TSTP Solution File: NUM858+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM858+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n016.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 : Thu Aug 31 10:41:06 EDT 2023
% Result : Theorem 45.72s 45.82s
% Output : CNFRefutation 45.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 26
% Syntax : Number of formulae : 144 ( 9 unt; 14 typ; 0 def)
% Number of atoms : 348 ( 59 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 330 ( 112 ~; 191 |; 16 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 11 >; 17 *; 0 +; 0 <<)
% 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 : 189 ( 4 sgn; 74 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
lesseq: ( $i * $i ) > $o ).
tff(decl_23,type,
sum: ( $i * $i ) > $i ).
tff(decl_24,type,
summation: $i > $i ).
tff(decl_25,type,
max: ( $i * $i ) > $i ).
tff(decl_26,type,
ub: ( $i * $i * $i ) > $o ).
tff(decl_27,type,
model_max: ( $i * $i * $i ) > $o ).
tff(decl_28,type,
model_ub: ( $i * $i * $i ) > $o ).
tff(decl_29,type,
minsol_model_max: ( $i * $i * $i ) > $o ).
tff(decl_30,type,
minsol_model_ub: ( $i * $i * $i ) > $o ).
tff(decl_31,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_32,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_33,type,
esk3_0: $i ).
tff(decl_34,type,
esk4_0: $i ).
tff(decl_35,type,
esk5_0: $i ).
fof(model_max_1,axiom,
! [X1,X2,X4] :
( model_max(X1,X2,X4)
<=> X4 = max(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',model_max_1) ).
fof(max_2,axiom,
! [X1,X2] :
( max(X1,X2) = X2
| ~ lesseq(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_2) ).
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/sandbox/benchmark/theBenchmark.p',minsol_model_max) ).
fof(lesseq_ref,axiom,
! [X1] : lesseq(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_ref) ).
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)
<=> ( model_ub(X1,X2,X4)
& ! [X3] :
( model_ub(X1,X2,X3)
=> lesseq(X4,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minsol_model_ub) ).
fof(model_ub_1,axiom,
! [X1,X2,X4] :
( model_ub(X1,X2,X4)
<=> ub(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',model_ub_1) ).
fof(ub,axiom,
! [X1,X2,X3] :
( ub(X1,X2,X3)
<=> ( lesseq(X1,X3)
& lesseq(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ub) ).
fof(lesseq_trans,axiom,
! [X1,X2,X3] :
( ( lesseq(X1,X2)
& lesseq(X2,X3) )
=> lesseq(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_trans) ).
fof(lesseq_total,axiom,
! [X1,X2] :
( lesseq(X1,X2)
| lesseq(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_total) ).
fof(max_1,axiom,
! [X1,X2] :
( max(X1,X2) = X1
| ~ lesseq(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_1) ).
fof(lesseq_antisymmetric,axiom,
! [X1,X2] :
( ( lesseq(X1,X2)
& lesseq(X2,X1) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_antisymmetric) ).
fof(c_0_12,plain,
! [X25,X26,X27] :
( ( ~ model_max(X25,X26,X27)
| X27 = max(X25,X26) )
& ( X27 != max(X25,X26)
| model_max(X25,X26,X27) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[model_max_1])]) ).
fof(c_0_13,plain,
! [X1,X2] :
( max(X1,X2) = X2
| ~ lesseq(X1,X2) ),
inference(fof_simplification,[status(thm)],[max_2]) ).
cnf(c_0_14,plain,
( model_max(X2,X3,X1)
| X1 != max(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_15,plain,
! [X20,X21] :
( max(X20,X21) = X21
| ~ lesseq(X20,X21) ),
inference(variable_rename,[status(thm)],[c_0_13]) ).
fof(c_0_16,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(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_17,plain,
model_max(X1,X2,max(X1,X2)),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
( max(X1,X2) = X2
| ~ lesseq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,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_16]) ).
cnf(c_0_20,plain,
( model_max(X1,X2,X2)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_21,plain,
! [X5] : lesseq(X5,X5),
inference(variable_rename,[status(thm)],[lesseq_ref]) ).
