%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : MGT021+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 : Thu Sep 24 08:50:36 AM UTC 2026
% Result : Theorem 0.09s 0.45s
% Output : Proof 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 82 ( 44 unt; 0 def)
% Number of atoms : 186 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 184 ( 80 ~; 70 |; 23 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 31 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mp_time_point_in_environment,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> in_environment(E,T) ),
file('theBenchmark.p',mp_time_point_in_environment) ).
fof(mp_environment_not_empty,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> greater(number_of_organizations(E,T),zero) ),
file('theBenchmark.p',mp_environment_not_empty) ).
fof(mp_increase_not_decrease,axiom,
! [X] :
( increases(X)
=> ~ decreases(X) ),
file('theBenchmark.p',mp_increase_not_decrease) ).
fof(a3,hypothesis,
! [E,T] :
( ( greater(number_of_organizations(E,T),zero)
& in_environment(E,T)
& environment(E) )
=> ( ( ~ greater(equilibrium(E),T)
=> constant(resources(E,T)) )
& ( greater(equilibrium(E),T)
=> decreases(resources(E,T)) ) ) ),
file('theBenchmark.p',a3) ).
fof(l4,hypothesis,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ( ( constant(resources(E,T))
=> ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) )
& ( decreases(resources(E,T))
=> increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ) ) ),
file('theBenchmark.p',l4) ).
fof(prove_l3,conjecture,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ),
file('theBenchmark.p',prove_l3) ).
fof(f_1_1,plain,
! [E,T] :
( in_environment(E,T)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[mp_time_point_in_environment]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( in_environment(U_1,U_0)
| ~ subpopulations(first_movers,efficient_producers,U_1,U_0)
| ~ environment(U_1) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( in_environment(U_1,U_0)
| ~ subpopulations(first_movers,efficient_producers,U_1,U_0)
| ~ environment(U_1) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [E,T] :
( greater(number_of_organizations(E,T),zero)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[mp_environment_not_empty]) ).
fof(f_2_2,plain,
! [U_3,U_2] :
( greater(number_of_organizations(U_3,U_2),zero)
| ~ subpopulations(first_movers,efficient_producers,U_3,U_2)
| ~ environment(U_3) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( greater(number_of_organizations(U_3,U_2),zero)
| ~ subpopulations(first_movers,efficient_producers,U_3,U_2)
| ~ environment(U_3) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [X] :
( ~ decreases(X)
| ~ increases(X) ),
inference(fof_nnf,[status(thm)],[mp_increase_not_decrease]) ).
fof(f_3_2,plain,
! [U_4] :
( ~ decreases(U_4)
| ~ increases(U_4) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( ~ decreases(U_4)
| ~ increases(U_4) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_5_1,plain,
! [E,T] :
( ( ( constant(resources(E,T))
| greater(equilibrium(E),T) )
& ( decreases(resources(E,T))
| ~ greater(equilibrium(E),T) ) )
| ~ greater(number_of_organizations(E,T),zero)
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[a3]) ).
fof(f_5_2,plain,
! [U_8,U_7] :
( ( ( constant(resources(U_8,U_7))
| greater(equilibrium(U_8),U_7) )
& ( decreases(resources(U_8,U_7))
| ~ greater(equilibrium(U_8),U_7) ) )
| ~ greater(number_of_organizations(U_8,U_7),zero)
| ~ in_environment(U_8,U_7)
| ~ environment(U_8) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( decreases(resources(U_8,U_7))
| ~ greater(equilibrium(U_8),U_7)
| ~ greater(number_of_organizations(U_8,U_7),zero)
| ~ in_environment(U_8,U_7)
| ~ environment(U_8) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( constant(resources(U_8,U_7))
| greater(equilibrium(U_8),U_7)
| ~ greater(number_of_organizations(U_8,U_7),zero)
| ~ in_environment(U_8,U_7)
| ~ environment(U_8) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [E,T] :
( ( ( ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
| ~ constant(resources(E,T)) )
& ( increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
| ~ decreases(resources(E,T)) ) )
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[l4]) ).
fof(f_6_2,plain,
! [U_10,U_9] :
( ( ( ~ decreases(difference(disbanding_rate(first_movers,U_9),disbanding_rate(efficient_producers,U_9)))
| ~ constant(resources(U_10,U_9)) )
& ( increases(difference(disbanding_rate(first_movers,U_9),disbanding_rate(efficient_producers,U_9)))
| ~ decreases(resources(U_10,U_9)) ) )
| ~ subpopulations(first_movers,efficient_producers,U_10,U_9)
| ~ environment(U_10) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( increases(difference(disbanding_rate(first_movers,U_9),disbanding_rate(efficient_producers,U_9)))
| ~ decreases(resources(U_10,U_9))
| ~ subpopulations(first_movers,efficient_producers,U_10,U_9)
| ~ environment(U_10) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( ~ decreases(difference(disbanding_rate(first_movers,U_9),disbanding_rate(efficient_producers,U_9)))
| ~ constant(resources(U_10,U_9))
| ~ subpopulations(first_movers,efficient_producers,U_10,U_9)
| ~ environment(U_10) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,negated_conjecture,
~ ! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ),
inference(negate,[status(cth)],[prove_l3]) ).
fof(f_7_2,negated_conjecture,
? [E,T] :
( decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ),
inference(fof_nnf,[status(thm)],[f_7_1]) ).
fof(f_7_3,negated_conjecture,
? [U_12,U_11] :
( decreases(difference(disbanding_rate(first_movers,U_11),disbanding_rate(efficient_producers,U_11)))
& subpopulations(first_movers,efficient_producers,U_12,U_11)
& environment(U_12) ),
inference(variable_rename,[status(thm)],[f_7_2]) ).
