%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : PRO009+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 01:59:31 PM UTC 2026
% Result : Theorem 1.07s 0.70s
% Output : CNFRefutation 1.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 20
% Syntax : Number of formulae : 131 ( 43 unt; 0 def)
% Number of atoms : 372 ( 17 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 397 ( 156 ~; 161 |; 58 &)
% ( 5 <=>; 17 =>; 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 : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 188 ( 5 sgn 99 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_27,axiom,
! [X77,X78] :
( ( ~ atomic(X77)
& occurrence_of(X78,X77) )
=> ? [X79] :
( subactivity_occurrence(X79,X78)
& root(X79,X77) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_27) ).
fof(goals,conjecture,
! [X110] :
( occurrence_of(X110,tptp0)
=> ? [X111,X112] :
( leaf_occ(X112,X110)
& min_precedes(X111,X112,tptp0)
& ( occurrence_of(X112,tptp1)
| occurrence_of(X112,tptp2) )
& root_occ(X111,X110)
& occurrence_of(X111,tptp3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(sos_37,axiom,
~ atomic(tptp0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_37) ).
fof(sos_24,axiom,
! [X68,X69] :
( subactivity_occurrence(X68,X69)
=> ( activity_occurrence(X69)
& activity_occurrence(X68) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_24) ).
fof(sos_35,axiom,
! [X106] :
( occurrence_of(X106,tptp0)
=> ? [X107,X108,X109] :
( leaf_occ(X109,X106)
& next_subocc(X108,X109,tptp0)
& ( occurrence_of(X109,tptp1)
| occurrence_of(X109,tptp2) )
& next_subocc(X107,X108,tptp0)
& occurrence_of(X108,tptp4)
& root_occ(X107,X106)
& occurrence_of(X107,tptp3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_35) ).
fof(sos_01,axiom,
! [X3] :
( activity_occurrence(X3)
=> ? [X4] :
( occurrence_of(X3,X4)
& activity(X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_01) ).
fof(sos_34,axiom,
! [X103,X104] :
( leaf_occ(X103,X104)
<=> ? [X105] :
( leaf(X103,X105)
& subactivity_occurrence(X103,X104)
& occurrence_of(X104,X105) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_34) ).
fof(sos_07,axiom,
! [X17,X18] :
( occurrence_of(X17,X18)
=> ( arboreal(X17)
<=> atomic(X18) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_07) ).
fof(sos_16,axiom,
! [X42,X43] :
( root(X42,X43)
=> legal(X42) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_16) ).
fof(sos_22,axiom,
! [X61,X62,X63] :
( next_subocc(X61,X62,X63)
<=> ( ~ ? [X64] :
( min_precedes(X64,X62,X63)
& min_precedes(X61,X64,X63) )
& min_precedes(X61,X62,X63) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_22) ).
fof(sos_08,axiom,
! [X19] :
( legal(X19)
=> arboreal(X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_08) ).
fof(sos_15,axiom,
! [X39,X40,X41] :
( min_precedes(X39,X40,X41)
=> precedes(X39,X40) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_15) ).
fof(sos_10,axiom,
! [X22,X23] :
( precedes(X22,X23)
<=> ( legal(X23)
& earlier(X22,X23) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_10) ).
fof(sos_28,axiom,
! [X80,X81,X82,X83] :
( ( subactivity_occurrence(X83,X81)
& subactivity_occurrence(X82,X81)
& arboreal(X83)
& arboreal(X82)
& occurrence_of(X81,X80) )
=> ( X82 = X83
| min_precedes(X83,X82,X80)
| min_precedes(X82,X83,X80) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_28) ).
fof(sos_33,axiom,
! [X100,X101] :
( root_occ(X100,X101)
<=> ? [X102] :
( root(X100,X102)
& subactivity_occurrence(X100,X101)
& occurrence_of(X101,X102) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_33) ).
fof(sos_02,axiom,
! [X5,X6,X7] :
( ( occurrence_of(X5,X7)
& occurrence_of(X5,X6) )
=> X6 = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_02) ).
fof(sos_41,axiom,
atomic(tptp3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_41) ).
fof(sos_14,axiom,
! [X36,X37,X38] :
( min_precedes(X36,X37,X38)
=> ~ root(X37,X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_14) ).
