%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM858+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 0.59s 0.51s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 12
% Syntax : Number of formulae : 105 ( 11 unt; 0 def)
% Number of atoms : 274 ( 31 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 275 ( 106 ~; 142 |; 16 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 184 ( 4 sgn 74 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(model_max_1,axiom,
! [X1,X2,X4] :
( model_max(X1,X2,X4)
<=> X4 = max(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',model_max_1) ).
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/sandbox2/benchmark/theBenchmark.p',minsol_model_max) ).
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(lesseq_ref,axiom,
! [X1] : lesseq(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lesseq_ref) ).
fof(max_1,axiom,
! [X1,X2] :
( ~ lesseq(X2,X1)
| max(X1,X2) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',max_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/sandbox2/benchmark/theBenchmark.p',minsol_model_ub) ).
fof(max_2,axiom,
! [X1,X2] :
( ~ lesseq(X1,X2)
| max(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',max_2) ).
fof(ub,axiom,
! [X1,X2,X3] :
( ub(X1,X2,X3)
<=> ( lesseq(X2,X3)
& lesseq(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ub) ).
fof(model_ub_1,axiom,
! [X1,X2,X4] :
( model_ub(X1,X2,X4)
<=> ub(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',model_ub_1) ).
fof(lesseq_trans,axiom,
! [X1,X2,X3] :
( ( lesseq(X2,X3)
& lesseq(X1,X2) )
=> lesseq(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lesseq_trans) ).
fof(lesseq_total,axiom,
! [X1,X2] :
( lesseq(X2,X1)
| lesseq(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lesseq_total) ).
fof(lesseq_antisymmetric,axiom,
! [X1,X2] :
( ( lesseq(X2,X1)
& lesseq(X1,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lesseq_antisymmetric) ).
fof(c_0_12,plain,
! [X32,X33,X34] :
( ( model_max(X32,X33,X34)
| X34 != max(X32,X33) )
& ( X34 = max(X32,X33)
| ~ model_max(X32,X33,X34) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[model_max_1])])]) ).
fof(c_0_13,plain,
! [X8,X9,X10,X11,X12,X13,X14] :
( ( minsol_model_max(X12,X13,X14)
| ~ model_max(X12,X13,X14)
| ~ lesseq(X14,esk4_3(X12,X13,X14)) )
& ( minsol_model_max(X12,X13,X14)
| ~ model_max(X12,X13,X14)
| model_max(X12,X13,esk4_3(X12,X13,X14)) )
& ( ~ minsol_model_max(X8,X9,X10)
| lesseq(X10,X11)
| ~ model_max(X8,X9,X11) )
& ( ~ minsol_model_max(X8,X9,X10)
| model_max(X8,X9,X10) ) ),
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_14,plain,
( ~ model_max(X1,X2,X3)
| X3 = max(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,plain,
( ~ model_max(X1,X2,X3)
| minsol_model_max(X1,X2,X3)
| model_max(X1,X2,esk4_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_16,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_17,plain,
( ~ model_max(X2,X3,X1)
| ~ lesseq(X1,esk4_3(X2,X3,X1))
| minsol_model_max(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( ~ model_max(X1,X2,X3)
| minsol_model_max(X1,X2,X3)
| esk4_3(X1,X2,X3) = max(X1,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_19,plain,
! [X24] : lesseq(X24,X24),
inference(variable_rename,[status(thm)],[lesseq_ref]) ).
cnf(c_0_20,plain,
( X1 != max(X2,X3)
| model_max(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_21,plain,
! [X1,X2] :
( ~ lesseq(X2,X1)
| max(X1,X2) = X1 ),
inference(fof_simplification,[status(thm)],[max_1]) ).
fof(c_0_22,plain,
! [X16,X17,X18,X19,X20,X21,X22] :
( ( minsol_model_ub(X20,X21,X22)
| ~ model_ub(X20,X21,X22)
| ~ lesseq(X22,esk5_3(X20,X21,X22)) )
& ( minsol_model_ub(X20,X21,X22)
| ~ model_ub(X20,X21,X22)
| model_ub(X20,X21,esk5_3(X20,X21,X22)) )
& ( ~ minsol_model_ub(X16,X17,X18)
| lesseq(X18,X19)
| ~ model_ub(X16,X17,X19) )
& ( ~ minsol_model_ub(X16,X17,X18)
| model_ub(X16,X17,X18) ) ),
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_23,negated_conjecture,
( ( 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)
| ~ minsol_model_ub(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_16])])])]) ).
