%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : MGT020+1 : 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 : n009.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 08:01:02 AM UTC 2026
% Result : Theorem 10.76s 3.07s
% Output : CNFRefutation 10.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 54 ( 10 unt; 0 def)
% Number of atoms : 177 ( 7 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 218 ( 95 ~; 93 |; 16 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l3,axiom,
! [X0,X1] :
( ( subpopulations('first$umovers','efficient$uproducers',X0,X1)
& environment(X0) )
=> ~ decreases(difference('disbanding$urate'('first$umovers',X1),'disbanding$urate'('efficient$uproducers',X1))) ) ).
fof(mp_earliest_time_point,axiom,
! [X0,X1] :
( environment(X0)
=> ( ( subpopulations('first$umovers','efficient$uproducers',X0,X1)
=> 'greater$uor$uequal'(X1,'initial$uFM$uEP'(X0)) )
& ( 'in$uenvironment'(X0,'initial$uFM$uEP'(X0))
=> subpopulations('first$umovers','efficient$uproducers',X0,'initial$uFM$uEP'(X0)) ) ) ) ).
fof(mp_positive_function_difference,axiom,
! [X0,X1,X2,X3] :
( ( greater('disbanding$urate'('first$umovers',X2),'disbanding$urate'('efficient$uproducers',X2))
& subpopulations('first$umovers','efficient$uproducers',X0,X3)
& 'greater$uor$uequal'(X3,X1)
& 'greater$uor$uequal'(X1,X2)
& environment(X0) )
=> ( ~ decreases(difference('disbanding$urate'('first$umovers',X1),'disbanding$urate'('efficient$uproducers',X1)))
=> greater('disbanding$urate'('first$umovers',X3),'disbanding$urate'('efficient$uproducers',X3)) ) ) ).
fof(mp_time_point_occurs,axiom,
! [X0,X1] :
( ( subpopulations('first$umovers','efficient$uproducers',X0,X1)
& environment(X0) )
=> 'in$uenvironment'(X0,X1) ) ).
fof(mp_initial_time,axiom,
! [X0] :
( environment(X0)
=> 'greater$uor$uequal'('initial$uFM$uEP'(X0),'start$utime'(X0)) ) ).
fof(mp_times_in_order,axiom,
! [X0,X1,X2] :
( ( 'in$uenvironment'(X0,X2)
& greater(X2,X1)
& 'greater$uor$uequal'(X1,'start$utime'(X0))
& environment(X0) )
=> 'in$uenvironment'(X0,X1) ) ).
fof(mp_greater_or_equal,axiom,
! [X0,X1] :
( 'greater$uor$uequal'(X0,X1)
=> ( X0 = X1
| greater(X0,X1) ) ) ).
fof(a8,hypothesis,
! [X0] :
( environment(X0)
=> greater('disbanding$urate'('first$umovers','initial$uFM$uEP'(X0)),'disbanding$urate'('efficient$uproducers','initial$uFM$uEP'(X0))) ) ).
fof(a10,hypothesis,
! [X0,X1,X2,X3] :
( ( 'greater$uor$uequal'(X2,X3)
& 'greater$uor$uequal'(X3,X1)
& subpopulations('first$umovers','efficient$uproducers',X0,X2)
& subpopulations('first$umovers','efficient$uproducers',X0,X1)
& environment(X0) )
=> subpopulations('first$umovers','efficient$uproducers',X0,X3) ) ).
fof(prove_l2,conjecture,
! [X0,X1] :
( ( subpopulations('first$umovers','efficient$uproducers',X0,X1)
& environment(X0) )
=> greater('disbanding$urate'('first$umovers',X1),'disbanding$urate'('efficient$uproducers',X1)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( ( subpopulations('first$umovers','efficient$uproducers',X0,X1)
& environment(X0) )
=> greater('disbanding$urate'('first$umovers',X1),'disbanding$urate'('efficient$uproducers',X1)) ),
inference(negate_conjecture,[status(cth)],[prove_l2]) ).
cnf(c0,plain,
( ~ decreases(difference('disbanding$urate'('first$umovers',X1),'disbanding$urate'('efficient$uproducers',X1)))
| ~ subpopulations('first$umovers','efficient$uproducers',X0,X1)
| ~ environment(X0) ),
inference(clausification,[status(esa)],[l3]) ).
