%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : PRO018+4 : 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 : n005.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 05:01:57 PM UTC 2026
% Result : Theorem 2.31s 1.95s
% Output : CNFRefutation 2.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 93 ( 27 unt; 0 def)
% Number of atoms : 477 ( 29 equ)
% Maximal formula atoms : 130 ( 5 avg)
% Number of connectives : 619 ( 235 ~; 272 |; 92 &)
% ( 4 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-3 aty)
% Number of variables : 163 ( 3 sgn 69 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_32,axiom,
! [X102,X103] :
( ( occurrence_of(X103,tptp0)
& subactivity_occurrence(X102,X103)
& arboreal(X102)
& ~ leaf_occ(X102,X103) )
=> ? [X104,X105,X106] :
( occurrence_of(X104,tptp3)
& next_subocc(X102,X104,tptp0)
& occurrence_of(X105,tptp4)
& min_precedes(X104,X105,tptp0)
& ( occurrence_of(X106,tptp1)
| occurrence_of(X106,tptp2) )
& min_precedes(X105,X106,tptp0)
& ! [X107] :
( min_precedes(X104,X107,tptp0)
=> ( X107 = X105
| X107 = X106 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_32) ).
fof(goals,conjecture,
! [X108,X109] :
( ( occurrence_of(X109,tptp0)
& subactivity_occurrence(X108,X109)
& arboreal(X108)
& ~ leaf_occ(X108,X109) )
=> ? [X110,X111] :
( occurrence_of(X110,tptp3)
& next_subocc(X108,X110,tptp0)
& ( occurrence_of(X111,tptp1)
| occurrence_of(X111,tptp2) )
& min_precedes(X110,X111,tptp0)
& leaf_occ(X111,X109)
& ( occurrence_of(X111,tptp1)
=> ~ ? [X112] :
( occurrence_of(X112,tptp2)
& min_precedes(X110,X112,tptp0) ) )
& ( occurrence_of(X111,tptp2)
=> ~ ? [X113] :
( occurrence_of(X113,tptp1)
& min_precedes(X110,X113,tptp0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(sos_08,axiom,
! [X29,X30,X31] :
( ( occurrence_of(X29,X30)
& occurrence_of(X29,X31) )
=> X30 = X31 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_08) ).
fof(sos_12,axiom,
! [X42] :
( activity_occurrence(X42)
=> ? [X43] :
( activity(X43)
& occurrence_of(X42,X43) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_12) ).
fof(sos_03,axiom,
! [X13,X14] :
( occurrence_of(X14,X13)
=> ( activity(X13)
& activity_occurrence(X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_03) ).
fof(sos_06,axiom,
! [X22,X23,X24] :
( min_precedes(X23,X24,X22)
=> ? [X25] :
( occurrence_of(X25,X22)
& subactivity_occurrence(X23,X25)
& subactivity_occurrence(X24,X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_06) ).
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/sandbox/benchmark/theBenchmark.p',sos_18) ).
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/sandbox/benchmark/theBenchmark.p',sos_26) ).
fof(sos_16,axiom,
! [X52,X53] :
( occurrence_of(X52,X53)
=> ( arboreal(X52)
<=> atomic(X53) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_16) ).
fof(sos_38,axiom,
atomic(tptp3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_38) ).
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/sandbox/benchmark/theBenchmark.p',sos_15) ).
fof(sos_09,axiom,
! [X32,X33,X34] :
( ( occurrence_of(X32,X34)
& leaf_occ(X33,X32) )
=> ~ ? [X35] : min_precedes(X33,X35,X34) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_09) ).
fof(sos_39,axiom,
tptp4 != tptp3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_39) ).
fof(sos_43,axiom,
tptp3 != tptp2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_43) ).
fof(sos_42,axiom,
tptp3 != tptp1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_42) ).
