TSTP Solution File: NUM858+1 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM858+1 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 01:17:36 EDT 2024
% Result : Theorem 0.71s 0.59s
% Output : CNFRefutation 0.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 12
% Syntax : Number of formulae : 136 ( 15 unt; 0 def)
% Number of atoms : 330 ( 75 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 273 ( 79 ~; 167 |; 16 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 3 ( 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 : 179 ( 2 sgn 74 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(max_is_ub_1,conjecture,
! [X1,X2,X3] :
( minsol_model_ub(X1,X2,X3)
<=> minsol_model_max(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',max_is_ub_1) ).
fof(minsol_model_ub,axiom,
! [X1,X2,X4] :
( minsol_model_ub(X1,X2,X4)
<=> ( model_ub(X1,X2,X4)
& ! [X3] :
( model_ub(X1,X2,X3)
=> lesseq(X4,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minsol_model_ub) ).
fof(ub,axiom,
! [X1,X2,X3] :
( ub(X1,X2,X3)
<=> ( lesseq(X1,X3)
& lesseq(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ub) ).
fof(lesseq_ref,axiom,
! [X1] : lesseq(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lesseq_ref) ).
fof(max_1,axiom,
! [X1,X2] :
( max(X1,X2) = X1
| ~ lesseq(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',max_1) ).
fof(minsol_model_max,axiom,
! [X1,X2,X4] :
( minsol_model_max(X1,X2,X4)
<=> ( model_max(X1,X2,X4)
& ! [X3] :
( model_max(X1,X2,X3)
=> lesseq(X4,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minsol_model_max) ).
fof(lesseq_total,axiom,
! [X1,X2] :
( lesseq(X1,X2)
| lesseq(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lesseq_total) ).
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(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(lesseq_antisymmetric,axiom,
! [X1,X2] :
( ( lesseq(X1,X2)
& lesseq(X2,X1) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lesseq_antisymmetric) ).
fof(max_2,axiom,
! [X1,X2] :
( max(X1,X2) = X2
| ~ lesseq(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',max_2) ).
fof(lesseq_trans,axiom,
! [X1,X2,X3] :
( ( lesseq(X1,X2)
& lesseq(X2,X3) )
=> lesseq(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lesseq_trans) ).
fof(c_0_12,negated_conjecture,
~ ! [X1,X2,X3] :
( minsol_model_ub(X1,X2,X3)
<=> minsol_model_max(X1,X2,X3) ),
inference(assume_negation,[status(cth)],[max_is_ub_1]) ).
fof(c_0_13,plain,
! [X39,X40,X41,X42,X43,X44,X45] :
( ( model_ub(X39,X40,X41)
| ~ minsol_model_ub(X39,X40,X41) )
& ( ~ model_ub(X39,X40,X42)
| lesseq(X41,X42)
| ~ minsol_model_ub(X39,X40,X41) )
& ( model_ub(X43,X44,esk2_3(X43,X44,X45))
| ~ model_ub(X43,X44,X45)
| minsol_model_ub(X43,X44,X45) )
& ( ~ lesseq(X45,esk2_3(X43,X44,X45))
| ~ model_ub(X43,X44,X45)
| minsol_model_ub(X43,X44,X45) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[minsol_model_ub])])])])])])]) ).
fof(c_0_14,negated_conjecture,
( ( ~ minsol_model_ub(esk3_0,esk4_0,esk5_0)
| ~ minsol_model_max(esk3_0,esk4_0,esk5_0) )
& ( minsol_model_ub(esk3_0,esk4_0,esk5_0)
| minsol_model_max(esk3_0,esk4_0,esk5_0) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).
fof(c_0_15,plain,
! [X22,X23,X24] :
( ( lesseq(X22,X24)
| ~ ub(X22,X23,X24) )
& ( lesseq(X23,X24)
| ~ ub(X22,X23,X24) )
& ( ~ lesseq(X22,X24)
| ~ lesseq(X23,X24)
| ub(X22,X23,X24) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ub])])])]) ).
fof(c_0_16,plain,
! [X5] : lesseq(X5,X5),
inference(variable_rename,[status(thm)],[lesseq_ref]) ).
fof(c_0_17,plain,
! [X1,X2] :
( max(X1,X2) = X1
| ~ lesseq(X2,X1) ),
inference(fof_simplification,[status(thm)],[max_1]) ).
