%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM862+1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n029.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 : Tue May 5 04:58:46 PM UTC 2026
% Result : Theorem 58.17s 34.25s
% Output : CNFRefutation 58.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 71
% Number of leaves : 14
% Syntax : Number of formulae : 292 ( 32 unt; 0 def)
% Number of atoms : 756 ( 34 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 773 ( 309 ~; 431 |; 20 &)
% ( 9 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 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 ( 10 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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',model_max_5) ).
fof(max_1,axiom,
! [X1,X2] :
( max(X1,X2) = X1
| ~ lesseq(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',minsol_model_max) ).
fof(lesseq_total,axiom,
! [X1,X2] :
( lesseq(X1,X2)
| lesseq(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_total) ).
fof(ub,axiom,
! [X1,X2,X3] :
( ub(X1,X2,X3)
<=> ( lesseq(X1,X3)
& lesseq(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ub) ).
fof(max_2,axiom,
! [X1,X2] :
( max(X1,X2) = X2
| ~ lesseq(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_2) ).
fof(lesseq_ref,axiom,
! [X1] : lesseq(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_ref) ).
fof(lesseq_trans,axiom,
! [X1,X2,X3] :
( ( lesseq(X1,X2)
& lesseq(X2,X3) )
=> lesseq(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_trans) ).
fof(lesseq_antisymmetric,axiom,
! [X1,X2] :
( ( lesseq(X1,X2)
& lesseq(X2,X1) )
=> X1 = X2 ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',sum_monotone_1) ).
fof(summation_monotone,axiom,
! [X1,X2] :
( lesseq(X1,X2)
<=> lesseq(summation(X1),summation(X2)) ),
file('/export/starexec/sandbox/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,
! [X66,X67,X68,X70,X71,X72,X73] :
( ( ub(X66,X67,esk1_3(X66,X67,X68))
| ~ model_ub(X66,X67,X68) )
& ( lesseq(sum(c,summation(esk1_3(X66,X67,X68))),X68)
| ~ model_ub(X66,X67,X68) )
& ( ~ ub(X70,X71,X73)
| ~ lesseq(sum(c,summation(X73)),X72)
| model_ub(X70,X71,X72) ) ),
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,
! [X63,X64,X65] :
( ( ~ model_max(X63,X64,X65)
| lesseq(sum(c,summation(max(X63,X64))),X65) )
& ( ~ lesseq(sum(c,summation(max(X63,X64))),X65)
| model_max(X63,X64,X65) ) ),
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,
! [X82,X83,X84,X85,X86,X87,X88] :
( ( model_ub(X82,X83,X84)
| ~ minsol_model_ub(X82,X83,X84) )
& ( ~ model_ub(X82,X83,X85)
| lesseq(X84,X85)
| ~ minsol_model_ub(X82,X83,X84) )
& ( model_ub(X86,X87,esk3_3(X86,X87,X88))
| ~ model_ub(X86,X87,X88)
| minsol_model_ub(X86,X87,X88) )
& ( ~ lesseq(X88,esk3_3(X86,X87,X88))
| ~ model_ub(X86,X87,X88)
| minsol_model_ub(X86,X87,X88) ) ),
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(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])])]) ).
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,
! [X56,X57] :
( max(X56,X57) = X56
| ~ lesseq(X57,X56) ),
inference(variable_rename,[status(thm)],[c_0_17]) ).
fof(c_0_23,plain,
! [X74,X75,X76,X77,X78,X79,X80] :
( ( model_max(X74,X75,X76)
| ~ minsol_model_max(X74,X75,X76) )
& ( ~ model_max(X74,X75,X77)
| lesseq(X76,X77)
| ~ minsol_model_max(X74,X75,X76) )
& ( model_max(X78,X79,esk2_3(X78,X79,X80))
| ~ model_max(X78,X79,X80)
| minsol_model_max(X78,X79,X80) )
& ( ~ lesseq(X80,esk2_3(X78,X79,X80))
| ~ model_max(X78,X79,X80)
| minsol_model_max(X78,X79,X80) ) ),
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(esk4_0,esk5_0,esk6_0)
| minsol_model_max(esk4_0,esk5_0,esk6_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(esk4_0,esk5_0,esk6_0)
| model_ub(esk4_0,esk5_0,esk6_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(esk4_0,esk5_0,esk6_0)
| model_max(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_32,plain,
! [X49,X50] :
( lesseq(X49,X50)
| lesseq(X50,X49) ),
inference(variable_rename,[status(thm)],[lesseq_total]) ).
cnf(c_0_33,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| model_ub(X1,X2,esk6_0)
| ~ ub(X1,X2,esk4_0)
| ~ lesseq(esk5_0,esk4_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,
! [X60,X61,X62] :
( ( lesseq(X60,X62)
| ~ ub(X60,X61,X62) )
& ( lesseq(X61,X62)
| ~ ub(X60,X61,X62) )
& ( ~ lesseq(X60,X62)
| ~ lesseq(X61,X62)
| ub(X60,X61,X62) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ub])])]) ).
cnf(c_0_36,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| model_ub(X1,X2,esk6_0)
| lesseq(esk4_0,esk5_0)
| ~ ub(X1,X2,esk4_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(esk4_0,esk5_0,esk6_0)
| model_ub(X1,X2,esk6_0)
| lesseq(esk4_0,esk5_0)
| ~ lesseq(X2,esk4_0)
| ~ lesseq(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
fof(c_0_40,plain,
! [X43] : lesseq(X43,X43),
inference(variable_rename,[status(thm)],[lesseq_ref]) ).
fof(c_0_41,plain,
! [X58,X59] :
( max(X58,X59) = X59
| ~ lesseq(X58,X59) ),
inference(variable_rename,[status(thm)],[c_0_38]) ).