fof(c_0_24,plain,
! [X1,X2] :
( ~ lesseq(X1,X2)
| max(X1,X2) = X2 ),
inference(fof_simplification,[status(thm)],[max_2]) ).
cnf(c_0_25,plain,
( ~ lesseq(X3,max(X1,X2))
| ~ model_max(X1,X2,X3)
| minsol_model_max(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_26,plain,
lesseq(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
model_max(X1,X2,max(X1,X2)),
inference(er,[status(thm)],[c_0_20]) ).
fof(c_0_28,plain,
! [X38,X39] :
( ~ lesseq(X39,X38)
| max(X38,X39) = X38 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_21])]) ).
fof(c_0_29,plain,
! [X42,X43,X44] :
( ( ub(X42,X43,X44)
| ~ lesseq(X43,X44)
| ~ lesseq(X42,X44) )
& ( ~ ub(X42,X43,X44)
| lesseq(X43,X44) )
& ( ~ ub(X42,X43,X44)
| lesseq(X42,X44) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ub])])])]) ).
fof(c_0_30,plain,
! [X35,X36,X37] :
( ( model_ub(X35,X36,X37)
| ~ ub(X35,X36,X37) )
& ( ub(X35,X36,X37)
| ~ model_ub(X35,X36,X37) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[model_ub_1])])]) ).
cnf(c_0_31,plain,
( ~ minsol_model_ub(X1,X2,X3)
| model_ub(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,negated_conjecture,
( minsol_model_max(esk1_0,esk2_0,esk3_0)
| minsol_model_ub(esk1_0,esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_33,plain,
! [X40,X41] :
( ~ lesseq(X40,X41)
| max(X40,X41) = X41 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_24])]) ).
cnf(c_0_34,plain,
minsol_model_max(X1,X2,max(X1,X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_35,plain,
( ~ lesseq(X2,X1)
| max(X1,X2) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,plain,
( ~ ub(X1,X3,X2)
| lesseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_37,plain,
( ~ model_ub(X1,X2,X3)
| ub(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_38,plain,
( ~ minsol_model_max(X1,X2,X3)
| model_max(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_39,negated_conjecture,
( model_ub(esk1_0,esk2_0,esk3_0)
| minsol_model_max(esk1_0,esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_40,plain,
( ~ lesseq(X1,X2)
| max(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,plain,
( ~ ub(X3,X1,X2)
| lesseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_42,plain,
( ~ minsol_model_max(X1,X2,X4)
| ~ model_max(X1,X2,X3)
| lesseq(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_43,plain,
( ~ lesseq(X2,X1)
| minsol_model_max(X1,X2,X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_44,plain,
( ~ model_ub(X1,X3,X2)
| lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_45,negated_conjecture,
( model_max(esk1_0,esk2_0,esk3_0)
| model_ub(esk1_0,esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_46,plain,
( ~ lesseq(X1,X2)
| minsol_model_max(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_40]) ).
cnf(c_0_47,plain,
( ~ model_ub(X3,X1,X2)
| lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_37]) ).
fof(c_0_48,plain,
! [X25,X26,X27] :
( lesseq(X25,X27)
| ~ lesseq(X26,X27)
| ~ lesseq(X25,X26) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[lesseq_trans])])]) ).
fof(c_0_49,plain,
! [X30,X31] :
( lesseq(X31,X30)
| lesseq(X30,X31) ),
inference(variable_rename,[status(thm)],[lesseq_total]) ).
cnf(c_0_50,plain,
( ~ lesseq(X3,X1)
| ~ model_max(X1,X3,X2)
| lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_51,negated_conjecture,
( lesseq(esk1_0,esk3_0)
| model_max(esk1_0,esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_52,plain,
( ~ lesseq(X3,X1)
| ~ model_max(X3,X1,X2)
| lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_42,c_0_46]) ).
cnf(c_0_53,negated_conjecture,
( lesseq(esk2_0,esk3_0)
| model_max(esk1_0,esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_47,c_0_45]) ).
cnf(c_0_54,plain,
( ~ lesseq(X2,X3)
| ~ lesseq(X1,X2)
| lesseq(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_55,plain,
( lesseq(X2,X1)
| lesseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_56,negated_conjecture,
( ~ lesseq(esk2_0,esk1_0)
| lesseq(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_57,negated_conjecture,
( ~ lesseq(esk1_0,esk2_0)
| lesseq(esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_58,plain,
( ~ lesseq(X3,X2)
| lesseq(X3,X1)
| lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_59,negated_conjecture,
( lesseq(esk1_0,esk3_0)
| lesseq(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_56,c_0_55]) ).
