%------------------------------------------------------------------------------
% File : PyRes---1.5
% Problem : MGT022+1 : 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 06:18:40 AM UTC 2026
% Result : Theorem 0.33s 0.60s
% Output : CNFRefutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 38 ( 9 unt; 0 def)
% Number of atoms : 135 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 156 ( 59 ~; 54 |; 29 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 26 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mp_constant_not_decrease,axiom,
! [X] :
( constant(X)
=> ~ decreases(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_constant_not_decrease) ).
fof(c18,plain,
! [X] :
( constant(X)
=> ~ decreases(X) ),
inference(fof_simplification,[status(thm)],[mp_constant_not_decrease]) ).
fof(c19,plain,
! [X] :
( ~ constant(X)
| ~ decreases(X) ),
inference(fof_nnf,[status(thm)],[c18]) ).
fof(c20,plain,
! [X8] :
( ~ constant(X8)
| ~ decreases(X8) ),
inference(variable_rename,[status(thm)],[c19]) ).
cnf(c21,plain,
( ~ constant(X9)
| ~ decreases(X9) ),
inference(split_conjunct,[status(thm)],[c20]) ).
fof(prove_l4,conjecture,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> ( ( decreases(resources(E,T))
=> increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) )
& ( constant(resources(E,T))
=> ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l4) ).
fof(c0,negated_conjecture,
~ ! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> ( ( decreases(resources(E,T))
=> increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) )
& ( constant(resources(E,T))
=> ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ) ) ),
inference(assume_negation,[status(cth)],[prove_l4]) ).
fof(c1,negated_conjecture,
~ ! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> ( ( decreases(resources(E,T))
=> increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) )
& ( constant(resources(E,T))
=> ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ) ) ),
inference(fof_simplification,[status(thm)],[c0]) ).
fof(c2,negated_conjecture,
? [E,T] :
( environment(E)
& subpopulations(first_movers,efficient_producers,E,T)
& ( ( decreases(resources(E,T))
& ~ increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) )
| ( constant(resources(E,T))
& decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ) ) ),
inference(fof_nnf,[status(thm)],[c1]) ).
fof(c3,negated_conjecture,
? [X2,X3] :
( environment(X2)
& subpopulations(first_movers,efficient_producers,X2,X3)
& ( ( decreases(resources(X2,X3))
& ~ increases(difference(disbanding_rate(first_movers,X3),disbanding_rate(efficient_producers,X3))) )
| ( constant(resources(X2,X3))
& decreases(difference(disbanding_rate(first_movers,X3),disbanding_rate(efficient_producers,X3))) ) ) ),
inference(variable_rename,[status(thm)],[c2]) ).
fof(c4,negated_conjecture,
( environment(skolem0001)
& subpopulations(first_movers,efficient_producers,skolem0001,skolem0002)
& ( ( decreases(resources(skolem0001,skolem0002))
& ~ increases(difference(disbanding_rate(first_movers,skolem0002),disbanding_rate(efficient_producers,skolem0002))) )
| ( constant(resources(skolem0001,skolem0002))
& decreases(difference(disbanding_rate(first_movers,skolem0002),disbanding_rate(efficient_producers,skolem0002))) ) ) ),
inference(skolemize,[status(esa)],[c3]) ).
fof(c5,negated_conjecture,
( environment(skolem0001)
& subpopulations(first_movers,efficient_producers,skolem0001,skolem0002)
& ( decreases(resources(skolem0001,skolem0002))
| constant(resources(skolem0001,skolem0002)) )
& ( decreases(resources(skolem0001,skolem0002))
| decreases(difference(disbanding_rate(first_movers,skolem0002),disbanding_rate(efficient_producers,skolem0002))) )
& ( ~ increases(difference(disbanding_rate(first_movers,skolem0002),disbanding_rate(efficient_producers,skolem0002)))
| constant(resources(skolem0001,skolem0002)) )
& ( ~ increases(difference(disbanding_rate(first_movers,skolem0002),disbanding_rate(efficient_producers,skolem0002)))
| decreases(difference(disbanding_rate(first_movers,skolem0002),disbanding_rate(efficient_producers,skolem0002))) ) ),
inference(distribute,[status(thm)],[c4]) ).
cnf(c9,negated_conjecture,
( decreases(resources(skolem0001,skolem0002))
| decreases(difference(disbanding_rate(first_movers,skolem0002),disbanding_rate(efficient_producers,skolem0002))) ),
inference(split_conjunct,[status(thm)],[c5]) ).
cnf(c23,plain,
( decreases(difference(disbanding_rate(first_movers,skolem0002),disbanding_rate(efficient_producers,skolem0002)))
| ~ constant(resources(skolem0001,skolem0002)) ),
inference(resolution,[status(thm)],[c9,c21]) ).
cnf(c10,negated_conjecture,
( ~ increases(difference(disbanding_rate(first_movers,skolem0002),disbanding_rate(efficient_producers,skolem0002)))
| constant(resources(skolem0001,skolem0002)) ),
inference(split_conjunct,[status(thm)],[c5]) ).
