%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : PRO004+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 01:59:14 PM UTC 2026
% Result : Theorem 64.92s 8.62s
% Output : CNFRefutation 64.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 21
% Syntax : Number of formulae : 156 ( 36 unt; 0 def)
% Number of atoms : 454 ( 35 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 501 ( 203 ~; 206 |; 73 &)
% ( 4 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 287 ( 264 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X7,X8,X9,X10] :
( ( root_occ(X8,X9)
& root_occ(X7,X9)
& occurrence_of(X9,X10) )
=> X7 = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X11,X12,X13,X14] :
( ( leaf_occ(X12,X13)
& leaf_occ(X11,X13)
& ~ atomic(X14)
& occurrence_of(X13,X14) )
=> X11 = X12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X15,X16,X17] :
( next_subocc(X15,X16,X17)
<=> ( ~ ? [X18] :
( min_precedes(X18,X16,X17)
& min_precedes(X15,X18,X17) )
& min_precedes(X15,X16,X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X22,X23,X24] :
( min_precedes(X22,X23,X24)
=> precedes(X22,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X28,X29] :
( precedes(X28,X29)
<=> ( legal(X29)
& earlier(X28,X29) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X32,X33] :
( root_occ(X32,X33)
<=> ? [X34] :
( root(X32,X34)
& subactivity_occurrence(X32,X33)
& occurrence_of(X33,X34) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X38,X39] :
( root(X38,X39)
=> legal(X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X51] :
( legal(X51)
=> arboreal(X51) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X52] :
( activity_occurrence(X52)
=> ? [X53] :
( occurrence_of(X52,X53)
& activity(X53) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X56,X57,X58] :
( ( root_occ(X57,X56)
& occurrence_of(X56,X58) )
=> ~ ? [X59] : min_precedes(X59,X57,X58) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X60,X61,X62] :
( ( leaf_occ(X61,X60)
& occurrence_of(X60,X62) )
=> ~ ? [X63] : min_precedes(X61,X63,X62) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X64,X65,X66] :
( ( occurrence_of(X64,X66)
& occurrence_of(X64,X65) )
=> X65 = X66 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [X70,X71,X72] :
( min_precedes(X71,X72,X70)
=> ? [X73] :
( subactivity_occurrence(X72,X73)
& subactivity_occurrence(X71,X73)
& occurrence_of(X73,X70) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [X89,X90] :
( occurrence_of(X90,X89)
=> ( activity_occurrence(X90)
& activity(X89) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [X91,X92] :
( ( ~ atomic(X91)
& occurrence_of(X92,X91) )
=> ? [X93] :
( subactivity_occurrence(X93,X92)
& root(X93,X91) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [X95] :
( occurrence_of(X95,tptp0)
=> ? [X96,X97] :
( next_subocc(X96,X97,tptp0)
& leaf_occ(X97,X95)
& occurrence_of(X97,tptp3)
& root_occ(X96,X95)
& occurrence_of(X96,tptp4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,axiom,
~ atomic(tptp0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,axiom,
tptp1 != tptp3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [X100,X101] :
( ( ~ leaf_occ(X100,X101)
& arboreal(X100)
& subactivity_occurrence(X100,X101)
& occurrence_of(X101,tptp0) )
=> root_occ(X100,X101) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [X102,X103] :
( ( ~ leaf_occ(X102,X103)
& arboreal(X102)
& subactivity_occurrence(X102,X103)
& occurrence_of(X103,tptp0) )
=> ? [X104] :
( next_subocc(X102,X104,tptp0)
& occurrence_of(X104,tptp1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,conjecture,
~ ? [X105] : occurrence_of(X105,tptp0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
~ ~ ? [X105] : occurrence_of(X105,tptp0),
inference(negated_conjecture,[status(cth)],[f49]) ).
fof(f57,plain,
! [X7,X8,X9,X10] :
( X7 = X8
| ~ root_occ(X8,X9)
| ~ root_occ(X7,X9)
| ~ occurrence_of(X9,X10) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f58,plain,
! [X7,X8] :
( X7 = X8
| ! [X9] :
( ~ root_occ(X8,X9)
| ~ root_occ(X7,X9)
| ! [X10] : ~ occurrence_of(X9,X10) ) ),
inference(miniscoping,[status(thm)],[f57]) ).