fof(c_0_18,plain,
! [X31,X32,X33,X34,X35,X36,X37] :
( ( model_max(X31,X32,X33)
| ~ minsol_model_max(X31,X32,X33) )
& ( ~ model_max(X31,X32,X34)
| lesseq(X33,X34)
| ~ minsol_model_max(X31,X32,X33) )
& ( model_max(X35,X36,esk1_3(X35,X36,X37))
| ~ model_max(X35,X36,X37)
| minsol_model_max(X35,X36,X37) )
& ( ~ lesseq(X37,esk1_3(X35,X36,X37))
| ~ model_max(X35,X36,X37)
| minsol_model_max(X35,X36,X37) ) ),
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_19,plain,
( model_ub(X1,X2,X3)
| ~ minsol_model_ub(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
( minsol_model_ub(esk3_0,esk4_0,esk5_0)
| minsol_model_max(esk3_0,esk4_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( ub(X1,X3,X2)
| ~ lesseq(X1,X2)
| ~ lesseq(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
lesseq(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_23,plain,
! [X11,X12] :
( lesseq(X11,X12)
| lesseq(X12,X11) ),
inference(variable_rename,[status(thm)],[lesseq_total]) ).
fof(c_0_24,plain,
! [X18,X19] :
( max(X18,X19) = X18
| ~ lesseq(X19,X18) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_17])]) ).
fof(c_0_25,plain,
! [X28,X29,X30] :
( ( ~ model_ub(X28,X29,X30)
| ub(X28,X29,X30) )
& ( ~ ub(X28,X29,X30)
| model_ub(X28,X29,X30) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[model_ub_1])])]) ).
cnf(c_0_26,plain,
( model_max(X1,X2,X3)
| ~ minsol_model_max(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,negated_conjecture,
( minsol_model_max(esk3_0,esk4_0,esk5_0)
| model_ub(esk3_0,esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_28,plain,
( ub(X1,X2,X1)
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,plain,
( lesseq(X1,X2)
| lesseq(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_30,plain,
! [X25,X26,X27] :
( ( ~ model_max(X25,X26,X27)
| X27 = max(X25,X26) )
& ( X27 != max(X25,X26)
| model_max(X25,X26,X27) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[model_max_1])])]) ).
cnf(c_0_31,plain,
( max(X1,X2) = X1
| ~ lesseq(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,plain,
( ub(X1,X2,X3)
| ~ model_ub(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_33,negated_conjecture,
( model_ub(esk3_0,esk4_0,esk5_0)
| model_max(esk3_0,esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,plain,
( model_ub(X1,X2,X3)
| ~ ub(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_35,plain,
( ub(X1,X2,X1)
| lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,plain,
( model_max(X2,X3,X1)
| X1 != max(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,plain,
( max(X1,X2) = X1
| lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_29]) ).
cnf(c_0_38,plain,
( lesseq(X1,X2)
| ~ ub(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_39,negated_conjecture,
( model_max(esk3_0,esk4_0,esk5_0)
| ub(esk3_0,esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_40,plain,
( lesseq(X4,X3)
| ~ model_ub(X1,X2,X3)
| ~ minsol_model_ub(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_41,plain,
( model_ub(X1,X2,X1)
| lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,plain,
( lesseq(X4,X3)
| ~ model_max(X1,X2,X3)
| ~ minsol_model_max(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_43,plain,
( model_max(X1,X2,X1)
| lesseq(X1,X2) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37])]) ).
cnf(c_0_44,plain,
( X3 = max(X1,X2)
| ~ model_max(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_45,negated_conjecture,
( model_max(esk3_0,esk4_0,esk5_0)
| lesseq(esk3_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
fof(c_0_46,plain,
! [X9,X10] :
( ~ lesseq(X9,X10)
| ~ lesseq(X10,X9)
| X9 = X10 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[lesseq_antisymmetric])])]) ).
cnf(c_0_47,plain,
( lesseq(X1,X2)
| lesseq(X3,X1)
| ~ minsol_model_ub(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,plain,
( lesseq(X1,X2)
| lesseq(X3,X1)
| ~ minsol_model_max(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,negated_conjecture,
( max(esk3_0,esk4_0) = esk5_0
| lesseq(esk3_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
fof(c_0_50,plain,
! [X1,X2] :
( max(X1,X2) = X2
| ~ lesseq(X1,X2) ),
inference(fof_simplification,[status(thm)],[max_2]) ).
