%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM860+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:50:53 PM UTC 2026
% Result : Theorem 93.68s 14.14s
% Output : CNFRefutation 93.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 67
% Number of leaves : 13
% Syntax : Number of formulae : 202 ( 16 unt; 0 def)
% Number of atoms : 549 ( 41 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 599 ( 252 ~; 316 |; 19 &)
% ( 8 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 330 ( 12 sgn 82 !; 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_3,axiom,
! [X1,X2,X4] :
( model_ub(X1,X2,X4)
<=> ? [X3] :
( lesseq(summation(X3),X4)
& ub(X1,X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',model_ub_3) ).
fof(lesseq_ref,axiom,
! [X1] : lesseq(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_ref) ).
fof(minsol_model_ub,axiom,
! [X1,X2,X4] :
( minsol_model_ub(X1,X2,X4)
<=> ( ! [X3] :
( model_ub(X1,X2,X3)
=> lesseq(X4,X3) )
& model_ub(X1,X2,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minsol_model_ub) ).
fof(ub,axiom,
! [X1,X2,X3] :
( ub(X1,X2,X3)
<=> ( lesseq(X2,X3)
& lesseq(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ub) ).
fof(model_max_3,axiom,
! [X1,X2,X4] :
( model_max(X1,X2,X4)
<=> lesseq(summation(max(X1,X2)),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',model_max_3) ).
fof(max_2,axiom,
! [X1,X2] :
( ~ lesseq(X1,X2)
| max(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_2) ).
fof(lesseq_total,axiom,
! [X1,X2] :
( lesseq(X2,X1)
| lesseq(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_total) ).
fof(minsol_model_max,axiom,
! [X1,X2,X4] :
( minsol_model_max(X1,X2,X4)
<=> ( ! [X3] :
( model_max(X1,X2,X3)
=> lesseq(X4,X3) )
& model_max(X1,X2,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minsol_model_max) ).
fof(max_1,axiom,
! [X1,X2] :
( ~ lesseq(X2,X1)
| max(X1,X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_1) ).
fof(lesseq_trans,axiom,
! [X1,X2,X3] :
( ( lesseq(X2,X3)
& lesseq(X1,X2) )
=> lesseq(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_trans) ).
fof(lesseq_antisymmetric,axiom,
! [X1,X2] :
( ( lesseq(X2,X1)
& lesseq(X1,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_antisymmetric) ).
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_13,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_14,plain,
! [X28,X29,X30,X32,X33,X34,X35] :
( ( model_ub(X32,X33,X34)
| ~ lesseq(summation(X35),X34)
| ~ ub(X32,X33,X35) )
& ( ~ model_ub(X28,X29,X30)
| lesseq(summation(esk1_3(X28,X29,X30)),X30) )
& ( ~ model_ub(X28,X29,X30)
| ub(X28,X29,esk1_3(X28,X29,X30)) ) ),
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_3])])])])])])]) ).
fof(c_0_15,plain,
! [X5] : lesseq(X5,X5),
inference(variable_rename,[status(thm)],[lesseq_ref]) ).
fof(c_0_16,plain,
! [X44,X45,X46,X47,X48,X49,X50] :
( ( minsol_model_ub(X48,X49,X50)
| ~ model_ub(X48,X49,X50)
| ~ lesseq(X50,esk3_3(X48,X49,X50)) )
& ( minsol_model_ub(X48,X49,X50)
| ~ model_ub(X48,X49,X50)
| model_ub(X48,X49,esk3_3(X48,X49,X50)) )
& ( ~ minsol_model_ub(X44,X45,X46)
| lesseq(X46,X47)
| ~ model_ub(X44,X45,X47) )
& ( ~ minsol_model_ub(X44,X45,X46)
| model_ub(X44,X45,X46) ) ),
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_17,negated_conjecture,
( ( 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)
| ~ minsol_model_ub(esk4_0,esk5_0,esk6_0) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
cnf(c_0_18,plain,
( ~ lesseq(summation(X3),X4)
| ~ ub(X1,X2,X3)
| model_ub(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
lesseq(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_20,plain,
! [X22,X23,X24] :
( ( ub(X22,X23,X24)
| ~ lesseq(X23,X24)
| ~ lesseq(X22,X24) )
& ( ~ ub(X22,X23,X24)
| lesseq(X23,X24) )
& ( ~ ub(X22,X23,X24)
| lesseq(X22,X24) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ub])])])]) ).
cnf(c_0_21,plain,
( ~ minsol_model_ub(X1,X2,X4)
| ~ model_ub(X1,X2,X3)
| lesseq(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
( minsol_model_max(esk4_0,esk5_0,esk6_0)
| minsol_model_ub(esk4_0,esk5_0,esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( ~ ub(X1,X2,X3)
| model_ub(X1,X2,summation(X3)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( ~ lesseq(X3,X2)
| ~ lesseq(X1,X2)
| ub(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
( ~ model_ub(esk4_0,esk5_0,X1)
| lesseq(esk6_0,X1)
| minsol_model_max(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
( ~ lesseq(X1,X3)
| ~ lesseq(X2,X3)
| model_ub(X1,X2,summation(X3)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
fof(c_0_27,plain,
! [X25,X26,X27] :
( ( model_max(X25,X26,X27)
| ~ lesseq(summation(max(X25,X26)),X27) )
& ( lesseq(summation(max(X25,X26)),X27)
| ~ model_max(X25,X26,X27) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[model_max_3])])]) ).
fof(c_0_28,plain,
! [X1,X2] :
( ~ lesseq(X1,X2)
| max(X1,X2) = X2 ),
inference(fof_simplification,[status(thm)],[max_2]) ).
fof(c_0_29,plain,
! [X11,X12] :
( lesseq(X12,X11)
| lesseq(X11,X12) ),
inference(variable_rename,[status(thm)],[lesseq_total]) ).
