%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : PRO009+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n014.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 5 05:01:53 PM UTC 2026
% Result : Theorem 1.63s 1.81s
% Output : CNFRefutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 19
% Syntax : Number of formulae : 118 ( 37 unt; 0 def)
% Number of atoms : 353 ( 14 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 378 ( 143 ~; 155 |; 59 &)
% ( 6 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 172 ( 6 sgn 93 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_27,axiom,
! [X77,X78] :
( ( occurrence_of(X78,X77)
& ~ atomic(X77) )
=> ? [X79] :
( root(X79,X77)
& subactivity_occurrence(X79,X78) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_27) ).
fof(goals,conjecture,
! [X110] :
( occurrence_of(X110,tptp0)
=> ? [X111,X112] :
( occurrence_of(X111,tptp3)
& root_occ(X111,X110)
& ( occurrence_of(X112,tptp2)
| occurrence_of(X112,tptp1) )
& min_precedes(X111,X112,tptp0)
& leaf_occ(X112,X110) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(sos_37,axiom,
~ atomic(tptp0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_37) ).
fof(sos_35,axiom,
! [X106] :
( occurrence_of(X106,tptp0)
=> ? [X107,X108,X109] :
( occurrence_of(X107,tptp3)
& root_occ(X107,X106)
& occurrence_of(X108,tptp4)
& next_subocc(X107,X108,tptp0)
& ( occurrence_of(X109,tptp2)
| occurrence_of(X109,tptp1) )
& next_subocc(X108,X109,tptp0)
& leaf_occ(X109,X106) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_35) ).
fof(sos_24,axiom,
! [X68,X69] :
( subactivity_occurrence(X68,X69)
=> ( activity_occurrence(X68)
& activity_occurrence(X69) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_24) ).
fof(sos_34,axiom,
! [X103,X104] :
( leaf_occ(X103,X104)
<=> ? [X105] :
( occurrence_of(X104,X105)
& subactivity_occurrence(X103,X104)
& leaf(X103,X105) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_34) ).
fof(sos_01,axiom,
! [X3] :
( activity_occurrence(X3)
=> ? [X4] :
( activity(X4)
& occurrence_of(X3,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_01) ).
fof(sos_22,axiom,
! [X61,X62,X63] :
( next_subocc(X61,X62,X63)
<=> ( min_precedes(X61,X62,X63)
& ~ ? [X64] :
( min_precedes(X61,X64,X63)
& min_precedes(X64,X62,X63) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_22) ).
fof(sos_07,axiom,
! [X17,X18] :
( occurrence_of(X17,X18)
=> ( arboreal(X17)
<=> atomic(X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_07) ).
fof(sos_16,axiom,
! [X42,X43] :
( root(X42,X43)
=> legal(X42) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_16) ).
fof(sos_15,axiom,
! [X39,X40,X41] :
( min_precedes(X39,X40,X41)
=> precedes(X39,X40) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_15) ).
fof(sos_08,axiom,
! [X19] :
( legal(X19)
=> arboreal(X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_08) ).
fof(sos_10,axiom,
! [X22,X23] :
( precedes(X22,X23)
<=> ( earlier(X22,X23)
& legal(X23) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_10) ).
fof(sos_28,axiom,
! [X80,X81,X82,X83] :
( ( occurrence_of(X81,X80)
& arboreal(X82)
& arboreal(X83)
& subactivity_occurrence(X82,X81)
& subactivity_occurrence(X83,X81) )
=> ( min_precedes(X82,X83,X80)
| min_precedes(X83,X82,X80)
| X82 = X83 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_28) ).
fof(sos_14,axiom,
! [X36,X37,X38] :
( min_precedes(X36,X37,X38)
=> ~ root(X37,X38) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_14) ).
fof(sos_33,axiom,
! [X100,X101] :
( root_occ(X100,X101)
<=> ? [X102] :
( occurrence_of(X101,X102)
& subactivity_occurrence(X100,X101)
& root(X100,X102) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_33) ).
fof(sos_41,axiom,
atomic(tptp3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_41) ).
fof(sos_02,axiom,
! [X5,X6,X7] :
( ( occurrence_of(X5,X6)
& occurrence_of(X5,X7) )
=> X6 = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_02) ).
fof(sos_21,axiom,
! [X57,X58] :
( leaf(X57,X58)
<=> ( ( root(X57,X58)
| ? [X59] : min_precedes(X59,X57,X58) )
& ~ ? [X60] : min_precedes(X57,X60,X58) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_21) ).
