%------------------------------------------------------------------------------
% File : PyRes---1.5
% Problem : MGT036+3 : TPTP v9.3.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% Computer : n018.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 : Tue Sep 8 06:18:44 AM UTC 2026
% Result : Theorem 0.31s 0.61s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 8 unt; 0 def)
% Number of atoms : 99 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 119 ( 50 ~; 44 |; 22 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 32 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(a13_star,plain,
? [E,T] :
( environment(E)
& subpopulations(first_movers,efficient_producers,E,T)
& greater_or_equal(growth_rate(first_movers,T),zero)
& greater(zero,growth_rate(efficient_producers,T)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a13_star) ).
fof(c4,plain,
? [X4,X5] :
( environment(X4)
& subpopulations(first_movers,efficient_producers,X4,X5)
& greater_or_equal(growth_rate(first_movers,X5),zero)
& greater(zero,growth_rate(efficient_producers,X5)) ),
inference(variable_rename,[status(thm)],[a13_star]) ).
fof(c5,plain,
( environment(skolem0001)
& subpopulations(first_movers,efficient_producers,skolem0001,skolem0002)
& greater_or_equal(growth_rate(first_movers,skolem0002),zero)
& greater(zero,growth_rate(efficient_producers,skolem0002)) ),
inference(skolemize,[status(esa)],[c4]) ).
cnf(c6,plain,
environment(skolem0001),
inference(split_conjunct,[status(thm)],[c5]) ).
cnf(c7,plain,
subpopulations(first_movers,efficient_producers,skolem0001,skolem0002),
inference(split_conjunct,[status(thm)],[c5]) ).
fof(prove_t5_star,conjecture,
? [E,T] :
( environment(E)
& subpopulations(first_movers,efficient_producers,E,T)
& outcompetes(first_movers,efficient_producers,T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t5_star) ).
fof(c0,negated_conjecture,
~ ? [E,T] :
( environment(E)
& subpopulations(first_movers,efficient_producers,E,T)
& outcompetes(first_movers,efficient_producers,T) ),
inference(assume_negation,[status(cth)],[prove_t5_star]) ).
fof(c1,negated_conjecture,
! [E,T] :
( ~ environment(E)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ outcompetes(first_movers,efficient_producers,T) ),
inference(fof_nnf,[status(thm)],[c0]) ).
fof(c2,negated_conjecture,
! [X2,X3] :
( ~ environment(X2)
| ~ subpopulations(first_movers,efficient_producers,X2,X3)
| ~ outcompetes(first_movers,efficient_producers,X3) ),
inference(variable_rename,[status(thm)],[c1]) ).
cnf(c3,negated_conjecture,
( ~ environment(X18)
| ~ subpopulations(first_movers,efficient_producers,X18,X19)
| ~ outcompetes(first_movers,efficient_producers,X19) ),
inference(split_conjunct,[status(thm)],[c2]) ).
cnf(c20,plain,
( ~ environment(skolem0001)
| ~ outcompetes(first_movers,efficient_producers,skolem0002) ),
inference(resolution,[status(thm)],[c3,c7]) ).
fof(mp_symmetry_of_subpopulations,axiom,
! [E,S1,S2,T] :
( ( environment(E)
& subpopulations(S1,S2,E,T) )
=> subpopulations(S2,S1,E,T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations) ).
fof(c16,plain,
! [E,S1,S2,T] :
( ~ environment(E)
| ~ subpopulations(S1,S2,E,T)
| subpopulations(S2,S1,E,T) ),
inference(fof_nnf,[status(thm)],[mp_symmetry_of_subpopulations]) ).
fof(c17,plain,
! [X10,X11,X12,X13] :
( ~ environment(X10)
| ~ subpopulations(X11,X12,X10,X13)
| subpopulations(X12,X11,X10,X13) ),
inference(variable_rename,[status(thm)],[c16]) ).
cnf(c18,plain,
( ~ environment(X17)
| ~ subpopulations(X16,X15,X17,X14)
| subpopulations(X15,X16,X17,X14) ),
inference(split_conjunct,[status(thm)],[c17]) ).