cnf(c_0_42,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| model_ub(X1,X2,esk6_0)
| lesseq(esk4_0,esk5_0)
| lesseq(esk4_0,X2)
| ~ lesseq(X1,esk4_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(esk4_0,esk5_0,esk6_0)
| model_ub(esk4_0,X1,esk6_0)
| lesseq(esk4_0,esk5_0)
| lesseq(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
fof(c_0_46,plain,
! [X44,X45,X46] :
( ~ lesseq(X44,X45)
| ~ lesseq(X45,X46)
| lesseq(X44,X46) ),
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(esk4_0,esk5_0,esk6_0)
| lesseq(esk4_0,esk5_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(esk4_0,esk5_0,esk6_0)
| lesseq(esk6_0,X1)
| ~ model_max(esk4_0,esk5_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(esk4_0,esk5_0,esk6_0)
| lesseq(sum(c,summation(esk5_0)),esk6_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(esk4_0,esk5_0,esk6_0)
| lesseq(esk6_0,sum(c,summation(max(esk4_0,esk5_0)))) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_58,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| model_max(esk5_0,X1,esk6_0)
| ~ lesseq(X1,esk5_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(esk4_0,esk5_0,esk6_0)
| lesseq(esk6_0,sum(c,summation(esk5_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,esk2_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(esk4_0,esk5_0,esk6_0)
| model_max(esk5_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_58,c_0_43]) ).
cnf(c_0_63,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| lesseq(esk6_0,X1)
| ~ model_max(X2,esk5_0,X1)
| ~ lesseq(X2,esk5_0) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_64,negated_conjecture,
( minsol_model_max(esk5_0,esk5_0,esk6_0)
| model_ub(esk4_0,esk5_0,esk6_0)
| model_max(esk5_0,esk5_0,esk2_3(esk5_0,esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
fof(c_0_65,plain,
! [X47,X48] :
( ~ lesseq(X47,X48)
| ~ lesseq(X48,X47)
| X47 = X48 ),
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,esk2_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(esk5_0,esk5_0,esk6_0)
| model_ub(esk4_0,esk5_0,esk6_0)
| lesseq(esk6_0,esk2_3(esk5_0,esk5_0,esk6_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,
! [X51,X52,X53] :
( ( ~ lesseq(X51,X52)
| lesseq(sum(X53,X51),sum(X53,X52)) )
& ( ~ lesseq(sum(X53,X51),sum(X53,X52))
| lesseq(X51,X52) ) ),
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(esk5_0,esk5_0,esk6_0)
| model_ub(esk4_0,esk5_0,esk6_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(esk5_0)) = esk6_0
| model_ub(esk4_0,esk5_0,esk6_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(esk4_0,esk5_0,esk6_0)
| lesseq(esk6_0,X1)
| ~ model_max(esk5_0,esk5_0,X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_70]) ).
fof(c_0_74,plain,
! [X54,X55] :
( ( ~ lesseq(X54,X55)
| lesseq(summation(X54),summation(X55)) )
& ( ~ lesseq(summation(X54),summation(X55))
| lesseq(X54,X55) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[summation_monotone])]) ).
cnf(c_0_75,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| lesseq(summation(esk5_0),X1)
| ~ lesseq(esk6_0,sum(c,X1)) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_76,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| lesseq(esk6_0,sum(c,summation(max(esk5_0,esk5_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(esk4_0,esk5_0,esk6_0)
| lesseq(summation(esk5_0),summation(max(esk5_0,esk5_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(esk4_0,esk5_0,esk6_0)
| lesseq(esk5_0,max(esk5_0,esk5_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(esk5_0,esk5_0) = esk5_0
| model_ub(esk4_0,esk5_0,esk6_0)
| ~ lesseq(max(esk5_0,esk5_0),esk5_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(esk4_0,esk5_0,esk6_0)
| model_ub(X1,X2,esk6_0)
| ~ ub(X1,X2,esk5_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(esk4_0,esk5_0,esk6_0)
| lesseq(summation(esk5_0),summation(max(esk4_0,esk5_0))) ),
inference(spm,[status(thm)],[c_0_75,c_0_57]) ).
cnf(c_0_93,negated_conjecture,
( max(esk5_0,esk5_0) = esk5_0
| model_ub(esk4_0,esk5_0,esk6_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(esk4_0,esk5_0,esk6_0)
| model_ub(X1,X2,esk6_0)
| ~ lesseq(X2,esk5_0)
| ~ lesseq(X1,esk5_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(esk4_0,esk5_0,esk6_0)
| lesseq(esk5_0,max(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_77,c_0_92]) ).
cnf(c_0_97,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| model_max(esk5_0,esk5_0,sum(c,summation(esk5_0))) ),
inference(spm,[status(thm)],[c_0_53,c_0_93]) ).
cnf(c_0_98,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| model_ub(X1,esk5_0,esk6_0)
| ~ lesseq(X1,esk5_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(esk4_0,esk5_0,esk6_0)
| lesseq(X1,max(esk4_0,esk5_0))
| ~ lesseq(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_51,c_0_96]) ).
cnf(c_0_101,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| lesseq(max(esk5_0,esk5_0),esk5_0) ),
inference(spm,[status(thm)],[c_0_82,c_0_97]) ).
cnf(c_0_102,plain,
( lesseq(X1,X2)
| ~ ub(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_103,plain,
( ub(X1,X2,esk1_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,esk5_0),esk5_0,esk6_0)
| model_ub(esk4_0,esk5_0,esk6_0)
| ~ lesseq(X1,esk5_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(esk4_0,esk5_0,esk6_0)
| lesseq(max(esk5_0,esk5_0),max(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_107,plain,
( lesseq(X1,esk1_3(X2,X1,X3))
| ~ model_ub(X2,X1,X3) ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_108,negated_conjecture,
( model_ub(max(esk5_0,esk5_0),esk5_0,esk6_0)
| model_ub(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_104,c_0_43]) ).
