%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : PRO005+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 01:59:30 PM UTC 2026
% Result : Theorem 0.61s 0.58s
% Output : CNFRefutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 21
% Syntax : Number of formulae : 113 ( 45 unt; 0 def)
% Number of atoms : 322 ( 21 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 346 ( 137 ~; 129 |; 60 &)
% ( 4 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 169 ( 4 sgn 93 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
~ ? [X110] : occurrence_of(X110,tptp0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(sos_32,axiom,
! [X102] :
( occurrence_of(X102,tptp0)
=> ? [X103,X104] :
( next_subocc(X103,X104,tptp0)
& leaf_occ(X104,X102)
& ( occurrence_of(X104,tptp2)
| occurrence_of(X104,tptp3) )
& root_occ(X103,X102)
& occurrence_of(X103,tptp4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_32) ).
fof(sos_26,axiom,
! [X79,X80,X81] :
( next_subocc(X79,X80,X81)
<=> ( ~ ? [X82] :
( min_precedes(X82,X80,X81)
& min_precedes(X79,X82,X81) )
& min_precedes(X79,X80,X81) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_26) ).
fof(sos_46,axiom,
! [X107,X108] :
( ( ~ leaf_occ(X107,X108)
& arboreal(X107)
& subactivity_occurrence(X107,X108)
& occurrence_of(X108,tptp0) )
=> ? [X109] :
( next_subocc(X107,X109,tptp0)
& occurrence_of(X109,tptp1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_46) ).
fof(sos_09,axiom,
! [X32,X33,X34] :
( ( leaf_occ(X33,X32)
& occurrence_of(X32,X34) )
=> ~ ? [X35] : min_precedes(X33,X35,X34) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_09) ).
fof(sos_19,axiom,
! [X59,X60] :
( root_occ(X59,X60)
<=> ? [X61] :
( root(X59,X61)
& subactivity_occurrence(X59,X60)
& occurrence_of(X60,X61) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_19) ).
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_35,axiom,
atomic(tptp4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_35) ).
fof(sos_15,axiom,
! [X48,X49] :
( leaf(X48,X49)
<=> ( ~ ? [X51] : min_precedes(X48,X51,X49)
& ( ? [X50] : min_precedes(X50,X48,X49)
| root(X48,X49) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_15) ).
fof(sos_45,axiom,
! [X105,X106] :
( ( ~ leaf_occ(X105,X106)
& arboreal(X105)
& subactivity_occurrence(X105,X106)
& occurrence_of(X106,tptp0) )
=> root_occ(X105,X106) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_45) ).
fof(sos_06,axiom,
! [X22,X23,X24] :
( min_precedes(X23,X24,X22)
=> ? [X25] :
( subactivity_occurrence(X24,X25)
& subactivity_occurrence(X23,X25)
& occurrence_of(X25,X22) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_06) ).
fof(sos_10,axiom,
! [X36,X37,X38] :
( ( root_occ(X37,X36)
& occurrence_of(X36,X38) )
=> ~ ? [X39] : min_precedes(X39,X37,X38) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_10) ).
fof(sos_38,axiom,
atomic(tptp1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_38) ).
fof(sos_07,axiom,
! [X26,X27] :
( ( ~ atomic(X27)
& leaf(X26,X27) )
=> ? [X28] :
( leaf_occ(X26,X28)
& occurrence_of(X28,X27) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_07) ).
fof(sos_34,axiom,
~ atomic(tptp0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_34) ).
fof(sos_28,axiom,
! [X87,X88,X89,X90] :
( ( leaf_occ(X88,X89)
& leaf_occ(X87,X89)
& ~ atomic(X90)
& occurrence_of(X89,X90) )
=> X87 = X88 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_28) ).
fof(sos_08,axiom,
! [X29,X30,X31] :
( ( occurrence_of(X29,X31)
& occurrence_of(X29,X30) )
=> X30 = X31 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_08) ).
fof(sos_12,axiom,
! [X42] :
( activity_occurrence(X42)
=> ? [X43] :
( occurrence_of(X42,X43)
& activity(X43) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_12) ).
fof(sos_03,axiom,
! [X13,X14] :
( occurrence_of(X14,X13)
=> ( activity_occurrence(X14)
& activity(X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_03) ).
fof(sos_43,axiom,
tptp1 != tptp2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_43) ).
fof(sos_42,axiom,
tptp1 != tptp3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_42) ).
