%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : MGT026+1 : 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 : n011.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 34.55s 34.86s
% Output : Proof 34.74s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% 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(mp2_favour_members,axiom,
! [E,S1,S2,T] :
( ( cardinality_at_time(S2,T) = zero
& greater(cardinality_at_time(S1,T),zero)
& subpopulation(S2,E,T)
& subpopulation(S1,E,T)
& environment(E) )
=> selection_favors(S1,S2,T) ),
file('theBenchmark.p',mp2_favour_members) ).
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_first_movers_exist,axiom,
! [E,T] :
( ( in_environment(E,T)
& environment(E) )
=> greater_or_equal(cardinality_at_time(first_movers,T),zero) ),
file('theBenchmark.p',mp_first_movers_exist) ).
fof(mp_subpopulations,axiom,
! [E,T] :
( ( in_environment(E,T)
& environment(E) )
=> ( subpopulation(efficient_producers,E,T)
& subpopulation(first_movers,E,T) ) ),
file('theBenchmark.p',mp_subpopulations) ).
fof(mp_critical_point_after_EP,axiom,
! [E] :
( environment(E)
=> greater_or_equal(critical_point(E),appear(efficient_producers,E)) ),
file('theBenchmark.p',mp_critical_point_after_EP) ).
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(d1,hypothesis,
! [E,Tc] :
( ( Tc = critical_point(E)
& environment(E) )
=> ( ! [T] :
( ( greater(T,Tc)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) )
& ~ greater(growth_rate(efficient_producers,Tc),growth_rate(first_movers,Tc)) ) ),
file('theBenchmark.p',d1) ).
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(prove_l8,conjecture,
! [E,T] :
( ( greater(T,critical_point(E))
& in_environment(E,T)
& environment(E) )
=> selection_favors(efficient_producers,first_movers,T) ),
file('theBenchmark.p',prove_l8) ).
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]) ).
fof(f_1_3,plain,
! [U_3,U_1,U_2,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(definitional_conversion,[status(esa)],[f_1_2]) ).
cnf(f_1_4,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_3]) ).
fof(f_2_1,plain,
! [E,S1,S2,T] :
( selection_favors(S1,S2,T)
| cardinality_at_time(S2,T) != zero
| ~ greater(cardinality_at_time(S1,T),zero)
| ~ subpopulation(S2,E,T)
| ~ subpopulation(S1,E,T)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[mp2_favour_members]) ).
fof(f_2_2,plain,
! [U_7,U_6,U_5,U_4] :
( selection_favors(U_6,U_5,U_4)
| cardinality_at_time(U_5,U_4) != zero
| ~ greater(cardinality_at_time(U_6,U_4),zero)
| ~ subpopulation(U_5,U_7,U_4)
| ~ subpopulation(U_6,U_7,U_4)
| ~ environment(U_7) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_4,U_5,U_6,U_7] :
( selection_favors(U_6,U_5,U_4)
| cardinality_at_time(U_5,U_4) != zero
| ~ greater(cardinality_at_time(U_6,U_4),zero)
| ~ subpopulation(U_5,U_7,U_4)
| ~ subpopulation(U_6,U_7,U_4)
| ~ environment(U_7) ),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
( selection_favors(U_6,U_5,U_4)
| cardinality_at_time(U_5,U_4) != zero
| ~ greater(cardinality_at_time(U_6,U_4),zero)
| ~ subpopulation(U_5,U_7,U_4)
| ~ subpopulation(U_6,U_7,U_4)
| ~ environment(U_7) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_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_3_2,plain,
! [U_9,U_8] :
( subpopulations(first_movers,efficient_producers,U_9,U_8)
| ~ greater(cardinality_at_time(efficient_producers,U_8),zero)
| ~ greater(cardinality_at_time(first_movers,U_8),zero)
| ~ in_environment(U_9,U_8)
| ~ environment(U_9) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_9,U_8] :
( subpopulations(first_movers,efficient_producers,U_9,U_8)
| ~ greater(cardinality_at_time(efficient_producers,U_8),zero)
| ~ greater(cardinality_at_time(first_movers,U_8),zero)
| ~ in_environment(U_9,U_8)
| ~ environment(U_9) ),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
( subpopulations(first_movers,efficient_producers,U_9,U_8)
| ~ greater(cardinality_at_time(efficient_producers,U_8),zero)
| ~ greater(cardinality_at_time(first_movers,U_8),zero)
| ~ in_environment(U_9,U_8)
| ~ environment(U_9) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [E,T] :
( greater_or_equal(cardinality_at_time(first_movers,T),zero)
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[mp_first_movers_exist]) ).