cnf(c_0_109,negated_conjecture,
( max(esk5_0,esk5_0) = max(esk4_0,esk5_0)
| model_ub(esk4_0,esk5_0,esk6_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_110,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| model_ub(X1,esk5_0,esk6_0)
| lesseq(esk5_0,X1) ),
inference(spm,[status(thm)],[c_0_98,c_0_34]) ).
cnf(c_0_111,plain,
( lesseq(X1,esk1_3(X2,X3,X4))
| ~ model_ub(X2,X3,X4)
| ~ lesseq(X1,X3) ),
inference(spm,[status(thm)],[c_0_51,c_0_107]) ).
cnf(c_0_112,negated_conjecture,
( model_ub(max(esk4_0,esk5_0),esk5_0,esk6_0)
| model_ub(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_113,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| lesseq(esk5_0,esk4_0) ),
inference(ef,[status(thm)],[c_0_110]) ).
cnf(c_0_114,plain,
( lesseq(X1,esk1_3(X2,X3,X4))
| ~ model_ub(X2,X3,X4)
| ~ lesseq(X1,X5)
| ~ lesseq(X5,X3) ),
inference(spm,[status(thm)],[c_0_51,c_0_111]) ).
cnf(c_0_115,negated_conjecture,
model_ub(esk4_0,esk5_0,esk6_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_27]),c_0_113]) ).
cnf(c_0_116,negated_conjecture,
( lesseq(X1,esk1_3(esk4_0,esk5_0,esk6_0))
| ~ lesseq(X2,esk5_0)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_117,plain,
( lesseq(sum(c,summation(esk1_3(X1,X2,X3))),X3)
| ~ model_ub(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_118,negated_conjecture,
( lesseq(X1,esk1_3(esk4_0,esk5_0,esk6_0))
| ~ lesseq(X1,max(X2,esk5_0))
| ~ lesseq(X2,esk5_0) ),
inference(spm,[status(thm)],[c_0_116,c_0_88]) ).
cnf(c_0_119,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_120,plain,
( lesseq(X1,X2)
| ~ ub(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_121,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_20,c_0_117]) ).
cnf(c_0_122,negated_conjecture,
( lesseq(max(X1,esk5_0),esk1_3(esk4_0,esk5_0,esk6_0))
| ~ lesseq(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_118,c_0_43]) ).
cnf(c_0_123,plain,
( lesseq(X1,X2)
| ~ model_ub(X3,X4,X2)
| ~ lesseq(X1,sum(c,summation(esk1_3(X3,X4,X2)))) ),
inference(spm,[status(thm)],[c_0_51,c_0_117]) ).
cnf(c_0_124,plain,
( lesseq(summation(X1),summation(X2))
| ~ lesseq(X3,X2)
| ~ lesseq(X1,X3) ),
inference(spm,[status(thm)],[c_0_119,c_0_91]) ).
cnf(c_0_125,plain,
( lesseq(X1,esk1_3(X1,X2,X3))
| ~ model_ub(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_120,c_0_103]) ).
cnf(c_0_126,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_121,c_0_37]) ).
cnf(c_0_127,negated_conjecture,
( lesseq(esk5_0,esk1_3(esk4_0,esk5_0,esk6_0))
| ~ lesseq(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_122,c_0_44]) ).
cnf(c_0_128,plain,
( lesseq(sum(c,X1),X2)
| ~ model_ub(X3,X4,X2)
| ~ lesseq(X1,summation(esk1_3(X3,X4,X2))) ),
inference(spm,[status(thm)],[c_0_123,c_0_80]) ).
cnf(c_0_129,plain,
( lesseq(summation(X1),summation(esk1_3(X2,X3,X4)))
| ~ model_ub(X2,X3,X4)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_130,plain,
( model_ub(X1,X2,X3)
| ~ model_ub(X2,X4,X3)
| ~ lesseq(X1,esk1_3(X2,X4,X3)) ),
inference(spm,[status(thm)],[c_0_126,c_0_125]) ).
cnf(c_0_131,negated_conjecture,
lesseq(esk5_0,esk1_3(esk4_0,esk5_0,esk6_0)),
inference(spm,[status(thm)],[c_0_127,c_0_43]) ).
cnf(c_0_132,plain,
( lesseq(sum(c,summation(X1)),X2)
| ~ model_ub(X3,X4,X2)
| ~ lesseq(X1,X3) ),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_133,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_18]) ).
cnf(c_0_134,negated_conjecture,
model_ub(esk5_0,esk4_0,esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_115])]) ).
cnf(c_0_135,negated_conjecture,
( lesseq(sum(c,summation(X1)),esk6_0)
| ~ lesseq(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_132,c_0_115]) ).
cnf(c_0_136,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_137,plain,
( model_ub(X1,X2,X3)
| ~ model_ub(X2,X1,X3) ),
inference(spm,[status(thm)],[c_0_130,c_0_107]) ).
cnf(c_0_138,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_133,c_0_134]) ).
cnf(c_0_139,plain,
( model_ub(X1,X1,X2)
| ~ model_ub(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_130,c_0_125]) ).
cnf(c_0_140,negated_conjecture,
( model_max(X1,X2,esk6_0)
| ~ lesseq(max(X1,X2),esk4_0) ),
inference(spm,[status(thm)],[c_0_48,c_0_135]) ).
