TSTP Solution File: NUM862+1 by E-SAT---3.1
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%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : NUM862+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n006.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 19:08:45 EDT 2023
% Result : Theorem 66.31s 8.92s
% Output : CNFRefutation 66.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 73
% Number of leaves : 14
% Syntax : Number of formulae : 283 ( 31 unt; 0 def)
% Number of atoms : 739 ( 34 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 762 ( 306 ~; 423 |; 20 &)
% ( 9 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% 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 : 532 ( 11 sgn; 88 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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/tmp/tmp.bB8GnfDvbU/E---3.1_28618.p',max_is_ub_1) ).
fof(model_ub_5,axiom,
! [X1,X2,X4] :
( model_ub(X1,X2,X4)
<=> ? [X3] :
( ub(X1,X2,X3)
& lesseq(sum(c,summation(X3)),X4) ) ),
file('/export/starexec/sandbox2/tmp/tmp.bB8GnfDvbU/E---3.1_28618.p',model_ub_5) ).
fof(model_max_5,axiom,
! [X1,X2,X4] :
( model_max(X1,X2,X4)
<=> lesseq(sum(c,summation(max(X1,X2))),X4) ),
file('/export/starexec/sandbox2/tmp/tmp.bB8GnfDvbU/E---3.1_28618.p',model_max_5) ).
fof(max_1,axiom,
! [X1,X2] :
( max(X1,X2) = X1
| ~ lesseq(X2,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.bB8GnfDvbU/E---3.1_28618.p',max_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/tmp/tmp.bB8GnfDvbU/E---3.1_28618.p',minsol_model_ub) ).
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/tmp/tmp.bB8GnfDvbU/E---3.1_28618.p',minsol_model_max) ).
fof(lesseq_total,axiom,
! [X1,X2] :
( lesseq(X1,X2)
| lesseq(X2,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.bB8GnfDvbU/E---3.1_28618.p',lesseq_total) ).
fof(ub,axiom,
! [X1,X2,X3] :
( ub(X1,X2,X3)
<=> ( lesseq(X1,X3)
& lesseq(X2,X3) ) ),
file('/export/starexec/sandbox2/tmp/tmp.bB8GnfDvbU/E---3.1_28618.p',ub) ).
fof(max_2,axiom,
! [X1,X2] :
( max(X1,X2) = X2
| ~ lesseq(X1,X2) ),
file('/export/starexec/sandbox2/tmp/tmp.bB8GnfDvbU/E---3.1_28618.p',max_2) ).
fof(lesseq_ref,axiom,
! [X1] : lesseq(X1,X1),
file('/export/starexec/sandbox2/tmp/tmp.bB8GnfDvbU/E---3.1_28618.p',lesseq_ref) ).
fof(lesseq_trans,axiom,
! [X1,X2,X3] :
( ( lesseq(X1,X2)
& lesseq(X2,X3) )
=> lesseq(X1,X3) ),
file('/export/starexec/sandbox2/tmp/tmp.bB8GnfDvbU/E---3.1_28618.p',lesseq_trans) ).
fof(lesseq_antisymmetric,axiom,
! [X1,X2] :
( ( lesseq(X1,X2)
& lesseq(X2,X1) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/tmp/tmp.bB8GnfDvbU/E---3.1_28618.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/tmp/tmp.bB8GnfDvbU/E---3.1_28618.p',sum_monotone_1) ).
fof(summation_monotone,axiom,
! [X1,X2] :
( lesseq(X1,X2)
<=> lesseq(summation(X1),summation(X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.bB8GnfDvbU/E---3.1_28618.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,X48,X49,X50,X51] :
( ( ub(X44,X45,esk6_3(X44,X45,X46))
| ~ model_ub(X44,X45,X46) )
& ( lesseq(sum(c,summation(esk6_3(X44,X45,X46))),X46)
| ~ model_ub(X44,X45,X46) )
& ( ~ ub(X48,X49,X51)
| ~ lesseq(sum(c,summation(X51)),X50)
| 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)],[model_ub_5])])])])])]) ).
fof(c_0_16,plain,
! [X41,X42,X43] :
( ( ~ model_max(X41,X42,X43)
| lesseq(sum(c,summation(max(X41,X42))),X43) )
& ( ~ lesseq(sum(c,summation(max(X41,X42))),X43)
| model_max(X41,X42,X43) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[model_max_5])]) ).
fof(c_0_17,plain,
! [X1,X2] :
( max(X1,X2) = X1
| ~ lesseq(X2,X1) ),
inference(fof_simplification,[status(thm)],[max_1]) ).
fof(c_0_18,plain,
! [X16,X17,X18,X19,X20,X21,X22] :
( ( model_ub(X16,X17,X18)
| ~ minsol_model_ub(X16,X17,X18) )
& ( ~ model_ub(X16,X17,X19)
| lesseq(X18,X19)
| ~ minsol_model_ub(X16,X17,X18) )
& ( model_ub(X20,X21,esk5_3(X20,X21,X22))
| ~ model_ub(X20,X21,X22)
| minsol_model_ub(X20,X21,X22) )
& ( ~ lesseq(X22,esk5_3(X20,X21,X22))
| ~ model_ub(X20,X21,X22)
| minsol_model_ub(X20,X21,X22) ) ),
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_19,negated_conjecture,
( ( ~ minsol_model_ub(esk1_0,esk2_0,esk3_0)
| ~ minsol_model_max(esk1_0,esk2_0,esk3_0) )
& ( minsol_model_ub(esk1_0,esk2_0,esk3_0)
| minsol_model_max(esk1_0,esk2_0,esk3_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
cnf(c_0_20,plain,
( model_ub(X1,X2,X4)
| ~ ub(X1,X2,X3)
| ~ lesseq(sum(c,summation(X3)),X4) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
( lesseq(sum(c,summation(max(X1,X2))),X3)
| ~ model_max(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_22,plain,
! [X37,X38] :
( max(X37,X38) = X37
| ~ lesseq(X38,X37) ),
inference(variable_rename,[status(thm)],[c_0_17]) ).
fof(c_0_23,plain,
! [X8,X9,X10,X11,X12,X13,X14] :
( ( model_max(X8,X9,X10)
| ~ minsol_model_max(X8,X9,X10) )
& ( ~ model_max(X8,X9,X11)
| lesseq(X10,X11)
| ~ minsol_model_max(X8,X9,X10) )
& ( model_max(X12,X13,esk4_3(X12,X13,X14))
| ~ model_max(X12,X13,X14)
| minsol_model_max(X12,X13,X14) )
& ( ~ lesseq(X14,esk4_3(X12,X13,X14))
| ~ model_max(X12,X13,X14)
| minsol_model_max(X12,X13,X14) ) ),
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_24,plain,
( model_ub(X1,X2,X3)
| ~ minsol_model_ub(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,negated_conjecture,
( minsol_model_ub(esk1_0,esk2_0,esk3_0)
| minsol_model_max(esk1_0,esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( model_ub(X1,X2,X3)
| ~ model_max(X4,X5,X3)
| ~ ub(X1,X2,max(X4,X5)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,plain,
( max(X1,X2) = X1
| ~ lesseq(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
( model_max(X1,X2,X3)
| ~ minsol_model_max(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,negated_conjecture,
( minsol_model_max(esk1_0,esk2_0,esk3_0)
| model_ub(esk1_0,esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,plain,
( model_ub(X1,X2,X3)
| ~ model_max(X4,X5,X3)
| ~ ub(X1,X2,X4)
| ~ lesseq(X5,X4) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| model_max(esk1_0,esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_32,plain,
! [X30,X31] :
( lesseq(X30,X31)
| lesseq(X31,X30) ),
inference(variable_rename,[status(thm)],[lesseq_total]) ).
