TSTP Solution File: LCL546+1 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : LCL546+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n007.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 : Thu Aug 31 07:10:05 EDT 2023
% Result : Theorem 230.24s 230.38s
% Output : Proof 230.38s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL546+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : duper %s
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 22:47:40 EDT 2023
% 0.14/0.35 % CPUTime :
% 230.24/230.38 SZS status Theorem for theBenchmark.p
% 230.24/230.38 SZS output start Proof for theBenchmark.p
% 230.24/230.38 Clause #0 (by assumption #[]): Eq (Iff modus_ponens (∀ (X Y : Iota), And (is_a_theorem X) (is_a_theorem (implies X Y)) → is_a_theorem Y)) True
% 230.24/230.38 Clause #5 (by assumption #[]): Eq (Iff implies_3 (∀ (X Y Z : Iota), is_a_theorem (implies (implies X Y) (implies (implies Y Z) (implies X Z))))) True
% 230.24/230.38 Clause #34 (by assumption #[]): Eq modus_ponens True
% 230.24/230.38 Clause #38 (by assumption #[]): Eq implies_3 True
% 230.24/230.38 Clause #49 (by assumption #[]): Eq (Iff necessitation (∀ (X : Iota), is_a_theorem X → is_a_theorem (necessarily X))) True
% 230.24/230.38 Clause #54 (by assumption #[]): Eq (Iff axiom_M (∀ (X : Iota), is_a_theorem (implies (necessarily X) X))) True
% 230.24/230.38 Clause #56 (by assumption #[]): Eq (Iff axiom_B (∀ (X : Iota), is_a_theorem (implies X (necessarily (possibly X))))) True
% 230.24/230.38 Clause #67 (by assumption #[]): Eq (Iff axiom_m6 (∀ (X : Iota), is_a_theorem (strict_implies X (possibly X)))) True
% 230.24/230.38 Clause #74 (by assumption #[]): Eq (op_strict_implies → ∀ (X Y : Iota), Eq (strict_implies X Y) (necessarily (implies X Y))) True
% 230.24/230.38 Clause #77 (by assumption #[]): Eq necessitation True
% 230.24/230.38 Clause #79 (by assumption #[]): Eq axiom_M True
% 230.24/230.38 Clause #81 (by assumption #[]): Eq axiom_B True
% 230.24/230.38 Clause #83 (by assumption #[]): Eq op_strict_implies True
% 230.24/230.38 Clause #85 (by assumption #[]): Eq (Not axiom_m6) True
% 230.24/230.38 Clause #87 (by clausification #[0]): Or (Eq modus_ponens False)
% 230.24/230.38 (Eq (∀ (X Y : Iota), And (is_a_theorem X) (is_a_theorem (implies X Y)) → is_a_theorem Y) True)
% 230.24/230.38 Clause #127 (by clausification #[85]): Eq axiom_m6 False
% 230.24/230.38 Clause #128 (by clausification #[87]): ∀ (a : Iota),
% 230.24/230.38 Or (Eq modus_ponens False)
% 230.24/230.38 (Eq (∀ (Y : Iota), And (is_a_theorem a) (is_a_theorem (implies a Y)) → is_a_theorem Y) True)
% 230.24/230.38 Clause #129 (by clausification #[128]): ∀ (a a_1 : Iota),
% 230.24/230.38 Or (Eq modus_ponens False) (Eq (And (is_a_theorem a) (is_a_theorem (implies a a_1)) → is_a_theorem a_1) True)
% 230.24/230.38 Clause #130 (by clausification #[129]): ∀ (a a_1 : Iota),
% 230.24/230.38 Or (Eq modus_ponens False)
% 230.24/230.38 (Or (Eq (And (is_a_theorem a) (is_a_theorem (implies a a_1))) False) (Eq (is_a_theorem a_1) True))
% 230.24/230.38 Clause #131 (by clausification #[130]): ∀ (a a_1 : Iota),
% 230.24/230.38 Or (Eq modus_ponens False)
% 230.24/230.38 (Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False)))
% 230.24/230.38 Clause #132 (by forward demodulation #[131, 34]): ∀ (a a_1 : Iota),
% 230.24/230.38 Or (Eq True False)
% 230.24/230.38 (Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False)))
% 230.24/230.38 Clause #133 (by clausification #[132]): ∀ (a a_1 : Iota),
% 230.24/230.38 Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False))