cnf(c_0_22,plain,
( minsol_model_max(X1,X2,X2)
| model_max(X1,X2,esk1_3(X1,X2,X2))
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
lesseq(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_24,plain,
( X3 = max(X1,X2)
| ~ model_max(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_25,plain,
( minsol_model_max(X1,X1,X1)
| model_max(X1,X1,esk1_3(X1,X1,X1)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,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_16]) ).
cnf(c_0_27,plain,
( esk1_3(X1,X1,X1) = max(X1,X1)
| minsol_model_max(X1,X1,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,plain,
( minsol_model_max(X1,X1,X1)
| ~ model_max(X1,X1,X1)
| ~ lesseq(X1,max(X1,X1)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_29,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_30,plain,
( lesseq(X4,X3)
| ~ model_max(X1,X2,X3)
| ~ minsol_model_max(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_31,plain,
( minsol_model_max(X1,X1,X1)
| ~ model_max(X1,X1,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_18]),c_0_23])]) ).
fof(c_0_32,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(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_33,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(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])]) ).
fof(c_0_34,plain,
! [X28,X29,X30] :
( ( ~ model_ub(X28,X29,X30)
| ub(X28,X29,X30) )
& ( ~ ub(X28,X29,X30)
| model_ub(X28,X29,X30) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[model_ub_1])]) ).
fof(c_0_35,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(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ub])])]) ).
fof(c_0_36,plain,
! [X6,X7,X8] :
( ~ lesseq(X6,X7)
| ~ lesseq(X7,X8)
| lesseq(X6,X8) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[lesseq_trans])]) ).
cnf(c_0_37,plain,
( lesseq(X1,X2)
| ~ model_max(X1,X1,X2)
| ~ model_max(X1,X1,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_38,plain,
( lesseq(X4,X3)
| ~ model_ub(X1,X2,X3)
| ~ minsol_model_ub(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_39,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_33]) ).
cnf(c_0_40,plain,
( model_ub(X1,X2,X3)
| ~ ub(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,plain,
( ub(X1,X3,X2)
| ~ lesseq(X1,X2)
| ~ lesseq(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_42,plain,
! [X11,X12] :
( lesseq(X11,X12)
| lesseq(X12,X11) ),
inference(variable_rename,[status(thm)],[lesseq_total]) ).
cnf(c_0_43,plain,
( lesseq(X1,X3)
| ~ lesseq(X1,X2)
| ~ lesseq(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_44,plain,
( lesseq(X1,max(X1,X1))
| ~ model_max(X1,X1,X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_17]) ).
cnf(c_0_45,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_38,c_0_39]) ).
cnf(c_0_46,plain,
( model_ub(X1,X2,X3)
| ~ lesseq(X2,X3)
| ~ lesseq(X1,X3) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,plain,
( lesseq(X1,X2)
| lesseq(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_48,plain,
( lesseq(X1,max(X2,X2))
| ~ model_max(X2,X2,X2)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_49,plain,
( model_ub(X1,X2,X3)
| ~ minsol_model_ub(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_50,negated_conjecture,
( minsol_model_max(esk3_0,esk4_0,esk5_0)
| lesseq(esk5_0,X1)
| ~ lesseq(esk4_0,X1)
| ~ lesseq(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,plain,
( lesseq(X1,X2)
| lesseq(X3,X1)
| ~ lesseq(X3,X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_47]) ).
cnf(c_0_52,plain,
( lesseq(X1,max(X2,X2))
| ~ lesseq(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_20]),c_0_23])]) ).
cnf(c_0_53,plain,
( lesseq(X1,X2)
| ~ ub(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_54,plain,
( ub(X1,X2,X3)
| ~ model_ub(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_55,plain,
( model_max(X1,X2,X3)
| ~ minsol_model_max(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_56,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_49,c_0_39]) ).
cnf(c_0_57,negated_conjecture,
( minsol_model_max(esk3_0,esk4_0,esk5_0)
| lesseq(esk5_0,max(esk4_0,esk4_0))
| ~ model_max(esk4_0,esk4_0,esk4_0)
| ~ lesseq(esk3_0,max(esk4_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_50,c_0_44]) ).
