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ConnectPP---0.7.2.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : ConnectPP---0.7.2
% Problem  : MGT025+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 : n015.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 08:50:37 AM UTC 2026

% Result   : Theorem 18.56s 18.84s
% Output   : Proof 19.08s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
fof(mp_only_members,axiom,
    ! [E,X,T] :
      ( ( ( greater(cardinality_at_time(X,T),zero)
         => ( X = first_movers
            | X = efficient_producers ) )
        & subpopulation(X,E,T)
        & environment(E) )
     => number_of_organizations(E,T) = sum(cardinality_at_time(first_movers,T),cardinality_at_time(efficient_producers,T)) ),
    file('theBenchmark.p',mp_only_members) ).

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_abc_sum_increase,axiom,
    ! [A,B,C] :
      ( ( constant(A)
        & A = sum(B,C) )
     => ( ( increases(C)
          & decreases(B) )
        | ( decreases(C)
          & increases(B) )
        | ( constant(C)
          & constant(B) ) ) ),
    file('theBenchmark.p',mp_abc_sum_increase) ).

fof(mp_growth_rate,axiom,
    ! [X,E,T] :
      ( ( greater(cardinality_at_time(X,T),zero)
        & subpopulation(X,E,T)
        & in_environment(E,T)
        & environment(E) )
     => ( ( decreases(cardinality_at_time(X,T))
         => greater(zero,growth_rate(X,T)) )
        & ( increases(cardinality_at_time(X,T))
         => greater(growth_rate(X,T),zero) )
        & ( constant(cardinality_at_time(X,T))
         => growth_rate(X,T) = zero ) ) ),
    file('theBenchmark.p',mp_growth_rate) ).

fof(mp_non_zero_producers,axiom,
    ! [E,T] :
      ( ( subpopulations(first_movers,efficient_producers,E,T)
        & environment(E) )
     => ( greater(cardinality_at_time(efficient_producers,T),zero)
        & greater(cardinality_at_time(first_movers,T),zero) ) ),
    file('theBenchmark.p',mp_non_zero_producers) ).

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(a9,hypothesis,
    ! [E,X,T] :
      ( ( greater(cardinality_at_time(X,T),zero)
        & subpopulation(X,E,T)
        & environment(E) )
     => ( X = first_movers
        | X = efficient_producers ) ),
    file('theBenchmark.p',a9) ).

fof(prove_l7,conjecture,
    ! [E,T] :
      ( ( constant(number_of_organizations(E,T))
        & subpopulations(first_movers,efficient_producers,E,T)
        & environment(E) )
     => ( ( greater(zero,growth_rate(first_movers,T))
          & greater(growth_rate(efficient_producers,T),zero) )
        | ( greater(zero,growth_rate(efficient_producers,T))
          & greater(growth_rate(first_movers,T),zero) )
        | ( growth_rate(efficient_producers,T) = zero
          & growth_rate(first_movers,T) = zero ) ) ),
    file('theBenchmark.p',prove_l7) ).

fof(f_1_1,plain,
    ! [E,X,T] :
      ( number_of_organizations(E,T) = sum(cardinality_at_time(first_movers,T),cardinality_at_time(efficient_producers,T))
      | ( X != first_movers
        & X != efficient_producers
        & greater(cardinality_at_time(X,T),zero) )
      | ~ subpopulation(X,E,T)
      | ~ environment(E) ),
    inference(fof_nnf,[status(thm)],[mp_only_members]) ).

fof(f_1_2,plain,
    ! [U_2,U_1,U_0] :
      ( number_of_organizations(U_2,U_0) = sum(cardinality_at_time(first_movers,U_0),cardinality_at_time(efficient_producers,U_0))
      | ( U_1 != first_movers
        & U_1 != efficient_producers
        & greater(cardinality_at_time(U_1,U_0),zero) )
      | ~ subpopulation(U_1,U_2,U_0)
      | ~ environment(U_2) ),
    inference(variable_rename,[status(thm)],[f_1_1]) ).

cnf(f_1_3,plain,
    ( greater(cardinality_at_time(U_1,U_0),zero)
    | ~ subpopulation(U_1,U_2,U_0)
    | ~ environment(U_2)
    | number_of_organizations(U_2,U_0) = sum(cardinality_at_time(first_movers,U_0),cardinality_at_time(efficient_producers,U_0)) ),
    inference(clausify,[status(thm)],[f_1_2]) ).

