TSTP Solution File: NUM861+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM861+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n013.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 10:41:07 EDT 2023
% Result : Theorem 16.74s 16.81s
% Output : CNFRefutation 16.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 30
% Syntax : Number of formulae : 273 ( 20 unt; 16 typ; 0 def)
% Number of atoms : 675 ( 36 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 695 ( 277 ~; 385 |; 20 &)
% ( 9 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 31 ( 12 >; 19 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 497 ( 16 sgn; 88 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
lesseq: ( $i * $i ) > $o ).
tff(decl_23,type,
sum: ( $i * $i ) > $i ).
tff(decl_24,type,
summation: $i > $i ).
tff(decl_25,type,
max: ( $i * $i ) > $i ).
tff(decl_26,type,
ub: ( $i * $i * $i ) > $o ).
tff(decl_27,type,
model_max: ( $i * $i * $i ) > $o ).
tff(decl_28,type,
c: $i ).
tff(decl_29,type,
model_ub: ( $i * $i * $i ) > $o ).
tff(decl_30,type,
minsol_model_max: ( $i * $i * $i ) > $o ).
tff(decl_31,type,
minsol_model_ub: ( $i * $i * $i ) > $o ).
tff(decl_32,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_33,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_34,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_35,type,
esk4_0: $i ).
tff(decl_36,type,
esk5_0: $i ).
tff(decl_37,type,
esk6_0: $i ).
fof(max_is_ub_1,conjecture,
! [X1,X2,X3] :
( minsol_model_ub(X1,X2,X3)
<=> minsol_model_max(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',max_is_ub_1) ).
fof(minsol_model_ub,axiom,
! [X1,X2,X4] :
( minsol_model_ub(X1,X2,X4)
<=> ( model_ub(X1,X2,X4)
& ! [X3] :
( model_ub(X1,X2,X3)
=> lesseq(X4,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minsol_model_ub) ).
fof(model_max_4,axiom,
! [X1,X2,X4] :
( model_max(X1,X2,X4)
<=> lesseq(sum(c,max(X1,X2)),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',model_max_4) ).
fof(lesseq_ref,axiom,
! [X1] : lesseq(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lesseq_ref) ).
fof(minsol_model_max,axiom,
! [X1,X2,X4] :
( minsol_model_max(X1,X2,X4)
<=> ( model_max(X1,X2,X4)
& ! [X3] :
( model_max(X1,X2,X3)
=> lesseq(X4,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minsol_model_max) ).
fof(max_2,axiom,
! [X1,X2] :
( max(X1,X2) = X2
| ~ lesseq(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',max_2) ).
fof(lesseq_antisymmetric,axiom,
! [X1,X2] :
( ( lesseq(X1,X2)
& lesseq(X2,X1) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lesseq_antisymmetric) ).
fof(sum_monotone_1,axiom,
! [X1,X2,X3] :
( lesseq(X1,X2)
<=> lesseq(sum(X3,X1),sum(X3,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_monotone_1) ).
fof(model_ub_4,axiom,
! [X1,X2,X4] :
( model_ub(X1,X2,X4)
<=> ? [X3] :
( ub(X1,X2,X3)
& lesseq(sum(c,X3),X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',model_ub_4) ).
fof(lesseq_trans,axiom,
! [X1,X2,X3] :
( ( lesseq(X1,X2)
& lesseq(X2,X3) )
=> lesseq(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lesseq_trans) ).
fof(lesseq_total,axiom,
! [X1,X2] :
( lesseq(X1,X2)
| lesseq(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lesseq_total) ).
fof(max_1,axiom,
! [X1,X2] :
( max(X1,X2) = X1
| ~ lesseq(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',max_1) ).
fof(ub,axiom,
! [X1,X2,X3] :
( ub(X1,X2,X3)
<=> ( lesseq(X1,X3)
& lesseq(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ub) ).
fof(summation_monotone,axiom,
! [X1,X2] :
( lesseq(X1,X2)
<=> lesseq(summation(X1),summation(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',summation_monotone) ).
fof(c_0_14,negated_conjecture,
~ ! [X1,X2,X3] :
( minsol_model_ub(X1,X2,X3)
<=> minsol_model_max(X1,X2,X3) ),
inference(assume_negation,[status(cth)],[max_is_ub_1]) ).
fof(c_0_15,plain,
! [X44,X45,X46,X47,X48,X49,X50] :
( ( model_ub(X44,X45,X46)
| ~ minsol_model_ub(X44,X45,X46) )
& ( ~ model_ub(X44,X45,X47)
| lesseq(X46,X47)
| ~ minsol_model_ub(X44,X45,X46) )
& ( model_ub(X48,X49,esk3_3(X48,X49,X50))
| ~ model_ub(X48,X49,X50)
| minsol_model_ub(X48,X49,X50) )
& ( ~ lesseq(X50,esk3_3(X48,X49,X50))
| ~ model_ub(X48,X49,X50)
| minsol_model_ub(X48,X49,X50) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[minsol_model_ub])])])])])]) ).
fof(c_0_16,negated_conjecture,
( ( ~ minsol_model_ub(esk4_0,esk5_0,esk6_0)
| ~ minsol_model_max(esk4_0,esk5_0,esk6_0) )
& ( minsol_model_ub(esk4_0,esk5_0,esk6_0)
| minsol_model_max(esk4_0,esk5_0,esk6_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
fof(c_0_17,plain,
! [X25,X26,X27] :
( ( ~ model_max(X25,X26,X27)
| lesseq(sum(c,max(X25,X26)),X27) )
& ( ~ lesseq(sum(c,max(X25,X26)),X27)
| model_max(X25,X26,X27) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[model_max_4])]) ).
fof(c_0_18,plain,
! [X5] : lesseq(X5,X5),
inference(variable_rename,[status(thm)],[lesseq_ref]) ).
fof(c_0_19,plain,
! [X36,X37,X38,X39,X40,X41,X42] :
( ( model_max(X36,X37,X38)
| ~ minsol_model_max(X36,X37,X38) )
& ( ~ model_max(X36,X37,X39)
| lesseq(X38,X39)
| ~ minsol_model_max(X36,X37,X38) )
& ( model_max(X40,X41,esk2_3(X40,X41,X42))
| ~ model_max(X40,X41,X42)
| minsol_model_max(X40,X41,X42) )
& ( ~ lesseq(X42,esk2_3(X40,X41,X42))
| ~ model_max(X40,X41,X42)
| minsol_model_max(X40,X41,X42) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[minsol_model_max])])])])])]) ).