fof(c_0_21,negated_conjecture,
~ ~ ? [X110] : occurrence_of(X110,tptp0),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_22,plain,
! [X229] :
( ( ~ occurrence_of(X229,tptp0)
| next_subocc(esk13_1(X229),esk14_1(X229),tptp0) )
& ( ~ occurrence_of(X229,tptp0)
| leaf_occ(esk14_1(X229),X229) )
& ( ~ occurrence_of(X229,tptp0)
| occurrence_of(esk14_1(X229),tptp2)
| occurrence_of(esk14_1(X229),tptp3) )
& ( ~ occurrence_of(X229,tptp0)
| root_occ(esk13_1(X229),X229) )
& ( ~ occurrence_of(X229,tptp0)
| occurrence_of(esk13_1(X229),tptp4) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_32])])])])]) ).
fof(c_0_23,negated_conjecture,
occurrence_of(esk16_0,tptp0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
fof(c_0_24,plain,
! [X202,X203,X204,X205,X206,X207,X208] :
( ( next_subocc(X206,X207,X208)
| ~ min_precedes(X206,X207,X208)
| min_precedes(esk12_3(X206,X207,X208),X207,X208) )
& ( next_subocc(X206,X207,X208)
| ~ min_precedes(X206,X207,X208)
| min_precedes(X206,esk12_3(X206,X207,X208),X208) )
& ( ~ next_subocc(X202,X203,X204)
| ~ min_precedes(X205,X203,X204)
| ~ min_precedes(X202,X205,X204) )
& ( ~ next_subocc(X202,X203,X204)
| min_precedes(X202,X203,X204) ) ),
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_26])])])])])])]) ).
cnf(c_0_25,plain,
( ~ occurrence_of(X1,tptp0)
| next_subocc(esk13_1(X1),esk14_1(X1),tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,negated_conjecture,
occurrence_of(esk16_0,tptp0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_27,plain,
! [X107,X108] :
( ( ~ leaf_occ(X107,X108)
& arboreal(X107)
& subactivity_occurrence(X107,X108)
& occurrence_of(X108,tptp0) )
=> ? [X109] :
( next_subocc(X107,X109,tptp0)
& occurrence_of(X109,tptp1) ) ),
inference(fof_simplification,[status(thm)],[sos_46]) ).
fof(c_0_28,plain,
! [X142,X143,X144,X145] :
( ~ min_precedes(X143,X145,X144)
| ~ leaf_occ(X143,X142)
| ~ occurrence_of(X142,X144) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_09])])])]) ).
cnf(c_0_29,plain,
( ~ next_subocc(X1,X2,X3)
| min_precedes(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,negated_conjecture,
next_subocc(esk13_1(esk16_0),esk14_1(esk16_0),tptp0),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
fof(c_0_31,plain,
! [X234,X235] :
( ( leaf_occ(X234,X235)
| ~ arboreal(X234)
| ~ subactivity_occurrence(X234,X235)
| ~ occurrence_of(X235,tptp0)
| next_subocc(X234,esk15_1(X234),tptp0) )
& ( leaf_occ(X234,X235)
| ~ arboreal(X234)
| ~ subactivity_occurrence(X234,X235)
| ~ occurrence_of(X235,tptp0)
| occurrence_of(esk15_1(X234),tptp1) ) ),
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)],[c_0_27])])])])])])]) ).
fof(c_0_32,plain,
! [X179,X180,X182,X183,X184] :
( ( root_occ(X182,X183)
| ~ root(X182,X184)
| ~ subactivity_occurrence(X182,X183)
| ~ occurrence_of(X183,X184) )
& ( ~ root_occ(X179,X180)
| root(X179,esk10_2(X179,X180)) )
& ( ~ root_occ(X179,X180)
| subactivity_occurrence(X179,X180) )
& ( ~ root_occ(X179,X180)
| occurrence_of(X180,esk10_2(X179,X180)) ) ),
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_19])])])])])])]) ).
cnf(c_0_33,plain,
( ~ occurrence_of(X1,tptp0)
| root_occ(esk13_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_34,plain,
! [X169,X170] :
( ( ~ occurrence_of(X169,X170)
| arboreal(X169)
| ~ atomic(X170) )
& ( ~ occurrence_of(X169,X170)
| atomic(X170)
| ~ arboreal(X169) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_16])])])]) ).
