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 v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n011.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 : Unsatisfiable 0.17s 0.58s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 32
% Syntax : Number of formulae : 68 ( 11 unt; 16 typ; 0 def)
% Number of atoms : 160 ( 14 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 215 ( 107 ~; 108 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 79 ( 0 sgn; 0 !; 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,
sk1: $i ).
tff(decl_37,type,
sk2: $i ).
cnf(d1_40,hypothesis,
( greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3))
| ~ environment(X1)
| X2 != critical_point(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X3)
| ~ greater(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_40) ).
cnf(mp_greater_or_equal_36,axiom,
( greater(X1,X2)
| X1 = X2
| ~ greater_or_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_36) ).
cnf(mp_critical_point_after_EP_34,axiom,
( greater_or_equal(critical_point(X1),appear(efficient_producers,X1))
| ~ environment(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_critical_point_after_EP_34) ).
cnf(mp_non_empty_fm_and_ep_30,axiom,
( 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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep_30) ).
cnf(t6_41,hypothesis,
( greater(cardinality_at_time(efficient_producers,X2),zero)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater_or_equal(X2,appear(efficient_producers,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_41) ).
cnf(mp_greater_or_equal_37,axiom,
( greater_or_equal(X1,X2)
| ~ greater(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_37) ).
cnf(mp_greater_transitivity_35,axiom,
( greater(X1,X3)
| ~ greater(X1,X2)
| ~ greater(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_transitivity_35) ).
cnf(prove_l8_44,negated_conjecture,
greater(sk2,critical_point(sk1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l8_44) ).
cnf(prove_l8_43,negated_conjecture,
in_environment(sk1,sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l8_43) ).
cnf(prove_l8_42,negated_conjecture,
environment(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l8_42) ).
cnf(mp2_favour_members_29,axiom,
( 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 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp2_favour_members_29) ).
cnf(mp_subpopulations_32,axiom,
( subpopulation(first_movers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_subpopulations_32) ).
cnf(mp1_high_growth_rates_28,axiom,
( selection_favors(X3,X2,X4)
| ~ environment(X1)
| ~ subpopulations(X2,X3,X1,X4)
| ~ greater(growth_rate(X3,X4),growth_rate(X2,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp1_high_growth_rates_28) ).
cnf(prove_l8_45,negated_conjecture,
~ selection_favors(efficient_producers,first_movers,sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l8_45) ).
cnf(mp_first_movers_exist_31,axiom,
( greater_or_equal(cardinality_at_time(first_movers,X2),zero)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_exist_31) ).
cnf(mp_subpopulations_33,axiom,
( subpopulation(efficient_producers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_subpopulations_33) ).
cnf(c_0_16,hypothesis,
( greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3))
| ~ environment(X1)
| X2 != critical_point(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X3)
| ~ greater(X3,X2) ),
d1_40 ).
cnf(c_0_17,axiom,
( greater(X1,X2)
| X1 = X2
| ~ greater_or_equal(X1,X2) ),
mp_greater_or_equal_36 ).
cnf(c_0_18,axiom,
( greater_or_equal(critical_point(X1),appear(efficient_producers,X1))
| ~ environment(X1) ),
mp_critical_point_after_EP_34 ).
cnf(c_0_19,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_16]) ).
cnf(c_0_20,axiom,
( 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) ),
mp_non_empty_fm_and_ep_30 ).
cnf(c_0_21,hypothesis,
( greater(cardinality_at_time(efficient_producers,X2),zero)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater_or_equal(X2,appear(efficient_producers,X1)) ),
t6_41 ).
cnf(c_0_22,axiom,
( greater_or_equal(X1,X2)
| ~ greater(X1,X2) ),
mp_greater_or_equal_37 ).
cnf(c_0_23,axiom,
( greater(X1,X3)
| ~ greater(X1,X2)
| ~ greater(X2,X3) ),
mp_greater_transitivity_35 ).
cnf(c_0_24,plain,
( appear(efficient_producers,X1) = critical_point(X1)
| greater(critical_point(X1),appear(efficient_producers,X1))
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_25,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_19,c_0_20]) ).
cnf(c_0_26,negated_conjecture,
greater(sk2,critical_point(sk1)),
prove_l8_44 ).
cnf(c_0_27,negated_conjecture,
in_environment(sk1,sk2),
prove_l8_43 ).