cnf(c_0_33,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| model_ub(X1,X2,esk3_0)
| ~ ub(X1,X2,esk1_0)
| ~ lesseq(esk2_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,plain,
( lesseq(X1,X2)
| lesseq(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_35,plain,
! [X52,X53,X54] :
( ( lesseq(X52,X54)
| ~ ub(X52,X53,X54) )
& ( lesseq(X53,X54)
| ~ ub(X52,X53,X54) )
& ( ~ lesseq(X52,X54)
| ~ lesseq(X53,X54)
| ub(X52,X53,X54) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ub])])]) ).
cnf(c_0_36,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| model_ub(X1,X2,esk3_0)
| lesseq(esk1_0,esk2_0)
| ~ ub(X1,X2,esk1_0) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,plain,
( ub(X1,X3,X2)
| ~ lesseq(X1,X2)
| ~ lesseq(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_38,plain,
! [X1,X2] :
( max(X1,X2) = X2
| ~ lesseq(X1,X2) ),
inference(fof_simplification,[status(thm)],[max_2]) ).
cnf(c_0_39,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| model_ub(X1,X2,esk3_0)
| lesseq(esk1_0,esk2_0)
| ~ lesseq(X2,esk1_0)
| ~ lesseq(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
fof(c_0_40,plain,
! [X24] : lesseq(X24,X24),
inference(variable_rename,[status(thm)],[lesseq_ref]) ).
fof(c_0_41,plain,
! [X39,X40] :
( max(X39,X40) = X40
| ~ lesseq(X39,X40) ),
inference(variable_rename,[status(thm)],[c_0_38]) ).
cnf(c_0_42,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| model_ub(X1,X2,esk3_0)
| lesseq(esk1_0,esk2_0)
| lesseq(esk1_0,X2)
| ~ lesseq(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_39,c_0_34]) ).
cnf(c_0_43,plain,
lesseq(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_44,plain,
( max(X1,X2) = X2
| ~ lesseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_45,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| model_ub(esk1_0,X1,esk3_0)
| lesseq(esk1_0,esk2_0)
| lesseq(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
fof(c_0_46,plain,
! [X25,X26,X27] :
( ~ lesseq(X25,X26)
| ~ lesseq(X26,X27)
| lesseq(X25,X27) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[lesseq_trans])]) ).
cnf(c_0_47,plain,
( lesseq(X4,X3)
| ~ model_max(X1,X2,X3)
| ~ minsol_model_max(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_48,plain,
( model_max(X1,X2,X3)
| ~ lesseq(sum(c,summation(max(X1,X2))),X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_49,plain,
( lesseq(sum(c,summation(X1)),X2)
| ~ model_max(X3,X1,X2)
| ~ lesseq(X3,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_44]) ).
cnf(c_0_50,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(esk1_0,esk2_0) ),
inference(ef,[status(thm)],[c_0_45]) ).
cnf(c_0_51,plain,
( lesseq(X1,X3)
| ~ lesseq(X1,X2)
| ~ lesseq(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_52,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(esk3_0,X1)
| ~ model_max(esk1_0,esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_29]) ).
cnf(c_0_53,plain,
model_max(X1,X2,sum(c,summation(max(X1,X2)))),
inference(spm,[status(thm)],[c_0_48,c_0_43]) ).
cnf(c_0_54,plain,
( model_max(X1,X2,X3)
| ~ lesseq(sum(c,summation(X1)),X3)
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_27]) ).
cnf(c_0_55,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(sum(c,summation(esk2_0)),esk3_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_31]),c_0_50]) ).
cnf(c_0_56,plain,
( lesseq(X1,X2)
| ~ model_max(X3,X4,X2)
| ~ lesseq(X1,sum(c,summation(max(X3,X4)))) ),
inference(spm,[status(thm)],[c_0_51,c_0_21]) ).
cnf(c_0_57,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(esk3_0,sum(c,summation(max(esk1_0,esk2_0)))) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_58,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| model_max(esk2_0,X1,esk3_0)
| ~ lesseq(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_59,plain,
( lesseq(X1,X2)
| ~ model_max(X3,X4,X2)
| ~ lesseq(X1,sum(c,summation(X4)))
| ~ lesseq(X3,X4) ),
inference(spm,[status(thm)],[c_0_56,c_0_44]) ).
cnf(c_0_60,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(esk3_0,sum(c,summation(esk2_0))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_44]),c_0_50]) ).
cnf(c_0_61,plain,
( model_max(X1,X2,esk4_3(X1,X2,X3))
| minsol_model_max(X1,X2,X3)
| ~ model_max(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_62,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| model_max(esk2_0,esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_58,c_0_43]) ).
cnf(c_0_63,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(esk3_0,X1)
| ~ model_max(X2,esk2_0,X1)
| ~ lesseq(X2,esk2_0) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_64,negated_conjecture,
( minsol_model_max(esk2_0,esk2_0,esk3_0)
| model_ub(esk1_0,esk2_0,esk3_0)
| model_max(esk2_0,esk2_0,esk4_3(esk2_0,esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
fof(c_0_65,plain,
! [X28,X29] :
( ~ lesseq(X28,X29)
| ~ lesseq(X29,X28)
| X28 = X29 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[lesseq_antisymmetric])]) ).
cnf(c_0_66,plain,
( minsol_model_max(X2,X3,X1)
| ~ lesseq(X1,esk4_3(X2,X3,X1))
| ~ model_max(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_67,negated_conjecture,
( minsol_model_max(esk2_0,esk2_0,esk3_0)
| model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(esk3_0,esk4_3(esk2_0,esk2_0,esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_43])]) ).
fof(c_0_68,plain,
! [X32,X33,X34] :
( ( ~ lesseq(X32,X33)
| lesseq(sum(X34,X32),sum(X34,X33)) )
& ( ~ lesseq(sum(X34,X32),sum(X34,X33))
| lesseq(X32,X33) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sum_monotone_1])]) ).
cnf(c_0_69,plain,
( X1 = X2
| ~ lesseq(X1,X2)
| ~ lesseq(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_70,negated_conjecture,
( minsol_model_max(esk2_0,esk2_0,esk3_0)
| model_ub(esk1_0,esk2_0,esk3_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_62]) ).
cnf(c_0_71,plain,
( lesseq(X2,X3)
| ~ lesseq(sum(X1,X2),sum(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_72,negated_conjecture,
( sum(c,summation(esk2_0)) = esk3_0
| model_ub(esk1_0,esk2_0,esk3_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_60]),c_0_55]) ).
cnf(c_0_73,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(esk3_0,X1)
| ~ model_max(esk2_0,esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_70]) ).
fof(c_0_74,plain,
! [X35,X36] :
( ( ~ lesseq(X35,X36)
| lesseq(summation(X35),summation(X36)) )
& ( ~ lesseq(summation(X35),summation(X36))
| lesseq(X35,X36) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[summation_monotone])]) ).
cnf(c_0_75,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(summation(esk2_0),X1)
| ~ lesseq(esk3_0,sum(c,X1)) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_76,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(esk3_0,sum(c,summation(max(esk2_0,esk2_0)))) ),
inference(spm,[status(thm)],[c_0_73,c_0_53]) ).
cnf(c_0_77,plain,
( lesseq(X1,X2)
| ~ lesseq(summation(X1),summation(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_78,plain,
( lesseq(summation(max(X1,X2)),X3)
| ~ model_max(X1,X2,sum(c,X3)) ),
inference(spm,[status(thm)],[c_0_71,c_0_21]) ).
cnf(c_0_79,plain,
( model_max(X1,X2,X3)
| ~ lesseq(sum(c,summation(X2)),X3)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_44]) ).
