TSTP Solution File: MGT028+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : MGT028+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 : n028.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 09:07:26 EDT 2023
% Result : Theorem 0.21s 0.58s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 19
% Syntax : Number of formulae : 53 ( 11 unt; 16 typ; 0 def)
% Number of atoms : 169 ( 0 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 222 ( 90 ~; 96 |; 27 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 12 >; 9 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn; 15 !; 5 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
environment: $i > $o ).
tff(decl_23,type,
stable: $i > $o ).
tff(decl_24,type,
in_environment: ( $i * $i ) > $o ).
tff(decl_25,type,
first_movers: $i ).
tff(decl_26,type,
efficient_producers: $i ).
tff(decl_27,type,
subpopulations: ( $i * $i * $i * $i ) > $o ).
tff(decl_28,type,
greater_or_equal: ( $i * $i ) > $o ).
tff(decl_29,type,
zero: $i ).
tff(decl_30,type,
growth_rate: ( $i * $i ) > $i ).
tff(decl_31,type,
greater: ( $i * $i ) > $o ).
tff(decl_32,type,
appear: ( $i * $i ) > $i ).
tff(decl_33,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_34,type,
esk2_1: $i > $i ).
tff(decl_35,type,
esk3_1: $i > $i ).
tff(decl_36,type,
esk4_0: $i ).
tff(decl_37,type,
esk5_1: $i > $i ).
fof(mp_first_movers_negative_growth,axiom,
! [X1] :
( ( environment(X1)
& stable(X1)
& ? [X2] :
( in_environment(X1,X2)
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater_or_equal(X3,X2) )
=> greater(zero,growth_rate(first_movers,X3)) ) ) )
=> ? [X4] :
( greater(X4,appear(efficient_producers,X1))
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater_or_equal(X3,X4) )
=> greater(zero,growth_rate(first_movers,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth) ).
fof(l11,hypothesis,
! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [X5] :
( in_environment(X1,X5)
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater_or_equal(X3,X5) )
=> ( greater(growth_rate(efficient_producers,X3),zero)
& greater(zero,growth_rate(first_movers,X3)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l11) ).
fof(prove_l10,conjecture,
! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [X5] :
( greater(X5,appear(efficient_producers,X1))
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater_or_equal(X3,X5) )
=> greater(zero,growth_rate(first_movers,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l10) ).
fof(c_0_3,plain,
! [X6,X7,X10] :
( ( greater(esk2_1(X6),appear(efficient_producers,X6))
| subpopulations(first_movers,efficient_producers,X6,esk1_2(X6,X7))
| ~ in_environment(X6,X7)
| ~ environment(X6)
| ~ stable(X6) )
& ( ~ subpopulations(first_movers,efficient_producers,X6,X10)
| ~ greater_or_equal(X10,esk2_1(X6))
| greater(zero,growth_rate(first_movers,X10))
| subpopulations(first_movers,efficient_producers,X6,esk1_2(X6,X7))
| ~ in_environment(X6,X7)
| ~ environment(X6)
| ~ stable(X6) )
& ( greater(esk2_1(X6),appear(efficient_producers,X6))
| greater_or_equal(esk1_2(X6,X7),X7)
| ~ in_environment(X6,X7)
| ~ environment(X6)
| ~ stable(X6) )
& ( ~ subpopulations(first_movers,efficient_producers,X6,X10)
| ~ greater_or_equal(X10,esk2_1(X6))
| greater(zero,growth_rate(first_movers,X10))
| greater_or_equal(esk1_2(X6,X7),X7)
| ~ in_environment(X6,X7)
| ~ environment(X6)
| ~ stable(X6) )
& ( greater(esk2_1(X6),appear(efficient_producers,X6))
| ~ greater(zero,growth_rate(first_movers,esk1_2(X6,X7)))
| ~ in_environment(X6,X7)
| ~ environment(X6)
| ~ stable(X6) )
& ( ~ subpopulations(first_movers,efficient_producers,X6,X10)
| ~ greater_or_equal(X10,esk2_1(X6))
| greater(zero,growth_rate(first_movers,X10))
| ~ greater(zero,growth_rate(first_movers,esk1_2(X6,X7)))
| ~ in_environment(X6,X7)
| ~ environment(X6)
| ~ stable(X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_first_movers_negative_growth])])])])]) ).