fof(sos_05,axiom,
! [X11,X12,X13] :
( ( earlier(X12,X13)
& earlier(X11,X12) )
=> earlier(X11,X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_05) ).
fof(sos_18,axiom,
! [X46,X47,X48,X49] :
( ( precedes(X47,X48)
& min_precedes(X46,X48,X49)
& min_precedes(X46,X47,X49) )
=> min_precedes(X47,X48,X49) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_18) ).
fof(c_0_20,plain,
! [X77,X78] :
( ( ~ atomic(X77)
& occurrence_of(X78,X77) )
=> ? [X79] :
( subactivity_occurrence(X79,X78)
& root(X79,X77) ) ),
inference(fof_simplification,[status(thm)],[sos_27]) ).
fof(c_0_21,negated_conjecture,
~ ! [X110] :
( occurrence_of(X110,tptp0)
=> ? [X111,X112] :
( leaf_occ(X112,X110)
& min_precedes(X111,X112,tptp0)
& ( occurrence_of(X112,tptp1)
| occurrence_of(X112,tptp2) )
& root_occ(X111,X110)
& occurrence_of(X111,tptp3) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_22,plain,
~ atomic(tptp0),
inference(fof_simplification,[status(thm)],[sos_37]) ).
fof(c_0_23,plain,
! [X200,X201] :
( ( atomic(X200)
| ~ occurrence_of(X201,X200)
| subactivity_occurrence(esk12_2(X200,X201),X201) )
& ( atomic(X200)
| ~ occurrence_of(X201,X200)
| root(esk12_2(X200,X201),X200) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])])]) ).
fof(c_0_24,negated_conjecture,
! [X240,X241] :
( ( ~ leaf_occ(X241,esk19_0)
| ~ min_precedes(X240,X241,tptp0)
| ~ root_occ(X240,esk19_0)
| ~ occurrence_of(X240,tptp3)
| ~ occurrence_of(X241,tptp1) )
& ( ~ leaf_occ(X241,esk19_0)
| ~ min_precedes(X240,X241,tptp0)
| ~ root_occ(X240,esk19_0)
| ~ occurrence_of(X240,tptp3)
| ~ occurrence_of(X241,tptp2) )
& occurrence_of(esk19_0,tptp0) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])])])]) ).
fof(c_0_25,plain,
~ atomic(tptp0),
inference(fof_nnf,[status(thm)],[c_0_22]) ).
fof(c_0_26,plain,
! [X191,X192] :
( ( ~ subactivity_occurrence(X191,X192)
| activity_occurrence(X192) )
& ( ~ subactivity_occurrence(X191,X192)
| activity_occurrence(X191) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_24])])])]) ).
cnf(c_0_27,plain,
( ~ occurrence_of(X2,X1)
| atomic(X1)
| subactivity_occurrence(esk12_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,negated_conjecture,
occurrence_of(esk19_0,tptp0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
~ atomic(tptp0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_30,plain,
! [X235] :
( ( ~ occurrence_of(X235,tptp0)
| leaf_occ(esk18_1(X235),X235) )
& ( ~ occurrence_of(X235,tptp0)
| next_subocc(esk17_1(X235),esk18_1(X235),tptp0) )
& ( ~ occurrence_of(X235,tptp0)
| occurrence_of(esk18_1(X235),tptp1)
| occurrence_of(esk18_1(X235),tptp2) )
& ( ~ occurrence_of(X235,tptp0)
| next_subocc(esk16_1(X235),esk17_1(X235),tptp0) )
& ( ~ occurrence_of(X235,tptp0)
| occurrence_of(esk17_1(X235),tptp4) )
& ( ~ occurrence_of(X235,tptp0)
| root_occ(esk16_1(X235),X235) )
& ( ~ occurrence_of(X235,tptp0)
| occurrence_of(esk16_1(X235),tptp3) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_35])])])])]) ).
fof(c_0_31,plain,
! [X115] :
( ( ~ activity_occurrence(X115)
| occurrence_of(X115,esk1_1(X115)) )
& ( ~ activity_occurrence(X115)
| activity(esk1_1(X115)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_01])])])])]) ).
