%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : MGT032+2 : 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 : n003.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 0.10s 0.40s
% Output : Proof 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 55 ( 26 unt; 0 def)
% Number of atoms : 150 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 156 ( 61 ~; 53 |; 35 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 32 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mp1_high_growth_rates,axiom,
! [E,S1,S2,T] :
( ( greater(growth_rate(S2,T),growth_rate(S1,T))
& subpopulations(S1,S2,E,T)
& environment(E) )
=> selection_favors(S2,S1,T) ),
file('theBenchmark.p',mp1_high_growth_rates) ).
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_t1,conjecture,
! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( ! [T] :
( ( greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> selection_favors(efficient_producers,first_movers,T) )
& in_environment(E,To) ) ),
file('theBenchmark.p',prove_t1) ).
fof(f_1_1,plain,
! [E,S1,S2,T] :
( selection_favors(S2,S1,T)
| ~ greater(growth_rate(S2,T),growth_rate(S1,T))
| ~ subpopulations(S1,S2,E,T)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[mp1_high_growth_rates]) ).
fof(f_1_2,plain,
! [U_3,U_2,U_1,U_0] :
( selection_favors(U_1,U_2,U_0)
| ~ greater(growth_rate(U_1,U_0),growth_rate(U_2,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,
( selection_favors(U_1,U_2,U_0)
| ~ greater(growth_rate(U_1,U_0),growth_rate(U_2,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] :
( ? [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_6] :
( ? [U_5] :
( ! [U_4] :
( greater(growth_rate(efficient_producers,U_4),growth_rate(first_movers,U_4))
| ~ greater_or_equal(U_4,U_5)
| ~ subpopulations(first_movers,efficient_producers,U_6,U_4) )
& in_environment(U_6,U_5) )
| ~ stable(U_6)
| ~ environment(U_6) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_6] :
( ( ! [U_4] :
( greater(growth_rate(efficient_producers,U_4),growth_rate(first_movers,U_4))
| ~ greater_or_equal(U_4,sK1(U_6))
| ~ subpopulations(first_movers,efficient_producers,U_6,U_4) )
& in_environment(U_6,sK1(U_6)) )
| ~ stable(U_6)
| ~ environment(U_6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_5,sK1(U_6))],[f_2_2]) ).
cnf(f_2_4,plain,
( in_environment(U_6,sK1(U_6))
| ~ stable(U_6)
| ~ environment(U_6) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_5,plain,
( greater(growth_rate(efficient_producers,U_4),growth_rate(first_movers,U_4))
| ~ greater_or_equal(U_4,sK1(U_6))
| ~ subpopulations(first_movers,efficient_producers,U_6,U_4)
| ~ stable(U_6)
| ~ environment(U_6) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,negated_conjecture,
~ ! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( ! [T] :
( ( greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> selection_favors(efficient_producers,first_movers,T) )
& in_environment(E,To) ) ),
inference(negate,[status(cth)],[prove_t1]) ).
fof(f_3_2,negated_conjecture,
? [E] :
( ! [To] :
( ? [T] :
( ~ selection_favors(efficient_producers,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)],[f_3_1]) ).
fof(f_3_3,negated_conjecture,
? [U_9] :
( ! [U_8] :
( ? [U_7] :
( ~ selection_favors(efficient_producers,first_movers,U_7)
& greater_or_equal(U_7,U_8)
& subpopulations(first_movers,efficient_producers,U_9,U_7) )
| ~ in_environment(U_9,U_8) )
& stable(U_9)
& environment(U_9) ),
inference(variable_rename,[status(thm)],[f_3_2]) ).
fof(f_3_4,negated_conjecture,
( ! [U_8] :
( ? [U_7] :
( ~ selection_favors(efficient_producers,first_movers,U_7)
& greater_or_equal(U_7,U_8)
& subpopulations(first_movers,efficient_producers,sK2,U_7) )
| ~ in_environment(sK2,U_8) )
& stable(sK2)
& environment(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_9,sK2)],[f_3_3]) ).
fof(f_3_5,negated_conjecture,
( ! [U_8] :
( ( ~ selection_favors(efficient_producers,first_movers,sK3(U_8))
& greater_or_equal(sK3(U_8),U_8)
& subpopulations(first_movers,efficient_producers,sK2,sK3(U_8)) )
| ~ in_environment(sK2,U_8) )
& stable(sK2)
& environment(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_7,sK3(U_8))],[f_3_4]) ).