cnf(c_0_51,plain,
( X1 = X2
| ~ lesseq(X1,X2)
| ~ lesseq(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_52,negated_conjecture,
( lesseq(esk5_0,esk3_0)
| lesseq(esk3_0,esk4_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_20]),c_0_48]) ).
cnf(c_0_53,negated_conjecture,
( esk5_0 = esk3_0
| lesseq(esk3_0,esk4_0)
| lesseq(esk3_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_49,c_0_37]) ).
fof(c_0_54,plain,
! [X20,X21] :
( max(X20,X21) = X21
| ~ lesseq(X20,X21) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_50])]) ).
cnf(c_0_55,plain,
( ub(X1,X2,X2)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_56,negated_conjecture,
( esk5_0 = esk3_0
| lesseq(esk3_0,esk4_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]) ).
cnf(c_0_57,plain,
( max(X1,X2) = X2
| ~ lesseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_58,negated_conjecture,
( esk5_0 = esk3_0
| ub(esk3_0,esk4_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_59,plain,
( ub(X1,X2,X2)
| lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_29]) ).
cnf(c_0_60,plain,
( max(X1,X2) = X2
| lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_29]) ).
cnf(c_0_61,plain,
( lesseq(X1,X2)
| ~ ub(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_62,negated_conjecture,
( minsol_model_max(esk3_0,esk4_0,esk5_0)
| lesseq(esk5_0,X1)
| ~ model_ub(esk3_0,esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_20]) ).
cnf(c_0_63,negated_conjecture,
( esk5_0 = esk3_0
| model_ub(esk3_0,esk4_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_34,c_0_58]) ).
cnf(c_0_64,plain,
( model_ub(X1,X2,X2)
| lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_59]) ).
cnf(c_0_65,plain,
( model_max(X1,X2,X2)
| lesseq(X2,X1) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_60])]) ).
cnf(c_0_66,negated_conjecture,
( model_max(esk3_0,esk4_0,esk5_0)
| lesseq(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_61,c_0_39]) ).
cnf(c_0_67,negated_conjecture,
( esk5_0 = esk3_0
| minsol_model_max(esk3_0,esk4_0,esk5_0)
| lesseq(esk5_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_68,plain,
model_max(X1,X2,max(X1,X2)),
inference(er,[status(thm)],[c_0_36]) ).
cnf(c_0_69,negated_conjecture,
( max(esk3_0,esk4_0) = esk4_0
| esk5_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_57,c_0_56]) ).
cnf(c_0_70,plain,
( lesseq(X1,X2)
| lesseq(X3,X1)
| ~ minsol_model_ub(X2,X1,X3) ),
inference(spm,[status(thm)],[c_0_40,c_0_64]) ).
cnf(c_0_71,plain,
( lesseq(X1,X2)
| lesseq(X3,X1)
| ~ minsol_model_max(X2,X1,X3) ),
inference(spm,[status(thm)],[c_0_42,c_0_65]) ).
cnf(c_0_72,negated_conjecture,
( max(esk3_0,esk4_0) = esk5_0
| lesseq(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_66]) ).
cnf(c_0_73,negated_conjecture,
( esk5_0 = esk3_0
| model_max(esk3_0,esk4_0,esk5_0)
| lesseq(esk5_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_67]) ).
cnf(c_0_74,plain,
( model_ub(X1,X2,esk2_3(X1,X2,X3))
| minsol_model_ub(X1,X2,X3)
| ~ model_ub(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_75,plain,
( model_max(X1,X2,esk1_3(X1,X2,X3))
| minsol_model_max(X1,X2,X3)
| ~ model_max(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_76,negated_conjecture,
( esk5_0 = esk3_0
| model_max(esk3_0,esk4_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_77,negated_conjecture,
( lesseq(esk5_0,esk4_0)
| lesseq(esk4_0,esk3_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_20]),c_0_71]) ).
cnf(c_0_78,negated_conjecture,
( esk5_0 = esk4_0
| lesseq(esk4_0,esk5_0)
| lesseq(esk4_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_60,c_0_72]) ).
cnf(c_0_79,negated_conjecture,
( max(esk3_0,esk4_0) = esk5_0
| esk5_0 = esk3_0
| lesseq(esk5_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_73]) ).