fof(c_0_15,plain,
! [X102,X103] :
( ( occurrence_of(X103,tptp0)
& subactivity_occurrence(X102,X103)
& arboreal(X102)
& ~ leaf_occ(X102,X103) )
=> ? [X104,X105,X106] :
( occurrence_of(X104,tptp3)
& next_subocc(X102,X104,tptp0)
& occurrence_of(X105,tptp4)
& min_precedes(X104,X105,tptp0)
& ( occurrence_of(X106,tptp1)
| occurrence_of(X106,tptp2) )
& min_precedes(X105,X106,tptp0)
& ! [X107] :
( min_precedes(X104,X107,tptp0)
=> ( X107 = X105
| X107 = X106 ) ) ) ),
inference(fof_simplification,[status(thm)],[sos_32]) ).
fof(c_0_16,negated_conjecture,
~ ! [X108,X109] :
( ( occurrence_of(X109,tptp0)
& subactivity_occurrence(X108,X109)
& arboreal(X108)
& ~ leaf_occ(X108,X109) )
=> ? [X110,X111] :
( occurrence_of(X110,tptp3)
& next_subocc(X108,X110,tptp0)
& ( occurrence_of(X111,tptp1)
| occurrence_of(X111,tptp2) )
& min_precedes(X110,X111,tptp0)
& leaf_occ(X111,X109)
& ( occurrence_of(X111,tptp1)
=> ~ ? [X112] :
( occurrence_of(X112,tptp2)
& min_precedes(X110,X112,tptp0) ) )
& ( occurrence_of(X111,tptp2)
=> ~ ? [X113] :
( occurrence_of(X113,tptp1)
& min_precedes(X110,X113,tptp0) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[goals])]) ).
fof(c_0_17,plain,
! [X345,X346,X350] :
( ( occurrence_of(esk13_1(X345),tptp3)
| ~ occurrence_of(X346,tptp0)
| ~ subactivity_occurrence(X345,X346)
| ~ arboreal(X345)
| leaf_occ(X345,X346) )
& ( next_subocc(X345,esk13_1(X345),tptp0)
| ~ occurrence_of(X346,tptp0)
| ~ subactivity_occurrence(X345,X346)
| ~ arboreal(X345)
| leaf_occ(X345,X346) )
& ( occurrence_of(esk14_1(X345),tptp4)
| ~ occurrence_of(X346,tptp0)
| ~ subactivity_occurrence(X345,X346)
| ~ arboreal(X345)
| leaf_occ(X345,X346) )
& ( min_precedes(esk13_1(X345),esk14_1(X345),tptp0)
| ~ occurrence_of(X346,tptp0)
| ~ subactivity_occurrence(X345,X346)
| ~ arboreal(X345)
| leaf_occ(X345,X346) )
& ( occurrence_of(esk15_1(X345),tptp1)
| occurrence_of(esk15_1(X345),tptp2)
| ~ occurrence_of(X346,tptp0)
| ~ subactivity_occurrence(X345,X346)
| ~ arboreal(X345)
| leaf_occ(X345,X346) )
& ( min_precedes(esk14_1(X345),esk15_1(X345),tptp0)
| ~ occurrence_of(X346,tptp0)
| ~ subactivity_occurrence(X345,X346)
| ~ arboreal(X345)
| leaf_occ(X345,X346) )
& ( ~ min_precedes(esk13_1(X345),X350,tptp0)
| X350 = esk14_1(X345)
| X350 = esk15_1(X345)
| ~ occurrence_of(X346,tptp0)
| ~ subactivity_occurrence(X345,X346)
| ~ arboreal(X345)
| leaf_occ(X345,X346) ) ),
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)],[c_0_15])])])])])]) ).
