TSTP Solution File: NUM861+1 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM861+1 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n025.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 21 01:17:37 EDT 2024
% Result : Theorem 117.66s 15.36s
% Output : CNFRefutation 117.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 12
% Syntax : Number of formulae : 233 ( 17 unt; 0 def)
% Number of atoms : 640 ( 23 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 679 ( 272 ~; 378 |; 18 &)
% ( 8 <=>; 3 =>; 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 : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 489 ( 13 sgn 80 !; 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/benchmark/theBenchmark.p',max_is_ub_1) ).
fof(minsol_model_ub,axiom,
! [X1,X2,X4] :
( minsol_model_ub(X1,X2,X4)
<=> ( model_ub(X1,X2,X4)
& ! [X3] :
( model_ub(X1,X2,X3)
=> lesseq(X4,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minsol_model_ub) ).
fof(max_2,axiom,
! [X1,X2] :
( max(X1,X2) = X2
| ~ lesseq(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',max_2) ).
fof(max_1,axiom,
! [X1,X2] :
( max(X1,X2) = X1
| ~ lesseq(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',max_1) ).
fof(minsol_model_max,axiom,
! [X1,X2,X4] :
( minsol_model_max(X1,X2,X4)
<=> ( model_max(X1,X2,X4)
& ! [X3] :
( model_max(X1,X2,X3)
=> lesseq(X4,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minsol_model_max) ).
fof(model_max_4,axiom,
! [X1,X2,X4] :
( model_max(X1,X2,X4)
<=> lesseq(sum(c,max(X1,X2)),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',model_max_4) ).
fof(lesseq_ref,axiom,
! [X1] : lesseq(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lesseq_ref) ).
fof(sum_monotone_1,axiom,
! [X1,X2,X3] :
( lesseq(X1,X2)
<=> lesseq(sum(X3,X1),sum(X3,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_monotone_1) ).
fof(model_ub_4,axiom,
! [X1,X2,X4] :
( model_ub(X1,X2,X4)
<=> ? [X3] :
( ub(X1,X2,X3)
& lesseq(sum(c,X3),X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',model_ub_4) ).
fof(lesseq_trans,axiom,
! [X1,X2,X3] :
( ( lesseq(X1,X2)
& lesseq(X2,X3) )
=> lesseq(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lesseq_trans) ).
fof(lesseq_total,axiom,
! [X1,X2] :
( lesseq(X1,X2)
| lesseq(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lesseq_total) ).
fof(ub,axiom,
! [X1,X2,X3] :
( ub(X1,X2,X3)
<=> ( lesseq(X1,X3)
& lesseq(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ub) ).
fof(c_0_12,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_13,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(fof_nnf,[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_14,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(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).
fof(c_0_15,plain,
! [X1,X2] :
( max(X1,X2) = X2
| ~ lesseq(X1,X2) ),
inference(fof_simplification,[status(thm)],[max_2]) ).
fof(c_0_16,plain,
! [X1,X2] :
( max(X1,X2) = X1
| ~ lesseq(X2,X1) ),
inference(fof_simplification,[status(thm)],[max_1]) ).
fof(c_0_17,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(fof_nnf,[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_18,plain,
( model_ub(X1,X2,X3)
| ~ minsol_model_ub(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,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_14]) ).
fof(c_0_20,plain,
! [X39,X40,X41] :
( ( ~ model_max(X39,X40,X41)
| lesseq(sum(c,max(X39,X40)),X41) )
& ( ~ lesseq(sum(c,max(X39,X40)),X41)
| model_max(X39,X40,X41) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[model_max_4])])]) ).
fof(c_0_21,plain,
! [X24] : lesseq(X24,X24),
inference(variable_rename,[status(thm)],[lesseq_ref]) ).
fof(c_0_22,plain,
! [X37,X38] :
( max(X37,X38) = X38
| ~ lesseq(X37,X38) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_15])]) ).
fof(c_0_23,plain,
! [X35,X36] :
( max(X35,X36) = X35
| ~ lesseq(X36,X35) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_16])]) ).
cnf(c_0_24,plain,
( lesseq(X4,X3)
| ~ model_max(X1,X2,X3)
| ~ minsol_model_max(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,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_18,c_0_19]) ).
cnf(c_0_26,plain,
( model_max(X1,X2,X3)
| ~ lesseq(sum(c,max(X1,X2)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
lesseq(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
( max(X1,X2) = X2
| ~ lesseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
( max(X1,X2) = X1
| ~ lesseq(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,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_24,c_0_25]) ).
cnf(c_0_31,plain,
model_max(X1,X2,sum(c,max(X1,X2))),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_32,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(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sum_monotone_1])])]) ).
cnf(c_0_33,plain,
( X1 = X2
| ~ lesseq(X1,X2)
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(esk3_0,sum(c,max(esk1_0,esk2_0))) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
( model_max(X1,X2,X3)
| ~ minsol_model_max(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_36,plain,
( lesseq(X2,X3)
| ~ lesseq(sum(X1,X2),sum(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,plain,
( lesseq(sum(c,max(X1,X2)),X3)
| ~ model_max(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_38,plain,
! [X42,X43,X44,X46,X47,X48,X49] :
( ( ub(X42,X43,esk6_3(X42,X43,X44))
| ~ model_ub(X42,X43,X44) )
& ( lesseq(sum(c,esk6_3(X42,X43,X44)),X44)
| ~ model_ub(X42,X43,X44) )
& ( ~ ub(X46,X47,X49)
| ~ lesseq(sum(c,X49),X48)
| model_ub(X46,X47,X48) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[model_ub_4])])])])])])]) ).