% 230.24/230.38 Clause #135 (by clausification #[49]): Or (Eq necessitation False) (Eq (∀ (X : Iota), is_a_theorem X → is_a_theorem (necessarily X)) True)
% 230.24/230.38 Clause #142 (by clausification #[5]): Or (Eq implies_3 False)
% 230.24/230.38 (Eq (∀ (X Y Z : Iota), is_a_theorem (implies (implies X Y) (implies (implies Y Z) (implies X Z)))) True)
% 230.24/230.38 Clause #150 (by clausification #[135]): ∀ (a : Iota), Or (Eq necessitation False) (Eq (is_a_theorem a → is_a_theorem (necessarily a)) True)
% 230.24/230.38 Clause #151 (by clausification #[150]): ∀ (a : Iota), Or (Eq necessitation False) (Or (Eq (is_a_theorem a) False) (Eq (is_a_theorem (necessarily a)) True))
% 230.24/230.38 Clause #152 (by forward demodulation #[151, 77]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (is_a_theorem a) False) (Eq (is_a_theorem (necessarily a)) True))
% 230.24/230.38 Clause #153 (by clausification #[152]): ∀ (a : Iota), Or (Eq (is_a_theorem a) False) (Eq (is_a_theorem (necessarily a)) True)
% 230.24/230.38 Clause #171 (by clausification #[54]): Or (Eq axiom_M False) (Eq (∀ (X : Iota), is_a_theorem (implies (necessarily X) X)) True)
% 230.24/230.38 Clause #175 (by clausification #[171]): ∀ (a : Iota), Or (Eq axiom_M False) (Eq (is_a_theorem (implies (necessarily a) a)) True)
% 230.24/230.38 Clause #176 (by forward demodulation #[175, 79]): ∀ (a : Iota), Or (Eq True False) (Eq (is_a_theorem (implies (necessarily a) a)) True)
% 230.24/230.38 Clause #177 (by clausification #[176]): ∀ (a : Iota), Eq (is_a_theorem (implies (necessarily a) a)) True
% 230.24/230.41 Clause #178 (by superposition #[177, 133]): ∀ (a a_1 : Iota),
% 230.24/230.41 Or (Eq (is_a_theorem a) True)
% 230.24/230.41 (Or (Eq True False) (Eq (is_a_theorem (implies (implies (necessarily a_1) a_1) a)) False))
% 230.24/230.41 Clause #190 (by clausification #[67]): Or (Eq axiom_m6 True) (Eq (∀ (X : Iota), is_a_theorem (strict_implies X (possibly X))) False)
% 230.24/230.41 Clause #192 (by clausification #[190]): ∀ (a : Iota), Or (Eq axiom_m6 True) (Eq (Not (is_a_theorem (strict_implies (skS.0 19 a) (possibly (skS.0 19 a))))) True)
% 230.24/230.41 Clause #193 (by clausification #[192]): ∀ (a : Iota), Or (Eq axiom_m6 True) (Eq (is_a_theorem (strict_implies (skS.0 19 a) (possibly (skS.0 19 a)))) False)
% 230.24/230.41 Clause #194 (by forward demodulation #[193, 127]): ∀ (a : Iota), Or (Eq False True) (Eq (is_a_theorem (strict_implies (skS.0 19 a) (possibly (skS.0 19 a)))) False)
% 230.24/230.41 Clause #195 (by clausification #[194]): ∀ (a : Iota), Eq (is_a_theorem (strict_implies (skS.0 19 a) (possibly (skS.0 19 a)))) False
% 230.24/230.41 Clause #246 (by clausification #[56]): Or (Eq axiom_B False) (Eq (∀ (X : Iota), is_a_theorem (implies X (necessarily (possibly X)))) True)
% 230.24/230.41 Clause #250 (by clausification #[246]): ∀ (a : Iota), Or (Eq axiom_B False) (Eq (is_a_theorem (implies a (necessarily (possibly a)))) True)
% 230.24/230.41 Clause #251 (by forward demodulation #[250, 81]): ∀ (a : Iota), Or (Eq True False) (Eq (is_a_theorem (implies a (necessarily (possibly a)))) True)
% 230.24/230.41 Clause #252 (by clausification #[251]): ∀ (a : Iota), Eq (is_a_theorem (implies a (necessarily (possibly a)))) True
% 230.24/230.41 Clause #253 (by superposition #[252, 133]): ∀ (a a_1 : Iota),
% 230.24/230.41 Or (Eq (is_a_theorem a) True)
% 230.24/230.41 (Or (Eq True False) (Eq (is_a_theorem (implies (implies a_1 (necessarily (possibly a_1))) a)) False))
% 230.24/230.41 Clause #1027 (by clausification #[74]): Or (Eq op_strict_implies False) (Eq (∀ (X Y : Iota), Eq (strict_implies X Y) (necessarily (implies X Y))) True)
