%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : MGT036+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 : n007.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 08:50:40 AM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 75 ( 39 unt; 0 def)
% Number of atoms : 187 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 190 ( 78 ~; 70 |; 33 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 91 ( 0 sgn 66 !; 5 ?)
% 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(mp_time_point_occur,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> in_environment(E,T) ),
file('theBenchmark.p',mp_time_point_occur) ).
fof(mp_growth_rate_relationships,axiom,
! [E,S1,S2,T] :
( ( ( subpopulations(S1,S2,E,T)
& environment(E) )
=> greater_or_equal(growth_rate(S1,T),zero) )
<=> ~ greater(zero,growth_rate(S1,T)) ),
file('theBenchmark.p',mp_growth_rate_relationships) ).
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(a2,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
file('theBenchmark.p',a2) ).
fof(a13,hypothesis,
! [E,S1,S2,T] :
( ( greater(resilience(S2),resilience(S1))
& ~ greater(zero,growth_rate(S1,T))
& in_environment(E,T)
& environment(E) )
=> ~ greater(zero,growth_rate(S2,T)) ),
file('theBenchmark.p',a13) ).
fof(prove_t5,conjecture,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ~ outcompetes(first_movers,efficient_producers,T) ),
file('theBenchmark.p',prove_t5) ).
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,T] :
( in_environment(E,T)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[mp_time_point_occur]) ).
fof(f_2_2,plain,
! [U_5,U_4] :
( in_environment(U_5,U_4)
| ~ subpopulations(first_movers,efficient_producers,U_5,U_4)
| ~ environment(U_5) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( in_environment(U_5,U_4)
| ~ subpopulations(first_movers,efficient_producers,U_5,U_4)
| ~ environment(U_5) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [E,S1,S2,T] :
( ( greater_or_equal(growth_rate(S1,T),zero)
| ~ subpopulations(S1,S2,E,T)
| ~ environment(E)
| greater(zero,growth_rate(S1,T)) )
& ( ~ greater(zero,growth_rate(S1,T))
| ( ~ greater_or_equal(growth_rate(S1,T),zero)
& subpopulations(S1,S2,E,T)
& environment(E) ) ) ),
inference(fof_nnf,[status(thm)],[mp_growth_rate_relationships]) ).
fof(f_3_2,plain,
! [U_9,U_8,U_7,U_6] :
( ( greater_or_equal(growth_rate(U_8,U_6),zero)
| ~ subpopulations(U_8,U_7,U_9,U_6)
| ~ environment(U_9)
| greater(zero,growth_rate(U_8,U_6)) )
& ( ~ greater(zero,growth_rate(U_8,U_6))
| ( ~ greater_or_equal(growth_rate(U_8,U_6),zero)
& subpopulations(U_8,U_7,U_9,U_6)
& environment(U_9) ) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_17,U_15,U_13,U_11] :
( greater_or_equal(growth_rate(U_15,U_11),zero)
| ~ subpopulations(U_15,U_13,U_17,U_11)
| ~ environment(U_17)
| greater(zero,growth_rate(U_15,U_11)) )
& ! [U_16,U_14,U_12,U_10] :
( ~ greater(zero,growth_rate(U_14,U_10))
| ( ~ greater_or_equal(growth_rate(U_14,U_10),zero)
& subpopulations(U_14,U_12,U_16,U_10)
& environment(U_16) ) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
cnf(f_3_6,plain,
( ~ greater_or_equal(growth_rate(U_14,U_10),zero)
| ~ greater(zero,growth_rate(U_14,U_10)) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_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_4_2,plain,
! [U_21,U_20,U_19,U_18] :
( ( ( ( greater(zero,growth_rate(U_20,U_18))
& greater_or_equal(growth_rate(U_19,U_18),zero) )
| ~ outcompetes(U_19,U_20,U_18) )
& ( outcompetes(U_19,U_20,U_18)
| ~ greater(zero,growth_rate(U_20,U_18))
| ~ greater_or_equal(growth_rate(U_19,U_18),zero) ) )
| ~ subpopulations(U_20,U_19,U_21,U_18)
| ~ environment(U_21) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_4,plain,
( greater_or_equal(growth_rate(U_19,U_18),zero)
| ~ outcompetes(U_19,U_20,U_18)
| ~ subpopulations(U_20,U_19,U_21,U_18)
| ~ environment(U_21) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_5,plain,
( greater(zero,growth_rate(U_20,U_18))
| ~ outcompetes(U_19,U_20,U_18)
| ~ subpopulations(U_20,U_19,U_21,U_18)
| ~ environment(U_21) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(fof_nnf,[status(thm)],[a2]) ).
cnf(f_5_2,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(clausify,[status(thm)],[f_5_1]) ).
fof(f_6_1,plain,
! [E,S1,S2,T] :
( ~ greater(zero,growth_rate(S2,T))
| ~ greater(resilience(S2),resilience(S1))
| greater(zero,growth_rate(S1,T))
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[a13]) ).
fof(f_6_2,plain,
! [U_25,U_24,U_23,U_22] :
( ~ greater(zero,growth_rate(U_23,U_22))
| ~ greater(resilience(U_23),resilience(U_24))
| greater(zero,growth_rate(U_24,U_22))
| ~ in_environment(U_25,U_22)
| ~ environment(U_25) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( ~ greater(zero,growth_rate(U_23,U_22))
| ~ greater(resilience(U_23),resilience(U_24))
| greater(zero,growth_rate(U_24,U_22))
| ~ in_environment(U_25,U_22)
| ~ environment(U_25) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,negated_conjecture,
~ ! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ~ outcompetes(first_movers,efficient_producers,T) ),
inference(negate,[status(cth)],[prove_t5]) ).