fof(c_0_18,negated_conjecture,
! [X353,X354] :
( occurrence_of(esk17_0,tptp0)
& subactivity_occurrence(esk16_0,esk17_0)
& arboreal(esk16_0)
& ~ leaf_occ(esk16_0,esk17_0)
& ( occurrence_of(X354,tptp2)
| occurrence_of(X354,tptp1)
| ~ occurrence_of(X354,tptp1)
| ~ occurrence_of(X353,tptp3)
| ~ next_subocc(esk16_0,X353,tptp0)
| ~ min_precedes(X353,X354,tptp0)
| ~ leaf_occ(X354,esk17_0) )
& ( occurrence_of(esk19_2(X353,X354),tptp1)
| occurrence_of(X354,tptp1)
| ~ occurrence_of(X354,tptp1)
| ~ occurrence_of(X353,tptp3)
| ~ next_subocc(esk16_0,X353,tptp0)
| ~ min_precedes(X353,X354,tptp0)
| ~ leaf_occ(X354,esk17_0) )
& ( min_precedes(X353,esk19_2(X353,X354),tptp0)
| occurrence_of(X354,tptp1)
| ~ occurrence_of(X354,tptp1)
| ~ occurrence_of(X353,tptp3)
| ~ next_subocc(esk16_0,X353,tptp0)
| ~ min_precedes(X353,X354,tptp0)
| ~ leaf_occ(X354,esk17_0) )
& ( occurrence_of(X354,tptp2)
| occurrence_of(esk18_2(X353,X354),tptp2)
| ~ occurrence_of(X354,tptp1)
| ~ occurrence_of(X353,tptp3)
| ~ next_subocc(esk16_0,X353,tptp0)
| ~ min_precedes(X353,X354,tptp0)
| ~ leaf_occ(X354,esk17_0) )
& ( occurrence_of(esk19_2(X353,X354),tptp1)
| occurrence_of(esk18_2(X353,X354),tptp2)
| ~ occurrence_of(X354,tptp1)
| ~ occurrence_of(X353,tptp3)
| ~ next_subocc(esk16_0,X353,tptp0)
| ~ min_precedes(X353,X354,tptp0)
| ~ leaf_occ(X354,esk17_0) )
& ( min_precedes(X353,esk19_2(X353,X354),tptp0)
| occurrence_of(esk18_2(X353,X354),tptp2)
| ~ occurrence_of(X354,tptp1)
| ~ occurrence_of(X353,tptp3)
| ~ next_subocc(esk16_0,X353,tptp0)
| ~ min_precedes(X353,X354,tptp0)
| ~ leaf_occ(X354,esk17_0) )
& ( occurrence_of(X354,tptp2)
| min_precedes(X353,esk18_2(X353,X354),tptp0)
| ~ occurrence_of(X354,tptp1)
| ~ occurrence_of(X353,tptp3)
| ~ next_subocc(esk16_0,X353,tptp0)
| ~ min_precedes(X353,X354,tptp0)
| ~ leaf_occ(X354,esk17_0) )
& ( occurrence_of(esk19_2(X353,X354),tptp1)
| min_precedes(X353,esk18_2(X353,X354),tptp0)
| ~ occurrence_of(X354,tptp1)
| ~ occurrence_of(X353,tptp3)
| ~ next_subocc(esk16_0,X353,tptp0)
| ~ min_precedes(X353,X354,tptp0)
| ~ leaf_occ(X354,esk17_0) )
& ( min_precedes(X353,esk19_2(X353,X354),tptp0)
| min_precedes(X353,esk18_2(X353,X354),tptp0)
| ~ occurrence_of(X354,tptp1)
| ~ occurrence_of(X353,tptp3)
| ~ next_subocc(esk16_0,X353,tptp0)
| ~ min_precedes(X353,X354,tptp0)
| ~ leaf_occ(X354,esk17_0) )
& ( occurrence_of(X354,tptp2)
| occurrence_of(X354,tptp1)
| ~ occurrence_of(X354,tptp2)
| ~ occurrence_of(X353,tptp3)
| ~ next_subocc(esk16_0,X353,tptp0)
| ~ min_precedes(X353,X354,tptp0)
| ~ leaf_occ(X354,esk17_0) )
& ( occurrence_of(esk19_2(X353,X354),tptp1)
