TSTP Solution File: MGT036+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : MGT036+2 : 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 09:08:32 EDT 2023
% Result : Theorem 0.18s 0.59s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 20
% Syntax : Number of formulae : 52 ( 13 unt; 13 typ; 0 def)
% Number of atoms : 120 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 142 ( 61 ~; 48 |; 21 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 8 >; 9 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 86 ( 9 sgn; 48 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
environment: $i > $o ).
tff(decl_23,type,
subpopulations: ( $i * $i * $i * $i ) > $o ).
tff(decl_24,type,
first_movers: $i ).
tff(decl_25,type,
efficient_producers: $i ).
tff(decl_26,type,
in_environment: ( $i * $i ) > $o ).
tff(decl_27,type,
growth_rate: ( $i * $i ) > $i ).
tff(decl_28,type,
zero: $i ).
tff(decl_29,type,
greater_or_equal: ( $i * $i ) > $o ).
tff(decl_30,type,
greater: ( $i * $i ) > $o ).
tff(decl_31,type,
outcompetes: ( $i * $i * $i ) > $o ).
tff(decl_32,type,
resilience: $i > $i ).
tff(decl_33,type,
esk1_0: $i ).
tff(decl_34,type,
esk2_0: $i ).
fof(prove_t5,conjecture,
! [X1,X4] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X4) )
=> ~ outcompetes(first_movers,efficient_producers,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t5) ).
fof(mp_symmetry_of_subpopulations,axiom,
! [X1,X2,X3,X4] :
( ( environment(X1)
& subpopulations(X2,X3,X1,X4) )
=> subpopulations(X3,X2,X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations) ).
fof(mp_growth_rate_relationships,axiom,
! [X1,X2,X3,X4] :
( ( ( environment(X1)
& subpopulations(X2,X3,X1,X4) )
=> greater_or_equal(growth_rate(X2,X4),zero) )
<=> ~ greater(zero,growth_rate(X2,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_relationships) ).
fof(d2,hypothesis,
! [X1,X2,X3,X4] :
( ( environment(X1)
& subpopulations(X2,X3,X1,X4) )
=> ( ( greater_or_equal(growth_rate(X3,X4),zero)
& greater(zero,growth_rate(X2,X4)) )
<=> outcompetes(X3,X2,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).
fof(a13,hypothesis,
! [X1,X2,X3,X4] :
( ( environment(X1)
& in_environment(X1,X4)
& ~ greater(zero,growth_rate(X2,X4))
& greater(resilience(X3),resilience(X2)) )
=> ~ greater(zero,growth_rate(X3,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13) ).
fof(mp_time_point_occur,axiom,
! [X1,X4] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X4) )
=> in_environment(X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_point_occur) ).
fof(a2,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X4] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X4) )
=> ~ outcompetes(first_movers,efficient_producers,X4) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[prove_t5])]) ).
fof(c_0_8,plain,
! [X5,X6,X7,X8] :
( ~ environment(X5)
| ~ subpopulations(X6,X7,X5,X8)
| subpopulations(X7,X6,X5,X8) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_symmetry_of_subpopulations])]) ).
fof(c_0_9,negated_conjecture,
( environment(esk1_0)
& subpopulations(first_movers,efficient_producers,esk1_0,esk2_0)
& outcompetes(first_movers,efficient_producers,esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_10,plain,
! [X1,X2,X3,X4] :
( ( ( environment(X1)
& subpopulations(X2,X3,X1,X4) )
=> greater_or_equal(growth_rate(X2,X4),zero) )
<=> ~ greater(zero,growth_rate(X2,X4)) ),
inference(fof_simplification,[status(thm)],[mp_growth_rate_relationships]) ).
fof(c_0_11,hypothesis,
! [X15,X16,X17,X18] :
( ( ~ greater_or_equal(growth_rate(X17,X18),zero)
| ~ greater(zero,growth_rate(X16,X18))
| outcompetes(X17,X16,X18)
| ~ environment(X15)
| ~ subpopulations(X16,X17,X15,X18) )
& ( greater_or_equal(growth_rate(X17,X18),zero)
| ~ outcompetes(X17,X16,X18)
| ~ environment(X15)
| ~ subpopulations(X16,X17,X15,X18) )
& ( greater(zero,growth_rate(X16,X18))
| ~ outcompetes(X17,X16,X18)
| ~ environment(X15)
| ~ subpopulations(X16,X17,X15,X18) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2])])]) ).