fof(c_0_19,plain,
! [X77,X78] :
( ( occurrence_of(X78,X77)
& ~ atomic(X77) )
=> ? [X79] :
( root(X79,X77)
& subactivity_occurrence(X79,X78) ) ),
inference(fof_simplification,[status(thm)],[sos_27]) ).
fof(c_0_20,negated_conjecture,
~ ! [X110] :
( occurrence_of(X110,tptp0)
=> ? [X111,X112] :
( occurrence_of(X111,tptp3)
& root_occ(X111,X110)
& ( occurrence_of(X112,tptp2)
| occurrence_of(X112,tptp1) )
& min_precedes(X111,X112,tptp0)
& leaf_occ(X112,X110) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_21,plain,
! [X312,X313] :
( ( root(esk12_2(X312,X313),X312)
| ~ occurrence_of(X313,X312)
| atomic(X312) )
& ( subactivity_occurrence(esk12_2(X312,X313),X313)
| ~ occurrence_of(X313,X312)
| atomic(X312) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])]) ).
fof(c_0_22,negated_conjecture,
! [X352,X353] :
( occurrence_of(esk19_0,tptp0)
& ( ~ occurrence_of(X353,tptp2)
| ~ occurrence_of(X352,tptp3)
| ~ root_occ(X352,esk19_0)
| ~ min_precedes(X352,X353,tptp0)
| ~ leaf_occ(X353,esk19_0) )
& ( ~ occurrence_of(X353,tptp1)
| ~ occurrence_of(X352,tptp3)
| ~ root_occ(X352,esk19_0)
| ~ min_precedes(X352,X353,tptp0)
| ~ leaf_occ(X353,esk19_0) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])])]) ).
fof(c_0_23,plain,
~ atomic(tptp0),
inference(fof_simplification,[status(thm)],[sos_37]) ).
fof(c_0_24,plain,
! [X347] :
( ( occurrence_of(esk16_1(X347),tptp3)
| ~ occurrence_of(X347,tptp0) )
& ( root_occ(esk16_1(X347),X347)
| ~ occurrence_of(X347,tptp0) )
& ( occurrence_of(esk17_1(X347),tptp4)
| ~ occurrence_of(X347,tptp0) )
& ( next_subocc(esk16_1(X347),esk17_1(X347),tptp0)
| ~ occurrence_of(X347,tptp0) )
& ( occurrence_of(esk18_1(X347),tptp2)
| occurrence_of(esk18_1(X347),tptp1)
| ~ occurrence_of(X347,tptp0) )
& ( next_subocc(esk17_1(X347),esk18_1(X347),tptp0)
| ~ occurrence_of(X347,tptp0) )
& ( leaf_occ(esk18_1(X347),X347)
| ~ occurrence_of(X347,tptp0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_35])])])]) ).
fof(c_0_25,plain,
! [X303,X304] :
( ( activity_occurrence(X303)
| ~ subactivity_occurrence(X303,X304) )
& ( activity_occurrence(X304)
| ~ subactivity_occurrence(X303,X304) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_24])])]) ).
cnf(c_0_26,plain,
( subactivity_occurrence(esk12_2(X1,X2),X2)
| atomic(X1)
| ~ occurrence_of(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,negated_conjecture,
occurrence_of(esk19_0,tptp0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
~ atomic(tptp0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_29,plain,
! [X341,X342,X344,X345,X346] :
( ( occurrence_of(X342,esk15_2(X341,X342))
| ~ leaf_occ(X341,X342) )
& ( subactivity_occurrence(X341,X342)
| ~ leaf_occ(X341,X342) )
& ( leaf(X341,esk15_2(X341,X342))
| ~ leaf_occ(X341,X342) )
& ( ~ occurrence_of(X345,X346)
| ~ subactivity_occurrence(X344,X345)
| ~ leaf(X344,X346)
| leaf_occ(X344,X345) ) ),
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)],[sos_34])])])])])]) ).
cnf(c_0_30,plain,
( leaf_occ(esk18_1(X1),X1)
| ~ occurrence_of(X1,tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_31,plain,
! [X227] :
( ( activity(esk1_1(X227))
| ~ activity_occurrence(X227) )
& ( occurrence_of(X227,esk1_1(X227))
| ~ activity_occurrence(X227) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_01])])])]) ).
