%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : MGT026+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 : n018.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 08:01:04 AM UTC 2026
% Result : Theorem 12.61s 2.01s
% Output : CNFRefutation 12.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 11
% Syntax : Number of formulae : 84 ( 10 unt; 0 def)
% Number of atoms : 311 ( 61 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 384 ( 157 ~; 192 |; 22 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 100 ( 0 sgn 29 !; 0 ?)
% 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$ufavors'(X2,X1,X3) ) ).
fof(mp2_favour_members,axiom,
! [X0,X1,X2,X3] :
( ( 'cardinality$uat$utime'(X2,X3) = zero
& greater('cardinality$uat$utime'(X1,X3),zero)
& subpopulation(X2,X0,X3)
& subpopulation(X1,X0,X3)
& environment(X0) )
=> 'selection$ufavors'(X1,X2,X3) ) ).
fof(mp_non_empty_fm_and_ep,axiom,
! [X0,X1] :
( ( greater('cardinality$uat$utime'('efficient$uproducers',X1),zero)
& greater('cardinality$uat$utime'('first$umovers',X1),zero)
& 'in$uenvironment'(X0,X1)
& environment(X0) )
=> subpopulations('first$umovers','efficient$uproducers',X0,X1) ) ).
fof(mp_first_movers_exist,axiom,
! [X0,X1] :
( ( 'in$uenvironment'(X0,X1)
& environment(X0) )
=> 'greater$uor$uequal'('cardinality$uat$utime'('first$umovers',X1),zero) ) ).
fof(mp_subpopulations,axiom,
! [X0,X1] :
( ( 'in$uenvironment'(X0,X1)
& environment(X0) )
=> ( subpopulation('efficient$uproducers',X0,X1)
& subpopulation('first$umovers',X0,X1) ) ) ).
fof(mp_critical_point_after_EP,axiom,
! [X0] :
( environment(X0)
=> 'greater$uor$uequal'('critical$upoint'(X0),appear('efficient$uproducers',X0)) ) ).
fof(mp_greater_transitivity,axiom,
! [X0,X1,X2] :
( ( greater(X1,X2)
& greater(X0,X1) )
=> greater(X0,X2) ) ).
fof(mp_greater_or_equal,axiom,
! [X0,X1] :
( 'greater$uor$uequal'(X0,X1)
<=> ( X0 = X1
| greater(X0,X1) ) ) ).
fof(d1,hypothesis,
! [X0,X1] :
( ( X1 = 'critical$upoint'(X0)
& environment(X0) )
=> ( ! [X2] :
( ( greater(X2,X1)
& subpopulations('first$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$umovers',X1)) ) ) ).
fof(t6,hypothesis,
! [X0,X1] :
( ( 'greater$uor$uequal'(X1,appear('efficient$uproducers',X0))
& 'in$uenvironment'(X0,X1)
& environment(X0) )
=> greater('cardinality$uat$utime'('efficient$uproducers',X1),zero) ) ).
fof(prove_l8,conjecture,
! [X0,X1] :
( ( greater(X1,'critical$upoint'(X0))
& 'in$uenvironment'(X0,X1)
& environment(X0) )
=> 'selection$ufavors'('efficient$uproducers','first$umovers',X1) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( ( greater(X1,'critical$upoint'(X0))
& 'in$uenvironment'(X0,X1)
& environment(X0) )
=> 'selection$ufavors'('efficient$uproducers','first$umovers',X1) ),
inference(negate_conjecture,[status(cth)],[prove_l8]) ).
cnf(c0,plain,
( 'selection$ufavors'(X2,X1,X3)
| ~ greater('growth$urate'(X2,X3),'growth$urate'(X1,X3))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(clausification,[status(esa)],[mp1_high_growth_rates]) ).
cnf(c1,plain,
( ~ environment(X3)
| 'cardinality$uat$utime'(X1,X2) != zero
| ~ greater('cardinality$uat$utime'(X0,X2),zero)
| ~ subpopulation(X1,X3,X2)
| ~ subpopulation(X0,X3,X2)
| 'selection$ufavors'(X0,X1,X2) ),
inference(clausification,[status(esa)],[mp2_favour_members]) ).