cnf(c_0_39,negated_conjecture,
( sum(c,max(esk1_0,esk2_0)) = esk3_0
| model_ub(esk1_0,esk2_0,esk3_0)
| ~ lesseq(sum(c,max(esk1_0,esk2_0)),esk3_0) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| model_max(esk1_0,esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_35,c_0_25]) ).
fof(c_0_41,plain,
! [X25,X26,X27] :
( ~ lesseq(X25,X26)
| ~ lesseq(X26,X27)
| lesseq(X25,X27) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[lesseq_trans])])]) ).
fof(c_0_42,plain,
! [X30,X31] :
( lesseq(X30,X31)
| lesseq(X31,X30) ),
inference(variable_rename,[status(thm)],[lesseq_total]) ).
cnf(c_0_43,plain,
( lesseq(max(X1,X2),X3)
| ~ model_max(X1,X2,sum(c,X3)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_44,plain,
( model_ub(X1,X2,X4)
| ~ ub(X1,X2,X3)
| ~ lesseq(sum(c,X3),X4) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_45,plain,
! [X50,X51,X52] :
( ( lesseq(X50,X52)
| ~ ub(X50,X51,X52) )
& ( lesseq(X51,X52)
| ~ ub(X50,X51,X52) )
& ( ~ lesseq(X50,X52)
| ~ lesseq(X51,X52)
| ub(X50,X51,X52) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ub])])])]) ).
cnf(c_0_46,plain,
( model_max(X1,X2,sum(c,X1))
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_29]) ).
cnf(c_0_47,negated_conjecture,
( sum(c,max(esk1_0,esk2_0)) = esk3_0
| model_ub(esk1_0,esk2_0,esk3_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_37]),c_0_40]) ).
cnf(c_0_48,plain,
( lesseq(X1,X3)
| ~ lesseq(X1,X2)
| ~ lesseq(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_49,plain,
( lesseq(X1,X2)
| lesseq(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_50,plain,
( lesseq(X1,X2)
| ~ model_max(X3,X1,sum(c,X2))
| ~ lesseq(X3,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_28]) ).
cnf(c_0_51,plain,
( model_ub(X1,X2,X3)
| ~ model_max(X4,X5,X3)
| ~ ub(X1,X2,max(X4,X5)) ),
inference(spm,[status(thm)],[c_0_44,c_0_37]) ).
cnf(c_0_52,plain,
( ub(X1,X3,X2)
| ~ lesseq(X1,X2)
| ~ lesseq(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_53,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| model_max(max(esk1_0,esk2_0),X1,esk3_0)
| ~ lesseq(X1,max(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_54,plain,
( lesseq(X1,X2)
| lesseq(X3,X1)
| ~ lesseq(X3,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_55,plain,
( lesseq(X1,max(X2,X1))
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_31]) ).
cnf(c_0_56,plain,
( lesseq(sum(c,esk6_3(X1,X2,X3)),X3)
| ~ model_ub(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_57,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_51,c_0_52]) ).
cnf(c_0_58,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| model_max(max(esk1_0,esk2_0),max(esk1_0,esk2_0),esk3_0) ),
inference(spm,[status(thm)],[c_0_53,c_0_27]) ).
cnf(c_0_59,plain,
( lesseq(X1,max(X2,X3))
| lesseq(X3,X1)
| ~ lesseq(X2,X3) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_60,plain,
( lesseq(X1,X2)
| ~ model_ub(X3,X4,X2)
| ~ lesseq(X1,sum(c,esk6_3(X3,X4,X2))) ),
inference(spm,[status(thm)],[c_0_48,c_0_56]) ).
cnf(c_0_61,plain,
( lesseq(sum(X3,X1),sum(X3,X2))
| ~ lesseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_62,plain,
( lesseq(X1,X2)
| ~ ub(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_63,plain,
( ub(X1,X2,esk6_3(X1,X2,X3))
| ~ model_ub(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_64,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_57,c_0_55]) ).
cnf(c_0_65,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| model_max(esk1_0,esk1_0,esk3_0)
| ~ lesseq(esk2_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_58,c_0_29]) ).
cnf(c_0_66,plain,
( lesseq(X1,X2)
| ~ ub(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_67,plain,
( lesseq(X1,X2)
| ~ model_max(X1,X3,sum(c,X2))
| ~ lesseq(X3,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_29]) ).
cnf(c_0_68,plain,
( lesseq(X1,max(X2,X2))
| lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_27]) ).
cnf(c_0_69,plain,
( lesseq(sum(c,X1),X2)
| ~ model_ub(X3,X4,X2)
| ~ lesseq(X1,esk6_3(X3,X4,X2)) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_70,plain,
( lesseq(X1,esk6_3(X1,X2,X3))
| ~ model_ub(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_71,plain,
( model_ub(X1,X1,X2)
| ~ model_max(X3,X1,X2)
| ~ lesseq(X3,X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_55]) ).
cnf(c_0_72,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| model_max(esk1_0,esk1_0,esk3_0)
| lesseq(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_65,c_0_49]) ).
cnf(c_0_73,plain,
( lesseq(X1,esk6_3(X2,X1,X3))
| ~ model_ub(X2,X1,X3) ),
inference(spm,[status(thm)],[c_0_66,c_0_63]) ).
cnf(c_0_74,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_44,c_0_56]) ).
cnf(c_0_75,plain,
( lesseq(X1,max(X1,X2))
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_67,c_0_31]) ).
cnf(c_0_76,plain,
( model_ub(X1,X2,X3)
| lesseq(X2,X1)
| ~ model_max(X2,X2,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_68]),c_0_27])]) ).
cnf(c_0_77,plain,
( model_max(X1,X2,X3)
| ~ lesseq(sum(c,X2),X3)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_28]) ).
