TSTP Solution File: MGT026+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : MGT026+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 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 : Thu Aug 31 09:07:25 EDT 2023
% Result : Theorem 0.22s 0.60s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 27
% Syntax : Number of formulae : 76 ( 7 unt; 16 typ; 0 def)
% Number of atoms : 219 ( 20 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 273 ( 114 ~; 112 |; 32 &)
% ( 1 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 11 >; 13 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 107 ( 0 sgn; 57 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
environment: $i > $o ).
tff(decl_23,type,
subpopulations: ( $i * $i * $i * $i ) > $o ).
tff(decl_24,type,
growth_rate: ( $i * $i ) > $i ).
tff(decl_25,type,
greater: ( $i * $i ) > $o ).
tff(decl_26,type,
selection_favors: ( $i * $i * $i ) > $o ).
tff(decl_27,type,
subpopulation: ( $i * $i * $i ) > $o ).
tff(decl_28,type,
cardinality_at_time: ( $i * $i ) > $i ).
tff(decl_29,type,
zero: $i ).
tff(decl_30,type,
in_environment: ( $i * $i ) > $o ).
tff(decl_31,type,
first_movers: $i ).
tff(decl_32,type,
efficient_producers: $i ).
tff(decl_33,type,
greater_or_equal: ( $i * $i ) > $o ).
tff(decl_34,type,
critical_point: $i > $i ).
tff(decl_35,type,
appear: ( $i * $i ) > $i ).
tff(decl_36,type,
esk1_0: $i ).
tff(decl_37,type,
esk2_0: $i ).
fof(d1,hypothesis,
! [X1,X8] :
( ( environment(X1)
& X8 = critical_point(X1) )
=> ( ~ greater(growth_rate(efficient_producers,X8),growth_rate(first_movers,X8))
& ! [X4] :
( ( subpopulations(first_movers,efficient_producers,X1,X4)
& greater(X4,X8) )
=> greater(growth_rate(efficient_producers,X4),growth_rate(first_movers,X4)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
fof(mp_greater_or_equal,axiom,
! [X5,X6] :
( greater_or_equal(X5,X6)
<=> ( greater(X5,X6)
| X5 = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal) ).
fof(mp_critical_point_after_EP,axiom,
! [X1] :
( environment(X1)
=> greater_or_equal(critical_point(X1),appear(efficient_producers,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_critical_point_after_EP) ).
fof(mp_non_empty_fm_and_ep,axiom,
! [X1,X4] :
( ( environment(X1)
& in_environment(X1,X4)
& greater(cardinality_at_time(first_movers,X4),zero)
& greater(cardinality_at_time(efficient_producers,X4),zero) )
=> subpopulations(first_movers,efficient_producers,X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep) ).
fof(prove_l8,conjecture,
! [X1,X4] :
( ( environment(X1)
& in_environment(X1,X4)
& greater(X4,critical_point(X1)) )
=> selection_favors(efficient_producers,first_movers,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l8) ).
fof(t6,hypothesis,
! [X1,X4] :
( ( environment(X1)
& in_environment(X1,X4)
& greater_or_equal(X4,appear(efficient_producers,X1)) )
=> greater(cardinality_at_time(efficient_producers,X4),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6) ).
fof(mp_greater_transitivity,axiom,
! [X5,X6,X7] :
( ( greater(X5,X6)
& greater(X6,X7) )
=> greater(X5,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_transitivity) ).
fof(mp2_favour_members,axiom,
! [X1,X2,X3,X4] :
( ( environment(X1)
& subpopulation(X2,X1,X4)
& subpopulation(X3,X1,X4)
& greater(cardinality_at_time(X2,X4),zero)
& cardinality_at_time(X3,X4) = zero )
=> selection_favors(X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp2_favour_members) ).
fof(mp_subpopulations,axiom,
! [X1,X4] :
( ( environment(X1)
& in_environment(X1,X4) )
=> ( subpopulation(first_movers,X1,X4)
& subpopulation(efficient_producers,X1,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_subpopulations) ).
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/sandbox2/benchmark/theBenchmark.p',mp1_high_growth_rates) ).
fof(mp_first_movers_exist,axiom,
! [X1,X4] :
( ( environment(X1)
& in_environment(X1,X4) )
=> greater_or_equal(cardinality_at_time(first_movers,X4),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_exist) ).
fof(c_0_11,hypothesis,
! [X1,X8] :
( ( environment(X1)
& X8 = critical_point(X1) )
=> ( ~ greater(growth_rate(efficient_producers,X8),growth_rate(first_movers,X8))
& ! [X4] :
( ( subpopulations(first_movers,efficient_producers,X1,X4)
& greater(X4,X8) )
=> greater(growth_rate(efficient_producers,X4),growth_rate(first_movers,X4)) ) ) ),
inference(fof_simplification,[status(thm)],[d1]) ).
