%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : MGT036+3 : 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 : n020.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 08:50:41 AM UTC 2026
% Result : Theorem 0.10s 0.41s
% Output : Proof 0.10s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(mp_symmetry_of_subpopulations,axiom,
! [E,S1,S2,T] :
( ( subpopulations(S1,S2,E,T)
& environment(E) )
=> subpopulations(S2,S1,E,T) ),
file('theBenchmark.p',mp_symmetry_of_subpopulations) ).
fof(d2,hypothesis,
! [E,S1,S2,T] :
( ( subpopulations(S1,S2,E,T)
& environment(E) )
=> ( ( greater(zero,growth_rate(S1,T))
& greater_or_equal(growth_rate(S2,T),zero) )
<=> outcompetes(S2,S1,T) ) ),
file('theBenchmark.p',d2) ).
fof(a13_star,hypothesis,
? [E,T] :
( greater(zero,growth_rate(efficient_producers,T))
& greater_or_equal(growth_rate(first_movers,T),zero)
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ),
file('theBenchmark.p',a13_star) ).
fof(prove_t5_star,conjecture,
? [E,T] :
( outcompetes(first_movers,efficient_producers,T)
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ),
file('theBenchmark.p',prove_t5_star) ).
fof(f_1_1,plain,
! [E,S1,S2,T] :
( subpopulations(S2,S1,E,T)
| ~ subpopulations(S1,S2,E,T)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[mp_symmetry_of_subpopulations]) ).
fof(f_1_2,plain,
! [U_3,U_2,U_1,U_0] :
( subpopulations(U_1,U_2,U_3,U_0)
| ~ subpopulations(U_2,U_1,U_3,U_0)
| ~ environment(U_3) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( subpopulations(U_1,U_2,U_3,U_0)
| ~ subpopulations(U_2,U_1,U_3,U_0)
| ~ environment(U_3) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [E,S1,S2,T] :
( ( ( ( greater(zero,growth_rate(S1,T))
& greater_or_equal(growth_rate(S2,T),zero) )
| ~ outcompetes(S2,S1,T) )
& ( outcompetes(S2,S1,T)
| ~ greater(zero,growth_rate(S1,T))
| ~ greater_or_equal(growth_rate(S2,T),zero) ) )
| ~ subpopulations(S1,S2,E,T)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[d2]) ).
fof(f_2_2,plain,
! [U_7,U_6,U_5,U_4] :
( ( ( ( greater(zero,growth_rate(U_6,U_4))
& greater_or_equal(growth_rate(U_5,U_4),zero) )
| ~ outcompetes(U_5,U_6,U_4) )
& ( outcompetes(U_5,U_6,U_4)
| ~ greater(zero,growth_rate(U_6,U_4))
| ~ greater_or_equal(growth_rate(U_5,U_4),zero) ) )
| ~ subpopulations(U_6,U_5,U_7,U_4)
| ~ environment(U_7) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( outcompetes(U_5,U_6,U_4)
| ~ greater(zero,growth_rate(U_6,U_4))
| ~ greater_or_equal(growth_rate(U_5,U_4),zero)
| ~ subpopulations(U_6,U_5,U_7,U_4)
| ~ environment(U_7) ),
inference(clausify,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( greater_or_equal(growth_rate(U_5,U_4),zero)
| ~ outcompetes(U_5,U_6,U_4)
| ~ subpopulations(U_6,U_5,U_7,U_4)
| ~ environment(U_7) ),
inference(clausify,[status(thm)],[f_2_2]) ).
cnf(f_2_5,plain,
( greater(zero,growth_rate(U_6,U_4))
| ~ outcompetes(U_5,U_6,U_4)
| ~ subpopulations(U_6,U_5,U_7,U_4)
| ~ environment(U_7) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
? [E,T] :
( greater(zero,growth_rate(efficient_producers,T))
& greater_or_equal(growth_rate(first_movers,T),zero)
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ),
inference(fof_nnf,[status(thm)],[a13_star]) ).
fof(f_3_2,plain,
? [U_9,U_8] :
( greater(zero,growth_rate(efficient_producers,U_8))
& greater_or_equal(growth_rate(first_movers,U_8),zero)
& subpopulations(first_movers,efficient_producers,U_9,U_8)
& environment(U_9) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
? [U_9] :
( ? [U_8] :
( greater(zero,growth_rate(efficient_producers,U_8))
& greater_or_equal(growth_rate(first_movers,U_8),zero)
& subpopulations(first_movers,efficient_producers,U_9,U_8) )
& environment(U_9) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ? [U_8] :
( greater(zero,growth_rate(efficient_producers,U_8))
& greater_or_equal(growth_rate(first_movers,U_8),zero)
& subpopulations(first_movers,efficient_producers,sK1,U_8) )
& environment(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_9,sK1)],[f_3_3]) ).
fof(f_3_5,plain,
( greater(zero,growth_rate(efficient_producers,sK2))
& greater_or_equal(growth_rate(first_movers,sK2),zero)
& subpopulations(first_movers,efficient_producers,sK1,sK2)
& environment(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_8,sK2)],[f_3_4]) ).
cnf(f_3_6,plain,
environment(sK1),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_7,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_8,plain,
greater_or_equal(growth_rate(first_movers,sK2),zero),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_9,plain,
greater(zero,growth_rate(efficient_producers,sK2)),
inference(clausify,[status(thm)],[f_3_5]) ).
fof(f_4_1,negated_conjecture,
~ ? [E,T] :
( outcompetes(first_movers,efficient_producers,T)
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ),
inference(negate,[status(cth)],[prove_t5_star]) ).
fof(f_4_2,negated_conjecture,
! [E,T] :
( ~ outcompetes(first_movers,efficient_producers,T)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[f_4_1]) ).
fof(f_4_3,negated_conjecture,
! [U_11,U_10] :
( ~ outcompetes(first_movers,efficient_producers,U_10)
| ~ subpopulations(first_movers,efficient_producers,U_11,U_10)
| ~ environment(U_11) ),
inference(variable_rename,[status(thm)],[f_4_2]) ).
fof(f_4_4,negated_conjecture,
! [U_11] :
( ! [U_10] :
( ~ outcompetes(first_movers,efficient_producers,U_10)
| ~ subpopulations(first_movers,efficient_producers,U_11,U_10) )
| ~ environment(U_11) ),
inference(miniscope,[status(thm)],[f_4_3]) ).
fof(f_4_5,negated_conjecture,
! [U_10,U_11] :
( ~ outcompetes(first_movers,efficient_producers,U_10)
| ~ subpopulations(first_movers,efficient_producers,U_11,U_10)
| ~ environment(U_11) ),
inference(definitional_conversion,[status(esa)],[f_4_4]) ).
cnf(f_4_6,negated_conjecture,
( ~ outcompetes(first_movers,efficient_producers,U_10)
| ~ subpopulations(first_movers,efficient_producers,U_11,U_10)
| ~ environment(U_11) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT036+3 : 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
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 16:14:46 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.41 % SZS status Theorem for theBenchmark
% 0.10/0.41 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------