%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM859+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 : n017.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 01:50:52 PM UTC 2026
% Result : Theorem 53.46s 8.25s
% Output : CNFRefutation 53.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 13
% Syntax : Number of formulae : 219 ( 16 unt; 0 def)
% Number of atoms : 598 ( 61 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 621 ( 242 ~; 348 |; 19 &)
% ( 8 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 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 : 426 ( 9 sgn 82 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(lesseq_antisymmetric,axiom,
! [X1,X2] :
( ( lesseq(X2,X1)
& lesseq(X1,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_antisymmetric) ).
fof(model_ub_2,axiom,
! [X1,X2,X4] :
( model_ub(X1,X2,X4)
<=> ? [X3] :
( lesseq(X3,X4)
& ub(X1,X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',model_ub_2) ).
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(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(model_max_2,axiom,
! [X1,X2,X4] :
( model_max(X1,X2,X4)
<=> lesseq(max(X1,X2),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',model_max_2) ).
fof(lesseq_ref,axiom,
! [X1] : lesseq(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_ref) ).
fof(max_2,axiom,
! [X1,X2] :
( ~ lesseq(X1,X2)
| max(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_2) ).
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(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(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(summation_monotone,axiom,
! [X1,X2] :
( lesseq(X1,X2)
<=> lesseq(summation(X1),summation(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',summation_monotone) ).
fof(lesseq_total,axiom,
! [X1,X2] :
( lesseq(X2,X1)
| lesseq(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_total) ).
fof(c_0_13,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])])]) ).
fof(c_0_14,plain,
! [X28,X29,X30,X32,X33,X34,X35] :
( ( model_ub(X32,X33,X34)
| ~ lesseq(X35,X34)
| ~ ub(X32,X33,X35) )
& ( ~ model_ub(X28,X29,X30)
| lesseq(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_2])])])])])])]) ).
fof(c_0_15,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_16,plain,
( ~ lesseq(X2,X1)
| ~ lesseq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
( ~ model_ub(X1,X2,X3)
| lesseq(esk1_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
( ~ ub(X1,X3,X2)
| lesseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( ~ model_ub(X1,X2,X3)
| ub(X1,X2,esk1_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_20,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])])]) ).
fof(c_0_21,plain,
! [X25,X26,X27] :
( ( model_max(X25,X26,X27)
| ~ lesseq(max(X25,X26),X27) )
& ( lesseq(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_2])])]) ).
cnf(c_0_22,plain,
( ~ lesseq(X3,esk1_3(X1,X2,X3))
| ~ model_ub(X1,X2,X3)
| esk1_3(X1,X2,X3) = X3 ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,plain,
( ~ model_ub(X1,X2,X3)
| lesseq(X1,esk1_3(X1,X2,X3)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( ~ lesseq(X2,X3)
| ~ lesseq(X1,X2)
| lesseq(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
( ~ model_max(X1,X2,X3)
| lesseq(max(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,plain,
( ~ model_ub(X1,X2,X1)
| esk1_3(X1,X2,X1) = X1 ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
( ~ lesseq(X3,X4)
| ~ ub(X1,X2,X3)
| model_ub(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_28,plain,
( ~ lesseq(X3,X2)
| ~ lesseq(X1,X2)
| ub(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_29,plain,
! [X5] : lesseq(X5,X5),
inference(variable_rename,[status(thm)],[lesseq_ref]) ).
fof(c_0_30,plain,
! [X1,X2] :
( ~ lesseq(X1,X2)
| max(X1,X2) = X2 ),
inference(fof_simplification,[status(thm)],[max_2]) ).
fof(c_0_31,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]) ).
cnf(c_0_32,plain,
( ~ lesseq(X1,max(X3,X4))
| ~ model_max(X3,X4,X2)
| lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_33,plain,
( ~ model_ub(X1,X2,X1)
| ub(X1,X2,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_26]) ).
cnf(c_0_34,plain,
( ~ lesseq(X1,X4)
| ~ lesseq(X2,X4)
| ~ lesseq(X4,X3)
| model_ub(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,plain,
lesseq(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_36,plain,
! [X20,X21] :
( ~ lesseq(X20,X21)
| max(X20,X21) = X21 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_30])]) ).
fof(c_0_37,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_38,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_31])])])]) ).
cnf(c_0_39,plain,
( ~ lesseq(esk1_3(X1,X2,X4),X3)
| ~ model_ub(X1,X2,X4)
| model_ub(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_27,c_0_19]) ).
cnf(c_0_40,plain,
( ~ model_max(X3,X4,X5)
| ~ model_ub(X1,X2,max(X3,X4))
| lesseq(esk1_3(X1,X2,max(X3,X4)),X5) ),
inference(spm,[status(thm)],[c_0_32,c_0_17]) ).
cnf(c_0_41,plain,
( ~ lesseq(X1,X3)
| ~ model_ub(X1,X2,X1)
| model_ub(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_27,c_0_33]) ).
cnf(c_0_42,plain,
( ~ lesseq(X1,X3)
| ~ lesseq(X2,X3)
| model_ub(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_43,plain,
( ~ lesseq(X1,X2)
| max(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_44,plain,
( ~ lesseq(max(X1,X2),X3)
| model_max(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_45,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_46,plain,
( ~ minsol_model_ub(X1,X2,X3)
| model_ub(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_47,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_38]) ).
fof(c_0_48,plain,
! [X1,X2] :
( ~ lesseq(X2,X1)
| max(X1,X2) = X1 ),
inference(fof_simplification,[status(thm)],[max_1]) ).
