%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : PLA053_5 : TPTP v9.2.0. Released v8.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n024.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 07:58:04 PM UTC 2025 % Result : Theorem 4.45s 4.90s % Output : Proof 4.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.20 % Problem : PLA053_5 : TPTP v9.2.0. Released v8.2.0. % 0.06/0.23 % Command : duper %s % 0.11/0.46 % Computer : n024.cluster.edu % 0.11/0.46 % Model : x86_64 x86_64 % 0.11/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.46 % Memory : 8042.1875MB % 0.11/0.46 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.46 % CPULimit : 300 % 0.11/0.46 % WCLimit : 300 % 0.11/0.46 % DateTime : Thu Oct 2 08:56:53 EDT 2025 % 0.11/0.46 % CPUTime : % 4.45/4.90 SZS status Theorem for theBenchmark.p % 4.45/4.90 SZS output start Proof for theBenchmark.p % 4.45/4.90 Clause #0 (by assumption #[]): Eq (∀ (W V : «$ki_world»), «$ki_accessible» W V) True % 4.45/4.90 Clause #1 (by assumption #[]): Eq (∀ (W : «$ki_world») (X : Iota), «$ki_exists_in_world_$i» W X) True % 4.45/4.90 Clause #4 (by assumption #[]): Eq % 4.45/4.90 (Exists fun A => % 4.45/4.90 And («$ki_exists_in_world_$i» «$ki_local_world» A) % 4.45/4.90 (∀ (W : «$ki_world»), % 4.45/4.90 «$ki_accessible» «$ki_local_world» W → % 4.45/4.90 ∀ (X : Iota), % 4.45/4.90 «$ki_exists_in_world_$i» W X → % 4.45/4.90 And (bomb W X) (h W A) → ∀ (W0 : «$ki_world»), «$ki_accessible» W W0 → bomb W0 X)) % 4.45/4.90 True % 4.45/4.90 Clause #5 (by assumption #[]): Eq % 4.45/4.90 (∀ (W : «$ki_world»), % 4.45/4.90 «$ki_accessible» «$ki_local_world» W → % 4.45/4.90 ∀ (X : Iota), % 4.45/4.90 «$ki_exists_in_world_$i» W X → % 4.45/4.90 Exists fun D => % 4.45/4.90 And («$ki_exists_in_world_$i» W D) % 4.45/4.90 (∀ (W0 : «$ki_world»), «$ki_accessible» W W0 → And (bomb W0 X) (h W0 D) → defused W0 X)) % 4.45/4.90 True % 4.45/4.90 Clause #6 (by assumption #[]): Eq % 4.45/4.90 (Not % 4.45/4.90 (∀ (W : «$ki_world»), % 4.45/4.90 «$ki_accessible» «$ki_local_world» W → % 4.45/4.90 ∀ (X : Iota), % 4.45/4.90 «$ki_exists_in_world_$i» W X → % 4.45/4.90 Exists fun D => And («$ki_exists_in_world_$i» W D) (And (bomb W X) (h W D) → defused W X))) % 4.45/4.90 True % 4.45/4.90 Clause #7 (by clausification #[1]): ∀ (a : «$ki_world»), Eq (∀ (X : Iota), «$ki_exists_in_world_$i» a X) True % 4.45/4.90 Clause #8 (by clausification #[7]): ∀ (a : «$ki_world») (a_1 : Iota), Eq («$ki_exists_in_world_$i» a a_1) True % 4.45/4.90 Clause #9 (by clausification #[0]): ∀ (a : «$ki_world»), Eq (∀ (V : «$ki_world»), «$ki_accessible» a V) True % 4.45/4.90 Clause #10 (by clausification #[9]): ∀ (a a_1 : «$ki_world»), Eq («$ki_accessible» a a_1) True % 4.45/4.90 Clause #23 (by clausification #[4]): ∀ (a : Iota), % 4.45/4.90 Eq % 4.45/4.90 (And («$ki_exists_in_world_$i» «$ki_local_world» (skS.0 2 a)) % 4.45/4.90 (∀ (W : «$ki_world»), % 4.45/4.90 «$ki_accessible» «$ki_local_world» W → % 4.45/4.90 ∀ (X : Iota), % 