cnf(c_0_20,plain,
( model_ub(X1,X2,X3)
| ~ minsol_model_ub(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
( minsol_model_ub(esk4_0,esk5_0,esk6_0)
| minsol_model_max(esk4_0,esk5_0,esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( model_max(X1,X2,X3)
| ~ lesseq(sum(c,max(X1,X2)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
lesseq(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
( lesseq(X4,X3)
| ~ model_max(X1,X2,X3)
| ~ minsol_model_max(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,negated_conjecture,
( minsol_model_max(esk4_0,esk5_0,esk6_0)
| model_ub(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
( minsol_model_max(X2,X3,X1)
| ~ lesseq(X1,esk2_3(X2,X3,X1))
| ~ model_max(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
( lesseq(sum(c,max(X1,X2)),X3)
| ~ model_max(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_28,plain,
( model_max(X1,X2,esk2_3(X1,X2,X3))
| minsol_model_max(X1,X2,X3)
| ~ model_max(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,plain,
model_max(X1,X2,sum(c,max(X1,X2))),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_30,plain,
! [X1,X2] :
( max(X1,X2) = X2
| ~ lesseq(X1,X2) ),
inference(fof_simplification,[status(thm)],[max_2]) ).
fof(c_0_31,plain,
! [X9,X10] :
( ~ lesseq(X9,X10)
| ~ lesseq(X10,X9)
| X9 = X10 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[lesseq_antisymmetric])]) ).
cnf(c_0_32,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| lesseq(esk6_0,X1)
| ~ model_max(esk4_0,esk5_0,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_33,plain,
! [X13,X14,X15] :
( ( ~ lesseq(X13,X14)
| lesseq(sum(X15,X13),sum(X15,X14)) )
& ( ~ lesseq(sum(X15,X13),sum(X15,X14))
| lesseq(X13,X14) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sum_monotone_1])]) ).
cnf(c_0_34,plain,
( minsol_model_max(X1,X2,sum(c,max(X3,X4)))
| ~ model_max(X3,X4,esk2_3(X1,X2,sum(c,max(X3,X4))))
| ~ model_max(X1,X2,sum(c,max(X3,X4))) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_35,plain,
( minsol_model_max(X1,X2,sum(c,max(X1,X2)))
| model_max(X1,X2,esk2_3(X1,X2,sum(c,max(X1,X2)))) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_36,plain,
! [X20,X21] :
( max(X20,X21) = X21
| ~ lesseq(X20,X21) ),
inference(variable_rename,[status(thm)],[c_0_30]) ).
cnf(c_0_37,plain,
( X1 = X2
| ~ lesseq(X1,X2)
| ~ lesseq(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| lesseq(esk6_0,sum(c,max(esk4_0,esk5_0))) ),
inference(spm,[status(thm)],[c_0_32,c_0_29]) ).
cnf(c_0_39,plain,
( model_max(X1,X2,X3)
| ~ minsol_model_max(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_40,plain,
( lesseq(X2,X3)
| ~ lesseq(sum(X1,X2),sum(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,plain,
minsol_model_max(X1,X2,sum(c,max(X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_29])]) ).
cnf(c_0_42,plain,
( max(X1,X2) = X2
| ~ lesseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_43,negated_conjecture,
( sum(c,max(esk4_0,esk5_0)) = esk6_0
| model_ub(esk4_0,esk5_0,esk6_0)
| ~ lesseq(sum(c,max(esk4_0,esk5_0)),esk6_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| model_max(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_39,c_0_25]) ).
fof(c_0_45,plain,
! [X28,X29,X30,X32,X33,X34,X35] :
( ( ub(X28,X29,esk1_3(X28,X29,X30))
| ~ model_ub(X28,X29,X30) )
& ( lesseq(sum(c,esk1_3(X28,X29,X30)),X30)
| ~ model_ub(X28,X29,X30) )
& ( ~ ub(X32,X33,X35)
| ~ lesseq(sum(c,X35),X34)
| model_ub(X32,X33,X34) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[model_ub_4])])])])])]) ).
fof(c_0_46,plain,
! [X6,X7,X8] :
( ~ lesseq(X6,X7)
| ~ lesseq(X7,X8)
| lesseq(X6,X8) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[lesseq_trans])]) ).
fof(c_0_47,plain,
! [X11,X12] :
( lesseq(X11,X12)
| lesseq(X12,X11) ),
inference(variable_rename,[status(thm)],[lesseq_total]) ).
cnf(c_0_48,plain,
( lesseq(max(X1,X2),X3)
| ~ model_max(X1,X2,sum(c,X3)) ),
inference(spm,[status(thm)],[c_0_40,c_0_27]) ).
cnf(c_0_49,plain,
( minsol_model_max(X1,X2,sum(c,X2))
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_50,negated_conjecture,
( sum(c,max(esk4_0,esk5_0)) = esk6_0
| model_ub(esk4_0,esk5_0,esk6_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_27]),c_0_44]) ).
fof(c_0_51,plain,
! [X1,X2] :
( max(X1,X2) = X1
| ~ lesseq(X2,X1) ),
inference(fof_simplification,[status(thm)],[max_1]) ).
cnf(c_0_52,plain,
( model_ub(X1,X2,X4)
| ~ ub(X1,X2,X3)
| ~ lesseq(sum(c,X3),X4) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
fof(c_0_53,plain,
! [X22,X23,X24] :
( ( lesseq(X22,X24)
| ~ ub(X22,X23,X24) )
& ( lesseq(X23,X24)
| ~ ub(X22,X23,X24) )
& ( ~ lesseq(X22,X24)
| ~ lesseq(X23,X24)
| ub(X22,X23,X24) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ub])])]) ).
cnf(c_0_54,plain,
( lesseq(X1,X3)
| ~ lesseq(X1,X2)
| ~ lesseq(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_55,plain,
( lesseq(X1,X2)
| lesseq(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_56,plain,
( lesseq(X1,X2)
| ~ model_max(X3,X1,sum(c,X2))
| ~ lesseq(X3,X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_42]) ).
cnf(c_0_57,negated_conjecture,
( minsol_model_max(X1,max(esk4_0,esk5_0),esk6_0)
| model_ub(esk4_0,esk5_0,esk6_0)
| ~ lesseq(X1,max(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
fof(c_0_58,plain,
! [X18,X19] :
( max(X18,X19) = X18
| ~ lesseq(X19,X18) ),
inference(variable_rename,[status(thm)],[c_0_51]) ).
