%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL546+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 : Sun Sep 27 07:54:49 AM UTC 2026
% Result : Theorem 41.42s 11.20s
% Output : CNFRefutation 41.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 57 ( 28 unt; 0 def)
% Number of atoms : 101 ( 3 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 70 ( 26 ~; 31 |; 2 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(s1_0_op_strict_implies,axiom,
'op$ustrict$uimplies' ).
fof(modus_ponens,axiom,
( 'modus$uponens'
<=> ! [X0,X1] :
( ( 'is$ua$utheorem'(implies(X0,X1))
& 'is$ua$utheorem'(X0) )
=> 'is$ua$utheorem'(X1) ) ) ).
fof(implies_3,axiom,
( 'implies$u3'
<=> ! [X0,X1,X2] : 'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ) ).
fof(hilbert_modus_ponens,axiom,
'modus$uponens' ).
fof(hilbert_implies_3,axiom,
'implies$u3' ).
fof(necessitation,axiom,
( necessitation
<=> ! [X0] :
( 'is$ua$utheorem'(X0)
=> 'is$ua$utheorem'(necessarily(X0)) ) ) ).
fof(modus_ponens_strict_implies,axiom,
( 'modus$uponens$ustrict$uimplies'
<=> ! [X0,X1] :
( ( 'is$ua$utheorem'('strict$uimplies'(X0,X1))
& 'is$ua$utheorem'(X0) )
=> 'is$ua$utheorem'(X1) ) ) ).
fof(axiom_M,axiom,
( 'axiom$uM'
<=> ! [X0] : 'is$ua$utheorem'(implies(necessarily(X0),X0)) ) ).
fof(axiom_B,axiom,
( 'axiom$uB'
<=> ! [X0] : 'is$ua$utheorem'(implies(X0,necessarily(possibly(X0)))) ) ).
fof(axiom_m6,axiom,
( 'axiom$um6'
<=> ! [X0] : 'is$ua$utheorem'('strict$uimplies'(X0,possibly(X0))) ) ).
fof(op_strict_implies,axiom,
( 'op$ustrict$uimplies'
=> ! [X0,X1] : 'strict$uimplies'(X0,X1) = necessarily(implies(X0,X1)) ) ).
fof(km4b_necessitation,axiom,
necessitation ).
fof(km4b_axiom_M,axiom,
'axiom$uM' ).
fof(km4b_axiom_B,axiom,
'axiom$uB' ).
fof(s1_0_m6s3m9b_axiom_m6,conjecture,
'axiom$um6' ).
fof(negated_conjecture,negated_conjecture,
~ 'axiom$um6',
inference(negate_conjecture,[status(cth)],[s1_0_m6s3m9b_axiom_m6]) ).
cnf(c3,plain,
'op$ustrict$uimplies',
inference(clausification,[status(esa)],[s1_0_op_strict_implies]) ).
cnf(c6,plain,
( 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0)
| ~ 'is$ua$utheorem'(implies(X0,X1))
| ~ 'modus$uponens' ),
inference(clausification,[status(esa)],[modus_ponens]) ).
cnf(c19,plain,
( 'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ 'implies$u3' ),
inference(clausification,[status(esa)],[implies_3]) ).
cnf(c69,plain,
'modus$uponens',
inference(clausification,[status(esa)],[hilbert_modus_ponens]) ).
cnf(c73,plain,
'implies$u3',
inference(clausification,[status(esa)],[hilbert_implies_3]) ).
cnf(c84,plain,
( 'is$ua$utheorem'(necessarily(X0))
| ~ 'is$ua$utheorem'(X0)
| ~ necessitation ),
inference(clausification,[status(esa)],[necessitation]) ).
cnf(c87,plain,
( 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0)
| ~ 'is$ua$utheorem'('strict$uimplies'(X0,X1))
| ~ 'modus$uponens$ustrict$uimplies' ),
inference(clausification,[status(esa)],[modus_ponens_strict_implies]) ).
cnf(c88,plain,
( 'is$ua$utheorem'('strict$uimplies'(sK124,sK125))
| 'modus$uponens$ustrict$uimplies' ),
inference(clausification,[status(esa)],[modus_ponens_strict_implies]) ).
cnf(c89,plain,
( 'is$ua$utheorem'(sK124)
| 'modus$uponens$ustrict$uimplies' ),
inference(clausification,[status(esa)],[modus_ponens_strict_implies]) ).
cnf(c90,plain,
( ~ 'is$ua$utheorem'(sK125)
| 'modus$uponens$ustrict$uimplies' ),
inference(clausification,[status(esa)],[modus_ponens_strict_implies]) ).
cnf(c100,plain,
( 'is$ua$utheorem'(implies(necessarily(X0),X0))
| ~ 'axiom$uM' ),
inference(clausification,[status(esa)],[axiom_M]) ).
cnf(c104,plain,
( 'is$ua$utheorem'(implies(X0,necessarily(possibly(X0))))
| ~ 'axiom$uB' ),
inference(clausification,[status(esa)],[axiom_B]) ).
cnf(c127,plain,
( ~ 'is$ua$utheorem'('strict$uimplies'(sK185,possibly(sK185)))
| 'axiom$um6' ),
inference(clausification,[status(esa)],[axiom_m6]) ).