cnf(c_0_80,plain,
( lesseq(sum(X3,X1),sum(X3,X2))
| ~ lesseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_81,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(summation(esk2_0),summation(max(esk2_0,esk2_0))) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_82,plain,
( lesseq(max(X1,X2),X3)
| ~ model_max(X1,X2,sum(c,summation(X3))) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_83,plain,
( model_max(X1,X2,sum(c,X3))
| ~ lesseq(summation(X2),X3)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_84,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(esk2_0,max(esk2_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_77,c_0_81]) ).
cnf(c_0_85,plain,
( model_max(X1,X2,sum(c,summation(X2)))
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_79,c_0_43]) ).
cnf(c_0_86,plain,
( lesseq(max(X1,X2),X3)
| ~ lesseq(summation(X2),summation(X3))
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_87,negated_conjecture,
( max(esk2_0,esk2_0) = esk2_0
| model_ub(esk1_0,esk2_0,esk3_0)
| ~ lesseq(max(esk2_0,esk2_0),esk2_0) ),
inference(spm,[status(thm)],[c_0_69,c_0_84]) ).
cnf(c_0_88,plain,
( lesseq(max(X1,X2),X2)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_82,c_0_85]) ).
cnf(c_0_89,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| model_ub(X1,X2,esk3_0)
| ~ ub(X1,X2,esk2_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_55]) ).
cnf(c_0_90,plain,
( lesseq(X1,X2)
| ~ lesseq(summation(X3),summation(X2))
| ~ lesseq(X1,max(X4,X3))
| ~ lesseq(X4,X3) ),
inference(spm,[status(thm)],[c_0_51,c_0_86]) ).
cnf(c_0_91,plain,
( lesseq(summation(X1),summation(X2))
| ~ lesseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_92,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(summation(esk2_0),summation(max(esk1_0,esk2_0))) ),
inference(spm,[status(thm)],[c_0_75,c_0_57]) ).
cnf(c_0_93,negated_conjecture,
( max(esk2_0,esk2_0) = esk2_0
| model_ub(esk1_0,esk2_0,esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_43])]) ).
cnf(c_0_94,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| model_ub(X1,X2,esk3_0)
| ~ lesseq(X2,esk2_0)
| ~ lesseq(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_89,c_0_37]) ).
cnf(c_0_95,plain,
( lesseq(X1,X2)
| ~ lesseq(X1,max(X3,X4))
| ~ lesseq(X3,X4)
| ~ lesseq(X4,X2) ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_96,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(esk2_0,max(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_77,c_0_92]) ).
cnf(c_0_97,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| model_max(esk2_0,esk2_0,sum(c,summation(esk2_0))) ),
inference(spm,[status(thm)],[c_0_53,c_0_93]) ).
cnf(c_0_98,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| model_ub(X1,esk2_0,esk3_0)
| ~ lesseq(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_94,c_0_43]) ).
cnf(c_0_99,plain,
( lesseq(max(X1,X2),X3)
| ~ lesseq(X1,X2)
| ~ lesseq(X2,X3) ),
inference(spm,[status(thm)],[c_0_95,c_0_43]) ).
cnf(c_0_100,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(X1,max(esk1_0,esk2_0))
| ~ lesseq(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_51,c_0_96]) ).
cnf(c_0_101,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(max(esk2_0,esk2_0),esk2_0) ),
inference(spm,[status(thm)],[c_0_82,c_0_97]) ).
cnf(c_0_102,plain,
( lesseq(X1,X2)
| ~ ub(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_103,plain,
( ub(X1,X2,esk6_3(X1,X2,X3))
| ~ model_ub(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_104,negated_conjecture,
( model_ub(max(X1,esk2_0),esk2_0,esk3_0)
| model_ub(esk1_0,esk2_0,esk3_0)
| ~ lesseq(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_98,c_0_88]) ).
cnf(c_0_105,plain,
( X1 = max(X2,X3)
| ~ lesseq(X1,max(X2,X3))
| ~ lesseq(X2,X3)
| ~ lesseq(X3,X1) ),
inference(spm,[status(thm)],[c_0_69,c_0_99]) ).
cnf(c_0_106,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(max(esk2_0,esk2_0),max(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_107,plain,
( lesseq(sum(c,summation(esk6_3(X1,X2,X3))),X3)
| ~ model_ub(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_108,plain,
( lesseq(X1,summation(X2))
| ~ lesseq(X1,summation(X3))
| ~ lesseq(X3,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_91]) ).
cnf(c_0_109,plain,
( lesseq(X1,X2)
| ~ ub(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_110,plain,
( lesseq(X1,esk6_3(X1,X2,X3))
| ~ model_ub(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_111,negated_conjecture,
( model_ub(max(esk2_0,esk2_0),esk2_0,esk3_0)
| model_ub(esk1_0,esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_104,c_0_43]) ).
cnf(c_0_112,negated_conjecture,
( max(esk2_0,esk2_0) = max(esk1_0,esk2_0)
| model_ub(esk1_0,esk2_0,esk3_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_50]),c_0_84]) ).
cnf(c_0_113,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| model_ub(X1,esk2_0,esk3_0)
| lesseq(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_98,c_0_34]) ).
cnf(c_0_114,plain,
( lesseq(X1,X2)
| ~ model_ub(X3,X4,X2)
| ~ lesseq(X1,sum(c,summation(esk6_3(X3,X4,X2)))) ),
inference(spm,[status(thm)],[c_0_51,c_0_107]) ).
cnf(c_0_115,plain,
( lesseq(summation(X1),summation(X2))
| ~ lesseq(X3,X2)
| ~ lesseq(X1,X3) ),
inference(spm,[status(thm)],[c_0_108,c_0_91]) ).
cnf(c_0_116,plain,
( lesseq(X1,esk6_3(X2,X1,X3))
| ~ model_ub(X2,X1,X3) ),
inference(spm,[status(thm)],[c_0_109,c_0_103]) ).
cnf(c_0_117,plain,
( lesseq(X1,esk6_3(X2,X3,X4))
| ~ model_ub(X2,X3,X4)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_110]) ).
cnf(c_0_118,negated_conjecture,
( model_ub(max(esk1_0,esk2_0),esk2_0,esk3_0)
| model_ub(esk1_0,esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_119,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(esk2_0,esk1_0) ),
inference(ef,[status(thm)],[c_0_113]) ).
cnf(c_0_120,plain,
( lesseq(sum(c,X1),X2)
| ~ model_ub(X3,X4,X2)
| ~ lesseq(X1,summation(esk6_3(X3,X4,X2))) ),
inference(spm,[status(thm)],[c_0_114,c_0_80]) ).
cnf(c_0_121,plain,
( lesseq(summation(X1),summation(esk6_3(X2,X3,X4)))
| ~ model_ub(X2,X3,X4)
| ~ lesseq(X1,X3) ),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_122,plain,
( lesseq(X1,esk6_3(X2,X3,X4))
| ~ model_ub(X2,X3,X4)
| ~ lesseq(X1,X5)
| ~ lesseq(X5,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_117]) ).
cnf(c_0_123,negated_conjecture,
model_ub(esk1_0,esk2_0,esk3_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_27]),c_0_119]) ).
cnf(c_0_124,plain,
( lesseq(sum(c,summation(X1)),X2)
| ~ model_ub(X3,X4,X2)
| ~ lesseq(X1,X4) ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_125,plain,
( lesseq(X1,X2)
| lesseq(X3,X1)
| ~ lesseq(X3,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_34]) ).
