%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : MGT032+2 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 08:01:16 AM UTC 2026
% Result : Theorem 7.90s 11.68s
% Output : CNFRefutation 7.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 4 unt; 0 def)
% Number of atoms : 76 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 93 ( 40 ~; 35 |; 11 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 10 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mp1_high_growth_rates,axiom,
! [X0,X1,X2,X3] :
( ( greater('growth$urate'(X2,X3),'growth$urate'(X1,X3))
& subpopulations(X1,X2,X0,X3)
& environment(X0) )
=> 'selection$ufavors'(X2,X1,X3) ) ).
fof(l1,hypothesis,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X1] :
( ! [X2] :
( ( 'greater$uor$uequal'(X2,X1)
& subpopulations('first$umovers','efficient$uproducers',X0,X2) )
=> greater('growth$urate'('efficient$uproducers',X2),'growth$urate'('first$umovers',X2)) )
& 'in$uenvironment'(X0,X1) ) ) ).
fof(prove_t1,conjecture,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X1] :
( ! [X2] :
( ( 'greater$uor$uequal'(X2,X1)
& subpopulations('first$umovers','efficient$uproducers',X0,X2) )
=> 'selection$ufavors'('efficient$uproducers','first$umovers',X2) )
& 'in$uenvironment'(X0,X1) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X1] :
( ! [X2] :
( ( 'greater$uor$uequal'(X2,X1)
& subpopulations('first$umovers','efficient$uproducers',X0,X2) )
=> 'selection$ufavors'('efficient$uproducers','first$umovers',X2) )
& 'in$uenvironment'(X0,X1) ) ),
inference(negate_conjecture,[status(cth)],[prove_t1]) ).
cnf(c0,plain,
( 'selection$ufavors'(X2,X1,X3)
| ~ greater('growth$urate'(X2,X3),'growth$urate'(X1,X3))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(clausification,[status(esa)],[mp1_high_growth_rates]) ).
cnf(c1,plain,
( 'in$uenvironment'(X0,sK5(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(clausification,[status(esa)],[l1]) ).
cnf(c2,plain,
( ~ 'greater$uor$uequal'(X0,sK5(X1))
| ~ subpopulations('first$umovers','efficient$uproducers',X1,X0)
| ~ environment(X1)
| ~ stable(X1)
| greater('growth$urate'('efficient$uproducers',X0),'growth$urate'('first$umovers',X0)) ),
inference(clausification,[status(esa)],[l1]) ).
cnf(c3,plain,
environment(sK7),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c4,plain,
stable(sK7),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c5,plain,
( subpopulations('first$umovers','efficient$uproducers',sK7,sK9(X0))
| ~ 'in$uenvironment'(sK7,X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c6,plain,
( 'greater$uor$uequal'(sK9(X0),X0)
| ~ 'in$uenvironment'(sK7,X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c7,plain,
( ~ 'selection$ufavors'('efficient$uproducers','first$umovers',sK9(X0))
| ~ 'in$uenvironment'(sK7,X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'greater$uor$uequal'(sK9(X0),sK5(sK7))
| ~ stable(sK7)
| ~ environment(sK7)
| greater('growth$urate'('efficient$uproducers',sK9(X0)),'growth$urate'('first$umovers',sK9(X0)))
| ~ 'in$uenvironment'(sK7,X0) ),
inference(resolution,[status(thm)],[c5,c2]) ).
cnf(d1,plain,
( ~ 'greater$uor$uequal'(sK9(X0),sK5(sK7))
| ~ 'in$uenvironment'(sK7,X0)
| ~ stable(sK7)
| greater('growth$urate'('efficient$uproducers',sK9(X0)),'growth$urate'('first$umovers',sK9(X0))) ),
inference(resolution,[status(thm)],[c3,d0]) ).
cnf(d2,plain,
( ~ 'greater$uor$uequal'(sK9(X0),sK5(sK7))
| ~ 'in$uenvironment'(sK7,X0)
| greater('growth$urate'('efficient$uproducers',sK9(X0)),'growth$urate'('first$umovers',sK9(X0))) ),
inference(resolution,[status(thm)],[c4,d1]) ).
cnf(d3,plain,
( 'selection$ufavors'('efficient$uproducers','first$umovers',sK9(X0))
| ~ subpopulations('first$umovers','efficient$uproducers',X1,sK9(X0))
| ~ environment(X1)
| ~ 'greater$uor$uequal'(sK9(X0),sK5(sK7))
| ~ 'in$uenvironment'(sK7,X0) ),
inference(resolution,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
( ~ 'in$uenvironment'(sK7,X0)
| ~ 'greater$uor$uequal'(sK9(X0),sK5(sK7))
| ~ 'in$uenvironment'(sK7,X0)
| 'selection$ufavors'('efficient$uproducers','first$umovers',sK9(X0))
| ~ environment(sK7) ),
inference(resolution,[status(thm)],[d3,c5]) ).
cnf(d5,plain,
( ~ 'greater$uor$uequal'(sK9(X0),sK5(sK7))
| ~ 'in$uenvironment'(sK7,X0)
| 'selection$ufavors'('efficient$uproducers','first$umovers',sK9(X0)) ),
inference(resolution,[status(thm)],[c3,d4]) ).
cnf(d6,plain,
( ~ 'in$uenvironment'(sK7,sK5(sK7))
| ~ 'in$uenvironment'(sK7,sK5(sK7))
| 'selection$ufavors'('efficient$uproducers','first$umovers',sK9(sK5(sK7))) ),
inference(resolution,[status(thm)],[d5,c6]) ).
cnf(d7,plain,
( ~ 'in$uenvironment'(sK7,sK5(sK7))
| ~ 'in$uenvironment'(sK7,sK5(sK7)) ),
inference(resolution,[status(thm)],[d6,c7]) ).
cnf(d8,plain,
( ~ stable(sK7)
| ~ environment(sK7) ),
inference(resolution,[status(thm)],[d7,c1]) ).
cnf(d9,plain,
~ stable(sK7),
inference(resolution,[status(thm)],[c3,d8]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[c4,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT032+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/10.37 % Computer : n001.cluster.edu
% 0.09/10.37 % Model : x86_64 x86_64
% 0.09/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.37 % Memory : 8046.5625MB
% 0.09/10.37 % OS : Linux 6.8.0-71-generic
% 0.09/10.37 % CPULimit : 300
% 0.09/10.37 % WCLimit : 300
% 0.09/10.37 % DateTime : Sat Sep 26 00:11:08 UTC 2026
% 0.09/10.37 % CPUTime :
% 0.09/10.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.90/11.68 % SZS status Theorem for theBenchmark.p
% 7.90/11.68 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------