fof(f59,plain,
! [X0,X1,X2,X3] :
( ~ occurrence_of(X1,X3)
| ~ root_occ(X2,X1)
| X0 = X2
| ~ root_occ(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f60,plain,
! [X11,X12,X13,X14] :
( X11 = X12
| ~ leaf_occ(X12,X13)
| ~ leaf_occ(X11,X13)
| atomic(X14)
| ~ occurrence_of(X13,X14) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f61,plain,
! [X11,X12] :
( X11 = X12
| ! [X13] :
( ~ leaf_occ(X12,X13)
| ~ leaf_occ(X11,X13)
| ! [X14] :
( atomic(X14)
| ~ occurrence_of(X13,X14) ) ) ),
inference(miniscoping,[status(thm)],[f60]) ).
fof(f62,plain,
! [X0,X1,X2,X3] :
( ~ leaf_occ(X1,X3)
| ~ leaf_occ(X2,X3)
| ~ occurrence_of(X3,X0)
| X1 = X2
| atomic(X0) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
! [X15,X16,X17] :
( next_subocc(X15,X16,X17)
<=> ( ! [X18] :
( ~ min_precedes(X18,X16,X17)
| ~ min_precedes(X15,X18,X17) )
& min_precedes(X15,X16,X17) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f64,plain,
! [X15,X16,X17] :
( ( ? [X18] :
( min_precedes(X18,X16,X17)
& min_precedes(X15,X18,X17) )
| ~ min_precedes(X15,X16,X17)
| next_subocc(X15,X16,X17) )
& ( ( ! [X18] :
( ~ min_precedes(X18,X16,X17)
| ~ min_precedes(X15,X18,X17) )
& min_precedes(X15,X16,X17) )
| ~ next_subocc(X15,X16,X17) ) ),
inference(NNF_transformation,[status(thm)],[f63]) ).
fof(f65,plain,
( ! [X15,X16,X17] :
( ? [X18] :
( min_precedes(X18,X16,X17)
& min_precedes(X15,X18,X17) )
| ~ min_precedes(X15,X16,X17)
| next_subocc(X15,X16,X17) )
& ! [X15,X16,X17] :
( ( ! [X18] :
( ~ min_precedes(X18,X16,X17)
| ~ min_precedes(X15,X18,X17) )
& min_precedes(X15,X16,X17) )
| ~ next_subocc(X15,X16,X17) ) ),
inference(miniscoping,[status(thm)],[f64]) ).
fof(f66,plain,
( ! [X15,X16,X17] :
( ( min_precedes(sK0_skl(X17,X16,X15),X16,X17)
& min_precedes(X15,sK0_skl(X17,X16,X15),X17) )
| ~ min_precedes(X15,X16,X17)
| next_subocc(X15,X16,X17) )
& ! [X15,X16,X17] :
( ( ! [X18] :
( ~ min_precedes(X18,X16,X17)
| ~ min_precedes(X15,X18,X17) )
& min_precedes(X15,X16,X17) )
| ~ next_subocc(X15,X16,X17) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X18,sK0_skl(X17,X16,X15))],[f65]) ).
fof(f67,plain,
! [X0,X1,X2] :
( min_precedes(X0,X1,X2)
| ~ next_subocc(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f75,plain,
! [X22,X23,X24] :
( precedes(X22,X23)
| ~ min_precedes(X22,X23,X24) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f76,plain,
! [X22,X23] :
( precedes(X22,X23)
| ! [X24] : ~ min_precedes(X22,X23,X24) ),
inference(miniscoping,[status(thm)],[f75]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ~ min_precedes(X0,X1,X2)
| precedes(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f81,plain,
! [X28,X29] :
( ( ~ legal(X29)
| ~ earlier(X28,X29)
| precedes(X28,X29) )
& ( ( legal(X29)
& earlier(X28,X29) )
| ~ precedes(X28,X29) ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f82,plain,
( ! [X28,X29] :
( ~ legal(X29)
| ~ earlier(X28,X29)
| precedes(X28,X29) )
& ! [X28,X29] :
( ( legal(X29)
& earlier(X28,X29) )
| ~ precedes(X28,X29) ) ),
inference(miniscoping,[status(thm)],[f81]) ).
