%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : MGT036+2 : TPTP v9.2.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:48:15 PM UTC 2026
% Result : Theorem 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 13 unt; 0 def)
% Number of atoms : 120 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 142 ( 61 ~; 48 |; 21 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 86 ( 9 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_t5,conjecture,
! [X1,X4] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X4) )
=> ~ outcompetes(first_movers,efficient_producers,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t5) ).
fof(mp_symmetry_of_subpopulations,axiom,
! [X1,X2,X3,X4] :
( ( environment(X1)
& subpopulations(X2,X3,X1,X4) )
=> subpopulations(X3,X2,X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations) ).
fof(mp_growth_rate_relationships,axiom,
! [X1,X2,X3,X4] :
( ( ( environment(X1)
& subpopulations(X2,X3,X1,X4) )
=> greater_or_equal(growth_rate(X2,X4),zero) )
<=> ~ greater(zero,growth_rate(X2,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_growth_rate_relationships) ).
fof(d2,hypothesis,
! [X1,X2,X3,X4] :
( ( environment(X1)
& subpopulations(X2,X3,X1,X4) )
=> ( ( greater_or_equal(growth_rate(X3,X4),zero)
& greater(zero,growth_rate(X2,X4)) )
<=> outcompetes(X3,X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
fof(a13,hypothesis,
! [X1,X2,X3,X4] :
( ( environment(X1)
& in_environment(X1,X4)
& ~ greater(zero,growth_rate(X2,X4))
& greater(resilience(X3),resilience(X2)) )
=> ~ greater(zero,growth_rate(X3,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a13) ).
fof(mp_time_point_occur,axiom,
! [X1,X4] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X4) )
=> in_environment(X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_occur) ).
fof(a2,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X4] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X4) )
=> ~ outcompetes(first_movers,efficient_producers,X4) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[prove_t5])]) ).
fof(c_0_8,plain,
! [X25,X26,X27,X28] :
( ~ environment(X25)
| ~ subpopulations(X26,X27,X25,X28)
| subpopulations(X27,X26,X25,X28) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_symmetry_of_subpopulations])]) ).
fof(c_0_9,negated_conjecture,
( environment(esk1_0)
& subpopulations(first_movers,efficient_producers,esk1_0,esk2_0)
& outcompetes(first_movers,efficient_producers,esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_10,plain,
! [X1,X2,X3,X4] :
( ( ( environment(X1)
& subpopulations(X2,X3,X1,X4) )
=> greater_or_equal(growth_rate(X2,X4),zero) )
<=> ~ greater(zero,growth_rate(X2,X4)) ),
inference(fof_simplification,[status(thm)],[mp_growth_rate_relationships]) ).
fof(c_0_11,hypothesis,
! [X35,X36,X37,X38] :
( ( ~ greater_or_equal(growth_rate(X37,X38),zero)
| ~ greater(zero,growth_rate(X36,X38))
| outcompetes(X37,X36,X38)
| ~ environment(X35)
| ~ subpopulations(X36,X37,X35,X38) )
& ( greater_or_equal(growth_rate(X37,X38),zero)
| ~ outcompetes(X37,X36,X38)
| ~ environment(X35)
| ~ subpopulations(X36,X37,X35,X38) )
& ( greater(zero,growth_rate(X36,X38))
| ~ outcompetes(X37,X36,X38)
| ~ environment(X35)
| ~ subpopulations(X36,X37,X35,X38) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2])])]) ).
cnf(c_0_12,plain,
( subpopulations(X3,X2,X1,X4)
| ~ environment(X1)
| ~ subpopulations(X2,X3,X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
subpopulations(first_movers,efficient_producers,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
environment(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_15,plain,
! [X31,X32,X33,X34] :
( ( environment(X31)
| ~ greater(zero,growth_rate(X32,X34)) )
& ( subpopulations(X32,X33,X31,X34)
| ~ greater(zero,growth_rate(X32,X34)) )
& ( ~ greater_or_equal(growth_rate(X32,X34),zero)
| ~ greater(zero,growth_rate(X32,X34)) )
& ( greater(zero,growth_rate(X32,X34))
| ~ environment(X31)
| ~ subpopulations(X32,X33,X31,X34)
| greater_or_equal(growth_rate(X32,X34),zero) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
cnf(c_0_16,hypothesis,
( greater(zero,growth_rate(X1,X2))
| ~ outcompetes(X3,X1,X2)
| ~ environment(X4)
| ~ subpopulations(X1,X3,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
subpopulations(efficient_producers,first_movers,esk1_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]) ).