fof(c_0_4,hypothesis,
! [X11,X13] :
( ( in_environment(X11,esk3_1(X11))
| ~ environment(X11)
| ~ stable(X11) )
& ( greater(growth_rate(efficient_producers,X13),zero)
| ~ subpopulations(first_movers,efficient_producers,X11,X13)
| ~ greater_or_equal(X13,esk3_1(X11))
| ~ environment(X11)
| ~ stable(X11) )
& ( greater(zero,growth_rate(first_movers,X13))
| ~ subpopulations(first_movers,efficient_producers,X11,X13)
| ~ greater_or_equal(X13,esk3_1(X11))
| ~ environment(X11)
| ~ stable(X11) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l11])])])])]) ).
cnf(c_0_5,plain,
( greater(esk2_1(X1),appear(efficient_producers,X1))
| subpopulations(first_movers,efficient_producers,X1,esk1_2(X1,X2))
| ~ in_environment(X1,X2)
| ~ environment(X1)
| ~ stable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,hypothesis,
( in_environment(X1,esk3_1(X1))
| ~ environment(X1)
| ~ stable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( greater(esk2_1(X1),appear(efficient_producers,X1))
| greater_or_equal(esk1_2(X1,X2),X2)
| ~ in_environment(X1,X2)
| ~ environment(X1)
| ~ stable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [X5] :
( greater(X5,appear(efficient_producers,X1))
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater_or_equal(X3,X5) )
=> greater(zero,growth_rate(first_movers,X3)) ) ) ),
inference(assume_negation,[status(cth)],[prove_l10]) ).
cnf(c_0_9,hypothesis,
( greater(zero,growth_rate(first_movers,X1))
| ~ subpopulations(first_movers,efficient_producers,X2,X1)
| ~ greater_or_equal(X1,esk3_1(X2))
| ~ environment(X2)
| ~ stable(X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,hypothesis,
( greater(esk2_1(X1),appear(efficient_producers,X1))
| subpopulations(first_movers,efficient_producers,X1,esk1_2(X1,esk3_1(X1)))
| ~ stable(X1)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_11,hypothesis,
( greater(esk2_1(X1),appear(efficient_producers,X1))
| greater_or_equal(esk1_2(X1,esk3_1(X1)),esk3_1(X1))
| ~ stable(X1)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
fof(c_0_12,negated_conjecture,
! [X15] :
( environment(esk4_0)
& stable(esk4_0)
& ( subpopulations(first_movers,efficient_producers,esk4_0,esk5_1(X15))
| ~ greater(X15,appear(efficient_producers,esk4_0)) )
& ( greater_or_equal(esk5_1(X15),X15)
| ~ greater(X15,appear(efficient_producers,esk4_0)) )
& ( ~ greater(zero,growth_rate(first_movers,esk5_1(X15)))
| ~ greater(X15,appear(efficient_producers,esk4_0)) ) ),
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_8])])])])]) ).
cnf(c_0_13,hypothesis,
( greater(zero,growth_rate(first_movers,esk1_2(X1,esk3_1(X1))))
| greater(esk2_1(X1),appear(efficient_producers,X1))
| ~ stable(X1)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_14,negated_conjecture,
stable(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,negated_conjecture,
environment(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( greater(esk2_1(X1),appear(efficient_producers,X1))
| ~ greater(zero,growth_rate(first_movers,esk1_2(X1,X2)))
| ~ in_environment(X1,X2)
| ~ environment(X1)
| ~ stable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_17,negated_conjecture,
( greater(zero,growth_rate(first_movers,esk1_2(esk4_0,esk3_1(esk4_0))))
| greater(esk2_1(esk4_0),appear(efficient_producers,esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).
cnf(c_0_18,negated_conjecture,
( greater(esk2_1(esk4_0),appear(efficient_producers,esk4_0))
| ~ in_environment(esk4_0,esk3_1(esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_14]),c_0_15])]) ).