fof(c_0_30,plain,
! [X36,X37,X38,X39,X40,X41,X42] :
( ( minsol_model_max(X40,X41,X42)
| ~ model_max(X40,X41,X42)
| ~ lesseq(X42,esk2_3(X40,X41,X42)) )
& ( minsol_model_max(X40,X41,X42)
| ~ model_max(X40,X41,X42)
| model_max(X40,X41,esk2_3(X40,X41,X42)) )
& ( ~ minsol_model_max(X36,X37,X38)
| lesseq(X38,X39)
| ~ model_max(X36,X37,X39) )
& ( ~ minsol_model_max(X36,X37,X38)
| model_max(X36,X37,X38) ) ),
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_31,negated_conjecture,
( ~ lesseq(esk4_0,X1)
| ~ lesseq(esk5_0,X1)
| lesseq(esk6_0,summation(X1))
| minsol_model_max(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
( ~ lesseq(summation(max(X1,X2)),X3)
| model_max(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_33,plain,
! [X20,X21] :
( ~ lesseq(X20,X21)
| max(X20,X21) = X21 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_28])]) ).
cnf(c_0_34,plain,
( lesseq(X2,X1)
| lesseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_35,plain,
! [X1,X2] :
( ~ lesseq(X2,X1)
| max(X1,X2) = X1 ),
inference(fof_simplification,[status(thm)],[max_1]) ).
cnf(c_0_36,plain,
( ~ minsol_model_max(X1,X2,X4)
| ~ model_max(X1,X2,X3)
| lesseq(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,negated_conjecture,
( ~ lesseq(esk4_0,esk5_0)
| lesseq(esk6_0,summation(esk5_0))
| minsol_model_max(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_31,c_0_19]) ).
cnf(c_0_38,plain,
model_max(X1,X2,summation(max(X1,X2))),
inference(spm,[status(thm)],[c_0_32,c_0_19]) ).
cnf(c_0_39,plain,
( ~ lesseq(X1,X2)
| max(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,negated_conjecture,
( ~ lesseq(esk4_0,X1)
| lesseq(X1,esk5_0)
| lesseq(esk6_0,summation(X1))
| minsol_model_max(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_31,c_0_34]) ).
fof(c_0_41,plain,
! [X18,X19] :
( ~ lesseq(X19,X18)
| max(X18,X19) = X18 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_35])]) ).
cnf(c_0_42,plain,
( ~ minsol_model_ub(X1,X2,X3)
| model_ub(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_43,plain,
! [X6,X7,X8] :
( lesseq(X6,X8)
| ~ lesseq(X7,X8)
| ~ lesseq(X6,X7) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[lesseq_trans])])]) ).
cnf(c_0_44,negated_conjecture,
( ~ lesseq(esk4_0,esk5_0)
| ~ model_max(esk4_0,esk5_0,X1)
| lesseq(esk6_0,X1)
| lesseq(esk6_0,summation(esk5_0)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_45,plain,
( ~ lesseq(X1,X2)
| model_max(X1,X2,summation(X2)) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_46,negated_conjecture,
( lesseq(esk4_0,esk5_0)
| lesseq(esk6_0,summation(esk4_0))
| minsol_model_max(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_40,c_0_19]) ).
cnf(c_0_47,plain,
( ~ lesseq(X2,X1)
| max(X1,X2) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_48,plain,
! [X9,X10] :
( X9 = X10
| ~ lesseq(X10,X9)
| ~ lesseq(X9,X10) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[lesseq_antisymmetric])])]) ).
cnf(c_0_49,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| minsol_model_max(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_42,c_0_22]) ).
fof(c_0_50,plain,
! [X16,X17] :
( ( lesseq(X16,X17)
| ~ lesseq(summation(X16),summation(X17)) )
& ( lesseq(summation(X16),summation(X17))
| ~ lesseq(X16,X17) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[summation_monotone])])]) ).
cnf(c_0_51,plain,
( ~ lesseq(X2,X3)
| ~ lesseq(X1,X2)
| lesseq(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_52,negated_conjecture,
( ~ lesseq(esk4_0,esk5_0)
| lesseq(esk6_0,summation(esk5_0)) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_53,negated_conjecture,
( ~ model_max(esk4_0,esk5_0,X1)
| lesseq(esk6_0,X1)
| lesseq(esk4_0,esk5_0)
| lesseq(esk6_0,summation(esk4_0)) ),
inference(spm,[status(thm)],[c_0_36,c_0_46]) ).
cnf(c_0_54,plain,
( ~ lesseq(X2,X1)
| model_max(X1,X2,summation(X1)) ),
inference(spm,[status(thm)],[c_0_38,c_0_47]) ).
cnf(c_0_55,plain,
( ~ lesseq(X2,X1)
| ~ lesseq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_56,plain,
( ~ model_max(X1,X2,X3)
| lesseq(summation(max(X1,X2)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_57,negated_conjecture,
( ~ model_max(esk4_0,esk5_0,X1)
| lesseq(esk6_0,X1)
| model_ub(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_36,c_0_49]) ).
cnf(c_0_58,plain,
( ~ minsol_model_max(X1,X2,X3)
| model_max(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_59,plain,
( ~ ub(X3,X1,X2)
| lesseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_60,plain,
( ~ model_ub(X1,X2,X3)
| ub(X1,X2,esk1_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_61,plain,
( ~ lesseq(summation(X1),summation(X2))
| lesseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_62,negated_conjecture,
( ~ lesseq(X1,esk6_0)
| ~ lesseq(esk4_0,esk5_0)
| lesseq(X1,summation(esk5_0)) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_63,negated_conjecture,
( lesseq(esk4_0,esk5_0)
| lesseq(esk6_0,summation(esk4_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_34]) ).
cnf(c_0_64,plain,
( ~ lesseq(X1,summation(max(X2,X3)))
| ~ model_max(X2,X3,X1)
| X1 = summation(max(X2,X3)) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_65,negated_conjecture,
( lesseq(esk6_0,summation(max(esk4_0,esk5_0)))
| model_ub(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_57,c_0_38]) ).
cnf(c_0_66,negated_conjecture,
( model_max(esk4_0,esk5_0,esk6_0)
| model_ub(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_58,c_0_49]) ).