cnf(c_0_78,plain,
( lesseq(sum(c,X1),X2)
| ~ model_ub(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_79,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| model_ub(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_71,c_0_72]),c_0_27])]) ).
cnf(c_0_80,plain,
( lesseq(sum(c,X1),X2)
| ~ model_ub(X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_69,c_0_73]) ).
cnf(c_0_81,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_74,c_0_52]) ).
cnf(c_0_82,plain,
( model_ub(X1,X2,X3)
| ~ model_max(X1,X2,X3)
| ~ lesseq(X1,X2)
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_75]) ).
cnf(c_0_83,plain,
( model_ub(X1,X2,X3)
| lesseq(X2,X1)
| ~ lesseq(sum(c,X2),X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_27])]) ).
cnf(c_0_84,negated_conjecture,
( lesseq(sum(c,esk1_0),esk3_0)
| lesseq(esk1_0,esk2_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80]) ).
cnf(c_0_85,plain,
( model_ub(X1,X2,X3)
| ~ model_ub(X2,X4,X3)
| ~ lesseq(X1,esk6_3(X2,X4,X3)) ),
inference(spm,[status(thm)],[c_0_81,c_0_70]) ).
cnf(c_0_86,plain,
( model_ub(X1,X2,X3)
| ~ lesseq(sum(c,X2),X3)
| ~ lesseq(X1,X2)
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_82,c_0_77]) ).
cnf(c_0_87,negated_conjecture,
( model_ub(X1,esk1_0,esk3_0)
| lesseq(esk1_0,esk2_0)
| lesseq(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_88,plain,
( model_ub(X1,X2,X3)
| ~ model_ub(X2,X1,X3) ),
inference(spm,[status(thm)],[c_0_85,c_0_73]) ).
cnf(c_0_89,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| ~ lesseq(esk1_0,esk2_0)
| ~ lesseq(esk2_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_82,c_0_40]) ).
cnf(c_0_90,negated_conjecture,
( model_ub(X1,esk1_0,esk3_0)
| lesseq(esk1_0,esk2_0)
| ~ lesseq(X1,esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_84]),c_0_87]) ).
cnf(c_0_91,plain,
( model_max(X1,X2,sum(c,X3))
| ~ lesseq(max(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_26,c_0_61]) ).
cnf(c_0_92,negated_conjecture,
( model_ub(esk2_0,esk1_0,esk3_0)
| ~ lesseq(esk2_0,esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90]) ).
cnf(c_0_93,plain,
( lesseq(X1,X2)
| ~ model_max(X3,X4,sum(c,X2))
| ~ lesseq(X1,max(X3,X4)) ),
inference(spm,[status(thm)],[c_0_48,c_0_43]) ).
cnf(c_0_94,plain,
( model_max(X1,X2,sum(c,X3))
| ~ lesseq(X2,X3)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_91,c_0_28]) ).
cnf(c_0_95,negated_conjecture,
( lesseq(sum(c,esk2_0),esk3_0)
| ~ lesseq(esk2_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_78,c_0_92]) ).
cnf(c_0_96,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(esk3_0,sum(c,esk1_0))
| ~ lesseq(esk2_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_34,c_0_29]) ).
cnf(c_0_97,plain,
( model_max(X1,X2,sum(c,X2))
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_28]) ).
cnf(c_0_98,plain,
( lesseq(X1,X2)
| ~ lesseq(X1,max(X3,X4))
| ~ lesseq(X4,X2)
| ~ lesseq(X3,X4) ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_99,plain,
( lesseq(esk6_3(X1,X2,sum(c,X3)),X3)
| ~ model_ub(X1,X2,sum(c,X3)) ),
inference(spm,[status(thm)],[c_0_36,c_0_56]) ).
cnf(c_0_100,plain,
( model_ub(X1,X1,sum(c,X2))
| ~ lesseq(X3,X1)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_71,c_0_94]) ).
cnf(c_0_101,plain,
( model_ub(X1,X2,X3)
| ~ model_ub(X4,X2,X3)
| ~ lesseq(X1,esk6_3(X4,X2,X3)) ),
inference(spm,[status(thm)],[c_0_81,c_0_73]) ).
cnf(c_0_102,negated_conjecture,
( model_ub(X1,esk2_0,esk3_0)
| lesseq(esk2_0,X1)
| ~ lesseq(esk2_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_83,c_0_95]) ).
cnf(c_0_103,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| model_max(esk1_0,esk2_0,X1)
| ~ lesseq(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_47]) ).
cnf(c_0_104,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(esk3_0,sum(c,esk1_0))
| lesseq(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_96,c_0_49]) ).
cnf(c_0_105,plain,
( lesseq(X1,X2)
| ~ lesseq(X1,max(X3,X2))
| ~ lesseq(X3,X2) ),
inference(spm,[status(thm)],[c_0_93,c_0_97]) ).
cnf(c_0_106,plain,
( lesseq(X1,X2)
| ~ lesseq(X1,max(X2,X3))
| ~ lesseq(X3,X2) ),
inference(spm,[status(thm)],[c_0_93,c_0_46]) ).
cnf(c_0_107,plain,
( lesseq(max(X1,X2),X3)
| ~ lesseq(X2,X3)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_98,c_0_27]) ).
cnf(c_0_108,plain,
( lesseq(X1,X2)
| ~ model_ub(X3,X4,sum(c,X2))
| ~ lesseq(X1,esk6_3(X3,X4,sum(c,X2))) ),
inference(spm,[status(thm)],[c_0_48,c_0_99]) ).
cnf(c_0_109,plain,
( model_ub(X1,X1,sum(c,X2))
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_100,c_0_27]) ).
