%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : MGT023+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 08:01:03 AM UTC 2026
% Result : Theorem 14.22s 2.38s
% Output : CNFRefutation 14.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 6 unt; 0 def)
% Number of atoms : 104 ( 14 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 134 ( 55 ~; 63 |; 10 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 7 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1,hypothesis,
! [X0,X1] :
( ( ! [X2] :
( ( greater(X2,X1)
& subpopulations('first$umovers','efficient$uproducers',X0,X2) )
=> greater('growth$urate'('efficient$uproducers',X2),'growth$urate'('first$umovers',X2)) )
& 'in$uenvironment'(X0,X1)
& ~ greater('growth$urate'('efficient$uproducers',X1),'growth$urate'('first$umovers',X1))
& environment(X0) )
=> X1 = 'critical$upoint'(X0) ) ).
fof(l12,hypothesis,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X1] :
( ! [X2] :
( ( greater(X2,X1)
& subpopulations('first$umovers','efficient$uproducers',X0,X2) )
=> greater('growth$urate'('efficient$uproducers',X2),'growth$urate'('first$umovers',X2)) )
& ~ greater('growth$urate'('efficient$uproducers',X1),'growth$urate'('first$umovers',X1))
& 'in$uenvironment'(X0,X1) ) ) ).
fof(prove_l5,conjecture,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> 'in$uenvironment'(X0,'critical$upoint'(X0)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ( stable(X0)
& environment(X0) )
=> 'in$uenvironment'(X0,'critical$upoint'(X0)) ),
inference(negate_conjecture,[status(cth)],[prove_l5]) ).
cnf(c0,plain,
( ~ 'in$uenvironment'(X1,X0)
| X0 = 'critical$upoint'(X1)
| subpopulations('first$umovers','efficient$uproducers',X1,sK2(X1,X0))
| ~ environment(X1)
| greater('growth$urate'('efficient$uproducers',X0),'growth$urate'('first$umovers',X0)) ),
inference(clausification,[status(esa)],[d1]) ).
cnf(c1,plain,
( ~ 'in$uenvironment'(X0,X1)
| X1 = 'critical$upoint'(X0)
| ~ environment(X0)
| greater('growth$urate'('efficient$uproducers',X1),'growth$urate'('first$umovers',X1))
| greater(sK2(X0,X1),X1) ),
inference(clausification,[status(esa)],[d1]) ).
cnf(c2,plain,
( ~ 'in$uenvironment'(X0,X1)
| X1 = 'critical$upoint'(X0)
| ~ environment(X0)
| greater('growth$urate'('efficient$uproducers',X1),'growth$urate'('first$umovers',X1))
| ~ greater('growth$urate'('efficient$uproducers',sK2(X0,X1)),'growth$urate'('first$umovers',sK2(X0,X1))) ),
inference(clausification,[status(esa)],[d1]) ).
cnf(c3,plain,
( 'in$uenvironment'(X0,sK4(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(clausification,[status(esa)],[l12]) ).
cnf(c4,plain,
( ~ greater('growth$urate'('efficient$uproducers',sK4(X0)),'growth$urate'('first$umovers',sK4(X0)))
| ~ stable(X0)
| ~ environment(X0) ),
inference(clausification,[status(esa)],[l12]) ).
cnf(c5,plain,
( ~ greater(X1,sK4(X0))
| ~ stable(X0)
| ~ environment(X0)
| greater('growth$urate'('efficient$uproducers',X1),'growth$urate'('first$umovers',X1))
| ~ subpopulations('first$umovers','efficient$uproducers',X0,X1) ),
inference(clausification,[status(esa)],[l12]) ).
cnf(c6,plain,
environment(sK6),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c7,plain,
stable(sK6),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c8,plain,
~ 'in$uenvironment'(sK6,'critical$upoint'(sK6)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d_0,plain,
( greater(sK2(X1,sK4(X0)),sK4(X0))
| ~ 'in$uenvironment'(X1,sK4(X0))
| ~ environment(X1)
| sK4(X0) = 'critical$upoint'(X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[c4,c1]) ).
cnf(d_1,plain,
( greater('growth$urate'('efficient$uproducers',X1),'growth$urate'('first$umovers',X1))
| ~ 'in$uenvironment'(X0,X1)
| ~ environment(X0)
| X1 = 'critical$upoint'(X0)
| ~ stable(X0)
| greater('growth$urate'('efficient$uproducers',sK2(X0,X1)),'growth$urate'('first$umovers',sK2(X0,X1)))
| ~ greater(sK2(X0,X1),sK4(X0))
| ~ environment(X0) ),
inference(resolution,[status(thm)],[c5,c0]) ).
cnf(d_2,plain,
( greater('growth$urate'('efficient$uproducers',X0),'growth$urate'('first$umovers',X0))
| ~ 'in$uenvironment'(X1,X0)
| ~ environment(X1)
| X0 = 'critical$upoint'(X1)
| ~ stable(X1)
| greater('growth$urate'('efficient$uproducers',X0),'growth$urate'('first$umovers',X0))
| ~ greater(sK2(X1,X0),sK4(X1))
| ~ 'in$uenvironment'(X1,X0)
| ~ environment(X1)
| X0 = 'critical$upoint'(X1) ),
inference(resolution,[status(thm)],[d_1,c2]) ).
cnf(d_3,plain,
( ~ stable(X0)
| ~ 'in$uenvironment'(X0,sK4(X0))
| ~ environment(X0)
| ~ environment(X0)
| sK4(X0) = 'critical$upoint'(X0)
| ~ stable(X0)
| greater('growth$urate'('efficient$uproducers',sK4(X0)),'growth$urate'('first$umovers',sK4(X0)))
| ~ 'in$uenvironment'(X0,sK4(X0))
| ~ environment(X0)
| sK4(X0) = 'critical$upoint'(X0) ),
inference(resolution,[status(thm)],[d_2,d_0]) ).
cnf(d_4,plain,
( ~ stable(X0)
| ~ environment(X0)
| ~ stable(X0)
| ~ 'in$uenvironment'(X0,sK4(X0))
| ~ environment(X0)
| sK4(X0) = 'critical$upoint'(X0) ),
inference(resolution,[status(thm)],[d_3,c4]) ).
cnf(d_5,plain,
( ~ stable(X0)
| ~ environment(X0)
| ~ stable(X0)
| ~ environment(X0)
| sK4(X0) = 'critical$upoint'(X0) ),
inference(resolution,[status(thm)],[d_4,c3]) ).
cnf(d_6,plain,
( ~ environment(sK6)
| sK4(sK6) = 'critical$upoint'(sK6) ),
inference(resolution,[status(thm)],[d_5,c7]) ).
cnf(d_7,plain,
sK4(sK6) = 'critical$upoint'(sK6),
inference(resolution,[status(thm)],[c6,d_6]) ).
cnf(d_8,plain,
( ~ stable(sK6)
| ~ environment(sK6)
| 'in$uenvironment'(sK6,'critical$upoint'(sK6)) ),
inference(superposition,[status(thm)],[d_7,c3]) ).
cnf(d_9,plain,
( ~ stable(sK6)
| 'in$uenvironment'(sK6,'critical$upoint'(sK6)) ),
inference(resolution,[status(thm)],[c6,d_8]) ).
cnf(d_10,plain,
'in$uenvironment'(sK6,'critical$upoint'(sK6)),
inference(resolution,[status(thm)],[c7,d_9]) ).
cnf(d_11,plain,
$false,
inference(resolution,[status(thm)],[c8,d_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT023+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 00:04:07 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.22/2.38 % SZS status Theorem for theBenchmark.p
% 14.22/2.38 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------