%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : MGT023+2 : 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 : n017.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 150.61s 150.96s
% Output : Proof 154.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(mp_earliest_time_growth_rate_exceeds,axiom,
! [E] :
( ( ? [To] :
( ! [T] :
( ( greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) )
& in_environment(E,To) )
& 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',mp_earliest_time_growth_rate_exceeds) ).
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(l1,hypothesis,
! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( ! [T] :
( ( greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) )
& in_environment(E,To) ) ),
file('theBenchmark.p',l1) ).
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] :
( ! [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) )
| ! [To] :
( ? [T] :
( ~ greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
& greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
| ~ in_environment(E,To) )
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[mp_earliest_time_growth_rate_exceeds]) ).
fof(f_1_2,plain,
! [U_4] :
( ? [U_3] :
( ! [U_2] :
( greater(growth_rate(efficient_producers,U_2),growth_rate(first_movers,U_2))
| ~ greater(U_2,U_3)
| ~ subpopulations(first_movers,efficient_producers,U_4,U_2) )
& ~ greater(growth_rate(efficient_producers,U_3),growth_rate(first_movers,U_3))
& in_environment(U_4,U_3) )
| ! [U_1] :
( ? [U_0] :
( ~ greater(growth_rate(efficient_producers,U_0),growth_rate(first_movers,U_0))
& greater_or_equal(U_0,U_1)
& subpopulations(first_movers,efficient_producers,U_4,U_0) )
| ~ in_environment(U_4,U_1) )
| ~ environment(U_4) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_4] :
( ? [U_3] :
( ! [U_2] :
( greater(growth_rate(efficient_producers,U_2),growth_rate(first_movers,U_2))
| ~ greater(U_2,U_3)
| ~ subpopulations(first_movers,efficient_producers,U_4,U_2) )
& ~ greater(growth_rate(efficient_producers,U_3),growth_rate(first_movers,U_3))
& in_environment(U_4,U_3) )
| ! [U_1] :
( ( ~ greater(growth_rate(efficient_producers,sK1(U_4,U_1)),growth_rate(first_movers,sK1(U_4,U_1)))
& greater_or_equal(sK1(U_4,U_1),U_1)
& subpopulations(first_movers,efficient_producers,U_4,sK1(U_4,U_1)) )
| ~ in_environment(U_4,U_1) )
| ~ environment(U_4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1(U_4,U_1))],[f_1_2]) ).
fof(f_1_4,plain,
! [U_4] :
( ( ! [U_2] :
( greater(growth_rate(efficient_producers,U_2),growth_rate(first_movers,U_2))
| ~ greater(U_2,sK2(U_4))
| ~ subpopulations(first_movers,efficient_producers,U_4,U_2) )
& ~ greater(growth_rate(efficient_producers,sK2(U_4)),growth_rate(first_movers,sK2(U_4)))
& in_environment(U_4,sK2(U_4)) )
| ! [U_1] :
( ( ~ greater(growth_rate(efficient_producers,sK1(U_4,U_1)),growth_rate(first_movers,sK1(U_4,U_1)))
& greater_or_equal(sK1(U_4,U_1),U_1)
& subpopulations(first_movers,efficient_producers,U_4,sK1(U_4,U_1)) )
| ~ in_environment(U_4,U_1) )
| ~ environment(U_4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_3,sK2(U_4))],[f_1_3]) ).
fof(f_1_5,plain,
( ! [U_4,U_2] :
( greater(growth_rate(efficient_producers,U_2),growth_rate(first_movers,U_2))
| ~ greater(U_2,sK2(U_4))
| ~ subpopulations(first_movers,efficient_producers,U_4,U_2)
| ~ sP1(U_4,U_2) )
& ! [U_4,U_2] :
( ~ greater(growth_rate(efficient_producers,sK2(U_4)),growth_rate(first_movers,sK2(U_4)))
| ~ sP1(U_4,U_2) )
& ! [U_4,U_2] :
( in_environment(U_4,sK2(U_4))
| ~ sP1(U_4,U_2) )
& ! [U_1,U_4] :
( ~ greater(growth_rate(efficient_producers,sK1(U_4,U_1)),growth_rate(first_movers,sK1(U_4,U_1)))
| ~ sP0(U_1,U_4) )
& ! [U_1,U_4] :
( greater_or_equal(sK1(U_4,U_1),U_1)
| ~ sP0(U_1,U_4) )
& ! [U_1,U_4] :
( subpopulations(first_movers,efficient_producers,U_4,sK1(U_4,U_1))
| ~ sP0(U_1,U_4) )
& ! [U_1,U_4,U_2] :
( sP1(U_4,U_2)
| sP0(U_1,U_4)
| ~ in_environment(U_4,U_1)
| ~ environment(U_4) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_1_4]) ).