cnf(c_0_35,plain,
( ~ occurrence_of(X1,tptp0)
| occurrence_of(esk13_1(X1),tptp4) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_36,plain,
( ~ min_precedes(X3,X4,X2)
| ~ leaf_occ(X3,X1)
| ~ occurrence_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_37,negated_conjecture,
min_precedes(esk13_1(esk16_0),esk14_1(esk16_0),tptp0),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_38,plain,
( ~ arboreal(X1)
| ~ subactivity_occurrence(X1,X2)
| ~ occurrence_of(X2,tptp0)
| leaf_occ(X1,X2)
| next_subocc(X1,esk15_1(X1),tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_39,plain,
( ~ root_occ(X1,X2)
| subactivity_occurrence(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,negated_conjecture,
root_occ(esk13_1(esk16_0),esk16_0),
inference(spm,[status(thm)],[c_0_33,c_0_26]) ).
cnf(c_0_41,plain,
( ~ occurrence_of(X2,X1)
| ~ atomic(X1)
| arboreal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,negated_conjecture,
occurrence_of(esk13_1(esk16_0),tptp4),
inference(spm,[status(thm)],[c_0_35,c_0_26]) ).
cnf(c_0_43,plain,
atomic(tptp4),
inference(split_conjunct,[status(thm)],[sos_35]) ).
cnf(c_0_44,negated_conjecture,
( ~ occurrence_of(X1,tptp0)
| ~ leaf_occ(esk13_1(esk16_0),X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_45,negated_conjecture,
( ~ subactivity_occurrence(X1,esk16_0)
| ~ arboreal(X1)
| leaf_occ(X1,esk16_0)
| next_subocc(X1,esk15_1(X1),tptp0) ),
inference(spm,[status(thm)],[c_0_38,c_0_26]) ).
cnf(c_0_46,negated_conjecture,
subactivity_occurrence(esk13_1(esk16_0),esk16_0),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_47,negated_conjecture,
arboreal(esk13_1(esk16_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]) ).
cnf(c_0_48,negated_conjecture,
~ leaf_occ(esk13_1(esk16_0),esk16_0),
inference(spm,[status(thm)],[c_0_44,c_0_26]) ).
fof(c_0_49,plain,
! [X161,X162,X164,X165,X166,X167] :
( ( leaf(X165,X166)
| min_precedes(X165,esk8_2(X165,X166),X166)
| ~ min_precedes(X167,X165,X166) )
& ( leaf(X165,X166)
| min_precedes(X165,esk8_2(X165,X166),X166)
| ~ root(X165,X166) )
& ( ~ leaf(X161,X162)
| ~ min_precedes(X161,X164,X162) )
& ( ~ leaf(X161,X162)
| min_precedes(esk7_2(X161,X162),X161,X162)
| root(X161,X162) ) ),
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_15])])])])])])]) ).
cnf(c_0_50,negated_conjecture,
next_subocc(esk13_1(esk16_0),esk15_1(esk13_1(esk16_0)),tptp0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47])]),c_0_48]) ).
fof(c_0_51,plain,
! [X105,X106] :
( ( ~ leaf_occ(X105,X106)
& arboreal(X105)
& subactivity_occurrence(X105,X106)
& occurrence_of(X106,tptp0) )
=> root_occ(X105,X106) ),
inference(fof_simplification,[status(thm)],[sos_45]) ).
fof(c_0_52,plain,
! [X132,X133,X134] :
( ( ~ min_precedes(X133,X134,X132)
| subactivity_occurrence(X134,esk3_3(X132,X133,X134)) )
& ( ~ min_precedes(X133,X134,X132)
| subactivity_occurrence(X133,esk3_3(X132,X133,X134)) )
& ( ~ min_precedes(X133,X134,X132)
| occurrence_of(esk3_3(X132,X133,X134),X132) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_06])])])])]) ).
cnf(c_0_53,plain,
( ~ arboreal(X1)
| ~ subactivity_occurrence(X1,X2)
| ~ occurrence_of(X2,tptp0)
| leaf_occ(X1,X2)
| occurrence_of(esk15_1(X1),tptp1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_54,plain,
! [X146,X147,X148,X149] :
( ~ min_precedes(X149,X147,X148)
| ~ root_occ(X147,X146)
| ~ occurrence_of(X146,X148) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_10])])])]) ).