cnf(c19,plain,
( ~ environment(skolem0001)
| subpopulations(efficient_producers,first_movers,skolem0001,skolem0002) ),
inference(resolution,[status(thm)],[c18,c7]) ).
cnf(c21,plain,
subpopulations(efficient_producers,first_movers,skolem0001,skolem0002),
inference(resolution,[status(thm)],[c19,c6]) ).
cnf(c8,plain,
greater_or_equal(growth_rate(first_movers,skolem0002),zero),
inference(split_conjunct,[status(thm)],[c5]) ).
cnf(c9,plain,
greater(zero,growth_rate(efficient_producers,skolem0002)),
inference(split_conjunct,[status(thm)],[c5]) ).
fof(d2,plain,
! [E,S1,S2,T] :
( ( environment(E)
& subpopulations(S1,S2,E,T) )
=> ( ( greater_or_equal(growth_rate(S2,T),zero)
& greater(zero,growth_rate(S1,T)) )
<=> outcompetes(S2,S1,T) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
fof(c10,plain,
! [E,S1,S2,T] :
( ~ environment(E)
| ~ subpopulations(S1,S2,E,T)
| ( ( ~ greater_or_equal(growth_rate(S2,T),zero)
| ~ greater(zero,growth_rate(S1,T))
| outcompetes(S2,S1,T) )
& ( ~ outcompetes(S2,S1,T)
| ( greater_or_equal(growth_rate(S2,T),zero)
& greater(zero,growth_rate(S1,T)) ) ) ) ),
inference(fof_nnf,[status(thm)],[d2]) ).
fof(c11,plain,
! [X6,X7,X8,X9] :
( ~ environment(X6)
| ~ subpopulations(X7,X8,X6,X9)
| ( ( ~ greater_or_equal(growth_rate(X8,X9),zero)
| ~ greater(zero,growth_rate(X7,X9))
| outcompetes(X8,X7,X9) )
& ( ~ outcompetes(X8,X7,X9)
| ( greater_or_equal(growth_rate(X8,X9),zero)
& greater(zero,growth_rate(X7,X9)) ) ) ) ),
inference(variable_rename,[status(thm)],[c10]) ).
fof(c12,plain,
! [X6,X7,X8,X9] :
( ( ~ environment(X6)
| ~ subpopulations(X7,X8,X6,X9)
| ~ greater_or_equal(growth_rate(X8,X9),zero)
| ~ greater(zero,growth_rate(X7,X9))
| outcompetes(X8,X7,X9) )
& ( ~ environment(X6)
| ~ subpopulations(X7,X8,X6,X9)
| ~ outcompetes(X8,X7,X9)
| greater_or_equal(growth_rate(X8,X9),zero) )
& ( ~ environment(X6)
| ~ subpopulations(X7,X8,X6,X9)
| ~ outcompetes(X8,X7,X9)
| greater(zero,growth_rate(X7,X9)) ) ),
inference(distribute,[status(thm)],[c11]) ).
cnf(c13,plain,
( ~ environment(X24)
| ~ subpopulations(X26,X25,X24,X27)
| ~ greater_or_equal(growth_rate(X25,X27),zero)
| ~ greater(zero,growth_rate(X26,X27))
| outcompetes(X25,X26,X27) ),
inference(split_conjunct,[status(thm)],[c12]) ).
cnf(c25,plain,
( ~ environment(X33)
| ~ subpopulations(efficient_producers,X32,X33,skolem0002)
| ~ greater_or_equal(growth_rate(X32,skolem0002),zero)
| outcompetes(X32,efficient_producers,skolem0002) ),
inference(resolution,[status(thm)],[c13,c9]) ).
cnf(c28,plain,
( ~ environment(X34)
| ~ subpopulations(efficient_producers,first_movers,X34,skolem0002)
| outcompetes(first_movers,efficient_producers,skolem0002) ),
inference(resolution,[status(thm)],[c25,c8]) ).
cnf(c29,plain,
( ~ environment(skolem0001)
| outcompetes(first_movers,efficient_producers,skolem0002) ),
inference(resolution,[status(thm)],[c28,c21]) ).
cnf(c30,plain,
outcompetes(first_movers,efficient_producers,skolem0002),
inference(resolution,[status(thm)],[c29,c6]) ).
cnf(c31,plain,
~ environment(skolem0001),
inference(resolution,[status(thm)],[c30,c20]) ).
cnf(c32,plain,
$false,
inference(resolution,[status(thm)],[c31,c6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT036+3 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.03 % Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 7 12:43:52 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.42 /export/starexec/sandbox2/solver/bin/lexer.py:155: SyntaxWarning: invalid escape sequence '\.'