cnf(c_0_126,negated_conjecture,
( lesseq(X1,esk6_3(esk1_0,esk2_0,esk3_0))
| ~ lesseq(X2,esk1_0)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_127,negated_conjecture,
( lesseq(sum(c,summation(X1)),esk3_0)
| ~ lesseq(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_124,c_0_123]) ).
cnf(c_0_128,plain,
( lesseq(max(X1,X2),X3)
| lesseq(X3,X2)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_125,c_0_88]) ).
cnf(c_0_129,negated_conjecture,
( lesseq(X1,esk6_3(esk1_0,esk2_0,esk3_0))
| ~ lesseq(X1,max(X2,esk1_0))
| ~ lesseq(X2,esk1_0) ),
inference(spm,[status(thm)],[c_0_126,c_0_88]) ).
cnf(c_0_130,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_26,c_0_37]) ).
cnf(c_0_131,negated_conjecture,
( model_max(X1,X2,esk3_0)
| ~ lesseq(max(X1,X2),esk2_0) ),
inference(spm,[status(thm)],[c_0_48,c_0_127]) ).
cnf(c_0_132,plain,
( lesseq(max(X1,X1),X2)
| lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_128,c_0_43]) ).
cnf(c_0_133,negated_conjecture,
( lesseq(max(X1,esk1_0),esk6_3(esk1_0,esk2_0,esk3_0))
| ~ lesseq(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_129,c_0_43]) ).
cnf(c_0_134,plain,
( model_ub(X1,X2,X3)
| ~ model_max(X4,X5,X3)
| ~ lesseq(X2,X5)
| ~ lesseq(X1,X5)
| ~ lesseq(X4,X5) ),
inference(spm,[status(thm)],[c_0_130,c_0_44]) ).
cnf(c_0_135,negated_conjecture,
( model_max(X1,X1,esk3_0)
| lesseq(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_136,negated_conjecture,
( lesseq(esk1_0,esk6_3(esk1_0,esk2_0,esk3_0))
| ~ lesseq(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_133,c_0_44]) ).
cnf(c_0_137,plain,
( model_ub(X1,X2,X3)
| ~ model_ub(X4,X5,X3)
| ~ ub(X1,X2,esk6_3(X4,X5,X3)) ),
inference(spm,[status(thm)],[c_0_20,c_0_107]) ).
cnf(c_0_138,negated_conjecture,
( model_ub(X1,X2,esk3_0)
| lesseq(esk2_0,X3)
| ~ lesseq(X2,X3)
| ~ lesseq(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_43])]) ).
cnf(c_0_139,negated_conjecture,
lesseq(esk1_0,esk6_3(esk1_0,esk2_0,esk3_0)),
inference(spm,[status(thm)],[c_0_136,c_0_43]) ).
cnf(c_0_140,plain,
( model_ub(X1,X2,X3)
| ~ model_ub(X4,X5,X3)
| ~ lesseq(X2,esk6_3(X4,X5,X3))
| ~ lesseq(X1,esk6_3(X4,X5,X3)) ),
inference(spm,[status(thm)],[c_0_137,c_0_37]) ).
cnf(c_0_141,negated_conjecture,
( model_ub(X1,esk1_0,esk3_0)
| lesseq(esk2_0,esk6_3(esk1_0,esk2_0,esk3_0))
| ~ lesseq(X1,esk6_3(esk1_0,esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_142,negated_conjecture,
( model_ub(X1,esk1_0,esk3_0)
| ~ lesseq(X1,esk6_3(esk1_0,esk2_0,esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_139]),c_0_123])]) ).
cnf(c_0_143,negated_conjecture,
( model_ub(esk2_0,esk1_0,esk3_0)
| lesseq(esk2_0,esk6_3(esk1_0,esk2_0,esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_116]),c_0_123])]) ).
cnf(c_0_144,plain,
( summation(X1) = summation(X2)
| ~ lesseq(summation(X1),summation(X2))
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_69,c_0_91]) ).
cnf(c_0_145,plain,
( model_ub(X1,X2,X3)
| ~ model_ub(X2,X4,X3)
| ~ lesseq(X1,esk6_3(X2,X4,X3)) ),
inference(spm,[status(thm)],[c_0_140,c_0_110]) ).
cnf(c_0_146,plain,
( model_ub(X1,X2,esk5_3(X1,X2,X3))
| minsol_model_ub(X1,X2,X3)
| ~ model_ub(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_147,negated_conjecture,
model_ub(esk2_0,esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_142,c_0_143]) ).
cnf(c_0_148,plain,
( summation(X1) = summation(X2)
| ~ lesseq(X2,X1)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_144,c_0_91]) ).
cnf(c_0_149,plain,
( lesseq(X4,X3)
| ~ model_ub(X1,X2,X3)
| ~ minsol_model_ub(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_150,plain,
( model_ub(X1,X2,X3)
| ~ model_ub(X2,X1,X3) ),
inference(spm,[status(thm)],[c_0_145,c_0_116]) ).
cnf(c_0_151,negated_conjecture,
( minsol_model_ub(esk2_0,esk1_0,esk3_0)
| model_ub(esk2_0,esk1_0,esk5_3(esk2_0,esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_152,negated_conjecture,
( lesseq(summation(X1),summation(esk6_3(esk1_0,esk2_0,esk3_0)))
| ~ lesseq(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_115,c_0_139]) ).
cnf(c_0_153,negated_conjecture,
( summation(esk6_3(esk1_0,esk2_0,esk3_0)) = summation(esk1_0)
| ~ lesseq(esk6_3(esk1_0,esk2_0,esk3_0),esk1_0) ),
inference(spm,[status(thm)],[c_0_148,c_0_139]) ).
cnf(c_0_154,plain,
( lesseq(summation(X1),summation(X2))
| lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_34]) ).
cnf(c_0_155,plain,
( model_max(X1,X2,sum(c,summation(X1)))
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_43]) ).
cnf(c_0_156,plain,
( lesseq(summation(X1),X2)
| ~ model_max(X3,X1,sum(c,X2))
| ~ lesseq(X3,X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_44]) ).
cnf(c_0_157,negated_conjecture,
( minsol_model_max(esk1_0,esk2_0,esk3_0)
| lesseq(esk3_0,X1)
| ~ model_ub(esk1_0,esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_149,c_0_25]) ).
cnf(c_0_158,negated_conjecture,
( minsol_model_ub(esk2_0,esk1_0,esk3_0)
| model_ub(esk1_0,esk2_0,esk5_3(esk2_0,esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_150,c_0_151]) ).
cnf(c_0_159,negated_conjecture,
model_ub(esk1_0,esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_142,c_0_139]) ).
cnf(c_0_160,negated_conjecture,
lesseq(summation(esk1_0),summation(esk6_3(esk1_0,esk2_0,esk3_0))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_154]) ).
cnf(c_0_161,plain,
( X1 = X2
| ~ lesseq(X1,X2)
| ~ lesseq(X2,X3)
| ~ lesseq(X3,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_27]),c_0_51]) ).
cnf(c_0_162,plain,
( lesseq(max(X1,X2),X1)
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_82,c_0_155]) ).
cnf(c_0_163,plain,
( lesseq(summation(X1),summation(max(X2,X1)))
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_156,c_0_53]) ).
cnf(c_0_164,plain,
( minsol_model_ub(X2,X3,X1)
| ~ lesseq(X1,esk5_3(X2,X3,X1))
| ~ model_ub(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_165,negated_conjecture,
( minsol_model_ub(esk2_0,esk1_0,esk3_0)
| minsol_model_max(esk1_0,esk2_0,esk3_0)
| lesseq(esk3_0,esk5_3(esk2_0,esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_157,c_0_158]) ).
cnf(c_0_166,plain,
( model_ub(X1,X2,X3)
| ~ model_ub(X2,X4,X3)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_145,c_0_117]) ).
