TSTP Solution File: MGT024-1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : MGT024-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n013.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 09:07:24 EDT 2023
% Result : Unsatisfiable 0.21s 0.57s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 34
% Syntax : Number of formulae : 74 ( 16 unt; 16 typ; 0 def)
% Number of atoms : 179 ( 32 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 203 ( 82 ~; 121 |; 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 : 20 ( 11 >; 9 *; 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 : 48 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
environment: $i > $o ).
tff(decl_23,type,
first_movers: $i ).
tff(decl_24,type,
efficient_producers: $i ).
tff(decl_25,type,
subpopulations: ( $i * $i * $i * $i ) > $o ).
tff(decl_26,type,
in_environment: ( $i * $i ) > $o ).
tff(decl_27,type,
number_of_organizations: ( $i * $i ) > $i ).
tff(decl_28,type,
zero: $i ).
tff(decl_29,type,
greater: ( $i * $i ) > $o ).
tff(decl_30,type,
equilibrium: $i > $i ).
tff(decl_31,type,
greater_or_equal: ( $i * $i ) > $o ).
tff(decl_32,type,
resources: ( $i * $i ) > $i ).
tff(decl_33,type,
decreases: $i > $o ).
tff(decl_34,type,
constant: $i > $o ).
tff(decl_35,type,
growth_rate: ( $i * $i ) > $i ).
tff(decl_36,type,
sk1: $i ).
tff(decl_37,type,
sk2: $i ).
cnf(mp_positive_number_of_organizations_25,axiom,
( greater(number_of_organizations(X1,X2),zero)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_positive_number_of_organizations_25) ).
cnf(prove_l6_40,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l6_40) ).
cnf(prove_l6_39,negated_conjecture,
environment(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l6_39) ).
cnf(mp_time_point_occur_24,axiom,
( in_environment(X1,X2)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_occur_24) ).
cnf(mp_equilibrium_26,axiom,
( ~ environment(X1)
| ~ greater_or_equal(X2,equilibrium(X1))
| ~ greater(equilibrium(X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_equilibrium_26) ).
cnf(prove_l6_41,negated_conjecture,
greater_or_equal(sk2,equilibrium(sk1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l6_41) ).
cnf(a3_28,hypothesis,
( greater(equilibrium(X1),X2)
| constant(resources(X1,X2))
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(number_of_organizations(X1,X2),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3_28) ).
cnf(a6_30,hypothesis,
( constant(number_of_organizations(X1,X2))
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ constant(resources(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a6_30) ).
cnf(l7_32,hypothesis,
( growth_rate(first_movers,X2) = zero
| greater(growth_rate(first_movers,X2),zero)
| greater(zero,growth_rate(first_movers,X2))
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ constant(number_of_organizations(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7_32) ).
cnf(l7_34,hypothesis,
( growth_rate(first_movers,X2) = zero
| greater(zero,growth_rate(efficient_producers,X2))
| greater(zero,growth_rate(first_movers,X2))
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ constant(number_of_organizations(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7_34) ).
cnf(l7_31,hypothesis,
( growth_rate(first_movers,X2) = zero
| greater(growth_rate(first_movers,X2),zero)
| greater(growth_rate(efficient_producers,X2),zero)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ constant(number_of_organizations(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7_31) ).
cnf(prove_l6_43,negated_conjecture,
( ~ greater(growth_rate(first_movers,sk2),zero)
| ~ greater(zero,growth_rate(efficient_producers,sk2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l6_43) ).
cnf(l7_33,hypothesis,
( growth_rate(first_movers,X2) = zero
| greater(zero,growth_rate(efficient_producers,X2))
| greater(growth_rate(efficient_producers,X2),zero)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ constant(number_of_organizations(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7_33) ).
cnf(l7_36,hypothesis,
( growth_rate(efficient_producers,X2) = zero
| greater(growth_rate(first_movers,X2),zero)
| greater(zero,growth_rate(first_movers,X2))
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ constant(number_of_organizations(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7_36) ).
cnf(l7_38,hypothesis,
( growth_rate(efficient_producers,X2) = zero
| greater(zero,growth_rate(efficient_producers,X2))
| greater(zero,growth_rate(first_movers,X2))
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ constant(number_of_organizations(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7_38) ).
