%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO378^5 : TPTP v9.2.0. Bugfixed v5.2.0. % 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 08:08:58 PM UTC 2025 % Result : Theorem 8.74s 8.95s % Output : Proof 8.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SYO378^5 : TPTP v9.2.0. Bugfixed v5.2.0. % 0.11/0.13 % Command : duper %s % 0.18/0.33 % Computer : n022.cluster.edu % 0.18/0.33 % Model : x86_64 x86_64 % 0.18/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.33 % Memory : 8042.1875MB % 0.18/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.33 % CPULimit : 300 % 0.18/0.33 % WCLimit : 300 % 0.18/0.33 % DateTime : Fri Oct 3 13:48:38 EDT 2025 % 0.18/0.33 % CPUTime : % 8.74/8.95 SZS status Theorem for theBenchmark.p % 8.74/8.95 SZS output start Proof for theBenchmark.p % 8.74/8.95 Clause #0 (by assumption #[]): Eq (Eq cQDP0 fun Xz => Eq Xz c) True % 8.74/8.95 Clause #1 (by assumption #[]): Eq (Eq cQDP1 fun Xz => And (Eq Xz cQDP0) (Exists fun Xt => Xz Xt)) True % 8.74/8.95 Clause #2 (by assumption #[]): Eq (Eq cQDP2 fun Xz => And (Eq Xz cQDP1) (Exists fun Xt => Xz Xt)) True % 8.74/8.95 Clause #3 (by assumption #[]): Eq (Not (Exists fun Xs => cQDP2 Xs)) True % 8.74/8.95 Clause #4 (by betaEtaReduce #[3]): Eq (Not (Exists cQDP2)) True % 8.74/8.95 Clause #5 (by clausification #[4]): Eq (Exists cQDP2) False % 8.74/8.95 Clause #6 (by clausification #[5]): ∀ (a : (Iota → Prop) → Prop), Eq (cQDP2 a) False % 8.74/8.95 Clause #7 (by clausification #[0]): Eq cQDP0 fun Xz => Eq Xz c % 8.74/8.95 Clause #8 (by argument congruence #[7]): ∀ (a : Iota), Eq (cQDP0 a) ((fun Xz => Eq Xz c) a) % 8.74/8.95 Clause #9 (by betaEtaReduce #[8]): ∀ (a : Iota), Eq (cQDP0 a) (Eq a c) % 8.74/8.95 Clause #10 (by clausify Prop equality #[9]): ∀ (a : Iota), Or (Eq (cQDP0 a) True) (Eq (Eq a c) False) % 8.74/8.95 Clause #13 (by betaEtaReduce #[1]): Eq (Eq cQDP1 fun Xz => And (Eq Xz cQDP0) (Exists Xz)) True % 8.74/8.95 Clause #14 (by clausification #[13]): Eq cQDP1 fun Xz => And (Eq Xz cQDP0) (Exists Xz) % 8.74/8.95 Clause #15 (by argument congruence #[14]): ∀ (a : Iota → Prop), Eq (cQDP1 a) ((fun Xz => And (Eq Xz cQDP0) (Exists Xz)) a) % 8.74/8.95 Clause #16 (by clausification #[10]): ∀ (a : Iota), Or (Eq (cQDP0 a) True) (Ne a c) % 8.74/8.95 Clause #17 (by destructive equality resolution #[16]): Eq (cQDP0 c) True % 8.74/8.95 Clause #18 (by betaEtaReduce #[15]): ∀ (a : Iota → Prop), Eq (cQDP1 a) (And (Eq a cQDP0) (Exists a)) % 8.74/8.95 Clause #19 (by identity loobHoist #[18]): ∀ (a : Iota → Prop), Or (Eq (cQDP1 a) (And (Eq a cQDP0) True)) (Eq (Exists a) False) % 8.74/8.95 Clause #21 (by clausification #[19]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (cQDP1 a) (And (Eq a cQDP0) True)) (Eq (a a_1) False) % 8.74/8.95 Clause #22 (by bool simp #[21]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (cQDP1 a) (Eq a cQDP0)) (Eq (a a_1) False) % 8.74/8.95 Clause #30 (by fluidSup #[22, 14]): ∀ (a : Iota → Prop) (a_1 : ((Iota → Prop) → Prop) → Iota), Or (Eq (cQDP1 a) (Eq a cQDP0)) (Eq (a (a_1 cQDP1)) False) % 8.74/8.95 Clause #42 (by superposition #[30, 17]): Or (Eq (cQDP1 fun x => cQDP0 x) (Eq (fun x => cQDP0 x) cQDP0)) (Eq False True) % 8.74/8.95 Clause #58 (by betaEtaReduce #[2]): Eq (Eq cQDP2 fun Xz => And (Eq Xz cQDP1) (Exists Xz)) True % 8.74/8.95 Clause #59 (by clausification #[58]): Eq cQDP2 fun Xz => And (Eq Xz cQDP1) (Exists Xz) % 8.74/8.95 Clause #60 (by argument congruence #[59]): ∀ (a : (Iota → Prop) → Prop), Eq (cQDP2 a) ((fun Xz => And (Eq Xz cQDP1) (Exists Xz)) a) % 8.74/8.95 Clause #161 (by betaEtaReduce #[42]): Or (Eq (cQDP1 cQDP0) (Eq cQDP0 cQDP0)) (Eq False True) % 8.74/8.95 Clause #162 (by clausification #[161]): Eq (cQDP1 cQDP0) (Eq cQDP0 cQDP0) % 8.74/8.95 Clause #163 (by bool simp #[162]): Eq (cQDP1 cQDP0) True % 8.74/8.95 Clause #453 (by betaEtaReduce #[60]): ∀ (a : (Iota → Prop) → Prop), Eq (cQDP2 a) (And (Eq a cQDP1) (Exists a)) % 8.74/8.95 Clause #454 (by forward demodulation #[453, 6]): ∀ (a : (Iota → Prop) → Prop), Eq False (And (Eq a cQDP1) (Exists a)) % 8.74/8.95 Clause #455 (by clausification #[454]): ∀ (a : (Iota → Prop) → Prop), Or (Eq (Eq a cQDP1) False) (Eq (Exists a) False) % 8.74/8.95 Clause #456 (by clausification #[455]): ∀ (a : (Iota → Prop) → Prop), Or (Eq (Exists a) False) (Ne a cQDP1) % 8.74/8.95 Clause #457 (by clausification #[456]): ∀ (a : (Iota → Prop) → Prop) (a_1 : Iota → Prop), Or (Ne a cQDP1) (Eq (a a_1) False) % 8.74/8.95 Clause #458 (by destructive equality resolution #[457]): ∀ (a : Iota → Prop), Eq (cQDP1 a) False % 8.74/8.95 Clause #467 (by superposition #[458, 163]): Eq False True % 8.74/8.95 Clause #473 (by clausification #[467]): False % 8.74/8.95 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------