cnf(c_0_141,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_142,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_143,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_144,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_136,c_0_25]) ).
cnf(c_0_145,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_137,c_0_138]) ).
cnf(c_0_146,negated_conjecture,
model_ub(esk4_0,esk4_0,esk6_0),
inference(spm,[status(thm)],[c_0_139,c_0_115]) ).
cnf(c_0_147,negated_conjecture,
( model_max(X1,esk4_0,esk6_0)
| ~ lesseq(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_140,c_0_88]) ).
cnf(c_0_148,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_149,plain,
( lesseq(X1,X2)
| lesseq(X3,X1)
| ~ lesseq(X3,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_34]) ).
cnf(c_0_150,plain,
( summation(X1) = summation(X2)
| ~ lesseq(X2,X1)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_141,c_0_91]) ).
cnf(c_0_151,plain,
( lesseq(max(X1,X2),X1)
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_82,c_0_142]) ).
cnf(c_0_152,plain,
( lesseq(summation(X1),summation(max(X2,X1)))
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_143,c_0_53]) ).
cnf(c_0_153,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_18]) ).
cnf(c_0_154,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_144,c_0_145]) ).
cnf(c_0_155,plain,
( model_ub(X1,X2,X3)
| ~ model_ub(X2,X4,X3)
| ~ lesseq(X1,X4) ),
inference(spm,[status(thm)],[c_0_130,c_0_111]) ).
cnf(c_0_156,negated_conjecture,
( minsol_model_ub(esk4_0,esk4_0,esk6_0)
| model_ub(esk4_0,esk4_0,esk3_3(esk4_0,esk4_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_133,c_0_146]) ).
cnf(c_0_157,negated_conjecture,
( lesseq(sum(c,summation(esk4_0)),esk6_0)
| ~ lesseq(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_49,c_0_147]) ).
cnf(c_0_158,plain,
( summation(X1) = summation(X2)
| ~ lesseq(summation(X2),X3)
| ~ lesseq(X3,summation(X1))
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_148,c_0_91]) ).
cnf(c_0_159,plain,
( lesseq(X1,X2)
| lesseq(X2,X3)
| lesseq(X3,X1) ),
inference(spm,[status(thm)],[c_0_149,c_0_34]) ).
cnf(c_0_160,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_161,plain,
( summation(max(X1,X2)) = summation(X1)
| ~ lesseq(X1,max(X1,X2))
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_150,c_0_151]) ).
cnf(c_0_162,plain,
( lesseq(X1,max(X2,X1))
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_152]) ).
cnf(c_0_163,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_153,c_0_154]),c_0_134])]) ).
cnf(c_0_164,negated_conjecture,
( minsol_model_ub(esk4_0,esk4_0,esk6_0)
| model_ub(X1,esk4_0,esk3_3(esk4_0,esk4_0,esk6_0))
| ~ lesseq(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_165,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_166,negated_conjecture,
lesseq(sum(c,summation(esk4_0)),esk6_0),
inference(spm,[status(thm)],[c_0_157,c_0_43]) ).
cnf(c_0_167,plain,
( summation(X1) = summation(X2)
| ~ lesseq(summation(X3),summation(X1))
| ~ lesseq(X1,X2)
| ~ lesseq(X2,X3) ),
inference(spm,[status(thm)],[c_0_158,c_0_91]) ).
cnf(c_0_168,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_169,plain,
( lesseq(X1,X2)
| lesseq(X3,X1)
| lesseq(X4,X3)
| ~ lesseq(X4,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_159]) ).
cnf(c_0_170,plain,
( lesseq(summation(X1),summation(max(X1,X2)))
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_160,c_0_53]) ).
cnf(c_0_171,plain,
summation(max(X1,X1)) = summation(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_43])]) ).
cnf(c_0_172,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_136,c_0_163]) ).
cnf(c_0_173,negated_conjecture,
( minsol_model_ub(esk4_0,esk4_0,esk6_0)
| model_ub(X1,esk4_0,esk3_3(esk4_0,esk4_0,esk6_0))
| lesseq(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_164,c_0_34]) ).
cnf(c_0_174,plain,
( model_ub(X1,max(X2,X3),X4)
| ~ model_max(X2,X3,X4)
| ~ lesseq(X1,max(X2,X3)) ),
inference(spm,[status(thm)],[c_0_165,c_0_43]) ).
cnf(c_0_175,negated_conjecture,
( minsol_model_max(X1,esk4_0,esk6_0)
| model_max(X1,esk4_0,esk2_3(X1,esk4_0,esk6_0))
| ~ lesseq(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_61,c_0_147]) ).
cnf(c_0_176,negated_conjecture,
( lesseq(X1,esk6_0)
| ~ lesseq(X1,sum(c,summation(esk4_0))) ),
inference(spm,[status(thm)],[c_0_51,c_0_166]) ).
cnf(c_0_177,plain,
( summation(X1) = summation(X2)
| ~ lesseq(X1,X2)
| ~ lesseq(X2,X3)
| ~ lesseq(X3,X1) ),
inference(spm,[status(thm)],[c_0_167,c_0_91]) ).
cnf(c_0_178,plain,
( lesseq(X1,X2)
| lesseq(X2,X3)
| ~ lesseq(X1,X4)
| ~ lesseq(X4,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_34]),c_0_169]) ).
cnf(c_0_179,plain,
( lesseq(summation(esk1_3(X1,X2,sum(c,X3))),X3)
| ~ model_ub(X1,X2,sum(c,X3)) ),
inference(spm,[status(thm)],[c_0_71,c_0_117]) ).
cnf(c_0_180,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_165,c_0_162]) ).
cnf(c_0_181,plain,
( lesseq(X1,max(X1,X2))
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_170]) ).