cnf(c1,plain,
( subpopulations('first$umovers','efficient$uproducers',X0,'initial$uFM$uEP'(X0))
| ~ 'in$uenvironment'(X0,'initial$uFM$uEP'(X0))
| ~ environment(X0) ),
inference(clausification,[status(esa)],[mp_earliest_time_point]) ).
cnf(c2,plain,
( 'greater$uor$uequal'(X1,'initial$uFM$uEP'(X0))
| ~ subpopulations('first$umovers','efficient$uproducers',X0,X1)
| ~ environment(X0) ),
inference(clausification,[status(esa)],[mp_earliest_time_point]) ).
cnf(c3,plain,
( decreases(difference('disbanding$urate'('first$umovers',X0),'disbanding$urate'('efficient$uproducers',X0)))
| ~ greater('disbanding$urate'('first$umovers',X1),'disbanding$urate'('efficient$uproducers',X1))
| ~ subpopulations('first$umovers','efficient$uproducers',X3,X2)
| greater('disbanding$urate'('first$umovers',X2),'disbanding$urate'('efficient$uproducers',X2))
| ~ environment(X3)
| ~ 'greater$uor$uequal'(X2,X0)
| ~ 'greater$uor$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[mp_positive_function_difference]) ).
cnf(c4,plain,
( 'in$uenvironment'(X0,X1)
| ~ subpopulations('first$umovers','efficient$uproducers',X0,X1)
| ~ environment(X0) ),
inference(clausification,[status(esa)],[mp_time_point_occurs]) ).
cnf(c5,plain,
( 'greater$uor$uequal'('initial$uFM$uEP'(X0),'start$utime'(X0))
| ~ environment(X0) ),
inference(clausification,[status(esa)],[mp_initial_time]) ).
cnf(c6,plain,
( ~ 'greater$uor$uequal'(X1,'start$utime'(X2))
| ~ environment(X2)
| 'in$uenvironment'(X2,X1)
| ~ 'in$uenvironment'(X2,X0)
| ~ greater(X0,X1) ),
inference(clausification,[status(esa)],[mp_times_in_order]) ).
cnf(c8,plain,
( X0 = X1
| greater(X0,X1)
| ~ 'greater$uor$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[mp_greater_or_equal]) ).
cnf(c9,plain,
( greater('disbanding$urate'('first$umovers','initial$uFM$uEP'(X0)),'disbanding$urate'('efficient$uproducers','initial$uFM$uEP'(X0)))
| ~ environment(X0) ),
inference(clausification,[status(esa)],[a8]) ).
cnf(c10,plain,
( subpopulations('first$umovers','efficient$uproducers',X2,X1)
| ~ 'greater$uor$uequal'(X1,X3)
| ~ subpopulations('first$umovers','efficient$uproducers',X2,X0)
| ~ subpopulations('first$umovers','efficient$uproducers',X2,X3)
| ~ environment(X2)
| ~ 'greater$uor$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[a10]) ).
cnf(c11,plain,
environment(sK24),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c12,plain,
subpopulations('first$umovers','efficient$uproducers',sK24,sK25),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c13,plain,
~ greater('disbanding$urate'('first$umovers',sK25),'disbanding$urate'('efficient$uproducers',sK25)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'greater$uor$uequal'(sK25,'initial$uFM$uEP'(sK24))
| ~ environment(sK24) ),
inference(resolution,[status(thm)],[c2,c12]) ).
cnf(d1,plain,
'greater$uor$uequal'(sK25,'initial$uFM$uEP'(sK24)),
inference(resolution,[status(thm)],[c11,d0]) ).
cnf(d2,plain,
( greater(sK25,'initial$uFM$uEP'(sK24))
| sK25 = 'initial$uFM$uEP'(sK24) ),
inference(resolution,[status(thm)],[c8,d1]) ).
cnf(d3,plain,
( ~ environment(X0)
| ~ greater(X1,'initial$uFM$uEP'(X0))
| ~ 'in$uenvironment'(X0,X1)
| 'in$uenvironment'(X0,'initial$uFM$uEP'(X0))
| ~ environment(X0) ),
inference(resolution,[status(thm)],[c6,c5]) ).