cnf(c_0_32,plain,
( activity_occurrence(X1)
| ~ subactivity_occurrence(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_33,negated_conjecture,
subactivity_occurrence(esk12_2(tptp0,esk19_0),esk19_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_34,plain,
( subactivity_occurrence(X1,X2)
| ~ leaf_occ(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,negated_conjecture,
leaf_occ(esk18_1(esk19_0),esk19_0),
inference(spm,[status(thm)],[c_0_30,c_0_27]) ).
fof(c_0_36,plain,
! [X289,X290,X291,X292,X293,X294,X295] :
( ( min_precedes(X289,X290,X291)
| ~ next_subocc(X289,X290,X291) )
& ( ~ min_precedes(X289,X292,X291)
| ~ min_precedes(X292,X290,X291)
| ~ next_subocc(X289,X290,X291) )
& ( min_precedes(X293,esk8_3(X293,X294,X295),X295)
| ~ min_precedes(X293,X294,X295)
| next_subocc(X293,X294,X295) )
& ( min_precedes(esk8_3(X293,X294,X295),X294,X295)
| ~ min_precedes(X293,X294,X295)
| next_subocc(X293,X294,X295) ) ),
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)],[sos_22])])])])])]) ).
cnf(c_0_37,plain,
( next_subocc(esk17_1(X1),esk18_1(X1),tptp0)
| ~ occurrence_of(X1,tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_38,plain,
! [X241,X242] :
( ( ~ arboreal(X241)
| atomic(X242)
| ~ occurrence_of(X241,X242) )
& ( ~ atomic(X242)
| arboreal(X241)
| ~ occurrence_of(X241,X242) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_07])])]) ).
cnf(c_0_39,plain,
( occurrence_of(X1,esk1_1(X1))
| ~ activity_occurrence(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_40,negated_conjecture,
activity_occurrence(esk12_2(tptp0,esk19_0)),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
fof(c_0_41,plain,
! [X266,X267] :
( ~ root(X266,X267)
| legal(X266) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_16])]) ).
cnf(c_0_42,plain,
( root(esk12_2(X1,X2),X1)
| atomic(X1)
| ~ occurrence_of(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_43,negated_conjecture,
subactivity_occurrence(esk18_1(esk19_0),esk19_0),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
fof(c_0_44,plain,
! [X263,X264,X265] :
( ~ min_precedes(X263,X264,X265)
| precedes(X263,X264) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_15])]) ).
cnf(c_0_45,plain,
( min_precedes(X1,X2,X3)
| ~ next_subocc(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_46,negated_conjecture,
next_subocc(esk17_1(esk19_0),esk18_1(esk19_0),tptp0),
inference(spm,[status(thm)],[c_0_37,c_0_27]) ).
cnf(c_0_47,plain,
( atomic(X2)
| ~ arboreal(X1)
| ~ occurrence_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_48,negated_conjecture,
occurrence_of(esk12_2(tptp0,esk19_0),esk1_1(esk12_2(tptp0,esk19_0))),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
fof(c_0_49,plain,
! [X243] :
( ~ legal(X243)
| arboreal(X243) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_08])]) ).
cnf(c_0_50,plain,
( legal(X1)
| ~ root(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_51,negated_conjecture,
root(esk12_2(tptp0,esk19_0),tptp0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_27]),c_0_28]) ).
cnf(c_0_52,negated_conjecture,
activity_occurrence(esk18_1(esk19_0)),
inference(spm,[status(thm)],[c_0_32,c_0_43]) ).
fof(c_0_53,plain,
! [X246,X247] :
( ( earlier(X246,X247)
| ~ precedes(X246,X247) )
& ( legal(X247)
| ~ precedes(X246,X247) )
& ( ~ earlier(X246,X247)
| ~ legal(X247)
| precedes(X246,X247) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_10])])]) ).
cnf(c_0_54,plain,
( precedes(X1,X2)
| ~ min_precedes(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_55,negated_conjecture,
min_precedes(esk17_1(esk19_0),esk18_1(esk19_0),tptp0),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_56,plain,
( arboreal(X2)
| ~ atomic(X1)
| ~ occurrence_of(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_57,negated_conjecture,
( atomic(esk1_1(esk12_2(tptp0,esk19_0)))
| ~ arboreal(esk12_2(tptp0,esk19_0)) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_58,plain,
( arboreal(X1)
| ~ legal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_59,negated_conjecture,
legal(esk12_2(tptp0,esk19_0)),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_60,negated_conjecture,
occurrence_of(esk18_1(esk19_0),esk1_1(esk18_1(esk19_0))),
inference(spm,[status(thm)],[c_0_39,c_0_52]) ).