cnf(prove_l6_44,negated_conjecture,
( ~ greater(growth_rate(efficient_producers,sk2),zero)
| ~ greater(zero,growth_rate(first_movers,sk2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l6_44) ).
cnf(l7_37,hypothesis,
( growth_rate(efficient_producers,X2) = zero
| greater(zero,growth_rate(efficient_producers,X2))
| greater(growth_rate(efficient_producers,X2),zero)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ constant(number_of_organizations(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7_37) ).
cnf(prove_l6_42,negated_conjecture,
( growth_rate(first_movers,sk2) != zero
| growth_rate(efficient_producers,sk2) != zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l6_42) ).
cnf(c_0_18,axiom,
( greater(number_of_organizations(X1,X2),zero)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
mp_positive_number_of_organizations_25 ).
cnf(c_0_19,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
prove_l6_40 ).
cnf(c_0_20,negated_conjecture,
environment(sk1),
prove_l6_39 ).
cnf(c_0_21,axiom,
( in_environment(X1,X2)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
mp_time_point_occur_24 ).
cnf(c_0_22,axiom,
( ~ environment(X1)
| ~ greater_or_equal(X2,equilibrium(X1))
| ~ greater(equilibrium(X1),X2) ),
mp_equilibrium_26 ).
cnf(c_0_23,negated_conjecture,
greater_or_equal(sk2,equilibrium(sk1)),
prove_l6_41 ).
cnf(c_0_24,hypothesis,
( greater(equilibrium(X1),X2)
| constant(resources(X1,X2))
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(number_of_organizations(X1,X2),zero) ),
a3_28 ).
cnf(c_0_25,negated_conjecture,
greater(number_of_organizations(sk1,sk2),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_26,negated_conjecture,
in_environment(sk1,sk2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_19]),c_0_20])]) ).
cnf(c_0_27,negated_conjecture,
~ greater(equilibrium(sk1),sk2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_20])]) ).
cnf(c_0_28,hypothesis,
( constant(number_of_organizations(X1,X2))
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ constant(resources(X1,X2)) ),
a6_30 ).
cnf(c_0_29,hypothesis,
constant(resources(sk1,sk2)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_20])]),c_0_27]) ).
cnf(c_0_30,hypothesis,
( growth_rate(first_movers,X2) = zero
| greater(growth_rate(first_movers,X2),zero)
| greater(zero,growth_rate(first_movers,X2))
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ constant(number_of_organizations(X1,X2)) ),
l7_32 ).
cnf(c_0_31,hypothesis,
constant(number_of_organizations(sk1,sk2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_26]),c_0_20])]) ).
cnf(c_0_32,hypothesis,
( growth_rate(first_movers,X2) = zero
| greater(zero,growth_rate(efficient_producers,X2))
| greater(zero,growth_rate(first_movers,X2))
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ constant(number_of_organizations(X1,X2)) ),
l7_34 ).
cnf(c_0_33,hypothesis,
( growth_rate(first_movers,X2) = zero
| greater(growth_rate(first_movers,X2),zero)
| greater(growth_rate(efficient_producers,X2),zero)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ constant(number_of_organizations(X1,X2)) ),
l7_31 ).
cnf(c_0_34,negated_conjecture,
( ~ greater(growth_rate(first_movers,sk2),zero)
| ~ greater(zero,growth_rate(efficient_producers,sk2)) ),
prove_l6_43 ).
cnf(c_0_35,negated_conjecture,
( growth_rate(first_movers,sk2) = zero
| greater(growth_rate(first_movers,sk2),zero)
| greater(zero,growth_rate(first_movers,sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_19]),c_0_20])]),c_0_31])]) ).
cnf(c_0_36,negated_conjecture,
( growth_rate(first_movers,sk2) = zero
| greater(zero,growth_rate(efficient_producers,sk2))
| greater(zero,growth_rate(first_movers,sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_19]),c_0_20])]),c_0_31])]) ).
cnf(c_0_37,hypothesis,
( growth_rate(first_movers,X2) = zero
| greater(zero,growth_rate(efficient_producers,X2))
| greater(growth_rate(efficient_producers,X2),zero)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ constant(number_of_organizations(X1,X2)) ),
l7_33 ).
cnf(c_0_38,hypothesis,
( growth_rate(efficient_producers,X2) = zero
| greater(growth_rate(first_movers,X2),zero)
| greater(zero,growth_rate(first_movers,X2))
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ constant(number_of_organizations(X1,X2)) ),
l7_36 ).