cnf(c_0_80,negated_conjecture,
( esk5_0 = esk3_0
| minsol_model_ub(esk3_0,esk4_0,esk4_0)
| model_ub(esk3_0,esk4_0,esk2_3(esk3_0,esk4_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_74,c_0_63]) ).
cnf(c_0_81,negated_conjecture,
( esk5_0 = esk3_0
| minsol_model_max(esk3_0,esk4_0,esk4_0)
| model_max(esk3_0,esk4_0,esk1_3(esk3_0,esk4_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_82,negated_conjecture,
( esk5_0 = esk4_0
| lesseq(esk4_0,esk3_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_77]),c_0_78]) ).
cnf(c_0_83,negated_conjecture,
( esk5_0 = esk3_0
| esk5_0 = esk4_0
| lesseq(esk5_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_69,c_0_79]) ).
cnf(c_0_84,negated_conjecture,
( esk5_0 = esk3_0
| esk5_0 = esk4_0
| lesseq(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_72,c_0_69]) ).
cnf(c_0_85,negated_conjecture,
( esk5_0 = esk3_0
| minsol_model_ub(esk3_0,esk4_0,esk4_0)
| ub(esk3_0,esk4_0,esk2_3(esk3_0,esk4_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_32,c_0_80]) ).
cnf(c_0_86,plain,
( minsol_model_max(X2,X3,X1)
| ~ lesseq(X1,esk1_3(X2,X3,X1))
| ~ model_max(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_87,negated_conjecture,
( esk1_3(esk3_0,esk4_0,esk4_0) = max(esk3_0,esk4_0)
| esk5_0 = esk3_0
| minsol_model_max(esk3_0,esk4_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_81]) ).
cnf(c_0_88,negated_conjecture,
( max(esk3_0,esk4_0) = esk3_0
| esk5_0 = esk4_0 ),
inference(spm,[status(thm)],[c_0_31,c_0_82]) ).
cnf(c_0_89,negated_conjecture,
( ~ minsol_model_ub(esk3_0,esk4_0,esk5_0)
| ~ minsol_model_max(esk3_0,esk4_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_90,negated_conjecture,
( esk5_0 = esk3_0
| esk5_0 = esk4_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_83]),c_0_84]) ).
cnf(c_0_91,plain,
( minsol_model_ub(X2,X3,X1)
| ~ lesseq(X1,esk2_3(X2,X3,X1))
| ~ model_ub(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_92,negated_conjecture,
( esk5_0 = esk3_0
| minsol_model_ub(esk3_0,esk4_0,esk4_0)
| lesseq(esk4_0,esk2_3(esk3_0,esk4_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_61,c_0_85]) ).
cnf(c_0_93,negated_conjecture,
( esk5_0 = esk3_0
| minsol_model_max(esk3_0,esk4_0,esk4_0)
| ~ lesseq(esk4_0,max(esk3_0,esk4_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_76]) ).
cnf(c_0_94,negated_conjecture,
( esk5_0 = esk4_0
| model_max(esk3_0,esk4_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_68,c_0_88]) ).
cnf(c_0_95,negated_conjecture,
( esk5_0 = esk3_0
| ~ minsol_model_ub(esk3_0,esk4_0,esk4_0)
| ~ minsol_model_max(esk3_0,esk4_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_96,negated_conjecture,
( esk5_0 = esk3_0
| minsol_model_ub(esk3_0,esk4_0,esk4_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_63]) ).
cnf(c_0_97,negated_conjecture,
( esk5_0 = esk3_0
| minsol_model_max(esk3_0,esk4_0,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_69]),c_0_22])]) ).
cnf(c_0_98,negated_conjecture,
( esk5_0 = esk4_0
| minsol_model_max(esk3_0,esk4_0,esk3_0)
| model_max(esk3_0,esk4_0,esk1_3(esk3_0,esk4_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_75,c_0_94]) ).
cnf(c_0_99,negated_conjecture,
esk5_0 = esk3_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97]) ).
cnf(c_0_100,negated_conjecture,
( esk1_3(esk3_0,esk4_0,esk3_0) = max(esk3_0,esk4_0)
| esk5_0 = esk4_0
| minsol_model_max(esk3_0,esk4_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_98]) ).