fof(c_0_12,hypothesis,
! [X29,X30,X31] :
( ( ~ greater(growth_rate(efficient_producers,X30),growth_rate(first_movers,X30))
| ~ environment(X29)
| X30 != critical_point(X29) )
& ( ~ subpopulations(first_movers,efficient_producers,X29,X31)
| ~ greater(X31,X30)
| greater(growth_rate(efficient_producers,X31),growth_rate(first_movers,X31))
| ~ environment(X29)
| X30 != critical_point(X29) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
fof(c_0_13,plain,
! [X27,X28] :
( ( ~ greater_or_equal(X27,X28)
| greater(X27,X28)
| X27 = X28 )
& ( ~ greater(X27,X28)
| greater_or_equal(X27,X28) )
& ( X27 != X28
| greater_or_equal(X27,X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_greater_or_equal])])]) ).
fof(c_0_14,plain,
! [X23] :
( ~ environment(X23)
| greater_or_equal(critical_point(X23),appear(efficient_producers,X23)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_critical_point_after_EP])]) ).
cnf(c_0_15,hypothesis,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater(X2,X3)
| ~ environment(X1)
| X3 != critical_point(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,plain,
! [X17,X18] :
( ~ environment(X17)
| ~ in_environment(X17,X18)
| ~ greater(cardinality_at_time(first_movers,X18),zero)
| ~ greater(cardinality_at_time(efficient_producers,X18),zero)
| subpopulations(first_movers,efficient_producers,X17,X18) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_non_empty_fm_and_ep])]) ).
fof(c_0_17,negated_conjecture,
~ ! [X1,X4] :
( ( environment(X1)
& in_environment(X1,X4)
& greater(X4,critical_point(X1)) )
=> selection_favors(efficient_producers,first_movers,X4) ),
inference(assume_negation,[status(cth)],[prove_l8]) ).
fof(c_0_18,hypothesis,
! [X32,X33] :
( ~ environment(X32)
| ~ in_environment(X32,X33)
| ~ greater_or_equal(X33,appear(efficient_producers,X32))
| greater(cardinality_at_time(efficient_producers,X33),zero) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6])]) ).
fof(c_0_19,plain,
! [X24,X25,X26] :
( ~ greater(X24,X25)
| ~ greater(X25,X26)
| greater(X24,X26) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_greater_transitivity])]) ).
cnf(c_0_20,plain,
( greater(X1,X2)
| X1 = X2
| ~ greater_or_equal(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( greater_or_equal(critical_point(X1),appear(efficient_producers,X1))
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,hypothesis,
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(X1,critical_point(X2))
| ~ subpopulations(first_movers,efficient_producers,X2,X1)
| ~ environment(X2) ),
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
( subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(cardinality_at_time(first_movers,X2),zero)
| ~ greater(cardinality_at_time(efficient_producers,X2),zero) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_24,negated_conjecture,
( environment(esk1_0)
& in_environment(esk1_0,esk2_0)
& greater(esk2_0,critical_point(esk1_0))
& ~ selection_favors(efficient_producers,first_movers,esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
fof(c_0_25,plain,
! [X13,X14,X15,X16] :
( ~ environment(X13)
| ~ subpopulation(X14,X13,X16)
| ~ subpopulation(X15,X13,X16)
| ~ greater(cardinality_at_time(X14,X16),zero)
| cardinality_at_time(X15,X16) != zero
| selection_favors(X14,X15,X16) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp2_favour_members])]) ).
fof(c_0_26,plain,
! [X21,X22] :
( ( subpopulation(first_movers,X21,X22)
| ~ environment(X21)
| ~ in_environment(X21,X22) )
& ( subpopulation(efficient_producers,X21,X22)
| ~ environment(X21)
| ~ in_environment(X21,X22) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_subpopulations])])]) ).
cnf(c_0_27,hypothesis,
( greater(cardinality_at_time(efficient_producers,X2),zero)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater_or_equal(X2,appear(efficient_producers,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,plain,
( greater_or_equal(X1,X2)
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_29,plain,
( greater(X1,X3)
| ~ greater(X1,X2)
| ~ greater(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_30,plain,
( appear(efficient_producers,X1) = critical_point(X1)
| greater(critical_point(X1),appear(efficient_producers,X1))
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_31,plain,
! [X9,X10,X11,X12] :
( ~ environment(X9)
| ~ subpopulations(X10,X11,X9,X12)
| ~ greater(growth_rate(X11,X12),growth_rate(X10,X12))
| selection_favors(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp1_high_growth_rates])]) ).
cnf(c_0_32,hypothesis,
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(X2,X1)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater(X1,critical_point(X2))
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_33,negated_conjecture,
greater(esk2_0,critical_point(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,negated_conjecture,
in_environment(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_35,negated_conjecture,
environment(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_36,plain,
! [X19,X20] :
( ~ environment(X19)
| ~ in_environment(X19,X20)
| greater_or_equal(cardinality_at_time(first_movers,X20),zero) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_first_movers_exist])]) ).