cnf(d4,plain,
( sK25 = 'initial$uFM$uEP'(sK24)
| 'in$uenvironment'(sK24,'initial$uFM$uEP'(sK24))
| ~ 'in$uenvironment'(sK24,sK25)
| ~ environment(sK24) ),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
( ~ 'in$uenvironment'(sK24,sK25)
| 'in$uenvironment'(sK24,'initial$uFM$uEP'(sK24))
| sK25 = 'initial$uFM$uEP'(sK24) ),
inference(resolution,[status(thm)],[c11,d4]) ).
cnf(d6,plain,
( 'in$uenvironment'(sK24,sK25)
| ~ environment(sK24) ),
inference(resolution,[status(thm)],[c4,c12]) ).
cnf(d7,plain,
'in$uenvironment'(sK24,sK25),
inference(resolution,[status(thm)],[c11,d6]) ).
cnf(d8,plain,
( 'in$uenvironment'(sK24,'initial$uFM$uEP'(sK24))
| sK25 = 'initial$uFM$uEP'(sK24) ),
inference(resolution,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
( ~ 'in$uenvironment'(X0,'initial$uFM$uEP'(X0))
| ~ environment(X0)
| 'greater$uor$uequal'('initial$uFM$uEP'(X0),'initial$uFM$uEP'(X0))
| ~ environment(X0) ),
inference(resolution,[status(thm)],[c2,c1]) ).
cnf(d10,plain,
( greater('disbanding$urate'('first$umovers',X3),'disbanding$urate'('efficient$uproducers',X3))
| ~ 'greater$uor$uequal'(X2,'initial$uFM$uEP'(X0))
| ~ 'greater$uor$uequal'(X3,X2)
| ~ subpopulations('first$umovers','efficient$uproducers',X1,X3)
| decreases(difference('disbanding$urate'('first$umovers',X2),'disbanding$urate'('efficient$uproducers',X2)))
| ~ environment(X1)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[c9,c3]) ).
cnf(d11,plain,
( greater('disbanding$urate'('first$umovers',sK25),'disbanding$urate'('efficient$uproducers',sK25))
| ~ 'greater$uor$uequal'(X1,'initial$uFM$uEP'(X0))
| ~ 'greater$uor$uequal'(sK25,X1)
| decreases(difference('disbanding$urate'('first$umovers',X1),'disbanding$urate'('efficient$uproducers',X1)))
| ~ environment(X0)
| ~ environment(sK24) ),
inference(resolution,[status(thm)],[d10,c12]) ).
cnf(d12,plain,
( greater('disbanding$urate'('first$umovers',sK25),'disbanding$urate'('efficient$uproducers',sK25))
| ~ 'greater$uor$uequal'(sK25,X1)
| ~ 'greater$uor$uequal'(X1,'initial$uFM$uEP'(X0))
| decreases(difference('disbanding$urate'('first$umovers',X1),'disbanding$urate'('efficient$uproducers',X1)))
| ~ environment(X0) ),
inference(resolution,[status(thm)],[c11,d11]) ).
cnf(d13,plain,
( ~ 'greater$uor$uequal'(sK25,X1)
| ~ 'greater$uor$uequal'(X1,'initial$uFM$uEP'(X0))
| decreases(difference('disbanding$urate'('first$umovers',X1),'disbanding$urate'('efficient$uproducers',X1)))
| ~ environment(X0) ),
inference(resolution,[status(thm)],[c13,d12]) ).
cnf(d14,plain,
( ~ 'in$uenvironment'(X0,'initial$uFM$uEP'(X0))
| ~ environment(X0)
| ~ 'greater$uor$uequal'(sK25,'initial$uFM$uEP'(X0))
| decreases(difference('disbanding$urate'('first$umovers','initial$uFM$uEP'(X0)),'disbanding$urate'('efficient$uproducers','initial$uFM$uEP'(X0))))
| ~ environment(X0) ),
inference(resolution,[status(thm)],[d13,d9]) ).