cnf(c2,plain,
( subpopulations('first$umovers','efficient$uproducers',X1,X0)
| ~ greater('cardinality$uat$utime'('first$umovers',X0),zero)
| ~ environment(X1)
| ~ 'in$uenvironment'(X1,X0)
| ~ greater('cardinality$uat$utime'('efficient$uproducers',X0),zero) ),
inference(clausification,[status(esa)],[mp_non_empty_fm_and_ep]) ).
cnf(c3,plain,
( 'greater$uor$uequal'('cardinality$uat$utime'('first$umovers',X1),zero)
| ~ 'in$uenvironment'(X0,X1)
| ~ environment(X0) ),
inference(clausification,[status(esa)],[mp_first_movers_exist]) ).
cnf(c4,plain,
( subpopulation('first$umovers',X0,X1)
| ~ 'in$uenvironment'(X0,X1)
| ~ environment(X0) ),
inference(clausification,[status(esa)],[mp_subpopulations]) ).
cnf(c5,plain,
( subpopulation('efficient$uproducers',X0,X1)
| ~ 'in$uenvironment'(X0,X1)
| ~ environment(X0) ),
inference(clausification,[status(esa)],[mp_subpopulations]) ).
cnf(c6,plain,
( 'greater$uor$uequal'('critical$upoint'(X0),appear('efficient$uproducers',X0))
| ~ environment(X0) ),
inference(clausification,[status(esa)],[mp_critical_point_after_EP]) ).
cnf(c7,plain,
( greater(X0,X2)
| ~ greater(X1,X2)
| ~ greater(X0,X1) ),
inference(clausification,[status(esa)],[mp_greater_transitivity]) ).
cnf(c8,plain,
( X0 = X1
| greater(X0,X1)
| ~ 'greater$uor$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[mp_greater_or_equal]) ).
cnf(c9,plain,
( ~ greater(X0,X1)
| 'greater$uor$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[mp_greater_or_equal]) ).
cnf(c12,plain,
( ~ greater(X1,X2)
| X2 != 'critical$upoint'(X0)
| ~ subpopulations('first$umovers','efficient$uproducers',X0,X1)
| greater('growth$urate'('efficient$uproducers',X1),'growth$urate'('first$umovers',X1))
| ~ environment(X0) ),
inference(clausification,[status(esa)],[d1]) ).
cnf(c13,plain,
( greater('cardinality$uat$utime'('efficient$uproducers',X1),zero)
| ~ 'greater$uor$uequal'(X1,appear('efficient$uproducers',X0))
| ~ 'in$uenvironment'(X0,X1)
| ~ environment(X0) ),
inference(clausification,[status(esa)],[t6]) ).
cnf(c14,plain,
environment(sK25),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c15,plain,
'in$uenvironment'(sK25,sK26),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c16,plain,
greater(sK26,'critical$upoint'(sK25)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c17,plain,
~ 'selection$ufavors'('efficient$uproducers','first$umovers',sK26),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d_0,plain,
( 'greater$uor$uequal'('cardinality$uat$utime'('first$umovers',sK26),zero)
| ~ environment(sK25) ),
inference(resolution,[status(thm)],[c3,c15]) ).
cnf(d_1,plain,
'greater$uor$uequal'('cardinality$uat$utime'('first$umovers',sK26),zero),
inference(resolution,[status(thm)],[c14,d_0]) ).
cnf(d_2,plain,
( greater('cardinality$uat$utime'('first$umovers',sK26),zero)
| 'cardinality$uat$utime'('first$umovers',sK26) = zero ),
inference(resolution,[status(thm)],[c8,d_1]) ).
cnf(d_3,plain,
( ~ environment(X0)
| greater('critical$upoint'(X0),appear('efficient$uproducers',X0))
| 'critical$upoint'(X0) = appear('efficient$uproducers',X0) ),
inference(resolution,[status(thm)],[c8,c6]) ).
cnf(d_4,plain,
( ~ greater(X1,'critical$upoint'(X0))
| greater(X1,appear('efficient$uproducers',X0))
| ~ environment(X0)
| 'critical$upoint'(X0) = appear('efficient$uproducers',X0) ),
inference(resolution,[status(thm)],[d_3,c7]) ).
cnf(d_5,plain,
( 'greater$uor$uequal'(X1,appear('efficient$uproducers',X0))
| ~ environment(X0)
| ~ greater(X1,'critical$upoint'(X0))
| 'critical$upoint'(X0) = appear('efficient$uproducers',X0) ),
inference(resolution,[status(thm)],[d_4,c9]) ).