fof(f_7_4,negated_conjecture,
? [U_11] :
( decreases(difference(disbanding_rate(first_movers,U_11),disbanding_rate(efficient_producers,U_11)))
& subpopulations(first_movers,efficient_producers,sK1,U_11)
& environment(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_12,sK1)],[f_7_3]) ).
fof(f_7_5,negated_conjecture,
( decreases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)))
& subpopulations(first_movers,efficient_producers,sK1,sK2)
& environment(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_11,sK2)],[f_7_4]) ).
fof(f_7_6,negated_conjecture,
( decreases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)))
& subpopulations(first_movers,efficient_producers,sK1,sK2)
& environment(sK1) ),
inference(definitional_conversion,[status(esa)],[f_7_5]) ).
cnf(f_7_7,negated_conjecture,
environment(sK1),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_8,negated_conjecture,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_9,negated_conjecture,
decreases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2))),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(t1,plain,
( ~ decreases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)))
| ~ increases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2))) ),
inference(start,[status(thm),parent(0:0)],[f_3_3]) ).
cnf(t2,plain,
( ~ subpopulations(first_movers,efficient_producers,sK1,sK2)
| ~ decreases(resources(sK1,sK2))
| ~ environment(sK1)
| increases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2))) ),
inference(extension,[status(thm),parent(t1:1)],[f_6_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
environment(sK1),
inference(extension,[status(thm),parent(t2:2)],[f_7_7]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(l2,lemma,
environment(sK1),
inference(lemma,[status(cth),parent(t2:2),below(t1:1)],[t2:2]) ).
cnf(t6,plain,
( ~ in_environment(sK1,sK2)
| ~ greater(number_of_organizations(sK1,sK2),zero)
| ~ greater(equilibrium(sK1),sK2)
| ~ environment(sK1)
| decreases(resources(sK1,sK2)) ),
inference(extension,[status(thm),parent(t2:3)],[f_5_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
environment(sK1),
inference(lemma_extension,[status(thm),parent(t6:2)],[l2:1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ in_environment(sK1,sK2)
| ~ greater(number_of_organizations(sK1,sK2),zero)
| constant(resources(sK1,sK2))
| ~ environment(sK1)
| greater(equilibrium(sK1),sK2) ),
inference(extension,[status(thm),parent(t6:3)],[f_5_4]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
environment(sK1),
inference(lemma_extension,[status(thm),parent(t10:2)],[l2:1]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( ~ subpopulations(first_movers,efficient_producers,sK1,sK2)
| ~ decreases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)))
| ~ environment(sK1)
| ~ constant(resources(sK1,sK2)) ),
inference(extension,[status(thm),parent(t10:3)],[f_6_4]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
environment(sK1),
inference(lemma_extension,[status(thm),parent(t14:2)],[l2:1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
decreases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2))),
inference(extension,[status(thm),parent(t14:3)],[f_7_9]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t14:3]) ).
cnf(t20,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(extension,[status(thm),parent(t14:4)],[f_7_8]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t14:4]) ).
cnf(t22,plain,
( ~ subpopulations(first_movers,efficient_producers,sK1,sK2)
| ~ environment(sK1)
| greater(number_of_organizations(sK1,sK2),zero) ),
inference(extension,[status(thm),parent(t10:4)],[f_2_3]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t10:4]) ).
cnf(t24,plain,
environment(sK1),
inference(lemma_extension,[status(thm),parent(t22:2)],[l2:1]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(extension,[status(thm),parent(t22:3)],[f_7_8]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t22:3]) ).
cnf(t28,plain,
( ~ subpopulations(first_movers,efficient_producers,sK1,sK2)
| ~ environment(sK1)
| in_environment(sK1,sK2) ),
inference(extension,[status(thm),parent(t10:5)],[f_1_3]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t10:5]) ).
cnf(t30,plain,
environment(sK1),
inference(lemma_extension,[status(thm),parent(t28:2)],[l2:1]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(extension,[status(thm),parent(t28:3)],[f_7_8]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t28:3]) ).
cnf(t34,plain,
( ~ subpopulations(first_movers,efficient_producers,sK1,sK2)
| ~ environment(sK1)
| greater(number_of_organizations(sK1,sK2),zero) ),
inference(extension,[status(thm),parent(t6:4)],[f_2_3]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t6:4]) ).
cnf(t36,plain,
environment(sK1),
inference(lemma_extension,[status(thm),parent(t34:2)],[l2:1]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(t38,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(extension,[status(thm),parent(t34:3)],[f_7_8]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t34:3]) ).
cnf(t40,plain,
( ~ subpopulations(first_movers,efficient_producers,sK1,sK2)
| ~ environment(sK1)
| in_environment(sK1,sK2) ),
inference(extension,[status(thm),parent(t6:5)],[f_1_3]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t6:5]) ).
cnf(t42,plain,
environment(sK1),
inference(lemma_extension,[status(thm),parent(t40:2)],[l2:1]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(extension,[status(thm),parent(t40:3)],[f_7_8]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t40:3]) ).
cnf(t46,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(extension,[status(thm),parent(t2:4)],[f_7_8]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t2:4]) ).
cnf(t48,plain,
decreases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2))),
inference(extension,[status(thm),parent(t1:2)],[f_7_9]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t1:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT021+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 19 16:14:23 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.45 % SZS status Theorem for theBenchmark
% 0.09/0.45 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------