cnf(c_0_49,plain,
( ~ model_max(X4,X5,X3)
| ~ model_ub(X1,X2,max(X4,X5))
| model_ub(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_50,plain,
( ~ lesseq(X2,X1)
| ~ lesseq(X1,X3)
| model_ub(X1,X2,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_35])]) ).
cnf(c_0_51,plain,
( ~ lesseq(X3,X1)
| ~ model_max(X3,X1,X2)
| lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_43]) ).
cnf(c_0_52,plain,
model_max(X1,X2,max(X1,X2)),
inference(spm,[status(thm)],[c_0_44,c_0_35]) ).
cnf(c_0_53,plain,
( ~ minsol_model_max(X1,X2,X4)
| ~ model_max(X1,X2,X3)
| lesseq(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_54,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_46,c_0_47]) ).
fof(c_0_55,plain,
! [X18,X19] :
( ~ lesseq(X19,X18)
| max(X18,X19) = X18 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_48])]) ).
fof(c_0_56,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_57,plain,
( ~ lesseq(X2,X1)
| ~ lesseq(X1,max(X4,X5))
| ~ model_max(X4,X5,X3)
| model_ub(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_58,plain,
( ~ lesseq(X2,X1)
| lesseq(X1,max(X2,X1)) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_59,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_53,c_0_54]) ).
cnf(c_0_60,plain,
( ~ lesseq(X2,X1)
| max(X1,X2) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_61,plain,
( ~ lesseq(X1,X2)
| lesseq(summation(X1),summation(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_62,plain,
( ~ lesseq(X4,X1)
| ~ lesseq(X2,X1)
| ~ model_max(X4,X1,X3)
| model_ub(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_63,plain,
( ~ lesseq(X1,X2)
| model_max(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_52,c_0_43]) ).
cnf(c_0_64,negated_conjecture,
( lesseq(esk6_0,max(esk4_0,esk5_0))
| model_ub(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_59,c_0_52]) ).
cnf(c_0_65,plain,
( ~ minsol_model_max(X1,X2,X3)
| model_max(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_66,plain,
( ~ ub(X3,X1,X2)
| lesseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_67,plain,
( ~ lesseq(X2,X1)
| model_max(X1,X2,X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_60]) ).
fof(c_0_68,plain,
! [X11,X12] :
( lesseq(X12,X11)
| lesseq(X11,X12) ),
inference(variable_rename,[status(thm)],[lesseq_total]) ).
cnf(c_0_69,plain,
( ~ lesseq(X2,X1)
| ~ lesseq(summation(X1),summation(X2))
| summation(X1) = summation(X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_61]) ).
cnf(c_0_70,plain,
( ~ lesseq(X3,X1)
| ~ lesseq(X2,X1)
| model_ub(X1,X2,X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_71,negated_conjecture,
( ~ lesseq(max(esk4_0,esk5_0),esk6_0)
| model_ub(esk4_0,esk5_0,esk6_0)
| max(esk4_0,esk5_0) = esk6_0 ),
inference(spm,[status(thm)],[c_0_16,c_0_64]) ).
cnf(c_0_72,negated_conjecture,
( model_max(esk4_0,esk5_0,esk6_0)
| model_ub(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_65,c_0_54]) ).
cnf(c_0_73,plain,
( ~ lesseq(X1,esk1_3(X3,X4,X2))
| ~ model_ub(X3,X4,X2)
| lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_17]) ).
cnf(c_0_74,plain,
( ~ model_ub(X2,X1,X3)
| lesseq(X1,esk1_3(X2,X1,X3)) ),
inference(spm,[status(thm)],[c_0_66,c_0_19]) ).
cnf(c_0_75,negated_conjecture,
( ~ lesseq(esk5_0,esk4_0)
| lesseq(esk6_0,esk4_0)
| model_ub(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_59,c_0_67]) ).
cnf(c_0_76,plain,
( lesseq(X2,X1)
| lesseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_77,plain,
( ~ lesseq(X1,X2)
| ~ lesseq(X2,X1)
| summation(X1) = summation(X2) ),
inference(spm,[status(thm)],[c_0_69,c_0_61]) ).
cnf(c_0_78,plain,
( ~ lesseq(X3,X1)
| ~ model_max(X1,X3,X2)
| lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_60]) ).
cnf(c_0_79,plain,
( ~ lesseq(X3,X2)
| ~ lesseq(X1,summation(X3))
| lesseq(X1,summation(X2)) ),
inference(spm,[status(thm)],[c_0_24,c_0_61]) ).
cnf(c_0_80,plain,
( ~ lesseq(X2,X1)
| model_ub(X1,X1,X1) ),
inference(spm,[status(thm)],[c_0_70,c_0_35]) ).
cnf(c_0_81,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk6_0)
| max(esk4_0,esk5_0) = esk6_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_25]),c_0_72]) ).
cnf(c_0_82,plain,
( ~ model_ub(X3,X1,X2)
| lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_83,negated_conjecture,
( lesseq(esk6_0,esk4_0)
| lesseq(esk4_0,esk5_0)
| model_ub(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_84,plain,
( ~ lesseq(X1,X4)
| ~ lesseq(X2,X4)
| lesseq(X3,X4)
| model_ub(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_76]) ).