cnf(c_0_182,plain,
( model_max(X1,X1,X2)
| ~ lesseq(sum(c,summation(X1)),X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_171]) ).
cnf(c_0_183,negated_conjecture,
( lesseq(summation(X1),summation(esk1_3(esk4_0,esk5_0,esk6_0)))
| ~ lesseq(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_124,c_0_131]) ).
cnf(c_0_184,negated_conjecture,
( summation(esk1_3(esk4_0,esk5_0,esk6_0)) = summation(esk5_0)
| ~ lesseq(esk1_3(esk4_0,esk5_0,esk6_0),esk5_0) ),
inference(spm,[status(thm)],[c_0_150,c_0_131]) ).
cnf(c_0_185,plain,
( lesseq(summation(X1),summation(X2))
| lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_34]) ).
cnf(c_0_186,negated_conjecture,
( minsol_model_ub(esk4_0,esk4_0,esk6_0)
| minsol_model_max(esk4_0,esk5_0,esk6_0)
| lesseq(esk6_0,esk3_3(esk4_0,esk4_0,esk6_0))
| lesseq(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_172,c_0_173]) ).
cnf(c_0_187,plain,
( model_ub(X1,X2,X3)
| ~ model_max(X4,X2,X3)
| ~ lesseq(X1,X2)
| ~ lesseq(X4,X2) ),
inference(spm,[status(thm)],[c_0_174,c_0_44]) ).
cnf(c_0_188,negated_conjecture,
( minsol_model_max(esk4_0,esk4_0,esk6_0)
| model_max(esk4_0,esk4_0,esk2_3(esk4_0,esk4_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_175,c_0_43]) ).
cnf(c_0_189,negated_conjecture,
( lesseq(sum(c,X1),esk6_0)
| ~ lesseq(X1,summation(esk4_0)) ),
inference(spm,[status(thm)],[c_0_176,c_0_80]) ).
cnf(c_0_190,plain,
( summation(max(X1,X2)) = summation(X2)
| ~ lesseq(X3,max(X1,X2))
| ~ lesseq(X2,X3)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_177,c_0_88]) ).
cnf(c_0_191,plain,
( lesseq(X1,X2)
| lesseq(X3,X1)
| ~ model_ub(X3,X4,X5)
| ~ lesseq(esk1_3(X3,X4,X5),X2) ),
inference(spm,[status(thm)],[c_0_178,c_0_125]) ).
cnf(c_0_192,plain,
( lesseq(esk1_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_179]) ).
cnf(c_0_193,plain,
( model_ub(X1,X2,X3)
| ~ model_max(X1,X2,X3)
| ~ lesseq(X1,X2)
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_180,c_0_181]) ).
cnf(c_0_194,plain,
( model_max(X1,X1,sum(c,X2))
| ~ lesseq(summation(X1),X2) ),
inference(spm,[status(thm)],[c_0_182,c_0_80]) ).
cnf(c_0_195,negated_conjecture,
lesseq(summation(esk5_0),summation(esk1_3(esk4_0,esk5_0,esk6_0))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_184]),c_0_185]) ).
cnf(c_0_196,negated_conjecture,
( minsol_model_ub(esk4_0,esk4_0,esk6_0)
| minsol_model_max(esk4_0,esk5_0,esk6_0)
| lesseq(esk4_0,esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_186]),c_0_146])]) ).
cnf(c_0_197,negated_conjecture,
( minsol_model_max(esk4_0,esk4_0,esk6_0)
| model_ub(X1,esk4_0,esk2_3(esk4_0,esk4_0,esk6_0))
| ~ lesseq(X1,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_188]),c_0_43])]) ).
cnf(c_0_198,negated_conjecture,
( model_max(X1,X2,esk6_0)
| ~ lesseq(summation(max(X1,X2)),summation(esk4_0)) ),
inference(spm,[status(thm)],[c_0_48,c_0_189]) ).
cnf(c_0_199,plain,
( summation(max(X1,X2)) = summation(X2)
| ~ lesseq(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_162]),c_0_43])]) ).
cnf(c_0_200,plain,
( lesseq(X1,X2)
| lesseq(X2,X3)
| ~ model_ub(X1,X4,sum(c,summation(X3))) ),
inference(spm,[status(thm)],[c_0_191,c_0_192]) ).
cnf(c_0_201,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_193,c_0_194]),c_0_43])]) ).
cnf(c_0_202,negated_conjecture,
lesseq(sum(c,summation(esk5_0)),esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_195]),c_0_115])]) ).
cnf(c_0_203,negated_conjecture,
( minsol_model_max(esk4_0,esk5_0,esk6_0)
| lesseq(esk4_0,esk5_0)
| lesseq(esk6_0,X1)
| ~ model_ub(esk4_0,esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_136,c_0_196]) ).
cnf(c_0_204,negated_conjecture,
( minsol_model_max(esk4_0,esk4_0,esk6_0)
| model_ub(esk4_0,esk4_0,esk2_3(esk4_0,esk4_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_197,c_0_43]) ).
cnf(c_0_205,negated_conjecture,
( model_max(X1,X1,esk6_0)
| ~ lesseq(summation(X1),summation(esk4_0)) ),
inference(spm,[status(thm)],[c_0_198,c_0_171]) ).
cnf(c_0_206,plain,
( lesseq(X1,X2)
| ~ lesseq(X1,max(X2,X3))
| ~ lesseq(X3,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_151]) ).
cnf(c_0_207,plain,
( lesseq(X1,max(X2,X3))
| ~ lesseq(summation(X1),summation(X3))
| ~ lesseq(X2,X3) ),
inference(spm,[status(thm)],[c_0_77,c_0_199]) ).