cnf(c_0_59,plain,
( model_ub(X1,X2,X3)
| ~ model_max(X4,X5,X3)
| ~ ub(X1,X2,max(X4,X5)) ),
inference(spm,[status(thm)],[c_0_52,c_0_27]) ).
cnf(c_0_60,plain,
( ub(X1,X3,X2)
| ~ lesseq(X1,X2)
| ~ lesseq(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_61,plain,
( lesseq(X1,X2)
| lesseq(X3,X1)
| ~ lesseq(X3,X2) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_62,plain,
( lesseq(X1,max(X2,X1))
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_29]) ).
cnf(c_0_63,negated_conjecture,
( minsol_model_max(max(esk4_0,esk5_0),max(esk4_0,esk5_0),esk6_0)
| model_ub(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_57,c_0_23]) ).
cnf(c_0_64,plain,
( max(X1,X2) = X1
| ~ lesseq(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_65,plain,
( model_ub(X1,X2,X3)
| ~ model_max(X4,X5,X3)
| ~ lesseq(X2,max(X4,X5))
| ~ lesseq(X1,max(X4,X5)) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_66,plain,
( lesseq(X1,max(X2,X3))
| lesseq(X3,X1)
| ~ lesseq(X2,X3) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_67,plain,
( lesseq(sum(c,esk1_3(X1,X2,X3)),X3)
| ~ model_ub(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_68,negated_conjecture,
( minsol_model_max(esk4_0,esk4_0,esk6_0)
| model_ub(esk4_0,esk5_0,esk6_0)
| ~ lesseq(esk5_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_69,plain,
( lesseq(X1,X2)
| ~ model_max(X1,X3,sum(c,X2))
| ~ lesseq(X3,X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_64]) ).
cnf(c_0_70,plain,
( model_ub(X1,X2,X3)
| ~ model_max(X4,X2,X3)
| ~ lesseq(X1,max(X4,X2))
| ~ lesseq(X4,X2) ),
inference(spm,[status(thm)],[c_0_65,c_0_62]) ).
cnf(c_0_71,plain,
( lesseq(X1,max(X2,X2))
| lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_66,c_0_23]) ).
cnf(c_0_72,plain,
( lesseq(X1,X2)
| ~ model_ub(X3,X4,X2)
| ~ lesseq(X1,sum(c,esk1_3(X3,X4,X2))) ),
inference(spm,[status(thm)],[c_0_54,c_0_67]) ).
cnf(c_0_73,plain,
( lesseq(sum(X3,X1),sum(X3,X2))
| ~ lesseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_74,plain,
( lesseq(X1,X2)
| ~ ub(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_75,plain,
( ub(X1,X2,esk1_3(X1,X2,X3))
| ~ model_ub(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_76,negated_conjecture,
( minsol_model_max(esk4_0,esk4_0,esk6_0)
| model_ub(esk4_0,esk5_0,esk6_0)
| lesseq(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_68,c_0_55]) ).
cnf(c_0_77,plain,
( lesseq(X1,X2)
| ~ ub(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_78,plain,
( model_ub(X1,X2,X3)
| ~ model_ub(X4,X5,X3)
| ~ ub(X1,X2,esk1_3(X4,X5,X3)) ),
inference(spm,[status(thm)],[c_0_52,c_0_67]) ).
cnf(c_0_79,plain,
( lesseq(X1,max(X1,X2))
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_69,c_0_29]) ).
cnf(c_0_80,plain,
( model_ub(X1,X2,X3)
| lesseq(X2,X1)
| ~ model_max(X2,X2,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_23])]) ).
cnf(c_0_81,plain,
( model_max(X1,X2,X3)
| ~ lesseq(sum(c,X2),X3)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_42]) ).
cnf(c_0_82,plain,
( lesseq(sum(c,X1),X2)
| ~ model_ub(X3,X4,X2)
| ~ lesseq(X1,esk1_3(X3,X4,X2)) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_83,plain,
( lesseq(X1,esk1_3(X1,X2,X3))
| ~ model_ub(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_84,plain,
( model_ub(X1,X1,X2)
| ~ model_max(X3,X1,X2)
| ~ lesseq(X3,X1) ),
inference(spm,[status(thm)],[c_0_70,c_0_62]) ).
cnf(c_0_85,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| model_max(esk4_0,esk4_0,esk6_0)
| lesseq(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_39,c_0_76]) ).
cnf(c_0_86,plain,
( lesseq(X1,esk1_3(X2,X1,X3))
| ~ model_ub(X2,X1,X3) ),
inference(spm,[status(thm)],[c_0_77,c_0_75]) ).
cnf(c_0_87,plain,
( model_ub(X1,X2,X3)
| ~ model_ub(X4,X5,X3)
| ~ lesseq(X2,esk1_3(X4,X5,X3))
| ~ lesseq(X1,esk1_3(X4,X5,X3)) ),
inference(spm,[status(thm)],[c_0_78,c_0_60]) ).
cnf(c_0_88,plain,
( model_ub(X1,X2,X3)
| ~ model_max(X1,X2,X3)
| ~ lesseq(X1,X2)
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_70,c_0_79]) ).
cnf(c_0_89,plain,
( model_ub(X1,X2,X3)
| lesseq(X2,X1)
| ~ lesseq(sum(c,X2),X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_23])]) ).
cnf(c_0_90,plain,
( lesseq(sum(c,X1),X2)
| ~ model_ub(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_91,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| model_ub(esk4_0,esk4_0,esk6_0)
| lesseq(esk4_0,esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_23])]) ).
cnf(c_0_92,plain,
( lesseq(sum(c,X1),X2)
| ~ model_ub(X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_82,c_0_86]) ).
cnf(c_0_93,plain,
( model_ub(X1,X2,X3)
| ~ model_ub(X2,X4,X3)
| ~ lesseq(X1,esk1_3(X2,X4,X3)) ),
inference(spm,[status(thm)],[c_0_87,c_0_83]) ).
cnf(c_0_94,plain,
( model_ub(X1,X2,X3)
| ~ lesseq(sum(c,X2),X3)
| ~ lesseq(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_81]),c_0_89]) ).
cnf(c_0_95,negated_conjecture,
( lesseq(sum(c,esk4_0),esk6_0)
| lesseq(esk4_0,esk5_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]) ).
cnf(c_0_96,plain,
( model_ub(X1,X2,X3)
| lesseq(X4,X2)
| ~ model_max(X4,X4,X3)
| ~ lesseq(X1,max(X4,X4)) ),
inference(spm,[status(thm)],[c_0_65,c_0_71]) ).