cnf(c_0_85,plain,
( ~ minsol_model_ub(X1,X2,X4)
| ~ model_ub(X1,X2,X3)
| lesseq(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_86,negated_conjecture,
( ~ lesseq(max(esk4_0,esk5_0),esk6_0)
| model_ub(esk4_0,esk5_0,esk6_0)
| summation(max(esk4_0,esk5_0)) = summation(esk6_0) ),
inference(spm,[status(thm)],[c_0_77,c_0_64]) ).
cnf(c_0_87,negated_conjecture,
( ~ lesseq(esk5_0,esk4_0)
| lesseq(esk4_0,esk6_0)
| model_ub(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_78,c_0_72]) ).
cnf(c_0_88,plain,
( ~ lesseq(X1,X3)
| ~ lesseq(X3,X2)
| lesseq(summation(X1),summation(X2)) ),
inference(spm,[status(thm)],[c_0_79,c_0_61]) ).
cnf(c_0_89,plain,
( ~ lesseq(X5,X4)
| ~ model_max(X5,X4,X3)
| ~ model_ub(X1,X2,X4)
| model_ub(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_49,c_0_43]) ).
cnf(c_0_90,plain,
model_ub(X1,X1,X1),
inference(spm,[status(thm)],[c_0_80,c_0_35]) ).
cnf(c_0_91,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_44,c_0_81]) ).
cnf(c_0_92,negated_conjecture,
( lesseq(esk5_0,esk6_0)
| lesseq(esk4_0,esk5_0)
| lesseq(esk6_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_93,negated_conjecture,
( ~ lesseq(esk4_0,esk5_0)
| lesseq(esk5_0,esk6_0)
| model_ub(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_51,c_0_72]) ).
cnf(c_0_94,plain,
( ~ lesseq(X1,X2)
| lesseq(X3,X2)
| model_ub(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_84,c_0_35]) ).
cnf(c_0_95,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_85,c_0_47]) ).
cnf(c_0_96,plain,
( ~ lesseq(X3,X2)
| lesseq(X3,X1)
| lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_76]) ).
cnf(c_0_97,negated_conjecture,
( ~ lesseq(esk5_0,esk4_0)
| model_ub(esk4_0,esk5_0,esk6_0)
| summation(esk6_0) = summation(esk4_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_60]),c_0_87]) ).
cnf(c_0_98,plain,
( ~ lesseq(X1,esk1_3(X3,X4,X2))
| ~ model_ub(X3,X4,X2)
| lesseq(summation(X1),summation(X2)) ),
inference(spm,[status(thm)],[c_0_88,c_0_17]) ).
cnf(c_0_99,plain,
( ~ lesseq(X3,X1)
| ~ model_max(X3,X1,X2)
| model_ub(X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_100,negated_conjecture,
( lesseq(esk5_0,esk6_0)
| model_max(esk4_0,esk5_0,esk4_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93]),c_0_82]) ).
cnf(c_0_101,plain,
( lesseq(X2,X1)
| model_ub(X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_94,c_0_35]) ).
cnf(c_0_102,negated_conjecture,
( ~ lesseq(esk4_0,X1)
| ~ lesseq(esk5_0,X1)
| lesseq(esk6_0,X1)
| minsol_model_max(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_95,c_0_42]) ).
cnf(c_0_103,plain,
( ~ lesseq(X2,X3)
| lesseq(X3,X1)
| lesseq(X1,max(X2,X3)) ),
inference(spm,[status(thm)],[c_0_96,c_0_58]) ).
cnf(c_0_104,plain,
( ~ lesseq(summation(X1),summation(X2))
| lesseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_105,negated_conjecture,
( lesseq(esk4_0,esk5_0)
| model_ub(esk4_0,esk5_0,esk6_0)
| summation(esk6_0) = summation(esk4_0) ),
inference(spm,[status(thm)],[c_0_97,c_0_76]) ).
cnf(c_0_106,plain,
( ~ model_ub(X3,X1,X2)
| lesseq(summation(X1),summation(X2)) ),
inference(spm,[status(thm)],[c_0_98,c_0_74]) ).
cnf(c_0_107,negated_conjecture,
( lesseq(esk5_0,esk6_0)
| model_ub(esk5_0,esk5_0,esk4_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_101]) ).
cnf(c_0_108,negated_conjecture,
( ~ lesseq(X1,esk5_0)
| ~ lesseq(esk4_0,max(X1,esk5_0))
| lesseq(esk6_0,max(X1,esk5_0))
| minsol_model_max(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_102,c_0_58]) ).
cnf(c_0_109,plain,
( lesseq(X2,X1)
| lesseq(X1,max(X2,X2)) ),
inference(spm,[status(thm)],[c_0_103,c_0_35]) ).
cnf(c_0_110,negated_conjecture,
( ~ lesseq(summation(X1),summation(esk4_0))
| lesseq(X1,esk6_0)
| lesseq(esk4_0,esk5_0)
| model_ub(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_111,negated_conjecture,
( lesseq(esk5_0,esk6_0)
| lesseq(summation(esk5_0),summation(esk4_0)) ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_112,plain,
( ~ lesseq(X1,max(X2,X3))
| ~ model_max(X2,X3,X1)
| X1 = max(X2,X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_25]) ).
cnf(c_0_113,negated_conjecture,
( lesseq(esk5_0,esk4_0)
| lesseq(esk6_0,max(esk5_0,esk5_0))
| minsol_model_max(esk4_0,esk5_0,esk6_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_35])]) ).
cnf(c_0_114,negated_conjecture,
lesseq(esk5_0,esk6_0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_93]),c_0_82]) ).