cnf(c_0_32,plain,
( ~ subactivity_occurrence(X1,X2)
| activity_occurrence(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
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_27,c_0_28]),c_0_29]) ).
fof(c_0_34,plain,
! [X229,X230,X232,X233,X234] :
( ( leaf_occ(X232,X233)
| ~ leaf(X232,X234)
| ~ subactivity_occurrence(X232,X233)
| ~ occurrence_of(X233,X234) )
& ( ~ leaf_occ(X229,X230)
| leaf(X229,esk15_2(X229,X230)) )
& ( ~ leaf_occ(X229,X230)
| subactivity_occurrence(X229,X230) )
& ( ~ leaf_occ(X229,X230)
| occurrence_of(X230,esk15_2(X229,X230)) ) ),
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)],[sos_34])])])])])])]) ).
cnf(c_0_35,plain,
( ~ occurrence_of(X1,tptp0)
| leaf_occ(esk18_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_36,plain,
! [X129,X130] :
( ( ~ occurrence_of(X129,X130)
| arboreal(X129)
| ~ atomic(X130) )
& ( ~ occurrence_of(X129,X130)
| atomic(X130)
| ~ arboreal(X129) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_07])])])]) ).
cnf(c_0_37,plain,
( ~ activity_occurrence(X1)
| occurrence_of(X1,esk1_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,negated_conjecture,
activity_occurrence(esk12_2(tptp0,esk19_0)),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
fof(c_0_39,plain,
! [X154,X155] :
( legal(X154)
| ~ root(X154,X155) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_16])])]) ).
cnf(c_0_40,plain,
( ~ occurrence_of(X2,X1)
| atomic(X1)
| root(esk12_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_41,plain,
( ~ leaf_occ(X1,X2)
| subactivity_occurrence(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,negated_conjecture,
leaf_occ(esk18_1(esk19_0),esk19_0),
inference(spm,[status(thm)],[c_0_35,c_0_28]) ).
fof(c_0_43,plain,
! [X177,X178,X179,X180,X181,X182,X183] :
( ( next_subocc(X181,X182,X183)
| ~ min_precedes(X181,X182,X183)
| min_precedes(esk8_3(X181,X182,X183),X182,X183) )
& ( next_subocc(X181,X182,X183)
| ~ min_precedes(X181,X182,X183)
| min_precedes(X181,esk8_3(X181,X182,X183),X183) )
& ( ~ next_subocc(X177,X178,X179)
| ~ min_precedes(X180,X178,X179)
| ~ min_precedes(X177,X180,X179) )
& ( ~ next_subocc(X177,X178,X179)
| min_precedes(X177,X178,X179) ) ),
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)],[sos_22])])])])])])]) ).
cnf(c_0_44,plain,
( ~ occurrence_of(X1,tptp0)
| next_subocc(esk17_1(X1),esk18_1(X1),tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_45,plain,
( ~ occurrence_of(X1,X2)
| ~ arboreal(X1)
| atomic(X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_46,negated_conjecture,
occurrence_of(esk12_2(tptp0,esk19_0),esk1_1(esk12_2(tptp0,esk19_0))),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
fof(c_0_47,plain,
! [X131] :
( arboreal(X131)
| ~ legal(X131) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_08])])]) ).
cnf(c_0_48,plain,
( ~ root(X1,X2)
| legal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_49,negated_conjecture,
root(esk12_2(tptp0,esk19_0),tptp0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_28]),c_0_29]) ).
cnf(c_0_50,negated_conjecture,
subactivity_occurrence(esk18_1(esk19_0),esk19_0),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
fof(c_0_51,plain,
! [X151,X152,X153] :
( precedes(X151,X152)
| ~ min_precedes(X151,X152,X153) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_15])])]) ).
cnf(c_0_52,plain,
( ~ next_subocc(X1,X2,X3)
| min_precedes(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_53,negated_conjecture,
next_subocc(esk17_1(esk19_0),esk18_1(esk19_0),tptp0),
inference(spm,[status(thm)],[c_0_44,c_0_28]) ).