cnf(c_0_28,negated_conjecture,
environment(sk1),
prove_l8_42 ).
cnf(c_0_29,axiom,
( 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 ),
mp2_favour_members_29 ).
cnf(c_0_30,axiom,
( subpopulation(first_movers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
mp_subpopulations_32 ).
cnf(c_0_31,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_21,c_0_22]) ).
cnf(c_0_32,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_23,c_0_24]) ).
cnf(c_0_33,axiom,
( selection_favors(X3,X2,X4)
| ~ environment(X1)
| ~ subpopulations(X2,X3,X1,X4)
| ~ greater(growth_rate(X3,X4),growth_rate(X2,X4)) ),
mp1_high_growth_rates_28 ).
cnf(c_0_34,negated_conjecture,
( greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2))
| ~ greater(cardinality_at_time(first_movers,sk2),zero)
| ~ greater(cardinality_at_time(efficient_producers,sk2),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28])]) ).
cnf(c_0_35,negated_conjecture,
~ selection_favors(efficient_producers,first_movers,sk2),
prove_l8_45 ).
cnf(c_0_36,axiom,
( greater_or_equal(cardinality_at_time(first_movers,X2),zero)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
mp_first_movers_exist_31 ).
cnf(c_0_37,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_29,c_0_30]) ).
cnf(c_0_38,axiom,
( subpopulation(efficient_producers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
mp_subpopulations_33 ).
cnf(c_0_39,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_31,c_0_32]) ).
cnf(c_0_40,negated_conjecture,
( ~ greater(cardinality_at_time(first_movers,sk2),zero)
| ~ greater(cardinality_at_time(efficient_producers,sk2),zero)
| ~ subpopulations(first_movers,efficient_producers,X1,sk2)
| ~ environment(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_41,negated_conjecture,
greater_or_equal(cardinality_at_time(first_movers,sk2),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_27]),c_0_28])]) ).
cnf(c_0_42,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_37,c_0_38]) ).
cnf(c_0_43,negated_conjecture,
( appear(efficient_producers,sk1) = critical_point(sk1)
| greater(cardinality_at_time(efficient_producers,sk2),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_26]),c_0_27]),c_0_28])]) ).
cnf(c_0_44,negated_conjecture,
( ~ in_environment(X1,sk2)
| ~ greater(cardinality_at_time(first_movers,sk2),zero)
| ~ greater(cardinality_at_time(efficient_producers,sk2),zero)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_20]) ).
cnf(c_0_45,negated_conjecture,
( cardinality_at_time(first_movers,sk2) = zero
| greater(cardinality_at_time(first_movers,sk2),zero) ),
inference(spm,[status(thm)],[c_0_17,c_0_41]) ).
cnf(c_0_46,negated_conjecture,
( cardinality_at_time(first_movers,sk2) != zero
| ~ greater(cardinality_at_time(efficient_producers,sk2),zero) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_27]),c_0_28])]),c_0_35]) ).
cnf(c_0_47,hypothesis,
( greater(cardinality_at_time(efficient_producers,sk2),zero)
| greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ in_environment(sk1,X1)
| ~ greater(X1,critical_point(sk1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_43]),c_0_28])]) ).
cnf(c_0_48,negated_conjecture,
( ~ in_environment(X1,sk2)
| ~ greater(cardinality_at_time(efficient_producers,sk2),zero)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).
cnf(c_0_49,negated_conjecture,
greater(cardinality_at_time(efficient_producers,sk2),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_26]),c_0_27])]) ).
cnf(c_0_50,negated_conjecture,
( ~ in_environment(X1,sk2)
| ~ environment(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49])]) ).
cnf(c_0_51,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_27]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.10 % Problem : MGT026-1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.11 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.10/0.32 % Computer : n011.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Mon Aug 28 06:15:55 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.17/0.57 start to proof: theBenchmark
% 0.17/0.58 % Version : CSE_E---1.5
% 0.17/0.58 % Problem : theBenchmark.p
% 0.17/0.58 % Proof found
% 0.17/0.58 % SZS status Theorem for theBenchmark.p
% 0.17/0.58 % SZS output start Proof
% See solution above
% 0.17/0.59 % Total time : 0.009000 s
% 0.17/0.59 % SZS output end Proof
% 0.17/0.59 % Total time : 0.011000 s
%------------------------------------------------------------------------------