cnf(f_1_4,plain,
    ( U_1 != efficient_producers
    | ~ subpopulation(U_1,U_2,U_0)
    | ~ environment(U_2)
    | number_of_organizations(U_2,U_0) = sum(cardinality_at_time(first_movers,U_0),cardinality_at_time(efficient_producers,U_0)) ),
    inference(clausify,[status(thm)],[f_1_2]) ).

cnf(f_1_5,plain,
    ( U_1 != first_movers
    | ~ subpopulation(U_1,U_2,U_0)
    | ~ environment(U_2)
    | number_of_organizations(U_2,U_0) = sum(cardinality_at_time(first_movers,U_0),cardinality_at_time(efficient_producers,U_0)) ),
    inference(clausify,[status(thm)],[f_1_2]) ).

fof(f_2_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_2_2,plain,
    ! [U_4,U_3] :
      ( ( subpopulation(efficient_producers,U_4,U_3)
        & subpopulation(first_movers,U_4,U_3) )
      | ~ in_environment(U_4,U_3)
      | ~ environment(U_4) ),
    inference(variable_rename,[status(thm)],[f_2_1]) ).

cnf(f_2_3,plain,
    ( subpopulation(first_movers,U_4,U_3)
    | ~ in_environment(U_4,U_3)
    | ~ environment(U_4) ),
    inference(clausify,[status(thm)],[f_2_2]) ).

cnf(f_2_4,plain,
    ( subpopulation(efficient_producers,U_4,U_3)
    | ~ in_environment(U_4,U_3)
    | ~ environment(U_4) ),
    inference(clausify,[status(thm)],[f_2_2]) ).

fof(f_3_1,plain,
    ! [A,B,C] :
      ( ( increases(C)
        & decreases(B) )
      | ( decreases(C)
        & increases(B) )
      | ( constant(C)
        & constant(B) )
      | ~ constant(A)
      | A != sum(B,C) ),
    inference(fof_nnf,[status(thm)],[mp_abc_sum_increase]) ).

fof(f_3_2,plain,
    ! [U_7,U_6,U_5] :
      ( ( increases(U_5)
        & decreases(U_6) )
      | ( decreases(U_5)
        & increases(U_6) )
      | ( constant(U_5)
        & constant(U_6) )
      | ~ constant(U_7)
      | U_7 != sum(U_6,U_5) ),
    inference(variable_rename,[status(thm)],[f_3_1]) ).

cnf(f_3_3,plain,
    ( increases(U_6)
    | constant(U_6)
    | decreases(U_6)
    | ~ constant(U_7)
    | U_7 != sum(U_6,U_5) ),
    inference(clausify,[status(thm)],[f_3_2]) ).

cnf(f_3_4,plain,
    ( decreases(U_5)
    | constant(U_6)
    | decreases(U_6)
    | ~ constant(U_7)
    | U_7 != sum(U_6,U_5) ),
    inference(clausify,[status(thm)],[f_3_2]) ).

cnf(f_3_5,plain,
    ( increases(U_6)
    | constant(U_5)
    | decreases(U_6)
    | ~ constant(U_7)
    | U_7 != sum(U_6,U_5) ),
    inference(clausify,[status(thm)],[f_3_2]) ).

cnf(f_3_6,plain,
    ( decreases(U_5)
    | constant(U_5)
    | decreases(U_6)
    | ~ constant(U_7)
    | U_7 != sum(U_6,U_5) ),
    inference(clausify,[status(thm)],[f_3_2]) ).

cnf(f_3_7,plain,
    ( increases(U_6)
    | constant(U_6)
    | increases(U_5)
    | ~ constant(U_7)
    | U_7 != sum(U_6,U_5) ),
    inference(clausify,[status(thm)],[f_3_2]) ).

cnf(f_3_8,plain,
    ( decreases(U_5)
    | constant(U_6)
    | increases(U_5)
    | ~ constant(U_7)
    | U_7 != sum(U_6,U_5) ),
    inference(clausify,[status(thm)],[f_3_2]) ).