cnf(c_0_54,plain,
( ~ occurrence_of(X2,X1)
| ~ atomic(X1)
| arboreal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_55,negated_conjecture,
( ~ arboreal(esk12_2(tptp0,esk19_0))
| atomic(esk1_1(esk12_2(tptp0,esk19_0))) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_56,plain,
( ~ legal(X1)
| arboreal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_57,negated_conjecture,
legal(esk12_2(tptp0,esk19_0)),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_58,negated_conjecture,
activity_occurrence(esk18_1(esk19_0)),
inference(spm,[status(thm)],[c_0_32,c_0_50]) ).
fof(c_0_59,plain,
! [X134,X135] :
( ( precedes(X134,X135)
| ~ legal(X135)
| ~ earlier(X134,X135) )
& ( ~ precedes(X134,X135)
| legal(X135) )
& ( ~ precedes(X134,X135)
| earlier(X134,X135) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_10])])])]) ).
cnf(c_0_60,plain,
( ~ min_precedes(X1,X2,X3)
| precedes(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_61,negated_conjecture,
min_precedes(esk17_1(esk19_0),esk18_1(esk19_0),tptp0),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
fof(c_0_62,plain,
! [X203,X204,X205,X206] :
( X205 = X206
| min_precedes(X206,X205,X203)
| min_precedes(X205,X206,X203)
| ~ subactivity_occurrence(X206,X204)
| ~ subactivity_occurrence(X205,X204)
| ~ arboreal(X206)
| ~ arboreal(X205)
| ~ occurrence_of(X204,X203) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_28])])]) ).
cnf(c_0_63,negated_conjecture,
( ~ atomic(esk1_1(esk12_2(tptp0,esk19_0)))
| arboreal(esk12_2(tptp0,esk19_0)) ),
inference(spm,[status(thm)],[c_0_54,c_0_46]) ).
cnf(c_0_64,negated_conjecture,
atomic(esk1_1(esk12_2(tptp0,esk19_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57])]) ).
fof(c_0_65,plain,
! [X223,X224,X226,X227,X228] :
( ( root_occ(X226,X227)
| ~ root(X226,X228)
| ~ subactivity_occurrence(X226,X227)
| ~ occurrence_of(X227,X228) )
& ( ~ root_occ(X223,X224)
| root(X223,esk14_2(X223,X224)) )
& ( ~ root_occ(X223,X224)
| subactivity_occurrence(X223,X224) )
& ( ~ root_occ(X223,X224)
| occurrence_of(X224,esk14_2(X223,X224)) ) ),
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)],[sos_33])])])])])])]) ).
cnf(c_0_66,plain,
( ~ occurrence_of(X1,tptp0)
| root_occ(esk16_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_67,plain,
( ~ occurrence_of(X1,tptp0)
| occurrence_of(esk16_1(X1),tptp3) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_68,plain,
! [X117,X118,X119] :
( X118 = X119
| ~ occurrence_of(X117,X119)
| ~ occurrence_of(X117,X118) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_02])])]) ).
cnf(c_0_69,plain,
( ~ occurrence_of(X1,tptp0)
| next_subocc(esk16_1(X1),esk17_1(X1),tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_70,negated_conjecture,
occurrence_of(esk18_1(esk19_0),esk1_1(esk18_1(esk19_0))),
inference(spm,[status(thm)],[c_0_37,c_0_58]) ).
cnf(c_0_71,plain,
( ~ precedes(X2,X1)
| legal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_72,negated_conjecture,
precedes(esk17_1(esk19_0),esk18_1(esk19_0)),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_73,plain,
( ~ subactivity_occurrence(X4,X1)
| ~ subactivity_occurrence(X3,X1)
| ~ arboreal(X4)
| ~ arboreal(X3)
| ~ occurrence_of(X1,X2)
| X3 = X4
| min_precedes(X4,X3,X2)
| min_precedes(X3,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_74,negated_conjecture,
arboreal(esk12_2(tptp0,esk19_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64])]) ).
cnf(c_0_75,plain,
( ~ root_occ(X1,X2)
| subactivity_occurrence(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_76,negated_conjecture,
root_occ(esk16_1(esk19_0),esk19_0),
inference(spm,[status(thm)],[c_0_66,c_0_28]) ).