4.45/4.90 «$ki_exists_in_world_$i» W X → % 4.45/4.90 And (bomb W X) (h W (skS.0 2 a)) → ∀ (W0 : «$ki_world»), «$ki_accessible» W W0 → bomb W0 X)) % 4.45/4.90 True % 4.45/4.90 Clause #24 (by clausification #[23]): ∀ (a : Iota), % 4.45/4.90 Eq % 4.45/4.90 (∀ (W : «$ki_world»), % 4.45/4.90 «$ki_accessible» «$ki_local_world» W → % 4.45/4.90 ∀ (X : Iota), % 4.45/4.90 «$ki_exists_in_world_$i» W X → % 4.45/4.90 And (bomb W X) (h W (skS.0 2 a)) → ∀ (W0 : «$ki_world»), «$ki_accessible» W W0 → bomb W0 X) % 4.45/4.90 True % 4.45/4.90 Clause #26 (by clausification #[24]): ∀ (a : «$ki_world») (a_1 : Iota), % 4.45/4.90 Eq % 4.45/4.90 («$ki_accessible» «$ki_local_world» a → % 4.45/4.90 ∀ (X : Iota), % 4.45/4.90 «$ki_exists_in_world_$i» a X → % 4.45/4.90 And (bomb a X) (h a (skS.0 2 a_1)) → ∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → bomb W0 X) % 4.45/4.90 True % 4.45/4.90 Clause #27 (by clausification #[26]): ∀ (a : «$ki_world») (a_1 : Iota), % 4.45/4.90 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.45/4.90 (Eq % 4.45/4.90 (∀ (X : Iota), % 4.45/4.90 «$ki_exists_in_world_$i» a X → % 4.45/4.90 And (bomb a X) (h a (skS.0 2 a_1)) → ∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → bomb W0 X) % 4.45/4.90 True) % 4.45/4.90 Clause #28 (by clausification #[27]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 4.45/4.90 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.45/4.90 (Eq % 4.45/4.90 («$ki_exists_in_world_$i» a a_1 → % 4.45/4.90 And (bomb a a_1) (h a (skS.0 2 a_2)) → ∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → bomb W0 a_1) % 4.45/4.90 True) % 4.45/4.90 Clause #29 (by clausification #[28]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 4.45/4.90 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.45/4.90 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.45/4.90 (Eq (And (bomb a a_1) (h a (skS.0 2 a_2)) → ∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → bomb W0 a_1) True)) % 4.45/4.90 Clause #30 (by clausification #[29]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 4.45/4.90 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.45/4.90 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.45/4.90 (Or (Eq (And (bomb a a_1) (h a (skS.0 2 a_2))) False) % 4.45/4.90 (Eq (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → bomb W0 a_1) True))) % 4.52/4.93 Clause #31 (by clausification #[30]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 4.52/4.93 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.52/4.93 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.52/4.93 (Or (Eq (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → bomb W0 a_1) True) % 4.52/4.93 (Or (Eq (bomb a a_1) False) (Eq (h a (skS.0 2 a_2)) False)))) % 4.52/4.93 Clause #32 (by clausification #[31]): ∀ (a : «$ki_world») (a_1 a_2 : Iota) (a_3 : «$ki_world»), % 4.52/4.93 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.52/4.93 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.52/4.93 (Or (Eq (bomb a a_1) False) % 4.52/4.93 (Or (Eq (h a (skS.0 2 a_2)) False) (Eq («$ki_accessible» a a_3 → bomb a_3 a_1) True)))) % 4.52/4.93 Clause #33 (by clausification #[32]): ∀ (a : «$ki_world») (a_1 a_2 : Iota) (a_3 : «$ki_world»), % 4.52/4.93 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.52/4.93 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.52/4.93 (Or (Eq (bomb a a_1) False) % 4.52/4.93 (Or (Eq (h a (skS.0 2 a_2)) False) (Or (Eq («$ki_accessible» a a_3) False) (Eq (bomb a_3 a_1) True))))) % 4.52/4.93 Clause #34 (by forward demodulation #[33, 10]): ∀ (a : «$ki_world») (a_1 a_2 : Iota) (a_3 : «$ki_world»), % 4.52/4.93 Or (Eq True False) % 4.52/4.93 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.52/4.93 (Or (Eq (bomb a a_1) False) % 4.52/4.93 (Or (Eq (h a (skS.0 2 a_2)) False) (Or (Eq («$ki_accessible» a a_3) False) (Eq (bomb a_3 a_1) True))))) % 4.52/4.93 Clause #35 (by clausification #[34]): ∀ (a : «$ki_world») (a_1 a_2 : Iota) (a_3 : «$ki_world»), % 4.52/4.93 Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.52/4.93 (Or (Eq (bomb a a_1) False) % 4.52/4.93 (Or (Eq (h a (skS.0 2 a_2)) False) (Or (Eq («$ki_accessible» a a_3) False) (Eq (bomb a_3 a_1) True)))) % 4.52/4.93 Clause #36 (by forward demodulation #[35, 8]): ∀ (a : «$ki_world») (a_1 a_2 : Iota) (a_3 : «$ki_world»), % 4.52/4.93 Or (Eq True False) % 4.52/4.93 (Or (Eq (bomb a a_1) False) % 4.52/4.93 (Or (Eq (h a (skS.0 2 a_2)) False) (Or (Eq («$ki_accessible» a a_3) False) (Eq (bomb a_3 a_1) True)))) % 4.52/4.93 Clause #37 (by clausification #[36]): ∀ (a : «$ki_world») (a_1 a_2 : Iota) (a_3 : «$ki_world»), % 4.52/4.93 Or (Eq (bomb a a_1) False) % 4.52/4.93 (Or (Eq (h a (skS.0 2 a_2)) False) (Or (Eq («$ki_accessible» a a_3) False) (Eq (bomb a_3 a_1) True))) % 4.52/4.93 Clause #39 (by clausification #[6]): Eq % 4.52/4.93 (∀ (W : «$ki_world»), % 4.52/4.93 «$ki_accessible» «$ki_local_world» W → % 4.52/4.93 ∀ (X : Iota), % 4.52/4.93 «$ki_exists_in_world_$i» W X → % 4.52/4.93 Exists fun D => And («$ki_exists_in_world_$i» W D) (And (bomb W X) (h W D) → defused W X)) % 4.52/4.93 False % 4.52/4.93 Clause #40 (by clausification #[39]): ∀ (a : «$ki_world»), % 4.52/4.93 Eq % 4.52/4.93 (Not % 4.52/4.93 («$ki_accessible» «$ki_local_world» (skS.0 3 a) → % 4.52/4.93 ∀ (X : Iota), % 4.52/4.93 «$ki_exists_in_world_$i» (skS.0 3 a) X → % 4.52/4.93 Exists fun D => % 4.52/4.93 And («$ki_exists_in_world_$i» (skS.0 3 a) D) % 4.52/4.93 (And (bomb (skS.0 3 a) X) (h (skS.0 3 a) D) → defused (skS.0 3 a) X))) % 4.52/4.93 True % 4.52/4.93 Clause #41 (by clausification #[40]): ∀ (a : «$ki_world»), % 4.52/4.93 Eq % 4.52/4.93 («$ki_accessible» «$ki_local_world» (skS.0 3 a) → % 4.52/4.93 ∀ (X : Iota), % 4.52/4.93 «$ki_exists_in_world_$i» (skS.0 3 a) X → % 4.52/4.93 Exists fun D => % 4.52/4.93 And («$ki_exists_in_world_$i» (skS.0 3 a) D) % 4.52/4.93 (And (bomb (skS.0 3 a) X) (h (skS.0 3 a) D) → defused (skS.0 3 a) X)) % 4.52/4.93 False % 4.52/4.93 Clause #43 (by clausification #[41]): ∀ (a : «$ki_world»), % 4.52/4.93 Eq % 4.52/4.93 (∀ (X : Iota), % 4.52/4.93 «$ki_exists_in_world_$i» (skS.0 3 a) X → % 4.52/4.93 Exists fun D => % 4.52/4.93 And («$ki_exists_in_world_$i» (skS.0 3 a) D) % 4.52/4.93 (And (bomb (skS.0 3 a) X) (h (skS.0 3 a) D) → defused (skS.0 3 a) X)) % 4.52/4.93 False % 4.52/4.93 Clause #44 (by clausification #[5]): ∀ (a : «$ki_world»), % 4.52/4.93 Eq % 4.52/4.93 («$ki_accessible» «$ki_local_world» a → % 4.52/4.93 ∀ (X : Iota), % 4.52/4.93 «$ki_exists_in_world_$i» a X → % 4.52/4.93 Exists fun D => % 4.52/4.93 And («$ki_exists_in_world_$i» a D) % 4.52/4.93 (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → And (bomb W0 X) (h W0 D) → defused W0 X)) % 4.52/4.93 True % 4.52/4.93 Clause #45 (by clausification #[44]): ∀ (a : «$ki_world»), % 4.52/4.96 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.52/4.96 (Eq % 4.52/4.96 (∀ (X : Iota), % 4.52/4.96 «$ki_exists_in_world_$i» a X → % 4.52/4.96 Exists fun D => % 4.52/4.96 And («$ki_exists_in_world_$i» a D) % 4.52/4.96 (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → And (bomb W0 X) (h W0 D) → defused W0 X)) % 4.52/4.96 True) % 4.52/4.96 Clause #46 (by clausification #[45]): ∀ (a : «$ki_world») (a_1 : Iota), % 4.52/4.96 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.52/4.96 (Eq % 4.52/4.96 («$ki_exists_in_world_$i» a a_1 → % 4.52/4.96 Exists fun D => % 4.52/4.96 And («$ki_exists_in_world_$i» a D) % 4.52/4.96 (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → And (bomb W0 a_1) (h W0 D) → defused W0 a_1)) % 4.52/4.96 True) % 4.52/4.96 Clause #47 (by clausification #[46]): ∀ (a : «$ki_world») (a_1 : Iota), % 4.52/4.96 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.52/4.96 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.52/4.96 (Eq % 4.52/4.96 (Exists fun D => % 4.52/4.96 And («$ki_exists_in_world_$i» a D) % 4.52/4.96 (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → And (bomb W0 a_1) (h W0 D) → defused W0 a_1)) % 4.52/4.96 True)) % 4.52/4.96 Clause #48 (by clausification #[47]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 4.52/4.96 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.52/4.96 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.52/4.96 (Eq % 4.52/4.96 (And («$ki_exists_in_world_$i» a (skS.0 4 a a_1 a_2)) % 4.52/4.96 (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → And (bomb W0 a_1) (h W0 (skS.0 4 a a_1 a_2)) → defused W0 a_1)) % 4.52/4.96 True)) % 4.52/4.96 Clause #49 (by clausification #[48]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 4.52/4.96 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.52/4.96 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.52/4.96 (Eq (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → And (bomb W0 a_1) (h W0 (skS.0 4 a a_1 a_2)) → defused W0 a_1) % 4.52/4.96 True)) % 4.52/4.96 Clause #51 (by clausification #[49]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world») (a_3 : Iota), % 