cnf(c_0_208,plain,
( lesseq(X1,X2)
| lesseq(X3,X1)
| ~ lesseq(summation(X3),summation(X2)) ),
inference(spm,[status(thm)],[c_0_200,c_0_201]) ).
cnf(c_0_209,negated_conjecture,
( lesseq(summation(X1),summation(esk6_0))
| ~ lesseq(X1,sum(c,summation(esk5_0))) ),
inference(spm,[status(thm)],[c_0_124,c_0_202]) ).
cnf(c_0_210,plain,
model_max(X1,X1,sum(c,summation(X1))),
inference(spm,[status(thm)],[c_0_53,c_0_171]) ).
cnf(c_0_211,negated_conjecture,
( minsol_model_max(esk4_0,esk4_0,esk6_0)
| minsol_model_max(esk4_0,esk5_0,esk6_0)
| lesseq(esk6_0,esk2_3(esk4_0,esk4_0,esk6_0))
| lesseq(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_203,c_0_204]) ).
cnf(c_0_212,negated_conjecture,
model_max(esk4_0,esk4_0,esk6_0),
inference(spm,[status(thm)],[c_0_205,c_0_43]) ).
cnf(c_0_213,plain,
( lesseq(X1,X2)
| ~ lesseq(summation(X1),summation(X3))
| ~ lesseq(X3,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_207]),c_0_208]) ).
cnf(c_0_214,negated_conjecture,
lesseq(summation(sum(c,summation(esk5_0))),summation(esk6_0)),
inference(spm,[status(thm)],[c_0_209,c_0_43]) ).
cnf(c_0_215,plain,
lesseq(max(X1,X1),X1),
inference(spm,[status(thm)],[c_0_82,c_0_210]) ).
cnf(c_0_216,negated_conjecture,
( minsol_model_max(esk4_0,esk5_0,esk6_0)
| minsol_model_max(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_66,c_0_211]),c_0_212])]) ).
cnf(c_0_217,negated_conjecture,
( model_max(X1,esk5_0,esk6_0)
| ~ lesseq(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_79,c_0_202]) ).
cnf(c_0_218,negated_conjecture,
( lesseq(sum(c,summation(esk5_0)),X1)
| ~ lesseq(esk6_0,X1) ),
inference(spm,[status(thm)],[c_0_213,c_0_214]) ).
cnf(c_0_219,plain,
( max(X1,X1) = X1
| ~ lesseq(X1,max(X1,X1)) ),
inference(spm,[status(thm)],[c_0_69,c_0_215]) ).
cnf(c_0_220,negated_conjecture,
( minsol_model_max(esk4_0,esk4_0,esk6_0)
| model_max(esk4_0,esk5_0,esk6_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_216]),c_0_217]) ).
cnf(c_0_221,negated_conjecture,
( model_max(esk5_0,esk5_0,X1)
| ~ lesseq(esk6_0,X1) ),
inference(spm,[status(thm)],[c_0_182,c_0_218]) ).
cnf(c_0_222,plain,
max(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_219,c_0_162]),c_0_43])]) ).
cnf(c_0_223,negated_conjecture,
( model_max(esk4_0,esk5_0,esk6_0)
| lesseq(esk6_0,X1)
| ~ model_max(esk4_0,esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_220]) ).
cnf(c_0_224,negated_conjecture,
( lesseq(esk5_0,X1)
| ~ lesseq(esk6_0,sum(c,summation(X1))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_221]),c_0_222]) ).
cnf(c_0_225,negated_conjecture,
( model_max(esk4_0,esk5_0,esk6_0)
| lesseq(esk6_0,sum(c,summation(esk4_0))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_223,c_0_53]),c_0_171]) ).
cnf(c_0_226,negated_conjecture,
( model_max(esk4_0,X1,esk6_0)
| ~ lesseq(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_140,c_0_151]) ).
cnf(c_0_227,plain,
( model_ub(X1,X1,X2)
| ~ model_max(X3,X4,X2)
| ~ lesseq(X1,max(X3,X4)) ),
inference(spm,[status(thm)],[c_0_139,c_0_174]) ).
cnf(c_0_228,negated_conjecture,
model_max(esk4_0,esk5_0,esk6_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_224,c_0_225]),c_0_226]) ).
cnf(c_0_229,plain,
( model_ub(X1,X1,X2)
| ~ model_max(X1,X3,X2)
| ~ lesseq(X3,X1) ),
inference(spm,[status(thm)],[c_0_227,c_0_181]) ).
cnf(c_0_230,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_61,c_0_228]) ).
cnf(c_0_231,negated_conjecture,
( minsol_model_max(esk4_0,esk5_0,esk6_0)
| model_ub(esk4_0,esk4_0,esk2_3(esk4_0,esk5_0,esk6_0))
| ~ lesseq(esk5_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_229,c_0_230]) ).
cnf(c_0_232,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_165,c_0_34]) ).
cnf(c_0_233,negated_conjecture,
( minsol_model_max(esk4_0,esk5_0,esk6_0)
| model_ub(esk4_0,esk4_0,esk2_3(esk4_0,esk5_0,esk6_0))
| lesseq(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_231,c_0_34]) ).
cnf(c_0_234,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_165,c_0_181]) ).
cnf(c_0_235,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_232,c_0_44]) ).
cnf(c_0_236,negated_conjecture,
( minsol_model_max(esk4_0,esk5_0,esk6_0)
| lesseq(esk6_0,esk2_3(esk4_0,esk5_0,esk6_0))
| lesseq(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_203,c_0_233]) ).
cnf(c_0_237,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_234,c_0_44]),c_0_235]) ).
