%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : LCL536+1 : TPTP v9.3.1. Bugfixed v9.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n015.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:36:05 AM UTC 2026 % Result : Theorem 15.35s 15.61s % Output : Proof 15.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL536+1 : TPTP v9.3.1. Bugfixed v9.2.0. % 0.00/0.05 % Command : duper %s % 0.11/0.38 % Computer : n015.cluster.edu % 0.11/0.38 % Model : x86_64 x86_64 % 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.38 % Memory : 8046.5625MB % 0.11/0.38 % OS : Linux 6.8.0-71-generic % 0.11/0.38 % CPULimit : 300 % 0.11/0.38 % WCLimit : 300 % 0.11/0.38 % DateTime : Sat Sep 5 02:53:12 UTC 2026 % 0.11/0.38 % CPUTime : % 15.35/15.61 SZS status Theorem for theBenchmark.p % 15.35/15.61 SZS output start Proof for theBenchmark.p % 15.35/15.61 Clause #49 (by assumption #[]): Eq (Iff necessitation (∀ (X : Iota), is_a_theorem X → is_a_theorem (necessarily X))) True % 15.35/15.61 Clause #57 (by assumption #[]): Eq (Iff axiom_5 (∀ (X : Iota), is_a_theorem (implies (possibly X) (necessarily (possibly X))))) True % 15.35/15.61 Clause #71 (by assumption #[]): Eq (Iff axiom_m10 (∀ (X : Iota), is_a_theorem (strict_implies (possibly X) (necessarily (possibly X))))) True % 15.35/15.61 Clause #74 (by assumption #[]): Eq (op_strict_implies → ∀ (X Y : Iota), Eq (strict_implies X Y) (necessarily (implies X Y))) True % 15.35/15.61 Clause #77 (by assumption #[]): Eq necessitation True % 15.35/15.61 Clause #80 (by assumption #[]): Eq axiom_5 True % 15.35/15.61 Clause #82 (by assumption #[]): Eq op_strict_implies True % 15.35/15.61 Clause #84 (by assumption #[]): Eq (Not axiom_m10) True % 15.35/15.61 Clause #126 (by clausification #[84]): Eq axiom_m10 False % 15.35/15.61 Clause #134 (by clausification #[49]): Or (Eq necessitation False) (Eq (∀ (X : Iota), is_a_theorem X → is_a_theorem (necessarily X)) True) % 15.35/15.61 Clause #140 (by clausification #[134]): ∀ (a : Iota), Or (Eq necessitation False) (Eq (is_a_theorem a → is_a_theorem (necessarily a)) True) % 15.35/15.61 Clause #141 (by clausification #[140]): ∀ (a : Iota), Or (Eq necessitation False) (Or (Eq (is_a_theorem a) False) (Eq (is_a_theorem (necessarily a)) True)) % 15.35/15.61 Clause #142 (by forward demodulation #[141, 77]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (is_a_theorem a) False) (Eq (is_a_theorem (necessarily a)) True)) % 15.35/15.61 Clause #143 (by clausification #[142]): ∀ (a : Iota), Or (Eq (is_a_theorem a) False) (Eq (is_a_theorem (necessarily a)) True) % 15.35/15.61 Clause #280 (by clausification #[57]): Or (Eq axiom_5 False) (Eq (∀ (X : Iota), is_a_theorem (implies (possibly X) (necessarily (possibly X)))) True) % 15.35/15.61 Clause #327 (by clausification #[280]): ∀ (a : Iota), Or (Eq axiom_5 False) (Eq (is_a_theorem (implies (possibly a) (necessarily (possibly a)))) True) % 15.35/15.61 Clause #328 (by forward demodulation #[327, 80]): ∀ (a : Iota), Or (Eq True False) (Eq (is_a_theorem (implies (possibly a) (necessarily (possibly a)))) True) % 15.35/15.61 Clause #329 (by clausification #[328]): ∀ (a : Iota), Eq (is_a_theorem (implies (possibly a) (necessarily (possibly a)))) True % 15.35/15.61 Clause #331 (by superposition #[329, 143]): ∀ (a : Iota), % 15.35/15.61 Or (Eq True False) (Eq (is_a_theorem (necessarily (implies (possibly a) (necessarily (possibly a))))) True) % 15.35/15.61 Clause #332 (by clausification #[331]): ∀ (a : Iota), Eq (is_a_theorem (necessarily (implies (possibly a) (necessarily (possibly a))))) True % 15.35/15.61 Clause #468 (by clausification #[71]): Or (Eq axiom_m10 True) (Eq (∀ (X : Iota), is_a_theorem (strict_implies (possibly X) (necessarily (possibly X)))) False) % 15.35/15.61 Clause #470 (by clausification #[468]): ∀ (a : Iota), % 15.35/15.61 Or (Eq axiom_m10 True) % 15.35/15.61 (Eq (Not (is_a_theorem (strict_implies (possibly (skS.0 62 a)) (necessarily (possibly (skS.0 62 a)))))) True) % 15.35/15.61 Clause #471 (by clausification #[470]): ∀ (a : Iota), % 15.35/15.61 Or (Eq axiom_m10 True) % 15.35/15.61 (Eq (is_a_theorem (strict_implies (possibly (skS.0 62 a)) (necessarily (possibly (skS.0 62 a))))) False) % 15.35/15.61 Clause #472 (by forward demodulation #[471, 126]): ∀ (a : Iota), % 15.35/15.61 Or (Eq False True) % 15.35/15.61 (Eq (is_a_theorem (strict_implies (possibly (skS.0 62 a)) (necessarily (possibly (skS.0 62 a))))) False) % 15.35/15.61 Clause #473 (by clausification #[472]): ∀ (a : Iota), Eq (is_a_theorem (strict_implies (possibly (skS.0 62 a)) (necessarily (possibly (skS.0 62 a))))) False % 15.35/15.61 Clause #969 (by clausification #[74]): Or (Eq op_strict_implies False) (Eq (∀ (X Y : Iota), Eq (strict_implies X Y) (necessarily (implies X Y))) True) % 15.35/15.61 Clause #970 (by clausification #[969]): ∀ (a : Iota), % 15.35/15.61 Or (Eq op_strict_implies False) (Eq (∀ (Y : Iota), Eq (strict_implies a Y) (necessarily (implies a Y))) True) % 15.35/15.61 Clause #971 (by clausification #[970]): ∀ (a a_1 : Iota), Or (Eq op_strict_implies False) (Eq (Eq (strict_implies a a_1) (necessarily (implies a a_1))) True) % 15.35/15.61 Clause #972 (by clausification #[971]): ∀ (a a_1 : Iota), Or (Eq op_strict_implies False) (Eq (strict_implies a a_1) (necessarily (implies a a_1))) % 15.35/15.61 Clause #973 (by forward demodulation #[972, 82]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (strict_implies a a_1) (necessarily (implies a a_1))) % 15.35/15.62 Clause #974 (by clausification #[973]): ∀ (a a_1 : Iota), Eq (strict_implies a a_1) (necessarily (implies a a_1)) % 15.35/15.62 Clause #982 (by backward demodulation #[974, 332]): ∀ (a : Iota), Eq (is_a_theorem (strict_implies (possibly a) (necessarily (possibly a)))) True % 15.35/15.62 Clause #1041 (by superposition #[982, 473]): Eq True False % 15.35/15.62 Clause #1048 (by clausification #[1041]): False % 15.35/15.62 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------