%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : KRS003_1 : TPTP v9.2.0. Released v5.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n019.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 07:52:30 PM UTC 2025 % Result : Theorem 3.83s 3.98s % Output : Proof 3.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : KRS003_1 : TPTP v9.2.0. Released v5.0.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n019.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Oct 2 10:16:38 EDT 2025 % 0.13/0.34 % CPUTime : % 3.83/3.98 SZS status Theorem for theBenchmark.p % 3.83/3.98 SZS output start Proof for theBenchmark.p % 3.83/3.98 Clause #0 (by assumption #[]): Eq (∀ (X1 : unreal), c X1 → s2least X1) True % 3.83/3.98 Clause #2 (by assumption #[]): Eq (∀ (X1 : unreal), Not (And (s2least X1) (equalish (u1r2 X1) (u1r1 X1)))) True % 3.83/3.98 Clause #3 (by assumption #[]): Eq (∀ (X1 : unreal), s2least X1 → s X1 (u1r1 X1)) True % 3.83/3.98 Clause #4 (by assumption #[]): Eq (∀ (X1 : unreal), s2least X1 → s X1 (u1r2 X1)) True % 3.83/3.98 Clause #6 (by assumption #[]): Eq (∀ (X1 : unreal), d X1 → s1most X1) True % 3.83/3.98 Clause #8 (by assumption #[]): Eq (∀ (X2 X3 : real) (X1 : unreal), And (And (s1most X1) (s X1 X3)) (s X1 X2) → equalish X3 X2) True % 3.83/3.98 Clause #12 (by assumption #[]): Eq (∀ (X1 : unreal), e X1 → c X1) True % 3.83/3.98 Clause #13 (by assumption #[]): Eq (∀ (X1 : unreal), f X1 → d X1) True % 3.83/3.98 Clause #14 (by assumption #[]): Eq (Not (Or (Not (e exist)) (Not (f exist)))) True % 3.83/3.98 Clause #15 (by clausification #[13]): ∀ (a : unreal), Eq (f a → d a) True % 3.83/3.98 Clause #16 (by clausification #[15]): ∀ (a : unreal), Or (Eq (f a) False) (Eq (d a) True) % 3.83/3.98 Clause #17 (by clausification #[12]): ∀ (a : unreal), Eq (e a → c a) True % 3.83/3.98 Clause #18 (by clausification #[17]): ∀ (a : unreal), Or (Eq (e a) False) (Eq (c a) True) % 3.83/3.98 Clause #23 (by clausification #[6]): ∀ (a : unreal), Eq (d a → s1most a) True % 3.83/3.98 Clause #24 (by clausification #[23]): ∀ (a : unreal), Or (Eq (d a) False) (Eq (s1most a) True) % 3.83/3.98 Clause #25 (by clausification #[0]): ∀ (a : unreal), Eq (c a → s2least a) True % 3.83/3.98 Clause #26 (by clausification #[25]): ∀ (a : unreal), Or (Eq (c a) False) (Eq (s2least a) True) % 3.83/3.98 Clause #29 (by clausification #[3]): ∀ (a : unreal), Eq (s2least a → s a (u1r1 a)) True % 3.83/3.98 Clause #30 (by clausification #[29]): ∀ (a : unreal), Or (Eq (s2least a) False) (Eq (s a (u1r1 a)) True) % 3.83/3.98 Clause #31 (by clausification #[4]): ∀ (a : unreal), Eq (s2least a → s a (u1r2 a)) True % 3.83/3.98 Clause #32 (by clausification #[31]): ∀ (a : unreal), Or (Eq (s2least a) False) (Eq (s a (u1r2 a)) True) % 3.83/3.98 Clause #33 (by clausification #[8]): ∀ (a : real), Eq (∀ (X3 : real) (X1 : unreal), And (And (s1most X1) (s X1 X3)) (s X1 a) → equalish X3 a) True % 3.83/3.99 Clause #34 (by clausification #[33]): ∀ (a a_1 : real), Eq (∀ (X1 : unreal), And (And (s1most X1) (s X1 a)) (s X1 a_1) → equalish a a_1) True % 3.83/3.99 Clause #35 (by clausification #[34]): ∀ (a : unreal) (a_1 a_2 : real), Eq (And (And (s1most a) (s a a_1)) (s a a_2) → equalish a_1 a_2) True % 3.83/3.99 Clause #36 (by clausification #[35]): ∀ (a : unreal) (a_1 a_2 : real), Or (Eq (And (And (s1most a) (s a a_1)) (s a a_2)) False) (Eq (equalish a_1 a_2) True) % 3.83/3.99 Clause #37 (by clausification #[36]): ∀ (a a_1 : real) (a_2 : unreal), % 3.83/3.99 Or (Eq (equalish a a_1) True) (Or (Eq (And (s1most a_2) (s a_2 a)) False) (Eq (s a_2 a_1) False)) % 3.83/3.99 Clause #38 (by clausification #[37]): ∀ (a a_1 : real) (a_2 : unreal), % 3.83/3.99 Or (Eq (equalish a a_1) True) (Or (Eq (s a_2 a_1) False) (Or (Eq (s1most a_2) False) (Eq (s a_2 a) False))) % 3.83/3.99 Clause #39 (by clausification #[14]): Eq (Or (Not (e exist)) (Not (f exist))) False % 3.83/3.99 Clause #40 (by clausification #[39]): Eq (Not (f exist)) False % 3.83/3.99 Clause #41 (by clausification #[39]): Eq (Not (e exist)) False % 3.83/3.99 Clause #42 (by clausification #[40]): Eq (f exist) True % 3.83/3.99 Clause #43 (by superposition #[42, 16]): Or (Eq True False) (Eq (d exist) True) % 3.83/3.99 Clause #44 (by clausification #[2]): ∀ (a : unreal), Eq (Not (And (s2least a) (equalish (u1r2 a) (u1r1 a)))) True % 3.83/3.99 Clause #45 (by clausification #[44]): ∀ (a : unreal), Eq (And (s2least a) (equalish (u1r2 a) (u1r1 a))) False % 3.83/3.99 Clause #46 (by clausification #[45]): ∀ (a : unreal), Or (Eq (s2least a) False) (Eq (equalish (u1r2 a) (u1r1 a)) False) % 3.83/3.99 Clause #47 (by clausification #[41]): Eq (e exist) True % 3.83/3.99 Clause #48 (by superposition #[47, 18]): Or (Eq True False) (Eq (c exist) True) % 3.83/3.99 Clause #49 (by clausification #[48]): Eq (c exist) True % 3.83/3.99 Clause #50 (by superposition #[49, 26]): Or (Eq True False) (Eq (s2least exist) True) % 3.83/3.99 Clause #51 (by clausification #[50]): Eq (s2least exist) True % 3.83/3.99 Clause #52 (by superposition #[51, 30]): Or (Eq True False) (Eq (s exist (u1r1 exist)) True) % 3.83/3.99 Clause #53 (by superposition #[51, 32]): Or (Eq True False) (Eq (s exist (u1r2 exist)) True) % 3.83/3.99 Clause #54 (by superposition #[51, 46]): Or (Eq True False) (Eq (equalish (u1r2 exist) (u1r1 exist)) False) % 3.83/3.99 Clause #55 (by clausification #[43]): Eq (d exist) True % 3.83/3.99 Clause #56 (by superposition #[55, 24]): Or (Eq True False) (Eq (s1most exist) True) % 3.83/3.99 Clause #57 (by clausification #[56]): Eq (s1most exist) True % 3.83/3.99 Clause #64 (by clausification #[53]): Eq (s exist (u1r2 exist)) True % 3.83/3.99 Clause #67 (by clausification #[52]): Eq (s exist (u1r1 exist)) True % 3.83/3.99 Clause #68 (by superposition #[67, 38]): ∀ (a : real), % 3.83/3.99 Or (Eq (equalish a (u1r1 exist)) True) (Or (Eq True False) (Or (Eq (s1most exist) False) (Eq (s exist a) False))) % 3.83/3.99 Clause #70 (by clausification #[54]): Eq (equalish (u1r2 exist) (u1r1 exist)) False % 3.83/3.99 Clause #94 (by clausification #[68]): ∀ (a : real), Or (Eq (equalish a (u1r1 exist)) True) (Or (Eq (s1most exist) False) (Eq (s exist a) False)) % 3.83/3.99 Clause #95 (by forward demodulation #[94, 57]): ∀ (a : real), Or (Eq (equalish a (u1r1 exist)) True) (Or (Eq True False) (Eq (s exist a) False)) % 3.83/3.99 Clause #96 (by clausification #[95]): ∀ (a : real), Or (Eq (equalish a (u1r1 exist)) True) (Eq (s exist a) False) % 3.83/3.99 Clause #97 (by superposition #[96, 64]): Or (Eq (equalish (u1r2 exist) (u1r1 exist)) True) (Eq False True) % 3.83/3.99 Clause #102 (by clausification #[97]): Eq (equalish (u1r2 exist) (u1r1 exist)) True % 3.83/3.99 Clause #103 (by superposition #[102, 70]): Eq True False % 3.83/3.99 Clause #104 (by clausification #[103]): False % 3.83/3.99 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------