cnf(c_0_101,plain,
( minsol_model_max(X1,X2,max(X1,X2))
| model_max(X1,X2,esk1_3(X1,X2,max(X1,X2))) ),
inference(spm,[status(thm)],[c_0_75,c_0_68]) ).
cnf(c_0_102,negated_conjecture,
max(esk3_0,esk4_0) = esk3_0,
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_99]),c_0_99]),c_0_31]) ).
cnf(c_0_103,negated_conjecture,
( esk5_0 = esk4_0
| minsol_model_max(esk3_0,esk4_0,esk3_0)
| ~ lesseq(esk3_0,max(esk3_0,esk4_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_100]),c_0_94]) ).
cnf(c_0_104,negated_conjecture,
( minsol_model_max(esk3_0,esk4_0,esk3_0)
| model_max(esk3_0,esk4_0,esk1_3(esk3_0,esk4_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_105,negated_conjecture,
( esk5_0 = esk4_0
| minsol_model_max(esk3_0,esk4_0,esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_88]),c_0_22])]) ).
fof(c_0_106,plain,
! [X6,X7,X8] :
( ~ lesseq(X6,X7)
| ~ lesseq(X7,X8)
| lesseq(X6,X8) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[lesseq_trans])])]) ).
cnf(c_0_107,negated_conjecture,
( esk5_0 = esk4_0
| ub(esk3_0,esk4_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_82]) ).
cnf(c_0_108,negated_conjecture,
( esk1_3(esk3_0,esk4_0,esk3_0) = esk3_0
| minsol_model_max(esk3_0,esk4_0,esk3_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_104]),c_0_102]) ).
cnf(c_0_109,negated_conjecture,
model_max(esk3_0,esk4_0,esk3_0),
inference(spm,[status(thm)],[c_0_68,c_0_102]) ).
cnf(c_0_110,negated_conjecture,
( esk5_0 = esk4_0
| lesseq(esk3_0,X1)
| ~ model_max(esk3_0,esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_105]) ).
cnf(c_0_111,plain,
( lesseq(X1,X3)
| ~ lesseq(X1,X2)
| ~ lesseq(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_112,negated_conjecture,
( esk5_0 = esk4_0
| model_ub(esk3_0,esk4_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_34,c_0_107]) ).
cnf(c_0_113,negated_conjecture,
( ~ minsol_model_ub(esk3_0,esk4_0,esk3_0)
| ~ minsol_model_max(esk3_0,esk4_0,esk3_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_99]),c_0_99]) ).
cnf(c_0_114,negated_conjecture,
minsol_model_max(esk3_0,esk4_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_108]),c_0_109]),c_0_22])]) ).
cnf(c_0_115,negated_conjecture,
( esk5_0 = esk4_0
| lesseq(esk3_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_110,c_0_45]) ).
cnf(c_0_116,negated_conjecture,
( esk5_0 = esk4_0
| lesseq(esk4_0,X1)
| ~ lesseq(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_111,c_0_82]) ).
cnf(c_0_117,negated_conjecture,
( esk5_0 = esk4_0
| minsol_model_ub(esk3_0,esk4_0,esk3_0)
| model_ub(esk3_0,esk4_0,esk2_3(esk3_0,esk4_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_74,c_0_112]) ).
cnf(c_0_118,negated_conjecture,
~ minsol_model_ub(esk3_0,esk4_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_114])]) ).
cnf(c_0_119,negated_conjecture,
( esk5_0 = esk4_0
| ub(esk3_0,X1,esk5_0)
| ~ lesseq(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_115]) ).
cnf(c_0_120,negated_conjecture,
( esk5_0 = esk4_0
| lesseq(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_116,c_0_115]) ).
cnf(c_0_121,plain,
ub(X1,X1,X1),
inference(spm,[status(thm)],[c_0_28,c_0_22]) ).
cnf(c_0_122,negated_conjecture,
( esk4_0 = esk3_0
| model_ub(esk3_0,esk4_0,esk2_3(esk3_0,esk4_0,esk3_0)) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_117,c_0_99]),c_0_118]) ).
cnf(c_0_123,negated_conjecture,
( esk5_0 = esk4_0
| ub(esk3_0,esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_124,plain,
model_ub(X1,X1,X1),
inference(spm,[status(thm)],[c_0_34,c_0_121]) ).
