%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : MSC012+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n008.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 07:55:23 PM UTC 2025 % Result : Theorem 7.05s 7.22s % Output : Proof 7.05s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : MSC012+1 : TPTP v9.2.0. Released v3.2.0. % 0.10/0.11 % Command : duper %s % 0.10/0.30 % Computer : n008.cluster.edu % 0.10/0.30 % Model : x86_64 x86_64 % 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.30 % Memory : 8042.1875MB % 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.30 % CPULimit : 300 % 0.10/0.30 % WCLimit : 300 % 0.10/0.30 % DateTime : Thu Oct 2 16:58:38 EDT 2025 % 0.10/0.30 % CPUTime : % 7.05/7.22 SZS status Theorem for theBenchmark.p % 7.05/7.22 SZS output start Proof for theBenchmark.p % 7.05/7.22 Clause #0 (by assumption #[]): Eq (∀ (A B : Iota), And (And (p A) (less A B)) (p B) → goal) True % 7.05/7.22 Clause #1 (by assumption #[]): Eq (∀ (A : Iota), Or (p A) (Exists fun B => And (less A B) (p B))) True % 7.05/7.22 Clause #2 (by assumption #[]): Eq (∀ (A B C : Iota), And (less A B) (less B C) → less A C) True % 7.05/7.22 Clause #3 (by assumption #[]): Eq (∀ (A : Iota), Exists fun B => less A B) True % 7.05/7.22 Clause #4 (by assumption #[]): Eq (Not goal) True % 7.05/7.22 Clause #5 (by clausification #[4]): Eq goal False % 7.05/7.22 Clause #6 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (B : Iota), And (And (p a) (less a B)) (p B) → goal) True % 7.05/7.22 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (And (And (p a) (less a a_1)) (p a_1) → goal) True % 7.05/7.22 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (And (And (p a) (less a a_1)) (p a_1)) False) (Eq goal True) % 7.05/7.22 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq goal True) (Or (Eq (And (p a) (less a a_1)) False) (Eq (p a_1) False)) % 7.05/7.22 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Or (Eq goal True) (Or (Eq (p a) False) (Or (Eq (p a_1) False) (Eq (less a_1 a) False))) % 7.05/7.22 Clause #11 (by forward demodulation #[10, 5]): ∀ (a a_1 : Iota), Or (Eq False True) (Or (Eq (p a) False) (Or (Eq (p a_1) False) (Eq (less a_1 a) False))) % 7.05/7.22 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Or (Eq (p a) False) (Or (Eq (p a_1) False) (Eq (less a_1 a) False)) % 7.05/7.22 Clause #13 (by betaEtaReduce #[3]): Eq (∀ (A : Iota), Exists (less A)) True % 7.05/7.22 Clause #14 (by clausification #[13]): ∀ (a : Iota), Eq (Exists (less a)) True % 7.05/7.22 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Eq (less a (skS.0 0 a a_1)) True % 7.05/7.22 Clause #16 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B C : Iota), And (less a B) (less B C) → less a C) True % 7.05/7.22 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), And (less a a_1) (less a_1 C) → less a C) True % 7.05/7.22 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), Eq (And (less a a_1) (less a_1 a_2) → less a a_2) True % 7.05/7.22 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (less a a_1) (less a_1 a_2)) False) (Eq (less a a_2) True) % 7.05/7.22 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), Or (Eq (less a a_1) True) (Or (Eq (less a a_2) False) (Eq (less a_2 a_1) False)) % 7.05/7.22 Clause #21 (by superposition #[20, 15]): ∀ (a a_1 a_2 : Iota), Or (Eq (less a a_1) True) (Or (Eq (less (skS.0 0 a a_2) a_1) False) (Eq False True)) % 7.05/7.22 Clause #22 (by clausification #[1]): ∀ (a : Iota), Eq (Or (p a) (Exists fun B => And (less a B) (p B))) True % 7.05/7.22 Clause #23 (by clausification #[22]): ∀ (a : Iota), Or (Eq (p a) True) (Eq (Exists fun B => And (less a B) (p B)) True) % 7.05/7.22 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (p a) True) (Eq (And (less a (skS.0 1 a a_1)) (p (skS.0 1 a a_1))) True) % 7.05/7.22 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (p a) True) (Eq (p (skS.0 1 a a_1)) True) % 7.05/7.22 Clause #26 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (p a) True) (Eq (less a (skS.0 1 a a_1)) True) % 7.05/7.22 Clause #27 (by superposition #[25, 12]): ∀ (a a_1 a_2 : Iota), % 7.05/7.22 Or (Eq (p a) True) (Or (Eq True False) (Or (Eq (p a_1) False) (Eq (less a_1 (skS.0 1 a a_2)) False))) % 7.05/7.22 Clause #28 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), Or (Eq (less a a_1) True) (Eq (less (skS.0 0 a a_2) a_1) False) % 7.05/7.22 Clause #31 (by superposition #[26, 28]): ∀ (a a_1 a_2 : Iota), % 7.05/7.22 Or (Eq (less a (skS.0 1 (skS.0 0 a a_1) a_2)) True) (Or (Eq (p (skS.0 0 a a_1)) True) (Eq False True)) % 7.05/7.22 Clause #32 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), Or (Eq (p a) True) (Or (Eq (p a_1) False) (Eq (less a_1 (skS.0 1 a a_2)) False)) % 7.05/7.22 Clause #33 (by superposition #[32, 25]): ∀ (a a_1 a_2 a_3 : Iota), % 7.05/7.22 Or (Eq (p a) True) (Or (Eq (less (skS.0 1 a_1 a_2) (skS.0 1 a a_3)) False) (Or (Eq (p a_1) True) (Eq False True))) % 7.05/7.22 Clause #45 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Or (Eq (less a (skS.0 1 (skS.0 0 a a_1) a_2)) True) (Eq (p (skS.0 0 a a_1)) True) % 7.05/7.22 Clause #55 (by clausification #[33]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (p a) True) (Or (Eq (less (skS.0 1 a_1 a_2) (skS.0 1 a a_3)) False) (Eq (p a_1) True)) % 7.05/7.26 Clause #56 (by superposition #[55, 26]): ∀ (a a_1 : Iota), % 7.05/7.26 Or (Eq (p (skS.0 1 a a_1)) True) (Or (Eq (p a) True) (Or (Eq (p (skS.0 1 a a_1)) True) (Eq False True))) % 7.05/7.26 Clause #57 (by superposition #[55, 45]): ∀ (a a_1 a_2 : Iota), % 7.05/7.26 Or (Eq (p (skS.0 0 (skS.0 1 a a_1) a_2)) True) % 7.05/7.26 (Or (Eq (p a) True) (Or (Eq False True) (Eq (p (skS.0 0 (skS.0 1 a a_1) a_2)) True))) % 7.05/7.26 Clause #58 (by clausification #[56]): ∀ (a a_1 : Iota), Or (Eq (p (skS.0 1 a a_1)) True) (Or (Eq (p a) True) (Eq (p (skS.0 1 a a_1)) True)) % 7.05/7.26 Clause #59 (by eliminate duplicate literals #[58]): ∀ (a a_1 : Iota), Or (Eq (p (skS.0 1 a a_1)) True) (Eq (p a) True) % 7.05/7.26 Clause #140 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), % 7.05/7.26 Or (Eq (p (skS.0 0 (skS.0 1 a a_1) a_2)) True) (Or (Eq (p a) True) (Eq (p (skS.0 0 (skS.0 1 a a_1) a_2)) True)) % 7.05/7.26 Clause #141 (by eliminate duplicate literals #[140]): ∀ (a a_1 a_2 : Iota), Or (Eq (p (skS.0 0 (skS.0 1 a a_1) a_2)) True) (Eq (p a) True) % 7.05/7.26 Clause #142 (by superposition #[141, 12]): ∀ (a a_1 a_2 a_3 : Iota), % 7.05/7.26 Or (Eq (p a) True) (Or (Eq True False) (Or (Eq (p a_1) False) (Eq (less a_1 (skS.0 0 (skS.0 1 a a_2) a_3)) False))) % 7.05/7.26 Clause #156 (by clausification #[142]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (p a) True) (Or (Eq (p a_1) False) (Eq (less a_1 (skS.0 0 (skS.0 1 a a_2) a_3)) False)) % 7.05/7.26 Clause #157 (by superposition #[156, 59]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 7.05/7.26 Or (Eq (p a) True) % 7.05/7.26 (Or (Eq (less (skS.0 1 a_1 a_2) (skS.0 0 (skS.0 1 a a_3) a_4)) False) (Or (Eq False True) (Eq (p a_1) True))) % 7.05/7.26 Clause #159 (by clausification #[157]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 7.05/7.26 Or (Eq (p a) True) (Or (Eq (less (skS.0 1 a_1 a_2) (skS.0 0 (skS.0 1 a a_3) a_4)) False) (Eq (p a_1) True)) % 7.05/7.26 Clause #160 (by superposition #[159, 15]): ∀ (a : Iota), Or (Eq (p a) True) (Or (Eq (p a) True) (Eq False True)) % 7.05/7.26 Clause #162 (by clausification #[160]): ∀ (a : Iota), Or (Eq (p a) True) (Eq (p a) True) % 7.05/7.26 Clause #163 (by eliminate duplicate literals #[162]): ∀ (a : Iota), Eq (p a) True % 7.05/7.26 Clause #168 (by backward demodulation #[163, 12]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (p a) False) (Eq (less a a_1) False)) % 7.05/7.26 Clause #183 (by clausification #[168]): ∀ (a a_1 : Iota), Or (Eq (p a) False) (Eq (less a a_1) False) % 7.05/7.26 Clause #184 (by forward demodulation #[183, 163]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (less a a_1) False) % 7.05/7.26 Clause #185 (by clausification #[184]): ∀ (a a_1 : Iota), Eq (less a a_1) False % 7.05/7.26 Clause #190 (by superposition #[185, 15]): Eq False True % 7.05/7.26 Clause #191 (by clausification #[190]): False % 7.05/7.26 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------