cnf(c_0_238,negated_conjecture,
( minsol_model_max(esk4_0,esk5_0,esk6_0)
| lesseq(esk4_0,esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_236]),c_0_228])]) ).
cnf(c_0_239,negated_conjecture,
( minsol_model_max(esk4_0,esk5_0,esk6_0)
| model_ub(X1,esk4_0,esk2_3(esk4_0,esk5_0,esk6_0))
| ~ lesseq(X1,esk5_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_237,c_0_230]),c_0_238]) ).
cnf(c_0_240,negated_conjecture,
( minsol_model_max(esk4_0,esk5_0,esk6_0)
| model_ub(esk5_0,esk4_0,esk2_3(esk4_0,esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_239,c_0_43]) ).
cnf(c_0_241,negated_conjecture,
( model_max(esk5_0,X1,esk6_0)
| ~ lesseq(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_54,c_0_202]) ).
cnf(c_0_242,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_172,c_0_240]) ).
cnf(c_0_243,plain,
( model_max(X1,max(X2,X3),X4)
| ~ model_max(X2,X3,X4)
| ~ lesseq(X1,max(X2,X3)) ),
inference(spm,[status(thm)],[c_0_79,c_0_21]) ).
cnf(c_0_244,negated_conjecture,
( minsol_model_max(esk5_0,X1,esk6_0)
| model_max(esk5_0,X1,esk2_3(esk5_0,X1,esk6_0))
| ~ lesseq(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_61,c_0_241]) ).
cnf(c_0_245,negated_conjecture,
( lesseq(X1,esk6_0)
| ~ lesseq(X1,sum(c,summation(esk5_0))) ),
inference(spm,[status(thm)],[c_0_51,c_0_202]) ).
cnf(c_0_246,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_66,c_0_242]),c_0_228])]) ).
cnf(c_0_247,plain,
( model_max(X1,X2,X3)
| ~ model_max(X2,X4,X3)
| ~ lesseq(X1,X2)
| ~ lesseq(X4,X2) ),
inference(spm,[status(thm)],[c_0_243,c_0_27]) ).
cnf(c_0_248,negated_conjecture,
( minsol_model_max(esk5_0,esk5_0,esk6_0)
| model_max(esk5_0,esk5_0,esk2_3(esk5_0,esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_244,c_0_43]) ).
cnf(c_0_249,negated_conjecture,
( lesseq(sum(c,X1),esk6_0)
| ~ lesseq(X1,summation(esk5_0)) ),
inference(spm,[status(thm)],[c_0_245,c_0_80]) ).
cnf(c_0_250,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_19]) ).
cnf(c_0_251,negated_conjecture,
( lesseq(esk6_0,X1)
| ~ model_max(esk4_0,esk5_0,X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_246]) ).
cnf(c_0_252,negated_conjecture,
( minsol_model_max(esk5_0,esk5_0,esk6_0)
| model_max(X1,esk5_0,esk2_3(esk5_0,esk5_0,esk6_0))
| ~ lesseq(X1,esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_247,c_0_248]),c_0_43])]) ).
cnf(c_0_253,negated_conjecture,
( model_max(X1,X2,esk6_0)
| ~ lesseq(summation(max(X1,X2)),summation(esk5_0)) ),
inference(spm,[status(thm)],[c_0_48,c_0_249]) ).
cnf(c_0_254,plain,
( lesseq(sum(c,summation(X1)),X2)
| ~ model_ub(X3,X4,X2)
| ~ lesseq(X1,esk1_3(X3,X4,X2)) ),
inference(spm,[status(thm)],[c_0_128,c_0_91]) ).
cnf(c_0_255,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_133,c_0_115]) ).
cnf(c_0_256,negated_conjecture,
~ minsol_model_ub(esk4_0,esk5_0,esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_250,c_0_246])]) ).
cnf(c_0_257,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_258,negated_conjecture,
lesseq(esk6_0,sum(c,summation(max(esk4_0,esk5_0)))),
inference(spm,[status(thm)],[c_0_251,c_0_53]) ).
cnf(c_0_259,negated_conjecture,
( minsol_model_max(esk5_0,esk5_0,esk6_0)
| model_max(X1,esk5_0,esk2_3(esk5_0,esk5_0,esk6_0))
| lesseq(esk5_0,X1) ),
inference(spm,[status(thm)],[c_0_252,c_0_34]) ).
cnf(c_0_260,negated_conjecture,
( model_max(X1,X1,esk6_0)
| ~ lesseq(summation(X1),summation(esk5_0)) ),
inference(spm,[status(thm)],[c_0_253,c_0_171]) ).
cnf(c_0_261,plain,
( lesseq(sum(c,summation(X1)),X2)
| ~ model_ub(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_254,c_0_125]) ).
cnf(c_0_262,negated_conjecture,
model_ub(esk4_0,esk5_0,esk3_3(esk4_0,esk5_0,esk6_0)),
inference(sr,[status(thm)],[c_0_255,c_0_256]) ).
cnf(c_0_263,negated_conjecture,
sum(c,summation(max(esk4_0,esk5_0))) = esk6_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_257,c_0_258]),c_0_228])]) ).
cnf(c_0_264,negated_conjecture,
( minsol_model_max(esk5_0,esk5_0,esk6_0)
| lesseq(esk6_0,esk2_3(esk5_0,esk5_0,esk6_0))
| lesseq(esk5_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_251,c_0_259]) ).
cnf(c_0_265,negated_conjecture,
model_max(esk5_0,esk5_0,esk6_0),
inference(spm,[status(thm)],[c_0_260,c_0_43]) ).
cnf(c_0_266,negated_conjecture,
( model_ub(X1,esk5_0,esk6_0)
| ~ lesseq(X1,esk1_3(esk4_0,esk5_0,esk6_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_131]),c_0_115])]) ).