cnf(d_6,plain,
( ~ 'in$uenvironment'(X0,X1)
| ~ environment(X0)
| greater('cardinality$uat$utime'('efficient$uproducers',X1),zero)
| ~ environment(X0)
| ~ greater(X1,'critical$upoint'(X0))
| 'critical$upoint'(X0) = appear('efficient$uproducers',X0) ),
inference(resolution,[status(thm)],[d_5,c13]) ).
cnf(d_7,plain,
( ~ 'in$uenvironment'(sK25,sK26)
| ~ environment(sK25)
| greater('cardinality$uat$utime'('efficient$uproducers',sK26),zero)
| 'critical$upoint'(sK25) = appear('efficient$uproducers',sK25) ),
inference(resolution,[status(thm)],[d_6,c16]) ).
cnf(d_8,plain,
( ~ 'in$uenvironment'(sK25,sK26)
| greater('cardinality$uat$utime'('efficient$uproducers',sK26),zero)
| 'critical$upoint'(sK25) = appear('efficient$uproducers',sK25) ),
inference(resolution,[status(thm)],[c14,d_7]) ).
cnf(d_9,plain,
( greater('cardinality$uat$utime'('efficient$uproducers',sK26),zero)
| 'critical$upoint'(sK25) = appear('efficient$uproducers',sK25) ),
inference(resolution,[status(thm)],[c15,d_8]) ).
cnf(d_10,plain,
( ~ 'in$uenvironment'(X0,sK26)
| subpopulations('first$umovers','efficient$uproducers',X0,sK26)
| ~ environment(X0)
| ~ greater('cardinality$uat$utime'('first$umovers',sK26),zero)
| 'critical$upoint'(sK25) = appear('efficient$uproducers',sK25) ),
inference(resolution,[status(thm)],[d_9,c2]) ).
cnf(d_11,plain,
( 'cardinality$uat$utime'('first$umovers',sK26) = zero
| ~ 'in$uenvironment'(X0,sK26)
| subpopulations('first$umovers','efficient$uproducers',X0,sK26)
| ~ environment(X0)
| 'critical$upoint'(sK25) = appear('efficient$uproducers',sK25) ),
inference(resolution,[status(thm)],[d_10,d_2]) ).
cnf(d_12,plain,
( ~ subpopulations('first$umovers','efficient$uproducers',X1,X0)
| ~ environment(X1)
| greater('growth$urate'('efficient$uproducers',X0),'growth$urate'('first$umovers',X0))
| ~ greater(X0,'critical$upoint'(X1)) ),
inference(equality_resolution,[status(thm)],[c12]) ).
cnf(d_13,plain,
( ~ environment(X0)
| greater('growth$urate'('efficient$uproducers',sK26),'growth$urate'('first$umovers',sK26))
| ~ greater(sK26,'critical$upoint'(X0))
| ~ 'in$uenvironment'(X0,sK26)
| ~ environment(X0)
| 'critical$upoint'(sK25) = appear('efficient$uproducers',sK25)
| 'cardinality$uat$utime'('first$umovers',sK26) = zero ),
inference(resolution,[status(thm)],[d_11,d_12]) ).
cnf(d_14,plain,
( ~ 'in$uenvironment'(sK25,sK26)
| ~ environment(sK25)
| greater('growth$urate'('efficient$uproducers',sK26),'growth$urate'('first$umovers',sK26))
| 'critical$upoint'(sK25) = appear('efficient$uproducers',sK25)
| 'cardinality$uat$utime'('first$umovers',sK26) = zero ),
inference(resolution,[status(thm)],[d_13,c16]) ).
cnf(d_15,plain,
( ~ 'in$uenvironment'(sK25,sK26)
| greater('growth$urate'('efficient$uproducers',sK26),'growth$urate'('first$umovers',sK26))
| 'critical$upoint'(sK25) = appear('efficient$uproducers',sK25)
| 'cardinality$uat$utime'('first$umovers',sK26) = zero ),
inference(resolution,[status(thm)],[c14,d_14]) ).
cnf(d_16,plain,
( greater('growth$urate'('efficient$uproducers',sK26),'growth$urate'('first$umovers',sK26))
| 'critical$upoint'(sK25) = appear('efficient$uproducers',sK25)
| 'cardinality$uat$utime'('first$umovers',sK26) = zero ),
inference(resolution,[status(thm)],[c15,d_15]) ).