cnf(c_0_61,plain,
( legal(X1)
| ~ precedes(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_62,negated_conjecture,
precedes(esk17_1(esk19_0),esk18_1(esk19_0)),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
fof(c_0_63,plain,
! [X315,X316,X317,X318] :
( ~ occurrence_of(X316,X315)
| ~ arboreal(X317)
| ~ arboreal(X318)
| ~ subactivity_occurrence(X317,X316)
| ~ subactivity_occurrence(X318,X316)
| min_precedes(X317,X318,X315)
| min_precedes(X318,X317,X315)
| X317 = X318 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_28])]) ).
cnf(c_0_64,negated_conjecture,
( arboreal(esk12_2(tptp0,esk19_0))
| ~ atomic(esk1_1(esk12_2(tptp0,esk19_0))) ),
inference(spm,[status(thm)],[c_0_56,c_0_48]) ).
cnf(c_0_65,negated_conjecture,
atomic(esk1_1(esk12_2(tptp0,esk19_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59])]) ).
cnf(c_0_66,negated_conjecture,
( atomic(esk1_1(esk18_1(esk19_0)))
| ~ arboreal(esk18_1(esk19_0)) ),
inference(spm,[status(thm)],[c_0_47,c_0_60]) ).
cnf(c_0_67,negated_conjecture,
legal(esk18_1(esk19_0)),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_68,plain,
( min_precedes(X3,X4,X2)
| min_precedes(X4,X3,X2)
| X3 = X4
| ~ occurrence_of(X1,X2)
| ~ arboreal(X3)
| ~ arboreal(X4)
| ~ subactivity_occurrence(X3,X1)
| ~ subactivity_occurrence(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_69,negated_conjecture,
arboreal(esk12_2(tptp0,esk19_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65])]) ).
cnf(c_0_70,negated_conjecture,
atomic(esk1_1(esk18_1(esk19_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_58]),c_0_67])]) ).
fof(c_0_71,plain,
! [X36,X37,X38] :
( min_precedes(X36,X37,X38)
=> ~ root(X37,X38) ),
inference(fof_simplification,[status(thm)],[sos_14]) ).
fof(c_0_72,plain,
! [X335,X336,X338,X339,X340] :
( ( occurrence_of(X336,esk14_2(X335,X336))
| ~ root_occ(X335,X336) )
& ( subactivity_occurrence(X335,X336)
| ~ root_occ(X335,X336) )
& ( root(X335,esk14_2(X335,X336))
| ~ root_occ(X335,X336) )
& ( ~ occurrence_of(X339,X340)
| ~ subactivity_occurrence(X338,X339)
| ~ root(X338,X340)
| root_occ(X338,X339) ) ),
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)],[sos_33])])])])])]) ).
cnf(c_0_73,plain,
( root_occ(esk16_1(X1),X1)
| ~ occurrence_of(X1,tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_74,plain,
( occurrence_of(esk16_1(X1),tptp3)
| ~ occurrence_of(X1,tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_75,negated_conjecture,
( X1 = esk12_2(tptp0,esk19_0)
| min_precedes(X1,esk12_2(tptp0,esk19_0),X2)
| min_precedes(esk12_2(tptp0,esk19_0),X1,X2)
| ~ subactivity_occurrence(X1,esk19_0)
| ~ arboreal(X1)
| ~ occurrence_of(esk19_0,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_33]),c_0_69])]) ).
cnf(c_0_76,negated_conjecture,
arboreal(esk18_1(esk19_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_60]),c_0_70])]) ).
fof(c_0_77,plain,
! [X260,X261,X262] :
( ~ min_precedes(X260,X261,X262)
| ~ root(X261,X262) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_71])]) ).
cnf(c_0_78,plain,
( subactivity_occurrence(X1,X2)
| ~ root_occ(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_79,negated_conjecture,
root_occ(esk16_1(esk19_0),esk19_0),
inference(spm,[status(thm)],[c_0_73,c_0_27]) ).
cnf(c_0_80,negated_conjecture,
occurrence_of(esk16_1(esk19_0),tptp3),
inference(spm,[status(thm)],[c_0_74,c_0_27]) ).
