%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : MGT036+3 : 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 08:01:17 AM UTC 2026
% Result : Theorem 12.28s 2.55s
% Output : CNFRefutation 12.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 8 unt; 0 def)
% Number of atoms : 50 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 51 ( 22 ~; 16 |; 10 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 8 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mp_symmetry_of_subpopulations,axiom,
! [X0,X1,X2,X3] :
( ( subpopulations(X1,X2,X0,X3)
& environment(X0) )
=> subpopulations(X2,X1,X0,X3) ) ).
fof(d2,hypothesis,
! [X0,X1,X2,X3] :
( ( subpopulations(X1,X2,X0,X3)
& environment(X0) )
=> ( ( greater(zero,'growth$urate'(X1,X3))
& 'greater$uor$uequal'('growth$urate'(X2,X3),zero) )
<=> outcompetes(X2,X1,X3) ) ) ).
fof(a13_star,hypothesis,
? [X0,X1] :
( greater(zero,'growth$urate'('efficient$uproducers',X1))
& 'greater$uor$uequal'('growth$urate'('first$umovers',X1),zero)
& subpopulations('first$umovers','efficient$uproducers',X0,X1)
& environment(X0) ) ).
fof(prove_t5_star,conjecture,
? [X0,X1] :
( outcompetes('first$umovers','efficient$uproducers',X1)
& subpopulations('first$umovers','efficient$uproducers',X0,X1)
& environment(X0) ) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0,X1] :
( outcompetes('first$umovers','efficient$uproducers',X1)
& subpopulations('first$umovers','efficient$uproducers',X0,X1)
& environment(X0) ),
inference(negate_conjecture,[status(cth)],[prove_t5_star]) ).
cnf(c0,plain,
( subpopulations(X2,X1,X0,X3)
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(clausification,[status(esa)],[mp_symmetry_of_subpopulations]) ).
cnf(c1,plain,
( ~ environment(X3)
| outcompetes(X2,X0,X1)
| ~ 'greater$uor$uequal'('growth$urate'(X2,X1),zero)
| ~ subpopulations(X0,X2,X3,X1)
| ~ greater(zero,'growth$urate'(X0,X1)) ),
inference(clausification,[status(esa)],[d2]) ).
cnf(c4,plain,
environment(sK8),
inference(clausification,[status(esa)],[a13_star]) ).
cnf(c5,plain,
subpopulations('first$umovers','efficient$uproducers',sK8,sK9),
inference(clausification,[status(esa)],[a13_star]) ).
cnf(c6,plain,
'greater$uor$uequal'('growth$urate'('first$umovers',sK9),zero),
inference(clausification,[status(esa)],[a13_star]) ).
cnf(c7,plain,
greater(zero,'growth$urate'('efficient$uproducers',sK9)),
inference(clausification,[status(esa)],[a13_star]) ).
cnf(c8,plain,
( ~ outcompetes('first$umovers','efficient$uproducers',X1)
| ~ subpopulations('first$umovers','efficient$uproducers',X0,X1)
| ~ environment(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d_0,plain,
( subpopulations('efficient$uproducers','first$umovers',sK8,sK9)
| ~ environment(sK8) ),
inference(resolution,[status(thm)],[c5,c0]) ).
cnf(d_1,plain,
subpopulations('efficient$uproducers','first$umovers',sK8,sK9),
inference(resolution,[status(thm)],[c4,d_0]) ).
cnf(d_2,plain,
( outcompetes('first$umovers',X1,sK9)
| ~ greater(zero,'growth$urate'(X1,sK9))
| ~ subpopulations(X1,'first$umovers',X0,sK9)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[c6,c1]) ).
cnf(d_3,plain,
( outcompetes('first$umovers','efficient$uproducers',sK9)
| ~ subpopulations('efficient$uproducers','first$umovers',X0,sK9)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[d_2,c7]) ).
cnf(d_4,plain,
( ~ outcompetes('first$umovers','efficient$uproducers',sK9)
| ~ environment(sK8) ),
inference(resolution,[status(thm)],[c5,c8]) ).
cnf(d_5,plain,
~ outcompetes('first$umovers','efficient$uproducers',sK9),
inference(resolution,[status(thm)],[c4,d_4]) ).
cnf(d_6,plain,
( ~ subpopulations('efficient$uproducers','first$umovers',X0,sK9)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[d_5,d_3]) ).
cnf(d_7,plain,
~ environment(sK8),
inference(resolution,[status(thm)],[d_6,d_1]) ).
cnf(d_8,plain,
$false,
inference(resolution,[status(thm)],[c4,d_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : MGT036+3 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.46 % Computer : n013.cluster.edu
% 0.21/0.46 % Model : x86_64 x86_64
% 0.21/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.46 % Memory : 8046.5625MB
% 0.21/0.46 % OS : Linux 6.8.0-71-generic
% 0.21/0.46 % CPULimit : 300
% 0.21/0.46 % WCLimit : 300
% 0.21/0.46 % DateTime : Sat Sep 26 00:05:51 UTC 2026
% 0.21/0.46 % CPUTime :
% 0.21/0.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.28/2.55 % SZS status Theorem for theBenchmark.p
% 12.28/2.55 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------