TSTP Solution File: LCL536+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : LCL536+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n010.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 07:10:04 EDT 2023
% Result : Theorem 6.50s 6.67s
% Output : Proof 6.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL536+1 : TPTP v8.1.2. Released v3.3.0.
% 0.14/0.15 % Command : duper %s
% 0.14/0.36 % Computer : n010.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Aug 25 05:58:20 EDT 2023
% 0.14/0.36 % CPUTime :
% 6.50/6.67 SZS status Theorem for theBenchmark.p
% 6.50/6.67 SZS output start Proof for theBenchmark.p
% 6.50/6.67 Clause #49 (by assumption #[]): Eq (Iff necessitation (∀ (X : Iota), is_a_theorem X → is_a_theorem (necessarily X))) True
% 6.50/6.67 Clause #57 (by assumption #[]): Eq (Iff axiom_5 (∀ (X : Iota), is_a_theorem (implies (possibly X) (necessarily (possibly X))))) True
% 6.50/6.67 Clause #71 (by assumption #[]): Eq (Iff axiom_m10 (∀ (X : Iota), is_a_theorem (strict_implies (possibly X) (necessarily (possibly X))))) True
% 6.50/6.67 Clause #74 (by assumption #[]): Eq (op_strict_implies → ∀ (X Y : Iota), Eq (strict_implies X Y) (necessarily (implies X Y))) True
% 6.50/6.67 Clause #77 (by assumption #[]): Eq necessitation True
% 6.50/6.67 Clause #80 (by assumption #[]): Eq axiom_5 True
% 6.50/6.67 Clause #82 (by assumption #[]): Eq op_strict_implies True
% 6.50/6.67 Clause #84 (by assumption #[]): Eq (Not axiom_m10) True
% 6.50/6.67 Clause #126 (by clausification #[84]): Eq axiom_m10 False
% 6.50/6.67 Clause #134 (by clausification #[49]): Or (Eq necessitation False) (Eq (∀ (X : Iota), is_a_theorem X → is_a_theorem (necessarily X)) True)
% 6.50/6.67 Clause #140 (by clausification #[134]): ∀ (a : Iota), Or (Eq necessitation False) (Eq (is_a_theorem a → is_a_theorem (necessarily a)) True)
% 6.50/6.67 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))
% 6.50/6.67 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))
% 6.50/6.67 Clause #143 (by clausification #[142]): ∀ (a : Iota), Or (Eq (is_a_theorem a) False) (Eq (is_a_theorem (necessarily a)) True)
% 6.50/6.67 Clause #280 (by clausification #[57]): Or (Eq axiom_5 False) (Eq (∀ (X : Iota), is_a_theorem (implies (possibly X) (necessarily (possibly X)))) True)
% 6.50/6.67 Clause #327 (by clausification #[280]): ∀ (a : Iota), Or (Eq axiom_5 False) (Eq (is_a_theorem (implies (possibly a) (necessarily (possibly a)))) True)
% 6.50/6.67 Clause #328 (by forward demodulation #[327, 80]): ∀ (a : Iota), Or (Eq True False) (Eq (is_a_theorem (implies (possibly a) (necessarily (possibly a)))) True)
% 6.50/6.67 Clause #329 (by clausification #[328]): ∀ (a : Iota), Eq (is_a_theorem (implies (possibly a) (necessarily (possibly a)))) True
% 6.50/6.67 Clause #331 (by superposition #[329, 143]): ∀ (a : Iota),
% 6.50/6.67 Or (Eq True False) (Eq (is_a_theorem (necessarily (implies (possibly a) (necessarily (possibly a))))) True)
% 6.50/6.67 Clause #332 (by clausification #[331]): ∀ (a : Iota), Eq (is_a_theorem (necessarily (implies (possibly a) (necessarily (possibly a))))) True
% 6.50/6.67 Clause #468 (by clausification #[71]): Or (Eq axiom_m10 True) (Eq (∀ (X : Iota), is_a_theorem (strict_implies (possibly X) (necessarily (possibly X)))) False)
% 6.50/6.67 Clause #470 (by clausification #[468]): ∀ (a : Iota),
% 6.50/6.67 Or (Eq axiom_m10 True)
% 6.50/6.67 (Eq (Not (is_a_theorem (strict_implies (possibly (skS.0 62 a)) (necessarily (possibly (skS.0 62 a)))))) True)
% 6.50/6.67 Clause #471 (by clausification #[470]): ∀ (a : Iota),
% 6.50/6.67 Or (Eq axiom_m10 True)
% 6.50/6.67 (Eq (is_a_theorem (strict_implies (possibly (skS.0 62 a)) (necessarily (possibly (skS.0 62 a))))) False)
% 6.50/6.67 Clause #472 (by forward demodulation #[471, 126]): ∀ (a : Iota),
% 6.50/6.67 Or (Eq False True)
% 6.50/6.67 (Eq (is_a_theorem (strict_implies (possibly (skS.0 62 a)) (necessarily (possibly (skS.0 62 a))))) False)
% 6.50/6.67 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
% 6.50/6.67 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)
% 6.50/6.67 Clause #970 (by clausification #[969]): ∀ (a : Iota),
% 6.50/6.67 Or (Eq op_strict_implies False) (Eq (∀ (Y : Iota), Eq (strict_implies a Y) (necessarily (implies a Y))) True)
% 6.50/6.67 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)
% 6.50/6.67 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)))
% 6.50/6.67 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)))
% 6.50/6.67 Clause #974 (by clausification #[973]): ∀ (a a_1 : Iota), Eq (strict_implies a a_1) (necessarily (implies a a_1))
% 6.50/6.67 Clause #982 (by backward demodulation #[974, 332]): ∀ (a : Iota), Eq (is_a_theorem (strict_implies (possibly a) (necessarily (possibly a)))) True
% 6.50/6.67 Clause #1041 (by superposition #[982, 473]): Eq True False
% 6.50/6.67 Clause #1048 (by clausification #[1041]): False
% 6.50/6.67 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------