%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : PRO009+4 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 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 : Tue May 5 05:01:53 PM UTC 2026
% Result : Theorem 1.77s 1.84s
% Output : CNFRefutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 20
% Syntax : Number of formulae : 130 ( 27 unt; 0 def)
% Number of atoms : 417 ( 30 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 473 ( 186 ~; 189 |; 75 &)
% ( 5 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 6 con; 0-3 aty)
% Number of variables : 234 ( 10 sgn 113 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos,axiom,
! [X1,X2] :
( ( occurrence_of(X2,X1)
& ~ atomic(X1) )
=> ? [X3] :
( root(X3,X1)
& subactivity_occurrence(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos) ).
fof(goals,conjecture,
! [X106] :
( occurrence_of(X106,tptp0)
=> ? [X107,X108] :
( occurrence_of(X107,tptp3)
& root_occ(X107,X106)
& ( occurrence_of(X108,tptp2)
| occurrence_of(X108,tptp1) )
& min_precedes(X107,X108,tptp0)
& leaf_occ(X108,X106) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(sos_34,axiom,
~ atomic(tptp0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_34) ).
fof(sos_08,axiom,
! [X29,X30,X31] :
( ( occurrence_of(X29,X30)
& occurrence_of(X29,X31) )
=> X30 = X31 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_08) ).
fof(sos_19,axiom,
! [X59,X60] :
( root_occ(X59,X60)
<=> ? [X61] :
( occurrence_of(X60,X61)
& subactivity_occurrence(X59,X60)
& root(X59,X61) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_19) ).
fof(sos_18,axiom,
! [X56,X57] :
( leaf_occ(X56,X57)
<=> ? [X58] :
( occurrence_of(X57,X58)
& subactivity_occurrence(X56,X57)
& leaf(X56,X58) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_18) ).
fof(sos_12,axiom,
! [X42] :
( activity_occurrence(X42)
=> ? [X43] :
( activity(X43)
& occurrence_of(X42,X43) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_12) ).
fof(sos_03,axiom,
! [X13,X14] :
( occurrence_of(X14,X13)
=> ( activity(X13)
& activity_occurrence(X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_03) ).
fof(sos_29,axiom,
! [X91,X92,X93,X94] :
( ( occurrence_of(X93,X94)
& root_occ(X91,X93)
& root_occ(X92,X93) )
=> X91 = X92 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_29) ).
fof(sos_26,axiom,
! [X79,X80,X81] :
( next_subocc(X79,X80,X81)
<=> ( min_precedes(X79,X80,X81)
& ~ ? [X82] :
( min_precedes(X79,X82,X81)
& min_precedes(X82,X80,X81) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_26) ).
fof(sos_32,axiom,
! [X102] :
( occurrence_of(X102,tptp0)
=> ? [X103,X104,X105] :
( occurrence_of(X103,tptp3)
& root_occ(X103,X102)
& occurrence_of(X104,tptp4)
& next_subocc(X103,X104,tptp0)
& ( occurrence_of(X105,tptp2)
| occurrence_of(X105,tptp1) )
& next_subocc(X104,X105,tptp0)
& leaf_occ(X105,X102) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_32) ).
fof(sos_14,axiom,
! [X45,X46] :
( atocc(X45,X46)
<=> ? [X47] :
( subactivity(X46,X47)
& atomic(X47)
& occurrence_of(X45,X47) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_14) ).
fof(sos_15,axiom,
! [X48,X49] :
( leaf(X48,X49)
<=> ( ( root(X48,X49)
| ? [X50] : min_precedes(X50,X48,X49) )
& ~ ? [X51] : min_precedes(X48,X51,X49) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_15) ).
fof(sos_02,axiom,
! [X9,X10,X11,X12] :
( ( occurrence_of(X10,X9)
& subactivity_occurrence(X11,X10)
& leaf_occ(X12,X10)
& arboreal(X11)
& ~ min_precedes(X11,X12,X9) )
=> X12 = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_02) ).
fof(sos_17,axiom,
! [X54,X55] :
( root(X54,X55)
=> legal(X54) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_17) ).
fof(sos_13,axiom,
! [X44] :
( legal(X44)
=> arboreal(X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_13) ).