fof(f_4_2,plain,
! [U_11,U_10] :
( greater_or_equal(cardinality_at_time(first_movers,U_10),zero)
| ~ in_environment(U_11,U_10)
| ~ environment(U_11) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_10,U_11] :
( greater_or_equal(cardinality_at_time(first_movers,U_10),zero)
| ~ in_environment(U_11,U_10)
| ~ environment(U_11) ),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
( greater_or_equal(cardinality_at_time(first_movers,U_10),zero)
| ~ in_environment(U_11,U_10)
| ~ environment(U_11) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [E,T] :
( ( subpopulation(efficient_producers,E,T)
& subpopulation(first_movers,E,T) )
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[mp_subpopulations]) ).
fof(f_5_2,plain,
! [U_13,U_12] :
( ( subpopulation(efficient_producers,U_13,U_12)
& subpopulation(first_movers,U_13,U_12) )
| ~ in_environment(U_13,U_12)
| ~ environment(U_13) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_13,U_12] :
( subpopulation(efficient_producers,U_13,U_12)
| ~ sP0(U_13,U_12) )
& ! [U_13,U_12] :
( subpopulation(first_movers,U_13,U_12)
| ~ sP0(U_13,U_12) )
& ! [U_13,U_12] :
( sP0(U_13,U_12)
| ~ in_environment(U_13,U_12)
| ~ environment(U_13) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_5_2]) ).
cnf(f_5_4,plain,
( sP0(U_13,U_12)
| ~ in_environment(U_13,U_12)
| ~ environment(U_13) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
( subpopulation(first_movers,U_13,U_12)
| ~ sP0(U_13,U_12) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_6,plain,
( subpopulation(efficient_producers,U_13,U_12)
| ~ sP0(U_13,U_12) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [E] :
( greater_or_equal(critical_point(E),appear(efficient_producers,E))
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[mp_critical_point_after_EP]) ).
fof(f_6_2,plain,
! [U_14] :
( greater_or_equal(critical_point(U_14),appear(efficient_producers,U_14))
| ~ environment(U_14) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_14] :
( greater_or_equal(critical_point(U_14),appear(efficient_producers,U_14))
| ~ environment(U_14) ),
inference(definitional_conversion,[status(esa)],[f_6_2]) ).
cnf(f_6_4,plain,
( greater_or_equal(critical_point(U_14),appear(efficient_producers,U_14))
| ~ environment(U_14) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [X,Y,Z] :
( greater(X,Z)
| ~ greater(Y,Z)
| ~ greater(X,Y) ),
inference(fof_nnf,[status(thm)],[mp_greater_transitivity]) ).
fof(f_7_2,plain,
! [U_17,U_16,U_15] :
( greater(U_17,U_15)
| ~ greater(U_16,U_15)
| ~ greater(U_17,U_16) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_16,U_17,U_15] :
( greater(U_17,U_15)
| ~ greater(U_16,U_15)
| ~ greater(U_17,U_16) ),
inference(definitional_conversion,[status(esa)],[f_7_2]) ).