cnf(c_0_60,plain,
( ~ minsol_model_ub(X1,X2,X4)
| ~ model_ub(X1,X2,X3)
| lesseq(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_61,plain,
( ~ ub(X1,X2,X3)
| model_ub(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_62,plain,
( ~ lesseq(X3,X2)
| ~ lesseq(X1,X2)
| ub(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_63,negated_conjecture,
( ~ lesseq(X1,esk2_0)
| ~ lesseq(esk1_0,esk2_0)
| lesseq(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_54,c_0_57]) ).
cnf(c_0_64,negated_conjecture,
( lesseq(X1,esk3_0)
| lesseq(esk1_0,X1)
| lesseq(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_65,negated_conjecture,
( ~ model_ub(esk1_0,esk2_0,X1)
| lesseq(esk3_0,X1)
| minsol_model_max(esk1_0,esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_60,c_0_32]) ).
cnf(c_0_66,plain,
( ~ lesseq(X1,X3)
| ~ lesseq(X2,X3)
| model_ub(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_67,negated_conjecture,
( ~ lesseq(X2,esk2_0)
| lesseq(X2,esk3_0)
| lesseq(esk1_0,X1)
| lesseq(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_68,negated_conjecture,
( ~ lesseq(esk1_0,X1)
| ~ lesseq(esk2_0,X1)
| lesseq(esk3_0,X1)
| minsol_model_max(esk1_0,esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_69,negated_conjecture,
( lesseq(X1,esk3_0)
| lesseq(esk1_0,X1)
| lesseq(esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_67,c_0_26]) ).
cnf(c_0_70,negated_conjecture,
( ~ lesseq(esk1_0,X1)
| lesseq(esk3_0,X1)
| lesseq(X1,esk2_0)
| minsol_model_max(esk1_0,esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_68,c_0_55]) ).
cnf(c_0_71,negated_conjecture,
lesseq(esk2_0,esk3_0),
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_69]),c_0_57]) ).
cnf(c_0_72,negated_conjecture,
( ~ lesseq(esk1_0,esk2_0)
| lesseq(esk3_0,esk2_0)
| minsol_model_max(esk1_0,esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_68,c_0_26]) ).
fof(c_0_73,plain,
! [X28,X29] :
( X28 = X29
| ~ lesseq(X29,X28)
| ~ lesseq(X28,X29) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[lesseq_antisymmetric])])]) ).
cnf(c_0_74,negated_conjecture,
( lesseq(esk2_0,esk3_0)
| max(esk1_0,esk2_0) = esk3_0 ),
inference(spm,[status(thm)],[c_0_14,c_0_53]) ).
cnf(c_0_75,negated_conjecture,
( lesseq(esk1_0,esk2_0)
| lesseq(esk3_0,esk1_0)
| minsol_model_max(esk1_0,esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_70,c_0_26]) ).
cnf(c_0_76,negated_conjecture,
( lesseq(X1,esk3_0)
| lesseq(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_71]) ).
cnf(c_0_77,negated_conjecture,
( ~ lesseq(esk1_0,esk2_0)
| lesseq(esk3_0,esk2_0)
| model_max(esk1_0,esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_38,c_0_72]) ).
cnf(c_0_78,plain,
( ~ lesseq(X2,X1)
| ~ lesseq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_79,negated_conjecture,
( ~ lesseq(esk1_0,esk2_0)
| lesseq(esk2_0,esk3_0)
| esk3_0 = esk2_0 ),
inference(spm,[status(thm)],[c_0_40,c_0_74]) ).
cnf(c_0_80,negated_conjecture,
( lesseq(esk3_0,esk1_0)
| lesseq(esk1_0,esk2_0)
| model_max(esk1_0,esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_38,c_0_75]) ).
cnf(c_0_81,negated_conjecture,
lesseq(esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_56,c_0_76]) ).
cnf(c_0_82,negated_conjecture,
( ~ lesseq(esk1_0,esk2_0)
| lesseq(esk3_0,esk2_0)
| max(esk1_0,esk2_0) = esk3_0 ),
inference(spm,[status(thm)],[c_0_14,c_0_77]) ).
cnf(c_0_83,negated_conjecture,
( ~ lesseq(esk1_0,esk2_0)
| ~ lesseq(esk3_0,esk2_0)
| esk3_0 = esk2_0 ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_84,negated_conjecture,
( lesseq(esk1_0,esk2_0)
| lesseq(esk3_0,esk1_0)
| max(esk1_0,esk2_0) = esk3_0 ),
inference(spm,[status(thm)],[c_0_14,c_0_80]) ).