cnf(c_0_115,negated_conjecture,
( ~ model_max(esk5_0,esk5_0,esk6_0)
| lesseq(esk5_0,esk4_0)
| minsol_model_max(esk4_0,esk5_0,esk6_0)
| max(esk5_0,esk5_0) = esk6_0 ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_116,plain,
( ~ lesseq(X1,X2)
| ~ lesseq(X2,X3)
| model_max(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_44,c_0_43]) ).
cnf(c_0_117,negated_conjecture,
( lesseq(esk5_0,esk4_0)
| lesseq(esk5_0,esk6_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_100]),c_0_76]) ).
cnf(c_0_118,negated_conjecture,
( lesseq(X1,esk6_0)
| lesseq(esk5_0,X1) ),
inference(spm,[status(thm)],[c_0_96,c_0_114]) ).
cnf(c_0_119,plain,
( ~ model_ub(X1,X3,X2)
| lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_73,c_0_23]) ).
cnf(c_0_120,plain,
( ~ lesseq(X1,max(X2,X3))
| ~ model_max(X2,X3,X1)
| summation(X1) = summation(max(X2,X3)) ),
inference(spm,[status(thm)],[c_0_77,c_0_25]) ).
cnf(c_0_121,plain,
( ~ lesseq(X2,X1)
| lesseq(X1,max(X1,X2)) ),
inference(spm,[status(thm)],[c_0_78,c_0_52]) ).
cnf(c_0_122,plain,
( ~ lesseq(X3,X2)
| ~ lesseq(X1,X2)
| ~ model_max(X3,X2,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_112,c_0_43]) ).
cnf(c_0_123,plain,
( ~ lesseq(X2,X1)
| ~ lesseq(X1,X3)
| model_max(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_44,c_0_60]) ).
cnf(c_0_124,plain,
( ~ lesseq(X3,X4)
| ~ lesseq(X1,X4)
| ~ model_max(X3,X4,X2)
| lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_43]) ).
cnf(c_0_125,negated_conjecture,
( lesseq(esk5_0,esk4_0)
| minsol_model_max(esk4_0,esk5_0,esk6_0)
| max(esk5_0,esk5_0) = esk6_0 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_35])]),c_0_117]) ).
cnf(c_0_126,plain,
( lesseq(X3,max(X1,X2))
| model_max(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_44,c_0_76]) ).
cnf(c_0_127,negated_conjecture,
lesseq(esk4_0,esk6_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_118]),c_0_119]) ).
cnf(c_0_128,plain,
( ~ lesseq(X2,X1)
| summation(max(X1,X2)) = summation(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_67]) ).
cnf(c_0_129,plain,
( ~ lesseq(X2,X3)
| ~ lesseq(X3,X1)
| ~ lesseq(X1,X2)
| X1 = X2 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_24]) ).
cnf(c_0_130,plain,
( ~ lesseq(X2,X3)
| ~ lesseq(X1,X3)
| lesseq(X1,max(X2,X3)) ),
inference(spm,[status(thm)],[c_0_124,c_0_52]) ).
cnf(c_0_131,negated_conjecture,
( lesseq(esk5_0,esk4_0)
| model_max(esk5_0,esk5_0,esk6_0)
| minsol_model_max(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_52,c_0_125]) ).
cnf(c_0_132,plain,
( ~ lesseq(X1,X2)
| lesseq(X3,X2)
| model_max(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_126,c_0_43]) ).
cnf(c_0_133,negated_conjecture,
( ~ lesseq(X1,esk4_0)
| lesseq(X1,esk6_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_127]) ).
cnf(c_0_134,plain,
( ~ lesseq(X2,X1)
| ~ lesseq(summation(X1),summation(X3))
| lesseq(max(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_104,c_0_128]) ).
cnf(c_0_135,plain,
( ~ lesseq(X1,X2)
| summation(max(X1,X2)) = summation(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_58]),c_0_63]) ).
cnf(c_0_136,negated_conjecture,
( ~ lesseq(esk6_0,X1)
| ~ lesseq(X1,esk4_0)
| esk6_0 = esk4_0 ),
inference(spm,[status(thm)],[c_0_129,c_0_127]) ).
cnf(c_0_137,plain,
( ~ lesseq(X2,X3)
| ~ lesseq(X1,X3)
| ~ model_max(X2,X3,X1)
| X1 = max(X2,X3) ),
inference(spm,[status(thm)],[c_0_112,c_0_130]) ).
cnf(c_0_138,negated_conjecture,
( lesseq(esk5_0,esk4_0)
| model_max(esk4_0,esk5_0,esk6_0)
| model_max(esk5_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_65,c_0_131]) ).
cnf(c_0_139,plain,
( lesseq(X3,X2)
| lesseq(X2,X1)
| model_max(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_132,c_0_76]) ).
cnf(c_0_140,negated_conjecture,
( ~ lesseq(max(X1,X2),esk4_0)
| model_max(X1,X2,esk6_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_133]) ).
cnf(c_0_141,plain,
( ~ lesseq(X2,X1)
| lesseq(max(X1,X2),X1) ),
inference(spm,[status(thm)],[c_0_134,c_0_35]) ).
cnf(c_0_142,negated_conjecture,
( ~ lesseq(X1,esk5_0)
| lesseq(X1,esk6_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_114]) ).
cnf(c_0_143,plain,
( ~ lesseq(X1,X2)
| ~ lesseq(summation(X2),summation(X3))
| lesseq(max(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_104,c_0_135]) ).