fof(f84,plain,
! [X0,X1] :
( ~ precedes(X1,X0)
| legal(X0) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f88,plain,
! [X32,X33] :
( ( ! [X34] :
( ~ root(X32,X34)
| ~ subactivity_occurrence(X32,X33)
| ~ occurrence_of(X33,X34) )
| root_occ(X32,X33) )
& ( ? [X34] :
( root(X32,X34)
& subactivity_occurrence(X32,X33)
& occurrence_of(X33,X34) )
| ~ root_occ(X32,X33) ) ),
inference(NNF_transformation,[status(thm)],[f11]) ).
fof(f89,plain,
( ! [X32,X33] :
( ! [X34] :
( ~ root(X32,X34)
| ~ subactivity_occurrence(X32,X33)
| ~ occurrence_of(X33,X34) )
| root_occ(X32,X33) )
& ! [X32,X33] :
( ? [X34] :
( root(X32,X34)
& subactivity_occurrence(X32,X33)
& occurrence_of(X33,X34) )
| ~ root_occ(X32,X33) ) ),
inference(miniscoping,[status(thm)],[f88]) ).
fof(f90,plain,
( ! [X32,X33] :
( ! [X34] :
( ~ root(X32,X34)
| ~ subactivity_occurrence(X32,X33)
| ~ occurrence_of(X33,X34) )
| root_occ(X32,X33) )
& ! [X32,X33] :
( ( root(X32,sK1_skl(X33,X32))
& subactivity_occurrence(X32,X33)
& occurrence_of(X33,sK1_skl(X33,X32)) )
| ~ root_occ(X32,X33) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(X34,sK1_skl(X33,X32))],[f89]) ).
fof(f91,plain,
! [X0,X1] :
( ~ root_occ(X1,X0)
| occurrence_of(X0,sK1_skl(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f92,plain,
! [X0,X1] :
( subactivity_occurrence(X0,X1)
| ~ root_occ(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f93,plain,
! [X0,X1] :
( root(X0,sK1_skl(X1,X0))
| ~ root_occ(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f94,plain,
! [X0,X1,X2] :
( root_occ(X2,X0)
| ~ root(X2,X1)
| ~ subactivity_occurrence(X2,X0)
| ~ occurrence_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f102,plain,
! [X38,X39] :
( legal(X38)
| ~ root(X38,X39) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f103,plain,
! [X38] :
( legal(X38)
| ! [X39] : ~ root(X38,X39) ),
inference(miniscoping,[status(thm)],[f102]) ).
fof(f104,plain,
! [X0,X1] :
( legal(X0)
| ~ root(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f126,plain,
! [X51] :
( arboreal(X51)
| ~ legal(X51) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f127,plain,
! [X0] :
( arboreal(X0)
| ~ legal(X0) ),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f128,plain,
! [X52] :
( ? [X53] :
( occurrence_of(X52,X53)
& activity(X53) )
| ~ activity_occurrence(X52) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f129,plain,
! [X52] :
( ( occurrence_of(X52,sK6_skl(X52))
& activity(sK6_skl(X52)) )
| ~ activity_occurrence(X52) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(X53,sK6_skl(X52))],[f128]) ).
fof(f131,plain,
! [X0] :
( occurrence_of(X0,sK6_skl(X0))
| ~ activity_occurrence(X0) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f135,plain,
! [X56,X57,X58] :
( ! [X59] : ~ min_precedes(X59,X57,X58)
| ~ root_occ(X57,X56)
| ~ occurrence_of(X56,X58) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f136,plain,
! [X57,X58] :
( ! [X59] : ~ min_precedes(X59,X57,X58)
| ! [X56] :
( ~ root_occ(X57,X56)
| ~ occurrence_of(X56,X58) ) ),
inference(miniscoping,[status(thm)],[f135]) ).
