TSTP Solution File: MGT023+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : MGT023+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 : n006.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 09:07:23 EDT 2023
% Result : Theorem 0.22s 0.61s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 35 ( 5 unt; 12 typ; 0 def)
% Number of atoms : 106 ( 11 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 130 ( 47 ~; 49 |; 24 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 9 >; 7 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn; 16 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
environment: $i > $o ).
tff(decl_23,type,
efficient_producers: $i ).
tff(decl_24,type,
growth_rate: ( $i * $i ) > $i ).
tff(decl_25,type,
first_movers: $i ).
tff(decl_26,type,
greater: ( $i * $i ) > $o ).
tff(decl_27,type,
in_environment: ( $i * $i ) > $o ).
tff(decl_28,type,
subpopulations: ( $i * $i * $i * $i ) > $o ).
tff(decl_29,type,
critical_point: $i > $i ).
tff(decl_30,type,
stable: $i > $o ).
tff(decl_31,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_32,type,
esk2_1: $i > $i ).
tff(decl_33,type,
esk3_0: $i ).
fof(d1,hypothesis,
! [X1,X2] :
( ( environment(X1)
& ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& in_environment(X1,X2)
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater(X3,X2) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) ) )
=> X2 = critical_point(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
fof(l12,hypothesis,
! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [X2] :
( in_environment(X1,X2)
& ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater(X3,X2) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12) ).
fof(prove_l5,conjecture,
! [X1] :
( ( environment(X1)
& stable(X1) )
=> in_environment(X1,critical_point(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5) ).
fof(c_0_3,hypothesis,
! [X1,X2] :
( ( environment(X1)
& ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& in_environment(X1,X2)
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater(X3,X2) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) ) )
=> X2 = critical_point(X1) ),
inference(fof_simplification,[status(thm)],[d1]) ).
fof(c_0_4,hypothesis,
! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [X2] :
( in_environment(X1,X2)
& ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater(X3,X2) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) ) ) ),
inference(fof_simplification,[status(thm)],[l12]) ).
fof(c_0_5,hypothesis,
! [X4,X5] :
( ( subpopulations(first_movers,efficient_producers,X4,esk1_2(X4,X5))
| ~ environment(X4)
| greater(growth_rate(efficient_producers,X5),growth_rate(first_movers,X5))
| ~ in_environment(X4,X5)
| X5 = critical_point(X4) )
& ( greater(esk1_2(X4,X5),X5)
| ~ environment(X4)
| greater(growth_rate(efficient_producers,X5),growth_rate(first_movers,X5))
| ~ in_environment(X4,X5)
| X5 = critical_point(X4) )
& ( ~ greater(growth_rate(efficient_producers,esk1_2(X4,X5)),growth_rate(first_movers,esk1_2(X4,X5)))
| ~ environment(X4)
| greater(growth_rate(efficient_producers,X5),growth_rate(first_movers,X5))
| ~ in_environment(X4,X5)
| X5 = critical_point(X4) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).
fof(c_0_6,hypothesis,
! [X7,X9] :
( ( in_environment(X7,esk2_1(X7))
| ~ environment(X7)
| ~ stable(X7) )
& ( ~ greater(growth_rate(efficient_producers,esk2_1(X7)),growth_rate(first_movers,esk2_1(X7)))
| ~ environment(X7)
| ~ stable(X7) )
& ( ~ subpopulations(first_movers,efficient_producers,X7,X9)
| ~ greater(X9,esk2_1(X7))
| greater(growth_rate(efficient_producers,X9),growth_rate(first_movers,X9))
| ~ environment(X7)
| ~ stable(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])]) ).
cnf(c_0_7,hypothesis,
( subpopulations(first_movers,efficient_producers,X1,esk1_2(X1,X2))
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| X2 = critical_point(X1)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,hypothesis,
( in_environment(X1,esk2_1(X1))
| ~ environment(X1)
| ~ stable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,hypothesis,
( ~ greater(growth_rate(efficient_producers,esk2_1(X1)),growth_rate(first_movers,esk2_1(X1)))
| ~ environment(X1)
| ~ stable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( ( environment(X1)
& stable(X1) )
=> in_environment(X1,critical_point(X1)) ),
inference(assume_negation,[status(cth)],[prove_l5]) ).
cnf(c_0_11,hypothesis,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater(X2,esk2_1(X1))
| ~ environment(X1)
| ~ stable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,hypothesis,
( critical_point(X1) = esk2_1(X1)
| subpopulations(first_movers,efficient_producers,X1,esk1_2(X1,esk2_1(X1)))
| ~ stable(X1)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).
fof(c_0_13,negated_conjecture,
( environment(esk3_0)
& stable(esk3_0)
& ~ in_environment(esk3_0,critical_point(esk3_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
cnf(c_0_14,hypothesis,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| X2 = critical_point(X1)
| ~ greater(growth_rate(efficient_producers,esk1_2(X1,X2)),growth_rate(first_movers,esk1_2(X1,X2)))
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_15,hypothesis,
( critical_point(X1) = esk2_1(X1)
| greater(growth_rate(efficient_producers,esk1_2(X1,esk2_1(X1))),growth_rate(first_movers,esk1_2(X1,esk2_1(X1))))
| ~ stable(X1)
| ~ greater(esk1_2(X1,esk2_1(X1)),esk2_1(X1))
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,hypothesis,
( greater(esk1_2(X1,X2),X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| X2 = critical_point(X1)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_17,negated_conjecture,
~ in_environment(esk3_0,critical_point(esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,hypothesis,
( critical_point(X1) = esk2_1(X1)
| ~ stable(X1)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_8]),c_0_9]) ).
cnf(c_0_19,negated_conjecture,
stable(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
environment(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,negated_conjecture,
~ in_environment(esk3_0,esk2_1(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])]) ).
cnf(c_0_22,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_8]),c_0_19]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : MGT023+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.15/0.36 % Computer : n006.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Aug 28 06:16:21 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.59 start to proof: theBenchmark
% 0.22/0.61 % Version : CSE_E---1.5
% 0.22/0.61 % Problem : theBenchmark.p
% 0.22/0.61 % Proof found
% 0.22/0.61 % SZS status Theorem for theBenchmark.p
% 0.22/0.61 % SZS output start Proof
% See solution above
% 0.22/0.61 % Total time : 0.007000 s
% 0.22/0.61 % SZS output end Proof
% 0.22/0.61 % Total time : 0.010000 s
%------------------------------------------------------------------------------