cnf(f_7_4,plain,
( greater(U_17,U_15)
| ~ greater(U_16,U_15)
| ~ greater(U_17,U_16) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_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_8_2,plain,
! [U_19,U_18] :
( ( greater_or_equal(U_19,U_18)
| ( U_19 != U_18
& ~ greater(U_19,U_18) ) )
& ( U_19 = U_18
| greater(U_19,U_18)
| ~ greater_or_equal(U_19,U_18) ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_23,U_21] :
( greater_or_equal(U_23,U_21)
| ( U_23 != U_21
& ~ greater(U_23,U_21) ) )
& ! [U_22,U_20] :
( U_22 = U_20
| greater(U_22,U_20)
| ~ greater_or_equal(U_22,U_20) ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
( ! [U_21,U_23] :
( U_23 != U_21
| ~ sP1(U_21,U_23) )
& ! [U_21,U_23] :
( ~ greater(U_23,U_21)
| ~ sP1(U_21,U_23) )
& ! [U_21,U_23] :
( greater_or_equal(U_23,U_21)
| sP1(U_21,U_23) )
& ! [U_22,U_20] :
( U_22 = U_20
| greater(U_22,U_20)
| ~ greater_or_equal(U_22,U_20) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_8_3]) ).
cnf(f_8_5,plain,
( U_22 = U_20
| greater(U_22,U_20)
| ~ greater_or_equal(U_22,U_20) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_6,plain,
( greater_or_equal(U_23,U_21)
| sP1(U_21,U_23) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_7,plain,
( ~ greater(U_23,U_21)
| ~ sP1(U_21,U_23) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_8,plain,
( U_23 != U_21
| ~ sP1(U_21,U_23) ),
inference(clausify,[status(thm)],[f_8_4]) ).
fof(f_9_1,plain,
! [E,Tc] :
( ( ! [T] :
( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater(T,Tc)
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& ~ greater(growth_rate(efficient_producers,Tc),growth_rate(first_movers,Tc)) )
| Tc != critical_point(E)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[d1]) ).
fof(f_9_2,plain,
! [U_26,U_25] :
( ( ! [U_24] :
( greater(growth_rate(efficient_producers,U_24),growth_rate(first_movers,U_24))
| ~ greater(U_24,U_25)
| ~ subpopulations(first_movers,efficient_producers,U_26,U_24) )
& ~ greater(growth_rate(efficient_producers,U_25),growth_rate(first_movers,U_25)) )
| U_25 != critical_point(U_26)
| ~ environment(U_26) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_26,U_25,U_24] :
( greater(growth_rate(efficient_producers,U_24),growth_rate(first_movers,U_24))
| ~ greater(U_24,U_25)
| ~ subpopulations(first_movers,efficient_producers,U_26,U_24)
| ~ sP2(U_26,U_25,U_24) )
& ! [U_26,U_25,U_24] :
( ~ greater(growth_rate(efficient_producers,U_25),growth_rate(first_movers,U_25))
| ~ sP2(U_26,U_25,U_24) )
& ! [U_26,U_25,U_24] :
( sP2(U_26,U_25,U_24)
| U_25 != critical_point(U_26)
| ~ environment(U_26) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_9_2]) ).
cnf(f_9_4,plain,
( sP2(U_26,U_25,U_24)
| U_25 != critical_point(U_26)
| ~ environment(U_26) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_5,plain,
( ~ greater(growth_rate(efficient_producers,U_25),growth_rate(first_movers,U_25))
| ~ sP2(U_26,U_25,U_24) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_6,plain,
( greater(growth_rate(efficient_producers,U_24),growth_rate(first_movers,U_24))
| ~ greater(U_24,U_25)
| ~ subpopulations(first_movers,efficient_producers,U_26,U_24)
| ~ sP2(U_26,U_25,U_24) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_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_10_2,plain,
! [U_28,U_27] :
( greater(cardinality_at_time(efficient_producers,U_27),zero)
| ~ greater_or_equal(U_27,appear(efficient_producers,U_28))
| ~ in_environment(U_28,U_27)
| ~ environment(U_28) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_27,U_28] :
( greater(cardinality_at_time(efficient_producers,U_27),zero)
| ~ greater_or_equal(U_27,appear(efficient_producers,U_28))
| ~ in_environment(U_28,U_27)
| ~ environment(U_28) ),
inference(definitional_conversion,[status(esa)],[f_10_2]) ).