fof(f137,plain,
! [X0,X1,X2,X3] :
( ~ occurrence_of(X3,X2)
| ~ root_occ(X1,X3)
| ~ min_precedes(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f138,plain,
! [X60,X61,X62] :
( ! [X63] : ~ min_precedes(X61,X63,X62)
| ~ leaf_occ(X61,X60)
| ~ occurrence_of(X60,X62) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f139,plain,
! [X61,X62] :
( ! [X63] : ~ min_precedes(X61,X63,X62)
| ! [X60] :
( ~ leaf_occ(X61,X60)
| ~ occurrence_of(X60,X62) ) ),
inference(miniscoping,[status(thm)],[f138]) ).
fof(f140,plain,
! [X0,X1,X2,X3] :
( ~ min_precedes(X2,X3,X1)
| ~ leaf_occ(X2,X0)
| ~ occurrence_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f141,plain,
! [X64,X65,X66] :
( X65 = X66
| ~ occurrence_of(X64,X66)
| ~ occurrence_of(X64,X65) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f142,plain,
! [X65,X66] :
( X65 = X66
| ! [X64] :
( ~ occurrence_of(X64,X66)
| ~ occurrence_of(X64,X65) ) ),
inference(miniscoping,[status(thm)],[f141]) ).
fof(f143,plain,
! [X0,X1,X2] :
( ~ occurrence_of(X0,X2)
| X2 = X1
| ~ occurrence_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f148,plain,
! [X70,X71,X72] :
( ? [X73] :
( subactivity_occurrence(X72,X73)
& subactivity_occurrence(X71,X73)
& occurrence_of(X73,X70) )
| ~ min_precedes(X71,X72,X70) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f149,plain,
! [X70,X71,X72] :
( ( subactivity_occurrence(X72,sK8_skl(X72,X71,X70))
& subactivity_occurrence(X71,sK8_skl(X72,X71,X70))
& occurrence_of(sK8_skl(X72,X71,X70),X70) )
| ~ min_precedes(X71,X72,X70) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(X73,sK8_skl(X72,X71,X70))],[f148]) ).
fof(f150,plain,
! [X0,X1,X2] :
( ~ min_precedes(X1,X0,X2)
| occurrence_of(sK8_skl(X0,X1,X2),X2) ),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f151,plain,
! [X0,X1,X2] :
( ~ min_precedes(X0,X1,X2)
| subactivity_occurrence(X0,sK8_skl(X1,X0,X2)) ),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f152,plain,
! [X0,X1,X2] :
( subactivity_occurrence(X1,sK8_skl(X1,X0,X2))
| ~ min_precedes(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f171,plain,
! [X89,X90] :
( ( activity_occurrence(X90)
& activity(X89) )
| ~ occurrence_of(X90,X89) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f173,plain,
! [X0,X1] :
( activity_occurrence(X0)
| ~ occurrence_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f174,plain,
! [X91,X92] :
( ? [X93] :
( subactivity_occurrence(X93,X92)
& root(X93,X91) )
| atomic(X91)
| ~ occurrence_of(X92,X91) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f175,plain,
! [X91,X92] :
( ( subactivity_occurrence(sK13_skl(X92,X91),X92)
& root(sK13_skl(X92,X91),X91) )
| atomic(X91)
| ~ occurrence_of(X92,X91) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl]),skolemize(X93,sK13_skl(X92,X91))],[f174]) ).
fof(f176,plain,
! [X0,X1] :
( atomic(X1)
| root(sK13_skl(X0,X1),X1)
| ~ occurrence_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f177,plain,
! [X0,X1] :
( subactivity_occurrence(sK13_skl(X0,X1),X0)
| atomic(X1)
| ~ occurrence_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f180,plain,
! [X95] :
( ? [X96,X97] :
( next_subocc(X96,X97,tptp0)
& leaf_occ(X97,X95)
& occurrence_of(X97,tptp3)
& root_occ(X96,X95)
& occurrence_of(X96,tptp4) )
| ~ occurrence_of(X95,tptp0) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f181,plain,
! [X95] :
( ( next_subocc(sK14_skl(X95),sK15_skl(X95),tptp0)
& leaf_occ(sK15_skl(X95),X95)
& occurrence_of(sK15_skl(X95),tptp3)
& root_occ(sK14_skl(X95),X95)
& occurrence_of(sK14_skl(X95),tptp4) )
| ~ occurrence_of(X95,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl]),skolemize(X96,sK14_skl(X95)),skolemize(X97,sK15_skl(X95))],[f180]) ).