cnf(c_0_77,negated_conjecture,
occurrence_of(esk16_1(esk19_0),tptp3),
inference(spm,[status(thm)],[c_0_67,c_0_28]) ).
cnf(c_0_78,plain,
atomic(tptp3),
inference(split_conjunct,[status(thm)],[sos_41]) ).
cnf(c_0_79,plain,
( ~ occurrence_of(X1,X3)
| ~ occurrence_of(X1,X2)
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_80,plain,
( ~ root_occ(X2,X1)
| occurrence_of(X1,esk14_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_81,negated_conjecture,
next_subocc(esk16_1(esk19_0),esk17_1(esk19_0),tptp0),
inference(spm,[status(thm)],[c_0_69,c_0_28]) ).
cnf(c_0_82,negated_conjecture,
( ~ arboreal(esk18_1(esk19_0))
| atomic(esk1_1(esk18_1(esk19_0))) ),
inference(spm,[status(thm)],[c_0_45,c_0_70]) ).
cnf(c_0_83,negated_conjecture,
legal(esk18_1(esk19_0)),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
fof(c_0_84,plain,
! [X36,X37,X38] :
( min_precedes(X36,X37,X38)
=> ~ root(X37,X38) ),
inference(fof_simplification,[status(thm)],[sos_14]) ).
cnf(c_0_85,negated_conjecture,
( ~ occurrence_of(esk19_0,X2)
| ~ arboreal(X1)
| ~ subactivity_occurrence(X1,esk19_0)
| min_precedes(esk12_2(tptp0,esk19_0),X1,X2)
| min_precedes(X1,esk12_2(tptp0,esk19_0),X2)
| X1 = esk12_2(tptp0,esk19_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_33]),c_0_74])]) ).
cnf(c_0_86,negated_conjecture,
subactivity_occurrence(esk16_1(esk19_0),esk19_0),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_87,negated_conjecture,
arboreal(esk16_1(esk19_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_77]),c_0_78])]) ).
cnf(c_0_88,negated_conjecture,
( ~ occurrence_of(esk19_0,X1)
| X1 = tptp0 ),
inference(spm,[status(thm)],[c_0_79,c_0_28]) ).
cnf(c_0_89,negated_conjecture,
occurrence_of(esk19_0,esk14_2(esk16_1(esk19_0),esk19_0)),
inference(spm,[status(thm)],[c_0_80,c_0_76]) ).
fof(c_0_90,plain,
! [X123,X124,X125] :
( earlier(X123,X125)
| ~ earlier(X124,X125)
| ~ earlier(X123,X124) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_05])])]) ).
cnf(c_0_91,plain,
( ~ precedes(X1,X2)
| earlier(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_92,negated_conjecture,
min_precedes(esk16_1(esk19_0),esk17_1(esk19_0),tptp0),
inference(spm,[status(thm)],[c_0_52,c_0_81]) ).
cnf(c_0_93,negated_conjecture,
atomic(esk1_1(esk18_1(esk19_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_56]),c_0_83])]) ).
fof(c_0_94,plain,
! [X148,X149,X150] :
( ~ root(X149,X150)
| ~ min_precedes(X148,X149,X150) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_84])])]) ).
cnf(c_0_95,negated_conjecture,
( ~ occurrence_of(esk19_0,X1)
| min_precedes(esk16_1(esk19_0),esk12_2(tptp0,esk19_0),X1)
| min_precedes(esk12_2(tptp0,esk19_0),esk16_1(esk19_0),X1)
| esk12_2(tptp0,esk19_0) = esk16_1(esk19_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87])]) ).
cnf(c_0_96,plain,
( ~ root_occ(X1,X2)
| root(X1,esk14_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_97,negated_conjecture,
esk14_2(esk16_1(esk19_0),esk19_0) = tptp0,
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_98,negated_conjecture,
( ~ leaf_occ(X1,esk19_0)
| ~ min_precedes(X2,X1,tptp0)
| ~ root_occ(X2,esk19_0)
| ~ occurrence_of(X2,tptp3)
| ~ occurrence_of(X1,tptp1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_99,plain,
( ~ occurrence_of(X1,tptp0)
| occurrence_of(esk18_1(X1),tptp1)
| occurrence_of(esk18_1(X1),tptp2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_100,negated_conjecture,
( ~ leaf_occ(X1,esk19_0)
| ~ min_precedes(X2,X1,tptp0)
| ~ root_occ(X2,esk19_0)
| ~ occurrence_of(X2,tptp3)
| ~ occurrence_of(X1,tptp2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_101,plain,
( ~ earlier(X2,X3)
| ~ earlier(X1,X2)
| earlier(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_102,negated_conjecture,
earlier(esk17_1(esk19_0),esk18_1(esk19_0)),
inference(spm,[status(thm)],[c_0_91,c_0_72]) ).