cnf(c6,negated_conjecture,
environment(skolem0001),
inference(split_conjunct,[status(thm)],[c5]) ).
cnf(c8,negated_conjecture,
( decreases(resources(skolem0001,skolem0002))
| constant(resources(skolem0001,skolem0002)) ),
inference(split_conjunct,[status(thm)],[c5]) ).
cnf(c7,negated_conjecture,
subpopulations(first_movers,efficient_producers,skolem0001,skolem0002),
inference(split_conjunct,[status(thm)],[c5]) ).
fof(a2,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
cnf(c12,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(split_conjunct,[status(thm)],[a2]) ).
fof(a5,plain,
! [E,S1,S2,T] :
( ( environment(E)
& subpopulations(S1,S2,E,T)
& greater(resilience(S2),resilience(S1)) )
=> ( ( decreases(resources(E,T))
=> increases(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) )
& ( constant(resources(E,T))
=> constant(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a5) ).
fof(c13,plain,
! [E,S1,S2,T] :
( ~ environment(E)
| ~ subpopulations(S1,S2,E,T)
| ~ greater(resilience(S2),resilience(S1))
| ( ( ~ decreases(resources(E,T))
| increases(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) )
& ( ~ constant(resources(E,T))
| constant(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) ) ) ),
inference(fof_nnf,[status(thm)],[a5]) ).
fof(c14,plain,
! [X4,X5,X6,X7] :
( ~ environment(X4)
| ~ subpopulations(X5,X6,X4,X7)
| ~ greater(resilience(X6),resilience(X5))
| ( ( ~ decreases(resources(X4,X7))
| increases(difference(disbanding_rate(X5,X7),disbanding_rate(X6,X7))) )
& ( ~ constant(resources(X4,X7))
| constant(difference(disbanding_rate(X5,X7),disbanding_rate(X6,X7))) ) ) ),
inference(variable_rename,[status(thm)],[c13]) ).
fof(c15,plain,
! [X4,X5,X6,X7] :
( ( ~ environment(X4)
| ~ subpopulations(X5,X6,X4,X7)
| ~ greater(resilience(X6),resilience(X5))
| ~ decreases(resources(X4,X7))
| increases(difference(disbanding_rate(X5,X7),disbanding_rate(X6,X7))) )
& ( ~ environment(X4)
| ~ subpopulations(X5,X6,X4,X7)
| ~ greater(resilience(X6),resilience(X5))
| ~ constant(resources(X4,X7))
| constant(difference(disbanding_rate(X5,X7),disbanding_rate(X6,X7))) ) ),
inference(distribute,[status(thm)],[c14]) ).
cnf(c16,plain,
( ~ environment(X11)
| ~ subpopulations(X13,X10,X11,X12)
| ~ greater(resilience(X10),resilience(X13))
| ~ decreases(resources(X11,X12))
| increases(difference(disbanding_rate(X13,X12),disbanding_rate(X10,X12))) ),
inference(split_conjunct,[status(thm)],[c15]) ).
cnf(c26,plain,
( ~ environment(X15)
| ~ subpopulations(first_movers,efficient_producers,X15,X14)
| ~ decreases(resources(X15,X14))
| increases(difference(disbanding_rate(first_movers,X14),disbanding_rate(efficient_producers,X14))) ),
inference(resolution,[status(thm)],[c16,c12]) ).
cnf(c27,plain,
( ~ environment(skolem0001)
| ~ decreases(resources(skolem0001,skolem0002))
| increases(difference(disbanding_rate(first_movers,skolem0002),disbanding_rate(efficient_producers,skolem0002))) ),
inference(resolution,[status(thm)],[c26,c7]) ).
cnf(c28,plain,
( ~ environment(skolem0001)
| increases(difference(disbanding_rate(first_movers,skolem0002),disbanding_rate(efficient_producers,skolem0002)))
| constant(resources(skolem0001,skolem0002)) ),
inference(resolution,[status(thm)],[c27,c8]) ).
cnf(c30,plain,
( increases(difference(disbanding_rate(first_movers,skolem0002),disbanding_rate(efficient_producers,skolem0002)))
| constant(resources(skolem0001,skolem0002)) ),
inference(resolution,[status(thm)],[c28,c6]) ).
cnf(c31,plain,
constant(resources(skolem0001,skolem0002)),
inference(resolution,[status(thm)],[c30,c10]) ).
cnf(c35,plain,
decreases(difference(disbanding_rate(first_movers,skolem0002),disbanding_rate(efficient_producers,skolem0002))),
inference(resolution,[status(thm)],[c31,c23]) ).
cnf(c36,plain,
~ constant(difference(disbanding_rate(first_movers,skolem0002),disbanding_rate(efficient_producers,skolem0002))),
inference(resolution,[status(thm)],[c35,c21]) ).
cnf(c17,plain,
( ~ environment(X17)
| ~ subpopulations(X19,X16,X17,X18)
| ~ greater(resilience(X16),resilience(X19))
| ~ constant(resources(X17,X18))
| constant(difference(disbanding_rate(X19,X18),disbanding_rate(X16,X18))) ),
inference(split_conjunct,[status(thm)],[c15]) ).
