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 v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n031.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 : Unsatisfiable 0.19s 0.64s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 29
% Syntax : Number of formulae : 59 ( 13 unt; 16 typ; 0 def)
% Number of atoms : 135 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 177 ( 85 ~; 92 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 48 ( 0 sgn; 0 !; 0 ?; 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,
sk1: ( $i * $i ) > $i ).
tff(decl_28,type,
subpopulations: ( $i * $i * $i * $i ) > $o ).
tff(decl_29,type,
sk2: $i > $i ).
tff(decl_30,type,
appear: ( $i * $i ) > $i ).
tff(decl_31,type,
greater: ( $i * $i ) > $o ).
tff(decl_32,type,
greater_or_equal: ( $i * $i ) > $o ).
tff(decl_33,type,
zero: $i ).
tff(decl_34,type,
growth_rate: ( $i * $i ) > $i ).
tff(decl_35,type,
sk3: $i > $i ).
tff(decl_36,type,
sk4: $i ).
tff(decl_37,type,
sk5: $i > $i ).
cnf(mp_first_movers_negative_growth_1,axiom,
( subpopulations(first_movers,efficient_producers,X1,sk1(X2,X1))
| greater(sk2(X1),appear(efficient_producers,X1))
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth_1) ).
cnf(l11_7,hypothesis,
( in_environment(X1,sk3(X1))
| ~ environment(X1)
| ~ stable(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l11_7) ).
cnf(mp_first_movers_negative_growth_2,axiom,
( greater_or_equal(sk1(X2,X1),X2)
| greater(sk2(X1),appear(efficient_producers,X1))
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth_2) ).
cnf(l11_9,hypothesis,
( greater(zero,growth_rate(first_movers,X2))
| ~ environment(X1)
| ~ stable(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater_or_equal(X2,sk3(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l11_9) ).
cnf(prove_l10_11,negated_conjecture,
stable(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l10_11) ).
cnf(prove_l10_10,negated_conjecture,
environment(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l10_10) ).
cnf(mp_first_movers_negative_growth_5,axiom,
( greater(sk2(X1),appear(efficient_producers,X1))
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2)
| ~ greater(zero,growth_rate(first_movers,sk1(X2,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth_5) ).
cnf(prove_l10_12,negated_conjecture,
( subpopulations(first_movers,efficient_producers,sk4,sk5(X1))
| ~ greater(X1,appear(efficient_producers,sk4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l10_12) ).
cnf(prove_l10_14,negated_conjecture,
( ~ greater(X1,appear(efficient_producers,sk4))
| ~ greater(zero,growth_rate(first_movers,sk5(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l10_14) ).
cnf(prove_l10_13,negated_conjecture,
( greater_or_equal(sk5(X1),X1)
| ~ greater(X1,appear(efficient_producers,sk4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l10_13) ).
cnf(mp_first_movers_negative_growth_3,axiom,
( subpopulations(first_movers,efficient_producers,X1,sk1(X2,X1))
| greater(zero,growth_rate(first_movers,X3))
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2)
| ~ subpopulations(first_movers,efficient_producers,X1,X3)
| ~ greater_or_equal(X3,sk2(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth_3) ).
cnf(mp_first_movers_negative_growth_4,axiom,
( greater_or_equal(sk1(X2,X1),X2)
| greater(zero,growth_rate(first_movers,X3))
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2)
| ~ subpopulations(first_movers,efficient_producers,X1,X3)
| ~ greater_or_equal(X3,sk2(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth_4) ).
cnf(mp_first_movers_negative_growth_6,axiom,
( greater(zero,growth_rate(first_movers,X3))
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2)
| ~ greater(zero,growth_rate(first_movers,sk1(X2,X1)))
| ~ subpopulations(first_movers,efficient_producers,X1,X3)
| ~ greater_or_equal(X3,sk2(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth_6) ).
cnf(c_0_13,axiom,
( subpopulations(first_movers,efficient_producers,X1,sk1(X2,X1))
| greater(sk2(X1),appear(efficient_producers,X1))
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2) ),
mp_first_movers_negative_growth_1 ).
cnf(c_0_14,hypothesis,
( in_environment(X1,sk3(X1))
| ~ environment(X1)
| ~ stable(X1) ),
l11_7 ).
cnf(c_0_15,axiom,
( greater_or_equal(sk1(X2,X1),X2)
| greater(sk2(X1),appear(efficient_producers,X1))
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2) ),
mp_first_movers_negative_growth_2 ).
cnf(c_0_16,hypothesis,
( greater(zero,growth_rate(first_movers,X2))
| ~ environment(X1)
| ~ stable(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater_or_equal(X2,sk3(X1)) ),
l11_9 ).
cnf(c_0_17,hypothesis,
( greater(sk2(X1),appear(efficient_producers,X1))
| subpopulations(first_movers,efficient_producers,X1,sk1(sk3(X1),X1))
| ~ stable(X1)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,hypothesis,
( greater_or_equal(sk1(sk3(X1),X1),sk3(X1))
| greater(sk2(X1),appear(efficient_producers,X1))
| ~ stable(X1)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_19,hypothesis,
( greater(zero,growth_rate(first_movers,sk1(sk3(X1),X1)))
| greater(sk2(X1),appear(efficient_producers,X1))
| ~ stable(X1)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_20,negated_conjecture,
stable(sk4),
prove_l10_11 ).