cnf(c_0_58,plain,
( lesseq(X1,max(X2,X2))
| lesseq(X3,X1)
| ~ lesseq(X3,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
fof(c_0_59,plain,
! [X1,X2] :
( max(X1,X2) = X1
| ~ lesseq(X2,X1) ),
inference(fof_simplification,[status(thm)],[max_1]) ).
cnf(c_0_60,plain,
( lesseq(X1,X2)
| ~ model_ub(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_61,negated_conjecture,
( model_ub(esk3_0,esk4_0,esk5_0)
| model_max(esk3_0,esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_62,negated_conjecture,
( minsol_model_max(esk3_0,esk4_0,esk5_0)
| lesseq(esk5_0,max(esk4_0,esk4_0))
| ~ lesseq(esk3_0,max(esk4_0,esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_20]),c_0_23])]) ).
cnf(c_0_63,plain,
( lesseq(X1,max(X2,X2))
| lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_23]) ).
fof(c_0_64,plain,
! [X18,X19] :
( max(X18,X19) = X18
| ~ lesseq(X19,X18) ),
inference(variable_rename,[status(thm)],[c_0_59]) ).
cnf(c_0_65,negated_conjecture,
( model_max(esk3_0,esk4_0,esk5_0)
| lesseq(esk3_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_66,negated_conjecture,
( minsol_model_max(esk3_0,esk4_0,esk5_0)
| lesseq(esk5_0,max(esk4_0,esk4_0))
| lesseq(esk4_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_67,plain,
( lesseq(X1,X2)
| ~ ub(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_68,negated_conjecture,
( minsol_model_max(esk3_0,esk4_0,esk5_0)
| lesseq(X1,esk4_0)
| lesseq(esk5_0,X1)
| ~ lesseq(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_47]) ).
cnf(c_0_69,plain,
( max(X1,X2) = X1
| ~ lesseq(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_70,negated_conjecture,
( max(esk3_0,esk4_0) = esk5_0
| lesseq(esk3_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_65]) ).
cnf(c_0_71,negated_conjecture,
( minsol_model_max(esk3_0,esk4_0,esk5_0)
| lesseq(esk4_0,esk3_0)
| lesseq(esk5_0,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_18]),c_0_23])]) ).
cnf(c_0_72,plain,
( lesseq(X1,X2)
| ~ model_ub(X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_67,c_0_54]) ).
cnf(c_0_73,negated_conjecture,
( minsol_model_max(esk3_0,esk4_0,esk5_0)
| lesseq(esk5_0,esk3_0)
| lesseq(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_68,c_0_23]) ).
fof(c_0_74,plain,
! [X9,X10] :
( ~ lesseq(X9,X10)
| ~ lesseq(X10,X9)
| X9 = X10 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[lesseq_antisymmetric])]) ).
cnf(c_0_75,negated_conjecture,
( esk5_0 = esk3_0
| lesseq(esk3_0,esk5_0)
| ~ lesseq(esk4_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_76,negated_conjecture,
( model_max(esk3_0,esk4_0,esk5_0)
| lesseq(esk5_0,esk4_0)
| lesseq(esk4_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_55,c_0_71]) ).
cnf(c_0_77,negated_conjecture,
( model_max(esk3_0,esk4_0,esk5_0)
| lesseq(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_72,c_0_61]) ).
cnf(c_0_78,negated_conjecture,
( model_max(esk3_0,esk4_0,esk5_0)
| lesseq(esk3_0,esk4_0)
| lesseq(esk5_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_55,c_0_73]) ).
cnf(c_0_79,plain,
( X1 = X2
| ~ lesseq(X1,X2)
| ~ lesseq(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_80,negated_conjecture,
( esk5_0 = esk3_0
| lesseq(esk3_0,esk4_0)
| lesseq(esk3_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_75,c_0_47]) ).