cnf(c_0_103,negated_conjecture,
precedes(esk16_1(esk19_0),esk17_1(esk19_0)),
inference(spm,[status(thm)],[c_0_60,c_0_92]) ).
cnf(c_0_104,negated_conjecture,
arboreal(esk18_1(esk19_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_70]),c_0_93])]) ).
cnf(c_0_105,plain,
( ~ root(X2,X3)
| ~ min_precedes(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_106,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)
| esk12_2(tptp0,esk19_0) = esk16_1(esk19_0) ),
inference(spm,[status(thm)],[c_0_95,c_0_28]) ).
cnf(c_0_107,negated_conjecture,
root(esk16_1(esk19_0),tptp0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_76]),c_0_97]) ).
cnf(c_0_108,negated_conjecture,
( ~ occurrence_of(X1,tptp3)
| ~ occurrence_of(esk18_1(esk19_0),tptp1)
| ~ min_precedes(X1,esk18_1(esk19_0),tptp0)
| ~ root_occ(X1,esk19_0) ),
inference(spm,[status(thm)],[c_0_98,c_0_42]) ).
cnf(c_0_109,negated_conjecture,
( occurrence_of(esk18_1(esk19_0),tptp2)
| occurrence_of(esk18_1(esk19_0),tptp1) ),
inference(spm,[status(thm)],[c_0_99,c_0_28]) ).
cnf(c_0_110,negated_conjecture,
( ~ occurrence_of(X1,tptp3)
| ~ occurrence_of(esk18_1(esk19_0),tptp2)
| ~ min_precedes(X1,esk18_1(esk19_0),tptp0)
| ~ root_occ(X1,esk19_0) ),
inference(spm,[status(thm)],[c_0_100,c_0_42]) ).
fof(c_0_111,plain,
! [X158,X159,X160,X161] :
( min_precedes(X159,X160,X161)
| ~ precedes(X159,X160)
| ~ min_precedes(X158,X160,X161)
| ~ min_precedes(X158,X159,X161) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_18])])]) ).
cnf(c_0_112,plain,
( ~ next_subocc(X1,X4,X3)
| ~ min_precedes(X2,X4,X3)
| ~ min_precedes(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_113,negated_conjecture,
( ~ earlier(X1,esk17_1(esk19_0))
| earlier(X1,esk18_1(esk19_0)) ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_114,negated_conjecture,
earlier(esk16_1(esk19_0),esk17_1(esk19_0)),
inference(spm,[status(thm)],[c_0_91,c_0_103]) ).
cnf(c_0_115,negated_conjecture,
( ~ occurrence_of(esk19_0,X1)
| min_precedes(esk18_1(esk19_0),esk12_2(tptp0,esk19_0),X1)
| min_precedes(esk12_2(tptp0,esk19_0),esk18_1(esk19_0),X1)
| esk12_2(tptp0,esk19_0) = esk18_1(esk19_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_50]),c_0_104])]) ).
cnf(c_0_116,negated_conjecture,
( min_precedes(esk16_1(esk19_0),esk12_2(tptp0,esk19_0),tptp0)
| esk12_2(tptp0,esk19_0) = esk16_1(esk19_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107])]) ).
cnf(c_0_117,negated_conjecture,
( ~ occurrence_of(X1,tptp3)
| ~ min_precedes(X1,esk18_1(esk19_0),tptp0)
| ~ root_occ(X1,esk19_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_110]) ).