cnf(c_0_55,plain,
( ~ min_precedes(X1,X2,X3)
| leaf(X2,X3)
| min_precedes(X2,esk8_2(X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_56,negated_conjecture,
min_precedes(esk13_1(esk16_0),esk15_1(esk13_1(esk16_0)),tptp0),
inference(spm,[status(thm)],[c_0_29,c_0_50]) ).
fof(c_0_57,plain,
! [X232,X233] :
( root_occ(X232,X233)
| leaf_occ(X232,X233)
| ~ arboreal(X232)
| ~ subactivity_occurrence(X232,X233)
| ~ occurrence_of(X233,tptp0) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_51])])]) ).
cnf(c_0_58,plain,
( ~ min_precedes(X2,X3,X1)
| occurrence_of(esk3_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_59,negated_conjecture,
( ~ subactivity_occurrence(X1,esk16_0)
| ~ arboreal(X1)
| occurrence_of(esk15_1(X1),tptp1)
| leaf_occ(X1,esk16_0) ),
inference(spm,[status(thm)],[c_0_53,c_0_26]) ).
cnf(c_0_60,plain,
( ~ min_precedes(X4,X3,X2)
| ~ root_occ(X3,X1)
| ~ occurrence_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_61,negated_conjecture,
( min_precedes(esk15_1(esk13_1(esk16_0)),esk8_2(esk15_1(esk13_1(esk16_0)),tptp0),tptp0)
| leaf(esk15_1(esk13_1(esk16_0)),tptp0) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_62,plain,
( ~ arboreal(X2)
| ~ subactivity_occurrence(X2,X1)
| ~ occurrence_of(X1,tptp0)
| root_occ(X2,X1)
| leaf_occ(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_63,negated_conjecture,
occurrence_of(esk3_3(tptp0,esk13_1(esk16_0),esk15_1(esk13_1(esk16_0))),tptp0),
inference(spm,[status(thm)],[c_0_58,c_0_56]) ).
cnf(c_0_64,plain,
( ~ min_precedes(X3,X1,X2)
| subactivity_occurrence(X1,esk3_3(X2,X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_65,negated_conjecture,
occurrence_of(esk15_1(esk13_1(esk16_0)),tptp1),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_46]),c_0_47])]),c_0_48]) ).
cnf(c_0_66,plain,
atomic(tptp1),
inference(split_conjunct,[status(thm)],[sos_38]) ).
cnf(c_0_67,negated_conjecture,
( ~ occurrence_of(X1,tptp0)
| ~ root_occ(esk15_1(esk13_1(esk16_0)),X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_56]) ).
fof(c_0_68,plain,
! [X26,X27] :
( ( ~ atomic(X27)
& leaf(X26,X27) )
=> ? [X28] :
( leaf_occ(X26,X28)
& occurrence_of(X28,X27) ) ),
inference(fof_simplification,[status(thm)],[sos_07]) ).
cnf(c_0_69,negated_conjecture,
( ~ occurrence_of(X1,tptp0)
| ~ leaf_occ(esk15_1(esk13_1(esk16_0)),X1)
| leaf(esk15_1(esk13_1(esk16_0)),tptp0) ),
inference(spm,[status(thm)],[c_0_36,c_0_61]) ).
cnf(c_0_70,negated_conjecture,
( ~ subactivity_occurrence(X1,esk3_3(tptp0,esk13_1(esk16_0),esk15_1(esk13_1(esk16_0))))
| ~ arboreal(X1)
| root_occ(X1,esk3_3(tptp0,esk13_1(esk16_0),esk15_1(esk13_1(esk16_0))))
| leaf_occ(X1,esk3_3(tptp0,esk13_1(esk16_0),esk15_1(esk13_1(esk16_0)))) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_71,negated_conjecture,
subactivity_occurrence(esk15_1(esk13_1(esk16_0)),esk3_3(tptp0,esk13_1(esk16_0),esk15_1(esk13_1(esk16_0)))),
inference(spm,[status(thm)],[c_0_64,c_0_56]) ).
cnf(c_0_72,negated_conjecture,
arboreal(esk15_1(esk13_1(esk16_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_65]),c_0_66])]) ).
cnf(c_0_73,negated_conjecture,
~ root_occ(esk15_1(esk13_1(esk16_0)),esk3_3(tptp0,esk13_1(esk16_0),esk15_1(esk13_1(esk16_0)))),
inference(spm,[status(thm)],[c_0_67,c_0_63]) ).