% 230.24/230.41 Clause #1028 (by clausification #[1027]): ∀ (a : Iota),
% 230.24/230.41 Or (Eq op_strict_implies False) (Eq (∀ (Y : Iota), Eq (strict_implies a Y) (necessarily (implies a Y))) True)
% 230.24/230.41 Clause #1029 (by clausification #[1028]): ∀ (a a_1 : Iota), Or (Eq op_strict_implies False) (Eq (Eq (strict_implies a a_1) (necessarily (implies a a_1))) True)
% 230.24/230.41 Clause #1030 (by clausification #[1029]): ∀ (a a_1 : Iota), Or (Eq op_strict_implies False) (Eq (strict_implies a a_1) (necessarily (implies a a_1)))
% 230.24/230.41 Clause #1031 (by forward demodulation #[1030, 83]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (strict_implies a a_1) (necessarily (implies a a_1)))
% 230.24/230.41 Clause #1032 (by clausification #[1031]): ∀ (a a_1 : Iota), Eq (strict_implies a a_1) (necessarily (implies a a_1))
% 230.24/230.41 Clause #1225 (by clausification #[142]): ∀ (a : Iota),
% 230.24/230.41 Or (Eq implies_3 False)
% 230.24/230.41 (Eq (∀ (Y Z : Iota), is_a_theorem (implies (implies a Y) (implies (implies Y Z) (implies a Z)))) True)
% 230.24/230.41 Clause #1226 (by clausification #[1225]): ∀ (a a_1 : Iota),
% 230.24/230.41 Or (Eq implies_3 False)
% 230.24/230.41 (Eq (∀ (Z : Iota), is_a_theorem (implies (implies a a_1) (implies (implies a_1 Z) (implies a Z)))) True)
% 230.24/230.41 Clause #1227 (by clausification #[1226]): ∀ (a a_1 a_2 : Iota),
% 230.24/230.41 Or (Eq implies_3 False) (Eq (is_a_theorem (implies (implies a a_1) (implies (implies a_1 a_2) (implies a a_2)))) True)
% 230.24/230.41 Clause #1228 (by forward demodulation #[1227, 38]): ∀ (a a_1 a_2 : Iota),
% 230.24/230.41 Or (Eq True False) (Eq (is_a_theorem (implies (implies a a_1) (implies (implies a_1 a_2) (implies a a_2)))) True)
% 230.24/230.41 Clause #1229 (by clausification #[1228]): ∀ (a a_1 a_2 : Iota), Eq (is_a_theorem (implies (implies a a_1) (implies (implies a_1 a_2) (implies a a_2)))) True
% 230.24/230.41 Clause #1295 (by clausification #[178]): ∀ (a a_1 : Iota), Or (Eq (is_a_theorem a) True) (Eq (is_a_theorem (implies (implies (necessarily a_1) a_1) a)) False)
% 230.24/230.41 Clause #1449 (by clausification #[253]): ∀ (a a_1 : Iota),
% 230.24/230.41 Or (Eq (is_a_theorem a) True) (Eq (is_a_theorem (implies (implies a_1 (necessarily (possibly a_1))) a)) False)
% 230.24/230.41 Clause #1454 (by superposition #[1449, 1229]): ∀ (a a_1 : Iota),
% 230.24/230.41 Or (Eq (is_a_theorem (implies (implies (necessarily (possibly a)) a_1) (implies a a_1))) True) (Eq False True)
% 230.24/230.41 Clause #22579 (by clausification #[1454]): ∀ (a a_1 : Iota), Eq (is_a_theorem (implies (implies (necessarily (possibly a)) a_1) (implies a a_1))) True
% 230.38/230.55 Clause #22580 (by superposition #[22579, 1295]): ∀ (a : Iota), Or (Eq (is_a_theorem (implies a (possibly a))) True) (Eq True False)
% 230.38/230.55 Clause #22601 (by clausification #[22580]): ∀ (a : Iota), Eq (is_a_theorem (implies a (possibly a))) True
% 230.38/230.55 Clause #22663 (by superposition #[22601, 153]): ∀ (a : Iota), Or (Eq True False) (Eq (is_a_theorem (necessarily (implies a (possibly a)))) True)
% 230.38/230.55 Clause #22816 (by clausification #[22663]): ∀ (a : Iota), Eq (is_a_theorem (necessarily (implies a (possibly a)))) True
% 230.38/230.55 Clause #22817 (by forward demodulation #[22816, 1032]): ∀ (a : Iota), Eq (is_a_theorem (strict_implies a (possibly a))) True
% 230.38/230.55 Clause #22818 (by superposition #[22817, 195]): Eq True False
% 230.38/230.55 Clause #22857 (by clausification #[22818]): False
% 230.38/230.55 SZS output end Proof for theBenchmark.p
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