4.52/4.96 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.52/4.96 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.52/4.96 (Eq («$ki_accessible» a a_2 → And (bomb a_2 a_1) (h a_2 (skS.0 4 a a_1 a_3)) → defused a_2 a_1) True)) % 4.52/4.96 Clause #52 (by clausification #[51]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world») (a_3 : Iota), % 4.52/4.96 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.52/4.96 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.52/4.96 (Or (Eq («$ki_accessible» a a_2) False) % 4.52/4.96 (Eq (And (bomb a_2 a_1) (h a_2 (skS.0 4 a a_1 a_3)) → defused a_2 a_1) True))) % 4.52/4.96 Clause #53 (by clausification #[52]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world») (a_3 : Iota), % 4.52/4.96 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.52/4.96 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.52/4.96 (Or (Eq («$ki_accessible» a a_2) False) % 4.52/4.96 (Or (Eq (And (bomb a_2 a_1) (h a_2 (skS.0 4 a a_1 a_3))) False) (Eq (defused a_2 a_1) True)))) % 4.52/4.96 Clause #54 (by clausification #[53]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world») (a_3 : Iota), % 4.52/4.96 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.52/4.96 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.52/4.96 (Or (Eq («$ki_accessible» a a_2) False) % 4.52/4.96 (Or (Eq (defused a_2 a_1) True) (Or (Eq (bomb a_2 a_1) False) (Eq (h a_2 (skS.0 4 a a_1 a_3)) False))))) % 4.52/4.96 Clause #55 (by forward demodulation #[54, 10]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world») (a_3 : Iota), % 4.52/4.96 Or (Eq True False) % 4.52/4.96 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.52/4.96 (Or (Eq («$ki_accessible» a a_2) False) % 4.52/4.96 (Or (Eq (defused a_2 a_1) True) (Or (Eq (bomb a_2 a_1) False) (Eq (h a_2 (skS.0 4 a a_1 a_3)) False))))) % 4.52/4.96 Clause #56 (by clausification #[55]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world») (a_3 : Iota), % 4.52/4.96 Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.52/4.96 (Or (Eq («$ki_accessible» a a_2) False) % 4.52/4.96 (Or (Eq (defused a_2 a_1) True) (Or (Eq (bomb a_2 a_1) False) (Eq (h a_2 (skS.0 4 a a_1 a_3)) False)))) % 4.52/4.96 Clause #57 (by forward demodulation #[56, 8]): ∀ (a a_1 : «$ki_world») (a_2 a_3 : Iota), % 4.56/4.99 Or (Eq True False) % 4.56/4.99 (Or (Eq («$ki_accessible» a a_1) False) % 4.56/4.99 (Or (Eq (defused a_1 a_2) True) (Or (Eq (bomb a_1 a_2) False) (Eq (h a_1 (skS.0 4 a a_2 a_3)) False)))) % 4.56/4.99 Clause #58 (by clausification #[57]): ∀ (a a_1 : «$ki_world») (a_2 a_3 : Iota), % 4.56/4.99 Or (Eq («$ki_accessible» a a_1) False) % 4.56/4.99 (Or (Eq (defused a_1 a_2) True) (Or (Eq (bomb a_1 a_2) False) (Eq (h a_1 (skS.0 4 a a_2 a_3)) False))) % 4.56/4.99 Clause #59 (by forward demodulation #[58, 10]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world») (a_3 : Iota), % 4.56/4.99 Or (Eq True False) (Or (Eq (defused a a_1) True) (Or (Eq (bomb a a_1) False) (Eq (h a (skS.0 4 a_2 a_1 a_3)) False))) % 4.56/4.99 Clause #60 (by clausification #[59]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world») (a_3 : Iota), % 4.56/4.99 Or (Eq (defused a a_1) True) (Or (Eq (bomb a a_1) False) (Eq (h a (skS.0 4 a_2 a_1 a_3)) False)) % 4.56/4.99 Clause #66 (by clausification #[43]): ∀ (a : «$ki_world») (a_1 : Iota), % 4.56/4.99 Eq % 4.56/4.99 (Not % 4.56/4.99 («$ki_exists_in_world_$i» (skS.0 3 a) (skS.0 5 a a_1) → % 4.56/4.99 Exists fun D => % 4.56/4.99 And («$ki_exists_in_world_$i» (skS.0 3 a) D) % 4.56/4.99 (And (bomb (skS.0 3 a) (skS.0 5 a a_1)) (h (skS.0 3 a) D) → defused (skS.0 3 a) (skS.0 5 a a_1)))) % 4.56/4.99 True % 4.56/4.99 Clause #67 (by clausification #[66]): ∀ (a : «$ki_world») (a_1 : Iota), % 4.56/4.99 Eq % 4.56/4.99 («$ki_exists_in_world_$i» (skS.0 3 a) (skS.0 5 a a_1) → % 4.56/4.99 Exists fun D => % 4.56/4.99 And («$ki_exists_in_world_$i» (skS.0 3 a) D) % 4.56/4.99 (And (bomb (skS.0 3 a) (skS.0 5 a a_1)) (h (skS.0 3 a) D) → defused (skS.0 3 a) (skS.0 5 a a_1))) % 4.56/4.99 False % 4.56/4.99 Clause #69 (by clausification #[67]): ∀ (a : «$ki_world») (a_1 : Iota), % 4.56/4.99 Eq % 4.56/4.99 (Exists fun D => % 4.56/4.99 And («$ki_exists_in_world_$i» (skS.0 3 a) D) % 4.56/4.99 (And (bomb (skS.0 3 a) (skS.0 5 a a_1)) (h (skS.0 3 a) D) → defused (skS.0 3 a) (skS.0 5 a a_1))) % 4.56/4.99 False % 4.56/4.99 Clause #73 (by clausification #[69]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 4.56/4.99 Eq % 4.56/4.99 (And («$ki_exists_in_world_$i» (skS.0 3 a) a_1) % 4.56/4.99 (And (bomb (skS.0 3 a) (skS.0 5 a a_2)) (h (skS.0 3 a) a_1) → defused (skS.0 3 a) (skS.0 5 a a_2))) % 4.56/4.99 False % 4.56/4.99 Clause #74 (by clausification #[73]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 4.56/4.99 Or (Eq («$ki_exists_in_world_$i» (skS.0 3 a) a_1) False) % 4.56/4.99 (Eq (And (bomb (skS.0 3 a) (skS.0 5 a a_2)) (h (skS.0 3 a) a_1) → defused (skS.0 3 a) (skS.0 5 a a_2)) False) % 4.56/4.99 Clause #75 (by clausification #[74]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 4.56/4.99 Or (Eq («$ki_exists_in_world_$i» (skS.0 3 a) a_1) False) % 4.56/4.99 (Eq (And (bomb (skS.0 3 a) (skS.0 5 a a_2)) (h (skS.0 3 a) a_1)) True) % 4.56/4.99 Clause #76 (by clausification #[74]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 4.56/4.99 Or (Eq («$ki_exists_in_world_$i» (skS.0 3 a) a_1) False) (Eq (defused (skS.0 3 a) (skS.0 5 a a_2)) False) % 4.56/4.99 Clause #77 (by clausification #[75]): ∀ (a : «$ki_world») (a_1 : Iota), Or (Eq («$ki_exists_in_world_$i» (skS.0 3 a) a_1) False) (Eq (h (skS.0 3 a) a_1) True) % 4.56/4.99 Clause #78 (by clausification #[75]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 4.56/4.99 Or (Eq («$ki_exists_in_world_$i» (skS.0 3 a) a_1) False) (Eq (bomb (skS.0 3 a) (skS.0 5 a a_2)) True) % 4.56/4.99 Clause #79 (by forward demodulation #[77, 8]): ∀ (a : «$ki_world») (a_1 : Iota), Or (Eq True False) (Eq (h (skS.0 3 a) a_1) True) % 4.56/4.99 