cnf(c_0_81,negated_conjecture,
( max(esk3_0,esk4_0) = esk5_0
| lesseq(esk4_0,esk3_0)
| lesseq(esk5_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_76]) ).
cnf(c_0_82,negated_conjecture,
( max(esk3_0,esk4_0) = esk5_0
| lesseq(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_77]) ).
cnf(c_0_83,negated_conjecture,
( max(esk3_0,esk4_0) = esk5_0
| lesseq(esk5_0,esk3_0)
| lesseq(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_78]) ).
cnf(c_0_84,negated_conjecture,
( esk5_0 = esk3_0
| lesseq(esk3_0,esk4_0)
| ~ lesseq(esk5_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_85,negated_conjecture,
( esk5_0 = esk4_0
| lesseq(esk5_0,esk4_0)
| lesseq(esk4_0,esk3_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_81]),c_0_47]) ).
cnf(c_0_86,negated_conjecture,
( esk5_0 = esk4_0
| lesseq(esk4_0,esk5_0)
| ~ lesseq(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_82]) ).
cnf(c_0_87,negated_conjecture,
( esk5_0 = esk3_0
| lesseq(esk3_0,esk4_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_83]),c_0_47]),c_0_84]) ).
cnf(c_0_88,negated_conjecture,
( esk5_0 = esk4_0
| lesseq(esk3_0,esk5_0)
| ~ lesseq(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_70]) ).
cnf(c_0_89,negated_conjecture,
( esk5_0 = esk4_0
| lesseq(esk4_0,esk3_0)
| ~ lesseq(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_79,c_0_85]) ).
cnf(c_0_90,negated_conjecture,
( esk5_0 = esk3_0
| esk5_0 = esk4_0
| lesseq(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_91,negated_conjecture,
( esk5_0 = esk3_0
| esk5_0 = esk4_0
| lesseq(esk3_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_88,c_0_87]) ).
cnf(c_0_92,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_32]) ).
cnf(c_0_93,negated_conjecture,
( esk5_0 = esk3_0
| esk5_0 = esk4_0
| lesseq(esk4_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_94,negated_conjecture,
( esk5_0 = esk4_0
| esk5_0 = esk3_0
| ~ lesseq(esk5_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_79,c_0_91]) ).
cnf(c_0_95,plain,
( minsol_model_ub(X1,X2,X3)
| model_ub(X1,X2,esk2_3(X1,X2,X3))
| ~ lesseq(X2,X3)
| ~ lesseq(X1,X3) ),
inference(spm,[status(thm)],[c_0_92,c_0_46]) ).
cnf(c_0_96,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_19,c_0_17]) ).
cnf(c_0_97,negated_conjecture,
( esk5_0 = esk4_0
| esk5_0 = esk3_0
| minsol_model_max(esk3_0,esk4_0,esk5_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_93]),c_0_23])]),c_0_94]) ).
cnf(c_0_98,plain,
( minsol_model_ub(X1,X2,X2)
| model_ub(X1,X2,esk2_3(X1,X2,X2))
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_95,c_0_23]) ).
cnf(c_0_99,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_22,c_0_87]) ).
cnf(c_0_100,plain,
( esk1_3(X1,X2,max(X1,X2)) = max(X1,X2)
| minsol_model_max(X1,X2,max(X1,X2)) ),
inference(spm,[status(thm)],[c_0_24,c_0_96]) ).
cnf(c_0_101,negated_conjecture,
( esk5_0 = esk3_0
| esk5_0 = esk4_0
| model_max(esk3_0,esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_55,c_0_97]) ).
cnf(c_0_102,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_98,c_0_87]) ).
cnf(c_0_103,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_24,c_0_99]) ).
cnf(c_0_104,plain,
minsol_model_max(X1,X2,max(X1,X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_100]),c_0_17]),c_0_23])]) ).
cnf(c_0_105,negated_conjecture,
( max(esk3_0,esk4_0) = esk5_0
| esk5_0 = esk4_0
| esk5_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_24,c_0_101]) ).
cnf(c_0_106,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_32]) ).
cnf(c_0_107,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_72,c_0_102]) ).