cnf(d_17,plain,
( 'selection$ufavors'('efficient$uproducers','first$umovers',sK26)
| ~ subpopulations('first$umovers','efficient$uproducers',X0,sK26)
| ~ environment(X0)
| 'critical$upoint'(sK25) = appear('efficient$uproducers',sK25)
| 'cardinality$uat$utime'('first$umovers',sK26) = zero ),
inference(resolution,[status(thm)],[d_16,c0]) ).
cnf(d_18,plain,
( ~ subpopulations('first$umovers','efficient$uproducers',X0,sK26)
| ~ environment(X0)
| 'critical$upoint'(sK25) = appear('efficient$uproducers',sK25)
| 'cardinality$uat$utime'('first$umovers',sK26) = zero ),
inference(resolution,[status(thm)],[c17,d_17]) ).
cnf(d_19,plain,
( ~ 'in$uenvironment'(X0,sK26)
| ~ environment(X0)
| 'critical$upoint'(sK25) = appear('efficient$uproducers',sK25)
| 'cardinality$uat$utime'('first$umovers',sK26) = zero
| ~ environment(X0)
| 'critical$upoint'(sK25) = appear('efficient$uproducers',sK25)
| 'cardinality$uat$utime'('first$umovers',sK26) = zero ),
inference(resolution,[status(thm)],[d_18,d_11]) ).
cnf(d_20,plain,
( ~ environment(sK25)
| 'critical$upoint'(sK25) = appear('efficient$uproducers',sK25)
| 'cardinality$uat$utime'('first$umovers',sK26) = zero ),
inference(resolution,[status(thm)],[d_19,c15]) ).
cnf(d_21,plain,
( 'critical$upoint'(sK25) = appear('efficient$uproducers',sK25)
| 'cardinality$uat$utime'('first$umovers',sK26) = zero ),
inference(resolution,[status(thm)],[c14,d_20]) ).
cnf(d_22,plain,
( 'cardinality$uat$utime'('first$umovers',sK26) = zero
| ~ 'in$uenvironment'(sK25,X0)
| ~ environment(sK25)
| greater('cardinality$uat$utime'('efficient$uproducers',X0),zero)
| ~ 'greater$uor$uequal'(X0,'critical$upoint'(sK25)) ),
inference(superposition,[status(thm)],[d_21,c13]) ).
cnf(d_23,plain,
( ~ 'greater$uor$uequal'(X0,'critical$upoint'(sK25))
| ~ 'in$uenvironment'(sK25,X0)
| greater('cardinality$uat$utime'('efficient$uproducers',X0),zero)
| 'cardinality$uat$utime'('first$umovers',sK26) = zero ),
inference(resolution,[status(thm)],[c14,d_22]) ).
cnf(d_24,plain,
( ~ 'in$uenvironment'(X1,X0)
| subpopulations('first$umovers','efficient$uproducers',X1,X0)
| ~ environment(X1)
| ~ greater('cardinality$uat$utime'('first$umovers',X0),zero)
| ~ 'greater$uor$uequal'(X0,'critical$upoint'(sK25))
| ~ 'in$uenvironment'(sK25,X0)
| 'cardinality$uat$utime'('first$umovers',sK26) = zero ),
inference(resolution,[status(thm)],[d_23,c2]) ).
cnf(d_25,plain,
( 'cardinality$uat$utime'('first$umovers',sK26) = zero
| ~ 'greater$uor$uequal'(sK26,'critical$upoint'(sK25))
| ~ 'in$uenvironment'(sK25,sK26)
| ~ 'in$uenvironment'(X0,sK26)
| subpopulations('first$umovers','efficient$uproducers',X0,sK26)
| ~ environment(X0)
| 'cardinality$uat$utime'('first$umovers',sK26) = zero ),
inference(resolution,[status(thm)],[d_24,d_2]) ).
cnf(d_26,plain,
( ~ 'greater$uor$uequal'(sK26,'critical$upoint'(sK25))
| ~ 'in$uenvironment'(X0,sK26)
| subpopulations('first$umovers','efficient$uproducers',X0,sK26)
| ~ environment(X0)
| 'cardinality$uat$utime'('first$umovers',sK26) = zero ),
inference(resolution,[status(thm)],[c15,d_25]) ).
