TSTP Solution File: MGT020+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : MGT020+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 : n027.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 09:07:21 EDT 2023
% Result : Theorem 0.20s 0.60s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 23
% Syntax : Number of formulae : 58 ( 5 unt; 14 typ; 0 def)
% Number of atoms : 148 ( 9 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 172 ( 68 ~; 68 |; 20 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 10 >; 8 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn; 44 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
environment: $i > $o ).
tff(decl_23,type,
first_movers: $i ).
tff(decl_24,type,
efficient_producers: $i ).
tff(decl_25,type,
subpopulations: ( $i * $i * $i * $i ) > $o ).
tff(decl_26,type,
disbanding_rate: ( $i * $i ) > $i ).
tff(decl_27,type,
difference: ( $i * $i ) > $i ).
tff(decl_28,type,
decreases: $i > $o ).
tff(decl_29,type,
initial_FM_EP: $i > $i ).
tff(decl_30,type,
in_environment: ( $i * $i ) > $o ).
tff(decl_31,type,
greater_or_equal: ( $i * $i ) > $o ).
tff(decl_32,type,
greater: ( $i * $i ) > $o ).
tff(decl_33,type,
start_time: $i > $i ).
tff(decl_34,type,
esk1_0: $i ).
tff(decl_35,type,
esk2_0: $i ).
fof(mp_positive_function_difference,axiom,
! [X1,X2,X3,X4] :
( ( environment(X1)
& greater_or_equal(X2,X3)
& greater_or_equal(X4,X2)
& subpopulations(first_movers,efficient_producers,X1,X4)
& greater(disbanding_rate(first_movers,X3),disbanding_rate(efficient_producers,X3)) )
=> ( ~ decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2)))
=> greater(disbanding_rate(first_movers,X4),disbanding_rate(efficient_producers,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_positive_function_difference) ).
fof(mp_times_in_order,axiom,
! [X1,X3,X4] :
( ( environment(X1)
& greater_or_equal(X3,start_time(X1))
& greater(X4,X3)
& in_environment(X1,X4) )
=> in_environment(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_times_in_order) ).
fof(mp_initial_time,axiom,
! [X1] :
( environment(X1)
=> greater_or_equal(initial_FM_EP(X1),start_time(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_initial_time) ).
fof(mp_greater_or_equal,axiom,
! [X5,X6] :
( greater_or_equal(X5,X6)
=> ( greater(X5,X6)
| X5 = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal) ).
fof(mp_earliest_time_point,axiom,
! [X1,X2] :
( environment(X1)
=> ( ( in_environment(X1,initial_FM_EP(X1))
=> subpopulations(first_movers,efficient_producers,X1,initial_FM_EP(X1)) )
& ( subpopulations(first_movers,efficient_producers,X1,X2)
=> greater_or_equal(X2,initial_FM_EP(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_point) ).
fof(a8,hypothesis,
! [X1] :
( environment(X1)
=> greater(disbanding_rate(first_movers,initial_FM_EP(X1)),disbanding_rate(efficient_producers,initial_FM_EP(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a8) ).
fof(prove_l2,conjecture,
! [X1,X2] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X2) )
=> greater(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l2) ).
fof(mp_time_point_occurs,axiom,
! [X1,X2] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X2) )
=> in_environment(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_point_occurs) ).
fof(l3,axiom,
! [X1,X2] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X2) )
=> ~ decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3) ).
fof(c_0_9,plain,
! [X1,X2,X3,X4] :
( ( environment(X1)
& greater_or_equal(X2,X3)
& greater_or_equal(X4,X2)
& subpopulations(first_movers,efficient_producers,X1,X4)
& greater(disbanding_rate(first_movers,X3),disbanding_rate(efficient_producers,X3)) )
=> ( ~ decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2)))
=> greater(disbanding_rate(first_movers,X4),disbanding_rate(efficient_producers,X4)) ) ),
inference(fof_simplification,[status(thm)],[mp_positive_function_difference]) ).
fof(c_0_10,plain,
! [X19,X20,X21] :
( ~ environment(X19)
| ~ greater_or_equal(X20,start_time(X19))
| ~ greater(X21,X20)
| ~ in_environment(X19,X21)
| in_environment(X19,X20) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_times_in_order])]) ).
fof(c_0_11,plain,
! [X18] :
( ~ environment(X18)
| greater_or_equal(initial_FM_EP(X18),start_time(X18)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_initial_time])]) ).
fof(c_0_12,plain,
! [X25,X26] :
( ~ greater_or_equal(X25,X26)
| greater(X25,X26)
| X25 = X26 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_greater_or_equal])]) ).
fof(c_0_13,plain,
! [X10,X11] :
( ( ~ in_environment(X10,initial_FM_EP(X10))
| subpopulations(first_movers,efficient_producers,X10,initial_FM_EP(X10))
| ~ environment(X10) )
& ( ~ subpopulations(first_movers,efficient_producers,X10,X11)
| greater_or_equal(X11,initial_FM_EP(X10))
| ~ environment(X10) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_earliest_time_point])])]) ).
fof(c_0_14,plain,
! [X12,X13,X14,X15] :
( ~ environment(X12)
| ~ greater_or_equal(X13,X14)
| ~ greater_or_equal(X15,X13)
| ~ subpopulations(first_movers,efficient_producers,X12,X15)
| ~ greater(disbanding_rate(first_movers,X14),disbanding_rate(efficient_producers,X14))
| decreases(difference(disbanding_rate(first_movers,X13),disbanding_rate(efficient_producers,X13)))
| greater(disbanding_rate(first_movers,X15),disbanding_rate(efficient_producers,X15)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])]) ).
