%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN937+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n029.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 08:08:16 PM UTC 2025 % Result : Theorem 3.38s 3.66s % Output : Proof 3.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.13 % Problem : SYN937+1 : TPTP v9.2.0. Released v3.1.0. % 0.06/0.14 % Command : duper %s % 0.13/0.39 % Computer : n029.cluster.edu % 0.13/0.39 % Model : x86_64 x86_64 % 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.39 % Memory : 8042.1875MB % 0.13/0.39 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.39 % CPULimit : 300 % 0.13/0.39 % WCLimit : 300 % 0.13/0.39 % DateTime : Thu Oct 2 15:11:53 EDT 2025 % 0.13/0.39 % CPUTime : % 3.38/3.66 SZS status Theorem for theBenchmark.p % 3.38/3.66 SZS output start Proof for theBenchmark.p % 3.38/3.66 Clause #0 (by assumption #[]): Eq (Not (Iff (∀ (X : Iota), p X → c) ((Exists fun X => p X) → c))) True % 3.38/3.66 Clause #1 (by betaEtaReduce #[0]): Eq (Not (Iff (∀ (X : Iota), p X → c) (Exists p → c))) True % 3.38/3.66 Clause #2 (by clausification #[1]): Eq (Iff (∀ (X : Iota), p X → c) (Exists p → c)) False % 3.38/3.66 Clause #3 (by clausification #[2]): Or (Eq (∀ (X : Iota), p X → c) False) (Eq (Exists p → c) False) % 3.38/3.66 Clause #4 (by clausification #[2]): Or (Eq (∀ (X : Iota), p X → c) True) (Eq (Exists p → c) True) % 3.38/3.66 Clause #5 (by clausification #[3]): ∀ (a : Iota), Or (Eq (Exists p → c) False) (Eq (Not (p (skS.0 0 a) → c)) True) % 3.38/3.66 Clause #6 (by clausification #[5]): ∀ (a : Iota), Or (Eq (Not (p (skS.0 0 a) → c)) True) (Eq (Exists p) True) % 3.38/3.66 Clause #7 (by clausification #[5]): ∀ (a : Iota), Or (Eq (Not (p (skS.0 0 a) → c)) True) (Eq c False) % 3.38/3.66 Clause #8 (by clausification #[6]): ∀ (a : Iota), Or (Eq (Exists p) True) (Eq (p (skS.0 0 a) → c) False) % 3.38/3.66 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq (p (skS.0 0 a) → c) False) (Eq (p (skS.0 1 a_1)) True) % 3.38/3.66 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Or (Eq (p (skS.0 1 a)) True) (Eq (p (skS.0 0 a_1)) True) % 3.38/3.66 Clause #12 (by clausification #[7]): ∀ (a : Iota), Or (Eq c False) (Eq (p (skS.0 0 a) → c) False) % 3.38/3.66 Clause #14 (by clausification #[12]): Or (Eq c False) (Eq c False) % 3.38/3.66 Clause #15 (by eliminate duplicate literals #[14]): Eq c False % 3.38/3.66 Clause #17 (by clausification #[4]): ∀ (a : Iota), Or (Eq (Exists p → c) True) (Eq (p a → c) True) % 3.38/3.66 Clause #18 (by clausification #[17]): ∀ (a : Iota), Or (Eq (p a → c) True) (Or (Eq (Exists p) False) (Eq c True)) % 3.38/3.66 Clause #19 (by clausification #[18]): ∀ (a : Iota), Or (Eq (Exists p) False) (Or (Eq c True) (Or (Eq (p a) False) (Eq c True))) % 3.38/3.66 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Or (Eq c True) (Or (Eq (p a) False) (Or (Eq c True) (Eq (p a_1) False))) % 3.38/3.66 Clause #21 (by eliminate duplicate literals #[20]): ∀ (a a_1 : Iota), Or (Eq c True) (Or (Eq (p a) False) (Eq (p a_1) False)) % 3.38/3.66 Clause #22 (by forward demodulation #[21, 15]): ∀ (a a_1 : Iota), Or (Eq False True) (Or (Eq (p a) False) (Eq (p a_1) False)) % 3.38/3.66 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Or (Eq (p a) False) (Eq (p a_1) False) % 3.38/3.66 Clause #25 (by superposition #[23, 10]): ∀ (a a_1 : Iota), Or (Eq (p a) False) (Or (Eq (p (skS.0 1 a_1)) True) (Eq False True)) % 3.38/3.66 Clause #27 (by clausification #[25]): ∀ (a a_1 : Iota), Or (Eq (p a) False) (Eq (p (skS.0 1 a_1)) True) % 3.38/3.66 Clause #29 (by superposition #[27, 10]): ∀ (a a_1 : Iota), Or (Eq (p (skS.0 1 a)) True) (Or (Eq (p (skS.0 1 a_1)) True) (Eq False True)) % 3.38/3.66 Clause #33 (by clausification #[29]): ∀ (a a_1 : Iota), Or (Eq (p (skS.0 1 a)) True) (Eq (p (skS.0 1 a_1)) True) % 3.38/3.66 Clause #37 (by equality factoring #[33]): ∀ (a : Iota), Or (Ne True True) (Eq (p (skS.0 1 a)) True) % 3.38/3.66 Clause #38 (by clausification #[37]): ∀ (a : Iota), Or (Eq (p (skS.0 1 a)) True) (Or (Eq True False) (Eq True False)) % 3.38/3.66 Clause #40 (by clausification #[38]): ∀ (a : Iota), Or (Eq (p (skS.0 1 a)) True) (Eq True False) % 3.38/3.66 Clause #41 (by clausification #[40]): ∀ (a : Iota), Eq (p (skS.0 1 a)) True % 3.38/3.66 Clause #42 (by superposition #[41, 23]): ∀ (a : Iota), Or (Eq True False) (Eq (p a) False) % 3.38/3.66 Clause #44 (by clausification #[42]): ∀ (a : Iota), Eq (p a) False % 3.38/3.66 Clause #45 (by superposition #[44, 41]): Eq False True % 3.38/3.66 Clause #46 (by clausification #[45]): False % 3.38/3.66 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------