fof(f_3_6,negated_conjecture,
( ! [U_8] :
( ~ selection_favors(efficient_producers,first_movers,sK3(U_8))
| ~ sP0(U_8) )
& ! [U_8] :
( greater_or_equal(sK3(U_8),U_8)
| ~ sP0(U_8) )
& ! [U_8] :
( subpopulations(first_movers,efficient_producers,sK2,sK3(U_8))
| ~ sP0(U_8) )
& ! [U_8] :
( sP0(U_8)
| ~ in_environment(sK2,U_8) )
& stable(sK2)
& environment(sK2) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_3_5]) ).
cnf(f_3_7,negated_conjecture,
environment(sK2),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_8,negated_conjecture,
stable(sK2),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_9,negated_conjecture,
( sP0(U_8)
| ~ in_environment(sK2,U_8) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_10,negated_conjecture,
( subpopulations(first_movers,efficient_producers,sK2,sK3(U_8))
| ~ sP0(U_8) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_11,negated_conjecture,
( greater_or_equal(sK3(U_8),U_8)
| ~ sP0(U_8) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_12,negated_conjecture,
( ~ selection_favors(efficient_producers,first_movers,sK3(U_8))
| ~ sP0(U_8) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(t1,plain,
( ~ selection_favors(efficient_producers,first_movers,sK3(sK1(sK2)))
| ~ sP0(sK1(sK2)) ),
inference(start,[status(thm),parent(0:0)],[f_3_12]) ).
cnf(t2,plain,
( ~ in_environment(sK2,sK1(sK2))
| sP0(sK1(sK2)) ),
inference(extension,[status(thm),parent(t1:1)],[f_3_9]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ stable(sK2)
| ~ environment(sK2)
| in_environment(sK2,sK1(sK2)) ),
inference(extension,[status(thm),parent(t2:2)],[f_2_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
environment(sK2),
inference(extension,[status(thm),parent(t4:2)],[f_3_7]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
stable(sK2),
inference(extension,[status(thm),parent(t4:3)],[f_3_8]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(l1_001,lemma,
sP0(sK1(sK2)),
inference(lemma,[status(cth),parent(t1:1),below(0:0)],[t1:1]) ).
cnf(t10,plain,
( ~ subpopulations(first_movers,efficient_producers,sK2,sK3(sK1(sK2)))
| ~ greater(growth_rate(efficient_producers,sK3(sK1(sK2))),growth_rate(first_movers,sK3(sK1(sK2))))
| ~ environment(sK2)
| selection_favors(efficient_producers,first_movers,sK3(sK1(sK2))) ),
inference(extension,[status(thm),parent(t1:2)],[f_1_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t1:2]) ).
cnf(t12,plain,
environment(sK2),
inference(extension,[status(thm),parent(t10:2)],[f_3_7]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( ~ stable(sK2)
| ~ subpopulations(first_movers,efficient_producers,sK2,sK3(sK1(sK2)))
| ~ greater_or_equal(sK3(sK1(sK2)),sK1(sK2))
| ~ environment(sK2)
| greater(growth_rate(efficient_producers,sK3(sK1(sK2))),growth_rate(first_movers,sK3(sK1(sK2)))) ),
inference(extension,[status(thm),parent(t10:3)],[f_2_5]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
environment(sK2),
inference(extension,[status(thm),parent(t14:2)],[f_3_7]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( ~ sP0(sK1(sK2))
| greater_or_equal(sK3(sK1(sK2)),sK1(sK2)) ),
inference(extension,[status(thm),parent(t14:3)],[f_3_11]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t14:3]) ).
cnf(t20,plain,
sP0(sK1(sK2)),
inference(lemma_extension,[status(thm),parent(t18:2)],[l1:1]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
( ~ sP0(sK1(sK2))
| subpopulations(first_movers,efficient_producers,sK2,sK3(sK1(sK2))) ),
inference(extension,[status(thm),parent(t14:4)],[f_3_10]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t14:4]) ).
cnf(t24,plain,
sP0(sK1(sK2)),
inference(lemma_extension,[status(thm),parent(t22:2)],[l1:1]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
stable(sK2),
inference(extension,[status(thm),parent(t14:5)],[f_3_8]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t14:5]) ).
cnf(t28,plain,
( ~ sP0(sK1(sK2))
| subpopulations(first_movers,efficient_producers,sK2,sK3(sK1(sK2))) ),
inference(extension,[status(thm),parent(t10:4)],[f_3_10]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t10:4]) ).
cnf(t30,plain,
sP0(sK1(sK2)),
inference(lemma_extension,[status(thm),parent(t28:2)],[l1:1]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT032+2 : 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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n003.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 16:13:45 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.40 % SZS status Theorem for theBenchmark
% 0.10/0.40 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------