TSTP Solution File: MGT021+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : MGT021+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n012.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 09:07:21 EDT 2023
% Result : Theorem 0.20s 0.59s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 24
% Syntax : Number of formulae : 51 ( 5 unt; 18 typ; 0 def)
% Number of atoms : 118 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 146 ( 61 ~; 49 |; 18 &)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 13 >; 10 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn; 27 !; 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,
increases: $i > $o ).
tff(decl_31,type,
decreases: $i > $o ).
tff(decl_32,type,
greater_or_equal: ( $i * $i ) > $o ).
tff(decl_33,type,
equilibrium: $i > $i ).
tff(decl_34,type,
resources: ( $i * $i ) > $i ).
tff(decl_35,type,
constant: $i > $o ).
tff(decl_36,type,
disbanding_rate: ( $i * $i ) > $i ).
tff(decl_37,type,
difference: ( $i * $i ) > $i ).
tff(decl_38,type,
esk1_0: $i ).
tff(decl_39,type,
esk2_0: $i ).
fof(l4,hypothesis,
! [X1,X2] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X2) )
=> ( ( decreases(resources(X1,X2))
=> increases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))) )
& ( constant(resources(X1,X2))
=> ~ decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4) ).
fof(prove_l3,conjecture,
! [X1,X2] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X2) )
=> ~ decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l3) ).
fof(a3,hypothesis,
! [X1,X2] :
( ( environment(X1)
& in_environment(X1,X2)
& greater(number_of_organizations(X1,X2),zero) )
=> ( ( greater(equilibrium(X1),X2)
=> decreases(resources(X1,X2)) )
& ( ~ greater(equilibrium(X1),X2)
=> constant(resources(X1,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3) ).
fof(mp_environment_not_empty,axiom,
! [X1,X2] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X2) )
=> greater(number_of_organizations(X1,X2),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_environment_not_empty) ).
fof(mp_time_point_in_environment,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_in_environment) ).
fof(mp_increase_not_decrease,axiom,
! [X3] :
( increases(X3)
=> ~ decreases(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_increase_not_decrease) ).
fof(c_0_6,hypothesis,
! [X1,X2] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X2) )
=> ( ( decreases(resources(X1,X2))
=> increases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))) )
& ( constant(resources(X1,X2))
=> ~ decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))) ) ) ),
inference(fof_simplification,[status(thm)],[l4]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X2) )
=> ~ decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[prove_l3])]) ).
fof(c_0_8,hypothesis,
! [X1,X2] :
( ( environment(X1)
& in_environment(X1,X2)
& greater(number_of_organizations(X1,X2),zero) )
=> ( ( greater(equilibrium(X1),X2)
=> decreases(resources(X1,X2)) )
& ( ~ greater(equilibrium(X1),X2)
=> constant(resources(X1,X2)) ) ) ),
inference(fof_simplification,[status(thm)],[a3]) ).
fof(c_0_9,hypothesis,
! [X14,X15] :
( ( ~ decreases(resources(X14,X15))
| increases(difference(disbanding_rate(first_movers,X15),disbanding_rate(efficient_producers,X15)))
| ~ environment(X14)
| ~ subpopulations(first_movers,efficient_producers,X14,X15) )
& ( ~ constant(resources(X14,X15))
| ~ decreases(difference(disbanding_rate(first_movers,X15),disbanding_rate(efficient_producers,X15)))
| ~ environment(X14)
| ~ subpopulations(first_movers,efficient_producers,X14,X15) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_10,negated_conjecture,
( environment(esk1_0)
& subpopulations(first_movers,efficient_producers,esk1_0,esk2_0)
& decreases(difference(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_11,hypothesis,
! [X12,X13] :
( ( ~ greater(equilibrium(X12),X13)
| decreases(resources(X12,X13))
| ~ environment(X12)
| ~ in_environment(X12,X13)
| ~ greater(number_of_organizations(X12,X13),zero) )
& ( greater(equilibrium(X12),X13)
| constant(resources(X12,X13))
| ~ environment(X12)
| ~ in_environment(X12,X13)
| ~ greater(number_of_organizations(X12,X13),zero) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_12,plain,
! [X7,X8] :
( ~ environment(X7)
| ~ subpopulations(first_movers,efficient_producers,X7,X8)
| greater(number_of_organizations(X7,X8),zero) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_environment_not_empty])]) ).
fof(c_0_13,plain,
! [X5,X6] :
( ~ environment(X5)
| ~ subpopulations(first_movers,efficient_producers,X5,X6)
| in_environment(X5,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_time_point_in_environment])]) ).
cnf(c_0_14,hypothesis,
( ~ constant(resources(X1,X2))
| ~ decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2)))
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
decreases(difference(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,hypothesis,
( decreases(resources(X1,X2))
| ~ greater(equilibrium(X1),X2)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(number_of_organizations(X1,X2),zero) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( greater(number_of_organizations(X1,X2),zero)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( in_environment(X1,X2)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
( ~ constant(resources(X1,esk2_0))
| ~ subpopulations(first_movers,efficient_producers,X1,esk2_0)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,hypothesis,
( greater(equilibrium(X1),X2)
| constant(resources(X1,X2))
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(number_of_organizations(X1,X2),zero) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,hypothesis,
( decreases(resources(X1,X2))
| ~ greater(equilibrium(X1),X2)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_22,negated_conjecture,
( greater(equilibrium(X1),esk2_0)
| ~ subpopulations(first_movers,efficient_producers,X1,esk2_0)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_18]),c_0_17]) ).
fof(c_0_23,plain,
! [X3] :
( increases(X3)
=> ~ decreases(X3) ),
inference(fof_simplification,[status(thm)],[mp_increase_not_decrease]) ).
cnf(c_0_24,hypothesis,
( increases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2)))
| ~ decreases(resources(X1,X2))
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_25,negated_conjecture,
( decreases(resources(X1,esk2_0))
| ~ subpopulations(first_movers,efficient_producers,X1,esk2_0)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_26,plain,
! [X9] :
( ~ increases(X9)
| ~ decreases(X9) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])]) ).
cnf(c_0_27,hypothesis,
( increases(difference(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0)))
| ~ subpopulations(first_movers,efficient_producers,X1,esk2_0)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
subpopulations(first_movers,efficient_producers,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_29,negated_conjecture,
environment(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_30,plain,
( ~ increases(X1)
| ~ decreases(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,negated_conjecture,
increases(difference(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT021+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n012.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 06:19:09 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.20/0.59 % Version : CSE_E---1.5
% 0.20/0.59 % Problem : theBenchmark.p
% 0.20/0.59 % Proof found
% 0.20/0.59 % SZS status Theorem for theBenchmark.p
% 0.20/0.59 % SZS output start Proof
% See solution above
% 0.20/0.59 % Total time : 0.008000 s
% 0.20/0.59 % SZS output end Proof
% 0.20/0.59 % Total time : 0.011000 s
%------------------------------------------------------------------------------