fof(c_0_15,hypothesis,
! [X27] :
( ~ environment(X27)
| greater(disbanding_rate(first_movers,initial_FM_EP(X27)),disbanding_rate(efficient_producers,initial_FM_EP(X27))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[a8])]) ).
fof(c_0_16,negated_conjecture,
~ ! [X1,X2] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X2) )
=> greater(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2)) ),
inference(assume_negation,[status(cth)],[prove_l2]) ).
cnf(c_0_17,plain,
( in_environment(X1,X2)
| ~ environment(X1)
| ~ greater_or_equal(X2,start_time(X1))
| ~ greater(X3,X2)
| ~ in_environment(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
( greater_or_equal(initial_FM_EP(X1),start_time(X1))
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
( greater(X1,X2)
| X1 = X2
| ~ greater_or_equal(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
( greater_or_equal(X2,initial_FM_EP(X1))
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_21,plain,
! [X16,X17] :
( ~ environment(X16)
| ~ subpopulations(first_movers,efficient_producers,X16,X17)
| in_environment(X16,X17) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_time_point_occurs])]) ).
cnf(c_0_22,plain,
( decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2)))
| greater(disbanding_rate(first_movers,X4),disbanding_rate(efficient_producers,X4))
| ~ environment(X1)
| ~ greater_or_equal(X2,X3)
| ~ greater_or_equal(X4,X2)
| ~ subpopulations(first_movers,efficient_producers,X1,X4)
| ~ greater(disbanding_rate(first_movers,X3),disbanding_rate(efficient_producers,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,hypothesis,
( greater(disbanding_rate(first_movers,initial_FM_EP(X1)),disbanding_rate(efficient_producers,initial_FM_EP(X1)))
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_24,negated_conjecture,
( environment(esk1_0)
& subpopulations(first_movers,efficient_producers,esk1_0,esk2_0)
& ~ greater(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
fof(c_0_25,plain,
! [X1,X2] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X2) )
=> ~ decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))) ),
inference(fof_simplification,[status(thm)],[l3]) ).
cnf(c_0_26,plain,
( in_environment(X1,initial_FM_EP(X1))
| ~ greater(X2,initial_FM_EP(X1))
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_27,plain,
( X1 = initial_FM_EP(X2)
| greater(X1,initial_FM_EP(X2))
| ~ subpopulations(first_movers,efficient_producers,X2,X1)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_28,plain,
( in_environment(X1,X2)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,hypothesis,
( greater(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))
| decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2)))
| ~ greater_or_equal(X2,initial_FM_EP(X3))
| ~ greater_or_equal(X1,X2)
| ~ subpopulations(first_movers,efficient_producers,X4,X1)
| ~ environment(X4)
| ~ environment(X3) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,negated_conjecture,
subpopulations(first_movers,efficient_producers,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,negated_conjecture,
environment(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,negated_conjecture,
~ greater(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_33,plain,
! [X8,X9] :
( ~ environment(X8)
| ~ subpopulations(first_movers,efficient_producers,X8,X9)
| ~ decreases(difference(disbanding_rate(first_movers,X9),disbanding_rate(efficient_producers,X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])]) ).
cnf(c_0_34,plain,
( X1 = initial_FM_EP(X2)
| in_environment(X2,initial_FM_EP(X2))
| ~ subpopulations(first_movers,efficient_producers,X2,X1)
| ~ environment(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_35,negated_conjecture,
( decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ greater_or_equal(X1,initial_FM_EP(X2))
| ~ greater_or_equal(esk2_0,X1)
| ~ environment(X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]),c_0_32]) ).
cnf(c_0_36,plain,
( ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_37,plain,
( subpopulations(first_movers,efficient_producers,X1,initial_FM_EP(X1))
| ~ in_environment(X1,initial_FM_EP(X1))
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_38,negated_conjecture,
( initial_FM_EP(esk1_0) = esk2_0
| in_environment(esk1_0,initial_FM_EP(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_30]),c_0_31])]) ).
cnf(c_0_39,negated_conjecture,
( ~ greater_or_equal(esk2_0,X1)
| ~ subpopulations(first_movers,efficient_producers,X2,X1)
| ~ environment(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_20]),c_0_36]) ).
cnf(c_0_40,negated_conjecture,
( initial_FM_EP(esk1_0) = esk2_0
| subpopulations(first_movers,efficient_producers,esk1_0,initial_FM_EP(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_31])]) ).
cnf(c_0_41,negated_conjecture,
( initial_FM_EP(esk1_0) = esk2_0
| ~ greater_or_equal(esk2_0,initial_FM_EP(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_31])]) ).
cnf(c_0_42,negated_conjecture,
initial_FM_EP(esk1_0) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_20]),c_0_30]),c_0_31])]) ).
cnf(c_0_43,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_42]),c_0_31])]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT020+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 : n027.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 07:00:21 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 0.20/0.60 % Version : CSE_E---1.5
% 0.20/0.60 % Problem : theBenchmark.p
% 0.20/0.60 % Proof found
% 0.20/0.60 % SZS status Theorem for theBenchmark.p
% 0.20/0.60 % SZS output start Proof
% See solution above
% 0.20/0.60 % Total time : 0.011000 s
% 0.20/0.60 % SZS output end Proof
% 0.20/0.60 % Total time : 0.014000 s
%------------------------------------------------------------------------------