cnf(d_27,plain,
'greater$uor$uequal'(sK26,'critical$upoint'(sK25)),
inference(resolution,[status(thm)],[c9,c16]) ).
cnf(d_28,plain,
( ~ 'in$uenvironment'(X0,sK26)
| subpopulations('first$umovers','efficient$uproducers',X0,sK26)
| ~ environment(X0)
| 'cardinality$uat$utime'('first$umovers',sK26) = zero ),
inference(resolution,[status(thm)],[d_27,d_26]) ).
cnf(d_29,plain,
( ~ environment(X0)
| greater('growth$urate'('efficient$uproducers',sK26),'growth$urate'('first$umovers',sK26))
| ~ greater(sK26,'critical$upoint'(X0))
| ~ 'in$uenvironment'(X0,sK26)
| ~ environment(X0)
| 'cardinality$uat$utime'('first$umovers',sK26) = zero ),
inference(resolution,[status(thm)],[d_28,d_12]) ).
cnf(d_30,plain,
( ~ 'in$uenvironment'(sK25,sK26)
| ~ environment(sK25)
| greater('growth$urate'('efficient$uproducers',sK26),'growth$urate'('first$umovers',sK26))
| 'cardinality$uat$utime'('first$umovers',sK26) = zero ),
inference(resolution,[status(thm)],[d_29,c16]) ).
cnf(d_31,plain,
( ~ 'in$uenvironment'(sK25,sK26)
| greater('growth$urate'('efficient$uproducers',sK26),'growth$urate'('first$umovers',sK26))
| 'cardinality$uat$utime'('first$umovers',sK26) = zero ),
inference(resolution,[status(thm)],[c14,d_30]) ).
cnf(d_32,plain,
( greater('growth$urate'('efficient$uproducers',sK26),'growth$urate'('first$umovers',sK26))
| 'cardinality$uat$utime'('first$umovers',sK26) = zero ),
inference(resolution,[status(thm)],[c15,d_31]) ).
cnf(d_33,plain,
( 'selection$ufavors'('efficient$uproducers','first$umovers',sK26)
| ~ subpopulations('first$umovers','efficient$uproducers',X0,sK26)
| ~ environment(X0)
| 'cardinality$uat$utime'('first$umovers',sK26) = zero ),
inference(resolution,[status(thm)],[d_32,c0]) ).
cnf(d_34,plain,
( ~ subpopulations('first$umovers','efficient$uproducers',X0,sK26)
| ~ environment(X0)
| 'cardinality$uat$utime'('first$umovers',sK26) = zero ),
inference(resolution,[status(thm)],[c17,d_33]) ).
cnf(d_35,plain,
( ~ 'in$uenvironment'(X0,sK26)
| ~ environment(X0)
| 'cardinality$uat$utime'('first$umovers',sK26) = zero
| ~ environment(X0)
| 'cardinality$uat$utime'('first$umovers',sK26) = zero ),
inference(resolution,[status(thm)],[d_34,d_28]) ).
cnf(d_36,plain,
( ~ environment(sK25)
| 'cardinality$uat$utime'('first$umovers',sK26) = zero ),
inference(resolution,[status(thm)],[d_35,c15]) ).
cnf(d_37,plain,
'cardinality$uat$utime'('first$umovers',sK26) = zero,
inference(resolution,[status(thm)],[c14,d_36]) ).
cnf(d_38,plain,
( ~ subpopulation(X0,X1,sK26)
| ~ subpopulation('first$umovers',X1,sK26)
| 'selection$ufavors'(X0,'first$umovers',sK26)
| ~ environment(X1)
| ~ greater('cardinality$uat$utime'(X0,sK26),zero)
| zero != zero ),
inference(superposition,[status(thm)],[d_37,c1]) ).
cnf(d_39,plain,
( ~ subpopulation('first$umovers',X1,sK26)
| ~ subpopulation(X0,X1,sK26)
| 'selection$ufavors'(X0,'first$umovers',sK26)
| ~ environment(X1)
| ~ greater('cardinality$uat$utime'(X0,sK26),zero) ),
inference(equality_resolution,[status(thm)],[d_38]) ).
cnf(d_40,plain,
( 'critical$upoint'(sK25) = appear('efficient$uproducers',sK25)
| ~ subpopulation('first$umovers',X0,sK26)
| ~ subpopulation('efficient$uproducers',X0,sK26)
| 'selection$ufavors'('efficient$uproducers','first$umovers',sK26)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[d_39,d_9]) ).