| occurrence_of(X354,tptp1)
| ~ occurrence_of(X354,tptp2)
| ~ occurrence_of(X353,tptp3)
| ~ next_subocc(esk16_0,X353,tptp0)
| ~ min_precedes(X353,X354,tptp0)
| ~ leaf_occ(X354,esk17_0) )
& ( min_precedes(X353,esk19_2(X353,X354),tptp0)
| occurrence_of(X354,tptp1)
| ~ occurrence_of(X354,tptp2)
| ~ occurrence_of(X353,tptp3)
| ~ next_subocc(esk16_0,X353,tptp0)
| ~ min_precedes(X353,X354,tptp0)
| ~ leaf_occ(X354,esk17_0) )
& ( occurrence_of(X354,tptp2)
| occurrence_of(esk18_2(X353,X354),tptp2)
| ~ occurrence_of(X354,tptp2)
| ~ occurrence_of(X353,tptp3)
| ~ next_subocc(esk16_0,X353,tptp0)
| ~ min_precedes(X353,X354,tptp0)
| ~ leaf_occ(X354,esk17_0) )
& ( occurrence_of(esk19_2(X353,X354),tptp1)
| occurrence_of(esk18_2(X353,X354),tptp2)
| ~ occurrence_of(X354,tptp2)
| ~ occurrence_of(X353,tptp3)
| ~ next_subocc(esk16_0,X353,tptp0)
| ~ min_precedes(X353,X354,tptp0)
| ~ leaf_occ(X354,esk17_0) )
& ( min_precedes(X353,esk19_2(X353,X354),tptp0)
| occurrence_of(esk18_2(X353,X354),tptp2)
| ~ occurrence_of(X354,tptp2)
| ~ occurrence_of(X353,tptp3)
| ~ next_subocc(esk16_0,X353,tptp0)
| ~ min_precedes(X353,X354,tptp0)
| ~ leaf_occ(X354,esk17_0) )
& ( occurrence_of(X354,tptp2)
| min_precedes(X353,esk18_2(X353,X354),tptp0)
| ~ occurrence_of(X354,tptp2)
| ~ occurrence_of(X353,tptp3)
| ~ next_subocc(esk16_0,X353,tptp0)
| ~ min_precedes(X353,X354,tptp0)
| ~ leaf_occ(X354,esk17_0) )
& ( occurrence_of(esk19_2(X353,X354),tptp1)
| min_precedes(X353,esk18_2(X353,X354),tptp0)
| ~ occurrence_of(X354,tptp2)
| ~ occurrence_of(X353,tptp3)
| ~ next_subocc(esk16_0,X353,tptp0)
| ~ min_precedes(X353,X354,tptp0)
| ~ leaf_occ(X354,esk17_0) )
& ( min_precedes(X353,esk19_2(X353,X354),tptp0)
| min_precedes(X353,esk18_2(X353,X354),tptp0)
| ~ occurrence_of(X354,tptp2)
| ~ occurrence_of(X353,tptp3)
| ~ next_subocc(esk16_0,X353,tptp0)
| ~ min_precedes(X353,X354,tptp0)
| ~ leaf_occ(X354,esk17_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_16])])])])]) ).
fof(c_0_19,plain,
! [X255,X256,X257] :
( ~ occurrence_of(X255,X256)
| ~ occurrence_of(X255,X257)
| X256 = X257 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_08])]) ).
fof(c_0_20,plain,
! [X268] :
( ( activity(esk5_1(X268))
| ~ activity_occurrence(X268) )
& ( occurrence_of(X268,esk5_1(X268))
| ~ activity_occurrence(X268) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_12])])])]) ).
fof(c_0_21,plain,
! [X239,X240] :
( ( activity(X239)
| ~ occurrence_of(X240,X239) )
& ( activity_occurrence(X240)
| ~ occurrence_of(X240,X239) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_03])])]) ).
