76 (Eq % 3.52/3.76 (Not % 3.52/3.76 (And (Or (Or (Not (big_p a)) (big_p (skS.0 1 a_1))) (big_p c)) % 3.52/3.76 (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c)))) % 3.52/3.76 True) % 3.52/3.76 (Eq (And (big_p a) (big_p (skS.0 0 a_2) → big_p b) → big_p c) False) % 3.52/3.76 Clause #7 (by clausification #[6]): ∀ (a_1 a_2 : Iota), % 3.52/3.76 Or (Eq (And (big_p a) (big_p (skS.0 0 a_1) → big_p b) → big_p c) False) % 3.52/3.76 (Eq % 3.52/3.76 (And (Or (Or (Not (big_p a)) (big_p (skS.0 1 a_2))) (big_p c)) % 3.52/3.76 (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c))) % 3.52/3.76 False) % 3.52/3.76 Clause #8 (by clausification #[7]): ∀ (a_1 a_2 : Iota), % 3.52/3.76 Or % 3.52/3.76 (Eq % 3.52/3.76 (And (Or (Or (Not (big_p a)) (big_p (skS.0 1 a_1))) (big_p c)) % 3.52/3.76 (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c))) % 3.52/3.76 False) % 3.52/3.76 (Eq (And (big_p a) (big_p (skS.0 0 a_2) → big_p b)) True) % 3.52/3.76 Clause #9 (by clausification #[7]): ∀ (a_1 : Iota), % 3.52/3.76 Or % 3.52/3.76 (Eq % 3.52/3.76 (And (Or (Or (Not (big_p a)) (big_p (skS.0 1 a_1))) (big_p c)) % 3.52/3.76 (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c))) % 3.52/3.76 False) % 3.52/3.76 (Eq (big_p c) False) % 3.52/3.76 Clause #10 (by clausification #[8]): ∀ (a_1 a_2 : Iota), % 3.52/3.76 Or (Eq (And (big_p a) (big_p (skS.0 0 a_1) → big_p b)) True) % 3.52/3.76 (Or (Eq (Or (Or (Not (big_p a)) (big_p (skS.0 1 a_2))) (big_p c)) False) % 3.52/3.76 (Eq (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c)) False)) % 3.52/3.76 Clause #12 (by clausification #[10]): ∀ (a_1 : Iota), % 3.52/3.76 Or (Eq (Or (Or (Not (big_p a)) (big_p (skS.0 1 a_1))) (big_p c)) False) % 3.52/3.76 (Or (Eq (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c)) False) (Eq (big_p a) True)) % 3.52/3.76 Clause #35 (by clausification #[3]): ∀ (a_1 : Iota), % 3.52/3.76 Or % 3.52/3.76 (Eq % 3.52/3.76 (∀ (X1 : Iota), % 3.52/3.76 And (Or (Or (Not (big_p a)) (big_p X1)) (big_p c)) (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c))) % 3.52/3.76 True) % 3.52/3.76 (Eq (And (big_p a) (big_p a_1 → big_p b) → big_p c) True) % 3.52/3.76 Clause #36 (by clausification #[35]): ∀ (a_1 a_2 : Iota), % 3.52/3.76 Or (Eq (And (big_p a) (big_p a_1 → big_p b) → big_p c) True) % 3.52/3.76 (Eq (And (Or (Or (Not (big_p a)) (big_p a_2)) (big_p c)) (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c))) True) % 3.52/3.76 Clause #37 (by clausification #[36]): ∀ (a_1 a_2 : Iota), % 3.52/3.76 Or (Eq (And (Or (Or (Not (big_p a)) (big_p a_1)) (big_p c)) (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c))) True) % 3.52/3.76 (Or (Eq (And (big_p a) (big_p a_2 → big_p b)) False) (Eq (big_p c) True)) % 3.62/3.78 Clause #39 (by clausification #[37]): ∀ (a_1 a_2 : Iota), % 3.62/3.78 Or (Eq (And (big_p a) (big_p a_1 → big_p b)) False) % 3.62/3.78 (Or (Eq (big_p c) True) (Eq (Or (Or (Not (big_p a)) (big_p a_2)) (big_p c)) True)) % 3.62/3.78 Clause #52 (by clausification #[39]): ∀ (a_1 a_2 : Iota), % 3.62/3.78 Or (Eq (big_p c) True) % 3.62/3.78 (Or (Eq (Or (Or (Not (big_p a)) (big_p a_1)) (big_p c)) True) % 3.62/3.78 (Or (Eq (big_p a) False) (Eq (big_p a_2 → big_p b) False))) % 3.62/3.78 Clause #53 (by clausification #[52]): ∀ (a_1 a_2 : Iota), % 3.62/3.78 Or (Eq (big_p c) True) % 3.62/3.78 (Or (Eq (big_p a) False) % 3.62/3.78 (Or (Eq (big_p a_1 → big_p b) False) (Or (Eq (Or (Not (big_p a)) (big_p a_2)) True) (Eq (big_p c) True)))) % 3.62/3.78 Clause #54 (by clausification #[53]): ∀ (a_1 a_2 : Iota), % 3.62/3.78 Or (Eq (big_p