fof(sos_05,axiom,
! [X19,X20] :
( root(X20,X19)
=> ? [X21] :
( subactivity(X21,X19)
& atocc(X20,X21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_05) ).
fof(sos_09,axiom,
! [X32,X33,X34] :
( ( occurrence_of(X32,X34)
& leaf_occ(X33,X32) )
=> ~ ? [X35] : min_precedes(X33,X35,X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_09) ).
fof(sos_07,axiom,
! [X26,X27] :
( ( leaf(X26,X27)
& ~ atomic(X27) )
=> ? [X28] :
( occurrence_of(X28,X27)
& leaf_occ(X26,X28) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_07) ).
fof(sos_10,axiom,
! [X36,X37,X38] :
( ( occurrence_of(X36,X38)
& root_occ(X37,X36) )
=> ~ ? [X39] : min_precedes(X39,X37,X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_10) ).
fof(c_0_20,plain,
! [X1,X2] :
( ( occurrence_of(X2,X1)
& ~ atomic(X1) )
=> ? [X3] :
( root(X3,X1)
& subactivity_occurrence(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[sos]) ).
fof(c_0_21,negated_conjecture,
~ ! [X106] :
( occurrence_of(X106,tptp0)
=> ? [X107,X108] :
( occurrence_of(X107,tptp3)
& root_occ(X107,X106)
& ( occurrence_of(X108,tptp2)
| occurrence_of(X108,tptp1) )
& min_precedes(X107,X108,tptp0)
& leaf_occ(X108,X106) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_22,plain,
! [X217,X218] :
( ( root(esk1_2(X217,X218),X217)
| ~ occurrence_of(X218,X217)
| atomic(X217) )
& ( subactivity_occurrence(esk1_2(X217,X218),X218)
| ~ occurrence_of(X218,X217)
| atomic(X217) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
fof(c_0_23,negated_conjecture,
! [X340,X341] :
( occurrence_of(esk16_0,tptp0)
& ( ~ occurrence_of(X341,tptp2)
| ~ occurrence_of(X340,tptp3)
| ~ root_occ(X340,esk16_0)
| ~ min_precedes(X340,X341,tptp0)
| ~ leaf_occ(X341,esk16_0) )
& ( ~ occurrence_of(X341,tptp1)
| ~ occurrence_of(X340,tptp3)
| ~ root_occ(X340,esk16_0)
| ~ min_precedes(X340,X341,tptp0)
| ~ leaf_occ(X341,esk16_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_21])])])])]) ).
fof(c_0_24,plain,
~ atomic(tptp0),
inference(fof_simplification,[status(thm)],[sos_34]) ).
fof(c_0_25,plain,
! [X245,X246,X247] :
( ~ occurrence_of(X245,X246)
| ~ occurrence_of(X245,X247)
| X246 = X247 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_08])]) ).
fof(c_0_26,plain,
! [X285,X286,X288,X289,X290] :
( ( occurrence_of(X286,esk10_2(X285,X286))
| ~ root_occ(X285,X286) )
& ( subactivity_occurrence(X285,X286)
| ~ root_occ(X285,X286) )
& ( root(X285,esk10_2(X285,X286))
| ~ root_occ(X285,X286) )
& ( ~ occurrence_of(X289,X290)
| ~ subactivity_occurrence(X288,X289)
| ~ root(X288,X290)
| root_occ(X288,X289) ) ),
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_19])])])])])]) ).
cnf(c_0_27,plain,
( subactivity_occurrence(esk1_2(X1,X2),X2)
| atomic(X1)
| ~ occurrence_of(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,negated_conjecture,
occurrence_of(esk16_0,tptp0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
~ atomic(tptp0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
( X2 = X3
| ~ occurrence_of(X1,X2)
| ~ occurrence_of(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_31,plain,
! [X279,X280,X282,X283,X284] :
( ( occurrence_of(X280,esk9_2(X279,X280))
| ~ leaf_occ(X279,X280) )
& ( subactivity_occurrence(X279,X280)
| ~ leaf_occ(X279,X280) )
& ( leaf(X279,esk9_2(X279,X280))
| ~ leaf_occ(X279,X280) )
& ( ~ occurrence_of(X283,X284)
| ~ subactivity_occurrence(X282,X283)
| ~ leaf(X282,X284)
| leaf_occ(X282,X283) ) ),
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_18])])])])])]) ).