cnf(c_0_110,plain,
( model_ub(X1,X1,X2)
| ~ model_ub(X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_101,c_0_73]) ).
cnf(c_0_111,negated_conjecture,
( model_ub(X1,esk2_0,esk3_0)
| lesseq(esk1_0,esk2_0)
| lesseq(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_102,c_0_49]) ).
cnf(c_0_112,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| model_max(esk1_0,esk2_0,sum(c,esk1_0))
| lesseq(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_113,plain,
( model_ub(X1,X1,X2)
| ~ lesseq(sum(c,X1),X2)
| ~ lesseq(X3,X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_77]) ).
cnf(c_0_114,plain,
( lesseq(max(X1,X2),X2)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_105,c_0_27]) ).
cnf(c_0_115,plain,
( lesseq(max(X1,X2),X3)
| ~ lesseq(X2,max(X3,X4))
| ~ lesseq(X4,X3)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_116,plain,
( lesseq(max(X1,X2),X3)
| lesseq(X3,X4)
| ~ lesseq(X2,X4)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_98,c_0_49]) ).
cnf(c_0_117,plain,
( lesseq(X1,X2)
| ~ model_ub(X1,X3,sum(c,X2)) ),
inference(spm,[status(thm)],[c_0_108,c_0_70]) ).
cnf(c_0_118,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| model_ub(X1,X1,esk3_0)
| ~ lesseq(X1,max(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_109,c_0_47]) ).
cnf(c_0_119,negated_conjecture,
( model_ub(esk2_0,esk2_0,esk3_0)
| lesseq(esk1_0,esk2_0)
| lesseq(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_120,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| model_ub(esk2_0,esk2_0,esk3_0)
| ~ lesseq(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_71,c_0_40]) ).
cnf(c_0_121,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(esk1_0,esk2_0)
| lesseq(X1,esk1_0)
| ~ lesseq(X1,max(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_93,c_0_112]) ).
cnf(c_0_122,negated_conjecture,
( model_ub(esk1_0,esk1_0,esk3_0)
| lesseq(esk1_0,esk2_0)
| ~ lesseq(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_113,c_0_84]) ).
cnf(c_0_123,plain,
( lesseq(X1,esk6_3(X2,X3,X4))
| ~ model_ub(X2,X3,X4)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_70]) ).
cnf(c_0_124,plain,
( lesseq(max(X1,max(X2,X3)),X3)
| ~ lesseq(X1,max(X2,X3))
| ~ lesseq(X2,X3) ),
inference(spm,[status(thm)],[c_0_105,c_0_114]) ).
cnf(c_0_125,plain,
( lesseq(max(X1,X2),X3)
| ~ lesseq(X2,X4)
| ~ lesseq(X4,X3)
| ~ lesseq(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_28]),c_0_116]) ).
cnf(c_0_126,plain,
( lesseq(X1,X2)
| lesseq(X2,X3)
| lesseq(X3,X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_49]) ).
cnf(c_0_127,plain,
( model_ub(X1,X2,X3)
| ~ model_max(X4,X2,X3)
| ~ lesseq(X1,X2)
| ~ lesseq(X4,X2) ),
inference(spm,[status(thm)],[c_0_64,c_0_28]) ).
cnf(c_0_128,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(X1,max(esk1_0,esk2_0))
| ~ model_ub(X1,X2,esk3_0) ),
inference(spm,[status(thm)],[c_0_117,c_0_47]) ).
cnf(c_0_129,negated_conjecture,
model_ub(esk2_0,esk2_0,esk3_0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_120]),c_0_110]) ).
cnf(c_0_130,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(max(esk1_0,esk2_0),esk1_0)
| lesseq(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_121,c_0_27]) ).
cnf(c_0_131,negated_conjecture,
( model_ub(esk1_0,esk1_0,esk3_0)
| lesseq(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_122,c_0_27]) ).
cnf(c_0_132,plain,
( model_ub(X1,X2,X3)
| ~ model_ub(X2,X4,X3)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_85,c_0_123]) ).
cnf(c_0_133,plain,
( lesseq(X1,X2)
| ~ lesseq(X1,max(X3,max(X4,X2)))
| ~ lesseq(X3,max(X4,X2))
| ~ lesseq(X4,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_124]) ).
cnf(c_0_134,plain,
( lesseq(max(X1,X2),X3)
| lesseq(X4,X2)
| ~ lesseq(X4,X3)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_125,c_0_49]) ).
cnf(c_0_135,plain,
( lesseq(X1,X2)
| ~ lesseq(X1,X3)
| ~ lesseq(X4,X2)
| ~ lesseq(X3,X4)
| ~ lesseq(X4,X3) ),
inference(spm,[status(thm)],[c_0_98,c_0_29]) ).
cnf(c_0_136,plain,
( lesseq(X1,X2)
| lesseq(X3,X1)
| lesseq(X4,X3)
| ~ lesseq(X4,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_126]) ).
cnf(c_0_137,plain,
( lesseq(max(X1,X2),X3)
| lesseq(X3,X2)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_105,c_0_49]) ).
cnf(c_0_138,negated_conjecture,
( model_ub(X1,max(esk1_0,esk2_0),esk3_0)
| model_ub(esk1_0,esk2_0,esk3_0)
| ~ lesseq(X1,max(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_58]),c_0_27])]) ).
cnf(c_0_139,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(esk2_0,max(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_140,negated_conjecture,
( max(esk1_0,esk2_0) = esk1_0
| model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(esk1_0,esk2_0)
| ~ lesseq(esk1_0,max(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_33,c_0_130]) ).
cnf(c_0_141,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(esk1_0,max(esk1_0,esk2_0))
| lesseq(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_128,c_0_131]) ).