cnf(c_0_167,negated_conjecture,
( minsol_model_ub(esk1_0,esk1_0,esk3_0)
| model_ub(esk1_0,esk1_0,esk5_3(esk1_0,esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_146,c_0_159]) ).
cnf(c_0_168,negated_conjecture,
lesseq(sum(c,summation(esk1_0)),esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_160]),c_0_123])]) ).
cnf(c_0_169,plain,
( summation(X1) = summation(X2)
| ~ lesseq(summation(X2),X3)
| ~ lesseq(X3,summation(X1))
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_161,c_0_91]) ).
cnf(c_0_170,plain,
( lesseq(X1,X2)
| lesseq(X2,X3)
| lesseq(X3,X1) ),
inference(spm,[status(thm)],[c_0_125,c_0_34]) ).
cnf(c_0_171,plain,
( lesseq(summation(X1),X2)
| ~ model_max(X1,X3,sum(c,X2))
| ~ lesseq(X3,X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_27]) ).
cnf(c_0_172,plain,
( summation(max(X1,X2)) = summation(X1)
| ~ lesseq(X1,max(X1,X2))
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_148,c_0_162]) ).
cnf(c_0_173,plain,
( lesseq(X1,max(X2,X1))
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_163]) ).
cnf(c_0_174,negated_conjecture,
( minsol_model_ub(esk2_0,esk1_0,esk3_0)
| minsol_model_max(esk1_0,esk2_0,esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_165]),c_0_147])]) ).
cnf(c_0_175,negated_conjecture,
( minsol_model_ub(esk1_0,esk1_0,esk3_0)
| model_ub(X1,esk1_0,esk5_3(esk1_0,esk1_0,esk3_0))
| ~ lesseq(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_166,c_0_167]) ).
cnf(c_0_176,negated_conjecture,
( model_max(esk1_0,X1,esk3_0)
| ~ lesseq(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_54,c_0_168]) ).
cnf(c_0_177,plain,
( summation(X1) = summation(X2)
| ~ lesseq(summation(X3),summation(X1))
| ~ lesseq(X1,X2)
| ~ lesseq(X2,X3) ),
inference(spm,[status(thm)],[c_0_169,c_0_91]) ).
cnf(c_0_178,plain,
( lesseq(X1,X2)
| ~ lesseq(X1,X3)
| ~ lesseq(X3,X4)
| ~ lesseq(X4,X2)
| ~ lesseq(X4,X3) ),
inference(spm,[status(thm)],[c_0_95,c_0_27]) ).
cnf(c_0_179,plain,
( lesseq(X1,X2)
| lesseq(X3,X1)
| lesseq(X4,X3)
| ~ lesseq(X4,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_170]) ).
cnf(c_0_180,plain,
( lesseq(summation(X1),summation(max(X1,X2)))
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_171,c_0_53]) ).
cnf(c_0_181,plain,
summation(max(X1,X1)) = summation(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_173]),c_0_43])]) ).
cnf(c_0_182,negated_conjecture,
( minsol_model_max(esk1_0,esk2_0,esk3_0)
| lesseq(esk3_0,X1)
| ~ model_ub(esk2_0,esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_149,c_0_174]) ).
cnf(c_0_183,negated_conjecture,
( minsol_model_ub(esk1_0,esk1_0,esk3_0)
| model_ub(X1,esk1_0,esk5_3(esk1_0,esk1_0,esk3_0))
| lesseq(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_175,c_0_34]) ).
cnf(c_0_184,plain,
( model_ub(X1,max(X2,X3),X4)
| ~ model_max(X2,X3,X4)
| ~ lesseq(X1,max(X2,X3)) ),
inference(spm,[status(thm)],[c_0_130,c_0_43]) ).
cnf(c_0_185,negated_conjecture,
( minsol_model_max(esk1_0,X1,esk3_0)
| model_max(esk1_0,X1,esk4_3(esk1_0,X1,esk3_0))
| ~ lesseq(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_61,c_0_176]) ).
cnf(c_0_186,negated_conjecture,
( lesseq(X1,esk3_0)
| ~ lesseq(X1,sum(c,summation(esk1_0))) ),
inference(spm,[status(thm)],[c_0_51,c_0_168]) ).
cnf(c_0_187,plain,
( summation(X1) = summation(X2)
| ~ lesseq(X1,X2)
| ~ lesseq(X2,X3)
| ~ lesseq(X3,X1) ),
inference(spm,[status(thm)],[c_0_177,c_0_91]) ).
cnf(c_0_188,plain,
( lesseq(X1,X2)
| lesseq(X2,X3)
| ~ lesseq(X1,X4)
| ~ lesseq(X4,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_34]),c_0_179]) ).
cnf(c_0_189,plain,
( lesseq(summation(esk6_3(X1,X2,sum(c,X3))),X3)
| ~ model_ub(X1,X2,sum(c,X3)) ),
inference(spm,[status(thm)],[c_0_71,c_0_107]) ).
cnf(c_0_190,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_130,c_0_173]) ).
cnf(c_0_191,plain,
( lesseq(X1,max(X1,X2))
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_180]) ).
cnf(c_0_192,plain,
( model_max(X1,X1,X2)
| ~ lesseq(sum(c,summation(X1)),X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_181]) ).
cnf(c_0_193,negated_conjecture,
( model_max(X1,esk2_0,esk3_0)
| ~ lesseq(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_131,c_0_88]) ).
cnf(c_0_194,negated_conjecture,
( minsol_model_ub(esk1_0,esk1_0,esk3_0)
| minsol_model_max(esk1_0,esk2_0,esk3_0)
| lesseq(esk3_0,esk5_3(esk1_0,esk1_0,esk3_0))
| lesseq(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_182,c_0_183]) ).
cnf(c_0_195,plain,
( model_ub(X1,X2,X3)
| ~ model_max(X4,X2,X3)
| ~ lesseq(X1,X2)
| ~ lesseq(X4,X2) ),
inference(spm,[status(thm)],[c_0_184,c_0_44]) ).
cnf(c_0_196,negated_conjecture,
( minsol_model_max(esk1_0,esk1_0,esk3_0)
| model_max(esk1_0,esk1_0,esk4_3(esk1_0,esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_185,c_0_43]) ).
cnf(c_0_197,negated_conjecture,
( lesseq(sum(c,X1),esk3_0)
| ~ lesseq(X1,summation(esk1_0)) ),
inference(spm,[status(thm)],[c_0_186,c_0_80]) ).
cnf(c_0_198,plain,
( summation(max(X1,X2)) = summation(X2)
| ~ lesseq(X3,max(X1,X2))
| ~ lesseq(X2,X3)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_187,c_0_88]) ).
cnf(c_0_199,plain,
( lesseq(X1,X2)
| lesseq(X3,X1)
| ~ model_ub(X3,X4,X5)
| ~ lesseq(esk6_3(X3,X4,X5),X2) ),
inference(spm,[status(thm)],[c_0_188,c_0_110]) ).
cnf(c_0_200,plain,
( lesseq(esk6_3(X1,X2,sum(c,summation(X3))),X3)
| ~ model_ub(X1,X2,sum(c,summation(X3))) ),
inference(spm,[status(thm)],[c_0_77,c_0_189]) ).
cnf(c_0_201,plain,
( model_ub(X1,X2,X3)
| ~ model_max(X1,X2,X3)
| ~ lesseq(X1,X2)
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_190,c_0_191]) ).
cnf(c_0_202,plain,
( model_max(X1,X1,sum(c,X2))
| ~ lesseq(summation(X1),X2) ),
inference(spm,[status(thm)],[c_0_192,c_0_80]) ).