fof(f183,plain,
! [X0] :
( root_occ(sK14_skl(X0),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[status(thm)],[f181]) ).
fof(f184,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| occurrence_of(sK15_skl(X0),tptp3) ),
inference(cnf_transformation,[status(thm)],[f181]) ).
fof(f185,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| leaf_occ(sK15_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f181]) ).
fof(f186,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| next_subocc(sK14_skl(X0),sK15_skl(X0),tptp0) ),
inference(cnf_transformation,[status(thm)],[f181]) ).
fof(f188,plain,
~ atomic(tptp0),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f196,plain,
tptp3 != tptp1,
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f201,plain,
! [X100,X101] :
( root_occ(X100,X101)
| leaf_occ(X100,X101)
| ~ arboreal(X100)
| ~ subactivity_occurrence(X100,X101)
| ~ occurrence_of(X101,tptp0) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f202,plain,
! [X0,X1] :
( leaf_occ(X0,X1)
| ~ subactivity_occurrence(X0,X1)
| ~ arboreal(X0)
| ~ occurrence_of(X1,tptp0)
| root_occ(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f203,plain,
! [X102,X103] :
( ? [X104] :
( next_subocc(X102,X104,tptp0)
& occurrence_of(X104,tptp1) )
| leaf_occ(X102,X103)
| ~ arboreal(X102)
| ~ subactivity_occurrence(X102,X103)
| ~ occurrence_of(X103,tptp0) ),
inference(pre_NNF_transformation,[status(thm)],[f48]) ).
fof(f204,plain,
! [X102] :
( ? [X104] :
( next_subocc(X102,X104,tptp0)
& occurrence_of(X104,tptp1) )
| ! [X103] :
( leaf_occ(X102,X103)
| ~ arboreal(X102)
| ~ subactivity_occurrence(X102,X103)
| ~ occurrence_of(X103,tptp0) ) ),
inference(miniscoping,[status(thm)],[f203]) ).
fof(f205,plain,
! [X102] :
( ( next_subocc(X102,sK16_skl(X102),tptp0)
& occurrence_of(sK16_skl(X102),tptp1) )
| ! [X103] :
( leaf_occ(X102,X103)
| ~ arboreal(X102)
| ~ subactivity_occurrence(X102,X103)
| ~ occurrence_of(X103,tptp0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl]),skolemize(X104,sK16_skl(X102))],[f204]) ).
fof(f206,plain,
! [X0,X1] :
( leaf_occ(X0,X1)
| occurrence_of(sK16_skl(X0),tptp1)
| ~ subactivity_occurrence(X0,X1)
| ~ occurrence_of(X1,tptp0)
| ~ arboreal(X0) ),
inference(cnf_transformation,[status(thm)],[f205]) ).
fof(f207,plain,
! [X0,X1] :
( leaf_occ(X0,X1)
| next_subocc(X0,sK16_skl(X0),tptp0)
| ~ arboreal(X0)
| ~ occurrence_of(X1,tptp0)
| ~ subactivity_occurrence(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f205]) ).
fof(f208,plain,
occurrence_of(sK17_skl,tptp0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl]),skolemize(X105,sK17_skl)],[f50]) ).
fof(f209,plain,
occurrence_of(sK17_skl,tptp0),
inference(cnf_transformation,[status(thm)],[f208]) ).
fof(f210,plain,
! [X0] :
( tptp0 = X0
| ~ occurrence_of(sK17_skl,X0) ),
inference(resolution,[status(thm)],[f143,f209]) ).