cnf(c_0_67,plain,
( ~ model_ub(X2,X1,X3)
| lesseq(X1,esk1_3(X2,X1,X3)) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_68,negated_conjecture,
( ~ lesseq(esk4_0,esk5_0)
| ~ lesseq(summation(X1),esk6_0)
| lesseq(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_69,plain,
( ~ model_ub(X1,X2,X3)
| lesseq(summation(esk1_3(X1,X2,X3)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_70,plain,
( ~ ub(X1,X3,X2)
| lesseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_71,negated_conjecture,
( ~ lesseq(X1,esk6_0)
| lesseq(esk4_0,esk5_0)
| lesseq(X1,summation(esk4_0)) ),
inference(spm,[status(thm)],[c_0_51,c_0_63]) ).
cnf(c_0_72,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| summation(max(esk4_0,esk5_0)) = esk6_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66]) ).
cnf(c_0_73,plain,
( ~ lesseq(esk1_3(X1,X2,X3),X2)
| ~ model_ub(X1,X2,X3)
| esk1_3(X1,X2,X3) = X2 ),
inference(spm,[status(thm)],[c_0_55,c_0_67]) ).
cnf(c_0_74,negated_conjecture,
( ~ lesseq(esk4_0,esk5_0)
| ~ model_ub(X1,X2,esk6_0)
| lesseq(esk1_3(X1,X2,esk6_0),esk5_0) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_75,plain,
( ~ model_ub(X1,X2,X3)
| lesseq(X1,esk1_3(X1,X2,X3)) ),
inference(spm,[status(thm)],[c_0_70,c_0_60]) ).
cnf(c_0_76,negated_conjecture,
( ~ lesseq(summation(X1),esk6_0)
| lesseq(X1,esk4_0)
| lesseq(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_61,c_0_71]) ).
cnf(c_0_77,plain,
( ~ lesseq(X3,X1)
| ~ model_max(X1,X3,X2)
| lesseq(summation(X1),X2) ),
inference(spm,[status(thm)],[c_0_56,c_0_47]) ).
cnf(c_0_78,negated_conjecture,
( ~ lesseq(esk6_0,X1)
| model_max(esk4_0,esk5_0,X1)
| model_ub(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_32,c_0_72]) ).
cnf(c_0_79,plain,
( ~ model_max(X2,X3,X1)
| ~ lesseq(X1,esk2_3(X2,X3,X1))
| minsol_model_max(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_80,plain,
( ~ model_max(X1,X2,X3)
| minsol_model_max(X1,X2,X3)
| model_max(X1,X2,esk2_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_81,negated_conjecture,
( ~ lesseq(esk4_0,esk5_0)
| ~ model_ub(X1,esk5_0,esk6_0)
| esk1_3(X1,esk5_0,esk6_0) = esk5_0 ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_82,plain,
( ~ lesseq(X3,X1)
| ~ model_max(X3,X1,X2)
| lesseq(summation(X1),X2) ),
inference(spm,[status(thm)],[c_0_56,c_0_39]) ).
cnf(c_0_83,plain,
( ~ lesseq(esk1_3(X1,X2,X3),X1)
| ~ model_ub(X1,X2,X3)
| esk1_3(X1,X2,X3) = X1 ),
inference(spm,[status(thm)],[c_0_55,c_0_75]) ).
cnf(c_0_84,negated_conjecture,
( ~ model_ub(X1,X2,esk6_0)
| lesseq(esk4_0,esk5_0)
| lesseq(esk1_3(X1,X2,esk6_0),esk4_0) ),
inference(spm,[status(thm)],[c_0_76,c_0_69]) ).
cnf(c_0_85,negated_conjecture,
( ~ lesseq(esk6_0,X1)
| ~ lesseq(esk5_0,esk4_0)
| lesseq(summation(esk4_0),X1)
| model_ub(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_86,plain,
( ~ model_max(X1,X2,summation(max(X3,X4)))
| ~ model_max(X3,X4,esk2_3(X1,X2,summation(max(X3,X4))))
| minsol_model_max(X1,X2,summation(max(X3,X4))) ),
inference(spm,[status(thm)],[c_0_79,c_0_56]) ).
cnf(c_0_87,plain,
( model_max(X1,X2,esk2_3(X1,X2,summation(max(X1,X2))))
| minsol_model_max(X1,X2,summation(max(X1,X2))) ),
inference(spm,[status(thm)],[c_0_80,c_0_38]) ).
cnf(c_0_88,negated_conjecture,
( ~ lesseq(esk4_0,esk5_0)
| ~ model_ub(X1,esk5_0,esk6_0)
| lesseq(summation(esk5_0),esk6_0) ),
inference(spm,[status(thm)],[c_0_69,c_0_81]) ).
cnf(c_0_89,negated_conjecture,
( ~ lesseq(esk4_0,esk5_0)
| lesseq(summation(esk5_0),esk6_0)
| model_ub(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_82,c_0_66]) ).
cnf(c_0_90,negated_conjecture,
( ~ model_ub(esk4_0,X1,esk6_0)
| lesseq(esk4_0,esk5_0)
| esk1_3(esk4_0,X1,esk6_0) = esk4_0 ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_91,negated_conjecture,
( ~ lesseq(esk6_0,X1)
| lesseq(esk4_0,esk5_0)
| lesseq(summation(esk4_0),X1)
| model_ub(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_85,c_0_34]) ).
cnf(c_0_92,plain,
( ~ model_ub(X1,X2,X3)
| minsol_model_ub(X1,X2,X3)
| model_ub(X1,X2,esk3_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_93,negated_conjecture,
( ~ lesseq(esk5_0,esk4_0)
| model_ub(esk4_0,esk5_0,esk6_0)
| summation(esk4_0) = esk6_0 ),
inference(spm,[status(thm)],[c_0_72,c_0_47]) ).
cnf(c_0_94,plain,
minsol_model_max(X1,X2,summation(max(X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_38])]) ).
