%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN931+1 : TPTP v9.2.0. Released v3.1.0. % 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 08:08:16 PM UTC 2025 % Result : Theorem 5.32s 5.51s % Output : Proof 5.32s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : SYN931+1 : TPTP v9.2.0. Released v3.1.0. % 0.09/0.11 % Command : duper %s % 0.10/0.31 % Computer : n022.cluster.edu % 0.10/0.31 % Model : x86_64 x86_64 % 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.31 % Memory : 8042.1875MB % 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.31 % CPULimit : 300 % 0.10/0.31 % WCLimit : 300 % 0.10/0.31 % DateTime : Thu Oct 2 15:36:53 EDT 2025 % 0.10/0.31 % CPUTime : % 5.32/5.51 SZS status Theorem for theBenchmark.p % 5.32/5.51 SZS output start Proof for theBenchmark.p % 5.32/5.51 Clause #0 (by assumption #[]): Eq (Not (Iff (Exists fun X => And (p X) c) (And (Exists fun X => p X) c))) True % 5.32/5.51 Clause #1 (by betaEtaReduce #[0]): Eq (Not (Iff (Exists fun X => And (p X) c) (And (Exists p) c))) True % 5.32/5.51 Clause #2 (by clausification #[1]): Eq (Iff (Exists fun X => And (p X) c) (And (Exists p) c)) False % 5.32/5.51 Clause #3 (by clausification #[2]): Or (Eq (Exists fun X => And (p X) c) False) (Eq (And (Exists p) c) False) % 5.32/5.51 Clause #4 (by clausification #[2]): Or (Eq (Exists fun X => And (p X) c) True) (Eq (And (Exists p) c) True) % 5.32/5.51 Clause #5 (by clausification #[3]): ∀ (a : Iota), Or (Eq (And (Exists p) c) False) (Eq (And (p a) c) False) % 5.32/5.51 Clause #6 (by clausification #[5]): ∀ (a : Iota), Or (Eq (And (p a) c) False) (Or (Eq (Exists p) False) (Eq c False)) % 5.32/5.51 Clause #7 (by clausification #[6]): ∀ (a : Iota), Or (Eq (Exists p) False) (Or (Eq c False) (Or (Eq (p a) False) (Eq c False))) % 5.32/5.51 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq c False) (Or (Eq (p a) False) (Or (Eq c False) (Eq (p a_1) False))) % 5.32/5.51 Clause #9 (by eliminate duplicate literals #[8]): ∀ (a a_1 : Iota), Or (Eq c False) (Or (Eq (p a) False) (Eq (p a_1) False)) % 5.32/5.51 Clause #10 (by clausification #[4]): ∀ (a : Iota), Or (Eq (And (Exists p) c) True) (Eq (And (p (skS.0 0 a)) c) True) % 5.32/5.51 Clause #11 (by clausification #[10]): ∀ (a : Iota), Or (Eq (And (p (skS.0 0 a)) c) True) (Eq c True) % 5.32/5.51 Clause #12 (by clausification #[10]): ∀ (a : Iota), Or (Eq (And (p (skS.0 0 a)) c) True) (Eq (Exists p) True) % 5.32/5.51 Clause #13 (by clausification #[11]): Or (Eq c True) (Eq c True) % 5.32/5.51 Clause #15 (by eliminate duplicate literals #[13]): Eq c True % 5.32/5.51 Clause #16 (by backward demodulation #[15, 9]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (p a) False) (Eq (p a_1) False)) % 5.32/5.51 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (p a) False) (Eq (p a_1) False) % 5.32/5.51 Clause #20 (by clausification #[12]): ∀ (a : Iota), Or (Eq (Exists p) True) (Eq (p (skS.0 0 a)) True) % 5.32/5.51 Clause #23 (by clausification #[20]): ∀ (a a_1 : Iota), Or (Eq (p (skS.0 0 a)) True) (Eq (p (skS.0 2 a_1)) True) % 5.32/5.51 Clause #24 (by superposition #[23, 17]): ∀ (a a_1 : Iota), Or (Eq (p (skS.0 2 a)) True) (Or (Eq True False) (Eq (p a_1) False)) % 5.32/5.51 Clause #29 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (p (skS.0 2 a)) True) (Eq (p a_1) False) % 5.32/5.51 Clause #30 (by superposition #[29, 23]): ∀ (a a_1 : Iota), Or (Eq (p (skS.0 2 a)) True) (Or (Eq False True) (Eq (p (skS.0 2 a_1)) True)) % 5.32/5.51 Clause #33 (by clausification #[30]): ∀ (a a_1 : Iota), Or (Eq (p (skS.0 2 a)) True) (Eq (p (skS.0 2 a_1)) True) % 5.32/5.51 Clause #36 (by equality factoring #[33]): ∀ (a : Iota), Or (Ne True True) (Eq (p (skS.0 2 a)) True) % 5.32/5.51 Clause #37 (by clausification #[36]): ∀ (a : Iota), Or (Eq (p (skS.0 2 a)) True) (Or (Eq True False) (Eq True False)) % 5.32/5.51 Clause #39 (by clausification #[37]): ∀ (a : Iota), Or (Eq (p (skS.0 2 a)) True) (Eq True False) % 5.32/5.51 Clause #40 (by clausification #[39]): ∀ (a : Iota), Eq (p (skS.0 2 a)) True % 5.32/5.51 Clause #41 (by superposition #[40, 17]): ∀ (a : Iota), Or (Eq True False) (Eq (p a) False) % 5.32/5.51 Clause #43 (by clausification #[41]): ∀ (a : Iota), Eq (p a) False % 5.32/5.51 Clause #44 (by superposition #[43, 40]): Eq False True % 5.32/5.51 Clause #45 (by clausification #[44]): False % 5.32/5.51 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------