TSTP Solution File: MGT032+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : MGT032+2 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n011.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 09:07:48 EDT 2023
% Result : Theorem 0.20s 0.57s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 16
% Syntax : Number of formulae : 33 ( 4 unt; 13 typ; 0 def)
% Number of atoms : 79 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 101 ( 42 ~; 36 |; 16 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 10 >; 9 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn; 17 !; 3 ?; 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,
greater: ( $i * $i ) > $o ).
tff(decl_26,type,
selection_favors: ( $i * $i * $i ) > $o ).
tff(decl_27,type,
stable: $i > $o ).
tff(decl_28,type,
in_environment: ( $i * $i ) > $o ).
tff(decl_29,type,
first_movers: $i ).
tff(decl_30,type,
efficient_producers: $i ).
tff(decl_31,type,
greater_or_equal: ( $i * $i ) > $o ).
tff(decl_32,type,
esk1_1: $i > $i ).
tff(decl_33,type,
esk2_0: $i ).
tff(decl_34,type,
esk3_1: $i > $i ).
fof(prove_t1,conjecture,
! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [X5] :
( in_environment(X1,X5)
& ! [X4] :
( ( subpopulations(first_movers,efficient_producers,X1,X4)
& greater_or_equal(X4,X5) )
=> selection_favors(efficient_producers,first_movers,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t1) ).
fof(l1,hypothesis,
! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [X5] :
( in_environment(X1,X5)
& ! [X4] :
( ( subpopulations(first_movers,efficient_producers,X1,X4)
& greater_or_equal(X4,X5) )
=> greater(growth_rate(efficient_producers,X4),growth_rate(first_movers,X4)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1) ).
fof(mp1_high_growth_rates,axiom,
! [X1,X2,X3,X4] :
( ( environment(X1)
& subpopulations(X2,X3,X1,X4)
& greater(growth_rate(X3,X4),growth_rate(X2,X4)) )
=> selection_favors(X3,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp1_high_growth_rates) ).
fof(c_0_3,negated_conjecture,
~ ! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [X5] :
( in_environment(X1,X5)
& ! [X4] :
( ( subpopulations(first_movers,efficient_producers,X1,X4)
& greater_or_equal(X4,X5) )
=> selection_favors(efficient_producers,first_movers,X4) ) ) ),
inference(assume_negation,[status(cth)],[prove_t1]) ).
fof(c_0_4,hypothesis,
! [X10,X12] :
( ( in_environment(X10,esk1_1(X10))
| ~ environment(X10)
| ~ stable(X10) )
& ( ~ subpopulations(first_movers,efficient_producers,X10,X12)
| ~ greater_or_equal(X12,esk1_1(X10))
| greater(growth_rate(efficient_producers,X12),growth_rate(first_movers,X12))
| ~ environment(X10)
| ~ stable(X10) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l1])])])])]) ).
fof(c_0_5,negated_conjecture,
! [X14] :
( environment(esk2_0)
& stable(esk2_0)
& ( subpopulations(first_movers,efficient_producers,esk2_0,esk3_1(X14))
| ~ in_environment(esk2_0,X14) )
& ( greater_or_equal(esk3_1(X14),X14)
| ~ in_environment(esk2_0,X14) )
& ( ~ selection_favors(efficient_producers,first_movers,esk3_1(X14))
| ~ in_environment(esk2_0,X14) ) ),
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_3])])])])]) ).
fof(c_0_6,plain,
! [X6,X7,X8,X9] :
( ~ environment(X6)
| ~ subpopulations(X7,X8,X6,X9)
| ~ greater(growth_rate(X8,X9),growth_rate(X7,X9))
| selection_favors(X8,X7,X9) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp1_high_growth_rates])]) ).
cnf(c_0_7,hypothesis,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater_or_equal(X2,esk1_1(X1))
| ~ environment(X1)
| ~ stable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,negated_conjecture,
( greater_or_equal(esk3_1(X1),X1)
| ~ in_environment(esk2_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( selection_favors(X3,X2,X4)
| ~ environment(X1)
| ~ subpopulations(X2,X3,X1,X4)
| ~ greater(growth_rate(X3,X4),growth_rate(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
( greater(growth_rate(efficient_producers,esk3_1(esk1_1(X1))),growth_rate(first_movers,esk3_1(esk1_1(X1))))
| ~ in_environment(esk2_0,esk1_1(X1))
| ~ stable(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,esk3_1(esk1_1(X1)))
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,negated_conjecture,
( ~ selection_favors(efficient_producers,first_movers,esk3_1(X1))
| ~ in_environment(esk2_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,negated_conjecture,
( ~ in_environment(esk2_0,esk1_1(X1))
| ~ stable(X1)
| ~ subpopulations(first_movers,efficient_producers,X2,esk3_1(esk1_1(X1)))
| ~ subpopulations(first_movers,efficient_producers,X1,esk3_1(esk1_1(X1)))
| ~ environment(X2)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_13,negated_conjecture,
( subpopulations(first_movers,efficient_producers,esk2_0,esk3_1(X1))
| ~ in_environment(esk2_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_14,negated_conjecture,
environment(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_15,negated_conjecture,
( ~ in_environment(esk2_0,esk1_1(X1))
| ~ stable(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,esk3_1(esk1_1(X1)))
| ~ environment(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]) ).
cnf(c_0_16,negated_conjecture,
stable(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_17,negated_conjecture,
~ in_environment(esk2_0,esk1_1(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_13]),c_0_16]),c_0_14])]) ).
cnf(c_0_18,hypothesis,
( in_environment(X1,esk1_1(X1))
| ~ environment(X1)
| ~ stable(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_19,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_16]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MGT032+2 : TPTP v8.1.2. Released v2.0.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n011.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 06:36:40 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.20/0.57 % Version : CSE_E---1.5
% 0.20/0.57 % Problem : theBenchmark.p
% 0.20/0.57 % Proof found
% 0.20/0.57 % SZS status Theorem for theBenchmark.p
% 0.20/0.57 % SZS output start Proof
% See solution above
% 0.20/0.57 % Total time : 0.007000 s
% 0.20/0.57 % SZS output end Proof
% 0.20/0.57 % Total time : 0.009000 s
%------------------------------------------------------------------------------