cnf(d_41,plain,
( ~ subpopulation('efficient$uproducers',X0,sK26)
| ~ subpopulation('first$umovers',X0,sK26)
| ~ environment(X0)
| 'critical$upoint'(sK25) = appear('efficient$uproducers',sK25) ),
inference(resolution,[status(thm)],[c17,d_40]) ).
cnf(d_42,plain,
( ~ 'in$uenvironment'(X0,sK26)
| ~ environment(X0)
| ~ subpopulation('first$umovers',X0,sK26)
| ~ environment(X0)
| 'critical$upoint'(sK25) = appear('efficient$uproducers',sK25) ),
inference(resolution,[status(thm)],[d_41,c5]) ).
cnf(d_43,plain,
( ~ 'in$uenvironment'(X0,sK26)
| ~ environment(X0)
| ~ 'in$uenvironment'(X0,sK26)
| ~ environment(X0)
| 'critical$upoint'(sK25) = appear('efficient$uproducers',sK25) ),
inference(resolution,[status(thm)],[d_42,c4]) ).
cnf(d_44,plain,
( ~ environment(sK25)
| 'critical$upoint'(sK25) = appear('efficient$uproducers',sK25) ),
inference(resolution,[status(thm)],[d_43,c15]) ).
cnf(d_45,plain,
'critical$upoint'(sK25) = appear('efficient$uproducers',sK25),
inference(resolution,[status(thm)],[c14,d_44]) ).
cnf(d_46,plain,
( ~ 'in$uenvironment'(sK25,X0)
| ~ environment(sK25)
| greater('cardinality$uat$utime'('efficient$uproducers',X0),zero)
| ~ 'greater$uor$uequal'(X0,'critical$upoint'(sK25)) ),
inference(superposition,[status(thm)],[d_45,c13]) ).
cnf(d_47,plain,
( ~ 'greater$uor$uequal'(X0,'critical$upoint'(sK25))
| ~ 'in$uenvironment'(sK25,X0)
| greater('cardinality$uat$utime'('efficient$uproducers',X0),zero) ),
inference(resolution,[status(thm)],[c14,d_46]) ).
cnf(d_48,plain,
( ~ subpopulation('first$umovers',X0,sK26)
| ~ subpopulation('efficient$uproducers',X0,sK26)
| 'selection$ufavors'('efficient$uproducers','first$umovers',sK26)
| ~ environment(X0)
| ~ 'greater$uor$uequal'(sK26,'critical$upoint'(sK25))
| ~ 'in$uenvironment'(sK25,sK26) ),
inference(resolution,[status(thm)],[d_47,d_39]) ).
cnf(d_49,plain,
( ~ 'greater$uor$uequal'(sK26,'critical$upoint'(sK25))
| ~ subpopulation('efficient$uproducers',X0,sK26)
| ~ subpopulation('first$umovers',X0,sK26)
| 'selection$ufavors'('efficient$uproducers','first$umovers',sK26)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[c15,d_48]) ).
cnf(d_50,plain,
( ~ 'greater$uor$uequal'(sK26,'critical$upoint'(sK25))
| ~ subpopulation('efficient$uproducers',X0,sK26)
| ~ subpopulation('first$umovers',X0,sK26)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[c17,d_49]) ).
cnf(d_51,plain,
( ~ subpopulation('efficient$uproducers',X0,sK26)
| ~ subpopulation('first$umovers',X0,sK26)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[d_27,d_50]) ).
cnf(d_52,plain,
( ~ 'in$uenvironment'(X0,sK26)
| ~ environment(X0)
| ~ subpopulation('first$umovers',X0,sK26)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[d_51,c5]) ).
cnf(d_53,plain,
( ~ 'in$uenvironment'(X0,sK26)
| ~ environment(X0)
| ~ 'in$uenvironment'(X0,sK26)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[d_52,c4]) ).
cnf(d_54,plain,
~ environment(sK25),
inference(resolution,[status(thm)],[d_53,c15]) ).
cnf(d_55,plain,
$false,
inference(resolution,[status(thm)],[c14,d_54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT026+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
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 00:06:51 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.61/2.01 % SZS status Theorem for theBenchmark.p
% 12.61/2.01 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------