cnf(c_0_32,plain,
( root_occ(X3,X1)
| ~ occurrence_of(X1,X2)
| ~ subactivity_occurrence(X3,X1)
| ~ root(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,negated_conjecture,
subactivity_occurrence(esk1_2(tptp0,esk16_0),esk16_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_34,plain,
( root(esk1_2(X1,X2),X1)
| atomic(X1)
| ~ occurrence_of(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_35,negated_conjecture,
( X1 = tptp0
| ~ occurrence_of(esk16_0,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_28]) ).
cnf(c_0_36,plain,
( occurrence_of(X1,esk9_2(X2,X1))
| ~ leaf_occ(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_37,plain,
! [X258] :
( ( activity(esk5_1(X258))
| ~ activity_occurrence(X258) )
& ( occurrence_of(X258,esk5_1(X258))
| ~ activity_occurrence(X258) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_12])])])]) ).
fof(c_0_38,plain,
! [X229,X230] :
( ( activity(X229)
| ~ occurrence_of(X230,X229) )
& ( activity_occurrence(X230)
| ~ occurrence_of(X230,X229) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_03])])]) ).
fof(c_0_39,plain,
! [X324,X325,X326,X327] :
( ~ occurrence_of(X326,X327)
| ~ root_occ(X324,X326)
| ~ root_occ(X325,X326)
| X324 = X325 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_29])]) ).
cnf(c_0_40,negated_conjecture,
( root_occ(esk1_2(tptp0,esk16_0),esk16_0)
| ~ root(esk1_2(tptp0,esk16_0),X1)
| ~ occurrence_of(esk16_0,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_41,negated_conjecture,
root(esk1_2(tptp0,esk16_0),tptp0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_28]),c_0_29]) ).
fof(c_0_42,plain,
! [X308,X309,X310,X311,X312,X313,X314] :
( ( min_precedes(X308,X309,X310)
| ~ next_subocc(X308,X309,X310) )
& ( ~ min_precedes(X308,X311,X310)
| ~ min_precedes(X311,X309,X310)
| ~ next_subocc(X308,X309,X310) )
& ( min_precedes(X312,esk12_3(X312,X313,X314),X314)
| ~ min_precedes(X312,X313,X314)
| next_subocc(X312,X313,X314) )
& ( min_precedes(esk12_3(X312,X313,X314),X313,X314)
| ~ min_precedes(X312,X313,X314)
| next_subocc(X312,X313,X314) ) ),
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_26])])])])])]) ).
fof(c_0_43,plain,
! [X335] :
( ( occurrence_of(esk13_1(X335),tptp3)
| ~ occurrence_of(X335,tptp0) )
& ( root_occ(esk13_1(X335),X335)
| ~ occurrence_of(X335,tptp0) )
& ( occurrence_of(esk14_1(X335),tptp4)
| ~ occurrence_of(X335,tptp0) )
& ( next_subocc(esk13_1(X335),esk14_1(X335),tptp0)
| ~ occurrence_of(X335,tptp0) )
& ( occurrence_of(esk15_1(X335),tptp2)
| occurrence_of(esk15_1(X335),tptp1)
| ~ occurrence_of(X335,tptp0) )
& ( next_subocc(esk14_1(X335),esk15_1(X335),tptp0)
| ~ occurrence_of(X335,tptp0) )
& ( leaf_occ(esk15_1(X335),X335)
| ~ occurrence_of(X335,tptp0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_32])])])]) ).
cnf(c_0_44,plain,
( leaf(X1,esk9_2(X1,X2))
| ~ leaf_occ(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_45,negated_conjecture,
( esk9_2(X1,esk16_0) = tptp0
| ~ leaf_occ(X1,esk16_0) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_46,plain,
( occurrence_of(X1,esk5_1(X1))
| ~ activity_occurrence(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_47,plain,
( activity_occurrence(X1)
| ~ occurrence_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_48,plain,
! [X261,X262,X264,X265,X266] :
( ( subactivity(X262,esk6_2(X261,X262))
| ~ atocc(X261,X262) )
& ( atomic(esk6_2(X261,X262))
| ~ atocc(X261,X262) )
& ( occurrence_of(X261,esk6_2(X261,X262))
| ~ atocc(X261,X262) )
& ( ~ subactivity(X265,X266)
| ~ atomic(X266)
| ~ occurrence_of(X264,X266)
| atocc(X264,X265) ) ),
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_14])])])])])]) ).