cnf(c_0_97,plain,
( model_ub(X1,X2,X3)
| ~ model_ub(X2,X1,X3) ),
inference(spm,[status(thm)],[c_0_93,c_0_86]) ).
cnf(c_0_98,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| ~ lesseq(esk4_0,esk5_0)
| ~ lesseq(esk5_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_88,c_0_44]) ).
cnf(c_0_99,negated_conjecture,
( model_ub(X1,esk4_0,esk6_0)
| lesseq(esk4_0,esk5_0)
| ~ lesseq(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_100,plain,
( model_max(X1,X2,sum(c,X3))
| ~ lesseq(max(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_22,c_0_73]) ).
cnf(c_0_101,plain,
( model_ub(X1,X2,X3)
| lesseq(X1,X2)
| ~ model_max(X1,X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_62]),c_0_23])]) ).
cnf(c_0_102,negated_conjecture,
( model_ub(esk5_0,esk4_0,esk6_0)
| ~ lesseq(esk5_0,esk4_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_99]) ).
cnf(c_0_103,plain,
( model_max(X1,X2,sum(c,X3))
| ~ lesseq(X2,X3)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_100,c_0_42]) ).
cnf(c_0_104,plain,
( model_ub(X1,X2,X3)
| lesseq(X1,X2)
| ~ lesseq(sum(c,X1),X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_81]),c_0_23])]) ).
cnf(c_0_105,negated_conjecture,
( lesseq(sum(c,esk5_0),esk6_0)
| ~ lesseq(esk5_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_90,c_0_102]) ).
cnf(c_0_106,plain,
( lesseq(sum(c,X1),X2)
| ~ model_max(X1,X3,X2)
| ~ lesseq(X3,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_64]) ).
fof(c_0_107,plain,
! [X16,X17] :
( ( ~ lesseq(X16,X17)
| lesseq(summation(X16),summation(X17)) )
& ( ~ lesseq(summation(X16),summation(X17))
| lesseq(X16,X17) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[summation_monotone])]) ).
cnf(c_0_108,plain,
( lesseq(esk1_3(X1,X2,sum(c,X3)),X3)
| ~ model_ub(X1,X2,sum(c,X3)) ),
inference(spm,[status(thm)],[c_0_40,c_0_67]) ).
cnf(c_0_109,plain,
( model_ub(X1,X1,sum(c,X2))
| ~ lesseq(X3,X1)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_84,c_0_103]) ).
cnf(c_0_110,negated_conjecture,
( model_ub(esk5_0,X1,esk6_0)
| lesseq(esk5_0,X1)
| ~ lesseq(esk5_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_111,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| lesseq(sum(c,esk4_0),esk6_0)
| ~ lesseq(esk5_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_106,c_0_44]) ).
cnf(c_0_112,plain,
( lesseq(summation(X1),summation(X2))
| ~ lesseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_113,plain,
( lesseq(X1,X2)
| ~ model_max(X3,X4,sum(c,X2))
| ~ lesseq(X1,max(X3,X4)) ),
inference(spm,[status(thm)],[c_0_54,c_0_48]) ).
cnf(c_0_114,plain,
( model_max(X1,X2,sum(c,X1))
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_64]) ).
cnf(c_0_115,plain,
( lesseq(X1,X2)
| ~ model_ub(X3,X4,sum(c,X2))
| ~ lesseq(X1,esk1_3(X3,X4,sum(c,X2))) ),
inference(spm,[status(thm)],[c_0_54,c_0_108]) ).
cnf(c_0_116,plain,
( model_ub(X1,X1,sum(c,X2))
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_109,c_0_23]) ).
cnf(c_0_117,plain,
( model_ub(X1,X1,X2)
| ~ model_ub(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_93,c_0_83]) ).
cnf(c_0_118,negated_conjecture,
( model_ub(esk5_0,X1,esk6_0)
| lesseq(esk4_0,esk5_0)
| lesseq(esk5_0,X1) ),
inference(spm,[status(thm)],[c_0_110,c_0_55]) ).
cnf(c_0_119,plain,
( model_ub(X1,X2,X3)
| ~ model_ub(X4,X2,X3)
| ~ lesseq(X1,esk1_3(X4,X2,X3)) ),
inference(spm,[status(thm)],[c_0_87,c_0_86]) ).
cnf(c_0_120,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| lesseq(X1,sum(c,max(esk4_0,esk5_0)))
| ~ lesseq(X1,esk6_0) ),
inference(spm,[status(thm)],[c_0_54,c_0_38]) ).
cnf(c_0_121,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| lesseq(sum(c,esk4_0),esk6_0)
| lesseq(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_111,c_0_55]) ).
cnf(c_0_122,plain,
( summation(X1) = summation(X2)
| ~ lesseq(summation(X1),summation(X2))
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_112]) ).
cnf(c_0_123,plain,
( lesseq(X1,X2)
| ~ lesseq(X1,max(X2,X3))
| ~ lesseq(X3,X2) ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_124,plain,
( lesseq(X1,X2)
| ~ model_ub(X1,X3,sum(c,X2)) ),
inference(spm,[status(thm)],[c_0_115,c_0_83]) ).
cnf(c_0_125,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| model_ub(X1,X1,esk6_0)
| ~ lesseq(X1,max(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_116,c_0_50]) ).
cnf(c_0_126,negated_conjecture,
( model_ub(esk5_0,esk5_0,esk6_0)
| lesseq(esk4_0,esk5_0)
| lesseq(esk5_0,X1) ),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_127,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| model_ub(esk5_0,esk5_0,esk6_0)
| ~ lesseq(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_84,c_0_44]) ).
cnf(c_0_128,plain,
( model_ub(X1,X1,X2)
| ~ model_ub(X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_119,c_0_86]) ).
cnf(c_0_129,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| lesseq(sum(c,esk4_0),sum(c,max(esk4_0,esk5_0)))
| lesseq(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_130,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| lesseq(esk6_0,sum(c,esk4_0))
| ~ lesseq(esk5_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_38,c_0_64]) ).
cnf(c_0_131,plain,
( lesseq(X1,esk1_3(X2,X3,X4))
| ~ model_ub(X2,X3,X4)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_54,c_0_83]) ).
cnf(c_0_132,plain,
( summation(X1) = summation(X2)
| ~ lesseq(X2,X1)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_122,c_0_112]) ).
cnf(c_0_133,plain,
( lesseq(max(X1,X2),X1)
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_123,c_0_23]) ).
