%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : MGT027+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 : n006.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 08:50:38 AM UTC 2026
% Result : Theorem 260.64s 261.01s
% Output : Proof 262.96s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(mp_contracts_from,axiom,
! [E,To] :
( ( ! [T] :
( ( greater_or_equal(T,To)
& greater(cardinality_at_time(first_movers,T),zero) )
=> greater(zero,growth_rate(first_movers,T)) )
& in_environment(E,To)
& stable(E)
& environment(E) )
=> contracts_from(To,first_movers) ),
file('theBenchmark.p',mp_contracts_from) ).
fof(mp_non_empty_fm_and_ep,axiom,
! [E,T] :
( ( greater(cardinality_at_time(efficient_producers,T),zero)
& greater(cardinality_at_time(first_movers,T),zero)
& in_environment(E,T)
& environment(E) )
=> subpopulations(first_movers,efficient_producers,E,T) ),
file('theBenchmark.p',mp_non_empty_fm_and_ep) ).
fof(mp_long_stable_environments,axiom,
! [E,T1,T2] :
( ( greater(T2,T1)
& in_environment(E,T1)
& stable(E)
& environment(E) )
=> in_environment(E,T2) ),
file('theBenchmark.p',mp_long_stable_environments) ).
fof(mp_EP_in_stable_environments,axiom,
! [E] :
( ( stable(E)
& environment(E) )
=> in_environment(E,appear(efficient_producers,E)) ),
file('theBenchmark.p',mp_EP_in_stable_environments) ).
fof(mp_greater_transitivity,axiom,
! [X,Y,Z] :
( ( greater(Y,Z)
& greater(X,Y) )
=> greater(X,Z) ),
file('theBenchmark.p',mp_greater_transitivity) ).
fof(mp_greater_or_equal,axiom,
! [X,Y] :
( greater_or_equal(X,Y)
<=> ( X = Y
| greater(X,Y) ) ),
file('theBenchmark.p',mp_greater_or_equal) ).
fof(t6,hypothesis,
! [E,T] :
( ( greater_or_equal(T,appear(efficient_producers,E))
& in_environment(E,T)
& environment(E) )
=> greater(cardinality_at_time(efficient_producers,T),zero) ),
file('theBenchmark.p',t6) ).
fof(l10,hypothesis,
! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( ! [T] :
( ( greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(zero,growth_rate(first_movers,T)) )
& greater(To,appear(efficient_producers,E)) ) ),
file('theBenchmark.p',l10) ).
fof(prove_l9,conjecture,
! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( contracts_from(To,first_movers)
& greater(To,appear(efficient_producers,E)) ) ),
file('theBenchmark.p',prove_l9) ).
fof(f_1_1,plain,
! [E,To] :
( contracts_from(To,first_movers)
| ? [T] :
( ~ greater(zero,growth_rate(first_movers,T))
& greater_or_equal(T,To)
& greater(cardinality_at_time(first_movers,T),zero) )
| ~ in_environment(E,To)
| ~ stable(E)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[mp_contracts_from]) ).
fof(f_1_2,plain,
! [U_2,U_1] :
( contracts_from(U_1,first_movers)
| ? [U_0] :
( ~ greater(zero,growth_rate(first_movers,U_0))
& greater_or_equal(U_0,U_1)
& greater(cardinality_at_time(first_movers,U_0),zero) )
| ~ in_environment(U_2,U_1)
| ~ stable(U_2)
| ~ environment(U_2) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_2,U_1] :
( contracts_from(U_1,first_movers)
| ( ~ greater(zero,growth_rate(first_movers,sK1(U_2,U_1)))
& greater_or_equal(sK1(U_2,U_1),U_1)
& greater(cardinality_at_time(first_movers,sK1(U_2,U_1)),zero) )
| ~ in_environment(U_2,U_1)
| ~ stable(U_2)
| ~ environment(U_2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1(U_2,U_1))],[f_1_2]) ).
cnf(f_1_4,plain,
( greater(cardinality_at_time(first_movers,sK1(U_2,U_1)),zero)
| ~ in_environment(U_2,U_1)
| ~ stable(U_2)
| ~ environment(U_2)
| contracts_from(U_1,first_movers) ),
inference(clausify,[status(thm)],[f_1_3]) ).