cnf(c_0_49,plain,
( X3 = X4
| ~ occurrence_of(X1,X2)
| ~ root_occ(X3,X1)
| ~ root_occ(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_50,negated_conjecture,
root_occ(esk1_2(tptp0,esk16_0),esk16_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_28])]) ).
fof(c_0_51,plain,
! [X267,X268,X270,X271,X272,X273] :
( ( root(X267,X268)
| min_precedes(esk7_2(X267,X268),X267,X268)
| ~ leaf(X267,X268) )
& ( ~ min_precedes(X267,X270,X268)
| ~ leaf(X267,X268) )
& ( ~ root(X271,X272)
| min_precedes(X271,esk8_2(X271,X272),X272)
| leaf(X271,X272) )
& ( ~ min_precedes(X273,X271,X272)
| min_precedes(X271,esk8_2(X271,X272),X272)
| leaf(X271,X272) ) ),
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_15])])])])])]) ).
cnf(c_0_52,plain,
( min_precedes(X1,X2,X3)
| ~ next_subocc(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_53,plain,
( next_subocc(esk14_1(X1),esk15_1(X1),tptp0)
| ~ occurrence_of(X1,tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
fof(c_0_54,plain,
! [X9,X10,X11,X12] :
( ( occurrence_of(X10,X9)
& subactivity_occurrence(X11,X10)
& leaf_occ(X12,X10)
& arboreal(X11)
& ~ min_precedes(X11,X12,X9) )
=> X12 = X11 ),
inference(fof_simplification,[status(thm)],[sos_02]) ).
cnf(c_0_55,plain,
( leaf_occ(X3,X1)
| ~ occurrence_of(X1,X2)
| ~ subactivity_occurrence(X3,X1)
| ~ leaf(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_56,negated_conjecture,
( leaf(X1,tptp0)
| ~ leaf_occ(X1,esk16_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
fof(c_0_57,plain,
! [X277,X278] :
( ~ root(X277,X278)
| legal(X277) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_17])]) ).
cnf(c_0_58,plain,
( X1 = esk5_1(X2)
| ~ occurrence_of(X2,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_46]),c_0_47]) ).
cnf(c_0_59,plain,
( occurrence_of(X1,esk6_2(X1,X2))
| ~ atocc(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_60,negated_conjecture,
( X1 = esk1_2(tptp0,esk16_0)
| ~ root_occ(X1,esk16_0)
| ~ occurrence_of(esk16_0,X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_61,plain,
( root_occ(esk13_1(X1),X1)
| ~ occurrence_of(X1,tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_62,plain,
( min_precedes(X2,esk8_2(X2,X3),X3)
| leaf(X2,X3)
| ~ min_precedes(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_63,plain,
( min_precedes(esk14_1(X1),esk15_1(X1),tptp0)
| ~ occurrence_of(X1,tptp0) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
fof(c_0_64,plain,
! [X225,X226,X227,X228] :
( ~ occurrence_of(X226,X225)
| ~ subactivity_occurrence(X227,X226)
| ~ leaf_occ(X228,X226)
| ~ arboreal(X227)
| min_precedes(X227,X228,X225)
| X228 = X227 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_54])]) ).
cnf(c_0_65,negated_conjecture,
( leaf_occ(X1,X2)
| ~ leaf_occ(X1,esk16_0)
| ~ subactivity_occurrence(X1,X2)
| ~ occurrence_of(X2,tptp0) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_66,plain,
( leaf_occ(esk15_1(X1),X1)
| ~ occurrence_of(X1,tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
fof(c_0_67,plain,
! [X260] :
( ~ legal(X260)
| arboreal(X260) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_13])]) ).