cnf(c_0_134,plain,
( model_ub(X1,X2,X3)
| ~ model_max(X4,X2,X3)
| ~ lesseq(X1,X2)
| ~ lesseq(X4,X2) ),
inference(spm,[status(thm)],[c_0_70,c_0_42]) ).
cnf(c_0_135,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| model_max(max(esk4_0,esk5_0),max(esk4_0,esk5_0),esk6_0) ),
inference(spm,[status(thm)],[c_0_39,c_0_63]) ).
cnf(c_0_136,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| lesseq(X1,max(esk4_0,esk5_0))
| ~ model_ub(X1,X2,esk6_0) ),
inference(spm,[status(thm)],[c_0_124,c_0_50]) ).
cnf(c_0_137,negated_conjecture,
model_ub(esk5_0,esk5_0,esk6_0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_127]),c_0_128]) ).
cnf(c_0_138,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| lesseq(esk4_0,max(esk4_0,esk5_0))
| lesseq(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_40,c_0_129]) ).
cnf(c_0_139,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| model_max(esk4_0,esk5_0,X1)
| ~ lesseq(esk6_0,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_50]) ).
cnf(c_0_140,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| lesseq(esk6_0,sum(c,esk4_0))
| lesseq(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_130,c_0_55]) ).
cnf(c_0_141,plain,
( model_ub(X1,X2,X3)
| ~ model_ub(X2,X4,X3)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_93,c_0_131]) ).
cnf(c_0_142,plain,
( lesseq(X1,X2)
| ~ lesseq(summation(X1),summation(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_143,plain,
( summation(max(X1,X2)) = summation(X1)
| ~ lesseq(X2,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_79]),c_0_133]) ).
cnf(c_0_144,negated_conjecture,
( model_ub(X1,max(esk4_0,esk5_0),esk6_0)
| model_ub(esk4_0,esk5_0,esk6_0)
| ~ lesseq(X1,max(esk4_0,esk5_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_23])]) ).
cnf(c_0_145,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| lesseq(esk5_0,max(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_146,negated_conjecture,
( max(esk4_0,esk5_0) = esk4_0
| model_ub(esk4_0,esk5_0,esk6_0)
| lesseq(esk4_0,esk5_0)
| ~ lesseq(max(esk4_0,esk5_0),esk4_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_138]) ).
cnf(c_0_147,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| model_max(esk4_0,esk5_0,sum(c,esk4_0))
| lesseq(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_148,negated_conjecture,
( model_ub(X1,esk5_0,esk6_0)
| ~ lesseq(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_141,c_0_137]) ).
cnf(c_0_149,plain,
( lesseq(X1,max(X2,X3))
| ~ lesseq(X1,X3)
| ~ lesseq(X2,X3) ),
inference(spm,[status(thm)],[c_0_54,c_0_62]) ).
cnf(c_0_150,plain,
( lesseq(max(X1,X2),X3)
| ~ lesseq(summation(X1),summation(X3))
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_142,c_0_143]) ).
cnf(c_0_151,plain,
( model_max(X1,X2,sum(c,X2))
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_42]) ).
cnf(c_0_152,negated_conjecture,
( model_ub(esk5_0,max(esk4_0,esk5_0),esk6_0)
| model_ub(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_153,negated_conjecture,
( max(esk4_0,esk5_0) = esk4_0
| model_ub(esk4_0,esk5_0,esk6_0)
| lesseq(esk4_0,esk5_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_48]),c_0_147]) ).
cnf(c_0_154,negated_conjecture,
( model_ub(esk5_0,X1,esk6_0)
| ~ lesseq(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_97,c_0_148]) ).
cnf(c_0_155,plain,
( max(X1,X2) = X3
| ~ lesseq(max(X1,X2),X3)
| ~ lesseq(X3,X2)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_149]) ).
cnf(c_0_156,plain,
( lesseq(max(X1,X2),X3)
| ~ lesseq(X2,X1)
| ~ lesseq(X1,X3) ),
inference(spm,[status(thm)],[c_0_150,c_0_112]) ).
cnf(c_0_157,plain,
( lesseq(X1,X2)
| ~ lesseq(X1,max(X3,X2))
| ~ lesseq(X3,X2) ),
inference(spm,[status(thm)],[c_0_113,c_0_151]) ).
cnf(c_0_158,negated_conjecture,
model_ub(esk5_0,esk4_0,esk6_0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_154]),c_0_97]) ).
cnf(c_0_159,plain,
( max(X1,X2) = X3
| ~ lesseq(X3,X2)
| ~ lesseq(X2,X1)
| ~ lesseq(X1,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_54]) ).
cnf(c_0_160,plain,
( lesseq(max(X1,X2),X2)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_157,c_0_23]) ).
cnf(c_0_161,plain,
( lesseq(X1,esk1_3(X2,X3,X4))
| ~ model_ub(X2,X3,X4)
| ~ lesseq(X1,X5)
| ~ lesseq(X5,X2) ),
inference(spm,[status(thm)],[c_0_54,c_0_131]) ).
cnf(c_0_162,negated_conjecture,
model_ub(esk4_0,esk5_0,esk6_0),
inference(spm,[status(thm)],[c_0_97,c_0_158]) ).
cnf(c_0_163,plain,
( max(X1,X2) = max(X3,X2)
| ~ lesseq(X1,max(X3,X2))
| ~ lesseq(X2,X1)
| ~ lesseq(X3,X2) ),
inference(spm,[status(thm)],[c_0_159,c_0_160]) ).
cnf(c_0_164,negated_conjecture,
( lesseq(X1,esk1_3(esk4_0,esk5_0,esk6_0))
| ~ lesseq(X2,esk4_0)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_161,c_0_162]) ).
cnf(c_0_165,plain,
( model_max(X1,X2,max(X3,X4))
| ~ lesseq(sum(c,max(X1,X2)),X4)
| ~ lesseq(X3,X4) ),
inference(spm,[status(thm)],[c_0_22,c_0_149]) ).
cnf(c_0_166,plain,
( lesseq(X1,X2)
| ~ model_max(X3,X4,X2)
| ~ lesseq(X1,sum(c,max(X3,X4))) ),
inference(spm,[status(thm)],[c_0_54,c_0_27]) ).
cnf(c_0_167,plain,
( model_max(X1,X2,X3)
| lesseq(X3,sum(c,max(X1,X2))) ),
inference(spm,[status(thm)],[c_0_22,c_0_55]) ).
cnf(c_0_168,plain,
( lesseq(max(X1,X2),X3)
| lesseq(X3,X2)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_157,c_0_55]) ).