fof(c_0_74,plain,
~ atomic(tptp0),
inference(fof_simplification,[status(thm)],[sos_34]) ).
fof(c_0_75,plain,
! [X87,X88,X89,X90] :
( ( leaf_occ(X88,X89)
& leaf_occ(X87,X89)
& ~ atomic(X90)
& occurrence_of(X89,X90) )
=> X87 = X88 ),
inference(fof_simplification,[status(thm)],[sos_28]) ).
fof(c_0_76,plain,
! [X136,X137] :
( ( atomic(X137)
| ~ leaf(X136,X137)
| leaf_occ(X136,esk4_2(X136,X137)) )
& ( atomic(X137)
| ~ leaf(X136,X137)
| occurrence_of(esk4_2(X136,X137),X137) ) ),
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_68])])])])]) ).
cnf(c_0_77,negated_conjecture,
( ~ leaf_occ(esk15_1(esk13_1(esk16_0)),esk3_3(tptp0,esk13_1(esk16_0),esk15_1(esk13_1(esk16_0))))
| leaf(esk15_1(esk13_1(esk16_0)),tptp0) ),
inference(spm,[status(thm)],[c_0_69,c_0_63]) ).
cnf(c_0_78,negated_conjecture,
leaf_occ(esk15_1(esk13_1(esk16_0)),esk3_3(tptp0,esk13_1(esk16_0),esk15_1(esk13_1(esk16_0)))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72])]),c_0_73]) ).
fof(c_0_79,plain,
~ atomic(tptp0),
inference(fof_nnf,[status(thm)],[c_0_74]) ).
fof(c_0_80,plain,
! [X214,X215,X216,X217] :
( X214 = X215
| ~ leaf_occ(X215,X216)
| ~ leaf_occ(X214,X216)
| atomic(X217)
| ~ occurrence_of(X216,X217) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_75])])]) ).
cnf(c_0_81,plain,
( ~ leaf(X1,X2)
| atomic(X2)
| leaf_occ(X1,esk4_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_82,negated_conjecture,
leaf(esk15_1(esk13_1(esk16_0)),tptp0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_78])]) ).
cnf(c_0_83,plain,
~ atomic(tptp0),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_84,plain,
( ~ leaf(X1,X2)
| atomic(X2)
| occurrence_of(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
fof(c_0_85,plain,
! [X139,X140,X141] :
( X140 = X141
| ~ occurrence_of(X139,X141)
| ~ occurrence_of(X139,X140) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_08])])]) ).
fof(c_0_86,plain,
! [X152] :
( ( ~ activity_occurrence(X152)
| occurrence_of(X152,esk5_1(X152)) )
& ( ~ activity_occurrence(X152)
| activity(esk5_1(X152)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_12])])])])]) ).
fof(c_0_87,plain,
! [X123,X124] :
( ( ~ occurrence_of(X124,X123)
| activity_occurrence(X124) )
& ( ~ occurrence_of(X124,X123)
| activity(X123) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_03])])])]) ).
cnf(c_0_88,plain,
( ~ leaf_occ(X4,X1)
| ~ leaf_occ(X3,X1)
| ~ occurrence_of(X1,X2)
| X3 = X4
| atomic(X2) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_89,negated_conjecture,
leaf_occ(esk15_1(esk13_1(esk16_0)),esk4_2(esk15_1(esk13_1(esk16_0)),tptp0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83]) ).
cnf(c_0_90,plain,
( ~ occurrence_of(X1,tptp0)
| leaf_occ(esk14_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_91,negated_conjecture,
occurrence_of(esk4_2(esk15_1(esk13_1(esk16_0)),tptp0),tptp0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_82]),c_0_83]) ).
cnf(c_0_92,plain,
( ~ occurrence_of(X1,X3)
| ~ occurrence_of(X1,X2)
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_93,plain,
( ~ activity_occurrence(X1)
| occurrence_of(X1,esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_94,plain,
( ~ occurrence_of(X1,X2)
| activity_occurrence(X1) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_95,negated_conjecture,
( ~ occurrence_of(esk4_2(esk15_1(esk13_1(esk16_0)),tptp0),X2)
| ~ leaf_occ(X1,esk4_2(esk15_1(esk13_1(esk16_0)),tptp0))
| atomic(X2)
| X1 = esk15_1(esk13_1(esk16_0)) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_96,negated_conjecture,
leaf_occ(esk14_1(esk4_2(esk15_1(esk13_1(esk16_0)),tptp0)),esk4_2(esk15_1(esk13_1(esk16_0)),tptp0)),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_97,plain,
( ~ occurrence_of(X2,X1)
| X1 = esk5_1(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_94]) ).