c) True) % 3.62/3.78 (Or (Eq (big_p a) False) % 3.62/3.78 (Or (Eq (Or (Not (big_p a)) (big_p a_1)) True) (Or (Eq (big_p c) True) (Eq (big_p a_2) True)))) % 3.62/3.78 Clause #56 (by clausification #[54]): ∀ (a_1 a_2 : Iota), % 3.62/3.78 Or (Eq (big_p c) True) % 3.62/3.78 (Or (Eq (big_p a) False) % 3.62/3.78 (Or (Eq (big_p c) True) (Or (Eq (big_p a_1) True) (Or (Eq (Not (big_p a)) True) (Eq (big_p a_2) True))))) % 3.62/3.78 Clause #57 (by clausification #[56]): ∀ (a_1 a_2 : Iota), % 3.62/3.78 Or (Eq (big_p c) True) % 3.62/3.78 (Or (Eq (big_p a) False) % 3.62/3.78 (Or (Eq (big_p c) True) (Or (Eq (big_p a_1) True) (Or (Eq (big_p a_2) True) (Eq (big_p a) False))))) % 3.62/3.78 Clause #58 (by eliminate duplicate literals #[57]): ∀ (a_1 a_2 : Iota), Or (Eq (big_p c) True) (Or (Eq (big_p a) False) (Or (Eq (big_p a_1) True) (Eq (big_p a_2) True))) % 3.62/3.78 Clause #68 (by clausification #[9]): ∀ (a_1 : Iota), % 3.62/3.78 Or (Eq (big_p c) False) % 3.62/3.78 (Or (Eq (Or (Or (Not (big_p a)) (big_p (skS.0 1 a_1))) (big_p c)) False) % 3.62/3.78 (Eq (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c)) False)) % 3.62/3.78 Clause #69 (by clausification #[68]): Or (Eq (big_p c) False) (Or (Eq (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c)) False) (Eq (big_p c) False)) % 3.62/3.78 Clause #71 (by clausification #[69]): Or (Eq (big_p c) False) (Or (Eq (big_p c) False) (Eq (big_p c) False)) % 3.62/3.78 Clause #73 (by eliminate duplicate literals #[71]): Eq (big_p c) False % 3.62/3.78 Clause #76 (by backward demodulation #[73, 58]): ∀ (a_1 a_2 : Iota), Or (Eq False True) (Or (Eq (big_p a) False) (Or (Eq (big_p a_1) True) (Eq (big_p a_2) True))) % 3.62/3.78 Clause #78 (by clausification #[76]): ∀ (a_1 a_2 : Iota), Or (Eq (big_p a) False) (Or (Eq (big_p a_1) True) (Eq (big_p a_2) True)) % 3.62/3.78 Clause #88 (by clausification #[12]): ∀ (a_1 : Iota), % 3.62/3.78 Or (Eq (Or (Or (Not (big_p a)) (Not (big_p b))) (big_p c)) False) % 3.62/3.78 (Or (Eq (big_p a) True) (Eq (Or (Not (big_p a)) (big_p (skS.0 1 a_1))) False)) % 3.62/3.78 Clause #101 (by clausification #[88]): ∀ (a_1 : Iota), % 3.62/3.78 Or (Eq (big_p a) True) % 3.62/3.78 (Or (Eq (Or (Not (big_p a)) (big_p (skS.0 1 a_1))) False) (Eq (Or (Not (big_p a)) (Not (big_p b))) False)) % 3.62/3.78 Clause #105 (by clausification #[101]): Or (Eq (big_p a) True) (Or (Eq (Or (Not (big_p a)) (Not (big_p b))) False) (Eq (Not (big_p a)) False)) % 3.62/3.78 Clause #117 (by clausification #[105]): Or (Eq (big_p a) True) (Or (Eq (Not (big_p a)) False) (Eq (Not (big_p a)) False)) % 3.62/3.78 Clause #121 (by clausification #[117]): Or (Eq (big_p a) True) (Or (Eq (Not (big_p a)) False) (Eq (big_p a) True)) % 3.62/3.78 Clause #122 (by clausification #[121]): Or (Eq (big_p a) True) (Or (Eq (big_p a) True) (Eq (big_p a) True)) % 3.62/3.78 Clause #123 (by eliminate duplicate literals #[122]): Eq (big_p a) True % 3.62/3.78 Clause #127 (by superposition #[123, 78]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (big_p a) True) (Eq (big_p a_1) True)) % 3.62/3.78 Clause #136 (by clausification #[127]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Eq (big_p a_1) True) % 3.62/3.78 Clause #137 (by superposition #[136, 73]): ∀ (a : Iota), Or (Eq (big_p a) True) (Eq True False) % 3.62/3.78 Clause #141 (by clausification #[137]): ∀ (a : Iota), Eq (big_p a) True % 3.62/3.78 Clause #142 (by superposition #[141, 73]): Eq True False % 3.62/3.78 Clause #143 (by clausification #[142]): False % 3.62/3.78 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------