%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : MGT023+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 08:50:37 AM UTC 2026
% Result : Theorem 0.09s 0.46s
% Output : Proof 0.21s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(d1,hypothesis,
! [E,To] :
( ( ! [T] :
( ( greater(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) )
& in_environment(E,To)
& ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
& environment(E) )
=> To = critical_point(E) ),
file('theBenchmark.p',d1) ).
fof(l12,hypothesis,
! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( ! [T] :
( ( greater(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) )
& ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
& in_environment(E,To) ) ),
file('theBenchmark.p',l12) ).
fof(prove_l5,conjecture,
! [E] :
( ( stable(E)
& environment(E) )
=> in_environment(E,critical_point(E)) ),
file('theBenchmark.p',prove_l5) ).
fof(f_1_1,plain,
! [E,To] :
( To = critical_point(E)
| ? [T] :
( ~ greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
& greater(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
| ~ in_environment(E,To)
| greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[d1]) ).
fof(f_1_2,plain,
! [U_2,U_1] :
( U_1 = critical_point(U_2)
| ? [U_0] :
( ~ greater(growth_rate(efficient_producers,U_0),growth_rate(first_movers,U_0))
& greater(U_0,U_1)
& subpopulations(first_movers,efficient_producers,U_2,U_0) )
| ~ in_environment(U_2,U_1)
| greater(growth_rate(efficient_producers,U_1),growth_rate(first_movers,U_1))
| ~ environment(U_2) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_2,U_1] :
( U_1 = critical_point(U_2)
| ( ~ greater(growth_rate(efficient_producers,sK1(U_2,U_1)),growth_rate(first_movers,sK1(U_2,U_1)))
& greater(sK1(U_2,U_1),U_1)
& subpopulations(first_movers,efficient_producers,U_2,sK1(U_2,U_1)) )
| ~ in_environment(U_2,U_1)
| greater(growth_rate(efficient_producers,U_1),growth_rate(first_movers,U_1))
| ~ environment(U_2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1(U_2,U_1))],[f_1_2]) ).
cnf(f_1_4,plain,
( subpopulations(first_movers,efficient_producers,U_2,sK1(U_2,U_1))
| ~ in_environment(U_2,U_1)
| greater(growth_rate(efficient_producers,U_1),growth_rate(first_movers,U_1))
| ~ environment(U_2)
| U_1 = critical_point(U_2) ),
inference(clausify,[status(thm)],[f_1_3]) ).
cnf(f_1_5,plain,
( greater(sK1(U_2,U_1),U_1)
| ~ in_environment(U_2,U_1)
| greater(growth_rate(efficient_producers,U_1),growth_rate(first_movers,U_1))
| ~ environment(U_2)
| U_1 = critical_point(U_2) ),
inference(clausify,[status(thm)],[f_1_3]) ).
cnf(f_1_6,plain,
( ~ greater(growth_rate(efficient_producers,sK1(U_2,U_1)),growth_rate(first_movers,sK1(U_2,U_1)))
| ~ in_environment(U_2,U_1)
| greater(growth_rate(efficient_producers,U_1),growth_rate(first_movers,U_1))
| ~ environment(U_2)
| U_1 = critical_point(U_2) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
! [E] :
( ? [To] :
( ! [T] :
( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater(T,To)
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
& in_environment(E,To) )
| ~ stable(E)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[l12]) ).
fof(f_2_2,plain,
! [U_5] :
( ? [U_4] :
( ! [U_3] :
( greater(growth_rate(efficient_producers,U_3),growth_rate(first_movers,U_3))
| ~ greater(U_3,U_4)
| ~ subpopulations(first_movers,efficient_producers,U_5,U_3) )
& ~ greater(growth_rate(efficient_producers,U_4),growth_rate(first_movers,U_4))
& in_environment(U_5,U_4) )
| ~ stable(U_5)
| ~ environment(U_5) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_5] :
( ( ! [U_3] :
( greater(growth_rate(efficient_producers,U_3),growth_rate(first_movers,U_3))
| ~ greater(U_3,sK2(U_5))
| ~ subpopulations(first_movers,efficient_producers,U_5,U_3) )
& ~ greater(growth_rate(efficient_producers,sK2(U_5)),growth_rate(first_movers,sK2(U_5)))
& in_environment(U_5,sK2(U_5)) )
| ~ stable(U_5)
| ~ environment(U_5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_4,sK2(U_5))],[f_2_2]) ).
cnf(f_2_4,plain,
( in_environment(U_5,sK2(U_5))
| ~ stable(U_5)
| ~ environment(U_5) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_5,plain,
( ~ greater(growth_rate(efficient_producers,sK2(U_5)),growth_rate(first_movers,sK2(U_5)))
| ~ stable(U_5)
| ~ environment(U_5) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_6,plain,
( greater(growth_rate(efficient_producers,U_3),growth_rate(first_movers,U_3))
| ~ greater(U_3,sK2(U_5))
| ~ subpopulations(first_movers,efficient_producers,U_5,U_3)
| ~ stable(U_5)
| ~ environment(U_5) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,negated_conjecture,
~ ! [E] :
( ( stable(E)
& environment(E) )
=> in_environment(E,critical_point(E)) ),
inference(negate,[status(cth)],[prove_l5]) ).
fof(f_3_2,negated_conjecture,
? [E] :
( ~ in_environment(E,critical_point(E))
& stable(E)
& environment(E) ),
inference(fof_nnf,[status(thm)],[f_3_1]) ).
fof(f_3_3,negated_conjecture,
? [U_6] :
( ~ in_environment(U_6,critical_point(U_6))
& stable(U_6)
& environment(U_6) ),
inference(variable_rename,[status(thm)],[f_3_2]) ).
fof(f_3_4,negated_conjecture,
( ~ in_environment(sK3,critical_point(sK3))
& stable(sK3)
& environment(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_6,sK3)],[f_3_3]) ).
fof(f_3_5,negated_conjecture,
( ~ in_environment(sK3,critical_point(sK3))
& stable(sK3)
& environment(sK3) ),
inference(definitional_conversion,[status(esa)],[f_3_4]) ).
cnf(f_3_6,negated_conjecture,
environment(sK3),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_7,negated_conjecture,
stable(sK3),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_8,negated_conjecture,
~ in_environment(sK3,critical_point(sK3)),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( growth_rate(Eq_x_0,Eq_x_1) = growth_rate(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( critical_point(Eq_x_0) = critical_point(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( sK1(Eq_x_0,Eq_x_1) = sK1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sK2(Eq_x_0) = sK2(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( environment(Eq_y_0)
| ~ environment(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_9,axiom,
( greater(Eq_y_0,Eq_y_1)
| ~ greater(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_10,axiom,
( in_environment(Eq_y_0,Eq_y_1)
| ~ in_environment(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_11,axiom,
( subpopulations(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ subpopulations(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_12,axiom,
( stable(Eq_y_0)
| ~ stable(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT023+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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 19 16:13:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.46 % SZS status Theorem for theBenchmark
% 0.09/0.46 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------