cnf(c_0_144,negated_conjecture,
( ~ lesseq(esk6_0,max(X1,X2))
| ~ model_max(X1,X2,esk4_0)
| esk6_0 = esk4_0 ),
inference(spm,[status(thm)],[c_0_136,c_0_25]) ).
cnf(c_0_145,negated_conjecture,
( lesseq(esk5_0,esk4_0)
| model_max(esk4_0,esk5_0,esk6_0)
| max(esk5_0,esk5_0) = esk6_0 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_35])]),c_0_139]) ).
cnf(c_0_146,negated_conjecture,
( ~ lesseq(X1,esk4_0)
| model_max(esk4_0,X1,esk6_0) ),
inference(spm,[status(thm)],[c_0_140,c_0_141]) ).
cnf(c_0_147,negated_conjecture,
( ~ lesseq(max(X1,X2),esk5_0)
| model_max(X1,X2,esk6_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_142]) ).
cnf(c_0_148,plain,
( ~ lesseq(X1,X2)
| lesseq(max(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_143,c_0_35]) ).
cnf(c_0_149,plain,
( ~ lesseq(X1,esk1_3(X4,X5,X3))
| ~ lesseq(X2,esk1_3(X4,X5,X3))
| ~ model_ub(X4,X5,X3)
| model_ub(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_17]) ).
cnf(c_0_150,negated_conjecture,
( ~ model_max(esk5_0,esk5_0,esk4_0)
| model_max(esk4_0,esk5_0,esk6_0)
| esk6_0 = esk4_0 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_35])]),c_0_146]) ).
cnf(c_0_151,plain,
( lesseq(X2,X1)
| model_max(X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_132,c_0_35]) ).
cnf(c_0_152,negated_conjecture,
( ~ lesseq(X1,esk5_0)
| model_max(X1,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_147,c_0_148]) ).
cnf(c_0_153,plain,
( ~ lesseq(X3,X1)
| lesseq(X1,X2)
| model_ub(X1,X2,X1) ),
inference(spm,[status(thm)],[c_0_70,c_0_76]) ).
cnf(c_0_154,plain,
( ~ lesseq(X1,esk1_3(X4,X2,X3))
| ~ model_ub(X4,X2,X3)
| model_ub(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_149,c_0_74]) ).
cnf(c_0_155,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_45]) ).
cnf(c_0_156,negated_conjecture,
( model_max(esk4_0,esk5_0,esk6_0)
| esk6_0 = esk4_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_151]),c_0_152]) ).
cnf(c_0_157,plain,
( lesseq(X1,X2)
| model_ub(X1,X2,X1) ),
inference(spm,[status(thm)],[c_0_153,c_0_35]) ).
cnf(c_0_158,plain,
( ~ lesseq(X1,X2)
| ~ model_ub(X2,X3,X4)
| lesseq(X1,esk1_3(X2,X3,X4)) ),
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_159,plain,
( ~ lesseq(X1,X3)
| ~ model_ub(X3,X2,X3)
| model_ub(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_154,c_0_26]) ).
cnf(c_0_160,negated_conjecture,
( model_max(esk4_0,esk5_0,esk2_3(esk4_0,esk5_0,esk6_0))
| minsol_model_max(esk4_0,esk5_0,esk6_0)
| esk6_0 = esk4_0 ),
inference(spm,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_161,negated_conjecture,
( lesseq(esk6_0,esk4_0)
| lesseq(esk4_0,esk5_0)
| minsol_model_max(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_95,c_0_157]) ).
cnf(c_0_162,plain,
( ~ lesseq(X1,X4)
| ~ model_ub(X4,X2,X3)
| model_ub(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_154,c_0_158]) ).
cnf(c_0_163,plain,
( ~ lesseq(X1,X2)
| model_ub(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_159,c_0_90]) ).
cnf(c_0_164,negated_conjecture,
( ~ lesseq(esk4_0,X1)
| ~ lesseq(esk5_0,esk4_0)
| lesseq(esk6_0,X1)
| minsol_model_max(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_95,c_0_50]) ).
cnf(c_0_165,negated_conjecture,
( ~ lesseq(esk5_0,esk4_0)
| lesseq(esk4_0,esk2_3(esk4_0,esk5_0,esk6_0))
| minsol_model_max(esk4_0,esk5_0,esk6_0)
| esk6_0 = esk4_0 ),
inference(spm,[status(thm)],[c_0_78,c_0_160]) ).
cnf(c_0_166,negated_conjecture,
( ~ model_max(esk4_0,esk5_0,X1)
| lesseq(esk6_0,X1)
| lesseq(esk4_0,esk5_0)
| lesseq(esk6_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_53,c_0_161]) ).
cnf(c_0_167,plain,
( ~ lesseq(X3,X2)
| ~ lesseq(X1,X3)
| model_ub(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_162,c_0_163]) ).
cnf(c_0_168,negated_conjecture,
( ~ lesseq(esk4_0,X1)
| lesseq(esk6_0,X1)
| lesseq(esk4_0,esk5_0)
| minsol_model_max(esk4_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_164,c_0_76]) ).
cnf(c_0_169,negated_conjecture,
( lesseq(esk4_0,esk5_0)
| lesseq(esk4_0,esk2_3(esk4_0,esk5_0,esk6_0))
| minsol_model_max(esk4_0,esk5_0,esk6_0)
| esk6_0 = esk4_0 ),
inference(spm,[status(thm)],[c_0_165,c_0_76]) ).
