%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : MGT036+1 : TPTP v9.2.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n031.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 1.71s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 11 unt; 0 def)
% Number of atoms : 131 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 159 ( 70 ~; 56 |; 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 : 91 ( 11 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d2,hypothesis,
! [X1,X3,X4,X2] :
( ( environment(X1)
& subpopulations(X3,X4,X1,X2) )
=> ( ( greater_or_equal(growth_rate(X4,X2),zero)
& greater(zero,growth_rate(X3,X2)) )
<=> outcompetes(X4,X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).
fof(mp_symmetry_of_FM_and_EP,axiom,
! [X1,X2] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X2) )
=> subpopulations(efficient_producers,first_movers,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_symmetry_of_FM_and_EP) ).
fof(prove_t5,conjecture,
! [X1,X2] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X2) )
=> ~ outcompetes(first_movers,efficient_producers,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t5) ).
fof(mp_growth_rate_relationships,axiom,
! [X1,X3,X4,X2] :
( ( ( environment(X1)
& subpopulations(X3,X4,X1,X2) )
=> greater_or_equal(growth_rate(X3,X2),zero) )
<=> ~ greater(zero,growth_rate(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_relationships) ).
fof(a12,hypothesis,
! [X1,X3,X4,X2] :
( ( environment(X1)
& in_environment(X1,X2)
& ~ greater(zero,growth_rate(X3,X2))
& greater(resilience(X4),resilience(X3)) )
=> ~ greater(zero,growth_rate(X4,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a12) ).
fof(mp_time_point_occur,axiom,
! [X1,X2] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X2) )
=> in_environment(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_point_occur) ).
fof(a2,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
fof(c_0_7,hypothesis,
! [X31,X32,X33,X34] :
( ( ~ greater_or_equal(growth_rate(X33,X34),zero)
| ~ greater(zero,growth_rate(X32,X34))
| outcompetes(X33,X32,X34)
| ~ environment(X31)
| ~ subpopulations(X32,X33,X31,X34) )
& ( greater_or_equal(growth_rate(X33,X34),zero)
| ~ outcompetes(X33,X32,X34)
| ~ environment(X31)
| ~ subpopulations(X32,X33,X31,X34) )
& ( greater(zero,growth_rate(X32,X34))
| ~ outcompetes(X33,X32,X34)
| ~ environment(X31)
| ~ subpopulations(X32,X33,X31,X34) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2])])]) ).
fof(c_0_8,plain,
! [X23,X24] :
( ~ environment(X23)
| ~ subpopulations(first_movers,efficient_producers,X23,X24)
| subpopulations(efficient_producers,first_movers,X23,X24) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_symmetry_of_FM_and_EP])]) ).
fof(c_0_9,negated_conjecture,
~ ! [X1,X2] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X2) )
=> ~ outcompetes(first_movers,efficient_producers,X2) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[prove_t5])]) ).
fof(c_0_10,plain,
! [X1,X3,X4,X2] :
( ( ( environment(X1)
& subpopulations(X3,X4,X1,X2) )
=> greater_or_equal(growth_rate(X3,X2),zero) )
<=> ~ greater(zero,growth_rate(X3,X2)) ),
inference(fof_simplification,[status(thm)],[mp_growth_rate_relationships]) ).
cnf(c_0_11,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_7]) ).
cnf(c_0_12,plain,
( subpopulations(efficient_producers,first_movers,X1,X2)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,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_9])])]) ).
fof(c_0_14,plain,
! [X27,X28,X29,X30] :
( ( environment(X27)
| ~ greater(zero,growth_rate(X28,X30)) )
& ( subpopulations(X28,X29,X27,X30)
| ~ greater(zero,growth_rate(X28,X30)) )
& ( ~ greater_or_equal(growth_rate(X28,X30),zero)
| ~ greater(zero,growth_rate(X28,X30)) )
& ( greater(zero,growth_rate(X28,X30))
| ~ environment(X27)
| ~ subpopulations(X28,X29,X27,X30)
| greater_or_equal(growth_rate(X28,X30),zero) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
cnf(c_0_15,hypothesis,
( greater(zero,growth_rate(efficient_producers,X1))
| ~ outcompetes(first_movers,efficient_producers,X1)
| ~ subpopulations(first_movers,efficient_producers,X2,X1)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,negated_conjecture,
subpopulations(first_movers,efficient_producers,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
outcompetes(first_movers,efficient_producers,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
environment(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( environment(X1)
| ~ greater(zero,growth_rate(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,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_15,c_0_16]),c_0_17]),c_0_18])]) ).
cnf(c_0_21,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_7]) ).
cnf(c_0_22,negated_conjecture,
environment(X1),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_23,hypothesis,
! [X1,X3,X4,X2] :
( ( environment(X1)
& in_environment(X1,X2)
& ~ greater(zero,growth_rate(X3,X2))
& greater(resilience(X4),resilience(X3)) )
=> ~ greater(zero,growth_rate(X4,X2)) ),
inference(fof_simplification,[status(thm)],[a12]) ).
cnf(c_0_24,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_21,c_0_22])]) ).
cnf(c_0_25,plain,
( subpopulations(X1,X2,X3,X4)
| ~ greater(zero,growth_rate(X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_26,hypothesis,
! [X35,X36,X37,X38] :
( ~ environment(X35)
| ~ in_environment(X35,X38)
| greater(zero,growth_rate(X36,X38))
| ~ greater(resilience(X37),resilience(X36))
| ~ greater(zero,growth_rate(X37,X38)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])]) ).
cnf(c_0_27,hypothesis,
( greater_or_equal(growth_rate(X1,X2),zero)
| ~ outcompetes(X1,X3,X2)
| ~ greater(zero,growth_rate(X3,X2)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,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_26]) ).
cnf(c_0_29,plain,
( ~ greater_or_equal(growth_rate(X1,X2),zero)
| ~ greater(zero,growth_rate(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_30,negated_conjecture,
( greater_or_equal(growth_rate(X1,esk2_0),zero)
| ~ outcompetes(X1,efficient_producers,esk2_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_20]) ).
cnf(c_0_31,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_28,c_0_19]) ).
cnf(c_0_32,negated_conjecture,
( ~ outcompetes(X1,efficient_producers,esk2_0)
| ~ greater(zero,growth_rate(X1,esk2_0)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
fof(c_0_33,plain,
! [X25,X26] :
( ~ environment(X25)
| ~ subpopulations(first_movers,efficient_producers,X25,X26)
| in_environment(X25,X26) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_time_point_occur])]) ).
cnf(c_0_34,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_31,c_0_20]) ).
cnf(c_0_35,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(split_conjunct,[status(thm)],[a2]) ).
cnf(c_0_36,negated_conjecture,
~ greater(zero,growth_rate(first_movers,esk2_0)),
inference(spm,[status(thm)],[c_0_32,c_0_17]) ).
cnf(c_0_37,plain,
( in_environment(X1,X2)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,hypothesis,
~ in_environment(X1,esk2_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_39,plain,
( in_environment(X1,X2)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_22])]) ).
cnf(c_0_40,hypothesis,
~ subpopulations(first_movers,efficient_producers,X1,esk2_0),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_16,c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT036+1 : TPTP v9.2.1. Released v2.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.32 % Computer : n031.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Mon May 4 23:30:38 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.26/1.71 % Version : CSE_E---1.7
% 1.26/1.71 % Problem : theBenchmark.p
% 1.26/1.71 % SZS status Theorem for theBenchmark.p
% 1.26/1.71 % SZS output start CNFRefutation
% See solution above
% 1.26/1.71 % Total time : 1.372s
%------------------------------------------------------------------------------