fof(c_0_22,plain,
! [X248,X249,X250] :
( ( occurrence_of(esk3_3(X248,X249,X250),X248)
| ~ min_precedes(X249,X250,X248) )
& ( subactivity_occurrence(X249,esk3_3(X248,X249,X250))
| ~ min_precedes(X249,X250,X248) )
& ( subactivity_occurrence(X250,esk3_3(X248,X249,X250))
| ~ min_precedes(X249,X250,X248) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_06])])])]) ).
cnf(c_0_23,plain,
( next_subocc(X1,esk13_1(X1),tptp0)
| leaf_occ(X1,X2)
| ~ occurrence_of(X2,tptp0)
| ~ subactivity_occurrence(X1,X2)
| ~ arboreal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,negated_conjecture,
occurrence_of(esk17_0,tptp0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( occurrence_of(esk13_1(X1),tptp3)
| leaf_occ(X1,X2)
| ~ occurrence_of(X2,tptp0)
| ~ subactivity_occurrence(X1,X2)
| ~ arboreal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,plain,
( X2 = X3
| ~ occurrence_of(X1,X2)
| ~ occurrence_of(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
( occurrence_of(X1,esk5_1(X1))
| ~ activity_occurrence(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
( activity_occurrence(X1)
| ~ occurrence_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_29,plain,
! [X289,X290,X292,X293,X294] :
( ( occurrence_of(X290,esk9_2(X289,X290))
| ~ leaf_occ(X289,X290) )
& ( subactivity_occurrence(X289,X290)
| ~ leaf_occ(X289,X290) )
& ( leaf(X289,esk9_2(X289,X290))
| ~ leaf_occ(X289,X290) )
& ( ~ occurrence_of(X293,X294)
| ~ subactivity_occurrence(X292,X293)
| ~ leaf(X292,X294)
| leaf_occ(X292,X293) ) ),
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_30,plain,
( occurrence_of(esk3_3(X1,X2,X3),X1)
| ~ min_precedes(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_31,plain,
! [X318,X319,X320,X321,X322,X323,X324] :
( ( min_precedes(X318,X319,X320)
| ~ next_subocc(X318,X319,X320) )
& ( ~ min_precedes(X318,X321,X320)
| ~ min_precedes(X321,X319,X320)
| ~ next_subocc(X318,X319,X320) )
& ( min_precedes(X322,esk12_3(X322,X323,X324),X324)
| ~ min_precedes(X322,X323,X324)
| next_subocc(X322,X323,X324) )
& ( min_precedes(esk12_3(X322,X323,X324),X323,X324)
| ~ min_precedes(X322,X323,X324)
| next_subocc(X322,X323,X324) ) ),
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])])])])])]) ).
cnf(c_0_32,negated_conjecture,
( next_subocc(X1,esk13_1(X1),tptp0)
| leaf_occ(X1,esk17_0)
| ~ arboreal(X1)
| ~ subactivity_occurrence(X1,esk17_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_33,negated_conjecture,
subactivity_occurrence(esk16_0,esk17_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_34,negated_conjecture,
arboreal(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_35,negated_conjecture,
~ leaf_occ(esk16_0,esk17_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_36,plain,
! [X285,X286] :
( ( ~ arboreal(X285)
| atomic(X286)
| ~ occurrence_of(X285,X286) )
& ( ~ atomic(X286)
| arboreal(X285)
| ~ occurrence_of(X285,X286) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_16])])]) ).
cnf(c_0_37,negated_conjecture,
( leaf_occ(X1,esk17_0)
| occurrence_of(esk13_1(X1),tptp3)
| ~ arboreal(X1)
| ~ subactivity_occurrence(X1,esk17_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_38,plain,
( X1 = esk5_1(X2)
| ~ occurrence_of(X2,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_39,plain,
( occurrence_of(X1,esk9_2(X2,X1))
| ~ leaf_occ(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_40,plain,
( next_subocc(X1,esk13_1(X1),tptp0)
| leaf_occ(X1,esk3_3(tptp0,X2,X3))
| ~ arboreal(X1)
| ~ min_precedes(X2,X3,tptp0)
| ~ subactivity_occurrence(X1,esk3_3(tptp0,X2,X3)) ),
inference(spm,[status(thm)],[c_0_23,c_0_30]) ).