cnf(c_0_95,negated_conjecture,
( ~ lesseq(esk4_0,esk5_0)
| ~ lesseq(summation(esk5_0),esk6_0)
| summation(esk5_0) = esk6_0 ),
inference(spm,[status(thm)],[c_0_55,c_0_52]) ).
cnf(c_0_96,negated_conjecture,
( ~ lesseq(esk4_0,esk5_0)
| lesseq(summation(esk5_0),esk6_0) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_97,negated_conjecture,
( ~ model_ub(esk4_0,X1,esk6_0)
| lesseq(esk4_0,esk5_0)
| lesseq(summation(esk4_0),esk6_0) ),
inference(spm,[status(thm)],[c_0_69,c_0_90]) ).
cnf(c_0_98,negated_conjecture,
( lesseq(esk4_0,esk5_0)
| lesseq(summation(esk4_0),esk6_0)
| model_ub(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_91,c_0_19]) ).
cnf(c_0_99,negated_conjecture,
( ~ minsol_model_max(esk4_0,esk5_0,esk6_0)
| ~ minsol_model_ub(esk4_0,esk5_0,esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_100,negated_conjecture,
( ~ lesseq(esk5_0,esk4_0)
| model_ub(esk4_0,esk5_0,esk3_3(esk4_0,esk5_0,esk6_0))
| minsol_model_ub(esk4_0,esk5_0,esk6_0)
| summation(esk4_0) = esk6_0 ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_101,plain,
( ~ lesseq(X1,X2)
| minsol_model_max(X1,X2,summation(X2)) ),
inference(spm,[status(thm)],[c_0_94,c_0_39]) ).
cnf(c_0_102,negated_conjecture,
( ~ lesseq(esk4_0,esk5_0)
| summation(esk5_0) = esk6_0 ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_103,negated_conjecture,
( ~ lesseq(summation(esk4_0),esk6_0)
| lesseq(esk4_0,esk5_0)
| summation(esk4_0) = esk6_0 ),
inference(spm,[status(thm)],[c_0_55,c_0_63]) ).
cnf(c_0_104,negated_conjecture,
( lesseq(esk4_0,esk5_0)
| lesseq(summation(esk4_0),esk6_0) ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_105,negated_conjecture,
( ~ lesseq(esk5_0,esk4_0)
| ~ minsol_model_max(esk4_0,esk5_0,esk6_0)
| model_ub(esk4_0,esk5_0,esk3_3(esk4_0,esk5_0,esk6_0))
| summation(esk4_0) = esk6_0 ),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_106,negated_conjecture,
( ~ lesseq(X1,esk5_0)
| ~ lesseq(esk4_0,esk5_0)
| minsol_model_max(X1,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_107,negated_conjecture,
( lesseq(esk4_0,esk5_0)
| summation(esk4_0) = esk6_0 ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_108,negated_conjecture,
( ~ lesseq(esk5_0,esk4_0)
| model_ub(esk4_0,esk5_0,esk3_3(esk4_0,esk5_0,esk6_0))
| summation(esk4_0) = esk6_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107]) ).
cnf(c_0_109,negated_conjecture,
( ~ lesseq(esk5_0,esk4_0)
| lesseq(esk6_0,esk3_3(esk4_0,esk5_0,esk6_0))
| minsol_model_max(esk4_0,esk5_0,esk6_0)
| summation(esk4_0) = esk6_0 ),
inference(spm,[status(thm)],[c_0_25,c_0_108]) ).
cnf(c_0_110,negated_conjecture,
( ~ lesseq(esk5_0,esk4_0)
| ~ model_max(esk4_0,esk5_0,X1)
| lesseq(esk6_0,X1)
| lesseq(esk6_0,esk3_3(esk4_0,esk5_0,esk6_0))
| summation(esk4_0) = esk6_0 ),
inference(spm,[status(thm)],[c_0_36,c_0_109]) ).
cnf(c_0_111,plain,
( ~ model_ub(X2,X3,X1)
| ~ lesseq(X1,esk3_3(X2,X3,X1))
| minsol_model_ub(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_112,negated_conjecture,
( ~ lesseq(esk5_0,esk4_0)
| lesseq(esk6_0,esk3_3(esk4_0,esk5_0,esk6_0))
| lesseq(esk6_0,summation(max(esk4_0,esk5_0)))
| summation(esk4_0) = esk6_0 ),
inference(spm,[status(thm)],[c_0_110,c_0_38]) ).
cnf(c_0_113,negated_conjecture,
( ~ lesseq(esk5_0,esk4_0)
| lesseq(esk6_0,summation(max(esk4_0,esk5_0)))
| minsol_model_ub(esk4_0,esk5_0,esk6_0)
| summation(esk4_0) = esk6_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_93]) ).
cnf(c_0_114,negated_conjecture,
( ~ lesseq(esk5_0,esk4_0)
| ~ minsol_model_max(esk4_0,esk5_0,esk6_0)
| lesseq(esk6_0,summation(max(esk4_0,esk5_0)))
| summation(esk4_0) = esk6_0 ),
inference(spm,[status(thm)],[c_0_99,c_0_113]) ).
cnf(c_0_115,negated_conjecture,
( ~ lesseq(esk5_0,esk4_0)
| lesseq(esk6_0,summation(max(esk4_0,esk5_0)))
| summation(esk4_0) = esk6_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_106]),c_0_107]) ).
cnf(c_0_116,negated_conjecture,
( ~ lesseq(esk5_0,esk4_0)
| lesseq(esk6_0,summation(esk4_0))
| summation(esk4_0) = esk6_0 ),
inference(spm,[status(thm)],[c_0_115,c_0_47]) ).
cnf(c_0_117,plain,
( ~ lesseq(X1,X2)
| lesseq(summation(X1),summation(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_118,negated_conjecture,
( ~ lesseq(esk5_0,esk4_0)
| ~ lesseq(summation(esk4_0),esk6_0)
| summation(esk4_0) = esk6_0 ),
inference(spm,[status(thm)],[c_0_55,c_0_116]) ).