cnf(c138,plain,
( necessarily(implies(X0,X1)) = 'strict$uimplies'(X0,X1)
| ~ 'op$ustrict$uimplies' ),
inference(clausification,[status(esa)],[op_strict_implies]) ).
cnf(c141,plain,
necessitation,
inference(clausification,[status(esa)],[km4b_necessitation]) ).
cnf(c143,plain,
'axiom$uM',
inference(clausification,[status(esa)],[km4b_axiom_M]) ).
cnf(c145,plain,
'axiom$uB',
inference(clausification,[status(esa)],[km4b_axiom_B]) ).
cnf(c146,plain,
~ 'axiom$um6',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
~ 'is$ua$utheorem'('strict$uimplies'(sK185,possibly(sK185))),
inference(resolution,[status(thm)],[c146,c127]) ).
cnf(d1,plain,
necessarily(implies(X0,X1)) = 'strict$uimplies'(X0,X1),
inference(resolution,[status(thm)],[c3,c138]) ).
cnf(d2,plain,
( 'is$ua$utheorem'(necessarily(X0))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[c141,c84]) ).
cnf(d3,plain,
'is$ua$utheorem'(implies(necessarily(X0),X0)),
inference(resolution,[status(thm)],[c143,c100]) ).
cnf(d4,plain,
( ~ 'is$ua$utheorem'(implies(X1,X0))
| ~ 'is$ua$utheorem'(X1)
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[c69,c6]) ).
cnf(d5,plain,
( ~ 'is$ua$utheorem'(implies(implies(necessarily(X1),X1),X0))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(resolution,[status(thm)],[c73,c19]) ).
cnf(d7,plain,
'is$ua$utheorem'(necessarily(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))),
inference(resolution,[status(thm)],[d2,d6]) ).
cnf(d8,plain,
'is$ua$utheorem'('strict$uimplies'(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(demodulation,[status(thm)],[d7,d1]) ).
cnf(d9,plain,
'is$ua$utheorem'(implies(X0,necessarily(possibly(X0)))),
inference(resolution,[status(thm)],[c145,c104]) ).
cnf(d10,plain,
( ~ 'modus$uponens$ustrict$uimplies'
| ~ 'is$ua$utheorem'('strict$uimplies'(implies(X1,necessarily(possibly(X1))),X0))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[c87,d9]) ).
cnf(d11,plain,
( ~ 'modus$uponens$ustrict$uimplies'
| 'is$ua$utheorem'(implies(implies(necessarily(possibly(X0)),X1),implies(X0,X1))) ),
inference(resolution,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
( 'modus$uponens$ustrict$uimplies'
| ~ 'is$ua$utheorem'(implies(sK124,X0))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d4,c89]) ).
cnf(d13,plain,
( 'modus$uponens$ustrict$uimplies'
| ~ 'is$ua$utheorem'(implies('strict$uimplies'(sK124,sK125),X0))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d4,c88]) ).
cnf(d14,plain,
'is$ua$utheorem'(implies('strict$uimplies'(X0,X1),implies(X0,X1))),
inference(superposition,[status(thm)],[d1,d3]) ).
cnf(d15,plain,
( 'modus$uponens$ustrict$uimplies'
| 'is$ua$utheorem'(implies(sK124,sK125)) ),
inference(resolution,[status(thm)],[d14,d13]) ).
cnf(d16,plain,
( 'modus$uponens$ustrict$uimplies'
| 'is$ua$utheorem'(sK125)
| 'modus$uponens$ustrict$uimplies' ),
inference(resolution,[status(thm)],[d15,d12]) ).
cnf(d17,plain,
( 'modus$uponens$ustrict$uimplies'
| 'modus$uponens$ustrict$uimplies' ),
inference(resolution,[status(thm)],[d16,c90]) ).
cnf(d18,plain,
'is$ua$utheorem'(implies(implies(necessarily(possibly(X0)),X1),implies(X0,X1))),
inference(resolution,[status(thm)],[d17,d11]) ).
cnf(d19,plain,
'is$ua$utheorem'(implies(X0,possibly(X0))),
inference(resolution,[status(thm)],[d18,d5]) ).
cnf(d20,plain,
'is$ua$utheorem'(necessarily(implies(X0,possibly(X0)))),
inference(resolution,[status(thm)],[d19,d2]) ).
cnf(d21,plain,
'is$ua$utheorem'('strict$uimplies'(X0,possibly(X0))),
inference(demodulation,[status(thm)],[d20,d1]) ).
cnf(d22,plain,
$false,
inference(resolution,[status(thm)],[d21,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL546+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.64 % Computer : n003.cluster.edu
% 0.18/0.64 % Model : x86_64 x86_64
% 0.18/0.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.64 % Memory : 8046.5625MB
% 0.18/0.64 % OS : Linux 6.8.0-71-generic
% 0.18/0.64 % CPULimit : 300
% 0.18/0.64 % WCLimit : 300
% 0.18/0.64 % DateTime : Fri Sep 25 22:45:40 UTC 2026
% 0.18/0.65 % CPUTime :
% 0.18/0.65 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 41.42/11.20 % SZS status Theorem for theBenchmark.p
% 41.42/11.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------