TSTP Solution File: MGT022+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : MGT022+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 : n009.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 09:07:22 EDT 2023
% Result : Theorem 0.50s 0.59s
% Output : CNFRefutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of formulae : 40 ( 8 unt; 14 typ; 0 def)
% Number of atoms : 83 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 94 ( 37 ~; 33 |; 13 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 10 >; 7 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn; 15 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
constant: $i > $o ).
tff(decl_23,type,
decreases: $i > $o ).
tff(decl_24,type,
environment: $i > $o ).
tff(decl_25,type,
subpopulations: ( $i * $i * $i * $i ) > $o ).
tff(decl_26,type,
resilience: $i > $i ).
tff(decl_27,type,
greater: ( $i * $i ) > $o ).
tff(decl_28,type,
resources: ( $i * $i ) > $i ).
tff(decl_29,type,
disbanding_rate: ( $i * $i ) > $i ).
tff(decl_30,type,
difference: ( $i * $i ) > $i ).
tff(decl_31,type,
increases: $i > $o ).
tff(decl_32,type,
efficient_producers: $i ).
tff(decl_33,type,
first_movers: $i ).
tff(decl_34,type,
esk1_0: $i ).
tff(decl_35,type,
esk2_0: $i ).
fof(a5,hypothesis,
! [X2,X3,X4,X5] :
( ( environment(X2)
& subpopulations(X3,X4,X2,X5)
& greater(resilience(X4),resilience(X3)) )
=> ( ( decreases(resources(X2,X5))
=> increases(difference(disbanding_rate(X3,X5),disbanding_rate(X4,X5))) )
& ( constant(resources(X2,X5))
=> constant(difference(disbanding_rate(X3,X5),disbanding_rate(X4,X5))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a5) ).
fof(prove_l4,conjecture,
! [X2,X5] :
( ( environment(X2)
& subpopulations(first_movers,efficient_producers,X2,X5) )
=> ( ( decreases(resources(X2,X5))
=> increases(difference(disbanding_rate(first_movers,X5),disbanding_rate(efficient_producers,X5))) )
& ( constant(resources(X2,X5))
=> ~ decreases(difference(disbanding_rate(first_movers,X5),disbanding_rate(efficient_producers,X5))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l4) ).
fof(mp_constant_not_decrease,axiom,
! [X1] :
( constant(X1)
=> ~ decreases(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_constant_not_decrease) ).
fof(a2,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
fof(c_0_4,hypothesis,
! [X7,X8,X9,X10] :
( ( ~ decreases(resources(X7,X10))
| increases(difference(disbanding_rate(X8,X10),disbanding_rate(X9,X10)))
| ~ environment(X7)
| ~ subpopulations(X8,X9,X7,X10)
| ~ greater(resilience(X9),resilience(X8)) )
& ( ~ constant(resources(X7,X10))
| constant(difference(disbanding_rate(X8,X10),disbanding_rate(X9,X10)))
| ~ environment(X7)
| ~ subpopulations(X8,X9,X7,X10)
| ~ greater(resilience(X9),resilience(X8)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[a5])])]) ).
fof(c_0_5,negated_conjecture,
~ ! [X2,X5] :
( ( environment(X2)
& subpopulations(first_movers,efficient_producers,X2,X5) )
=> ( ( decreases(resources(X2,X5))
=> increases(difference(disbanding_rate(first_movers,X5),disbanding_rate(efficient_producers,X5))) )
& ( constant(resources(X2,X5))
=> ~ decreases(difference(disbanding_rate(first_movers,X5),disbanding_rate(efficient_producers,X5))) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[prove_l4])]) ).
fof(c_0_6,plain,
! [X1] :
( constant(X1)
=> ~ decreases(X1) ),
inference(fof_simplification,[status(thm)],[mp_constant_not_decrease]) ).
cnf(c_0_7,hypothesis,
( constant(difference(disbanding_rate(X3,X2),disbanding_rate(X4,X2)))
| ~ constant(resources(X1,X2))
| ~ environment(X1)
| ~ subpopulations(X3,X4,X1,X2)
| ~ greater(resilience(X4),resilience(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(split_conjunct,[status(thm)],[a2]) ).
fof(c_0_9,negated_conjecture,
( environment(esk1_0)
& subpopulations(first_movers,efficient_producers,esk1_0,esk2_0)
& ( constant(resources(esk1_0,esk2_0))
| decreases(resources(esk1_0,esk2_0)) )
& ( decreases(difference(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0)))
| decreases(resources(esk1_0,esk2_0)) )
& ( constant(resources(esk1_0,esk2_0))
| ~ increases(difference(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0))) )
& ( decreases(difference(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0)))
| ~ increases(difference(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_10,plain,
! [X6] :
( ~ constant(X6)
| ~ decreases(X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])]) ).
cnf(c_0_11,hypothesis,
( constant(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X2,X1)
| ~ environment(X2)
| ~ constant(resources(X2,X1)) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,negated_conjecture,
subpopulations(first_movers,efficient_producers,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,negated_conjecture,
environment(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( ~ constant(X1)
| ~ decreases(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
( constant(difference(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0)))
| ~ constant(resources(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]) ).
cnf(c_0_16,hypothesis,
( increases(difference(disbanding_rate(X3,X2),disbanding_rate(X4,X2)))
| ~ decreases(resources(X1,X2))
| ~ environment(X1)
| ~ subpopulations(X3,X4,X1,X2)
| ~ greater(resilience(X4),resilience(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_17,negated_conjecture,
( ~ decreases(difference(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0)))
| ~ constant(resources(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
( decreases(difference(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0)))
| decreases(resources(esk1_0,esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,negated_conjecture,
( constant(resources(esk1_0,esk2_0))
| decreases(resources(esk1_0,esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,hypothesis,
( increases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X2,X1)
| ~ environment(X2)
| ~ decreases(resources(X2,X1)) ),
inference(spm,[status(thm)],[c_0_16,c_0_8]) ).
cnf(c_0_21,negated_conjecture,
decreases(resources(esk1_0,esk2_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_22,negated_conjecture,
( constant(resources(esk1_0,esk2_0))
| ~ increases(difference(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0))) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_23,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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_12]),c_0_13])]),c_0_21])]) ).
cnf(c_0_24,negated_conjecture,
constant(resources(esk1_0,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_24]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : MGT022+1 : TPTP v8.1.2. Released v2.0.0.
% 0.03/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 06:27:35 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.50/0.58 start to proof: theBenchmark
% 0.50/0.59 % Version : CSE_E---1.5
% 0.50/0.59 % Problem : theBenchmark.p
% 0.50/0.59 % Proof found
% 0.50/0.59 % SZS status Theorem for theBenchmark.p
% 0.50/0.59 % SZS output start Proof
% See solution above
% 0.50/0.60 % Total time : 0.006000 s
% 0.50/0.60 % SZS output end Proof
% 0.50/0.60 % Total time : 0.009000 s
%------------------------------------------------------------------------------