cnf(c_0_12,plain,
( subpopulations(X3,X2,X1,X4)
| ~ environment(X1)
| ~ subpopulations(X2,X3,X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
subpopulations(first_movers,efficient_producers,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
environment(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_15,plain,
! [X11,X12,X13,X14] :
( ( environment(X11)
| ~ greater(zero,growth_rate(X12,X14)) )
& ( subpopulations(X12,X13,X11,X14)
| ~ greater(zero,growth_rate(X12,X14)) )
& ( ~ greater_or_equal(growth_rate(X12,X14),zero)
| ~ greater(zero,growth_rate(X12,X14)) )
& ( greater(zero,growth_rate(X12,X14))
| ~ environment(X11)
| ~ subpopulations(X12,X13,X11,X14)
| greater_or_equal(growth_rate(X12,X14),zero) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
cnf(c_0_16,hypothesis,
( greater(zero,growth_rate(X1,X2))
| ~ outcompetes(X3,X1,X2)
| ~ environment(X4)
| ~ subpopulations(X1,X3,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
subpopulations(efficient_producers,first_movers,esk1_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]) ).
cnf(c_0_18,negated_conjecture,
outcompetes(first_movers,efficient_producers,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_19,hypothesis,
! [X1,X2,X3,X4] :
( ( environment(X1)
& in_environment(X1,X4)
& ~ greater(zero,growth_rate(X2,X4))
& greater(resilience(X3),resilience(X2)) )
=> ~ greater(zero,growth_rate(X3,X4)) ),
inference(fof_simplification,[status(thm)],[a13]) ).
cnf(c_0_20,plain,
( environment(X1)
| ~ greater(zero,growth_rate(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
greater(zero,growth_rate(efficient_producers,esk2_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_18]),c_0_14])]) ).
fof(c_0_22,hypothesis,
! [X19,X20,X21,X22] :
( ~ environment(X19)
| ~ in_environment(X19,X22)
| greater(zero,growth_rate(X20,X22))
| ~ greater(resilience(X21),resilience(X20))
| ~ greater(zero,growth_rate(X21,X22)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])]) ).
cnf(c_0_23,hypothesis,
( greater_or_equal(growth_rate(X1,X2),zero)
| ~ outcompetes(X1,X3,X2)
| ~ environment(X4)
| ~ subpopulations(X3,X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_24,negated_conjecture,
environment(X1),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,hypothesis,
( greater(zero,growth_rate(X3,X2))
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(resilience(X4),resilience(X3))
| ~ greater(zero,growth_rate(X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,hypothesis,
( greater_or_equal(growth_rate(X1,X2),zero)
| ~ outcompetes(X1,X3,X2)
| ~ subpopulations(X3,X1,X4,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]) ).
cnf(c_0_27,hypothesis,
( greater(zero,growth_rate(X1,X2))
| ~ greater(zero,growth_rate(X3,X2))
| ~ greater(resilience(X3),resilience(X1))
| ~ in_environment(X4,X2) ),
inference(csr,[status(thm)],[c_0_25,c_0_20]) ).
cnf(c_0_28,plain,
( ~ greater_or_equal(growth_rate(X1,X2),zero)
| ~ greater(zero,growth_rate(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_29,negated_conjecture,
greater_or_equal(growth_rate(first_movers,esk2_0),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_17]),c_0_18])]) ).
fof(c_0_30,plain,
! [X9,X10] :
( ~ environment(X9)
| ~ subpopulations(first_movers,efficient_producers,X9,X10)
| in_environment(X9,X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_time_point_occur])]) ).
cnf(c_0_31,negated_conjecture,
( greater(zero,growth_rate(X1,esk2_0))
| ~ greater(resilience(efficient_producers),resilience(X1))
| ~ in_environment(X2,esk2_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_21]) ).
cnf(c_0_32,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(split_conjunct,[status(thm)],[a2]) ).
cnf(c_0_33,negated_conjecture,
~ greater(zero,growth_rate(first_movers,esk2_0)),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
( in_environment(X1,X2)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,hypothesis,
~ in_environment(X1,esk2_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_36,plain,
( in_environment(X1,X2)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_24])]) ).
cnf(c_0_37,hypothesis,
~ subpopulations(first_movers,efficient_producers,X1,esk2_0),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_13,c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT036+2 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n028.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 06:51:39 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.57 start to proof: theBenchmark
% 0.18/0.59 % Version : CSE_E---1.5
% 0.18/0.59 % Problem : theBenchmark.p
% 0.18/0.59 % Proof found
% 0.18/0.59 % SZS status Theorem for theBenchmark.p
% 0.18/0.59 % SZS output start Proof
% See solution above
% 0.18/0.59 % Total time : 0.008000 s
% 0.18/0.59 % SZS output end Proof
% 0.18/0.59 % Total time : 0.010000 s
%------------------------------------------------------------------------------