cnf(d15,plain,
( ~ subpopulations('first$umovers','efficient$uproducers',X1,'initial$uFM$uEP'(X0))
| ~ environment(X1)
| ~ 'greater$uor$uequal'(sK25,'initial$uFM$uEP'(X0))
| ~ 'in$uenvironment'(X0,'initial$uFM$uEP'(X0))
| ~ environment(X0) ),
inference(resolution,[status(thm)],[d14,c0]) ).
cnf(d16,plain,
( ~ 'in$uenvironment'(X0,'initial$uFM$uEP'(X0))
| ~ environment(X0)
| ~ 'greater$uor$uequal'(sK25,'initial$uFM$uEP'(X0))
| ~ 'in$uenvironment'(X0,'initial$uFM$uEP'(X0))
| ~ environment(X0)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[d15,c1]) ).
cnf(d17,plain,
( ~ 'in$uenvironment'(sK24,'initial$uFM$uEP'(sK24))
| ~ environment(sK24) ),
inference(resolution,[status(thm)],[d16,d1]) ).
cnf(d18,plain,
~ 'in$uenvironment'(sK24,'initial$uFM$uEP'(sK24)),
inference(resolution,[status(thm)],[c11,d17]) ).
cnf(d19,plain,
sK25 = 'initial$uFM$uEP'(sK24),
inference(resolution,[status(thm)],[d18,d8]) ).
cnf(d20,plain,
'greater$uor$uequal'(sK25,sK25),
inference(demodulation,[status(thm)],[d1,d19]) ).
cnf(d21,plain,
( ~ 'greater$uor$uequal'(X1,X0)
| ~ 'greater$uor$uequal'(X0,sK25)
| ~ subpopulations('first$umovers','efficient$uproducers',sK24,X1)
| subpopulations('first$umovers','efficient$uproducers',sK24,X0)
| ~ environment(sK24) ),
inference(resolution,[status(thm)],[c10,c12]) ).
cnf(d22,plain,
( ~ 'greater$uor$uequal'(X1,sK25)
| ~ 'greater$uor$uequal'(X0,X1)
| subpopulations('first$umovers','efficient$uproducers',sK24,X1)
| ~ subpopulations('first$umovers','efficient$uproducers',sK24,X0) ),
inference(resolution,[status(thm)],[c11,d21]) ).
cnf(d23,plain,
( ~ 'greater$uor$uequal'(sK25,X0)
| ~ 'greater$uor$uequal'(X0,sK25)
| subpopulations('first$umovers','efficient$uproducers',sK24,X0) ),
inference(resolution,[status(thm)],[d22,c12]) ).
cnf(d24,plain,
( ~ 'greater$uor$uequal'(sK25,sK25)
| decreases(difference('disbanding$urate'('first$umovers',sK25),'disbanding$urate'('efficient$uproducers',sK25)))
| ~ environment(sK24) ),
inference(resolution,[status(thm)],[d13,d1]) ).
cnf(d25,plain,
( ~ 'greater$uor$uequal'(sK25,sK25)
| decreases(difference('disbanding$urate'('first$umovers',sK25),'disbanding$urate'('efficient$uproducers',sK25))) ),
inference(resolution,[status(thm)],[c11,d24]) ).
cnf(d26,plain,
( ~ subpopulations('first$umovers','efficient$uproducers',X0,sK25)
| ~ environment(X0)
| ~ 'greater$uor$uequal'(sK25,sK25) ),
inference(resolution,[status(thm)],[d25,c0]) ).
cnf(d27,plain,
( ~ 'greater$uor$uequal'(sK25,sK25)
| ~ 'greater$uor$uequal'(sK25,sK25)
| ~ 'greater$uor$uequal'(sK25,sK25)
| ~ environment(sK24) ),
inference(resolution,[status(thm)],[d26,d23]) ).
cnf(d28,plain,
~ 'greater$uor$uequal'(sK25,sK25),
inference(resolution,[status(thm)],[c11,d27]) ).
cnf(d29,plain,
$false,
inference(resolution,[status(thm)],[d28,d20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT020+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n009.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 00:04:00 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.76/3.07 % SZS status Theorem for theBenchmark.p
% 10.76/3.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------