cnf(c_0_68,plain,
( legal(X1)
| ~ root(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_69,plain,
( esk6_2(X1,X2) = esk5_1(X1)
| ~ atocc(X1,X2) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
fof(c_0_70,plain,
! [X235,X236] :
( ( subactivity(esk2_2(X235,X236),X235)
| ~ root(X236,X235) )
& ( atocc(X236,esk2_2(X235,X236))
| ~ root(X236,X235) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_05])])])]) ).
cnf(c_0_71,negated_conjecture,
( esk1_2(tptp0,esk16_0) = esk13_1(esk16_0)
| ~ occurrence_of(esk16_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_28])]) ).
cnf(c_0_72,negated_conjecture,
activity_occurrence(esk16_0),
inference(spm,[status(thm)],[c_0_47,c_0_28]) ).
fof(c_0_73,plain,
! [X248,X249,X250,X251] :
( ~ occurrence_of(X248,X250)
| ~ leaf_occ(X249,X248)
| ~ min_precedes(X249,X251,X250) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_09])])]) ).
cnf(c_0_74,plain,
( leaf(esk15_1(X1),tptp0)
| min_precedes(esk15_1(X1),esk8_2(esk15_1(X1),tptp0),tptp0)
| ~ occurrence_of(X1,tptp0) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_75,plain,
( min_precedes(X3,X4,X2)
| X4 = X3
| ~ occurrence_of(X1,X2)
| ~ subactivity_occurrence(X3,X1)
| ~ leaf_occ(X4,X1)
| ~ arboreal(X3) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_76,negated_conjecture,
( leaf_occ(esk15_1(esk16_0),X1)
| ~ subactivity_occurrence(esk15_1(esk16_0),X1)
| ~ occurrence_of(X1,tptp0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_28])]) ).
cnf(c_0_77,plain,
( subactivity_occurrence(X1,X2)
| ~ leaf_occ(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_78,plain,
( arboreal(X1)
| ~ legal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_79,negated_conjecture,
legal(esk1_2(tptp0,esk16_0)),
inference(spm,[status(thm)],[c_0_68,c_0_41]) ).
cnf(c_0_80,plain,
( occurrence_of(X1,esk5_1(X1))
| ~ atocc(X1,X2) ),
inference(spm,[status(thm)],[c_0_59,c_0_69]) ).
cnf(c_0_81,plain,
( atocc(X1,esk2_2(X2,X1))
| ~ root(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_82,negated_conjecture,
esk1_2(tptp0,esk16_0) = esk13_1(esk16_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_46]),c_0_72])]) ).
fof(c_0_83,plain,
! [X26,X27] :
( ( leaf(X26,X27)
& ~ atomic(X27) )
=> ? [X28] :
( occurrence_of(X28,X27)
& leaf_occ(X26,X28) ) ),
inference(fof_simplification,[status(thm)],[sos_07]) ).
cnf(c_0_84,plain,
( ~ occurrence_of(X1,X2)
| ~ leaf_occ(X3,X1)
| ~ min_precedes(X3,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_85,negated_conjecture,
( leaf(esk15_1(esk16_0),tptp0)
| min_precedes(esk15_1(esk16_0),esk8_2(esk15_1(esk16_0),tptp0),tptp0) ),
inference(spm,[status(thm)],[c_0_74,c_0_28]) ).
cnf(c_0_86,negated_conjecture,
( X1 = esk15_1(esk16_0)
| min_precedes(X1,esk15_1(esk16_0),X2)
| ~ arboreal(X1)
| ~ subactivity_occurrence(esk15_1(esk16_0),X3)
| ~ subactivity_occurrence(X1,X3)
| ~ occurrence_of(X3,tptp0)
| ~ occurrence_of(X3,X2) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_87,plain,
( subactivity_occurrence(esk15_1(X1),X1)
| ~ occurrence_of(X1,tptp0) ),
inference(spm,[status(thm)],[c_0_77,c_0_66]) ).
cnf(c_0_88,plain,
( subactivity_occurrence(X1,X2)
| ~ root_occ(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_89,negated_conjecture,
arboreal(esk1_2(tptp0,esk16_0)),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_90,plain,
( occurrence_of(esk13_1(X1),tptp3)
| ~ occurrence_of(X1,tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_91,plain,
( occurrence_of(X1,esk5_1(X1))
| ~ root(X1,X2) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_92,negated_conjecture,
root(esk13_1(esk16_0),tptp0),
inference(rw,[status(thm)],[c_0_41,c_0_82]) ).