cnf(c_0_203,negated_conjecture,
( lesseq(sum(c,summation(esk2_0)),esk3_0)
| ~ lesseq(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_49,c_0_193]) ).
cnf(c_0_204,negated_conjecture,
( minsol_model_ub(esk1_0,esk1_0,esk3_0)
| minsol_model_max(esk1_0,esk2_0,esk3_0)
| lesseq(esk1_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_194]),c_0_159])]) ).
cnf(c_0_205,negated_conjecture,
( minsol_model_max(esk1_0,esk1_0,esk3_0)
| model_ub(X1,esk1_0,esk4_3(esk1_0,esk1_0,esk3_0))
| ~ lesseq(X1,esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_196]),c_0_43])]) ).
cnf(c_0_206,negated_conjecture,
( model_max(X1,X2,esk3_0)
| ~ lesseq(summation(max(X1,X2)),summation(esk1_0)) ),
inference(spm,[status(thm)],[c_0_48,c_0_197]) ).
cnf(c_0_207,plain,
( summation(max(X1,X2)) = summation(X2)
| ~ lesseq(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_198,c_0_173]),c_0_43])]) ).
cnf(c_0_208,plain,
( lesseq(X1,X2)
| lesseq(X2,X3)
| ~ model_ub(X1,X4,sum(c,summation(X3))) ),
inference(spm,[status(thm)],[c_0_199,c_0_200]) ).
cnf(c_0_209,plain,
( model_ub(X1,X1,sum(c,X2))
| ~ lesseq(summation(X1),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_202]),c_0_43])]) ).
cnf(c_0_210,negated_conjecture,
lesseq(sum(c,summation(esk2_0)),esk3_0),
inference(spm,[status(thm)],[c_0_203,c_0_43]) ).
cnf(c_0_211,negated_conjecture,
( minsol_model_max(esk1_0,esk2_0,esk3_0)
| lesseq(esk1_0,esk2_0)
| lesseq(esk3_0,X1)
| ~ model_ub(esk1_0,esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_149,c_0_204]) ).
cnf(c_0_212,negated_conjecture,
( minsol_model_max(esk1_0,esk1_0,esk3_0)
| model_ub(esk1_0,esk1_0,esk4_3(esk1_0,esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_205,c_0_43]) ).
cnf(c_0_213,negated_conjecture,
( model_max(X1,X1,esk3_0)
| ~ lesseq(summation(X1),summation(esk1_0)) ),
inference(spm,[status(thm)],[c_0_206,c_0_181]) ).
cnf(c_0_214,plain,
( lesseq(X1,X2)
| ~ lesseq(X1,max(X2,X3))
| ~ lesseq(X3,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_162]) ).
cnf(c_0_215,plain,
( lesseq(X1,max(X2,X3))
| ~ lesseq(summation(X1),summation(X3))
| ~ lesseq(X2,X3) ),
inference(spm,[status(thm)],[c_0_77,c_0_207]) ).
cnf(c_0_216,plain,
( lesseq(X1,X2)
| lesseq(X3,X1)
| ~ lesseq(summation(X3),summation(X2)) ),
inference(spm,[status(thm)],[c_0_208,c_0_209]) ).
cnf(c_0_217,negated_conjecture,
( lesseq(summation(X1),summation(esk3_0))
| ~ lesseq(X1,sum(c,summation(esk2_0))) ),
inference(spm,[status(thm)],[c_0_115,c_0_210]) ).
cnf(c_0_218,plain,
model_max(X1,X1,sum(c,summation(X1))),
inference(spm,[status(thm)],[c_0_53,c_0_181]) ).
cnf(c_0_219,negated_conjecture,
( minsol_model_max(esk1_0,esk1_0,esk3_0)
| minsol_model_max(esk1_0,esk2_0,esk3_0)
| lesseq(esk3_0,esk4_3(esk1_0,esk1_0,esk3_0))
| lesseq(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_211,c_0_212]) ).
cnf(c_0_220,negated_conjecture,
model_max(esk1_0,esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_213,c_0_43]) ).
cnf(c_0_221,plain,
( lesseq(X1,X2)
| ~ lesseq(summation(X1),summation(X3))
| ~ lesseq(X3,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_215]),c_0_216]) ).
cnf(c_0_222,negated_conjecture,
lesseq(summation(sum(c,summation(esk2_0))),summation(esk3_0)),
inference(spm,[status(thm)],[c_0_217,c_0_43]) ).
cnf(c_0_223,plain,
lesseq(max(X1,X1),X1),
inference(spm,[status(thm)],[c_0_82,c_0_218]) ).
cnf(c_0_224,negated_conjecture,
( minsol_model_max(esk1_0,esk2_0,esk3_0)
| minsol_model_max(esk1_0,esk1_0,esk3_0)
| lesseq(esk1_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_219]),c_0_220])]) ).
cnf(c_0_225,negated_conjecture,
( lesseq(sum(c,summation(esk2_0)),X1)
| ~ lesseq(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_221,c_0_222]) ).
cnf(c_0_226,plain,
( max(X1,X1) = X1
| ~ lesseq(X1,max(X1,X1)) ),
inference(spm,[status(thm)],[c_0_69,c_0_223]) ).
cnf(c_0_227,negated_conjecture,
( minsol_model_max(esk1_0,esk1_0,esk3_0)
| model_max(esk1_0,esk2_0,esk3_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_224]),c_0_193]) ).
cnf(c_0_228,negated_conjecture,
( model_max(esk2_0,esk2_0,X1)
| ~ lesseq(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_192,c_0_225]) ).
cnf(c_0_229,plain,
max(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_226,c_0_173]),c_0_43])]) ).
cnf(c_0_230,negated_conjecture,
( model_max(esk1_0,esk2_0,esk3_0)
| lesseq(esk3_0,X1)
| ~ model_max(esk1_0,esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_227]) ).
cnf(c_0_231,plain,
( model_ub(X1,X1,X2)
| ~ model_ub(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_145,c_0_110]) ).
cnf(c_0_232,negated_conjecture,
( lesseq(esk2_0,X1)
| ~ lesseq(esk3_0,sum(c,summation(X1))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_228]),c_0_229]) ).
cnf(c_0_233,negated_conjecture,
( model_max(esk1_0,esk2_0,esk3_0)
| lesseq(esk3_0,sum(c,summation(esk1_0))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_230,c_0_53]),c_0_181]) ).
cnf(c_0_234,plain,
( model_ub(X1,X1,X2)
| ~ model_max(X3,X4,X2)
| ~ lesseq(X1,max(X3,X4)) ),
inference(spm,[status(thm)],[c_0_231,c_0_184]) ).
cnf(c_0_235,negated_conjecture,
model_max(esk1_0,esk2_0,esk3_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_232,c_0_233]),c_0_176]) ).
cnf(c_0_236,plain,
( model_ub(X1,X1,X2)
| ~ model_max(X1,X3,X2)
| ~ lesseq(X3,X1) ),
inference(spm,[status(thm)],[c_0_234,c_0_191]) ).
cnf(c_0_237,negated_conjecture,
( minsol_model_max(esk1_0,esk2_0,esk3_0)
| model_max(esk1_0,esk2_0,esk4_3(esk1_0,esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_61,c_0_235]) ).
cnf(c_0_238,negated_conjecture,
( minsol_model_max(esk1_0,esk2_0,esk3_0)
| model_ub(esk1_0,esk1_0,esk4_3(esk1_0,esk2_0,esk3_0))
| ~ lesseq(esk2_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_236,c_0_237]) ).