cnf(f_1_5,plain,
( greater_or_equal(sK1(U_2,U_1),U_1)
| ~ in_environment(U_2,U_1)
| ~ stable(U_2)
| ~ environment(U_2)
| contracts_from(U_1,first_movers) ),
inference(clausify,[status(thm)],[f_1_3]) ).
cnf(f_1_6,plain,
( ~ greater(zero,growth_rate(first_movers,sK1(U_2,U_1)))
| ~ in_environment(U_2,U_1)
| ~ stable(U_2)
| ~ environment(U_2)
| contracts_from(U_1,first_movers) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
! [E,T] :
( subpopulations(first_movers,efficient_producers,E,T)
| ~ greater(cardinality_at_time(efficient_producers,T),zero)
| ~ greater(cardinality_at_time(first_movers,T),zero)
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[mp_non_empty_fm_and_ep]) ).
fof(f_2_2,plain,
! [U_4,U_3] :
( subpopulations(first_movers,efficient_producers,U_4,U_3)
| ~ greater(cardinality_at_time(efficient_producers,U_3),zero)
| ~ greater(cardinality_at_time(first_movers,U_3),zero)
| ~ in_environment(U_4,U_3)
| ~ environment(U_4) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( subpopulations(first_movers,efficient_producers,U_4,U_3)
| ~ greater(cardinality_at_time(efficient_producers,U_3),zero)
| ~ greater(cardinality_at_time(first_movers,U_3),zero)
| ~ in_environment(U_4,U_3)
| ~ environment(U_4) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [E,T1,T2] :
( in_environment(E,T2)
| ~ greater(T2,T1)
| ~ in_environment(E,T1)
| ~ stable(E)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[mp_long_stable_environments]) ).
fof(f_3_2,plain,
! [U_7,U_6,U_5] :
( in_environment(U_7,U_5)
| ~ greater(U_5,U_6)
| ~ in_environment(U_7,U_6)
| ~ stable(U_7)
| ~ environment(U_7) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( in_environment(U_7,U_5)
| ~ greater(U_5,U_6)
| ~ in_environment(U_7,U_6)
| ~ stable(U_7)
| ~ environment(U_7) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [E] :
( in_environment(E,appear(efficient_producers,E))
| ~ stable(E)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[mp_EP_in_stable_environments]) ).
fof(f_4_2,plain,
! [U_8] :
( in_environment(U_8,appear(efficient_producers,U_8))
| ~ stable(U_8)
| ~ environment(U_8) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( in_environment(U_8,appear(efficient_producers,U_8))
| ~ stable(U_8)
| ~ environment(U_8) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [X,Y,Z] :
( greater(X,Z)
| ~ greater(Y,Z)
| ~ greater(X,Y) ),
inference(fof_nnf,[status(thm)],[mp_greater_transitivity]) ).
fof(f_5_2,plain,
! [U_11,U_10,U_9] :
( greater(U_11,U_9)
| ~ greater(U_10,U_9)
| ~ greater(U_11,U_10) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( greater(U_11,U_9)
| ~ greater(U_10,U_9)
| ~ greater(U_11,U_10) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [X,Y] :
( ( greater_or_equal(X,Y)
| ( X != Y
& ~ greater(X,Y) ) )
& ( X = Y
| greater(X,Y)
| ~ greater_or_equal(X,Y) ) ),
inference(fof_nnf,[status(thm)],[mp_greater_or_equal]) ).
fof(f_6_2,plain,
! [U_13,U_12] :
( ( greater_or_equal(U_13,U_12)
| ( U_13 != U_12
& ~ greater(U_13,U_12) ) )
& ( U_13 = U_12
| greater(U_13,U_12)
| ~ greater_or_equal(U_13,U_12) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_17,U_15] :
( greater_or_equal(U_17,U_15)
| ( U_17 != U_15
& ~ greater(U_17,U_15) ) )
& ! [U_16,U_14] :
( U_16 = U_14
| greater(U_16,U_14)
| ~ greater_or_equal(U_16,U_14) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( U_16 = U_14
| greater(U_16,U_14)
| ~ greater_or_equal(U_16,U_14) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( ~ greater(U_17,U_15)
| greater_or_equal(U_17,U_15) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_6,plain,
( U_17 != U_15
| greater_or_equal(U_17,U_15) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [E,T] :
( greater(cardinality_at_time(efficient_producers,T),zero)
| ~ greater_or_equal(T,appear(efficient_producers,E))
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[t6]) ).