cnf(c_0_118,plain,
( ~ precedes(X2,X4)
| ~ min_precedes(X1,X4,X3)
| ~ min_precedes(X1,X2,X3)
| min_precedes(X2,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_119,negated_conjecture,
( ~ min_precedes(esk17_1(esk19_0),X1,tptp0)
| ~ min_precedes(X1,esk18_1(esk19_0),tptp0) ),
inference(spm,[status(thm)],[c_0_112,c_0_53]) ).
cnf(c_0_120,plain,
( ~ legal(X2)
| ~ earlier(X1,X2)
| precedes(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_121,negated_conjecture,
earlier(esk16_1(esk19_0),esk18_1(esk19_0)),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_122,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)
| esk12_2(tptp0,esk19_0) = esk18_1(esk19_0) ),
inference(spm,[status(thm)],[c_0_115,c_0_28]) ).
cnf(c_0_123,negated_conjecture,
esk12_2(tptp0,esk19_0) = esk16_1(esk19_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_116]),c_0_49])]) ).
cnf(c_0_124,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_117,c_0_76]),c_0_77])]) ).
cnf(c_0_125,negated_conjecture,
( ~ precedes(X1,esk18_1(esk19_0))
| ~ min_precedes(esk17_1(esk19_0),X1,tptp0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_61]),c_0_119]) ).
cnf(c_0_126,negated_conjecture,
precedes(esk16_1(esk19_0),esk18_1(esk19_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_83])]) ).
cnf(c_0_127,negated_conjecture,
( min_precedes(esk18_1(esk19_0),esk16_1(esk19_0),tptp0)
| esk16_1(esk19_0) = esk18_1(esk19_0) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_123]),c_0_123]),c_0_123]),c_0_124]) ).
cnf(c_0_128,negated_conjecture,
~ min_precedes(esk17_1(esk19_0),esk16_1(esk19_0),tptp0),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_129,negated_conjecture,
esk16_1(esk19_0) = esk18_1(esk19_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_127]),c_0_107])]) ).
cnf(c_0_130,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_128,c_0_129]),c_0_61])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PRO009+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.52 % Computer : n019.cluster.edu
% 0.09/0.52 % Model : x86_64 x86_64
% 0.09/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.52 % Memory : 8046.5625MB
% 0.09/0.52 % OS : Linux 6.8.0-71-generic
% 0.09/0.52 % CPULimit : 300
% 0.09/0.52 % WCLimit : 300
% 0.09/0.52 % DateTime : Mon Sep 21 03:42:21 UTC 2026
% 0.09/0.52 % CPUTime :
% 0.09/0.52 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.57 Running first-order theorem proving
% 0.15/0.57 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
% 1.07/0.70 % Version: 3.5.1
% 1.07/0.70 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.07/0.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.07/0.70 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.07/0.70 % Starting new_bool_3 with 300s (1) cores
% 1.07/0.70 % Starting new_bool_1 with 300s (1) cores
% 1.07/0.70 % Starting sh5l with 300s (1) cores
% 1.07/0.70 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1610044 completed with status 0
% 1.07/0.70 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.07/0.70 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.07/0.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.07/0.70 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.07/0.70 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.07/0.70 % No SInE strategy applied
% 1.07/0.70 % Search class: FGHSF-FFMM32-SFFFFFNN
% 1.07/0.70 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.07/0.70 % Starting SubtermCWHack with 136s (1) cores
% 1.07/0.70 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.07/0.70 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2SI with 136s (1) cores
% 1.07/0.70 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2g with 136s (1) cores
% 1.07/0.70 % Starting G-E--_107_C48_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 1.07/0.70 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2SI with pid 1610052 completed with status 0
% 1.07/0.70 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2SI
% 1.07/0.70 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.07/0.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.07/0.70 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.07/0.70 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.07/0.70 % No SInE strategy applied
% 1.07/0.70 % Search class: FGHSF-FFMM32-SFFFFFNN
% 1.07/0.70 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.07/0.70 % Starting SubtermCWHack with 136s (1) cores
% 1.07/0.70 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.07/0.70 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2SI with 136s (1) cores
% 1.07/0.70 % Preprocessing time : 0.002 s
% 1.07/0.70 % Presaturation interreduction done
% 1.07/0.70
% 1.07/0.70 % Proof found!