cnf(c_0_142,negated_conjecture,
( model_ub(X1,esk2_0,esk3_0)
| ~ lesseq(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_132,c_0_129]) ).
cnf(c_0_143,plain,
( lesseq(X1,X2)
| ~ lesseq(X3,max(X4,X2))
| ~ lesseq(X1,X3)
| ~ lesseq(X4,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_29]),c_0_134]) ).
cnf(c_0_144,plain,
( lesseq(X1,X2)
| lesseq(X2,X3)
| ~ lesseq(X4,X3)
| ~ lesseq(X1,X4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_49]),c_0_136]) ).
cnf(c_0_145,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_13]) ).
cnf(c_0_146,plain,
( lesseq(max(X1,X1),X2)
| lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_137,c_0_27]) ).
cnf(c_0_147,negated_conjecture,
( model_ub(esk2_0,max(esk1_0,esk2_0),esk3_0)
| model_ub(esk1_0,esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_148,negated_conjecture,
( max(esk1_0,esk2_0) = esk1_0
| model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_140,c_0_141]) ).
cnf(c_0_149,negated_conjecture,
( model_ub(esk2_0,X1,esk3_0)
| ~ lesseq(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_88,c_0_142]) ).
cnf(c_0_150,plain,
( lesseq(X1,X2)
| ~ lesseq(X3,X4)
| ~ lesseq(X1,X3)
| ~ lesseq(X4,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_29]),c_0_144]) ).
cnf(c_0_151,plain,
( lesseq(X1,max(X2,X3))
| ~ lesseq(X1,X3)
| ~ lesseq(X2,X3) ),
inference(spm,[status(thm)],[c_0_48,c_0_55]) ).
cnf(c_0_152,plain,
( minsol_model_ub(X1,X2,max(X3,X3))
| lesseq(esk5_3(X1,X2,max(X3,X3)),X3)
| ~ model_ub(X1,X2,max(X3,X3)) ),
inference(spm,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_153,negated_conjecture,
model_ub(esk2_0,esk1_0,esk3_0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_149]),c_0_88]) ).
cnf(c_0_154,plain,
( lesseq(X4,X3)
| ~ model_ub(X1,X2,X3)
| ~ minsol_model_ub(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_155,plain,
( lesseq(X1,X2)
| ~ model_max(X3,X4,X5)
| ~ lesseq(X1,sum(c,max(X3,X4)))
| ~ lesseq(X5,X2) ),
inference(spm,[status(thm)],[c_0_150,c_0_37]) ).
cnf(c_0_156,plain,
( model_max(X1,X2,X3)
| lesseq(X3,sum(c,max(X1,X2))) ),
inference(spm,[status(thm)],[c_0_26,c_0_49]) ).
cnf(c_0_157,plain,
( X1 = max(X2,X3)
| ~ lesseq(max(X2,X3),X1)
| ~ lesseq(X1,X3)
| ~ lesseq(X2,X3) ),
inference(spm,[status(thm)],[c_0_33,c_0_151]) ).
cnf(c_0_158,plain,
( minsol_model_ub(X1,X2,X3)
| lesseq(esk5_3(X1,X2,X3),X3)
| ~ model_ub(X1,X2,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_28]),c_0_27])]) ).
cnf(c_0_159,negated_conjecture,
model_ub(esk1_0,esk2_0,esk3_0),
inference(spm,[status(thm)],[c_0_88,c_0_153]) ).
cnf(c_0_160,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_13]) ).
cnf(c_0_161,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_154,c_0_19]) ).
cnf(c_0_162,plain,
( model_ub(X1,X2,sum(c,X2))
| lesseq(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_97]),c_0_27])]) ).
cnf(c_0_163,plain,
( model_max(X1,X2,X3)
| lesseq(X3,X4)
| ~ model_max(X1,X2,X5)
| ~ lesseq(X5,X4) ),
inference(spm,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_164,plain,
( X1 = X2
| ~ lesseq(X2,X1)
| ~ lesseq(X1,X3)
| ~ lesseq(X3,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_29]),c_0_48]) ).
cnf(c_0_165,negated_conjecture,
( minsol_model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(esk5_3(esk1_0,esk2_0,esk3_0),esk3_0) ),
inference(spm,[status(thm)],[c_0_158,c_0_159]) ).
cnf(c_0_166,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_160,c_0_159]) ).
cnf(c_0_167,negated_conjecture,
( minsol_model_max(esk1_0,esk2_0,esk3_0)
| lesseq(esk3_0,sum(c,esk2_0))
| lesseq(esk2_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_161,c_0_162]) ).
cnf(c_0_168,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_17]) ).
cnf(c_0_169,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_17]) ).
cnf(c_0_170,plain,
( model_max(X1,X2,max(X3,X4))
| ~ lesseq(sum(c,max(X1,X2)),X4)
| ~ lesseq(X3,X4) ),
inference(spm,[status(thm)],[c_0_26,c_0_151]) ).
cnf(c_0_171,plain,
( model_max(X1,X2,X3)
| lesseq(X3,X4)
| ~ lesseq(sum(c,max(X1,X2)),X4) ),
inference(spm,[status(thm)],[c_0_163,c_0_31]) ).
cnf(c_0_172,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_160,c_0_153]) ).
cnf(c_0_173,negated_conjecture,
( esk5_3(esk1_0,esk2_0,esk3_0) = esk3_0
| minsol_model_ub(esk1_0,esk2_0,esk3_0)
| ~ lesseq(X1,esk5_3(esk1_0,esk2_0,esk3_0))
| ~ lesseq(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_164,c_0_165]) ).