cnf(c34,plain,
( ~ environment(X20)
| ~ subpopulations(first_movers,efficient_producers,X20,X21)
| ~ constant(resources(X20,X21))
| constant(difference(disbanding_rate(first_movers,X21),disbanding_rate(efficient_producers,X21))) ),
inference(resolution,[status(thm)],[c17,c12]) ).
cnf(c37,plain,
( ~ environment(skolem0001)
| ~ constant(resources(skolem0001,skolem0002))
| constant(difference(disbanding_rate(first_movers,skolem0002),disbanding_rate(efficient_producers,skolem0002))) ),
inference(resolution,[status(thm)],[c34,c7]) ).
cnf(c38,plain,
( ~ environment(skolem0001)
| constant(difference(disbanding_rate(first_movers,skolem0002),disbanding_rate(efficient_producers,skolem0002))) ),
inference(resolution,[status(thm)],[c37,c31]) ).
cnf(c39,plain,
constant(difference(disbanding_rate(first_movers,skolem0002),disbanding_rate(efficient_producers,skolem0002))),
inference(resolution,[status(thm)],[c38,c6]) ).
cnf(c40,plain,
$false,
inference(resolution,[status(thm)],[c39,c36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT022+1 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.04 % Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 7 12:05:52 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.41 /export/starexec/sandbox2/solver/bin/lexer.py:155: SyntaxWarning: invalid escape sequence '\.'
% 0.12/0.41 (re.compile("\."), Token.FullStop),
% 0.12/0.41 /export/starexec/sandbox2/solver/bin/lexer.py:156: SyntaxWarning: invalid escape sequence '\('
% 0.12/0.41 (re.compile("\("), Token.OpenPar),
% 0.12/0.41 /export/starexec/sandbox2/solver/bin/lexer.py:157: SyntaxWarning: invalid escape sequence '\)'
% 0.12/0.41 (re.compile("\)"), Token.ClosePar),
% 0.12/0.41 /export/starexec/sandbox2/solver/bin/lexer.py:158: SyntaxWarning: invalid escape sequence '\['
% 0.12/0.41 (re.compile("\["), Token.OpenSquare),
% 0.12/0.41 /export/starexec/sandbox2/solver/bin/lexer.py:159: SyntaxWarning: invalid escape sequence '\]'
% 0.12/0.41 (re.compile("\]"), Token.CloseSquare),
% 0.12/0.41 /export/starexec/sandbox2/solver/bin/lexer.py:162: SyntaxWarning: invalid escape sequence '\|'
% 0.12/0.41 (re.compile("~\|"), Token.Nor),
% 0.12/0.41 /export/starexec/sandbox2/solver/bin/lexer.py:164: SyntaxWarning: invalid escape sequence '\|'
% 0.12/0.41 (re.compile("\|"), Token.Or),
% 0.12/0.41 /export/starexec/sandbox2/solver/bin/lexer.py:175: SyntaxWarning: invalid escape sequence '\?'
% 0.12/0.41 (re.compile("\?"), Token.Existential),
% 0.12/0.41 /export/starexec/sandbox2/solver/bin/lexer.py:176: SyntaxWarning: invalid escape sequence '\s'
% 0.12/0.41 (re.compile("\s+"), Token.WhiteSpace),
% 0.12/0.41 /export/starexec/sandbox2/solver/bin/lexer.py:180: SyntaxWarning: invalid escape sequence '\$'
% 0.12/0.41 (re.compile("\$[_a-z0-9_A-Z]*"), Token.DefFunctor),
% 0.23/0.48 /export/starexec/sandbox2/solver/bin/signature.py:6: SyntaxWarning: invalid escape sequence '\c'
% 0.23/0.48 """
% 0.23/0.48 /export/starexec/sandbox2/solver/bin/literals.py:6: SyntaxWarning: invalid escape sequence '\c'
% 0.23/0.48 """
% 0.23/0.57 /export/starexec/sandbox2/solver/bin/unification.py:6: SyntaxWarning: invalid escape sequence '\c'
% 0.23/0.57 """
% 0.33/0.60 % Version: 1.5
% 0.33/0.60 % SZS status Theorem
% 0.33/0.60 % SZS output start CNFRefutation
% See solution above
% 0.33/0.60
% 0.33/0.60 % Initial clauses : 10
% 0.33/0.60 % Processed clauses : 23
% 0.33/0.60 % Factors computed : 0
% 0.33/0.60 % Resolvents computed: 19
% 0.33/0.60 % Tautologies deleted: 1
% 0.33/0.60 % Forward subsumed : 3
% 0.33/0.60 % Backward subsumed : 10
% 0.33/0.60 % -------- CPU Time ---------
% 0.33/0.60 % User time : 0.229 s
% 0.33/0.60 % System time : 0.020 s
% 0.33/0.60 % Total time : 0.249 s
%------------------------------------------------------------------------------