cnf(f_10_4,plain,
( greater(cardinality_at_time(efficient_producers,U_27),zero)
| ~ greater_or_equal(U_27,appear(efficient_producers,U_28))
| ~ in_environment(U_28,U_27)
| ~ environment(U_28) ),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,negated_conjecture,
~ ! [E,T] :
( ( greater(T,critical_point(E))
& in_environment(E,T)
& environment(E) )
=> selection_favors(efficient_producers,first_movers,T) ),
inference(negate,[status(cth)],[prove_l8]) ).
fof(f_11_2,negated_conjecture,
? [E,T] :
( ~ selection_favors(efficient_producers,first_movers,T)
& greater(T,critical_point(E))
& in_environment(E,T)
& environment(E) ),
inference(fof_nnf,[status(thm)],[f_11_1]) ).
fof(f_11_3,negated_conjecture,
? [U_30,U_29] :
( ~ selection_favors(efficient_producers,first_movers,U_29)
& greater(U_29,critical_point(U_30))
& in_environment(U_30,U_29)
& environment(U_30) ),
inference(variable_rename,[status(thm)],[f_11_2]) ).
fof(f_11_4,negated_conjecture,
? [U_29] :
( ~ selection_favors(efficient_producers,first_movers,U_29)
& greater(U_29,critical_point(sK1))
& in_environment(sK1,U_29)
& environment(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_30,sK1)],[f_11_3]) ).
fof(f_11_5,negated_conjecture,
( ~ selection_favors(efficient_producers,first_movers,sK2)
& greater(sK2,critical_point(sK1))
& in_environment(sK1,sK2)
& environment(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_29,sK2)],[f_11_4]) ).
fof(f_11_6,negated_conjecture,
( ~ selection_favors(efficient_producers,first_movers,sK2)
& greater(sK2,critical_point(sK1))
& in_environment(sK1,sK2)
& environment(sK1) ),
inference(definitional_conversion,[status(esa)],[f_11_5]) ).
cnf(f_11_7,negated_conjecture,
environment(sK1),
inference(clausify,[status(thm)],[f_11_6]) ).
cnf(f_11_8,negated_conjecture,
in_environment(sK1,sK2),
inference(clausify,[status(thm)],[f_11_6]) ).
cnf(f_11_9,negated_conjecture,
greater(sK2,critical_point(sK1)),
inference(clausify,[status(thm)],[f_11_6]) ).
cnf(f_11_10,negated_conjecture,
~ selection_favors(efficient_producers,first_movers,sK2),
inference(clausify,[status(thm)],[f_11_6]) ).
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,
( 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_5,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_6,axiom,
( critical_point(Eq_x_0) = critical_point(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,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_8,axiom,
( environment(Eq_y_0)
| ~ environment(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_9,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(equality_10,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_11,axiom,
( selection_favors(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ selection_favors(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_12,axiom,
( subpopulation(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ subpopulation(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_13,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_14,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_15,axiom,
( sP0(Eq_y_0,Eq_y_1)
| ~ sP0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_16,axiom,
( sP1(Eq_y_0,Eq_y_1)
| ~ sP1(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,axiom,
( sP2(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP2(Eq_x_0,Eq_x_1,Eq_x_2)
| 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 : MGT026+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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 19 16:12:24 UTC 2026
% 0.09/0.36 % CPUTime :
% 34.55/34.86 % SZS status Theorem for theBenchmark
% 34.55/34.86 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------