cnf(c_0_170,plain,
( ~ lesseq(X3,X4)
| ~ lesseq(X4,X2)
| ~ lesseq(X4,X3)
| ~ lesseq(X1,X3)
| lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_124,c_0_123]) ).
cnf(c_0_171,negated_conjecture,
( lesseq(esk6_0,esk4_0)
| lesseq(esk4_0,esk5_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_67]),c_0_76]) ).
cnf(c_0_172,plain,
( ~ lesseq(X3,X1)
| ~ lesseq(max(X3,X1),X2)
| model_ub(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_167,c_0_58]) ).
cnf(c_0_173,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_45]) ).
cnf(c_0_174,negated_conjecture,
( lesseq(esk4_0,esk5_0)
| lesseq(esk6_0,esk2_3(esk4_0,esk5_0,esk6_0))
| minsol_model_max(esk4_0,esk5_0,esk6_0)
| esk6_0 = esk4_0 ),
inference(spm,[status(thm)],[c_0_168,c_0_169]) ).
cnf(c_0_175,plain,
( ~ lesseq(X5,X2)
| ~ lesseq(esk1_3(X1,X3,X4),X5)
| ~ lesseq(X5,esk1_3(X1,X3,X4))
| ~ model_ub(X1,X3,X4)
| lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_170,c_0_23]) ).
cnf(c_0_176,negated_conjecture,
( lesseq(esk4_0,esk5_0)
| esk6_0 = esk4_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_171]),c_0_127])]) ).
cnf(c_0_177,plain,
( ~ lesseq(X3,X1)
| ~ model_max(X3,X1,X2)
| model_ub(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_172,c_0_25]) ).
cnf(c_0_178,negated_conjecture,
( lesseq(esk4_0,esk5_0)
| minsol_model_max(esk4_0,esk5_0,esk6_0)
| esk6_0 = esk4_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_174]),c_0_156]) ).
cnf(c_0_179,plain,
( ~ lesseq(esk1_3(X1,X3,X4),X2)
| ~ model_ub(X1,X3,X4)
| lesseq(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_35]),c_0_35])]) ).
cnf(c_0_180,plain,
( ~ model_ub(X1,X2,X2)
| esk1_3(X1,X2,X2) = X2 ),
inference(spm,[status(thm)],[c_0_22,c_0_74]) ).
cnf(c_0_181,negated_conjecture,
( ~ lesseq(esk5_0,X1)
| model_ub(esk4_0,X1,X1)
| esk6_0 = esk4_0 ),
inference(spm,[status(thm)],[c_0_167,c_0_176]) ).
cnf(c_0_182,negated_conjecture,
( model_ub(esk5_0,esk2_3(esk4_0,esk5_0,esk6_0),esk2_3(esk4_0,esk5_0,esk6_0))
| minsol_model_max(esk4_0,esk5_0,esk6_0)
| esk6_0 = esk4_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_160]),c_0_178]) ).
cnf(c_0_183,plain,
( ~ lesseq(X3,X2)
| ~ model_ub(X1,X3,X3)
| lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_179,c_0_180]) ).
cnf(c_0_184,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk5_0)
| esk6_0 = esk4_0 ),
inference(spm,[status(thm)],[c_0_181,c_0_35]) ).
cnf(c_0_185,negated_conjecture,
( lesseq(esk5_0,esk2_3(esk4_0,esk5_0,esk6_0))
| minsol_model_max(esk4_0,esk5_0,esk6_0)
| esk6_0 = esk4_0 ),
inference(spm,[status(thm)],[c_0_119,c_0_182]) ).
cnf(c_0_186,negated_conjecture,
( ~ lesseq(esk5_0,X1)
| lesseq(esk4_0,X1)
| esk6_0 = esk4_0 ),
inference(spm,[status(thm)],[c_0_183,c_0_184]) ).
cnf(c_0_187,negated_conjecture,
( ~ lesseq(esk4_0,esk2_3(esk4_0,esk5_0,esk6_0))
| lesseq(esk6_0,esk2_3(esk4_0,esk5_0,esk6_0))
| minsol_model_max(esk4_0,esk5_0,esk6_0)
| esk6_0 = esk4_0 ),
inference(spm,[status(thm)],[c_0_102,c_0_185]) ).
cnf(c_0_188,negated_conjecture,
( lesseq(esk4_0,esk2_3(esk4_0,esk5_0,esk6_0))
| minsol_model_max(esk4_0,esk5_0,esk6_0)
| esk6_0 = esk4_0 ),
inference(spm,[status(thm)],[c_0_186,c_0_185]) ).
cnf(c_0_189,negated_conjecture,
( lesseq(esk6_0,esk2_3(esk4_0,esk5_0,esk6_0))
| minsol_model_max(esk4_0,esk5_0,esk6_0)
| esk6_0 = esk4_0 ),
inference(spm,[status(thm)],[c_0_187,c_0_188]) ).
cnf(c_0_190,plain,
( ~ lesseq(X1,esk1_3(X2,X4,X3))
| ~ model_ub(X2,X4,X3)
| model_ub(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_149,c_0_23]) ).
cnf(c_0_191,negated_conjecture,
( ~ lesseq(X1,esk5_0)
| model_ub(esk5_0,esk6_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_177,c_0_152]) ).
cnf(c_0_192,negated_conjecture,
( minsol_model_max(esk4_0,esk5_0,esk6_0)
| esk6_0 = esk4_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_189]),c_0_156]) ).
cnf(c_0_193,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_37]) ).
