%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO379^5 : TPTP v9.2.0. Bugfixed v5.2.0. % 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 08:08:58 PM UTC 2025 % Result : Theorem 3.66s 3.81s % Output : Proof 3.66s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SYO379^5 : TPTP v9.2.0. Bugfixed v5.2.0. % 0.11/0.13 % Command : duper %s % 0.14/0.34 % Computer : n021.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Oct 3 13:53:23 EDT 2025 % 0.14/0.35 % CPUTime : % 3.66/3.81 SZS status Theorem for theBenchmark.p % 3.66/3.81 SZS output start Proof for theBenchmark.p % 3.66/3.81 Clause #0 (by assumption #[]): Eq (Eq cQDP0 fun Xz => Eq Xz c) True % 3.66/3.81 Clause #1 (by assumption #[]): Eq (Eq cQDP1 fun Xz => And (Eq Xz cQDP0) (Exists fun Xt => Xz Xt)) True % 3.66/3.81 Clause #2 (by assumption #[]): Eq (Not (Exists fun Xs => cQDP1 Xs)) True % 3.66/3.81 Clause #3 (by betaEtaReduce #[2]): Eq (Not (Exists cQDP1)) True % 3.66/3.81 Clause #4 (by clausification #[3]): Eq (Exists cQDP1) False % 3.66/3.81 Clause #5 (by clausification #[4]): ∀ (a : Iota → Prop), Eq (cQDP1 a) False % 3.66/3.81 Clause #6 (by clausification #[0]): Eq cQDP0 fun Xz => Eq Xz c % 3.66/3.81 Clause #7 (by argument congruence #[6]): ∀ (a : Iota), Eq (cQDP0 a) ((fun Xz => Eq Xz c) a) % 3.66/3.81 Clause #8 (by betaEtaReduce #[7]): ∀ (a : Iota), Eq (cQDP0 a) (Eq a c) % 3.66/3.81 Clause #9 (by clausify Prop equality #[8]): ∀ (a : Iota), Or (Eq (cQDP0 a) True) (Eq (Eq a c) False) % 3.66/3.81 Clause #12 (by betaEtaReduce #[1]): Eq (Eq cQDP1 fun Xz => And (Eq Xz cQDP0) (Exists Xz)) True % 3.66/3.81 Clause #13 (by clausification #[12]): Eq cQDP1 fun Xz => And (Eq Xz cQDP0) (Exists Xz) % 3.66/3.81 Clause #14 (by argument congruence #[13]): ∀ (a : Iota → Prop), Eq (cQDP1 a) ((fun Xz => And (Eq Xz cQDP0) (Exists Xz)) a) % 3.66/3.81 Clause #15 (by clausification #[9]): ∀ (a : Iota), Or (Eq (cQDP0 a) True) (Ne a c) % 3.66/3.81 Clause #16 (by destructive equality resolution #[15]): Eq (cQDP0 c) True % 3.66/3.81 Clause #17 (by betaEtaReduce #[14]): ∀ (a : Iota → Prop), Eq (cQDP1 a) (And (Eq a cQDP0) (Exists a)) % 3.66/3.81 Clause #18 (by forward demodulation #[17, 5]): ∀ (a : Iota → Prop), Eq False (And (Eq a cQDP0) (Exists a)) % 3.66/3.81 Clause #19 (by clausification #[18]): ∀ (a : Iota → Prop), Or (Eq (Eq a cQDP0) False) (Eq (Exists a) False) % 3.66/3.81 Clause #20 (by clausification #[19]): ∀ (a : Iota → Prop), Or (Eq (Exists a) False) (Ne a cQDP0) % 3.66/3.81 Clause #21 (by clausification #[20]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Ne a cQDP0) (Eq (a a_1) False) % 3.66/3.81 Clause #22 (by destructive equality resolution #[21]): ∀ (a : Iota), Eq (cQDP0 a) False % 3.66/3.81 Clause #24 (by superposition #[22, 16]): Eq False True % 3.66/3.81 Clause #25 (by clausification #[24]): False % 3.66/3.81 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------