cnf(c_0_119,negated_conjecture,
( ~ lesseq(X1,esk5_0)
| ~ lesseq(esk4_0,esk5_0)
| lesseq(summation(X1),esk6_0) ),
inference(spm,[status(thm)],[c_0_117,c_0_102]) ).
cnf(c_0_120,plain,
( ~ model_ub(X1,X2,summation(X3))
| lesseq(esk1_3(X1,X2,summation(X3)),X3) ),
inference(spm,[status(thm)],[c_0_61,c_0_69]) ).
cnf(c_0_121,negated_conjecture,
( ~ lesseq(esk5_0,esk4_0)
| summation(esk4_0) = esk6_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_107]) ).
cnf(c_0_122,negated_conjecture,
( ~ lesseq(esk5_0,esk4_0)
| ~ model_ub(X1,X2,esk6_0)
| lesseq(esk1_3(X1,X2,esk6_0),esk4_0) ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_123,plain,
( ~ model_ub(X1,X2,summation(X1))
| esk1_3(X1,X2,summation(X1)) = X1 ),
inference(spm,[status(thm)],[c_0_83,c_0_120]) ).
cnf(c_0_124,negated_conjecture,
( ~ lesseq(esk5_0,esk4_0)
| ~ model_ub(X1,esk4_0,esk6_0)
| esk1_3(X1,esk4_0,esk6_0) = esk4_0 ),
inference(spm,[status(thm)],[c_0_73,c_0_122]) ).
cnf(c_0_125,negated_conjecture,
( ~ lesseq(esk4_0,esk5_0)
| ~ ub(X1,X2,esk5_0)
| model_ub(X1,X2,esk6_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_96]) ).
cnf(c_0_126,plain,
( ~ model_ub(X1,X2,summation(X1))
| ub(X1,X2,X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_123]) ).
cnf(c_0_127,negated_conjecture,
( ~ lesseq(esk6_0,X3)
| ~ lesseq(esk5_0,esk4_0)
| ~ ub(X1,X2,esk4_0)
| model_ub(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_121]) ).
cnf(c_0_128,negated_conjecture,
( ~ lesseq(esk5_0,esk4_0)
| ~ model_ub(X1,esk4_0,esk6_0)
| ub(X1,esk4_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_60,c_0_124]) ).
cnf(c_0_129,negated_conjecture,
( ~ lesseq(esk4_0,esk5_0)
| ~ model_ub(esk5_0,X1,summation(esk5_0))
| model_ub(esk5_0,X1,esk6_0) ),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_130,plain,
( ~ lesseq(X1,summation(esk1_3(X3,X4,X2)))
| ~ model_ub(X3,X4,X2)
| lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_69]) ).
cnf(c_0_131,negated_conjecture,
( ~ lesseq(esk6_0,X2)
| ~ lesseq(esk5_0,esk4_0)
| ~ model_ub(X1,esk4_0,esk6_0)
| model_ub(X1,esk4_0,X2) ),
inference(spm,[status(thm)],[c_0_127,c_0_128]) ).
cnf(c_0_132,negated_conjecture,
( ~ lesseq(X1,esk5_0)
| ~ lesseq(esk4_0,esk5_0)
| model_ub(esk5_0,X1,esk6_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_26]),c_0_19])]) ).
cnf(c_0_133,plain,
( ~ lesseq(X1,esk1_3(X3,X4,X2))
| ~ model_ub(X3,X4,X2)
| lesseq(summation(X1),X2) ),
inference(spm,[status(thm)],[c_0_130,c_0_117]) ).
cnf(c_0_134,negated_conjecture,
( ~ lesseq(esk6_0,X1)
| ~ lesseq(esk4_0,esk5_0)
| ~ lesseq(esk5_0,esk4_0)
| model_ub(esk5_0,esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_135,negated_conjecture,
( ~ lesseq(esk5_0,esk4_0)
| ~ lesseq(esk6_0,summation(X1))
| lesseq(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_121]) ).
cnf(c_0_136,plain,
( ~ model_ub(X1,X3,X2)
| lesseq(summation(X1),X2) ),
inference(spm,[status(thm)],[c_0_133,c_0_75]) ).
cnf(c_0_137,negated_conjecture,
( ~ lesseq(esk5_0,esk4_0)
| ~ lesseq(esk6_0,summation(esk5_0))
| model_ub(esk5_0,esk4_0,esk6_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_134]),c_0_135]) ).
cnf(c_0_138,negated_conjecture,
( ~ lesseq(esk5_0,esk4_0)
| lesseq(summation(esk5_0),esk6_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_34]) ).
cnf(c_0_139,plain,
( ~ lesseq(X1,esk1_3(X3,X4,summation(X2)))
| ~ model_ub(X3,X4,summation(X2))
| lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_120]) ).
cnf(c_0_140,negated_conjecture,
( ~ lesseq(esk5_0,esk4_0)
| ~ ub(X1,X2,esk5_0)
| model_ub(X1,X2,esk6_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_138]) ).
cnf(c_0_141,plain,
( ~ model_ub(X1,X3,summation(X2))
| lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_139,c_0_75]) ).
cnf(c_0_142,negated_conjecture,
( ~ lesseq(esk5_0,esk4_0)
| ~ model_ub(esk5_0,X1,summation(esk5_0))
| model_ub(esk5_0,X1,esk6_0) ),
inference(spm,[status(thm)],[c_0_140,c_0_126]) ).
cnf(c_0_143,negated_conjecture,
( ~ model_ub(X1,X2,esk6_0)
| lesseq(X1,max(esk4_0,esk5_0))
| model_ub(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_141,c_0_72]) ).
cnf(c_0_144,negated_conjecture,
( ~ lesseq(X1,esk5_0)
| ~ lesseq(esk5_0,esk4_0)
| model_ub(esk5_0,X1,esk6_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_26]),c_0_19])]) ).
cnf(c_0_145,plain,
( ~ lesseq(X2,X1)
| ~ lesseq(summation(X1),summation(X2))
| summation(X1) = summation(X2) ),
inference(spm,[status(thm)],[c_0_55,c_0_117]) ).