cnf(c_0_85,negated_conjecture,
( ~ lesseq(esk3_0,esk1_0)
| esk3_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_78,c_0_81]) ).
cnf(c_0_86,negated_conjecture,
( ~ lesseq(esk1_0,esk2_0)
| esk3_0 = esk2_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_82]),c_0_83]) ).
cnf(c_0_87,negated_conjecture,
( lesseq(esk1_0,esk2_0)
| esk3_0 = esk1_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_84]),c_0_55]),c_0_85]) ).
cnf(c_0_88,plain,
( ~ model_ub(X1,X2,X3)
| minsol_model_ub(X1,X2,X3)
| model_ub(X1,X2,esk5_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_89,negated_conjecture,
( ~ minsol_model_max(esk1_0,esk2_0,esk3_0)
| ~ minsol_model_ub(esk1_0,esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_90,negated_conjecture,
( esk3_0 = esk2_0
| esk3_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_91,plain,
( ~ model_ub(X2,X3,X1)
| ~ lesseq(X1,esk5_3(X2,X3,X1))
| minsol_model_ub(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_92,plain,
( ~ model_ub(X1,X2,X3)
| lesseq(X2,esk5_3(X1,X2,X3))
| minsol_model_ub(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_47,c_0_88]) ).
cnf(c_0_93,negated_conjecture,
( ~ minsol_model_max(esk1_0,esk2_0,esk2_0)
| ~ minsol_model_ub(esk1_0,esk2_0,esk2_0)
| esk3_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_94,plain,
( ~ model_ub(X1,X2,X2)
| minsol_model_ub(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_95,negated_conjecture,
( ~ model_ub(esk1_0,esk2_0,esk2_0)
| ~ minsol_model_max(esk1_0,esk2_0,esk2_0)
| esk3_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_96,negated_conjecture,
( ~ model_ub(esk1_0,esk2_0,esk2_0)
| esk3_0 = esk1_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_46]),c_0_87]) ).
cnf(c_0_97,negated_conjecture,
esk3_0 = esk1_0,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_66]),c_0_26])]),c_0_87]) ).
cnf(c_0_98,plain,
( ~ model_ub(X1,X2,X3)
| lesseq(X1,esk5_3(X1,X2,X3))
| minsol_model_ub(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_44,c_0_88]) ).
cnf(c_0_99,negated_conjecture,
( ~ minsol_model_max(esk1_0,esk2_0,esk1_0)
| ~ minsol_model_ub(esk1_0,esk2_0,esk1_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_97]),c_0_97]) ).
cnf(c_0_100,plain,
( ~ model_ub(X1,X2,X1)
| minsol_model_ub(X1,X2,X1) ),
inference(spm,[status(thm)],[c_0_91,c_0_98]) ).
cnf(c_0_101,negated_conjecture,
( ~ model_ub(esk1_0,esk2_0,esk1_0)
| ~ minsol_model_max(esk1_0,esk2_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_102,negated_conjecture,
lesseq(esk2_0,esk1_0),
inference(rw,[status(thm)],[c_0_71,c_0_97]) ).
cnf(c_0_103,negated_conjecture,
~ model_ub(esk1_0,esk2_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_43]),c_0_102])]) ).
cnf(c_0_104,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_66]),c_0_102]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM858+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 03:13:07 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.59/0.51 % Version: 3.5.1
% 0.59/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.59/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.59/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.59/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.59/0.51 % Starting new_bool_1 with 300s (1) cores
% 0.59/0.51 % Starting sh5l with 300s (1) cores
% 0.59/0.51 % new_bool_3 with pid 4018150 completed with status 0
% 0.59/0.51 % Result found by new_bool_3
% 0.59/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.59/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.59/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.59/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.59/0.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.59/0.51 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.59/0.51 % Search class: FGHSF-FFMF32-SFFFFFNN
% 0.59/0.51 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.59/0.51 % Starting SubtermCWHack with 31s (1) cores
% 0.59/0.51 % SubtermCWHack with pid 4018153 completed with status 0
% 0.59/0.51 % Result found by SubtermCWHack
% 0.59/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.59/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.59/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.59/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.59/0.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.59/0.51 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.59/0.51 % Search class: FGHSF-FFMF32-SFFFFFNN
% 0.59/0.51 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.59/0.51 % Starting SubtermCWHack with 31s (1) cores
% 0.59/0.51 % Preprocessing time : 0.001 s
% 0.59/0.51
% 0.59/0.51 % Proof found!