cnf(c_0_239,plain,
( model_ub(X1,X2,X3)
| lesseq(max(X4,X5),X2)
| ~ model_max(X4,X5,X3)
| ~ lesseq(X1,max(X4,X5)) ),
inference(spm,[status(thm)],[c_0_130,c_0_34]) ).
cnf(c_0_240,negated_conjecture,
( minsol_model_max(esk1_0,esk2_0,esk3_0)
| model_ub(esk1_0,esk1_0,esk4_3(esk1_0,esk2_0,esk3_0))
| lesseq(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_238,c_0_34]) ).
cnf(c_0_241,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_130,c_0_191]) ).
cnf(c_0_242,plain,
( model_ub(X1,X2,X3)
| lesseq(X4,X2)
| ~ model_max(X5,X4,X3)
| ~ lesseq(X1,X4)
| ~ lesseq(X5,X4) ),
inference(spm,[status(thm)],[c_0_239,c_0_44]) ).
cnf(c_0_243,negated_conjecture,
( minsol_model_max(esk1_0,esk2_0,esk3_0)
| lesseq(esk3_0,esk4_3(esk1_0,esk2_0,esk3_0))
| lesseq(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_211,c_0_240]) ).
cnf(c_0_244,plain,
( model_ub(X1,X2,X3)
| ~ model_max(X2,X4,X3)
| ~ lesseq(X1,X4)
| ~ lesseq(X2,X4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_241,c_0_44]),c_0_242]) ).
cnf(c_0_245,negated_conjecture,
( minsol_model_max(esk1_0,esk2_0,esk3_0)
| lesseq(esk1_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_243]),c_0_235])]) ).
cnf(c_0_246,negated_conjecture,
( minsol_model_max(esk1_0,esk2_0,esk3_0)
| model_ub(X1,esk1_0,esk4_3(esk1_0,esk2_0,esk3_0))
| ~ lesseq(X1,esk2_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_244,c_0_237]),c_0_245]) ).
cnf(c_0_247,negated_conjecture,
( minsol_model_max(esk1_0,esk2_0,esk3_0)
| model_ub(esk2_0,esk1_0,esk4_3(esk1_0,esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_246,c_0_43]) ).
cnf(c_0_248,negated_conjecture,
( minsol_model_max(esk1_0,esk2_0,esk3_0)
| lesseq(esk3_0,esk4_3(esk1_0,esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_182,c_0_247]) ).
cnf(c_0_249,negated_conjecture,
minsol_model_max(esk1_0,esk2_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_248]),c_0_235])]) ).
cnf(c_0_250,negated_conjecture,
( ~ minsol_model_ub(esk1_0,esk2_0,esk3_0)
| ~ minsol_model_max(esk1_0,esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_251,negated_conjecture,
( lesseq(esk3_0,X1)
| ~ model_max(esk1_0,esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_249]) ).
cnf(c_0_252,plain,
( lesseq(sum(c,summation(X1)),X2)
| ~ model_ub(X3,X4,X2)
| ~ lesseq(X1,esk6_3(X3,X4,X2)) ),
inference(spm,[status(thm)],[c_0_120,c_0_91]) ).
cnf(c_0_253,negated_conjecture,
( minsol_model_ub(esk1_0,esk2_0,esk3_0)
| model_ub(esk1_0,esk2_0,esk5_3(esk1_0,esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_146,c_0_123]) ).
cnf(c_0_254,negated_conjecture,
~ minsol_model_ub(esk1_0,esk2_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_250,c_0_249])]) ).
cnf(c_0_255,plain,
( X1 = sum(c,summation(max(X2,X3)))
| ~ model_max(X2,X3,X1)
| ~ lesseq(X1,sum(c,summation(max(X2,X3)))) ),
inference(spm,[status(thm)],[c_0_69,c_0_21]) ).
cnf(c_0_256,negated_conjecture,
lesseq(esk3_0,sum(c,summation(max(esk1_0,esk2_0)))),
inference(spm,[status(thm)],[c_0_251,c_0_53]) ).
cnf(c_0_257,plain,
( lesseq(sum(c,summation(X1)),X2)
| ~ model_ub(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_252,c_0_110]) ).
cnf(c_0_258,negated_conjecture,
model_ub(esk1_0,esk2_0,esk5_3(esk1_0,esk2_0,esk3_0)),
inference(sr,[status(thm)],[c_0_253,c_0_254]) ).
cnf(c_0_259,negated_conjecture,
sum(c,summation(max(esk1_0,esk2_0))) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_255,c_0_256]),c_0_235])]) ).
cnf(c_0_260,negated_conjecture,
lesseq(sum(c,summation(esk1_0)),esk5_3(esk1_0,esk2_0,esk3_0)),
inference(spm,[status(thm)],[c_0_257,c_0_258]) ).
cnf(c_0_261,negated_conjecture,
( sum(c,summation(esk1_0)) = esk3_0
| ~ lesseq(esk2_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_259,c_0_27]) ).
cnf(c_0_262,negated_conjecture,
model_ub(esk2_0,esk2_0,esk3_0),
inference(spm,[status(thm)],[c_0_231,c_0_147]) ).
cnf(c_0_263,negated_conjecture,
( lesseq(esk3_0,esk5_3(esk1_0,esk2_0,esk3_0))
| ~ lesseq(esk2_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_260,c_0_261]) ).
cnf(c_0_264,negated_conjecture,
( minsol_model_ub(esk2_0,esk2_0,esk3_0)
| model_ub(esk2_0,esk2_0,esk5_3(esk2_0,esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_146,c_0_262]) ).
cnf(c_0_265,negated_conjecture,
~ lesseq(esk2_0,esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_263]),c_0_123])]),c_0_254]) ).
cnf(c_0_266,negated_conjecture,
( minsol_model_ub(esk2_0,esk2_0,esk3_0)
| model_ub(X1,esk2_0,esk5_3(esk2_0,esk2_0,esk3_0))
| ~ lesseq(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_166,c_0_264]) ).
cnf(c_0_267,negated_conjecture,
lesseq(esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_265,c_0_34]) ).
cnf(c_0_268,negated_conjecture,
( sum(c,summation(esk2_0)) = esk3_0
| ~ lesseq(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_259,c_0_44]) ).
cnf(c_0_269,plain,
( lesseq(sum(c,summation(X1)),X2)
| ~ model_ub(X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_252,c_0_116]) ).
cnf(c_0_270,negated_conjecture,
( minsol_model_ub(esk2_0,esk2_0,esk3_0)
| model_ub(esk1_0,esk2_0,esk5_3(esk2_0,esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_266,c_0_267]) ).
cnf(c_0_271,negated_conjecture,
sum(c,summation(esk2_0)) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_268,c_0_267])]) ).
cnf(c_0_272,plain,
( model_ub(X1,X1,X2)
| ~ model_max(X3,X3,X2)
| ~ lesseq(X1,X3) ),
inference(spm,[status(thm)],[c_0_234,c_0_229]) ).
cnf(c_0_273,plain,
( model_max(esk6_3(X1,X2,X3),X4,X3)
| ~ model_ub(X1,X2,X3)
| ~ lesseq(X4,esk6_3(X1,X2,X3)) ),
inference(spm,[status(thm)],[c_0_54,c_0_107]) ).
cnf(c_0_274,negated_conjecture,
( minsol_model_ub(esk2_0,esk2_0,esk3_0)
| lesseq(esk3_0,esk5_3(esk2_0,esk2_0,esk3_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_269,c_0_270]),c_0_271]) ).
cnf(c_0_275,plain,
( model_ub(X1,X1,X2)
| ~ model_ub(X3,X4,X2)
| ~ lesseq(X1,esk6_3(X3,X4,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_272,c_0_273]),c_0_43])]) ).