cnf(c_0_39,hypothesis,
( growth_rate(efficient_producers,X2) = zero
| greater(zero,growth_rate(efficient_producers,X2))
| greater(zero,growth_rate(first_movers,X2))
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ constant(number_of_organizations(X1,X2)) ),
l7_38 ).
cnf(c_0_40,negated_conjecture,
( ~ greater(growth_rate(efficient_producers,sk2),zero)
| ~ greater(zero,growth_rate(first_movers,sk2)) ),
prove_l6_44 ).
cnf(c_0_41,negated_conjecture,
( growth_rate(first_movers,sk2) = zero
| greater(growth_rate(efficient_producers,sk2),zero)
| greater(growth_rate(first_movers,sk2),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_19]),c_0_20])]),c_0_31])]) ).
cnf(c_0_42,negated_conjecture,
( growth_rate(first_movers,sk2) = zero
| greater(zero,growth_rate(first_movers,sk2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_43,negated_conjecture,
( growth_rate(first_movers,sk2) = zero
| greater(growth_rate(efficient_producers,sk2),zero)
| greater(zero,growth_rate(efficient_producers,sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_19]),c_0_20])]),c_0_31])]) ).
cnf(c_0_44,hypothesis,
( growth_rate(efficient_producers,X2) = zero
| greater(zero,growth_rate(efficient_producers,X2))
| greater(growth_rate(efficient_producers,X2),zero)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ constant(number_of_organizations(X1,X2)) ),
l7_37 ).
cnf(c_0_45,negated_conjecture,
( growth_rate(efficient_producers,sk2) = zero
| greater(growth_rate(first_movers,sk2),zero)
| greater(zero,growth_rate(first_movers,sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_19]),c_0_20])]),c_0_31])]) ).
cnf(c_0_46,negated_conjecture,
( growth_rate(efficient_producers,sk2) = zero
| greater(zero,growth_rate(efficient_producers,sk2))
| greater(zero,growth_rate(first_movers,sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_19]),c_0_20])]),c_0_31])]) ).
cnf(c_0_47,negated_conjecture,
( growth_rate(first_movers,sk2) = zero
| greater(growth_rate(first_movers,sk2),zero) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_48,negated_conjecture,
( growth_rate(first_movers,sk2) = zero
| greater(zero,growth_rate(efficient_producers,sk2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_43]),c_0_42]) ).
cnf(c_0_49,negated_conjecture,
( growth_rate(efficient_producers,sk2) = zero
| greater(growth_rate(efficient_producers,sk2),zero)
| greater(zero,growth_rate(efficient_producers,sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_19]),c_0_20])]),c_0_31])]) ).
cnf(c_0_50,negated_conjecture,
( growth_rate(efficient_producers,sk2) = zero
| greater(zero,growth_rate(first_movers,sk2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_45]),c_0_46]) ).
cnf(c_0_51,negated_conjecture,
( growth_rate(first_movers,sk2) != zero
| growth_rate(efficient_producers,sk2) != zero ),
prove_l6_42 ).
cnf(c_0_52,negated_conjecture,
growth_rate(first_movers,sk2) = zero,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_47]),c_0_48]) ).
cnf(c_0_53,negated_conjecture,
( growth_rate(efficient_producers,sk2) = zero
| greater(zero,growth_rate(efficient_producers,sk2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_49]),c_0_50]) ).
cnf(c_0_54,negated_conjecture,
growth_rate(efficient_producers,sk2) != zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52])]) ).
cnf(c_0_55,negated_conjecture,
greater(zero,growth_rate(efficient_producers,sk2)),
inference(sr,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_56,negated_conjecture,
greater(zero,zero),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_52]),c_0_54]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_52]),c_0_55]),c_0_56])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT024-1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 06:14:17 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.21/0.56 start to proof: theBenchmark
% 0.21/0.57 % Version : CSE_E---1.5
% 0.21/0.57 % Problem : theBenchmark.p
% 0.21/0.57 % Proof found
% 0.21/0.57 % SZS status Theorem for theBenchmark.p
% 0.21/0.57 % SZS output start Proof
% See solution above
% 0.21/0.58 % Total time : 0.008000 s
% 0.21/0.58 % SZS output end Proof
% 0.21/0.58 % Total time : 0.011000 s
%------------------------------------------------------------------------------