cnf(f_3_9,plain,
    ( increases(U_6)
    | constant(U_5)
    | increases(U_5)
    | ~ constant(U_7)
    | U_7 != sum(U_6,U_5) ),
    inference(clausify,[status(thm)],[f_3_2]) ).

cnf(f_3_10,plain,
    ( decreases(U_5)
    | constant(U_5)
    | increases(U_5)
    | ~ constant(U_7)
    | U_7 != sum(U_6,U_5) ),
    inference(clausify,[status(thm)],[f_3_2]) ).

fof(f_4_1,plain,
    ! [X,E,T] :
      ( ( ( greater(zero,growth_rate(X,T))
          | ~ decreases(cardinality_at_time(X,T)) )
        & ( greater(growth_rate(X,T),zero)
          | ~ increases(cardinality_at_time(X,T)) )
        & ( growth_rate(X,T) = zero
          | ~ constant(cardinality_at_time(X,T)) ) )
      | ~ greater(cardinality_at_time(X,T),zero)
      | ~ subpopulation(X,E,T)
      | ~ in_environment(E,T)
      | ~ environment(E) ),
    inference(fof_nnf,[status(thm)],[mp_growth_rate]) ).

fof(f_4_2,plain,
    ! [U_10,U_9,U_8] :
      ( ( ( greater(zero,growth_rate(U_10,U_8))
          | ~ decreases(cardinality_at_time(U_10,U_8)) )
        & ( greater(growth_rate(U_10,U_8),zero)
          | ~ increases(cardinality_at_time(U_10,U_8)) )
        & ( growth_rate(U_10,U_8) = zero
          | ~ constant(cardinality_at_time(U_10,U_8)) ) )
      | ~ greater(cardinality_at_time(U_10,U_8),zero)
      | ~ subpopulation(U_10,U_9,U_8)
      | ~ in_environment(U_9,U_8)
      | ~ environment(U_9) ),
    inference(variable_rename,[status(thm)],[f_4_1]) ).

cnf(f_4_3,plain,
    ( growth_rate(U_10,U_8) = zero
    | ~ constant(cardinality_at_time(U_10,U_8))
    | ~ greater(cardinality_at_time(U_10,U_8),zero)
    | ~ subpopulation(U_10,U_9,U_8)
    | ~ in_environment(U_9,U_8)
    | ~ environment(U_9) ),
    inference(clausify,[status(thm)],[f_4_2]) ).

cnf(f_4_4,plain,
    ( greater(growth_rate(U_10,U_8),zero)
    | ~ increases(cardinality_at_time(U_10,U_8))
    | ~ greater(cardinality_at_time(U_10,U_8),zero)
    | ~ subpopulation(U_10,U_9,U_8)
    | ~ in_environment(U_9,U_8)
    | ~ environment(U_9) ),
    inference(clausify,[status(thm)],[f_4_2]) ).

cnf(f_4_5,plain,
    ( greater(zero,growth_rate(U_10,U_8))
    | ~ decreases(cardinality_at_time(U_10,U_8))
    | ~ greater(cardinality_at_time(U_10,U_8),zero)
    | ~ subpopulation(U_10,U_9,U_8)
    | ~ in_environment(U_9,U_8)
    | ~ environment(U_9) ),
    inference(clausify,[status(thm)],[f_4_2]) ).

fof(f_5_1,plain,
    ! [E,T] :
      ( ( greater(cardinality_at_time(efficient_producers,T),zero)
        & greater(cardinality_at_time(first_movers,T),zero) )
      | ~ subpopulations(first_movers,efficient_producers,E,T)
      | ~ environment(E) ),
    inference(fof_nnf,[status(thm)],[mp_non_zero_producers]) ).

fof(f_5_2,plain,
    ! [U_12,U_11] :
      ( ( greater(cardinality_at_time(efficient_producers,U_11),zero)
        & greater(cardinality_at_time(first_movers,U_11),zero) )
      | ~ subpopulations(first_movers,efficient_producers,U_12,U_11)
      | ~ environment(U_12) ),
    inference(variable_rename,[status(thm)],[f_5_1]) ).

cnf(f_5_3,plain,
    ( greater(cardinality_at_time(first_movers,U_11),zero)
    | ~ subpopulations(first_movers,efficient_producers,U_12,U_11)
    | ~ environment(U_12) ),
    inference(clausify,[status(thm)],[f_5_2]) ).