cnf(c_0_81,plain,
atomic(tptp3),
inference(split_conjunct,[status(thm)],[sos_41]) ).
cnf(c_0_82,negated_conjecture,
( ~ occurrence_of(X1,tptp1)
| ~ occurrence_of(X2,tptp3)
| ~ root_occ(X2,esk19_0)
| ~ min_precedes(X2,X1,tptp0)
| ~ leaf_occ(X1,esk19_0) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_83,plain,
( occurrence_of(esk18_1(X1),tptp2)
| occurrence_of(esk18_1(X1),tptp1)
| ~ occurrence_of(X1,tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_84,negated_conjecture,
( ~ occurrence_of(X1,tptp2)
| ~ occurrence_of(X2,tptp3)
| ~ root_occ(X2,esk19_0)
| ~ min_precedes(X2,X1,tptp0)
| ~ leaf_occ(X1,esk19_0) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_85,plain,
! [X229,X230,X231] :
( ~ occurrence_of(X229,X230)
| ~ occurrence_of(X229,X231)
| X230 = X231 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_02])]) ).
cnf(c_0_86,negated_conjecture,
( esk12_2(tptp0,esk19_0) = esk18_1(esk19_0)
| min_precedes(esk12_2(tptp0,esk19_0),esk18_1(esk19_0),X1)
| min_precedes(esk18_1(esk19_0),esk12_2(tptp0,esk19_0),X1)
| ~ occurrence_of(esk19_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_43]),c_0_76])]) ).
cnf(c_0_87,plain,
( ~ min_precedes(X1,X2,X3)
| ~ root(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_88,negated_conjecture,
subactivity_occurrence(esk16_1(esk19_0),esk19_0),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_89,negated_conjecture,
arboreal(esk16_1(esk19_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_80]),c_0_81])]) ).
cnf(c_0_90,negated_conjecture,
( ~ root_occ(X1,esk19_0)
| ~ min_precedes(X1,esk18_1(esk19_0),tptp0)
| ~ occurrence_of(esk18_1(esk19_0),tptp1)
| ~ occurrence_of(X1,tptp3) ),
inference(spm,[status(thm)],[c_0_82,c_0_35]) ).
cnf(c_0_91,negated_conjecture,
( occurrence_of(esk18_1(esk19_0),tptp1)
| occurrence_of(esk18_1(esk19_0),tptp2) ),
inference(spm,[status(thm)],[c_0_83,c_0_27]) ).
cnf(c_0_92,negated_conjecture,
( ~ root_occ(X1,esk19_0)
| ~ min_precedes(X1,esk18_1(esk19_0),tptp0)
| ~ occurrence_of(esk18_1(esk19_0),tptp2)
| ~ occurrence_of(X1,tptp3) ),
inference(spm,[status(thm)],[c_0_84,c_0_35]) ).
cnf(c_0_93,plain,
( X2 = X3
| ~ occurrence_of(X1,X2)
| ~ occurrence_of(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_94,plain,
( occurrence_of(X1,esk14_2(X2,X1))
| ~ root_occ(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_95,negated_conjecture,
( esk12_2(tptp0,esk19_0) = esk18_1(esk19_0)
| min_precedes(esk18_1(esk19_0),esk12_2(tptp0,esk19_0),tptp0)
| min_precedes(esk12_2(tptp0,esk19_0),esk18_1(esk19_0),tptp0) ),
inference(spm,[status(thm)],[c_0_86,c_0_27]) ).
cnf(c_0_96,negated_conjecture,
~ root(esk18_1(esk19_0),tptp0),
inference(spm,[status(thm)],[c_0_87,c_0_55]) ).
cnf(c_0_97,negated_conjecture,
( esk12_2(tptp0,esk19_0) = esk16_1(esk19_0)
| min_precedes(esk12_2(tptp0,esk19_0),esk16_1(esk19_0),X1)
| min_precedes(esk16_1(esk19_0),esk12_2(tptp0,esk19_0),X1)
| ~ occurrence_of(esk19_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_88]),c_0_89])]) ).
cnf(c_0_98,negated_conjecture,
( ~ root_occ(X1,esk19_0)
| ~ min_precedes(X1,esk18_1(esk19_0),tptp0)
| ~ occurrence_of(X1,tptp3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]) ).