cnf(c_0_98,negated_conjecture,
( ~ occurrence_of(esk4_2(esk15_1(esk13_1(esk16_0)),tptp0),X1)
| atomic(X1)
| esk14_1(esk4_2(esk15_1(esk13_1(esk16_0)),tptp0)) = esk15_1(esk13_1(esk16_0)) ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_99,negated_conjecture,
esk5_1(esk4_2(esk15_1(esk13_1(esk16_0)),tptp0)) = tptp0,
inference(spm,[status(thm)],[c_0_97,c_0_91]) ).
cnf(c_0_100,negated_conjecture,
activity_occurrence(esk4_2(esk15_1(esk13_1(esk16_0)),tptp0)),
inference(spm,[status(thm)],[c_0_94,c_0_91]) ).
fof(c_0_101,plain,
tptp1 != tptp2,
inference(fof_simplification,[status(thm)],[sos_43]) ).
cnf(c_0_102,plain,
( ~ occurrence_of(X1,tptp0)
| occurrence_of(esk14_1(X1),tptp2)
| occurrence_of(esk14_1(X1),tptp3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_103,negated_conjecture,
esk14_1(esk4_2(esk15_1(esk13_1(esk16_0)),tptp0)) = esk15_1(esk13_1(esk16_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_93]),c_0_99]),c_0_100])]),c_0_83]) ).
fof(c_0_104,plain,
tptp1 != tptp2,
inference(fof_nnf,[status(thm)],[c_0_101]) ).
fof(c_0_105,plain,
tptp1 != tptp3,
inference(fof_simplification,[status(thm)],[sos_42]) ).
cnf(c_0_106,negated_conjecture,
( occurrence_of(esk15_1(esk13_1(esk16_0)),tptp3)
| occurrence_of(esk15_1(esk13_1(esk16_0)),tptp2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_91]),c_0_103]),c_0_103]) ).
cnf(c_0_107,negated_conjecture,
esk5_1(esk15_1(esk13_1(esk16_0))) = tptp1,
inference(spm,[status(thm)],[c_0_97,c_0_65]) ).
cnf(c_0_108,plain,
tptp1 != tptp2,
inference(split_conjunct,[status(thm)],[c_0_104]) ).
fof(c_0_109,plain,
tptp1 != tptp3,
inference(fof_nnf,[status(thm)],[c_0_105]) ).
cnf(c_0_110,negated_conjecture,
occurrence_of(esk15_1(esk13_1(esk16_0)),tptp3),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_106]),c_0_107]),c_0_108]) ).
cnf(c_0_111,plain,
tptp1 != tptp3,
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_112,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_110]),c_0_107]),c_0_111]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PRO005+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n026.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 03:44:06 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.61/0.58 % Version: 3.5.1
% 0.61/0.58 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.61/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.61/0.58 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.61/0.58 % Starting new_bool_3 with 300s (1) cores
% 0.61/0.58 % Starting new_bool_1 with 300s (1) cores
% 0.61/0.58 % Starting sh5l with 300s (1) cores
% 0.61/0.58 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1288091 completed with status 0
% 0.61/0.58 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.61/0.58 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.61/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.61/0.58 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.61/0.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.61/0.58 % No SInE strategy applied
% 0.61/0.58 % Search class: FGHSF-FFMM31-SFFFFFNN
% 0.61/0.58 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.61/0.58 % Starting SubtermCWHack with 136s (1) cores
% 0.61/0.58 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.61/0.58 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2g with 136s (1) cores
% 0.61/0.58 % Starting new_bool_3 with 136s (1) cores
% 0.61/0.58 % Starting new_bool_1 with 136s (1) cores
% 0.61/0.58 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1288098 completed with status 0
% 0.61/0.58 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.61/0.58 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.61/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.61/0.58 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.61/0.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.61/0.58 % No SInE strategy applied
% 0.61/0.58 % Search class: FGHSF-FFMM31-SFFFFFNN
% 0.61/0.58 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.61/0.58 % Starting SubtermCWHack with 136s (1) cores
% 0.61/0.58 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.61/0.58 % Preprocessing time : 0.002 s
% 0.61/0.58 % Presaturation interreduction done
% 0.61/0.58
% 0.61/0.58 % Proof found!