cnf(c_0_146,plain,
( ~ lesseq(X1,summation(max(X3,X4)))
| ~ model_max(X3,X4,X2)
| lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_56]) ).
cnf(c_0_147,negated_conjecture,
( ~ lesseq(X1,esk5_0)
| ~ lesseq(esk5_0,esk4_0)
| lesseq(esk5_0,max(esk4_0,esk5_0))
| model_ub(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_143,c_0_144]) ).
cnf(c_0_148,plain,
( ~ lesseq(X1,X2)
| ~ lesseq(X2,X1)
| summation(X1) = summation(X2) ),
inference(spm,[status(thm)],[c_0_145,c_0_117]) ).
cnf(c_0_149,plain,
( ~ lesseq(X1,max(X3,X4))
| ~ model_max(X3,X4,X2)
| lesseq(summation(X1),X2) ),
inference(spm,[status(thm)],[c_0_146,c_0_117]) ).
cnf(c_0_150,negated_conjecture,
( ~ lesseq(esk5_0,esk4_0)
| lesseq(esk5_0,max(esk4_0,esk5_0))
| model_ub(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_147,c_0_19]) ).
cnf(c_0_151,negated_conjecture,
( ~ lesseq(esk4_0,esk5_0)
| summation(summation(esk5_0)) = summation(esk6_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_96]),c_0_52]) ).
cnf(c_0_152,negated_conjecture,
( ~ lesseq(esk5_0,esk4_0)
| ~ model_max(esk4_0,esk5_0,X1)
| lesseq(summation(esk5_0),X1)
| model_ub(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_153,negated_conjecture,
( ~ lesseq(esk4_0,esk5_0)
| ~ lesseq(summation(esk6_0),summation(X1))
| lesseq(summation(esk5_0),X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_151]) ).
cnf(c_0_154,negated_conjecture,
( ~ lesseq(esk6_0,X1)
| ~ lesseq(esk5_0,esk4_0)
| lesseq(summation(esk5_0),X1)
| model_ub(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_152,c_0_78]) ).
cnf(c_0_155,negated_conjecture,
( ~ lesseq(esk6_0,X1)
| ~ lesseq(esk4_0,esk5_0)
| lesseq(summation(esk5_0),X1) ),
inference(spm,[status(thm)],[c_0_153,c_0_117]) ).
cnf(c_0_156,negated_conjecture,
( ~ lesseq(esk6_0,X1)
| lesseq(summation(esk5_0),X1)
| model_ub(esk4_0,esk5_0,esk6_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_34]),c_0_155]) ).
cnf(c_0_157,plain,
( ~ model_ub(X3,X1,X2)
| lesseq(summation(X1),X2) ),
inference(spm,[status(thm)],[c_0_133,c_0_67]) ).
cnf(c_0_158,plain,
( ~ lesseq(X3,X2)
| ~ lesseq(X1,summation(X3))
| lesseq(X1,summation(X2)) ),
inference(spm,[status(thm)],[c_0_51,c_0_117]) ).
cnf(c_0_159,negated_conjecture,
lesseq(summation(esk5_0),esk6_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_19]),c_0_157]) ).
cnf(c_0_160,plain,
( ~ lesseq(X1,X3)
| ~ lesseq(X3,X2)
| lesseq(summation(X1),summation(X2)) ),
inference(spm,[status(thm)],[c_0_158,c_0_117]) ).
cnf(c_0_161,plain,
( ~ model_ub(X1,X2,X3)
| model_ub(X1,X2,summation(esk1_3(X1,X2,X3))) ),
inference(spm,[status(thm)],[c_0_23,c_0_60]) ).
cnf(c_0_162,negated_conjecture,
( ~ ub(X1,X2,esk5_0)
| model_ub(X1,X2,esk6_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_159]) ).
cnf(c_0_163,plain,
( ~ lesseq(X1,summation(esk1_3(X3,X4,X2)))
| ~ model_ub(X3,X4,X2)
| lesseq(summation(X1),summation(X2)) ),
inference(spm,[status(thm)],[c_0_160,c_0_69]) ).
cnf(c_0_164,plain,
( ~ model_ub(X1,X2,X3)
| lesseq(summation(X1),summation(esk1_3(X1,X2,X3))) ),
inference(spm,[status(thm)],[c_0_136,c_0_161]) ).
cnf(c_0_165,negated_conjecture,
( ~ model_ub(esk5_0,X1,summation(esk5_0))
| model_ub(esk5_0,X1,esk6_0) ),
inference(spm,[status(thm)],[c_0_162,c_0_126]) ).
cnf(c_0_166,plain,
( ~ model_ub(X1,X3,X2)
| lesseq(summation(summation(X1)),summation(X2)) ),
inference(spm,[status(thm)],[c_0_163,c_0_164]) ).
cnf(c_0_167,negated_conjecture,
( ~ lesseq(X1,esk5_0)
| model_ub(esk5_0,X1,esk6_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_26]),c_0_19])]) ).
cnf(c_0_168,negated_conjecture,
( ~ lesseq(X1,esk5_0)
| lesseq(summation(summation(esk5_0)),summation(esk6_0)) ),
inference(spm,[status(thm)],[c_0_166,c_0_167]) ).
cnf(c_0_169,negated_conjecture,
lesseq(summation(summation(esk5_0)),summation(esk6_0)),
inference(spm,[status(thm)],[c_0_168,c_0_19]) ).
cnf(c_0_170,negated_conjecture,
( ~ lesseq(esk6_0,X1)
| lesseq(summation(summation(esk5_0)),summation(X1)) ),
inference(spm,[status(thm)],[c_0_158,c_0_169]) ).
cnf(c_0_171,negated_conjecture,
( ~ lesseq(esk6_0,X1)
| lesseq(summation(esk5_0),X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_170]) ).
cnf(c_0_172,plain,
( ~ model_ub(X1,X2,summation(X2))
| esk1_3(X1,X2,summation(X2)) = X2 ),
inference(spm,[status(thm)],[c_0_73,c_0_120]) ).
