%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL538+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 : n011.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 15.99s 2.37s
% Output : CNFRefutation 15.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 17 unt; 0 def)
% Number of atoms : 52 ( 3 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 36 ( 15 ~; 13 |; 2 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 7 !; 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$utheorem'(X1) ) ) ).
fof(hilbert_modus_ponens,axiom,
'modus$uponens' ).
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$utheorem'(implies(necessarily(X0),X0)) ) ).
fof(op_strict_implies,axiom,
( 'op$ustrict$uimplies'
=> ! [X0,X1] : 'strict$uimplies'(X0,X1) = necessarily(implies(X0,X1)) ) ).
fof(km4b_axiom_M,axiom,
'axiom$uM' ).
fof(s1_0_modus_ponens_strict_implies,conjecture,
'modus$uponens$ustrict$uimplies' ).
fof(negated_conjecture,negated_conjecture,
~ 'modus$uponens$ustrict$uimplies',
inference(negate_conjecture,[status(cth)],[s1_0_modus_ponens_strict_implies]) ).
cnf(c3,plain,
'op$ustrict$uimplies',
inference(clausification,[status(esa)],[s1_0_op_strict_implies]) ).
cnf(c6,plain,
( 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(implies(X0,X1))
| ~ 'is$ua$utheorem'(X0)
| ~ 'modus$uponens' ),
inference(clausification,[status(esa)],[modus_ponens]) ).
cnf(c69,plain,
'modus$uponens',
inference(clausification,[status(esa)],[hilbert_modus_ponens]) ).
cnf(c88,plain,
( 'is$ua$utheorem'(sK124)
| 'modus$uponens$ustrict$uimplies' ),
inference(clausification,[status(esa)],[modus_ponens_strict_implies]) ).
cnf(c89,plain,
( 'is$ua$utheorem'('strict$uimplies'(sK124,sK125))
| 'modus$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(c138,plain,
( 'strict$uimplies'(X0,X1) = necessarily(implies(X0,X1))
| ~ 'op$ustrict$uimplies' ),
inference(clausification,[status(esa)],[op_strict_implies]) ).
cnf(c143,plain,
'axiom$uM',
inference(clausification,[status(esa)],[km4b_axiom_M]) ).
cnf(c146,plain,
~ 'modus$uponens$ustrict$uimplies',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'is$ua$utheorem'(implies(X1,X0))
| ~ 'is$ua$utheorem'(X1)
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[c69,c6]) ).
cnf(d1,plain,
'is$ua$utheorem'('strict$uimplies'(sK124,sK125)),
inference(resolution,[status(thm)],[c146,c89]) ).
cnf(d2,plain,
'is$ua$utheorem'(implies(necessarily(X0),X0)),
inference(resolution,[status(thm)],[c143,c100]) ).
cnf(d3,plain,
( 'is$ua$utheorem'(X0)
| ~ 'is$ua$utheorem'(necessarily(X0)) ),
inference(resolution,[status(thm)],[d0,d2]) ).
cnf(d4,plain,
'strict$uimplies'(X0,X1) = necessarily(implies(X0,X1)),
inference(resolution,[status(thm)],[c3,c138]) ).
cnf(d5,plain,
( 'is$ua$utheorem'(implies(X0,X1))
| ~ 'is$ua$utheorem'('strict$uimplies'(X0,X1)) ),
inference(superposition,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
'is$ua$utheorem'(implies(sK124,sK125)),
inference(resolution,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
( 'is$ua$utheorem'(sK125)
| ~ 'is$ua$utheorem'(sK124) ),
inference(resolution,[status(thm)],[d6,d0]) ).
cnf(d8,plain,
~ 'is$ua$utheorem'(sK125),
inference(resolution,[status(thm)],[c146,c90]) ).
cnf(d9,plain,
~ 'is$ua$utheorem'(sK124),
inference(resolution,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
'is$ua$utheorem'(sK124),
inference(resolution,[status(thm)],[c146,c88]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[d10,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL538+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 25 22:42:43 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.99/2.37 % SZS status Theorem for theBenchmark.p
% 15.99/2.37 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------