% 0.61/0.58 % SZS status Theorem
% 0.61/0.58 % SZS output start CNFRefutation
% See solution above
% 0.61/0.58 % Parsed axioms : 48
% 0.61/0.58 % Removed by relevancy pruning/SinE : 0
% 0.61/0.58 % Initial clauses : 81
% 0.61/0.58 % Removed in clause preprocessing : 0
% 0.61/0.58 % Initial clauses in saturation : 81
% 0.61/0.58 % Processed clauses : 1515
% 0.61/0.58 % ...of these trivial : 75
% 0.61/0.58 % ...subsumed : 271
% 0.61/0.58 % ...remaining for further processing : 1169
% 0.61/0.58 % Other redundant clauses eliminated : 0
% 0.61/0.58 % Clauses deleted for lack of memory : 0
% 0.61/0.58 % Backward-subsumed : 0
% 0.61/0.58 % Backward-rewritten : 261
% 0.61/0.58 % Generated clauses : 3129
% 0.61/0.58 % ...of the previous two non-redundant : 2550
% 0.61/0.58 % ...aggressively subsumed : 0
% 0.61/0.58 % Contextual simplify-reflections : 6
% 0.61/0.58 % Paramodulations : 3129
% 0.61/0.58 % Factorizations : 0
% 0.61/0.58 % NegExts : 0
% 0.61/0.58 % Equation resolutions : 0
% 0.61/0.58 % Disequality decompositions : 0
% 0.61/0.58 % Total rewrite steps : 2172
% 0.61/0.58 % ...of those cached : 1939
% 0.61/0.58 % Propositional unsat checks : 0
% 0.61/0.58 % Propositional check models : 0
% 0.61/0.58 % Propositional check unsatisfiable : 0
% 0.61/0.58 % Propositional clauses : 0
% 0.61/0.58 % Propositional clauses after purity: 0
% 0.61/0.58 % Propositional unsat core size : 0
% 0.61/0.58 % Propositional preprocessing time : 0.000
% 0.61/0.58 % Propositional encoding time : 0.000
% 0.61/0.58 % Propositional solver time : 0.000
% 0.61/0.58 % Success case prop preproc time : 0.000
% 0.61/0.58 % Success case prop encoding time : 0.000
% 0.61/0.58 % Success case prop solver time : 0.000
% 0.61/0.58 % Current number of processed clauses : 827
% 0.61/0.58 % Positive orientable unit clauses : 262
% 0.61/0.58 % Positive unorientable unit clauses: 0
% 0.61/0.58 % Negative unit clauses : 253
% 0.61/0.58 % Non-unit-clauses : 312
% 0.61/0.58 % Current number of unprocessed clauses: 1105
% 0.61/0.58 % ...number of literals in the above : 2727
% 0.61/0.58 % Current number of archived formulas : 0
% 0.61/0.58 % Current number of archived clauses : 342
% 0.61/0.58 % Clause-clause subsumption calls (NU) : 27741
% 0.61/0.58 % Rec. Clause-clause subsumption calls : 17654
% 0.61/0.58 % Non-unit clause-clause subsumptions : 109
% 0.61/0.58 % Unit Clause-clause subsumption calls : 7423
% 0.61/0.58 % Rewrite failures with RHS unbound : 0
% 0.61/0.58 % BW rewrite match attempts : 220
% 0.61/0.58 % BW rewrite match successes : 32
% 0.61/0.58 % Condensation attempts : 0
% 0.61/0.58 % Condensation successes : 0
% 0.61/0.58 % Termbank termtop insertions : 86597
% 0.61/0.58 % Search garbage collected termcells : 1324
% 0.61/0.58
% 0.61/0.58 % -------------------------------------------------
% 0.61/0.58 % User time : 0.147 s
% 0.61/0.58 % System time : 0.010 s
% 0.61/0.58 % Total time : 0.157 s
% 0.61/0.58 % Maximum resident set size: 3996 pages
% 0.61/0.58
% 0.61/0.58 % -------------------------------------------------
% 0.61/0.58 % User time : 0.586 s
% 0.61/0.58 % System time : 0.037 s
% 0.61/0.58 % Total time : 0.623 s
% 0.61/0.58 % Maximum resident set size: 4608 pages
% 0.61/0.58 % E exiting
%------------------------------------------------------------------------------