cnf(f_5_4,plain,
    ( greater(cardinality_at_time(efficient_producers,U_11),zero)
    | ~ subpopulations(first_movers,efficient_producers,U_12,U_11)
    | ~ environment(U_12) ),
    inference(clausify,[status(thm)],[f_5_2]) ).

fof(f_6_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_6_2,plain,
    ! [U_14,U_13] :
      ( in_environment(U_14,U_13)
      | ~ subpopulations(first_movers,efficient_producers,U_14,U_13)
      | ~ environment(U_14) ),
    inference(variable_rename,[status(thm)],[f_6_1]) ).

cnf(f_6_3,plain,
    ( in_environment(U_14,U_13)
    | ~ subpopulations(first_movers,efficient_producers,U_14,U_13)
    | ~ environment(U_14) ),
    inference(clausify,[status(thm)],[f_6_2]) ).

fof(f_7_1,plain,
    ! [E,X,T] :
      ( X = first_movers
      | X = efficient_producers
      | ~ greater(cardinality_at_time(X,T),zero)
      | ~ subpopulation(X,E,T)
      | ~ environment(E) ),
    inference(fof_nnf,[status(thm)],[a9]) ).

fof(f_7_2,plain,
    ! [U_17,U_16,U_15] :
      ( U_16 = first_movers
      | U_16 = efficient_producers
      | ~ greater(cardinality_at_time(U_16,U_15),zero)
      | ~ subpopulation(U_16,U_17,U_15)
      | ~ environment(U_17) ),
    inference(variable_rename,[status(thm)],[f_7_1]) ).

fof(f_7_3,plain,
    ! [U_17,U_16] :
      ( ! [U_15] :
          ( ~ greater(cardinality_at_time(U_16,U_15),zero)
          | ~ subpopulation(U_16,U_17,U_15) )
      | ~ environment(U_17)
      | U_16 = first_movers
      | U_16 = efficient_producers ),
    inference(miniscope,[status(thm)],[f_7_2]) ).

cnf(f_7_4,plain,
    ( ~ greater(cardinality_at_time(U_16,U_15),zero)
    | ~ subpopulation(U_16,U_17,U_15)
    | ~ environment(U_17)
    | U_16 = first_movers
    | U_16 = efficient_producers ),
    inference(clausify,[status(thm)],[f_7_3]) ).

fof(f_8_1,negated_conjecture,
    ~ ! [E,T] :
        ( ( constant(number_of_organizations(E,T))
          & subpopulations(first_movers,efficient_producers,E,T)
          & environment(E) )
       => ( ( greater(zero,growth_rate(first_movers,T))
            & greater(growth_rate(efficient_producers,T),zero) )
          | ( greater(zero,growth_rate(efficient_producers,T))
            & greater(growth_rate(first_movers,T),zero) )
          | ( growth_rate(efficient_producers,T) = zero
            & growth_rate(first_movers,T) = zero ) ) ),
    inference(negate,[status(cth)],[prove_l7]) ).

fof(f_8_2,negated_conjecture,
    ? [E,T] :
      ( ( ~ greater(zero,growth_rate(first_movers,T))
        | ~ greater(growth_rate(efficient_producers,T),zero) )
      & ( ~ greater(zero,growth_rate(efficient_producers,T))
        | ~ greater(growth_rate(first_movers,T),zero) )
      & ( growth_rate(efficient_producers,T) != zero
        | growth_rate(first_movers,T) != zero )
      & constant(number_of_organizations(E,T))
      & subpopulations(first_movers,efficient_producers,E,T)
      & environment(E) ),
    inference(fof_nnf,[status(thm)],[f_8_1]) ).

fof(f_8_3,negated_conjecture,
    ? [U_19,U_18] :
      ( ( ~ greater(zero,growth_rate(first_movers,U_18))
        | ~ greater(growth_rate(efficient_producers,U_18),zero) )
      & ( ~ greater(zero,growth_rate(efficient_producers,U_18))
        | ~ greater(growth_rate(first_movers,U_18),zero) )
      & ( growth_rate(efficient_producers,U_18) != zero
        | growth_rate(first_movers,U_18) != zero )
      & constant(number_of_organizations(U_19,U_18))
      & subpopulations(first_movers,efficient_producers,U_19,U_18)
      & environment(U_19) ),
    inference(variable_rename,[status(thm)],[f_8_2]) ).

