TSTP Solution File: MGT036+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : MGT036+3 : 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 : n023.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 0.51s 0.60s
% Output : CNFRefutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 15
% Syntax : Number of formulae : 32 ( 7 unt; 11 typ; 0 def)
% Number of atoms : 65 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 75 ( 31 ~; 26 |; 15 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 6 >; 8 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn; 18 !; 6 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
environment: $i > $o ).
tff(decl_23,type,
subpopulations: ( $i * $i * $i * $i ) > $o ).
tff(decl_24,type,
growth_rate: ( $i * $i ) > $i ).
tff(decl_25,type,
zero: $i ).
tff(decl_26,type,
greater_or_equal: ( $i * $i ) > $o ).
tff(decl_27,type,
greater: ( $i * $i ) > $o ).
tff(decl_28,type,
outcompetes: ( $i * $i * $i ) > $o ).
tff(decl_29,type,
first_movers: $i ).
tff(decl_30,type,
efficient_producers: $i ).
tff(decl_31,type,
esk1_0: $i ).
tff(decl_32,type,
esk2_0: $i ).
fof(prove_t5_star,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_star) ).
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_star,hypothesis,
? [X1,X4] :
( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X4)
& greater_or_equal(growth_rate(first_movers,X4),zero)
& greater(zero,growth_rate(efficient_producers,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_star) ).
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(c_0_4,negated_conjecture,
~ ? [X1,X4] :
( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X4)
& outcompetes(first_movers,efficient_producers,X4) ),
inference(assume_negation,[status(cth)],[prove_t5_star]) ).
fof(c_0_5,hypothesis,
! [X9,X10,X11,X12] :
( ( ~ greater_or_equal(growth_rate(X11,X12),zero)
| ~ greater(zero,growth_rate(X10,X12))
| outcompetes(X11,X10,X12)
| ~ environment(X9)
| ~ subpopulations(X10,X11,X9,X12) )
& ( greater_or_equal(growth_rate(X11,X12),zero)
| ~ outcompetes(X11,X10,X12)
| ~ environment(X9)
| ~ subpopulations(X10,X11,X9,X12) )
& ( greater(zero,growth_rate(X10,X12))
| ~ outcompetes(X11,X10,X12)
| ~ environment(X9)
| ~ subpopulations(X10,X11,X9,X12) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2])])]) ).
fof(c_0_6,hypothesis,
( environment(esk1_0)
& subpopulations(first_movers,efficient_producers,esk1_0,esk2_0)
& greater_or_equal(growth_rate(first_movers,esk2_0),zero)
& greater(zero,growth_rate(efficient_producers,esk2_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[a13_star])]) ).
fof(c_0_7,negated_conjecture,
! [X15,X16] :
( ~ environment(X15)
| ~ subpopulations(first_movers,efficient_producers,X15,X16)
| ~ outcompetes(first_movers,efficient_producers,X16) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])]) ).
cnf(c_0_8,hypothesis,
( outcompetes(X1,X3,X2)
| ~ greater_or_equal(growth_rate(X1,X2),zero)
| ~ greater(zero,growth_rate(X3,X2))
| ~ environment(X4)
| ~ subpopulations(X3,X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,hypothesis,
greater(zero,growth_rate(efficient_producers,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
( ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ outcompetes(first_movers,efficient_producers,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,hypothesis,
subpopulations(first_movers,efficient_producers,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,hypothesis,
environment(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_13,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])]) ).
cnf(c_0_14,hypothesis,
( outcompetes(X1,efficient_producers,esk2_0)
| ~ greater_or_equal(growth_rate(X1,esk2_0),zero)
| ~ subpopulations(efficient_producers,X1,X2,esk2_0)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_15,hypothesis,
greater_or_equal(growth_rate(first_movers,esk2_0),zero),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,negated_conjecture,
~ outcompetes(first_movers,efficient_producers,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]) ).
cnf(c_0_17,plain,
( subpopulations(X3,X2,X1,X4)
| ~ environment(X1)
| ~ subpopulations(X2,X3,X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,hypothesis,
( ~ subpopulations(efficient_producers,first_movers,X1,esk2_0)
| ~ environment(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_19,hypothesis,
subpopulations(efficient_producers,first_movers,esk1_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_11]),c_0_12])]) ).
cnf(c_0_20,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_12])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : MGT036+3 : TPTP v8.1.2. Released v2.0.0.
% 0.04/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 06:26:25 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.51/0.58 start to proof: theBenchmark
% 0.51/0.60 % Version : CSE_E---1.5
% 0.51/0.60 % Problem : theBenchmark.p
% 0.51/0.60 % Proof found
% 0.51/0.60 % SZS status Theorem for theBenchmark.p
% 0.51/0.60 % SZS output start Proof
% See solution above
% 0.51/0.60 % Total time : 0.006000 s
% 0.51/0.60 % SZS output end Proof
% 0.51/0.60 % Total time : 0.009000 s
%------------------------------------------------------------------------------