Clause #80 (by clausification #[79]): ∀ (a : «$ki_world») (a_1 : Iota), Eq (h (skS.0 3 a) a_1) True % 4.56/4.99 Clause #85 (by superposition #[78, 8]): ∀ (a : «$ki_world») (a_1 : Iota), Or (Eq (bomb (skS.0 3 a) (skS.0 5 a a_1)) True) (Eq False True) % 4.56/4.99 Clause #86 (by clausification #[85]): ∀ (a : «$ki_world») (a_1 : Iota), Eq (bomb (skS.0 3 a) (skS.0 5 a a_1)) True % 4.56/4.99 Clause #87 (by superposition #[86, 37]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world») (a_3 : Iota), % 4.56/4.99 Or (Eq True False) % 4.56/4.99 (Or (Eq (h (skS.0 3 a) (skS.0 2 a_1)) False) % 4.56/4.99 (Or (Eq («$ki_accessible» (skS.0 3 a) a_2) False) (Eq (bomb a_2 (skS.0 5 a a_3)) True))) % 4.56/4.99 Clause #89 (by superposition #[76, 8]): ∀ (a : «$ki_world») (a_1 : Iota), Or (Eq (defused (skS.0 3 a) (skS.0 5 a a_1)) False) (Eq False True) % 4.56/4.99 Clause #92 (by clausification #[89]): ∀ (a : «$ki_world») (a_1 : Iota), Eq (defused (skS.0 3 a) (skS.0 5 a a_1)) False % 4.56/5.00 Clause #95 (by clausification #[87]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world») (a_3 : Iota), % 4.56/5.00 Or (Eq (h (skS.0 3 a) (skS.0 2 a_1)) False) % 4.56/5.00 (Or (Eq («$ki_accessible» (skS.0 3 a) a_2) False) (Eq (bomb a_2 (skS.0 5 a a_3)) True)) % 4.56/5.00 Clause #96 (by forward demodulation #[95, 10]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world») (a_3 : Iota), % 4.56/5.00 Or (Eq (h (skS.0 3 a) (skS.0 2 a_1)) False) (Or (Eq True False) (Eq (bomb a_2 (skS.0 5 a a_3)) True)) % 4.56/5.00 Clause #97 (by clausification #[96]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world») (a_3 : Iota), % 4.56/5.00 Or (Eq (h (skS.0 3 a) (skS.0 2 a_1)) False) (Eq (bomb a_2 (skS.0 5 a a_3)) True) % 4.56/5.00 Clause #98 (by superposition #[97, 80]): ∀ (a a_1 : «$ki_world») (a_2 : Iota), Or (Eq (bomb a (skS.0 5 a_1 a_2)) True) (Eq False True) % 4.56/5.00 Clause #99 (by clausification #[98]): ∀ (a a_1 : «$ki_world») (a_2 : Iota), Eq (bomb a (skS.0 5 a_1 a_2)) True % 4.56/5.00 Clause #101 (by superposition #[99, 60]): ∀ (a a_1 : «$ki_world») (a_2 : Iota) (a_3 : «$ki_world») (a_4 : Iota), % 4.56/5.00 Or (Eq (defused a (skS.0 5 a_1 a_2)) True) (Or (Eq True False) (Eq (h a (skS.0 4 a_3 (skS.0 5 a_1 a_2) a_4)) False)) % 4.56/5.00 Clause #106 (by clausification #[101]): ∀ (a a_1 : «$ki_world») (a_2 : Iota) (a_3 : «$ki_world») (a_4 : Iota), % 4.56/5.00 Or (Eq (defused a (skS.0 5 a_1 a_2)) True) (Eq (h a (skS.0 4 a_3 (skS.0 5 a_1 a_2) a_4)) False) % 4.56/5.00 Clause #107 (by superposition #[106, 80]): ∀ (a a_1 : «$ki_world») (a_2 : Iota), Or (Eq (defused (skS.0 3 a) (skS.0 5 a_1 a_2)) True) (Eq False True) % 4.56/5.00 Clause #108 (by clausification #[107]): ∀ (a a_1 : «$ki_world») (a_2 : Iota), Eq (defused (skS.0 3 a) (skS.0 5 a_1 a_2)) True % 4.56/5.00 Clause #109 (by superposition #[108, 92]): Eq True False % 4.56/5.00 Clause #110 (by clausification #[109]): False % 4.56/5.00 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------