cnf(c_0_194,plain,
( ~ model_ub(X2,X1,X3)
| model_ub(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_190,c_0_74]) ).
cnf(c_0_195,negated_conjecture,
model_ub(esk5_0,esk6_0,esk6_0),
inference(spm,[status(thm)],[c_0_191,c_0_35]) ).
cnf(c_0_196,negated_conjecture,
( ~ model_max(esk4_0,esk5_0,X1)
| lesseq(esk6_0,X1)
| esk6_0 = esk4_0 ),
inference(spm,[status(thm)],[c_0_53,c_0_192]) ).
cnf(c_0_197,negated_conjecture,
( model_ub(esk4_0,esk5_0,esk3_3(esk4_0,esk5_0,esk5_0))
| minsol_model_ub(esk4_0,esk5_0,esk5_0)
| esk6_0 = esk4_0 ),
inference(spm,[status(thm)],[c_0_193,c_0_184]) ).
cnf(c_0_198,negated_conjecture,
model_ub(esk6_0,esk5_0,esk6_0),
inference(spm,[status(thm)],[c_0_194,c_0_195]) ).
cnf(c_0_199,negated_conjecture,
( lesseq(esk6_0,esk5_0)
| esk6_0 = esk4_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_63]),c_0_176]) ).
cnf(c_0_200,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_37]) ).
cnf(c_0_201,negated_conjecture,
( lesseq(esk5_0,esk3_3(esk4_0,esk5_0,esk5_0))
| minsol_model_ub(esk4_0,esk5_0,esk5_0)
| esk6_0 = esk4_0 ),
inference(spm,[status(thm)],[c_0_82,c_0_197]) ).
cnf(c_0_202,negated_conjecture,
( model_ub(esk6_0,esk5_0,esk3_3(esk6_0,esk5_0,esk6_0))
| minsol_model_ub(esk6_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_193,c_0_198]) ).
cnf(c_0_203,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_38]) ).
cnf(c_0_204,negated_conjecture,
( esk6_0 = esk5_0
| esk6_0 = esk4_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_199]),c_0_114])]) ).
cnf(c_0_205,negated_conjecture,
( minsol_model_ub(esk4_0,esk5_0,esk5_0)
| esk6_0 = esk4_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_201]),c_0_184]) ).
cnf(c_0_206,negated_conjecture,
( lesseq(esk6_0,esk3_3(esk6_0,esk5_0,esk6_0))
| minsol_model_ub(esk6_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_119,c_0_202]) ).
cnf(c_0_207,negated_conjecture,
( ~ minsol_model_max(esk4_0,esk5_0,esk5_0)
| esk6_0 = esk4_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_203,c_0_204]),c_0_205]) ).
cnf(c_0_208,negated_conjecture,
( esk5_0 != esk4_0
| esk6_0 = esk4_0 ),
inference(ef,[status(thm)],[c_0_204]) ).
cnf(c_0_209,negated_conjecture,
minsol_model_ub(esk6_0,esk5_0,esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_206]),c_0_198])]) ).
cnf(c_0_210,negated_conjecture,
esk6_0 = esk4_0,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_204]),c_0_207]),c_0_208]) ).
cnf(c_0_211,plain,
( ~ model_max(X1,X2,max(X3,X4))
| ~ model_max(X3,X4,esk2_3(X1,X2,max(X3,X4)))
| minsol_model_max(X1,X2,max(X3,X4)) ),
inference(spm,[status(thm)],[c_0_173,c_0_25]) ).
cnf(c_0_212,plain,
( model_max(X1,X2,esk2_3(X1,X2,max(X1,X2)))
| minsol_model_max(X1,X2,max(X1,X2)) ),
inference(spm,[status(thm)],[c_0_155,c_0_52]) ).
cnf(c_0_213,negated_conjecture,
minsol_model_ub(esk4_0,esk5_0,esk4_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_209,c_0_210]),c_0_210]) ).
cnf(c_0_214,plain,
minsol_model_max(X1,X2,max(X1,X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_211,c_0_212]),c_0_52])]) ).
cnf(c_0_215,negated_conjecture,
~ minsol_model_max(esk4_0,esk5_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_203,c_0_210]),c_0_210]),c_0_213])]) ).
cnf(c_0_216,plain,
( ~ lesseq(X2,X1)
| minsol_model_max(X1,X2,X1) ),
inference(spm,[status(thm)],[c_0_214,c_0_60]) ).
cnf(c_0_217,negated_conjecture,
lesseq(esk5_0,esk4_0),
inference(rw,[status(thm)],[c_0_114,c_0_210]) ).
cnf(c_0_218,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_216]),c_0_217])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM859+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n017.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 03:08:57 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 53.46/8.25 % Version: 3.5.1
% 53.46/8.25 % Preprocessing class: FSMSSMSSSSSNFFN.
% 53.46/8.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 53.46/8.25 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 53.46/8.25 % Starting new_bool_3 with 300s (1) cores
% 53.46/8.25 % Starting new_bool_1 with 300s (1) cores
% 53.46/8.25 % Starting sh5l with 300s (1) cores
% 53.46/8.25 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1294551 completed with status 0
% 53.46/8.25 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 53.46/8.25 % Preprocessing class: FSMSSMSSSSSNFFN.