fof(f_8_4,negated_conjecture,
    ? [U_18] :
      ( ( ~ greater(zero,growth_rate(first_movers,U_18))
        | ~ greater(growth_rate(efficient_producers,U_18),zero) )
      & ( ~ greater(zero,growth_rate(efficient_producers,U_18))
        | ~ greater(growth_rate(first_movers,U_18),zero) )
      & ( growth_rate(efficient_producers,U_18) != zero
        | growth_rate(first_movers,U_18) != zero )
      & constant(number_of_organizations(sK1,U_18))
      & subpopulations(first_movers,efficient_producers,sK1,U_18)
      & environment(sK1) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_19,sK1)],[f_8_3]) ).

fof(f_8_5,negated_conjecture,
    ( ( ~ greater(zero,growth_rate(first_movers,sK2))
      | ~ greater(growth_rate(efficient_producers,sK2),zero) )
    & ( ~ greater(zero,growth_rate(efficient_producers,sK2))
      | ~ greater(growth_rate(first_movers,sK2),zero) )
    & ( growth_rate(efficient_producers,sK2) != zero
      | growth_rate(first_movers,sK2) != zero )
    & constant(number_of_organizations(sK1,sK2))
    & subpopulations(first_movers,efficient_producers,sK1,sK2)
    & environment(sK1) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_18,sK2)],[f_8_4]) ).

fof(f_8_6,negated_conjecture,
    ( ( ~ greater(zero,growth_rate(first_movers,sK2))
      | ~ greater(growth_rate(efficient_producers,sK2),zero) )
    & ( ~ greater(zero,growth_rate(efficient_producers,sK2))
      | ~ greater(growth_rate(first_movers,sK2),zero) )
    & ( growth_rate(efficient_producers,sK2) != zero
      | growth_rate(first_movers,sK2) != zero )
    & constant(number_of_organizations(sK1,sK2))
    & subpopulations(first_movers,efficient_producers,sK1,sK2)
    & environment(sK1) ),
    inference(definitional_conversion,[status(esa)],[f_8_5]) ).

cnf(f_8_7,negated_conjecture,
    environment(sK1),
    inference(clausify,[status(thm)],[f_8_6]) ).

cnf(f_8_8,negated_conjecture,
    subpopulations(first_movers,efficient_producers,sK1,sK2),
    inference(clausify,[status(thm)],[f_8_6]) ).

cnf(f_8_9,negated_conjecture,
    constant(number_of_organizations(sK1,sK2)),
    inference(clausify,[status(thm)],[f_8_6]) ).

cnf(f_8_10,negated_conjecture,
    ( growth_rate(efficient_producers,sK2) != zero
    | growth_rate(first_movers,sK2) != zero ),
    inference(clausify,[status(thm)],[f_8_6]) ).

cnf(f_8_11,negated_conjecture,
    ( ~ greater(zero,growth_rate(efficient_producers,sK2))
    | ~ greater(growth_rate(first_movers,sK2),zero) ),
    inference(clausify,[status(thm)],[f_8_6]) ).

cnf(f_8_12,negated_conjecture,
    ( ~ greater(zero,growth_rate(first_movers,sK2))
    | ~ greater(growth_rate(efficient_producers,sK2),zero) ),
    inference(clausify,[status(thm)],[f_8_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,
    ( 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,
    ( number_of_organizations(Eq_x_0,Eq_x_1) = number_of_organizations(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,
    ( sum(Eq_x_0,Eq_x_1) = sum(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,
    ( 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_8,axiom,
    ( environment(Eq_y_0)
    | ~ environment(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_9,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_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,
    ( 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,
    ( constant(Eq_y_0)
    | ~ constant(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_13,axiom,
    ( increases(Eq_y_0)
    | ~ increases(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_14,axiom,
    ( decreases(Eq_y_0)
    | ~ decreases(Eq_x_0)
    | 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  : MGT025+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
% 0.09/0.35  % Computer : n015.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 16:15:33 UTC 2026
% 0.09/0.36  % CPUTime  : 
% 18.56/18.84  % SZS status Theorem for theBenchmark
% 18.56/18.84  % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------