% 0.10/0.42 (re.compile("\."), Token.FullStop),
% 0.10/0.42 /export/starexec/sandbox2/solver/bin/lexer.py:156: SyntaxWarning: invalid escape sequence '\('
% 0.10/0.43 (re.compile("\("), Token.OpenPar),
% 0.10/0.43 /export/starexec/sandbox2/solver/bin/lexer.py:157: SyntaxWarning: invalid escape sequence '\)'
% 0.10/0.43 (re.compile("\)"), Token.ClosePar),
% 0.10/0.43 /export/starexec/sandbox2/solver/bin/lexer.py:158: SyntaxWarning: invalid escape sequence '\['
% 0.10/0.43 (re.compile("\["), Token.OpenSquare),
% 0.10/0.43 /export/starexec/sandbox2/solver/bin/lexer.py:159: SyntaxWarning: invalid escape sequence '\]'
% 0.10/0.43 (re.compile("\]"), Token.CloseSquare),
% 0.10/0.43 /export/starexec/sandbox2/solver/bin/lexer.py:162: SyntaxWarning: invalid escape sequence '\|'
% 0.10/0.43 (re.compile("~\|"), Token.Nor),
% 0.10/0.43 /export/starexec/sandbox2/solver/bin/lexer.py:164: SyntaxWarning: invalid escape sequence '\|'
% 0.10/0.43 (re.compile("\|"), Token.Or),
% 0.10/0.43 /export/starexec/sandbox2/solver/bin/lexer.py:175: SyntaxWarning: invalid escape sequence '\?'
% 0.10/0.43 (re.compile("\?"), Token.Existential),
% 0.10/0.43 /export/starexec/sandbox2/solver/bin/lexer.py:176: SyntaxWarning: invalid escape sequence '\s'
% 0.10/0.43 (re.compile("\s+"), Token.WhiteSpace),
% 0.10/0.43 /export/starexec/sandbox2/solver/bin/lexer.py:180: SyntaxWarning: invalid escape sequence '\$'
% 0.10/0.43 (re.compile("\$[_a-z0-9_A-Z]*"), Token.DefFunctor),
% 0.21/0.50 /export/starexec/sandbox2/solver/bin/signature.py:6: SyntaxWarning: invalid escape sequence '\c'
% 0.21/0.50 """
% 0.21/0.50 /export/starexec/sandbox2/solver/bin/literals.py:6: SyntaxWarning: invalid escape sequence '\c'
% 0.21/0.50 """
% 0.31/0.59 /export/starexec/sandbox2/solver/bin/unification.py:6: SyntaxWarning: invalid escape sequence '\c'
% 0.31/0.59 """
% 0.31/0.61 % Version: 1.5
% 0.31/0.61 % SZS status Theorem
% 0.31/0.61 % SZS output start CNFRefutation
% See solution above
% 0.31/0.61
% 0.31/0.61 % Initial clauses : 9
% 0.31/0.61 % Processed clauses : 19
% 0.31/0.61 % Factors computed : 0
% 0.31/0.61 % Resolvents computed: 14
% 0.31/0.61 % Tautologies deleted: 0
% 0.31/0.61 % Forward subsumed : 3
% 0.31/0.61 % Backward subsumed : 6
% 0.31/0.61 % -------- CPU Time ---------
% 0.31/0.61 % User time : 0.213 s
% 0.31/0.61 % System time : 0.035 s
% 0.31/0.61 % Total time : 0.248 s
%------------------------------------------------------------------------------