cnf(c_0_18,negated_conjecture,
outcompetes(first_movers,efficient_producers,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_19,hypothesis,
! [X1,X2,X3,X4] :
( ( environment(X1)
& in_environment(X1,X4)
& ~ greater(zero,growth_rate(X2,X4))
& greater(resilience(X3),resilience(X2)) )
=> ~ greater(zero,growth_rate(X3,X4)) ),
inference(fof_simplification,[status(thm)],[a13]) ).
cnf(c_0_20,plain,
( environment(X1)
| ~ greater(zero,growth_rate(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
greater(zero,growth_rate(efficient_producers,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_14])]) ).
fof(c_0_22,hypothesis,
! [X39,X40,X41,X42] :
( ~ environment(X39)
| ~ in_environment(X39,X42)
| greater(zero,growth_rate(X40,X42))
| ~ greater(resilience(X41),resilience(X40))
| ~ greater(zero,growth_rate(X41,X42)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])]) ).
cnf(c_0_23,hypothesis,
( greater_or_equal(growth_rate(X1,X2),zero)
| ~ outcompetes(X1,X3,X2)
| ~ environment(X4)
| ~ subpopulations(X3,X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_24,negated_conjecture,
environment(X1),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,hypothesis,
( greater(zero,growth_rate(X3,X2))
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(resilience(X4),resilience(X3))
| ~ greater(zero,growth_rate(X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,hypothesis,
( greater_or_equal(growth_rate(X1,X2),zero)
| ~ outcompetes(X1,X3,X2)
| ~ subpopulations(X3,X1,X4,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]) ).
cnf(c_0_27,hypothesis,
( greater(zero,growth_rate(X1,X2))
| ~ greater(zero,growth_rate(X3,X2))
| ~ greater(resilience(X3),resilience(X1))
| ~ in_environment(X4,X2) ),
inference(csr,[status(thm)],[c_0_25,c_0_20]) ).
cnf(c_0_28,plain,
( ~ greater_or_equal(growth_rate(X1,X2),zero)
| ~ greater(zero,growth_rate(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_29,negated_conjecture,
greater_or_equal(growth_rate(first_movers,esk2_0),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_17]),c_0_18])]) ).
fof(c_0_30,plain,
! [X29,X30] :
( ~ environment(X29)
| ~ subpopulations(first_movers,efficient_producers,X29,X30)
| in_environment(X29,X30) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_time_point_occur])]) ).
cnf(c_0_31,negated_conjecture,
( greater(zero,growth_rate(X1,esk2_0))
| ~ greater(resilience(efficient_producers),resilience(X1))
| ~ in_environment(X2,esk2_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_21]) ).
cnf(c_0_32,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(split_conjunct,[status(thm)],[a2]) ).
cnf(c_0_33,negated_conjecture,
~ greater(zero,growth_rate(first_movers,esk2_0)),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
( in_environment(X1,X2)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,hypothesis,
~ in_environment(X1,esk2_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_36,plain,
( in_environment(X1,X2)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_24])]) ).
cnf(c_0_37,hypothesis,
~ subpopulations(first_movers,efficient_producers,X1,esk2_0),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_13,c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT036+2 : TPTP v9.2.1. Released v2.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n004.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 23:28:32 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.26/1.72 % Version : CSE_E---1.7
% 1.26/1.72 % Problem : theBenchmark.p
% 1.26/1.72 % SZS status Theorem for theBenchmark.p
% 1.26/1.72 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.373s
%------------------------------------------------------------------------------