cnf(c_0_41,plain,
( subactivity_occurrence(X1,esk3_3(X2,X3,X1))
| ~ min_precedes(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_42,plain,
( min_precedes(X1,X2,X3)
| ~ next_subocc(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_43,negated_conjecture,
next_subocc(esk16_0,esk13_1(esk16_0),tptp0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]),c_0_35]) ).
cnf(c_0_44,plain,
( arboreal(X2)
| ~ atomic(X1)
| ~ occurrence_of(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_45,negated_conjecture,
occurrence_of(esk13_1(esk16_0),tptp3),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_33]),c_0_34])]),c_0_35]) ).
cnf(c_0_46,plain,
atomic(tptp3),
inference(split_conjunct,[status(thm)],[sos_38]) ).
cnf(c_0_47,plain,
( min_precedes(esk13_1(X1),esk14_1(X1),tptp0)
| leaf_occ(X1,X2)
| ~ occurrence_of(X2,tptp0)
| ~ subactivity_occurrence(X1,X2)
| ~ arboreal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_48,plain,
( leaf(X1,esk9_2(X1,X2))
| ~ leaf_occ(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_49,plain,
( esk9_2(X1,X2) = esk5_1(X2)
| ~ leaf_occ(X1,X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_50,plain,
( next_subocc(X1,esk13_1(X1),tptp0)
| leaf_occ(X1,esk3_3(tptp0,X2,X1))
| ~ arboreal(X1)
| ~ min_precedes(X2,X1,tptp0) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_51,negated_conjecture,
min_precedes(esk16_0,esk13_1(esk16_0),tptp0),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_52,negated_conjecture,
arboreal(esk13_1(esk16_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46])]) ).
fof(c_0_53,plain,
! [X277,X278,X280,X281,X282,X283] :
( ( root(X277,X278)
| min_precedes(esk7_2(X277,X278),X277,X278)
| ~ leaf(X277,X278) )
& ( ~ min_precedes(X277,X280,X278)
| ~ leaf(X277,X278) )
& ( ~ root(X281,X282)
| min_precedes(X281,esk8_2(X281,X282),X282)
| leaf(X281,X282) )
& ( ~ min_precedes(X283,X281,X282)
| min_precedes(X281,esk8_2(X281,X282),X282)
| leaf(X281,X282) ) ),
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_54,negated_conjecture,
( min_precedes(esk13_1(X1),esk14_1(X1),tptp0)
| leaf_occ(X1,esk17_0)
| ~ arboreal(X1)
| ~ subactivity_occurrence(X1,esk17_0) ),
inference(spm,[status(thm)],[c_0_47,c_0_24]) ).
fof(c_0_55,plain,
! [X258,X259,X260,X261] :
( ~ occurrence_of(X258,X260)
| ~ leaf_occ(X259,X258)
| ~ min_precedes(X259,X261,X260) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_09])])]) ).
cnf(c_0_56,plain,
( leaf_occ(X1,esk3_3(tptp0,X2,X3))
| occurrence_of(esk13_1(X1),tptp3)
| ~ arboreal(X1)
| ~ min_precedes(X2,X3,tptp0)
| ~ subactivity_occurrence(X1,esk3_3(tptp0,X2,X3)) ),
inference(spm,[status(thm)],[c_0_25,c_0_30]) ).
cnf(c_0_57,plain,
( leaf(X1,esk5_1(X2))
| ~ leaf_occ(X1,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_58,plain,
( esk5_1(esk3_3(X1,X2,X3)) = X1
| ~ min_precedes(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_30]) ).