cnf(c_0_174,negated_conjecture,
( minsol_model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(sum(c,esk2_0),esk5_3(esk1_0,esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_80,c_0_166]) ).
cnf(c_0_175,negated_conjecture,
( lesseq(esk3_0,sum(c,esk2_0))
| lesseq(esk2_0,esk1_0)
| lesseq(esk3_0,X1)
| ~ model_max(esk1_0,esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_167]) ).
cnf(c_0_176,plain,
( minsol_model_max(X1,X2,sum(c,max(X3,X4)))
| ~ model_max(X3,X4,esk4_3(X1,X2,sum(c,max(X3,X4))))
| ~ model_max(X1,X2,sum(c,max(X3,X4))) ),
inference(spm,[status(thm)],[c_0_168,c_0_37]) ).
cnf(c_0_177,plain,
( minsol_model_max(X1,X2,sum(c,max(X1,X2)))
| model_max(X1,X2,esk4_3(X1,X2,sum(c,max(X1,X2)))) ),
inference(spm,[status(thm)],[c_0_169,c_0_31]) ).
cnf(c_0_178,plain,
( model_max(X1,X2,X3)
| ~ lesseq(sum(c,max(X1,X2)),X4)
| ~ lesseq(X4,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_29]),c_0_171]) ).
cnf(c_0_179,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_88,c_0_172]) ).
cnf(c_0_180,plain,
( lesseq(sum(c,X1),X2)
| ~ model_max(X1,X3,X2)
| ~ lesseq(X3,X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_29]) ).
cnf(c_0_181,negated_conjecture,
( esk5_3(esk1_0,esk2_0,esk3_0) = esk3_0
| minsol_model_ub(esk1_0,esk2_0,esk3_0)
| ~ lesseq(esk3_0,sum(c,esk2_0)) ),
inference(spm,[status(thm)],[c_0_173,c_0_174]) ).
cnf(c_0_182,negated_conjecture,
( lesseq(esk3_0,sum(c,esk2_0))
| lesseq(esk2_0,esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_97]),c_0_49]) ).
cnf(c_0_183,plain,
minsol_model_max(X1,X2,sum(c,max(X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_177]),c_0_31])]) ).
cnf(c_0_184,negated_conjecture,
lesseq(sum(c,esk2_0),esk3_0),
inference(spm,[status(thm)],[c_0_78,c_0_129]) ).
cnf(c_0_185,plain,
( model_max(X1,X2,X3)
| ~ lesseq(sum(c,X2),X4)
| ~ lesseq(X4,X3)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_178,c_0_28]) ).
cnf(c_0_186,negated_conjecture,
lesseq(sum(c,esk1_0),esk3_0),
inference(spm,[status(thm)],[c_0_80,c_0_153]) ).
cnf(c_0_187,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_161,c_0_179]) ).
cnf(c_0_188,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_57,c_0_75]) ).
cnf(c_0_189,plain,
( lesseq(sum(c,X1),sum(c,max(X1,X2)))
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_180,c_0_31]) ).
cnf(c_0_190,negated_conjecture,
( esk5_3(esk1_0,esk2_0,esk3_0) = esk3_0
| minsol_model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(esk2_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_181,c_0_182]) ).
cnf(c_0_191,plain,
( minsol_model_max(X1,X2,sum(c,X2))
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_183,c_0_28]) ).
cnf(c_0_192,negated_conjecture,
( sum(c,esk2_0) = esk3_0
| lesseq(esk2_0,esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_182]),c_0_184])]) ).
cnf(c_0_193,negated_conjecture,
( model_max(X1,esk1_0,X2)
| ~ lesseq(esk3_0,X2)
| ~ lesseq(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_185,c_0_186]) ).
cnf(c_0_194,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_145,c_0_187]),c_0_153])]) ).
cnf(c_0_195,plain,
( model_ub(X1,X2,X3)
| ~ model_max(X2,X1,X3)
| ~ lesseq(X1,X2)
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_188,c_0_55]) ).
cnf(c_0_196,plain,
( model_ub(X1,X2,sum(c,max(X2,X3)))
| lesseq(X2,X1)
| ~ lesseq(X3,X2) ),
inference(spm,[status(thm)],[c_0_83,c_0_189]) ).
cnf(c_0_197,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_14]) ).
cnf(c_0_198,negated_conjecture,
( minsol_model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(esk2_0,esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_190]),c_0_159]),c_0_27])]) ).
cnf(c_0_199,negated_conjecture,
( minsol_model_max(X1,esk2_0,esk3_0)
| lesseq(esk2_0,esk1_0)
| ~ lesseq(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_191,c_0_192]) ).
cnf(c_0_200,plain,
( model_max(X1,X2,sum(c,X3))
| ~ lesseq(X1,X3)
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_91,c_0_29]) ).
cnf(c_0_201,negated_conjecture,
( model_ub(esk1_0,esk1_0,X1)
| ~ lesseq(X2,esk1_0)
| ~ lesseq(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_193]) ).
cnf(c_0_202,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_154,c_0_194]) ).
cnf(c_0_203,plain,
( model_ub(X1,X2,sum(c,max(X2,X1)))
| ~ lesseq(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_31]),c_0_196]) ).
cnf(c_0_204,negated_conjecture,
( lesseq(esk2_0,esk1_0)
| ~ minsol_model_max(esk1_0,esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_197,c_0_198]) ).
cnf(c_0_205,negated_conjecture,
( minsol_model_max(X1,esk2_0,esk3_0)
| lesseq(esk2_0,esk1_0)
| lesseq(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_199,c_0_49]) ).
cnf(c_0_206,plain,
( lesseq(X1,X2)
| ~ lesseq(X1,max(X3,X4))
| ~ lesseq(X3,X2)
| ~ lesseq(X4,X3) ),
inference(spm,[status(thm)],[c_0_93,c_0_200]) ).