cnf(c_0_169,plain,
( max(X1,X1) = max(X2,X1)
| ~ lesseq(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_62]),c_0_23])]) ).
cnf(c_0_170,negated_conjecture,
( lesseq(X1,esk1_3(esk4_0,esk5_0,esk6_0))
| ~ lesseq(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_164,c_0_23]) ).
cnf(c_0_171,plain,
( model_max(X1,X2,X3)
| ~ lesseq(sum(c,max(X1,X2)),X4)
| ~ lesseq(X3,X4)
| ~ lesseq(X4,X3) ),
inference(spm,[status(thm)],[c_0_165,c_0_64]) ).
cnf(c_0_172,plain,
( model_max(X1,X2,X3)
| lesseq(X3,X4)
| ~ model_max(X1,X2,X4) ),
inference(spm,[status(thm)],[c_0_166,c_0_167]) ).
cnf(c_0_173,plain,
( lesseq(X4,X3)
| ~ model_ub(X1,X2,X3)
| ~ minsol_model_ub(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_174,plain,
( minsol_model_ub(X2,X3,X1)
| ~ lesseq(X1,esk3_3(X2,X3,X1))
| ~ model_ub(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_175,plain,
( lesseq(max(X1,X1),X2)
| lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_168,c_0_23]) ).
cnf(c_0_176,plain,
( max(X1,X1) = X1
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_169]) ).
cnf(c_0_177,negated_conjecture,
( model_ub(X1,X2,esk6_0)
| ~ lesseq(X1,esk1_3(esk4_0,esk5_0,esk6_0))
| ~ lesseq(X2,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_170]),c_0_162])]) ).
cnf(c_0_178,plain,
( model_max(X1,X2,X3)
| ~ model_max(X1,X2,X4)
| ~ lesseq(X4,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_27]),c_0_172]) ).
cnf(c_0_179,negated_conjecture,
( minsol_model_max(esk4_0,esk5_0,esk6_0)
| lesseq(esk6_0,X1)
| ~ model_ub(esk4_0,esk5_0,X1) ),
inference(spm,[status(thm)],[c_0_173,c_0_21]) ).
cnf(c_0_180,plain,
( model_ub(X1,X2,sum(c,X2))
| lesseq(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_151]),c_0_23])]) ).
cnf(c_0_181,plain,
( minsol_model_ub(X1,X2,max(X3,X3))
| lesseq(esk3_3(X1,X2,max(X3,X3)),X3)
| ~ model_ub(X1,X2,max(X3,X3)) ),
inference(spm,[status(thm)],[c_0_174,c_0_175]) ).
cnf(c_0_182,plain,
max(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_176,c_0_23]) ).
cnf(c_0_183,plain,
( model_ub(X1,X2,sum(c,X3))
| ~ ub(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_52,c_0_23]) ).
cnf(c_0_184,negated_conjecture,
( model_ub(esk1_3(esk4_0,esk5_0,esk6_0),X1,esk6_0)
| ~ lesseq(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_177,c_0_23]) ).
cnf(c_0_185,plain,
( model_max(X1,X2,X3)
| ~ lesseq(sum(c,X2),X4)
| ~ lesseq(X4,X3)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_178,c_0_81]) ).
cnf(c_0_186,negated_conjecture,
lesseq(sum(c,esk4_0),esk6_0),
inference(spm,[status(thm)],[c_0_92,c_0_158]) ).
cnf(c_0_187,negated_conjecture,
( minsol_model_max(esk4_0,esk5_0,esk6_0)
| lesseq(esk6_0,sum(c,esk5_0))
| lesseq(esk5_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_179,c_0_180]) ).
cnf(c_0_188,plain,
( minsol_model_ub(X1,X2,X3)
| lesseq(esk3_3(X1,X2,X3),X3)
| ~ model_ub(X1,X2,X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_181,c_0_182]),c_0_182]),c_0_182]) ).
cnf(c_0_189,plain,
( model_ub(X1,X2,esk3_3(X1,X2,X3))
| minsol_model_ub(X1,X2,X3)
| ~ model_ub(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_190,plain,
( model_ub(X1,X2,sum(c,esk1_3(X1,X2,X3)))
| ~ model_ub(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_183,c_0_75]) ).
cnf(c_0_191,negated_conjecture,
( model_ub(esk1_3(esk4_0,esk5_0,esk6_0),esk1_3(esk4_0,esk5_0,esk6_0),esk6_0)
| ~ lesseq(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_117,c_0_184]) ).
cnf(c_0_192,negated_conjecture,
( model_max(X1,esk4_0,X2)
| ~ lesseq(esk6_0,X2)
| ~ lesseq(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_185,c_0_186]) ).
cnf(c_0_193,negated_conjecture,
( lesseq(esk6_0,sum(c,esk5_0))
| lesseq(esk5_0,esk4_0)
| lesseq(esk6_0,X1)
| ~ model_max(esk4_0,esk5_0,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_187]) ).
cnf(c_0_194,plain,
( X1 = X2
| ~ lesseq(X1,X2)
| ~ lesseq(X2,X3)
| ~ lesseq(X3,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_64]),c_0_54]) ).
cnf(c_0_195,negated_conjecture,
( minsol_model_ub(esk4_0,esk5_0,esk6_0)
| lesseq(esk3_3(esk4_0,esk5_0,esk6_0),esk6_0) ),
inference(spm,[status(thm)],[c_0_188,c_0_162]) ).
cnf(c_0_196,negated_conjecture,
( minsol_model_ub(esk4_0,esk5_0,esk6_0)
| model_ub(esk4_0,esk5_0,esk3_3(esk4_0,esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_189,c_0_162]) ).
cnf(c_0_197,negated_conjecture,
( minsol_model_ub(esk5_0,esk4_0,esk6_0)
| model_ub(esk5_0,esk4_0,esk3_3(esk5_0,esk4_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_189,c_0_158]) ).
cnf(c_0_198,negated_conjecture,
( minsol_model_max(esk4_0,esk5_0,esk6_0)
| lesseq(esk6_0,sum(c,esk1_3(esk4_0,esk5_0,X1)))
| ~ model_ub(esk4_0,esk5_0,X1) ),
inference(spm,[status(thm)],[c_0_179,c_0_190]) ).
cnf(c_0_199,negated_conjecture,
model_ub(esk1_3(esk4_0,esk5_0,esk6_0),esk1_3(esk4_0,esk5_0,esk6_0),esk6_0),
inference(spm,[status(thm)],[c_0_191,c_0_23]) ).