cnf(f_1_6,plain,
( sP1(U_4,U_2)
| sP0(U_1,U_4)
| ~ in_environment(U_4,U_1)
| ~ environment(U_4) ),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_7,plain,
( subpopulations(first_movers,efficient_producers,U_4,sK1(U_4,U_1))
| ~ sP0(U_1,U_4) ),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_8,plain,
( greater_or_equal(sK1(U_4,U_1),U_1)
| ~ sP0(U_1,U_4) ),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_9,plain,
( ~ greater(growth_rate(efficient_producers,sK1(U_4,U_1)),growth_rate(first_movers,sK1(U_4,U_1)))
| ~ sP0(U_1,U_4) ),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_10,plain,
( in_environment(U_4,sK2(U_4))
| ~ sP1(U_4,U_2) ),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_11,plain,
( ~ greater(growth_rate(efficient_producers,sK2(U_4)),growth_rate(first_movers,sK2(U_4)))
| ~ sP1(U_4,U_2) ),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_12,plain,
( greater(growth_rate(efficient_producers,U_2),growth_rate(first_movers,U_2))
| ~ greater(U_2,sK2(U_4))
| ~ subpopulations(first_movers,efficient_producers,U_4,U_2)
| ~ sP1(U_4,U_2) ),
inference(clausify,[status(thm)],[f_1_5]) ).
fof(f_2_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_2_2,plain,
! [U_7,U_6] :
( U_6 = critical_point(U_7)
| ? [U_5] :
( ~ greater(growth_rate(efficient_producers,U_5),growth_rate(first_movers,U_5))
& greater(U_5,U_6)
& subpopulations(first_movers,efficient_producers,U_7,U_5) )
| ~ in_environment(U_7,U_6)
| greater(growth_rate(efficient_producers,U_6),growth_rate(first_movers,U_6))
| ~ environment(U_7) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_7,U_6] :
( U_6 = critical_point(U_7)
| ( ~ greater(growth_rate(efficient_producers,sK3(U_7,U_6)),growth_rate(first_movers,sK3(U_7,U_6)))
& greater(sK3(U_7,U_6),U_6)
& subpopulations(first_movers,efficient_producers,U_7,sK3(U_7,U_6)) )
| ~ in_environment(U_7,U_6)
| greater(growth_rate(efficient_producers,U_6),growth_rate(first_movers,U_6))
| ~ environment(U_7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_5,sK3(U_7,U_6))],[f_2_2]) ).
fof(f_2_4,plain,
( ! [U_6,U_7] :
( ~ greater(growth_rate(efficient_producers,sK3(U_7,U_6)),growth_rate(first_movers,sK3(U_7,U_6)))
| ~ sP2(U_6,U_7) )
& ! [U_6,U_7] :
( greater(sK3(U_7,U_6),U_6)
| ~ sP2(U_6,U_7) )
& ! [U_6,U_7] :
( subpopulations(first_movers,efficient_producers,U_7,sK3(U_7,U_6))
| ~ sP2(U_6,U_7) )
& ! [U_6,U_7] :
( U_6 = critical_point(U_7)
| sP2(U_6,U_7)
| ~ in_environment(U_7,U_6)
| greater(growth_rate(efficient_producers,U_6),growth_rate(first_movers,U_6))
| ~ environment(U_7) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_2_3]) ).
cnf(f_2_5,plain,
( U_6 = critical_point(U_7)
| sP2(U_6,U_7)
| ~ in_environment(U_7,U_6)
| greater(growth_rate(efficient_producers,U_6),growth_rate(first_movers,U_6))
| ~ environment(U_7) ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_6,plain,
( subpopulations(first_movers,efficient_producers,U_7,sK3(U_7,U_6))
| ~ sP2(U_6,U_7) ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_7,plain,
( greater(sK3(U_7,U_6),U_6)
| ~ sP2(U_6,U_7) ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_8,plain,
( ~ greater(growth_rate(efficient_producers,sK3(U_7,U_6)),growth_rate(first_movers,sK3(U_7,U_6)))
| ~ sP2(U_6,U_7) ),
inference(clausify,[status(thm)],[f_2_4]) ).
fof(f_3_1,plain,
! [E] :
( ? [To] :
( ! [T] :
( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater_or_equal(T,To)
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& in_environment(E,To) )
| ~ stable(E)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[l1]) ).
