%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : MGT032+2 : 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 : n010.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 04:47:31 PM UTC 2026
% Result : Theorem 1.24s 1.71s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 4 unt; 0 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 89 ( 36 ~; 30 |; 16 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 17 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_t1,conjecture,
! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [X5] :
( in_environment(X1,X5)
& ! [X4] :
( ( subpopulations(first_movers,efficient_producers,X1,X4)
& greater_or_equal(X4,X5) )
=> selection_favors(efficient_producers,first_movers,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t1) ).
fof(l1,hypothesis,
! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [X5] :
( in_environment(X1,X5)
& ! [X4] :
( ( subpopulations(first_movers,efficient_producers,X1,X4)
& greater_or_equal(X4,X5) )
=> greater(growth_rate(efficient_producers,X4),growth_rate(first_movers,X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1) ).
fof(mp1_high_growth_rates,axiom,
! [X1,X2,X3,X4] :
( ( environment(X1)
& subpopulations(X2,X3,X1,X4)
& greater(growth_rate(X3,X4),growth_rate(X2,X4)) )
=> selection_favors(X3,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp1_high_growth_rates) ).
fof(c_0_3,negated_conjecture,
~ ! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [X5] :
( in_environment(X1,X5)
& ! [X4] :
( ( subpopulations(first_movers,efficient_producers,X1,X4)
& greater_or_equal(X4,X5) )
=> selection_favors(efficient_producers,first_movers,X4) ) ) ),
inference(assume_negation,[status(cth)],[prove_t1]) ).
fof(c_0_4,hypothesis,
! [X20,X22] :
( ( in_environment(X20,esk1_1(X20))
| ~ environment(X20)
| ~ stable(X20) )
& ( ~ subpopulations(first_movers,efficient_producers,X20,X22)
| ~ greater_or_equal(X22,esk1_1(X20))
| greater(growth_rate(efficient_producers,X22),growth_rate(first_movers,X22))
| ~ environment(X20)
| ~ stable(X20) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l1])])])])]) ).
fof(c_0_5,negated_conjecture,
! [X24] :
( environment(esk2_0)
& stable(esk2_0)
& ( subpopulations(first_movers,efficient_producers,esk2_0,esk3_1(X24))
| ~ in_environment(esk2_0,X24) )
& ( greater_or_equal(esk3_1(X24),X24)
| ~ in_environment(esk2_0,X24) )
& ( ~ selection_favors(efficient_producers,first_movers,esk3_1(X24))
| ~ in_environment(esk2_0,X24) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])])]) ).
fof(c_0_6,plain,
! [X16,X17,X18,X19] :
( ~ environment(X16)
| ~ subpopulations(X17,X18,X16,X19)
| ~ greater(growth_rate(X18,X19),growth_rate(X17,X19))
| selection_favors(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp1_high_growth_rates])]) ).
cnf(c_0_7,hypothesis,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater_or_equal(X2,esk1_1(X1))
| ~ environment(X1)
| ~ stable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,negated_conjecture,
( subpopulations(first_movers,efficient_producers,esk2_0,esk3_1(X1))
| ~ in_environment(esk2_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
stable(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
environment(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,plain,
( selection_favors(X3,X2,X4)
| ~ environment(X1)
| ~ subpopulations(X2,X3,X1,X4)
| ~ greater(growth_rate(X3,X4),growth_rate(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,negated_conjecture,
( greater(growth_rate(efficient_producers,esk3_1(X1)),growth_rate(first_movers,esk3_1(X1)))
| ~ greater_or_equal(esk3_1(X1),esk1_1(esk2_0))
| ~ in_environment(esk2_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]),c_0_10])]) ).
cnf(c_0_13,negated_conjecture,
( ~ selection_favors(efficient_producers,first_movers,esk3_1(X1))
| ~ in_environment(esk2_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_14,negated_conjecture,
( ~ greater_or_equal(esk3_1(X1),esk1_1(esk2_0))
| ~ in_environment(esk2_0,X1)
| ~ subpopulations(first_movers,efficient_producers,X2,esk3_1(X1))
| ~ environment(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
cnf(c_0_15,negated_conjecture,
( ~ greater_or_equal(esk3_1(X1),esk1_1(esk2_0))
| ~ in_environment(esk2_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_8]),c_0_10])]) ).
cnf(c_0_16,negated_conjecture,
( greater_or_equal(esk3_1(X1),X1)
| ~ in_environment(esk2_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_17,negated_conjecture,
~ in_environment(esk2_0,esk1_1(esk2_0)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,hypothesis,
( in_environment(X1,esk1_1(X1))
| ~ environment(X1)
| ~ stable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_19,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_9]),c_0_10])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT032+2 : 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
% 0.15/0.32 % Computer : n010.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 23:27:36 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.24/1.71 % Version : CSE_E---1.7
% 1.24/1.71 % Problem : theBenchmark.p
% 1.24/1.71 % SZS status Theorem for theBenchmark.p
% 1.24/1.71 % SZS output start CNFRefutation
% See solution above
% 1.24/1.71 % Total time : 1.371s
%------------------------------------------------------------------------------