cnf(c_0_200,negated_conjecture,
( model_ub(esk4_0,esk4_0,X1)
| ~ lesseq(X2,esk4_0)
| ~ lesseq(esk6_0,X1) ),
inference(spm,[status(thm)],[c_0_84,c_0_192]) ).
cnf(c_0_201,negated_conjecture,
( lesseq(esk6_0,sum(c,esk5_0))
| lesseq(esk5_0,esk4_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_151]),c_0_55]) ).
cnf(c_0_202,negated_conjecture,
lesseq(sum(c,esk5_0),esk6_0),
inference(spm,[status(thm)],[c_0_90,c_0_137]) ).
cnf(c_0_203,negated_conjecture,
( esk3_3(esk4_0,esk5_0,esk6_0) = esk6_0
| minsol_model_ub(esk4_0,esk5_0,esk6_0)
| ~ lesseq(X1,esk3_3(esk4_0,esk5_0,esk6_0))
| ~ lesseq(esk6_0,X1) ),
inference(spm,[status(thm)],[c_0_194,c_0_195]) ).
cnf(c_0_204,negated_conjecture,
( minsol_model_ub(esk4_0,esk5_0,esk6_0)
| lesseq(sum(c,esk5_0),esk3_3(esk4_0,esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_92,c_0_196]) ).
cnf(c_0_205,negated_conjecture,
( minsol_model_ub(esk5_0,esk4_0,esk6_0)
| model_ub(esk4_0,esk5_0,esk3_3(esk5_0,esk4_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_97,c_0_197]) ).
cnf(c_0_206,negated_conjecture,
( minsol_model_max(esk4_0,esk5_0,esk6_0)
| lesseq(esk6_0,sum(c,esk1_3(esk4_0,esk5_0,esk6_0))) ),
inference(spm,[status(thm)],[c_0_198,c_0_162]) ).
cnf(c_0_207,negated_conjecture,
lesseq(sum(c,esk1_3(esk4_0,esk5_0,esk6_0)),esk6_0),
inference(spm,[status(thm)],[c_0_90,c_0_199]) ).
cnf(c_0_208,negated_conjecture,
( model_ub(esk4_0,esk4_0,X1)
| ~ lesseq(esk6_0,X1) ),
inference(spm,[status(thm)],[c_0_200,c_0_23]) ).
cnf(c_0_209,negated_conjecture,
( sum(c,esk5_0) = esk6_0
| lesseq(esk5_0,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_201]),c_0_202])]) ).
cnf(c_0_210,negated_conjecture,
( esk3_3(esk4_0,esk5_0,esk6_0) = esk6_0
| minsol_model_ub(esk4_0,esk5_0,esk6_0)
| ~ lesseq(esk6_0,sum(c,esk5_0)) ),
inference(spm,[status(thm)],[c_0_203,c_0_204]) ).
cnf(c_0_211,negated_conjecture,
( minsol_model_ub(esk5_0,esk4_0,esk6_0)
| minsol_model_max(esk4_0,esk5_0,esk6_0)
| lesseq(esk6_0,esk3_3(esk5_0,esk4_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_179,c_0_205]) ).
cnf(c_0_212,plain,
( model_ub(X1,X2,X3)
| ~ model_max(X2,X4,X3)
| ~ lesseq(X1,max(X2,X4))
| ~ lesseq(X4,X2) ),
inference(spm,[status(thm)],[c_0_65,c_0_79]) ).
cnf(c_0_213,plain,
( lesseq(sum(c,X1),sum(c,max(X1,X2)))
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_29]) ).
cnf(c_0_214,negated_conjecture,
( sum(c,esk1_3(esk4_0,esk5_0,esk6_0)) = esk6_0
| minsol_model_max(esk4_0,esk5_0,esk6_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_206]),c_0_207])]) ).
cnf(c_0_215,negated_conjecture,
( lesseq(esk4_0,X1)
| ~ lesseq(esk6_0,sum(c,X1)) ),
inference(spm,[status(thm)],[c_0_124,c_0_208]) ).
cnf(c_0_216,negated_conjecture,
( lesseq(esk5_0,esk4_0)
| lesseq(X1,esk5_0)
| ~ model_ub(X1,X2,esk6_0) ),
inference(spm,[status(thm)],[c_0_124,c_0_209]) ).
cnf(c_0_217,negated_conjecture,
( esk3_3(esk4_0,esk5_0,esk6_0) = esk6_0
| minsol_model_ub(esk4_0,esk5_0,esk6_0)
| lesseq(esk5_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_210,c_0_201]) ).
cnf(c_0_218,negated_conjecture,
( minsol_model_ub(esk5_0,esk4_0,esk6_0)
| minsol_model_max(esk4_0,esk5_0,esk6_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_211]),c_0_158])]) ).
cnf(c_0_219,plain,
( model_ub(X1,X2,X3)
| ~ model_max(X2,X1,X3)
| ~ lesseq(X1,X2)
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_212,c_0_62]) ).
cnf(c_0_220,plain,
( model_ub(X1,X2,sum(c,max(X2,X3)))
| lesseq(X2,X1)
| ~ lesseq(X3,X2) ),
inference(spm,[status(thm)],[c_0_89,c_0_213]) ).
cnf(c_0_221,negated_conjecture,
( minsol_model_max(X1,esk1_3(esk4_0,esk5_0,esk6_0),esk6_0)
| minsol_model_max(esk4_0,esk5_0,esk6_0)
| ~ lesseq(X1,esk1_3(esk4_0,esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_49,c_0_214]) ).
cnf(c_0_222,negated_conjecture,
( minsol_model_max(esk4_0,esk5_0,esk6_0)
| lesseq(esk4_0,esk1_3(esk4_0,esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_215,c_0_206]) ).
cnf(c_0_223,plain,
( esk1_3(X1,X2,X3) = X2
| ~ model_ub(X1,X2,X3)
| ~ lesseq(esk1_3(X1,X2,X3),X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_86]) ).
cnf(c_0_224,negated_conjecture,
( lesseq(esk1_3(esk4_0,esk5_0,esk6_0),esk5_0)
| lesseq(esk5_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_216,c_0_199]) ).
cnf(c_0_225,negated_conjecture,
( ~ minsol_model_ub(esk4_0,esk5_0,esk6_0)
| ~ minsol_model_max(esk4_0,esk5_0,esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_226,negated_conjecture,
( minsol_model_ub(esk4_0,esk5_0,esk6_0)
| lesseq(esk5_0,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_217]),c_0_162]),c_0_23])]) ).