cnf(c_0_21,negated_conjecture,
environment(sk4),
prove_l10_10 ).
cnf(c_0_22,axiom,
( greater(sk2(X1),appear(efficient_producers,X1))
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2)
| ~ greater(zero,growth_rate(first_movers,sk1(X2,X1))) ),
mp_first_movers_negative_growth_5 ).
cnf(c_0_23,negated_conjecture,
( greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| greater(sk2(sk4),appear(efficient_producers,sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_24,negated_conjecture,
( greater(sk2(sk4),appear(efficient_producers,sk4))
| ~ in_environment(sk4,sk3(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_20]),c_0_21])]) ).
cnf(c_0_25,negated_conjecture,
( subpopulations(first_movers,efficient_producers,sk4,sk5(X1))
| ~ greater(X1,appear(efficient_producers,sk4)) ),
prove_l10_12 ).
cnf(c_0_26,hypothesis,
greater(sk2(sk4),appear(efficient_producers,sk4)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_14]),c_0_20]),c_0_21])]) ).
cnf(c_0_27,negated_conjecture,
( ~ greater(X1,appear(efficient_producers,sk4))
| ~ greater(zero,growth_rate(first_movers,sk5(X1))) ),
prove_l10_14 ).
cnf(c_0_28,negated_conjecture,
( greater_or_equal(sk5(X1),X1)
| ~ greater(X1,appear(efficient_producers,sk4)) ),
prove_l10_13 ).
cnf(c_0_29,axiom,
( subpopulations(first_movers,efficient_producers,X1,sk1(X2,X1))
| greater(zero,growth_rate(first_movers,X3))
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2)
| ~ subpopulations(first_movers,efficient_producers,X1,X3)
| ~ greater_or_equal(X3,sk2(X1)) ),
mp_first_movers_negative_growth_3 ).
cnf(c_0_30,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4))),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,negated_conjecture,
~ greater(zero,growth_rate(first_movers,sk5(sk2(sk4)))),
inference(spm,[status(thm)],[c_0_27,c_0_26]) ).
cnf(c_0_32,negated_conjecture,
greater_or_equal(sk5(sk2(sk4)),sk2(sk4)),
inference(spm,[status(thm)],[c_0_28,c_0_26]) ).
cnf(c_0_33,axiom,
( greater_or_equal(sk1(X2,X1),X2)
| greater(zero,growth_rate(first_movers,X3))
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2)
| ~ subpopulations(first_movers,efficient_producers,X1,X3)
| ~ greater_or_equal(X3,sk2(X1)) ),
mp_first_movers_negative_growth_4 ).
cnf(c_0_34,negated_conjecture,
( subpopulations(first_movers,efficient_producers,sk4,sk1(X1,sk4))
| ~ in_environment(sk4,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_29,c_0_30]),c_0_20]),c_0_21])]),c_0_31]),c_0_32])]) ).
cnf(c_0_35,negated_conjecture,
( greater_or_equal(sk1(X1,sk4),X1)
| ~ in_environment(sk4,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_33,c_0_30]),c_0_20]),c_0_21])]),c_0_31]),c_0_32])]) ).
cnf(c_0_36,axiom,
( greater(zero,growth_rate(first_movers,X3))
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2)
| ~ greater(zero,growth_rate(first_movers,sk1(X2,X1)))
| ~ subpopulations(first_movers,efficient_producers,X1,X3)
| ~ greater_or_equal(X3,sk2(X1)) ),
mp_first_movers_negative_growth_6 ).
cnf(c_0_37,hypothesis,
subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_14]),c_0_20]),c_0_21])]) ).
cnf(c_0_38,hypothesis,
greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_14]),c_0_20]),c_0_21])]) ).
cnf(c_0_39,negated_conjecture,
( ~ greater(zero,growth_rate(first_movers,sk1(X1,sk4)))
| ~ in_environment(sk4,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_36,c_0_30]),c_0_20]),c_0_21])]),c_0_31]),c_0_32])]) ).
cnf(c_0_40,hypothesis,
greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_37]),c_0_38]),c_0_20]),c_0_21])]) ).
cnf(c_0_41,negated_conjecture,
~ in_environment(sk4,sk3(sk4)),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_42,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_14]),c_0_20]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT028-1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n031.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 06:53:39 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.62 start to proof: theBenchmark
% 0.19/0.64 % Version : CSE_E---1.5
% 0.19/0.64 % Problem : theBenchmark.p
% 0.19/0.64 % Proof found
% 0.19/0.64 % SZS status Theorem for theBenchmark.p
% 0.19/0.64 % SZS output start Proof
% See solution above
% 0.19/0.64 % Total time : 0.007000 s
% 0.19/0.64 % SZS output end Proof
% 0.19/0.64 % Total time : 0.010000 s
%------------------------------------------------------------------------------