cnf(c_0_125,negated_conjecture,
( esk4_0 = esk3_0
| ub(esk3_0,esk4_0,esk2_3(esk3_0,esk4_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_32,c_0_122]) ).
cnf(c_0_126,negated_conjecture,
( esk5_0 = esk4_0
| model_ub(esk3_0,esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_34,c_0_123]) ).
cnf(c_0_127,plain,
( minsol_model_ub(X1,X1,X1)
| model_ub(X1,X1,esk2_3(X1,X1,X1)) ),
inference(spm,[status(thm)],[c_0_74,c_0_124]) ).
cnf(c_0_128,negated_conjecture,
( esk4_0 = esk3_0
| lesseq(esk3_0,esk2_3(esk3_0,esk4_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_38,c_0_125]) ).
cnf(c_0_129,negated_conjecture,
( esk4_0 = esk3_0
| model_ub(esk3_0,esk4_0,esk3_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_126,c_0_99]),c_0_99]) ).
cnf(c_0_130,plain,
( minsol_model_ub(X1,X1,X1)
| ub(X1,X1,esk2_3(X1,X1,X1)) ),
inference(spm,[status(thm)],[c_0_32,c_0_127]) ).
cnf(c_0_131,negated_conjecture,
esk4_0 = esk3_0,
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_128]),c_0_118]),c_0_129]) ).
cnf(c_0_132,plain,
( minsol_model_ub(X1,X1,X1)
| lesseq(X1,esk2_3(X1,X1,X1)) ),
inference(spm,[status(thm)],[c_0_38,c_0_130]) ).
cnf(c_0_133,negated_conjecture,
~ minsol_model_ub(esk3_0,esk3_0,esk3_0),
inference(rw,[status(thm)],[c_0_118,c_0_131]) ).
cnf(c_0_134,plain,
minsol_model_ub(X1,X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_132]),c_0_124])]) ).
cnf(c_0_135,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_133,c_0_134])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM858+1 : TPTP v8.2.0. Released v4.1.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 20 05:40:53 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 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
% 0.71/0.59 # Version: 3.1.0
% 0.71/0.59 # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.71/0.59 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.71/0.59 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.71/0.59 # Starting new_bool_3 with 300s (1) cores
% 0.71/0.59 # Starting new_bool_1 with 300s (1) cores
% 0.71/0.59 # Starting sh5l with 300s (1) cores
% 0.71/0.59 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 23376 completed with status 0
% 0.71/0.59 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.71/0.59 # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.71/0.59 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.71/0.59 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.71/0.59 # No SInE strategy applied
% 0.71/0.59 # Search class: FGHSF-FFMF32-SFFFFFNN
% 0.71/0.59 # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.71/0.59 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 901s (1) cores
% 0.71/0.59 # Starting G-E--_107_C36_F1_PI_AE_Q4_CS_SP_PS_S0Y with 151s (1) cores
% 0.71/0.59 # Starting new_bool_3 with 151s (1) cores
% 0.71/0.59 # Starting new_bool_1 with 151s (1) cores
% 0.71/0.59 # Starting G-E--_208_C18_F1_AE_CS_SP_PI_S0a with 146s (1) cores
% 0.71/0.59 # G-E--_208_C18_F1_AE_CS_SP_PI_S0a with pid 23387 completed with status 0
% 0.71/0.59 # Result found by G-E--_208_C18_F1_AE_CS_SP_PI_S0a
% 0.71/0.59 # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.71/0.59 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.71/0.59 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.71/0.59 # No SInE strategy applied
% 0.71/0.59 # Search class: FGHSF-FFMF32-SFFFFFNN
% 0.71/0.59 # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.71/0.59 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 901s (1) cores
% 0.71/0.59 # Starting G-E--_107_C36_F1_PI_AE_Q4_CS_SP_PS_S0Y with 151s (1) cores
% 0.71/0.59 # Starting new_bool_3 with 151s (1) cores
% 0.71/0.59 # Starting new_bool_1 with 151s (1) cores
% 0.71/0.59 # Starting G-E--_208_C18_F1_AE_CS_SP_PI_S0a with 146s (1) cores
% 0.71/0.59 # Preprocessing time : 0.001 s
% 0.71/0.59
% 0.71/0.59 # Proof found!
