%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : MGT030+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 08:50:39 AM UTC 2026
% Result : Theorem 0.23s 0.51s
% Output : Proof 0.23s
% 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(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_l12,conjecture,
! [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',prove_l12) ).
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]) ).
cnf(f_1_5,plain,
( subpopulations(first_movers,efficient_producers,U_4,sK1(U_4,U_1))
| ~ in_environment(U_4,U_1)
| ~ environment(U_4)
| in_environment(U_4,sK2(U_4)) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_6,plain,
( greater_or_equal(sK1(U_4,U_1),U_1)
| ~ in_environment(U_4,U_1)
| ~ environment(U_4)
| in_environment(U_4,sK2(U_4)) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_7,plain,
( ~ greater(growth_rate(efficient_producers,sK1(U_4,U_1)),growth_rate(first_movers,sK1(U_4,U_1)))
| ~ in_environment(U_4,U_1)
| ~ environment(U_4)
| in_environment(U_4,sK2(U_4)) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_8,plain,
( subpopulations(first_movers,efficient_producers,U_4,sK1(U_4,U_1))
| ~ in_environment(U_4,U_1)
| ~ environment(U_4)
| ~ greater(growth_rate(efficient_producers,sK2(U_4)),growth_rate(first_movers,sK2(U_4))) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_9,plain,
( greater_or_equal(sK1(U_4,U_1),U_1)
| ~ in_environment(U_4,U_1)
| ~ environment(U_4)
| ~ greater(growth_rate(efficient_producers,sK2(U_4)),growth_rate(first_movers,sK2(U_4))) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_10,plain,
( ~ greater(growth_rate(efficient_producers,sK1(U_4,U_1)),growth_rate(first_movers,sK1(U_4,U_1)))
| ~ in_environment(U_4,U_1)
| ~ environment(U_4)
| ~ greater(growth_rate(efficient_producers,sK2(U_4)),growth_rate(first_movers,sK2(U_4))) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_11,plain,
( subpopulations(first_movers,efficient_producers,U_4,sK1(U_4,U_1))
| ~ in_environment(U_4,U_1)
| ~ environment(U_4)
| 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) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_12,plain,
( greater_or_equal(sK1(U_4,U_1),U_1)
| ~ in_environment(U_4,U_1)
| ~ environment(U_4)
| 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) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_13,plain,
( ~ greater(growth_rate(efficient_producers,sK1(U_4,U_1)),growth_rate(first_movers,sK1(U_4,U_1)))
| ~ in_environment(U_4,U_1)
| ~ environment(U_4)
| 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) ),
inference(clausify,[status(thm)],[f_1_4]) ).
fof(f_2_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_2_2,plain,
! [U_7] :
( ? [U_6] :
( ! [U_5] :
( greater(growth_rate(efficient_producers,U_5),growth_rate(first_movers,U_5))
| ~ greater_or_equal(U_5,U_6)
| ~ subpopulations(first_movers,efficient_producers,U_7,U_5) )
& in_environment(U_7,U_6) )
| ~ stable(U_7)
| ~ environment(U_7) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_7] :
( ( ! [U_5] :
( greater(growth_rate(efficient_producers,U_5),growth_rate(first_movers,U_5))
| ~ greater_or_equal(U_5,sK3(U_7))
| ~ subpopulations(first_movers,efficient_producers,U_7,U_5) )
& in_environment(U_7,sK3(U_7)) )
| ~ stable(U_7)
| ~ environment(U_7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_6,sK3(U_7))],[f_2_2]) ).
cnf(f_2_4,plain,
( in_environment(U_7,sK3(U_7))
| ~ stable(U_7)
| ~ environment(U_7) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_5,plain,
( greater(growth_rate(efficient_producers,U_5),growth_rate(first_movers,U_5))
| ~ greater_or_equal(U_5,sK3(U_7))
| ~ subpopulations(first_movers,efficient_producers,U_7,U_5)
| ~ stable(U_7)
| ~ environment(U_7) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,negated_conjecture,
~ ! [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) ) ),
inference(negate,[status(cth)],[prove_l12]) ).
fof(f_3_2,negated_conjecture,
? [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)],[f_3_1]) ).
fof(f_3_3,negated_conjecture,
? [U_10] :
( ! [U_9] :
( ? [U_8] :
( ~ greater(growth_rate(efficient_producers,U_8),growth_rate(first_movers,U_8))
& greater(U_8,U_9)
& subpopulations(first_movers,efficient_producers,U_10,U_8) )
| greater(growth_rate(efficient_producers,U_9),growth_rate(first_movers,U_9))
| ~ in_environment(U_10,U_9) )
& stable(U_10)
& environment(U_10) ),
inference(variable_rename,[status(thm)],[f_3_2]) ).
fof(f_3_4,negated_conjecture,
( ! [U_9] :
( ? [U_8] :
( ~ greater(growth_rate(efficient_producers,U_8),growth_rate(first_movers,U_8))
& greater(U_8,U_9)
& subpopulations(first_movers,efficient_producers,sK4,U_8) )
| greater(growth_rate(efficient_producers,U_9),growth_rate(first_movers,U_9))
| ~ in_environment(sK4,U_9) )
& stable(sK4)
& environment(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_10,sK4)],[f_3_3]) ).
fof(f_3_5,negated_conjecture,
( ! [U_9] :
( ( ~ greater(growth_rate(efficient_producers,sK5(U_9)),growth_rate(first_movers,sK5(U_9)))
& greater(sK5(U_9),U_9)
& subpopulations(first_movers,efficient_producers,sK4,sK5(U_9)) )
| greater(growth_rate(efficient_producers,U_9),growth_rate(first_movers,U_9))
| ~ in_environment(sK4,U_9) )
& stable(sK4)
& environment(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_8,sK5(U_9))],[f_3_4]) ).
fof(f_3_6,negated_conjecture,
( ! [U_9] :
( ~ greater(growth_rate(efficient_producers,sK5(U_9)),growth_rate(first_movers,sK5(U_9)))
| ~ sP0(U_9) )
& ! [U_9] :
( greater(sK5(U_9),U_9)
| ~ sP0(U_9) )
& ! [U_9] :
( subpopulations(first_movers,efficient_producers,sK4,sK5(U_9))
| ~ sP0(U_9) )
& ! [U_9] :
( sP0(U_9)
| greater(growth_rate(efficient_producers,U_9),growth_rate(first_movers,U_9))
| ~ in_environment(sK4,U_9) )
& stable(sK4)
& environment(sK4) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_3_5]) ).
cnf(f_3_7,negated_conjecture,
environment(sK4),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_8,negated_conjecture,
stable(sK4),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_9,negated_conjecture,
( sP0(U_9)
| greater(growth_rate(efficient_producers,U_9),growth_rate(first_movers,U_9))
| ~ in_environment(sK4,U_9) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_10,negated_conjecture,
( subpopulations(first_movers,efficient_producers,sK4,sK5(U_9))
| ~ sP0(U_9) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_11,negated_conjecture,
( greater(sK5(U_9),U_9)
| ~ sP0(U_9) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_12,negated_conjecture,
( ~ greater(growth_rate(efficient_producers,sK5(U_9)),growth_rate(first_movers,sK5(U_9)))
| ~ sP0(U_9) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT030+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_NEQ 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
% 0.11/0.37 % Computer : n019.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 19 16:12:20 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.23/0.51 % SZS status Theorem for theBenchmark
% 0.23/0.51 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------