% 1.07/0.70 % SZS status Theorem
% 1.07/0.70 % SZS output start CNFRefutation
% See solution above
% 1.07/0.70 % Parsed axioms : 49
% 1.07/0.70 % Removed by relevancy pruning/SinE : 0
% 1.07/0.70 % Initial clauses : 88
% 1.07/0.70 % Removed in clause preprocessing : 0
% 1.07/0.70 % Initial clauses in saturation : 88
% 1.07/0.70 % Processed clauses : 1203
% 1.07/0.70 % ...of these trivial : 21
% 1.07/0.70 % ...subsumed : 281
% 1.07/0.70 % ...remaining for further processing : 901
% 1.07/0.70 % Other redundant clauses eliminated : 0
% 1.07/0.70 % Clauses deleted for lack of memory : 0
% 1.07/0.70 % Backward-subsumed : 5
% 1.07/0.70 % Backward-rewritten : 179
% 1.07/0.70 % Generated clauses : 2667
% 1.07/0.70 % ...of the previous two non-redundant : 2123
% 1.07/0.70 % ...aggressively subsumed : 0
% 1.07/0.70 % Contextual simplify-reflections : 3
% 1.07/0.70 % Paramodulations : 2664
% 1.07/0.70 % Factorizations : 3
% 1.07/0.70 % NegExts : 0
% 1.07/0.70 % Equation resolutions : 0
% 1.07/0.70 % Disequality decompositions : 0
% 1.07/0.70 % Total rewrite steps : 942
% 1.07/0.70 % ...of those cached : 777
% 1.07/0.70 % Propositional unsat checks : 0
% 1.07/0.70 % Propositional check models : 0
% 1.07/0.70 % Propositional check unsatisfiable : 0
% 1.07/0.70 % Propositional clauses : 0
% 1.07/0.70 % Propositional clauses after purity: 0
% 1.07/0.70 % Propositional unsat core size : 0
% 1.07/0.70 % Propositional preprocessing time : 0.000
% 1.07/0.70 % Propositional encoding time : 0.000
% 1.07/0.70 % Propositional solver time : 0.000
% 1.07/0.70 % Success case prop preproc time : 0.000
% 1.07/0.70 % Success case prop encoding time : 0.000
% 1.07/0.70 % Success case prop solver time : 0.000
% 1.07/0.70 % Current number of processed clauses : 629
% 1.07/0.70 % Positive orientable unit clauses : 254
% 1.07/0.70 % Positive unorientable unit clauses: 0
% 1.07/0.70 % Negative unit clauses : 50
% 1.07/0.70 % Non-unit-clauses : 325
% 1.07/0.70 % Current number of unprocessed clauses: 1007
% 1.07/0.70 % ...number of literals in the above : 2291
% 1.07/0.70 % Current number of archived formulas : 0
% 1.07/0.70 % Current number of archived clauses : 272
% 1.07/0.70 % Clause-clause subsumption calls (NU) : 18622
% 1.07/0.70 % Rec. Clause-clause subsumption calls : 12329
% 1.07/0.70 % Non-unit clause-clause subsumptions : 215
% 1.07/0.70 % Unit Clause-clause subsumption calls : 1563
% 1.07/0.70 % Rewrite failures with RHS unbound : 0
% 1.07/0.70 % BW rewrite match attempts : 198
% 1.07/0.70 % BW rewrite match successes : 28
% 1.07/0.70 % Condensation attempts : 0
% 1.07/0.70 % Condensation successes : 0
% 1.07/0.70 % Termbank termtop insertions : 52682
% 1.07/0.70 % Search garbage collected termcells : 1353
% 1.07/0.70
% 1.07/0.70 % -------------------------------------------------
% 1.07/0.70 % User time : 0.104 s
% 1.07/0.70 % System time : 0.009 s
% 1.07/0.70 % Total time : 0.113 s
% 1.07/0.70 % Maximum resident set size: 3948 pages
% 1.07/0.70
% 1.07/0.70 % -------------------------------------------------
% 1.07/0.70 % User time : 0.501 s
% 1.07/0.70 % System time : 0.043 s
% 1.07/0.70 % Total time : 0.544 s
% 1.07/0.70 % Maximum resident set size: 4608 pages
% 1.07/0.70 % E exiting
%------------------------------------------------------------------------------