fof(f_3_2,plain,
! [U_10] :
( ? [U_9] :
( ! [U_8] :
( greater(growth_rate(efficient_producers,U_8),growth_rate(first_movers,U_8))
| ~ greater_or_equal(U_8,U_9)
| ~ subpopulations(first_movers,efficient_producers,U_10,U_8) )
& in_environment(U_10,U_9) )
| ~ stable(U_10)
| ~ environment(U_10) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_10] :
( ( ! [U_8] :
( greater(growth_rate(efficient_producers,U_8),growth_rate(first_movers,U_8))
| ~ greater_or_equal(U_8,sK4(U_10))
| ~ subpopulations(first_movers,efficient_producers,U_10,U_8) )
& in_environment(U_10,sK4(U_10)) )
| ~ stable(U_10)
| ~ environment(U_10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_9,sK4(U_10))],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_8,U_10] :
( greater(growth_rate(efficient_producers,U_8),growth_rate(first_movers,U_8))
| ~ greater_or_equal(U_8,sK4(U_10))
| ~ subpopulations(first_movers,efficient_producers,U_10,U_8)
| ~ sP3(U_8,U_10) )
& ! [U_8,U_10] :
( in_environment(U_10,sK4(U_10))
| ~ sP3(U_8,U_10) )
& ! [U_8,U_10] :
( sP3(U_8,U_10)
| ~ stable(U_10)
| ~ environment(U_10) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_3_3]) ).
cnf(f_3_5,plain,
( sP3(U_8,U_10)
| ~ stable(U_10)
| ~ environment(U_10) ),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_6,plain,
( in_environment(U_10,sK4(U_10))
| ~ sP3(U_8,U_10) ),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_7,plain,
( greater(growth_rate(efficient_producers,U_8),growth_rate(first_movers,U_8))
| ~ greater_or_equal(U_8,sK4(U_10))
| ~ subpopulations(first_movers,efficient_producers,U_10,U_8)
| ~ sP3(U_8,U_10) ),
inference(clausify,[status(thm)],[f_3_4]) ).
fof(f_4_1,negated_conjecture,
~ ! [E] :
( ( stable(E)
& environment(E) )
=> in_environment(E,critical_point(E)) ),
inference(negate,[status(cth)],[prove_l5]) ).
fof(f_4_2,negated_conjecture,
? [E] :
( ~ in_environment(E,critical_point(E))
& stable(E)
& environment(E) ),
inference(fof_nnf,[status(thm)],[f_4_1]) ).
fof(f_4_3,negated_conjecture,
? [U_11] :
( ~ in_environment(U_11,critical_point(U_11))
& stable(U_11)
& environment(U_11) ),
inference(variable_rename,[status(thm)],[f_4_2]) ).
fof(f_4_4,negated_conjecture,
( ~ in_environment(sK5,critical_point(sK5))
& stable(sK5)
& environment(sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_11,sK5)],[f_4_3]) ).
fof(f_4_5,negated_conjecture,
( ~ in_environment(sK5,critical_point(sK5))
& stable(sK5)
& environment(sK5) ),
inference(definitional_conversion,[status(esa)],[f_4_4]) ).
cnf(f_4_6,negated_conjecture,
environment(sK5),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_7,negated_conjecture,
stable(sK5),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_8,negated_conjecture,
~ in_environment(sK5,critical_point(sK5)),
inference(clausify,[status(thm)],[f_4_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,
( sK3(Eq_x_0,Eq_x_1) = sK3(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK4(Eq_x_0) = sK4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( environment(Eq_y_0)
| ~ environment(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_11,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_12,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_13,axiom,
( greater_or_equal(Eq_y_0,Eq_y_1)
| ~ greater_or_equal(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_14,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_15,axiom,
( stable(Eq_y_0)
| ~ stable(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_16,axiom,
( sP0(Eq_y_0,Eq_y_1)
| ~ sP0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,axiom,
( sP1(Eq_y_0,Eq_y_1)
| ~ sP1(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,axiom,
( sP2(Eq_y_0,Eq_y_1)
| ~ sP2(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,axiom,
( sP3(Eq_y_0,Eq_y_1)
| ~ sP3(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| 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+2 : 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
% 0.10/0.36 % Computer : n017.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 19 16:08:26 UTC 2026
% 0.10/0.37 % CPUTime :
% 150.61/150.96 % SZS status Theorem for theBenchmark
% 150.61/150.96 % SZS output start Proof for theBenchmark
% See solution above
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