cnf(c_0_108,negated_conjecture,
( esk5_0 = esk3_0
| minsol_model_max(esk3_0,esk4_0,esk4_0)
| ~ model_max(esk3_0,esk4_0,esk4_0)
| ~ lesseq(esk4_0,max(esk3_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_26,c_0_103]) ).
cnf(c_0_109,plain,
( minsol_model_max(X1,X2,X2)
| ~ lesseq(X1,X2) ),
inference(spm,[status(thm)],[c_0_104,c_0_18]) ).
cnf(c_0_110,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_33]) ).
cnf(c_0_111,negated_conjecture,
( esk5_0 = esk3_0
| esk5_0 = esk4_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_105]),c_0_87]) ).
cnf(c_0_112,negated_conjecture,
( esk5_0 = esk3_0
| minsol_model_ub(esk3_0,esk4_0,esk4_0)
| ~ model_ub(esk3_0,esk4_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_113,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_108,c_0_20]),c_0_87]) ).
cnf(c_0_114,plain,
( lesseq(X1,X2)
| ~ model_max(X3,X1,X2)
| ~ lesseq(X3,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_109]) ).
cnf(c_0_115,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_110,c_0_111]) ).
cnf(c_0_116,negated_conjecture,
( esk5_0 = esk3_0
| minsol_model_ub(esk3_0,esk4_0,esk4_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_46]),c_0_23])]),c_0_87]) ).
cnf(c_0_117,negated_conjecture,
( esk5_0 = esk3_0
| minsol_model_max(esk3_0,esk4_0,esk4_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_18]),c_0_23])]),c_0_87]) ).
cnf(c_0_118,negated_conjecture,
( lesseq(esk4_0,esk5_0)
| ~ lesseq(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_114,c_0_77]) ).
cnf(c_0_119,negated_conjecture,
esk5_0 = esk3_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_117]) ).
cnf(c_0_120,negated_conjecture,
lesseq(esk4_0,esk3_0),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_118,c_0_119]),c_0_47]) ).
cnf(c_0_121,negated_conjecture,
( minsol_model_ub(X1,esk4_0,esk3_0)
| model_ub(X1,esk4_0,esk2_3(X1,esk4_0,esk3_0))
| ~ lesseq(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_95,c_0_120]) ).
cnf(c_0_122,negated_conjecture,
( 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_121,c_0_23]) ).
cnf(c_0_123,negated_conjecture,
( minsol_model_ub(esk3_0,esk4_0,esk3_0)
| lesseq(esk3_0,esk2_3(esk3_0,esk4_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_60,c_0_122]) ).
cnf(c_0_124,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_110,c_0_119]),c_0_119]) ).
cnf(c_0_125,negated_conjecture,
( minsol_model_ub(esk3_0,esk4_0,esk3_0)
| ~ model_ub(esk3_0,esk4_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_106,c_0_123]) ).
cnf(c_0_126,negated_conjecture,
( ~ minsol_model_max(esk3_0,esk4_0,esk3_0)
| ~ model_ub(esk3_0,esk4_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_127,plain,
( minsol_model_max(X1,X2,X1)
| ~ lesseq(X2,X1) ),
inference(spm,[status(thm)],[c_0_104,c_0_69]) ).
cnf(c_0_128,negated_conjecture,
~ model_ub(esk3_0,esk4_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_120])]) ).
cnf(c_0_129,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_46]),c_0_120]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM858+1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.36 % Computer : n016.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Aug 25 13:18:10 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.55 start to proof: theBenchmark
% 45.72/45.82 % Version : CSE_E---1.5
% 45.72/45.82 % Problem : theBenchmark.p
% 45.72/45.82 % Proof found
% 45.72/45.82 % SZS status Theorem for theBenchmark.p
% 45.72/45.82 % SZS output start Proof
% See solution above
% 45.72/45.83 % Total time : 45.245000 s
% 45.72/45.83 % SZS output end Proof
% 45.72/45.83 % Total time : 45.250000 s
%------------------------------------------------------------------------------