% 0.59/0.51 % SZS status Theorem
% 0.59/0.51 % SZS output start CNFRefutation
% See solution above
% 0.59/0.51 % Parsed axioms : 14
% 0.59/0.51 % Removed by relevancy pruning/SinE : 2
% 0.59/0.51 % Initial clauses : 23
% 0.59/0.51 % Removed in clause preprocessing : 0
% 0.59/0.51 % Initial clauses in saturation : 23
% 0.59/0.51 % Processed clauses : 734
% 0.59/0.51 % ...of these trivial : 2
% 0.59/0.51 % ...subsumed : 468
% 0.59/0.51 % ...remaining for further processing : 264
% 0.59/0.51 % Other redundant clauses eliminated : 1
% 0.59/0.51 % Clauses deleted for lack of memory : 0
% 0.59/0.51 % Backward-subsumed : 70
% 0.59/0.51 % Backward-rewritten : 122
% 0.59/0.51 % Generated clauses : 4470
% 0.59/0.51 % ...of the previous two non-redundant : 3759
% 0.59/0.51 % ...aggressively subsumed : 0
% 0.59/0.51 % Contextual simplify-reflections : 10
% 0.59/0.51 % Paramodulations : 4360
% 0.59/0.51 % Factorizations : 107
% 0.59/0.51 % NegExts : 0
% 0.59/0.51 % Equation resolutions : 1
% 0.59/0.51 % Disequality decompositions : 0
% 0.59/0.51 % Total rewrite steps : 921
% 0.59/0.51 % ...of those cached : 879
% 0.59/0.51 % Propositional unsat checks : 0
% 0.59/0.51 % Propositional check models : 0
% 0.59/0.51 % Propositional check unsatisfiable : 0
% 0.59/0.51 % Propositional clauses : 0
% 0.59/0.51 % Propositional clauses after purity: 0
% 0.59/0.51 % Propositional unsat core size : 0
% 0.59/0.51 % Propositional preprocessing time : 0.000
% 0.59/0.51 % Propositional encoding time : 0.000
% 0.59/0.51 % Propositional solver time : 0.000
% 0.59/0.51 % Success case prop preproc time : 0.000
% 0.59/0.51 % Success case prop encoding time : 0.000
% 0.59/0.51 % Success case prop solver time : 0.000
% 0.59/0.51 % Current number of processed clauses : 69
% 0.59/0.51 % Positive orientable unit clauses : 5
% 0.59/0.51 % Positive unorientable unit clauses: 0
% 0.59/0.51 % Negative unit clauses : 1
% 0.59/0.51 % Non-unit-clauses : 63
% 0.59/0.51 % Current number of unprocessed clauses: 2689
% 0.59/0.51 % ...number of literals in the above : 14457
% 0.59/0.51 % Current number of archived formulas : 0
% 0.59/0.51 % Current number of archived clauses : 194
% 0.59/0.51 % Clause-clause subsumption calls (NU) : 9075
% 0.59/0.51 % Rec. Clause-clause subsumption calls : 6753
% 0.59/0.51 % Non-unit clause-clause subsumptions : 535
% 0.59/0.51 % Unit Clause-clause subsumption calls : 124
% 0.59/0.51 % Rewrite failures with RHS unbound : 0
% 0.59/0.51 % BW rewrite match attempts : 10
% 0.59/0.51 % BW rewrite match successes : 4
% 0.59/0.51 % Condensation attempts : 0
% 0.59/0.51 % Condensation successes : 0
% 0.59/0.51 % Termbank termtop insertions : 57093
% 0.59/0.51 % Search garbage collected termcells : 394
% 0.59/0.51
% 0.59/0.51 % -------------------------------------------------
% 0.59/0.51 % User time : 0.075 s
% 0.59/0.51 % System time : 0.005 s
% 0.59/0.51 % Total time : 0.080 s
% 0.59/0.51 % Maximum resident set size: 3592 pages
% 0.59/0.51
% 0.59/0.51 % -------------------------------------------------
% 0.59/0.51 % User time : 0.076 s
% 0.59/0.51 % System time : 0.010 s
% 0.59/0.51 % Total time : 0.086 s
% 0.59/0.51 % Maximum resident set size: 4608 pages
% 0.59/0.51 % E exiting
%------------------------------------------------------------------------------