cnf(c_0_19,negated_conjecture,
( subpopulations(first_movers,efficient_producers,esk4_0,esk5_1(X1))
| ~ greater(X1,appear(efficient_producers,esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,hypothesis,
greater(esk2_1(esk4_0),appear(efficient_producers,esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_6]),c_0_14]),c_0_15])]) ).
cnf(c_0_21,negated_conjecture,
( ~ greater(zero,growth_rate(first_movers,esk5_1(X1)))
| ~ greater(X1,appear(efficient_producers,esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_22,negated_conjecture,
( greater_or_equal(esk5_1(X1),X1)
| ~ greater(X1,appear(efficient_producers,esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_23,plain,
( greater(zero,growth_rate(first_movers,X2))
| subpopulations(first_movers,efficient_producers,X1,esk1_2(X1,X3))
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater_or_equal(X2,esk2_1(X1))
| ~ in_environment(X1,X3)
| ~ environment(X1)
| ~ stable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_24,negated_conjecture,
subpopulations(first_movers,efficient_producers,esk4_0,esk5_1(esk2_1(esk4_0))),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
~ greater(zero,growth_rate(first_movers,esk5_1(esk2_1(esk4_0)))),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_26,negated_conjecture,
greater_or_equal(esk5_1(esk2_1(esk4_0)),esk2_1(esk4_0)),
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_27,plain,
( greater(zero,growth_rate(first_movers,X2))
| greater_or_equal(esk1_2(X1,X3),X3)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater_or_equal(X2,esk2_1(X1))
| ~ in_environment(X1,X3)
| ~ environment(X1)
| ~ stable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_28,negated_conjecture,
( subpopulations(first_movers,efficient_producers,esk4_0,esk1_2(esk4_0,X1))
| ~ in_environment(esk4_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_14]),c_0_15])]),c_0_25]),c_0_26])]) ).
cnf(c_0_29,negated_conjecture,
( greater_or_equal(esk1_2(esk4_0,X1),X1)
| ~ in_environment(esk4_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_24]),c_0_14]),c_0_15])]),c_0_25]),c_0_26])]) ).
cnf(c_0_30,plain,
( greater(zero,growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater_or_equal(X2,esk2_1(X1))
| ~ greater(zero,growth_rate(first_movers,esk1_2(X1,X3)))
| ~ in_environment(X1,X3)
| ~ environment(X1)
| ~ stable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_31,hypothesis,
subpopulations(first_movers,efficient_producers,esk4_0,esk1_2(esk4_0,esk3_1(esk4_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_6]),c_0_14]),c_0_15])]) ).
cnf(c_0_32,hypothesis,
greater_or_equal(esk1_2(esk4_0,esk3_1(esk4_0)),esk3_1(esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_6]),c_0_14]),c_0_15])]) ).
cnf(c_0_33,negated_conjecture,
( ~ greater(zero,growth_rate(first_movers,esk1_2(esk4_0,X1)))
| ~ in_environment(esk4_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_24]),c_0_14]),c_0_15])]),c_0_25]),c_0_26])]) ).
cnf(c_0_34,hypothesis,
greater(zero,growth_rate(first_movers,esk1_2(esk4_0,esk3_1(esk4_0)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_31]),c_0_32]),c_0_14]),c_0_15])]) ).
cnf(c_0_35,negated_conjecture,
~ in_environment(esk4_0,esk3_1(esk4_0)),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_36,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_6]),c_0_14]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT028+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 : n028.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 06:36:09 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.21/0.57 start to proof: theBenchmark
% 0.21/0.58 % Version : CSE_E---1.5
% 0.21/0.58 % Problem : theBenchmark.p
% 0.21/0.58 % Proof found
% 0.21/0.58 % SZS status Theorem for theBenchmark.p
% 0.21/0.58 % SZS output start Proof
% See solution above
% 0.21/0.59 % Total time : 0.008000 s
% 0.21/0.59 % SZS output end Proof
% 0.21/0.59 % Total time : 0.010000 s
%------------------------------------------------------------------------------