% 53.46/8.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 53.46/8.25 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 53.46/8.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 53.46/8.25 % No SInE strategy applied
% 53.46/8.25 % Search class: FGHSF-FFMF32-SFFFFFNN
% 53.46/8.25 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 53.46/8.25 % Starting SubtermCWHack with 151s (1) cores
% 53.46/8.25 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 901s (1) cores
% 53.46/8.25 % Starting G-E--_107_C36_F1_PI_AE_Q4_CS_SP_PS_S0Y with 151s (1) cores
% 53.46/8.25 % Starting new_bool_3 with 151s (1) cores
% 53.46/8.25 % Starting new_bool_1 with 146s (1) cores
% 53.46/8.25 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1294556 completed with status 0
% 53.46/8.25 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 53.46/8.25 % Preprocessing class: FSMSSMSSSSSNFFN.
% 53.46/8.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 53.46/8.25 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 53.46/8.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 53.46/8.25 % No SInE strategy applied
% 53.46/8.25 % Search class: FGHSF-FFMF32-SFFFFFNN
% 53.46/8.25 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 53.46/8.25 % Starting SubtermCWHack with 151s (1) cores
% 53.46/8.25 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 901s (1) cores
% 53.46/8.25 % Preprocessing time : 0.002 s
% 53.46/8.25 % Presaturation interreduction done
% 53.46/8.25
% 53.46/8.25 % Proof found!
% 53.46/8.25 % SZS status Theorem
% 53.46/8.25 % SZS output start CNFRefutation
% See solution above
% 53.46/8.25 % Parsed axioms : 14
% 53.46/8.25 % Removed by relevancy pruning/SinE : 0
% 53.46/8.25 % Initial clauses : 28
% 53.46/8.25 % Removed in clause preprocessing : 0
% 53.46/8.25 % Initial clauses in saturation : 28
% 53.46/8.25 % Processed clauses : 15525
% 53.46/8.25 % ...of these trivial : 23
% 53.46/8.25 % ...subsumed : 12417
% 53.46/8.25 % ...remaining for further processing : 3085
% 53.46/8.25 % Other redundant clauses eliminated : 0
% 53.46/8.25 % Clauses deleted for lack of memory : 0
% 53.46/8.25 % Backward-subsumed : 489
% 53.46/8.25 % Backward-rewritten : 1386
% 53.46/8.25 % Generated clauses : 439170
% 53.46/8.25 % ...of the previous two non-redundant : 423263
% 53.46/8.25 % ...aggressively subsumed : 0
% 53.46/8.25 % Contextual simplify-reflections : 116
% 53.46/8.25 % Paramodulations : 438795
% 53.46/8.25 % Factorizations : 375
% 53.46/8.25 % NegExts : 0
% 53.46/8.25 % Equation resolutions : 0
% 53.46/8.25 % Disequality decompositions : 0
% 53.46/8.25 % Total rewrite steps : 32324
% 53.46/8.25 % ...of those cached : 32160
% 53.46/8.25 % Propositional unsat checks : 0
% 53.46/8.25 % Propositional check models : 0
% 53.46/8.25 % Propositional check unsatisfiable : 0
% 53.46/8.25 % Propositional clauses : 0
% 53.46/8.25 % Propositional clauses after purity: 0
% 53.46/8.25 % Propositional unsat core size : 0
% 53.46/8.25 % Propositional preprocessing time : 0.000
% 53.46/8.25 % Propositional encoding time : 0.000
% 53.46/8.25 % Propositional solver time : 0.000
% 53.46/8.25 % Success case prop preproc time : 0.000
% 53.46/8.25 % Success case prop encoding time : 0.000
% 53.46/8.25 % Success case prop solver time : 0.000
% 53.46/8.25 % Current number of processed clauses : 1182
% 53.46/8.25 % Positive orientable unit clauses : 11
% 53.46/8.25 % Positive unorientable unit clauses: 0
% 53.46/8.25 % Negative unit clauses : 3
% 53.46/8.25 % Non-unit-clauses : 1168
% 53.46/8.25 % Current number of unprocessed clauses: 405423
% 53.46/8.25 % ...number of literals in the above : 1995050
% 53.46/8.25 % Current number of archived formulas : 0
% 53.46/8.25 % Current number of archived clauses : 1903
% 53.46/8.25 % Clause-clause subsumption calls (NU) : 1051442
% 53.46/8.25 % Rec. Clause-clause subsumption calls : 583910
% 53.46/8.25 % Non-unit clause-clause subsumptions : 12978
% 53.46/8.25 % Unit Clause-clause subsumption calls : 3386
% 53.46/8.25 % Rewrite failures with RHS unbound : 0
% 53.46/8.25 % BW rewrite match attempts : 70
% 53.46/8.25 % BW rewrite match successes : 21
% 53.46/8.25 % Condensation attempts : 0
% 53.46/8.25 % Condensation successes : 0
% 53.46/8.25 % Termbank termtop insertions : 6490378
% 53.46/8.25 % Search garbage collected termcells : 477
% 53.46/8.25
% 53.46/8.25 % -------------------------------------------------
% 53.46/8.25 % User time : 7.281 s
% 53.46/8.25 % System time : 0.276 s
% 53.46/8.25 % Total time : 7.557 s
% 53.46/8.25 % Maximum resident set size: 3644 pages
% 53.46/8.25
% 53.46/8.25 % -------------------------------------------------
% 53.46/8.25 % User time : 36.143 s
% 53.46/8.25 % System time : 1.655 s
% 53.46/8.25 % Total time : 37.798 s
% 53.46/8.25 % Maximum resident set size: 4864 pages
% 53.46/8.25 % E exiting
%------------------------------------------------------------------------------