cnf(c_0_37,plain,
( selection_favors(X2,X4,X3)
| ~ environment(X1)
| ~ subpopulation(X2,X1,X3)
| ~ subpopulation(X4,X1,X3)
| ~ greater(cardinality_at_time(X2,X3),zero)
| cardinality_at_time(X4,X3) != zero ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_38,plain,
( subpopulation(first_movers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_39,hypothesis,
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ in_environment(X2,X1)
| ~ greater(X1,appear(efficient_producers,X2))
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_40,plain,
( appear(efficient_producers,X1) = critical_point(X1)
| greater(X2,appear(efficient_producers,X1))
| ~ greater(X2,critical_point(X1))
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_41,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_31]) ).
cnf(c_0_42,negated_conjecture,
( greater(growth_rate(efficient_producers,esk2_0),growth_rate(first_movers,esk2_0))
| ~ greater(cardinality_at_time(first_movers,esk2_0),zero)
| ~ greater(cardinality_at_time(efficient_producers,esk2_0),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_35])]) ).
cnf(c_0_43,negated_conjecture,
~ selection_favors(efficient_producers,first_movers,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_44,plain,
( greater_or_equal(cardinality_at_time(first_movers,X2),zero)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_45,plain,
( selection_favors(X1,first_movers,X2)
| cardinality_at_time(first_movers,X2) != zero
| ~ in_environment(X3,X2)
| ~ subpopulation(X1,X3,X2)
| ~ greater(cardinality_at_time(X1,X2),zero)
| ~ environment(X3) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_46,plain,
( subpopulation(efficient_producers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_47,hypothesis,
( appear(efficient_producers,X1) = critical_point(X1)
| greater(cardinality_at_time(efficient_producers,X2),zero)
| ~ in_environment(X1,X2)
| ~ greater(X2,critical_point(X1))
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_48,negated_conjecture,
( ~ greater(cardinality_at_time(first_movers,esk2_0),zero)
| ~ greater(cardinality_at_time(efficient_producers,esk2_0),zero)
| ~ subpopulations(first_movers,efficient_producers,X1,esk2_0)
| ~ environment(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
cnf(c_0_49,negated_conjecture,
greater_or_equal(cardinality_at_time(first_movers,esk2_0),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_34]),c_0_35])]) ).
cnf(c_0_50,plain,
( selection_favors(efficient_producers,first_movers,X1)
| cardinality_at_time(first_movers,X1) != zero
| ~ in_environment(X2,X1)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,negated_conjecture,
( appear(efficient_producers,esk1_0) = critical_point(esk1_0)
| greater(cardinality_at_time(efficient_producers,esk2_0),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_33]),c_0_34]),c_0_35])]) ).
cnf(c_0_52,negated_conjecture,
( ~ in_environment(X1,esk2_0)
| ~ greater(cardinality_at_time(first_movers,esk2_0),zero)
| ~ greater(cardinality_at_time(efficient_producers,esk2_0),zero)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_23]) ).
cnf(c_0_53,negated_conjecture,
( cardinality_at_time(first_movers,esk2_0) = zero
| greater(cardinality_at_time(first_movers,esk2_0),zero) ),
inference(spm,[status(thm)],[c_0_20,c_0_49]) ).
cnf(c_0_54,negated_conjecture,
( cardinality_at_time(first_movers,esk2_0) != zero
| ~ greater(cardinality_at_time(efficient_producers,esk2_0),zero) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_34]),c_0_35])]),c_0_43]) ).
cnf(c_0_55,hypothesis,
( greater(cardinality_at_time(efficient_producers,esk2_0),zero)
| greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ in_environment(esk1_0,X1)
| ~ greater(X1,critical_point(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_51]),c_0_35])]) ).
cnf(c_0_56,negated_conjecture,
( ~ in_environment(X1,esk2_0)
| ~ greater(cardinality_at_time(efficient_producers,esk2_0),zero)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]) ).
cnf(c_0_57,negated_conjecture,
greater(cardinality_at_time(efficient_producers,esk2_0),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_33]),c_0_34])]) ).
cnf(c_0_58,negated_conjecture,
( ~ in_environment(X1,esk2_0)
| ~ environment(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57])]) ).
cnf(c_0_59,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_34]),c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : MGT026+1 : TPTP v8.1.2. Released v2.0.0.
% 0.12/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.35 % Computer : n010.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon Aug 28 06:28:34 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.22/0.58 start to proof: theBenchmark
% 0.22/0.60 % Version : CSE_E---1.5
% 0.22/0.60 % Problem : theBenchmark.p
% 0.22/0.60 % Proof found
% 0.22/0.60 % SZS status Theorem for theBenchmark.p
% 0.22/0.60 % SZS output start Proof
% See solution above
% 0.22/0.61 % Total time : 0.013000 s
% 0.22/0.61 % SZS output end Proof
% 0.22/0.61 % Total time : 0.017000 s
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