%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN934+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n021.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 3.58s 3.78s % Output : Proof 3.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SYN934+1 : TPTP v9.2.0. Released v3.1.0. % 0.12/0.13 % Command : duper %s % 0.12/0.33 % Computer : n021.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Thu Oct 2 15:48:38 EDT 2025 % 0.12/0.34 % CPUTime : % 3.58/3.78 SZS status Theorem for theBenchmark.p % 3.58/3.78 SZS output start Proof for theBenchmark.p % 3.58/3.78 Clause #0 (by assumption #[]): Eq (Not (Iff (Exists fun X => c → p X) (c → Exists fun X => p X))) True % 3.58/3.78 Clause #1 (by betaEtaReduce #[0]): Eq (Not (Iff (Exists fun X => c → p X) (c → Exists p))) True % 3.58/3.78 Clause #2 (by clausification #[1]): Eq (Iff (Exists fun X => c → p X) (c → Exists p)) False % 3.58/3.78 Clause #3 (by clausification #[2]): Or (Eq (Exists fun X => c → p X) False) (Eq (c → Exists p) False) % 3.58/3.78 Clause #4 (by clausification #[2]): Or (Eq (Exists fun X => c → p X) True) (Eq (c → Exists p) True) % 3.58/3.78 Clause #5 (by clausification #[3]): ∀ (a : Iota), Or (Eq (c → Exists p) False) (Eq (c → p a) False) % 3.58/3.78 Clause #6 (by clausification #[5]): ∀ (a : Iota), Or (Eq (c → p a) False) (Eq c True) % 3.58/3.78 Clause #7 (by clausification #[5]): ∀ (a : Iota), Or (Eq (c → p a) False) (Eq (Exists p) False) % 3.58/3.78 Clause #8 (by clausification #[6]): Or (Eq c True) (Eq c True) % 3.58/3.78 Clause #10 (by eliminate duplicate literals #[8]): Eq c True % 3.58/3.78 Clause #13 (by clausification #[7]): ∀ (a : Iota), Or (Eq (Exists p) False) (Eq (p a) False) % 3.58/3.78 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (p a) False) (Eq (p a_1) False) % 3.58/3.78 Clause #15 (by clausification #[4]): ∀ (a : Iota), Or (Eq (c → Exists p) True) (Eq (c → p (skS.0 0 a)) True) % 3.58/3.78 Clause #16 (by clausification #[15]): ∀ (a : Iota), Or (Eq (c → p (skS.0 0 a)) True) (Or (Eq c False) (Eq (Exists p) True)) % 3.58/3.78 Clause #17 (by clausification #[16]): ∀ (a : Iota), Or (Eq c False) (Or (Eq (Exists p) True) (Or (Eq c False) (Eq (p (skS.0 0 a)) True))) % 3.58/3.78 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq c False) (Or (Eq c False) (Or (Eq (p (skS.0 0 a)) True) (Eq (p (skS.0 1 a_1)) True))) % 3.58/3.78 Clause #19 (by eliminate duplicate literals #[18]): ∀ (a a_1 : Iota), Or (Eq c False) (Or (Eq (p (skS.0 0 a)) True) (Eq (p (skS.0 1 a_1)) True)) % 3.58/3.78 Clause #20 (by forward demodulation #[19, 10]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (p (skS.0 0 a)) True) (Eq (p (skS.0 1 a_1)) True)) % 3.58/3.78 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Or (Eq (p (skS.0 0 a)) True) (Eq (p (skS.0 1 a_1)) True) % 3.58/3.78 Clause #22 (by superposition #[21, 14]): ∀ (a a_1 : Iota), Or (Eq (p (skS.0 1 a)) True) (Or (Eq True False) (Eq (p a_1) False)) % 3.58/3.78 Clause #24 (by clausification #[22]): ∀ (a a_1 : Iota), Or (Eq (p (skS.0 1 a)) True) (Eq (p a_1) False) % 3.58/3.78 Clause #25 (by superposition #[24, 21]): ∀ (a a_1 : Iota), Or (Eq (p (skS.0 1 a)) True) (Or (Eq False True) (Eq (p (skS.0 1 a_1)) True)) % 3.58/3.78 Clause #31 (by clausification #[25]): ∀ (a a_1 : Iota), Or (Eq (p (skS.0 1 a)) True) (Eq (p (skS.0 1 a_1)) True) % 3.58/3.78 Clause #34 (by equality factoring #[31]): ∀ (a : Iota), Or (Ne True True) (Eq (p (skS.0 1 a)) True) % 3.58/3.78 Clause #35 (by clausification #[34]): ∀ (a : Iota), Or (Eq (p (skS.0 1 a)) True) (Or (Eq True False) (Eq True False)) % 3.58/3.78 Clause #37 (by clausification #[35]): ∀ (a : Iota), Or (Eq (p (skS.0 1 a)) True) (Eq True False) % 3.58/3.78 Clause #38 (by clausification #[37]): ∀ (a : Iota), Eq (p (skS.0 1 a)) True % 3.58/3.78 Clause #39 (by superposition #[38, 14]): ∀ (a : Iota), Or (Eq True False) (Eq (p a) False) % 3.58/3.78 Clause #41 (by clausification #[39]): ∀ (a : Iota), Eq (p a) False % 3.58/3.78 Clause #42 (by superposition #[41, 38]): Eq False True % 3.58/3.78 Clause #43 (by clausification #[42]): False % 3.58/3.78 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------