cnf(c_0_267,negated_conjecture,
lesseq(sum(c,summation(esk4_0)),esk3_3(esk4_0,esk5_0,esk6_0)),
inference(spm,[status(thm)],[c_0_261,c_0_262]) ).
cnf(c_0_268,negated_conjecture,
( sum(c,summation(esk4_0)) = esk6_0
| ~ lesseq(esk5_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_263,c_0_27]) ).
cnf(c_0_269,negated_conjecture,
( minsol_model_max(esk5_0,esk5_0,esk6_0)
| lesseq(esk5_0,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_264]),c_0_265])]) ).
cnf(c_0_270,negated_conjecture,
model_ub(esk5_0,esk5_0,esk6_0),
inference(spm,[status(thm)],[c_0_266,c_0_131]) ).
cnf(c_0_271,negated_conjecture,
( lesseq(esk6_0,esk3_3(esk4_0,esk5_0,esk6_0))
| ~ lesseq(esk5_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_267,c_0_268]) ).
cnf(c_0_272,negated_conjecture,
( lesseq(esk5_0,esk4_0)
| lesseq(esk6_0,X1)
| ~ model_max(esk5_0,esk5_0,X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_269]) ).
cnf(c_0_273,negated_conjecture,
( minsol_model_ub(esk5_0,esk5_0,esk6_0)
| model_ub(esk5_0,esk5_0,esk3_3(esk5_0,esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_133,c_0_270]) ).
cnf(c_0_274,negated_conjecture,
~ lesseq(esk5_0,esk4_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_271]),c_0_115])]),c_0_256]) ).
cnf(c_0_275,negated_conjecture,
( lesseq(esk6_0,sum(c,summation(esk5_0)))
| lesseq(esk5_0,esk4_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_272,c_0_53]),c_0_171]) ).
cnf(c_0_276,negated_conjecture,
( minsol_model_ub(esk5_0,esk5_0,esk6_0)
| model_ub(X1,esk5_0,esk3_3(esk5_0,esk5_0,esk6_0))
| ~ lesseq(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_155,c_0_273]) ).
cnf(c_0_277,negated_conjecture,
lesseq(esk4_0,esk5_0),
inference(spm,[status(thm)],[c_0_274,c_0_34]) ).
cnf(c_0_278,negated_conjecture,
( sum(c,summation(esk5_0)) = esk6_0
| lesseq(esk5_0,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_275]),c_0_202])]) ).
cnf(c_0_279,plain,
( lesseq(sum(c,summation(X1)),X2)
| ~ model_ub(X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_254,c_0_107]) ).
cnf(c_0_280,negated_conjecture,
( minsol_model_ub(esk5_0,esk5_0,esk6_0)
| model_ub(esk4_0,esk5_0,esk3_3(esk5_0,esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_276,c_0_277]) ).
cnf(c_0_281,negated_conjecture,
sum(c,summation(esk5_0)) = esk6_0,
inference(sr,[status(thm)],[c_0_278,c_0_274]) ).
cnf(c_0_282,plain,
( model_ub(X1,X1,X2)
| ~ model_max(X3,X3,X2)
| ~ lesseq(X1,X3) ),
inference(spm,[status(thm)],[c_0_227,c_0_222]) ).
cnf(c_0_283,plain,
( model_max(esk1_3(X1,X2,X3),X4,X3)
| ~ model_ub(X1,X2,X3)
| ~ lesseq(X4,esk1_3(X1,X2,X3)) ),
inference(spm,[status(thm)],[c_0_54,c_0_117]) ).
cnf(c_0_284,negated_conjecture,
( minsol_model_ub(esk5_0,esk5_0,esk6_0)
| lesseq(esk6_0,esk3_3(esk5_0,esk5_0,esk6_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_279,c_0_280]),c_0_281]) ).
cnf(c_0_285,plain,
( model_ub(X1,X1,X2)
| ~ model_ub(X3,X4,X2)
| ~ lesseq(X1,esk1_3(X3,X4,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_282,c_0_283]),c_0_43])]) ).
cnf(c_0_286,negated_conjecture,
minsol_model_ub(esk5_0,esk5_0,esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_284]),c_0_270])]) ).
cnf(c_0_287,plain,
( model_ub(X1,X1,X2)
| ~ model_ub(X3,X4,X2)
| ~ lesseq(X1,X4) ),
inference(spm,[status(thm)],[c_0_285,c_0_111]) ).
cnf(c_0_288,negated_conjecture,
( lesseq(esk6_0,X1)
| ~ model_ub(esk5_0,esk5_0,X1) ),
inference(spm,[status(thm)],[c_0_136,c_0_286]) ).
cnf(c_0_289,negated_conjecture,
( model_ub(X1,X1,esk3_3(esk4_0,esk5_0,esk6_0))
| ~ lesseq(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_287,c_0_262]) ).
cnf(c_0_290,negated_conjecture,
lesseq(esk6_0,esk3_3(esk4_0,esk5_0,esk6_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_288,c_0_289]),c_0_43])]) ).
cnf(c_0_291,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_290]),c_0_115])]),c_0_256]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : NUM862+1 : TPTP v9.2.1. Released v4.1.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.34 % Computer : n029.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 01:16:29 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.20/0.35 % start to proof: theBenchmark
% 58.17/34.25 % Version : CSE_E---1.7
% 58.17/34.25 % Problem : theBenchmark.p
% 58.17/34.25 % SZS status Theorem for theBenchmark.p
% 58.17/34.25 % SZS output start CNFRefutation
% See solution above
% 58.37/34.49 % Total time : 25.415s
%------------------------------------------------------------------------------