fof(c_0_93,plain,
! [X242,X243] :
( ( occurrence_of(esk4_2(X242,X243),X243)
| ~ leaf(X242,X243)
| atomic(X243) )
& ( leaf_occ(X242,esk4_2(X242,X243))
| ~ leaf(X242,X243)
| atomic(X243) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_83])])])]) ).
cnf(c_0_94,negated_conjecture,
( leaf(esk15_1(esk16_0),tptp0)
| ~ leaf_occ(esk15_1(esk16_0),X1)
| ~ occurrence_of(X1,tptp0) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_95,negated_conjecture,
( X1 = esk15_1(esk16_0)
| min_precedes(X1,esk15_1(esk16_0),X2)
| ~ arboreal(X1)
| ~ subactivity_occurrence(X1,esk16_0)
| ~ occurrence_of(esk16_0,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_28])]) ).
cnf(c_0_96,plain,
( subactivity_occurrence(esk13_1(X1),X1)
| ~ occurrence_of(X1,tptp0) ),
inference(spm,[status(thm)],[c_0_88,c_0_61]) ).
cnf(c_0_97,negated_conjecture,
arboreal(esk13_1(esk16_0)),
inference(rw,[status(thm)],[c_0_89,c_0_82]) ).
cnf(c_0_98,plain,
( X1 = tptp3
| ~ occurrence_of(esk13_1(X2),X1)
| ~ occurrence_of(X2,tptp0) ),
inference(spm,[status(thm)],[c_0_30,c_0_90]) ).
cnf(c_0_99,negated_conjecture,
occurrence_of(esk13_1(esk16_0),esk5_1(esk13_1(esk16_0))),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_100,plain,
( leaf_occ(X1,esk4_2(X1,X2))
| atomic(X2)
| ~ leaf(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_101,negated_conjecture,
leaf(esk15_1(esk16_0),tptp0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_66]),c_0_28])]) ).
cnf(c_0_102,negated_conjecture,
( esk13_1(esk16_0) = esk15_1(esk16_0)
| min_precedes(esk13_1(esk16_0),esk15_1(esk16_0),X1)
| ~ occurrence_of(esk16_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97]),c_0_28])]) ).
cnf(c_0_103,negated_conjecture,
esk5_1(esk16_0) = tptp0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_46]),c_0_72])]) ).
cnf(c_0_104,negated_conjecture,
esk5_1(esk13_1(esk16_0)) = tptp3,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_28])]) ).
cnf(c_0_105,negated_conjecture,
leaf_occ(esk15_1(esk16_0),esk4_2(esk15_1(esk16_0),tptp0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_29]) ).
cnf(c_0_106,plain,
( occurrence_of(esk4_2(X1,X2),X2)
| atomic(X2)
| ~ leaf(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_107,negated_conjecture,
( ~ occurrence_of(X1,tptp1)
| ~ occurrence_of(X2,tptp3)
| ~ root_occ(X2,esk16_0)
| ~ min_precedes(X2,X1,tptp0)
| ~ leaf_occ(X1,esk16_0) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_108,negated_conjecture,
( esk13_1(esk16_0) = esk15_1(esk16_0)
| min_precedes(esk13_1(esk16_0),esk15_1(esk16_0),tptp0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_46]),c_0_103]),c_0_72])]) ).
cnf(c_0_109,negated_conjecture,
root_occ(esk13_1(esk16_0),esk16_0),
inference(rw,[status(thm)],[c_0_50,c_0_82]) ).
cnf(c_0_110,negated_conjecture,
occurrence_of(esk13_1(esk16_0),tptp3),
inference(rw,[status(thm)],[c_0_99,c_0_104]) ).
cnf(c_0_111,negated_conjecture,
( ~ occurrence_of(X1,tptp2)
| ~ occurrence_of(X2,tptp3)
| ~ root_occ(X2,esk16_0)
| ~ min_precedes(X2,X1,tptp0)
| ~ leaf_occ(X1,esk16_0) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_112,plain,
! [X252,X253,X254,X255] :
( ~ occurrence_of(X252,X254)
| ~ root_occ(X253,X252)
| ~ min_precedes(X255,X253,X254) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_10])])]) ).