cnf(c_0_227,negated_conjecture,
( minsol_model_max(esk4_0,esk5_0,esk6_0)
| lesseq(esk6_0,X1)
| ~ model_ub(esk5_0,esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_173,c_0_218]) ).
cnf(c_0_228,plain,
( model_ub(X1,X2,sum(c,max(X2,X1)))
| ~ lesseq(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_219,c_0_29]),c_0_220]) ).
cnf(c_0_229,negated_conjecture,
( minsol_model_max(esk4_0,esk1_3(esk4_0,esk5_0,esk6_0),esk6_0)
| minsol_model_max(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_221,c_0_222]) ).
cnf(c_0_230,negated_conjecture,
( esk1_3(esk4_0,esk5_0,esk6_0) = esk5_0
| lesseq(esk5_0,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_223,c_0_224]),c_0_162])]) ).
cnf(c_0_231,negated_conjecture,
( lesseq(esk5_0,esk4_0)
| ~ minsol_model_max(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_225,c_0_226]) ).
cnf(c_0_232,plain,
( lesseq(X1,esk1_3(X2,X3,X4))
| ~ model_ub(X2,X3,X4)
| ~ lesseq(X1,X3) ),
inference(spm,[status(thm)],[c_0_54,c_0_86]) ).
cnf(c_0_233,negated_conjecture,
( minsol_model_max(esk4_0,esk5_0,esk6_0)
| lesseq(esk6_0,sum(c,max(esk4_0,esk5_0)))
| ~ lesseq(esk5_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_227,c_0_228]) ).
cnf(c_0_234,negated_conjecture,
lesseq(esk5_0,esk4_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_229,c_0_230]),c_0_231]) ).
cnf(c_0_235,plain,
( lesseq(sum(c,X1),X2)
| ~ model_ub(X3,X4,X2)
| ~ lesseq(X1,X4) ),
inference(spm,[status(thm)],[c_0_82,c_0_232]) ).
cnf(c_0_236,negated_conjecture,
( minsol_model_max(esk4_0,esk5_0,esk6_0)
| lesseq(esk6_0,sum(c,max(esk4_0,esk5_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_233,c_0_234])]) ).
cnf(c_0_237,negated_conjecture,
( lesseq(sum(c,X1),esk6_0)
| ~ lesseq(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_235,c_0_158]) ).
cnf(c_0_238,plain,
( X1 = max(X2,X3)
| ~ lesseq(X1,max(X2,X3))
| ~ lesseq(X3,X2)
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_156]) ).
cnf(c_0_239,negated_conjecture,
( minsol_model_max(esk4_0,esk5_0,esk6_0)
| lesseq(esk4_0,max(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_215,c_0_236]) ).
cnf(c_0_240,plain,
( lesseq(X1,max(X2,X1))
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_124,c_0_228]) ).
cnf(c_0_241,negated_conjecture,
( model_max(X1,X2,esk6_0)
| ~ lesseq(max(X1,X2),esk4_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_237]) ).
cnf(c_0_242,negated_conjecture,
( max(esk4_0,esk5_0) = esk4_0
| minsol_model_max(esk4_0,esk5_0,esk6_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_238,c_0_239]),c_0_234]),c_0_23])]) ).
cnf(c_0_243,plain,
( model_ub(X1,X2,X3)
| ~ model_max(X4,X2,X3)
| ~ lesseq(X1,max(X4,X2))
| ~ lesseq(X2,X4) ),
inference(spm,[status(thm)],[c_0_65,c_0_240]) ).
cnf(c_0_244,negated_conjecture,
model_max(esk4_0,esk5_0,esk6_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_241,c_0_242]),c_0_23])]),c_0_39]) ).
cnf(c_0_245,plain,
( model_ub(X1,X2,X3)
| ~ model_max(X1,X2,X3)
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_243,c_0_79]) ).
cnf(c_0_246,negated_conjecture,
( minsol_model_max(esk4_0,esk5_0,esk6_0)
| model_max(esk4_0,esk5_0,esk2_3(esk4_0,esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_28,c_0_244]) ).
cnf(c_0_247,negated_conjecture,
( minsol_model_max(esk4_0,esk5_0,esk6_0)
| model_ub(esk4_0,esk5_0,esk2_3(esk4_0,esk5_0,esk6_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_245,c_0_246]),c_0_234])]) ).
cnf(c_0_248,negated_conjecture,
( minsol_model_max(esk4_0,esk5_0,esk6_0)
| lesseq(esk6_0,esk2_3(esk4_0,esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_179,c_0_247]) ).
cnf(c_0_249,negated_conjecture,
minsol_model_max(esk4_0,esk5_0,esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_248]),c_0_244])]) ).
cnf(c_0_250,negated_conjecture,
( minsol_model_ub(esk4_0,esk5_0,esk6_0)
| lesseq(sum(c,esk4_0),esk3_3(esk4_0,esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_90,c_0_196]) ).
cnf(c_0_251,negated_conjecture,
( lesseq(esk6_0,X1)
| ~ model_max(esk4_0,esk5_0,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_249]) ).
cnf(c_0_252,negated_conjecture,
( esk3_3(esk4_0,esk5_0,esk6_0) = esk6_0
| minsol_model_ub(esk4_0,esk5_0,esk6_0)
| ~ lesseq(esk6_0,sum(c,esk4_0)) ),
inference(spm,[status(thm)],[c_0_203,c_0_250]) ).
cnf(c_0_253,negated_conjecture,
lesseq(esk6_0,sum(c,esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_251,c_0_114]),c_0_234])]) ).
cnf(c_0_254,negated_conjecture,
~ minsol_model_ub(esk4_0,esk5_0,esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_225,c_0_249])]) ).
cnf(c_0_255,negated_conjecture,
esk3_3(esk4_0,esk5_0,esk6_0) = esk6_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_252,c_0_253])]),c_0_254]) ).
cnf(c_0_256,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_255]),c_0_162]),c_0_23])]),c_0_254]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : NUM861+1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 17:31:17 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.55 start to proof: theBenchmark
% 16.74/16.81 % Version : CSE_E---1.5
% 16.74/16.81 % Problem : theBenchmark.p
% 16.74/16.81 % Proof found
% 16.74/16.81 % SZS status Theorem for theBenchmark.p
% 16.74/16.81 % SZS output start Proof
% See solution above
% 16.74/16.82 % Total time : 16.238000 s
% 16.74/16.82 % SZS output end Proof
% 16.74/16.82 % Total time : 16.242000 s
%------------------------------------------------------------------------------