cnf(c_0_173,negated_conjecture,
( ~ lesseq(esk6_0,summation(X1))
| lesseq(esk5_0,X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_171]) ).
cnf(c_0_174,plain,
( ~ model_ub(X1,X2,summation(X2))
| ub(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_60,c_0_172]) ).
cnf(c_0_175,negated_conjecture,
( ~ lesseq(X1,max(esk4_0,esk5_0))
| ~ lesseq(X2,max(esk4_0,esk5_0))
| model_ub(X1,X2,esk6_0)
| model_ub(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_72]) ).
cnf(c_0_176,negated_conjecture,
( lesseq(esk5_0,max(esk4_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_173,c_0_72]),c_0_19])]) ).
cnf(c_0_177,negated_conjecture,
( ~ lesseq(esk6_0,summation(X1))
| lesseq(esk4_0,X1)
| lesseq(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_61,c_0_107]) ).
cnf(c_0_178,negated_conjecture,
( ~ model_ub(X1,esk5_0,summation(esk5_0))
| model_ub(X1,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_162,c_0_174]) ).
cnf(c_0_179,negated_conjecture,
( ~ lesseq(X1,max(esk4_0,esk5_0))
| model_ub(X1,esk5_0,esk6_0)
| model_ub(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_175,c_0_176]) ).
cnf(c_0_180,negated_conjecture,
( lesseq(esk4_0,esk5_0)
| lesseq(esk4_0,max(esk4_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_177,c_0_72]),c_0_19])]) ).
cnf(c_0_181,negated_conjecture,
( ~ lesseq(X1,esk5_0)
| model_ub(X1,esk5_0,esk6_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_26]),c_0_19])]) ).
cnf(c_0_182,negated_conjecture,
model_ub(esk4_0,esk5_0,esk6_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_180]),c_0_181]) ).
cnf(c_0_183,negated_conjecture,
( ~ lesseq(esk5_0,X1)
| ~ lesseq(esk4_0,esk5_0)
| lesseq(esk6_0,summation(X1)) ),
inference(spm,[status(thm)],[c_0_158,c_0_52]) ).
cnf(c_0_184,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk3_3(esk4_0,esk5_0,esk6_0))
| minsol_model_ub(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_92,c_0_182]) ).
cnf(c_0_185,negated_conjecture,
( ~ lesseq(esk4_0,esk5_0)
| ~ lesseq(esk5_0,esk1_3(X2,X3,X1))
| ~ model_ub(X2,X3,X1)
| lesseq(esk6_0,X1) ),
inference(spm,[status(thm)],[c_0_130,c_0_183]) ).
cnf(c_0_186,negated_conjecture,
( ~ minsol_model_max(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_99,c_0_184]) ).
cnf(c_0_187,negated_conjecture,
( ~ lesseq(esk4_0,esk5_0)
| ~ model_ub(X2,esk5_0,X1)
| lesseq(esk6_0,X1) ),
inference(spm,[status(thm)],[c_0_185,c_0_67]) ).
cnf(c_0_188,negated_conjecture,
( ~ lesseq(esk4_0,esk5_0)
| model_ub(esk4_0,esk5_0,esk3_3(esk4_0,esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_186,c_0_106]) ).
cnf(c_0_189,negated_conjecture,
( ~ lesseq(esk4_0,esk5_0)
| lesseq(esk6_0,esk3_3(esk4_0,esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_187,c_0_188]) ).
cnf(c_0_190,negated_conjecture,
( ~ lesseq(esk4_0,esk5_0)
| minsol_model_ub(esk4_0,esk5_0,esk6_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_189]),c_0_182])]) ).
cnf(c_0_191,negated_conjecture,
( ~ lesseq(esk4_0,esk5_0)
| ~ minsol_model_max(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_99,c_0_190]) ).
cnf(c_0_192,negated_conjecture,
~ lesseq(esk4_0,esk5_0),
inference(spm,[status(thm)],[c_0_191,c_0_106]) ).
cnf(c_0_193,plain,
( ~ lesseq(X2,X1)
| minsol_model_max(X1,X2,summation(X1)) ),
inference(spm,[status(thm)],[c_0_94,c_0_47]) ).
cnf(c_0_194,negated_conjecture,
summation(esk4_0) = esk6_0,
inference(sr,[status(thm)],[c_0_107,c_0_192]) ).
cnf(c_0_195,negated_conjecture,
( ~ lesseq(X1,esk4_0)
| minsol_model_max(esk4_0,X1,esk6_0) ),
inference(spm,[status(thm)],[c_0_193,c_0_194]) ).
cnf(c_0_196,negated_conjecture,
lesseq(esk5_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_194]),c_0_19])]) ).
cnf(c_0_197,negated_conjecture,
model_ub(esk4_0,esk5_0,esk3_3(esk4_0,esk5_0,esk6_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_186,c_0_195]),c_0_196])]) ).
cnf(c_0_198,negated_conjecture,
lesseq(esk6_0,esk3_3(esk4_0,esk5_0,esk6_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_197]),c_0_194]) ).
cnf(c_0_199,negated_conjecture,
minsol_model_ub(esk4_0,esk5_0,esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_198]),c_0_182])]) ).
cnf(c_0_200,negated_conjecture,
~ minsol_model_max(esk4_0,esk5_0,esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_199])]) ).
cnf(c_0_201,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_195]),c_0_196])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM860+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.34 % Computer : n014.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 03:13:49 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.43 Running first-order theorem proving
% 0.19/0.43 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 93.68/14.14 % Version: 3.5.1
% 93.68/14.14 % Preprocessing class: FSMSSMSSSSSNFFN.
% 93.68/14.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 93.68/14.14 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 93.68/14.14 % Starting new_bool_3 with 300s (1) cores
% 93.68/14.14 % Starting new_bool_1 with 300s (1) cores
% 93.68/14.14 % Starting sh5l with 300s (1) cores
% 93.68/14.14 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3020430 completed with status 0
% 93.68/14.14 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 93.68/14.14 % Preprocessing class: FSMSSMSSSSSNFFN.