cnf(c_0_207,negated_conjecture,
( model_ub(esk1_0,esk1_0,X1)
| ~ lesseq(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_201,c_0_27]) ).
cnf(c_0_208,negated_conjecture,
( minsol_model_max(esk1_0,esk2_0,esk3_0)
| lesseq(esk3_0,sum(c,max(esk1_0,esk2_0)))
| ~ lesseq(esk2_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_202,c_0_203]) ).
cnf(c_0_209,negated_conjecture,
lesseq(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_204,c_0_205]) ).
cnf(c_0_210,plain,
( lesseq(max(X1,X2),X3)
| ~ lesseq(X1,X3)
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_206,c_0_27]) ).
cnf(c_0_211,negated_conjecture,
( lesseq(esk1_0,X1)
| ~ lesseq(esk3_0,sum(c,X1)) ),
inference(spm,[status(thm)],[c_0_117,c_0_207]) ).
cnf(c_0_212,negated_conjecture,
( minsol_model_max(esk1_0,esk2_0,esk3_0)
| lesseq(esk3_0,sum(c,max(esk1_0,esk2_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_208,c_0_209])]) ).
cnf(c_0_213,plain,
( model_max(X1,X2,X3)
| ~ lesseq(sum(c,X4),X3)
| ~ lesseq(max(X1,X2),X4) ),
inference(spm,[status(thm)],[c_0_178,c_0_61]) ).
cnf(c_0_214,plain,
( max(X1,X2) = X3
| ~ lesseq(X3,max(X1,X2))
| ~ lesseq(X1,X3)
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_210]) ).
cnf(c_0_215,negated_conjecture,
( minsol_model_max(esk1_0,esk2_0,esk3_0)
| lesseq(esk1_0,max(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_211,c_0_212]) ).
cnf(c_0_216,plain,
( lesseq(X1,max(X2,X1))
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_117,c_0_203]) ).
cnf(c_0_217,negated_conjecture,
( model_max(X1,X2,esk3_0)
| ~ lesseq(max(X1,X2),esk1_0) ),
inference(spm,[status(thm)],[c_0_213,c_0_186]) ).
cnf(c_0_218,negated_conjecture,
( max(esk1_0,esk2_0) = esk1_0
| minsol_model_max(esk1_0,esk2_0,esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_215]),c_0_27]),c_0_209])]) ).
cnf(c_0_219,plain,
( model_ub(X1,X2,X3)
| ~ model_max(X4,X2,X3)
| ~ lesseq(X1,max(X4,X2))
| ~ lesseq(X2,X4) ),
inference(spm,[status(thm)],[c_0_57,c_0_216]) ).
cnf(c_0_220,negated_conjecture,
model_max(esk1_0,esk2_0,esk3_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_218]),c_0_27])]),c_0_35]) ).
cnf(c_0_221,plain,
( model_ub(X1,X2,X3)
| ~ model_max(X1,X2,X3)
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_219,c_0_75]) ).
cnf(c_0_222,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_169,c_0_220]) ).
cnf(c_0_223,negated_conjecture,
( minsol_model_max(esk1_0,esk2_0,esk3_0)
| model_ub(esk1_0,esk2_0,esk4_3(esk1_0,esk2_0,esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_222]),c_0_209])]) ).
cnf(c_0_224,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_161,c_0_223]) ).
cnf(c_0_225,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_168,c_0_224]),c_0_220])]) ).
cnf(c_0_226,negated_conjecture,
( minsol_model_ub(esk1_0,esk2_0,esk3_0)
| lesseq(sum(c,esk1_0),esk5_3(esk1_0,esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_78,c_0_166]) ).
cnf(c_0_227,negated_conjecture,
( lesseq(esk3_0,X1)
| ~ model_max(esk1_0,esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_225]) ).
cnf(c_0_228,negated_conjecture,
( esk5_3(esk1_0,esk2_0,esk3_0) = esk3_0
| minsol_model_ub(esk1_0,esk2_0,esk3_0)
| ~ lesseq(esk3_0,sum(c,esk1_0)) ),
inference(spm,[status(thm)],[c_0_173,c_0_226]) ).
cnf(c_0_229,negated_conjecture,
lesseq(esk3_0,sum(c,esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_227,c_0_46]),c_0_209])]) ).
cnf(c_0_230,negated_conjecture,
~ minsol_model_ub(esk1_0,esk2_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_197,c_0_225])]) ).
cnf(c_0_231,negated_conjecture,
esk5_3(esk1_0,esk2_0,esk3_0) = esk3_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_228,c_0_229])]),c_0_230]) ).
cnf(c_0_232,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_231]),c_0_159]),c_0_27])]),c_0_230]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM861+1 : TPTP v8.2.0. Released v4.1.0.
% 0.09/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n025.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon May 20 07:26:53 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.17/0.44 Running first-order theorem proving
% 0.17/0.44 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 117.66/15.36 # Version: 3.1.0
% 117.66/15.36 # Preprocessing class: FSMSSMSSSSSNFFN.
% 117.66/15.36 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 117.66/15.36 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 117.66/15.36 # Starting new_bool_3 with 300s (1) cores
% 117.66/15.36 # Starting new_bool_1 with 300s (1) cores
% 117.66/15.36 # Starting sh5l with 300s (1) cores
% 117.66/15.36 # sh5l with pid 11195 completed with status 0
% 117.66/15.36 # Result found by sh5l
% 117.66/15.36 # Preprocessing class: FSMSSMSSSSSNFFN.