cnf(c_0_59,negated_conjecture,
( next_subocc(esk13_1(esk16_0),esk13_1(esk13_1(esk16_0)),tptp0)
| leaf_occ(esk13_1(esk16_0),esk3_3(tptp0,esk16_0,esk13_1(esk16_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52])]) ).
cnf(c_0_60,plain,
( ~ min_precedes(X1,X2,X3)
| ~ leaf(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_61,negated_conjecture,
min_precedes(esk13_1(esk16_0),esk14_1(esk16_0),tptp0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_33]),c_0_34])]),c_0_35]) ).
cnf(c_0_62,plain,
( ~ occurrence_of(X1,X2)
| ~ leaf_occ(X3,X1)
| ~ min_precedes(X3,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_63,plain,
( leaf_occ(X1,esk3_3(tptp0,X2,X1))
| occurrence_of(esk13_1(X1),tptp3)
| ~ arboreal(X1)
| ~ min_precedes(X2,X1,tptp0) ),
inference(spm,[status(thm)],[c_0_56,c_0_41]) ).
cnf(c_0_64,plain,
( leaf(X1,X2)
| ~ min_precedes(X3,X4,X2)
| ~ leaf_occ(X1,esk3_3(X2,X3,X4)) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_65,negated_conjecture,
( min_precedes(esk13_1(esk16_0),esk13_1(esk13_1(esk16_0)),tptp0)
| leaf_occ(esk13_1(esk16_0),esk3_3(tptp0,esk16_0,esk13_1(esk16_0))) ),
inference(spm,[status(thm)],[c_0_42,c_0_59]) ).
cnf(c_0_66,negated_conjecture,
~ leaf(esk13_1(esk16_0),tptp0),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_67,negated_conjecture,
( ~ leaf_occ(esk13_1(esk16_0),X1)
| ~ occurrence_of(X1,tptp0) ),
inference(spm,[status(thm)],[c_0_62,c_0_61]) ).
cnf(c_0_68,negated_conjecture,
( leaf_occ(esk13_1(esk16_0),esk3_3(tptp0,esk16_0,esk13_1(esk16_0)))
| occurrence_of(esk13_1(esk13_1(esk16_0)),tptp3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_51]),c_0_52])]) ).
cnf(c_0_69,plain,
( X2 = esk14_1(X1)
| X2 = esk15_1(X1)
| leaf_occ(X1,X3)
| ~ min_precedes(esk13_1(X1),X2,tptp0)
| ~ occurrence_of(X3,tptp0)
| ~ subactivity_occurrence(X1,X3)
| ~ arboreal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_70,negated_conjecture,
min_precedes(esk13_1(esk16_0),esk13_1(esk13_1(esk16_0)),tptp0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_51])]),c_0_66]) ).
cnf(c_0_71,negated_conjecture,
( ~ leaf_occ(esk16_0,X1)
| ~ occurrence_of(X1,tptp0) ),
inference(spm,[status(thm)],[c_0_62,c_0_51]) ).
cnf(c_0_72,plain,
( occurrence_of(esk14_1(X1),tptp4)
| leaf_occ(X1,X2)
| ~ occurrence_of(X2,tptp0)
| ~ subactivity_occurrence(X1,X2)
| ~ arboreal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_73,plain,
( occurrence_of(esk15_1(X1),tptp1)
| occurrence_of(esk15_1(X1),tptp2)
| leaf_occ(X1,X2)
| ~ occurrence_of(X2,tptp0)
| ~ subactivity_occurrence(X1,X2)
| ~ arboreal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_74,negated_conjecture,
( occurrence_of(esk13_1(esk13_1(esk16_0)),tptp3)
| ~ occurrence_of(esk3_3(tptp0,esk16_0,esk13_1(esk16_0)),tptp0) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_75,negated_conjecture,
( esk13_1(esk13_1(esk16_0)) = esk15_1(esk16_0)
| esk13_1(esk13_1(esk16_0)) = esk14_1(esk16_0)
| ~ subactivity_occurrence(esk16_0,X1)
| ~ occurrence_of(X1,tptp0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_34])]),c_0_71]) ).