fof(f_7_2,plain,
! [U_19,U_18] :
( greater(cardinality_at_time(efficient_producers,U_18),zero)
| ~ greater_or_equal(U_18,appear(efficient_producers,U_19))
| ~ in_environment(U_19,U_18)
| ~ environment(U_19) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( greater(cardinality_at_time(efficient_producers,U_18),zero)
| ~ greater_or_equal(U_18,appear(efficient_producers,U_19))
| ~ in_environment(U_19,U_18)
| ~ environment(U_19) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [E] :
( ? [To] :
( ! [T] :
( greater(zero,growth_rate(first_movers,T))
| ~ greater_or_equal(T,To)
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& greater(To,appear(efficient_producers,E)) )
| ~ stable(E)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[l10]) ).
fof(f_8_2,plain,
! [U_22] :
( ? [U_21] :
( ! [U_20] :
( greater(zero,growth_rate(first_movers,U_20))
| ~ greater_or_equal(U_20,U_21)
| ~ subpopulations(first_movers,efficient_producers,U_22,U_20) )
& greater(U_21,appear(efficient_producers,U_22)) )
| ~ stable(U_22)
| ~ environment(U_22) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_22] :
( ( ! [U_20] :
( greater(zero,growth_rate(first_movers,U_20))
| ~ greater_or_equal(U_20,sK2(U_22))
| ~ subpopulations(first_movers,efficient_producers,U_22,U_20) )
& greater(sK2(U_22),appear(efficient_producers,U_22)) )
| ~ stable(U_22)
| ~ environment(U_22) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_21,sK2(U_22))],[f_8_2]) ).
cnf(f_8_4,plain,
( greater(sK2(U_22),appear(efficient_producers,U_22))
| ~ stable(U_22)
| ~ environment(U_22) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
( greater(zero,growth_rate(first_movers,U_20))
| ~ greater_or_equal(U_20,sK2(U_22))
| ~ subpopulations(first_movers,efficient_producers,U_22,U_20)
| ~ stable(U_22)
| ~ environment(U_22) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,negated_conjecture,
~ ! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( contracts_from(To,first_movers)
& greater(To,appear(efficient_producers,E)) ) ),
inference(negate,[status(cth)],[prove_l9]) ).
fof(f_9_2,negated_conjecture,
? [E] :
( ! [To] :
( ~ contracts_from(To,first_movers)
| ~ greater(To,appear(efficient_producers,E)) )
& stable(E)
& environment(E) ),
inference(fof_nnf,[status(thm)],[f_9_1]) ).
fof(f_9_3,negated_conjecture,
? [U_24] :
( ! [U_23] :
( ~ contracts_from(U_23,first_movers)
| ~ greater(U_23,appear(efficient_producers,U_24)) )
& stable(U_24)
& environment(U_24) ),
inference(variable_rename,[status(thm)],[f_9_2]) ).
fof(f_9_4,negated_conjecture,
( ! [U_23] :
( ~ contracts_from(U_23,first_movers)
| ~ greater(U_23,appear(efficient_producers,sK3)) )
& stable(sK3)
& environment(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_24,sK3)],[f_9_3]) ).
cnf(f_9_5,negated_conjecture,
environment(sK3),
inference(clausify,[status(thm)],[f_9_4]) ).
cnf(f_9_6,negated_conjecture,
stable(sK3),
inference(clausify,[status(thm)],[f_9_4]) ).
cnf(f_9_7,negated_conjecture,
( ~ contracts_from(U_23,first_movers)
| ~ greater(U_23,appear(efficient_producers,sK3)) ),
inference(clausify,[status(thm)],[f_9_4]) ).
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,
( cardinality_at_time(Eq_x_0,Eq_x_1) = cardinality_at_time(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,
( 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_6,axiom,
( appear(Eq_x_0,Eq_x_1) = appear(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,
( 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_8,axiom,
( sK2(Eq_x_0) = sK2(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( environment(Eq_y_0)
| ~ environment(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_10,axiom,
( stable(Eq_y_0)
| ~ stable(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,
( 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_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,
( contracts_from(Eq_y_0,Eq_y_1)
| ~ contracts_from(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,
( 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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT027+1 : 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
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 19 16:12:13 UTC 2026
% 0.09/0.37 % CPUTime :
% 260.64/261.01 % SZS status Theorem for theBenchmark
% 260.64/261.01 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------