% 0.71/0.59 # SZS status Theorem
% 0.71/0.59 # SZS output start CNFRefutation
% See solution above
% 0.71/0.59 # Parsed axioms : 14
% 0.71/0.59 # Removed by relevancy pruning/SinE : 0
% 0.71/0.59 # Initial clauses : 27
% 0.71/0.59 # Removed in clause preprocessing : 0
% 0.71/0.59 # Initial clauses in saturation : 27
% 0.71/0.59 # Processed clauses : 1592
% 0.71/0.59 # ...of these trivial : 38
% 0.71/0.59 # ...subsumed : 930
% 0.71/0.59 # ...remaining for further processing : 624
% 0.71/0.59 # Other redundant clauses eliminated : 7
% 0.71/0.59 # Clauses deleted for lack of memory : 0
% 0.71/0.59 # Backward-subsumed : 98
% 0.71/0.59 # Backward-rewritten : 423
% 0.71/0.59 # Generated clauses : 5659
% 0.71/0.59 # ...of the previous two non-redundant : 5123
% 0.71/0.59 # ...aggressively subsumed : 0
% 0.71/0.59 # Contextual simplify-reflections : 16
% 0.71/0.59 # Paramodulations : 5591
% 0.71/0.59 # Factorizations : 18
% 0.71/0.59 # NegExts : 0
% 0.71/0.59 # Equation resolutions : 50
% 0.71/0.59 # Disequality decompositions : 0
% 0.71/0.59 # Total rewrite steps : 1669
% 0.71/0.59 # ...of those cached : 1624
% 0.71/0.59 # Propositional unsat checks : 0
% 0.71/0.59 # Propositional check models : 0
% 0.71/0.59 # Propositional check unsatisfiable : 0
% 0.71/0.59 # Propositional clauses : 0
% 0.71/0.59 # Propositional clauses after purity: 0
% 0.71/0.59 # Propositional unsat core size : 0
% 0.71/0.59 # Propositional preprocessing time : 0.000
% 0.71/0.59 # Propositional encoding time : 0.000
% 0.71/0.59 # Propositional solver time : 0.000
% 0.71/0.59 # Success case prop preproc time : 0.000
% 0.71/0.59 # Success case prop encoding time : 0.000
% 0.71/0.59 # Success case prop solver time : 0.000
% 0.71/0.59 # Current number of processed clauses : 103
% 0.71/0.59 # Positive orientable unit clauses : 10
% 0.71/0.59 # Positive unorientable unit clauses: 0
% 0.71/0.59 # Negative unit clauses : 0
% 0.71/0.59 # Non-unit-clauses : 93
% 0.71/0.59 # Current number of unprocessed clauses: 1275
% 0.71/0.59 # ...number of literals in the above : 5010
% 0.71/0.59 # Current number of archived formulas : 0
% 0.71/0.59 # Current number of archived clauses : 521
% 0.71/0.59 # Clause-clause subsumption calls (NU) : 53968
% 0.71/0.59 # Rec. Clause-clause subsumption calls : 26320
% 0.71/0.59 # Non-unit clause-clause subsumptions : 1040
% 0.71/0.59 # Unit Clause-clause subsumption calls : 409
% 0.71/0.59 # Rewrite failures with RHS unbound : 0
% 0.71/0.59 # BW rewrite match attempts : 46
% 0.71/0.59 # BW rewrite match successes : 8
% 0.71/0.59 # Condensation attempts : 0
% 0.71/0.59 # Condensation successes : 0
% 0.71/0.59 # Termbank termtop insertions : 64500
% 0.71/0.59 # Search garbage collected termcells : 419
% 0.71/0.59
% 0.71/0.59 # -------------------------------------------------
% 0.71/0.59 # User time : 0.095 s
% 0.71/0.59 # System time : 0.005 s
% 0.71/0.59 # Total time : 0.100 s
% 0.71/0.59 # Maximum resident set size: 1756 pages
% 0.71/0.59
% 0.71/0.59 # -------------------------------------------------
% 0.71/0.59 # User time : 0.468 s
% 0.71/0.59 # System time : 0.017 s
% 0.71/0.59 # Total time : 0.486 s
% 0.71/0.59 # Maximum resident set size: 1700 pages
% 0.71/0.59 % E---3.1 exiting
% 0.71/0.59 % E exiting
%------------------------------------------------------------------------------