cnf(c_0_113,negated_conjecture,
subactivity_occurrence(esk15_1(esk16_0),esk4_2(esk15_1(esk16_0),tptp0)),
inference(spm,[status(thm)],[c_0_77,c_0_105]) ).
cnf(c_0_114,negated_conjecture,
occurrence_of(esk4_2(esk15_1(esk16_0),tptp0),tptp0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_101]),c_0_29]) ).
cnf(c_0_115,negated_conjecture,
( esk13_1(esk16_0) = esk15_1(esk16_0)
| ~ leaf_occ(esk15_1(esk16_0),esk16_0)
| ~ occurrence_of(esk15_1(esk16_0),tptp1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_109]),c_0_110])]) ).
cnf(c_0_116,plain,
( occurrence_of(esk15_1(X1),tptp2)
| occurrence_of(esk15_1(X1),tptp1)
| ~ occurrence_of(X1,tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_117,negated_conjecture,
( esk13_1(esk16_0) = esk15_1(esk16_0)
| ~ leaf_occ(esk15_1(esk16_0),esk16_0)
| ~ occurrence_of(esk15_1(esk16_0),tptp2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_108]),c_0_109]),c_0_110])]) ).
cnf(c_0_118,plain,
( ~ occurrence_of(X1,X2)
| ~ root_occ(X3,X1)
| ~ min_precedes(X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_119,negated_conjecture,
( root_occ(esk15_1(esk16_0),esk4_2(esk15_1(esk16_0),tptp0))
| ~ root(esk15_1(esk16_0),X1)
| ~ occurrence_of(esk4_2(esk15_1(esk16_0),tptp0),X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_113]) ).
cnf(c_0_120,negated_conjecture,
esk5_1(esk4_2(esk15_1(esk16_0),tptp0)) = tptp0,
inference(spm,[status(thm)],[c_0_58,c_0_114]) ).
cnf(c_0_121,negated_conjecture,
activity_occurrence(esk4_2(esk15_1(esk16_0),tptp0)),
inference(spm,[status(thm)],[c_0_47,c_0_114]) ).
cnf(c_0_122,negated_conjecture,
( esk13_1(esk16_0) = esk15_1(esk16_0)
| ~ occurrence_of(esk15_1(esk16_0),tptp1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_66]),c_0_28])]) ).
cnf(c_0_123,negated_conjecture,
( occurrence_of(esk15_1(esk16_0),tptp1)
| occurrence_of(esk15_1(esk16_0),tptp2) ),
inference(spm,[status(thm)],[c_0_116,c_0_28]) ).
cnf(c_0_124,negated_conjecture,
( esk13_1(esk16_0) = esk15_1(esk16_0)
| ~ occurrence_of(esk15_1(esk16_0),tptp2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_66]),c_0_28])]) ).
cnf(c_0_125,plain,
( ~ root_occ(esk15_1(X1),X2)
| ~ occurrence_of(X2,tptp0)
| ~ occurrence_of(X1,tptp0) ),
inference(spm,[status(thm)],[c_0_118,c_0_63]) ).
cnf(c_0_126,negated_conjecture,
( root_occ(esk15_1(esk16_0),esk4_2(esk15_1(esk16_0),tptp0))
| ~ root(esk15_1(esk16_0),tptp0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_46]),c_0_120]),c_0_121])]) ).
cnf(c_0_127,negated_conjecture,
esk13_1(esk16_0) = esk15_1(esk16_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_124]) ).
cnf(c_0_128,negated_conjecture,
~ root(esk15_1(esk16_0),tptp0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_114]),c_0_28])]) ).
cnf(c_0_129,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_127]),c_0_128]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PRO009+4 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n016.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 01:31:06 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.77/1.84 % Version : CSE_E---1.7
% 1.77/1.84 % Problem : theBenchmark.p
% 1.77/1.84 % SZS status Theorem for theBenchmark.p
% 1.77/1.84 % SZS output start CNFRefutation
% See solution above
% 1.77/1.84 % Total time : 1.371s
%------------------------------------------------------------------------------