cnf(c_0_76,negated_conjecture,
( leaf_occ(X1,esk17_0)
| occurrence_of(esk14_1(X1),tptp4)
| ~ arboreal(X1)
| ~ subactivity_occurrence(X1,esk17_0) ),
inference(spm,[status(thm)],[c_0_72,c_0_24]) ).
cnf(c_0_77,negated_conjecture,
( leaf_occ(X1,esk17_0)
| occurrence_of(esk15_1(X1),tptp2)
| occurrence_of(esk15_1(X1),tptp1)
| ~ arboreal(X1)
| ~ subactivity_occurrence(X1,esk17_0) ),
inference(spm,[status(thm)],[c_0_73,c_0_24]) ).
cnf(c_0_78,negated_conjecture,
occurrence_of(esk13_1(esk13_1(esk16_0)),tptp3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_30]),c_0_51])]) ).
cnf(c_0_79,negated_conjecture,
( esk13_1(esk13_1(esk16_0)) = esk14_1(esk16_0)
| esk13_1(esk13_1(esk16_0)) = esk15_1(esk16_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_33]),c_0_24])]) ).
cnf(c_0_80,negated_conjecture,
occurrence_of(esk14_1(esk16_0),tptp4),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_33]),c_0_34])]),c_0_35]) ).
cnf(c_0_81,negated_conjecture,
( occurrence_of(esk15_1(esk16_0),tptp1)
| occurrence_of(esk15_1(esk16_0),tptp2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_33]),c_0_34])]),c_0_35]) ).
cnf(c_0_82,negated_conjecture,
esk5_1(esk13_1(esk13_1(esk16_0))) = tptp3,
inference(spm,[status(thm)],[c_0_38,c_0_78]) ).
cnf(c_0_83,negated_conjecture,
( esk13_1(esk13_1(esk16_0)) = esk14_1(esk16_0)
| occurrence_of(esk15_1(esk16_0),tptp3) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_84,negated_conjecture,
esk5_1(esk14_1(esk16_0)) = tptp4,
inference(spm,[status(thm)],[c_0_38,c_0_80]) ).
cnf(c_0_85,plain,
tptp4 != tptp3,
inference(split_conjunct,[status(thm)],[sos_39]) ).
cnf(c_0_86,negated_conjecture,
( X1 = tptp2
| occurrence_of(esk15_1(esk16_0),tptp1)
| ~ occurrence_of(esk15_1(esk16_0),X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_81]) ).
cnf(c_0_87,negated_conjecture,
occurrence_of(esk15_1(esk16_0),tptp3),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84]),c_0_85]) ).
cnf(c_0_88,plain,
tptp3 != tptp2,
inference(split_conjunct,[status(thm)],[sos_43]) ).
cnf(c_0_89,negated_conjecture,
occurrence_of(esk15_1(esk16_0),tptp1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88]) ).
cnf(c_0_90,negated_conjecture,
esk5_1(esk15_1(esk16_0)) = tptp3,
inference(spm,[status(thm)],[c_0_38,c_0_87]) ).
cnf(c_0_91,plain,
tptp3 != tptp1,
inference(split_conjunct,[status(thm)],[sos_42]) ).
cnf(c_0_92,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_89]),c_0_90]),c_0_91]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PRO018+4 : 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
% 0.17/0.33 % Computer : n005.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue May 5 01:31:15 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 % start to proof: theBenchmark
% 2.31/1.95 % Version : CSE_E---1.7
% 2.31/1.95 % Problem : theBenchmark.p
% 2.31/1.95 % SZS status Theorem for theBenchmark.p
% 2.31/1.95 % SZS output start CNFRefutation
% See solution above
% 2.31/1.96 % Total time : 1.371s
%------------------------------------------------------------------------------