fof(f_7_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_7_1]) ).
fof(f_7_3,negated_conjecture,
? [U_27,U_26] :
( outcompetes(first_movers,efficient_producers,U_26)
& subpopulations(first_movers,efficient_producers,U_27,U_26)
& environment(U_27) ),
inference(variable_rename,[status(thm)],[f_7_2]) ).
fof(f_7_4,negated_conjecture,
? [U_26] :
( outcompetes(first_movers,efficient_producers,U_26)
& subpopulations(first_movers,efficient_producers,sK1,U_26)
& environment(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_27,sK1)],[f_7_3]) ).
fof(f_7_5,negated_conjecture,
( outcompetes(first_movers,efficient_producers,sK2)
& subpopulations(first_movers,efficient_producers,sK1,sK2)
& environment(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_26,sK2)],[f_7_4]) ).
fof(f_7_6,negated_conjecture,
( outcompetes(first_movers,efficient_producers,sK2)
& subpopulations(first_movers,efficient_producers,sK1,sK2)
& environment(sK1) ),
inference(definitional_conversion,[status(esa)],[f_7_5]) ).
cnf(f_7_7,negated_conjecture,
environment(sK1),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_8,negated_conjecture,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_9,negated_conjecture,
outcompetes(first_movers,efficient_producers,sK2),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(t1,plain,
( ~ greater_or_equal(growth_rate(first_movers,sK2),zero)
| ~ greater(zero,growth_rate(first_movers,sK2)) ),
inference(start,[status(thm),parent(0:0)],[f_3_6]) ).
cnf(t2,plain,
( ~ in_environment(sK1,sK2)
| ~ greater(zero,growth_rate(efficient_producers,sK2))
| ~ greater(resilience(efficient_producers),resilience(first_movers))
| ~ environment(sK1)
| greater(zero,growth_rate(first_movers,sK2)) ),
inference(extension,[status(thm),parent(t1:1)],[f_6_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
environment(sK1),
inference(extension,[status(thm),parent(t2:2)],[f_7_7]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(l2,lemma,
environment(sK1),
inference(lemma,[status(cth),parent(t2:2),below(t1:1)],[t2:2]) ).
cnf(t6,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(extension,[status(thm),parent(t2:3)],[f_5_2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
( ~ subpopulations(efficient_producers,first_movers,sK1,sK2)
| ~ outcompetes(first_movers,efficient_producers,sK2)
| ~ environment(sK1)
| greater(zero,growth_rate(efficient_producers,sK2)) ),
inference(extension,[status(thm),parent(t2:4)],[f_4_5]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:4]) ).
cnf(t10,plain,
environment(sK1),
inference(extension,[status(thm),parent(t8:2)],[f_7_7]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(l5,lemma,
environment(sK1),
inference(lemma,[status(cth),parent(t8:2),below(t2:4)],[t8:2]) ).
cnf(t12,plain,
outcompetes(first_movers,efficient_producers,sK2),
inference(extension,[status(thm),parent(t8:3)],[f_7_9]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
( ~ subpopulations(first_movers,efficient_producers,sK1,sK2)
| ~ environment(sK1)
| subpopulations(efficient_producers,first_movers,sK1,sK2) ),
inference(extension,[status(thm),parent(t8:4)],[f_1_3]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t8:4]) ).
cnf(t16,plain,
environment(sK1),
inference(lemma_extension,[status(thm),parent(t14:2)],[l5:1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(extension,[status(thm),parent(t14:3)],[f_7_8]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t14:3]) ).
cnf(t20,plain,
( ~ subpopulations(first_movers,efficient_producers,sK1,sK2)
| ~ environment(sK1)
| in_environment(sK1,sK2) ),
inference(extension,[status(thm),parent(t2:5)],[f_2_3]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t2:5]) ).
cnf(t22,plain,
environment(sK1),
inference(lemma_extension,[status(thm),parent(t20:2)],[l2:1]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(extension,[status(thm),parent(t20:3)],[f_7_8]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t20:3]) ).
cnf(t26,plain,
( ~ subpopulations(efficient_producers,first_movers,sK1,sK2)
| ~ outcompetes(first_movers,efficient_producers,sK2)
| ~ environment(sK1)
| greater_or_equal(growth_rate(first_movers,sK2),zero) ),
inference(extension,[status(thm),parent(t1:2)],[f_4_4]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t1:2]) ).
cnf(t28,plain,
environment(sK1),
inference(extension,[status(thm),parent(t26:2)],[f_7_7]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(l12,lemma,
environment(sK1),
inference(lemma,[status(cth),parent(t26:2),below(t1:2)],[t26:2]) ).
cnf(t30,plain,
outcompetes(first_movers,efficient_producers,sK2),
inference(extension,[status(thm),parent(t26:3)],[f_7_9]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t26:3]) ).
cnf(t32,plain,
( ~ subpopulations(first_movers,efficient_producers,sK1,sK2)
| ~ environment(sK1)
| subpopulations(efficient_producers,first_movers,sK1,sK2) ),
inference(extension,[status(thm),parent(t26:4)],[f_1_3]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t26:4]) ).
cnf(t34,plain,
environment(sK1),
inference(lemma_extension,[status(thm),parent(t32:2)],[l12:1]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(extension,[status(thm),parent(t32:3)],[f_7_8]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t32:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT036+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_NEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 19 16:12:04 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.39 % SZS status Theorem for theBenchmark
% 0.13/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------