cnf(c_0_99,negated_conjecture,
( X1 = tptp0
| ~ occurrence_of(esk19_0,X1) ),
inference(spm,[status(thm)],[c_0_93,c_0_27]) ).
cnf(c_0_100,negated_conjecture,
occurrence_of(esk19_0,esk14_2(esk16_1(esk19_0),esk19_0)),
inference(spm,[status(thm)],[c_0_94,c_0_79]) ).
cnf(c_0_101,negated_conjecture,
( min_precedes(esk12_2(tptp0,esk19_0),esk18_1(esk19_0),tptp0)
| min_precedes(esk18_1(esk19_0),esk12_2(tptp0,esk19_0),tptp0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_95]),c_0_96]) ).
cnf(c_0_102,negated_conjecture,
( esk12_2(tptp0,esk19_0) = esk16_1(esk19_0)
| min_precedes(esk16_1(esk19_0),esk12_2(tptp0,esk19_0),tptp0)
| min_precedes(esk12_2(tptp0,esk19_0),esk16_1(esk19_0),tptp0) ),
inference(spm,[status(thm)],[c_0_97,c_0_27]) ).
cnf(c_0_103,negated_conjecture,
~ min_precedes(esk16_1(esk19_0),esk18_1(esk19_0),tptp0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_79]),c_0_80])]) ).
cnf(c_0_104,plain,
( root(X1,esk14_2(X1,X2))
| ~ root_occ(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_105,negated_conjecture,
esk14_2(esk16_1(esk19_0),esk19_0) = tptp0,
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_106,plain,
( occurrence_of(X1,esk15_2(X2,X1))
| ~ leaf_occ(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_107,negated_conjecture,
( min_precedes(esk12_2(tptp0,esk19_0),esk16_1(esk19_0),tptp0)
| min_precedes(esk16_1(esk19_0),esk12_2(tptp0,esk19_0),tptp0)
| min_precedes(esk18_1(esk19_0),esk16_1(esk19_0),tptp0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_103]) ).
cnf(c_0_108,negated_conjecture,
root(esk16_1(esk19_0),tptp0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_79]),c_0_105]) ).
cnf(c_0_109,negated_conjecture,
occurrence_of(esk19_0,esk15_2(esk18_1(esk19_0),esk19_0)),
inference(spm,[status(thm)],[c_0_106,c_0_35]) ).
fof(c_0_110,plain,
! [X281,X282,X284,X285,X286,X287] :
( ( root(X281,X282)
| min_precedes(esk6_2(X281,X282),X281,X282)
| ~ leaf(X281,X282) )
& ( ~ min_precedes(X281,X284,X282)
| ~ leaf(X281,X282) )
& ( ~ root(X285,X286)
| min_precedes(X285,esk7_2(X285,X286),X286)
| leaf(X285,X286) )
& ( ~ min_precedes(X287,X285,X286)
| min_precedes(X285,esk7_2(X285,X286),X286)
| leaf(X285,X286) ) ),
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)],[sos_21])])])])])]) ).
cnf(c_0_111,negated_conjecture,
( min_precedes(esk16_1(esk19_0),esk12_2(tptp0,esk19_0),tptp0)
| min_precedes(esk18_1(esk19_0),esk16_1(esk19_0),tptp0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_107]),c_0_108])]) ).
cnf(c_0_112,plain,
( leaf(X1,esk15_2(X1,X2))
| ~ leaf_occ(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_113,negated_conjecture,
esk15_2(esk18_1(esk19_0),esk19_0) = tptp0,
inference(spm,[status(thm)],[c_0_99,c_0_109]) ).
cnf(c_0_114,plain,
( ~ min_precedes(X1,X2,X3)
| ~ leaf(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_115,negated_conjecture,
min_precedes(esk18_1(esk19_0),esk16_1(esk19_0),tptp0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_111]),c_0_51])]) ).
cnf(c_0_116,negated_conjecture,
leaf(esk18_1(esk19_0),tptp0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_35]),c_0_113]) ).
cnf(c_0_117,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_116])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PRO009+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n014.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 01:31:36 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.63/1.81 % Version : CSE_E---1.7
% 1.63/1.81 % Problem : theBenchmark.p
% 1.63/1.81 % SZS status Theorem for theBenchmark.p
% 1.63/1.81 % SZS output start CNFRefutation
% See solution above
% 1.63/1.81 % Total time : 1.369s
%------------------------------------------------------------------------------