cnf(c_0_276,plain,
( lesseq(X1,esk6_3(X2,X3,X4))
| ~ model_ub(X2,X3,X4)
| ~ lesseq(X1,X3) ),
inference(spm,[status(thm)],[c_0_51,c_0_116]) ).
cnf(c_0_277,negated_conjecture,
minsol_model_ub(esk2_0,esk2_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_274]),c_0_262])]) ).
cnf(c_0_278,plain,
( model_ub(X1,X1,X2)
| ~ model_ub(X3,X4,X2)
| ~ lesseq(X1,X4) ),
inference(spm,[status(thm)],[c_0_275,c_0_276]) ).
cnf(c_0_279,negated_conjecture,
( lesseq(esk3_0,X1)
| ~ model_ub(esk2_0,esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_149,c_0_277]) ).
cnf(c_0_280,negated_conjecture,
( model_ub(X1,X1,esk5_3(esk1_0,esk2_0,esk3_0))
| ~ lesseq(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_278,c_0_258]) ).
cnf(c_0_281,negated_conjecture,
lesseq(esk3_0,esk5_3(esk1_0,esk2_0,esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_279,c_0_280]),c_0_43])]) ).
cnf(c_0_282,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_281]),c_0_123])]),c_0_254]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM862+1 : TPTP v8.1.2. Released v4.1.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n006.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 : 2400
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Oct 2 14:45:40 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.47 Running first-order model finding
% 0.20/0.47 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.bB8GnfDvbU/E---3.1_28618.p
% 66.31/8.92 # Version: 3.1pre001
% 66.31/8.92 # Preprocessing class: FSMSSMSSSSSNFFN.
% 66.31/8.92 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 66.31/8.92 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 66.31/8.92 # Starting new_bool_3 with 300s (1) cores
% 66.31/8.92 # Starting new_bool_1 with 300s (1) cores
% 66.31/8.92 # Starting sh5l with 300s (1) cores
% 66.31/8.92 # sh5l with pid 28700 completed with status 0
% 66.31/8.92 # Result found by sh5l
% 66.31/8.92 # Preprocessing class: FSMSSMSSSSSNFFN.
% 66.31/8.92 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 66.31/8.92 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 66.31/8.92 # Starting new_bool_3 with 300s (1) cores
% 66.31/8.92 # Starting new_bool_1 with 300s (1) cores
% 66.31/8.92 # Starting sh5l with 300s (1) cores
% 66.31/8.92 # SinE strategy is gf500_gu_R04_F100_L20000
% 66.31/8.92 # Search class: FGHSF-FFMF32-MFFFFFNN
% 66.31/8.92 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 66.31/8.92 # Starting G-E--_208_C18CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 66.31/8.92 # G-E--_208_C18CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 28706 completed with status 0
% 66.31/8.92 # Result found by G-E--_208_C18CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 66.31/8.92 # Preprocessing class: FSMSSMSSSSSNFFN.
% 66.31/8.92 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 66.31/8.92 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 66.31/8.92 # Starting new_bool_3 with 300s (1) cores
% 66.31/8.92 # Starting new_bool_1 with 300s (1) cores
% 66.31/8.92 # Starting sh5l with 300s (1) cores
% 66.31/8.92 # SinE strategy is gf500_gu_R04_F100_L20000
% 66.31/8.92 # Search class: FGHSF-FFMF32-MFFFFFNN
% 66.31/8.92 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 66.31/8.92 # Starting G-E--_208_C18CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 66.31/8.92 # Preprocessing time : 0.001 s
% 66.31/8.92 # Presaturation interreduction done
% 66.31/8.92
% 66.31/8.92 # Proof found!
% 66.31/8.92 # SZS status Theorem
% 66.31/8.92 # SZS output start CNFRefutation
% See solution above
% 66.31/8.92 # Parsed axioms : 14
% 66.31/8.92 # Removed by relevancy pruning/SinE : 0
% 66.31/8.92 # Initial clauses : 28
% 66.31/8.92 # Removed in clause preprocessing : 0
% 66.31/8.92 # Initial clauses in saturation : 28
% 66.31/8.92 # Processed clauses : 15621
% 66.31/8.92 # ...of these trivial : 17
% 66.31/8.92 # ...subsumed : 11497
% 66.31/8.92 # ...remaining for further processing : 4107
% 66.31/8.92 # Other redundant clauses eliminated : 0
% 66.31/8.92 # Clauses deleted for lack of memory : 0
% 66.31/8.92 # Backward-subsumed : 259
% 66.31/8.92 # Backward-rewritten : 816
% 66.31/8.92 # Generated clauses : 805611
% 66.31/8.92 # ...of the previous two non-redundant : 783056
% 66.31/8.92 # ...aggressively subsumed : 0
% 66.31/8.92 # Contextual simplify-reflections : 40
% 66.31/8.92 # Paramodulations : 804781
% 66.31/8.92 # Factorizations : 778
% 66.31/8.92 # NegExts : 0
% 66.31/8.92 # Equation resolutions : 0
% 66.31/8.92 # Total rewrite steps : 43003
% 66.31/8.92 # Propositional unsat checks : 0
% 66.31/8.92 # Propositional check models : 0
% 66.31/8.92 # Propositional check unsatisfiable : 0
% 66.31/8.92 # Propositional clauses : 0
% 66.31/8.92 # Propositional clauses after purity: 0
% 66.31/8.92 # Propositional unsat core size : 0
% 66.31/8.92 # Propositional preprocessing time : 0.000
% 66.31/8.92 # Propositional encoding time : 0.000
% 66.31/8.92 # Propositional solver time : 0.000
% 66.31/8.92 # Success case prop preproc time : 0.000
% 66.31/8.92 # Success case prop encoding time : 0.000
% 66.31/8.92 # Success case prop solver time : 0.000
% 66.31/8.92 # Current number of processed clauses : 2952
% 66.31/8.92 # Positive orientable unit clauses : 54
% 66.31/8.92 # Positive unorientable unit clauses: 0
% 66.31/8.92 # Negative unit clauses : 3
% 66.31/8.92 # Non-unit-clauses : 2895
% 66.31/8.92 # Current number of unprocessed clauses: 764360
% 66.31/8.92 # ...number of literals in the above : 3696407
% 66.31/8.92 # Current number of archived formulas : 0
% 66.31/8.92 # Current number of archived clauses : 1155
% 66.31/8.92 # Clause-clause subsumption calls (NU) : 1273484
% 66.31/8.92 # Rec. Clause-clause subsumption calls : 698143
% 66.31/8.92 # Non-unit clause-clause subsumptions : 11714
% 66.31/8.92 # Unit Clause-clause subsumption calls : 14625
% 66.31/8.92 # Rewrite failures with RHS unbound : 0
% 66.31/8.92 # BW rewrite match attempts : 496
% 66.31/8.92 # BW rewrite match successes : 31
% 66.31/8.92 # Condensation attempts : 0
% 66.31/8.92 # Condensation successes : 0
% 66.31/8.92 # Termbank termtop insertions : 14937816
% 66.31/8.92
% 66.31/8.92 # -------------------------------------------------
% 66.31/8.92 # User time : 7.861 s
% 66.31/8.92 # System time : 0.333 s
% 66.31/8.92 # Total time : 8.194 s
% 66.31/8.92 # Maximum resident set size: 1848 pages
% 66.31/8.92
% 66.31/8.92 # -------------------------------------------------
% 66.31/8.92 # User time : 7.863 s
% 66.31/8.92 # System time : 0.335 s
% 66.31/8.92 # Total time : 8.198 s
% 66.31/8.92 # Maximum resident set size: 1732 pages
% 66.31/8.92 % E---3.1 exiting
%------------------------------------------------------------------------------