% 117.66/15.36 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 117.66/15.36 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 117.66/15.36 # Starting new_bool_3 with 300s (1) cores
% 117.66/15.36 # Starting new_bool_1 with 300s (1) cores
% 117.66/15.36 # Starting sh5l with 300s (1) cores
% 117.66/15.36 # SinE strategy is gf500_gu_R04_F100_L20000
% 117.66/15.36 # Search class: FGHSF-FFMF32-SFFFFFNN
% 117.66/15.36 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 117.66/15.36 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 163s (1) cores
% 117.66/15.36 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 11204 completed with status 0
% 117.66/15.36 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 117.66/15.36 # Preprocessing class: FSMSSMSSSSSNFFN.
% 117.66/15.36 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 117.66/15.36 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 117.66/15.36 # Starting new_bool_3 with 300s (1) cores
% 117.66/15.36 # Starting new_bool_1 with 300s (1) cores
% 117.66/15.36 # Starting sh5l with 300s (1) cores
% 117.66/15.36 # SinE strategy is gf500_gu_R04_F100_L20000
% 117.66/15.36 # Search class: FGHSF-FFMF32-SFFFFFNN
% 117.66/15.36 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 117.66/15.36 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 163s (1) cores
% 117.66/15.36 # Preprocessing time : 0.001 s
% 117.66/15.36 # Presaturation interreduction done
% 117.66/15.36
% 117.66/15.36 # Proof found!
% 117.66/15.36 # SZS status Theorem
% 117.66/15.36 # SZS output start CNFRefutation
% See solution above
% 117.66/15.37 # Parsed axioms : 14
% 117.66/15.37 # Removed by relevancy pruning/SinE : 1
% 117.66/15.37 # Initial clauses : 26
% 117.66/15.37 # Removed in clause preprocessing : 0
% 117.66/15.37 # Initial clauses in saturation : 26
% 117.66/15.37 # Processed clauses : 27985
% 117.66/15.37 # ...of these trivial : 95
% 117.66/15.37 # ...subsumed : 22530
% 117.66/15.37 # ...remaining for further processing : 5360
% 117.66/15.37 # Other redundant clauses eliminated : 0
% 117.66/15.37 # Clauses deleted for lack of memory : 0
% 117.66/15.37 # Backward-subsumed : 826
% 117.66/15.37 # Backward-rewritten : 1179
% 117.66/15.37 # Generated clauses : 898017
% 117.66/15.37 # ...of the previous two non-redundant : 881343
% 117.66/15.37 # ...aggressively subsumed : 0
% 117.66/15.37 # Contextual simplify-reflections : 129
% 117.66/15.37 # Paramodulations : 897588
% 117.66/15.37 # Factorizations : 374
% 117.66/15.37 # NegExts : 0
% 117.66/15.37 # Equation resolutions : 0
% 117.66/15.37 # Disequality decompositions : 0
% 117.66/15.37 # Total rewrite steps : 88488
% 117.66/15.37 # ...of those cached : 88169
% 117.66/15.37 # Propositional unsat checks : 1
% 117.66/15.37 # Propositional check models : 0
% 117.66/15.37 # Propositional check unsatisfiable : 0
% 117.66/15.37 # Propositional clauses : 0
% 117.66/15.37 # Propositional clauses after purity: 0
% 117.66/15.37 # Propositional unsat core size : 0
% 117.66/15.37 # Propositional preprocessing time : 0.000
% 117.66/15.37 # Propositional encoding time : 0.803
% 117.66/15.37 # Propositional solver time : 0.257
% 117.66/15.37 # Success case prop preproc time : 0.000
% 117.66/15.37 # Success case prop encoding time : 0.000
% 117.66/15.37 # Success case prop solver time : 0.000
% 117.66/15.37 # Current number of processed clauses : 3274
% 117.66/15.37 # Positive orientable unit clauses : 20
% 117.66/15.37 # Positive unorientable unit clauses: 0
% 117.66/15.37 # Negative unit clauses : 1
% 117.66/15.37 # Non-unit-clauses : 3253
% 117.66/15.37 # Current number of unprocessed clauses: 847745
% 117.66/15.37 # ...number of literals in the above : 4266448
% 117.66/15.37 # Current number of archived formulas : 0
% 117.66/15.37 # Current number of archived clauses : 2086
% 117.66/15.37 # Clause-clause subsumption calls (NU) : 1557179
% 117.66/15.37 # Rec. Clause-clause subsumption calls : 739552
% 117.66/15.37 # Non-unit clause-clause subsumptions : 23448
% 117.66/15.37 # Unit Clause-clause subsumption calls : 8374
% 117.66/15.37 # Rewrite failures with RHS unbound : 0
% 117.66/15.37 # BW rewrite match attempts : 596
% 117.66/15.37 # BW rewrite match successes : 26
% 117.66/15.37 # Condensation attempts : 0
% 117.66/15.37 # Condensation successes : 0
% 117.66/15.37 # Termbank termtop insertions : 21411662
% 117.66/15.37 # Search garbage collected termcells : 466
% 117.66/15.37
% 117.66/15.37 # -------------------------------------------------
% 117.66/15.37 # User time : 13.961 s
% 117.66/15.37 # System time : 0.523 s
% 117.66/15.37 # Total time : 14.484 s
% 117.66/15.37 # Maximum resident set size: 1724 pages
% 117.66/15.37
% 117.66/15.37 # -------------------------------------------------
% 117.66/15.37 # User time : 13.962 s
% 117.66/15.37 # System time : 0.525 s
% 117.66/15.37 # Total time : 14.487 s
% 117.66/15.37 # Maximum resident set size: 1752 pages
% 117.66/15.37 % E---3.1 exiting
% 117.66/15.37 % E exiting
%------------------------------------------------------------------------------