% 93.68/14.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 93.68/14.14 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 93.68/14.14 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 93.68/14.14 % No SInE strategy applied
% 93.68/14.14 % Search class: FGHSF-FFMF32-SFFFFFNN
% 93.68/14.14 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 93.68/14.14 % Starting SubtermCWHack with 151s (1) cores
% 93.68/14.14 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 901s (1) cores
% 93.68/14.14 % Starting G-E--_107_C36_F1_PI_AE_Q4_CS_SP_PS_S0Y with 151s (1) cores
% 93.68/14.14 % Starting new_bool_3 with 151s (1) cores
% 93.68/14.14 % Starting new_bool_1 with 146s (1) cores
% 93.68/14.14 % G-E--_107_C36_F1_PI_AE_Q4_CS_SP_PS_S0Y with pid 3020437 completed with status 0
% 93.68/14.14 % Result found by G-E--_107_C36_F1_PI_AE_Q4_CS_SP_PS_S0Y
% 93.68/14.14 % Preprocessing class: FSMSSMSSSSSNFFN.
% 93.68/14.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 93.68/14.14 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 93.68/14.14 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 93.68/14.14 % No SInE strategy applied
% 93.68/14.14 % Search class: FGHSF-FFMF32-SFFFFFNN
% 93.68/14.14 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 93.68/14.14 % Starting SubtermCWHack with 151s (1) cores
% 93.68/14.14 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 901s (1) cores
% 93.68/14.14 % Starting G-E--_107_C36_F1_PI_AE_Q4_CS_SP_PS_S0Y with 151s (1) cores
% 93.68/14.14 % Preprocessing time : 0.002 s
% 93.68/14.14 % Presaturation interreduction done
% 93.68/14.14
% 93.68/14.14 % Proof found!
% 93.68/14.14 % SZS status Theorem
% 93.68/14.14 % SZS output start CNFRefutation
% See solution above
% 93.68/14.14 % Parsed axioms : 14
% 93.68/14.14 % Removed by relevancy pruning/SinE : 0
% 93.68/14.14 % Initial clauses : 28
% 93.68/14.14 % Removed in clause preprocessing : 0
% 93.68/14.14 % Initial clauses in saturation : 28
% 93.68/14.14 % Processed clauses : 10272
% 93.68/14.14 % ...of these trivial : 3
% 93.68/14.14 % ...subsumed : 7608
% 93.68/14.14 % ...remaining for further processing : 2661
% 93.68/14.14 % Other redundant clauses eliminated : 0
% 93.68/14.14 % Clauses deleted for lack of memory : 0
% 93.68/14.14 % Backward-subsumed : 893
% 93.68/14.14 % Backward-rewritten : 670
% 93.68/14.14 % Generated clauses : 348099
% 93.68/14.14 % ...of the previous two non-redundant : 322227
% 93.68/14.14 % ...aggressively subsumed : 0
% 93.68/14.14 % Contextual simplify-reflections : 127
% 93.68/14.14 % Paramodulations : 347547
% 93.68/14.14 % Factorizations : 492
% 93.68/14.14 % NegExts : 0
% 93.68/14.14 % Equation resolutions : 0
% 93.68/14.14 % Disequality decompositions : 0
% 93.68/14.14 % Total rewrite steps : 21766
% 93.68/14.14 % ...of those cached : 21596
% 93.68/14.14 % Propositional unsat checks : 0
% 93.68/14.14 % Propositional check models : 0
% 93.68/14.14 % Propositional check unsatisfiable : 0
% 93.68/14.14 % Propositional clauses : 0
% 93.68/14.14 % Propositional clauses after purity: 0
% 93.68/14.14 % Propositional unsat core size : 0
% 93.68/14.14 % Propositional preprocessing time : 0.000
% 93.68/14.14 % Propositional encoding time : 0.000
% 93.68/14.14 % Propositional solver time : 0.000
% 93.68/14.14 % Success case prop preproc time : 0.000
% 93.68/14.14 % Success case prop encoding time : 0.000
% 93.68/14.14 % Success case prop solver time : 0.000
% 93.68/14.14 % Current number of processed clauses : 1010
% 93.68/14.14 % Positive orientable unit clauses : 13
% 93.68/14.14 % Positive unorientable unit clauses: 0
% 93.68/14.14 % Negative unit clauses : 2
% 93.68/14.14 % Non-unit-clauses : 995
% 93.68/14.14 % Current number of unprocessed clauses: 310843
% 93.68/14.14 % ...number of literals in the above : 1877483
% 93.68/14.14 % Current number of archived formulas : 0
% 93.68/14.14 % Current number of archived clauses : 1651
% 93.68/14.14 % Clause-clause subsumption calls (NU) : 710996
% 93.68/14.14 % Rec. Clause-clause subsumption calls : 244382
% 93.68/14.14 % Non-unit clause-clause subsumptions : 8281
% 93.68/14.14 % Unit Clause-clause subsumption calls : 4188
% 93.68/14.14 % Rewrite failures with RHS unbound : 0
% 93.68/14.14 % BW rewrite match attempts : 40
% 93.68/14.14 % BW rewrite match successes : 11
% 93.68/14.14 % Condensation attempts : 0
% 93.68/14.14 % Condensation successes : 0
% 93.68/14.14 % Termbank termtop insertions : 6563933
% 93.68/14.14 % Search garbage collected termcells : 478
% 93.68/14.14
% 93.68/14.14 % -------------------------------------------------
% 93.68/14.14 % User time : 12.799 s
% 93.68/14.14 % System time : 0.388 s
% 93.68/14.14 % Total time : 13.187 s
% 93.68/14.14 % Maximum resident set size: 3644 pages
% 93.68/14.14
% 93.68/14.14 % -------------------------------------------------
% 93.68/14.14 % User time : 63.946 s
% 93.68/14.14 % System time : 2.398 s
% 93.68/14.14 % Total time : 66.345 s
% 93.68/14.14 % Maximum resident set size: 4864 pages
% 93.68/14.14 % E exiting
%------------------------------------------------------------------------------