fof(f212,plain,
! [X0,X1,X2] :
( legal(X1)
| ~ min_precedes(X0,X1,X2) ),
inference(resolution,[status(thm)],[f84,f77]) ).
fof(f215,plain,
! [X0,X1,X2] :
( ~ occurrence_of(X1,tptp0)
| ~ leaf_occ(X2,X1)
| X0 = X2
| ~ leaf_occ(X0,X1) ),
inference(resolution,[status(thm)],[f62,f188]) ).
fof(f222,plain,
! [X0,X1] :
( sK6_skl(X0) = X1
| ~ occurrence_of(X0,X1)
| ~ activity_occurrence(X0) ),
inference(resolution,[status(thm)],[f131,f143]) ).
fof(f223,plain,
! [X0,X1] :
( ~ occurrence_of(X1,X0)
| X0 = sK6_skl(X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f222,f173]) ).
fof(f234,plain,
! [X0] :
( root(sK13_skl(X0,tptp0),tptp0)
| ~ occurrence_of(X0,tptp0) ),
inference(resolution,[status(thm)],[f176,f188]) ).
fof(f235,plain,
root_occ(sK14_skl(sK17_skl),sK17_skl),
inference(resolution,[status(thm)],[f183,f209]) ).
fof(f236,plain,
occurrence_of(sK17_skl,sK1_skl(sK17_skl,sK14_skl(sK17_skl))),
inference(resolution,[status(thm)],[f235,f91]) ).
fof(f237,plain,
root(sK14_skl(sK17_skl),sK1_skl(sK17_skl,sK14_skl(sK17_skl))),
inference(resolution,[status(thm)],[f235,f93]) ).
fof(f238,plain,
subactivity_occurrence(sK14_skl(sK17_skl),sK17_skl),
inference(resolution,[status(thm)],[f235,f92]) ).
fof(f239,plain,
tptp0 = sK1_skl(sK17_skl,sK14_skl(sK17_skl)),
inference(resolution,[status(thm)],[f236,f210]) ).
fof(f244,plain,
root(sK14_skl(sK17_skl),tptp0),
inference(forward_demodulation,[status(thm)],[f239,f237]) ).
fof(f246,plain,
legal(sK14_skl(sK17_skl)),
inference(resolution,[status(thm)],[f244,f104]) ).
fof(f248,plain,
arboreal(sK14_skl(sK17_skl)),
inference(resolution,[status(thm)],[f246,f127]) ).
fof(f255,plain,
root(sK13_skl(sK17_skl,tptp0),tptp0),
inference(resolution,[status(thm)],[f234,f209]) ).
fof(f295,plain,
! [X0,X1] :
( ~ occurrence_of(sK17_skl,X1)
| ~ root_occ(X0,sK17_skl)
| sK14_skl(sK17_skl) = X0 ),
inference(resolution,[status(thm)],[f59,f235]) ).
fof(f325,plain,
next_subocc(sK14_skl(sK17_skl),sK15_skl(sK17_skl),tptp0),
inference(resolution,[status(thm)],[f186,f209]) ).
fof(f327,plain,
min_precedes(sK14_skl(sK17_skl),sK15_skl(sK17_skl),tptp0),
inference(resolution,[status(thm)],[f325,f67]) ).
fof(f335,plain,
occurrence_of(sK8_skl(sK15_skl(sK17_skl),sK14_skl(sK17_skl),tptp0),tptp0),
inference(resolution,[status(thm)],[f327,f150]) ).
fof(f340,plain,
! [X0] :
( ~ leaf_occ(sK14_skl(sK17_skl),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(resolution,[status(thm)],[f327,f140]) ).
fof(f440,plain,
! [X0] :
( root_occ(sK13_skl(sK17_skl,tptp0),X0)
| ~ subactivity_occurrence(sK13_skl(sK17_skl,tptp0),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(resolution,[status(thm)],[f94,f255]) ).
fof(f586,plain,
! [X0,X1] :
( min_precedes(X1,sK16_skl(X1),tptp0)
| ~ arboreal(X1)
| leaf_occ(X1,X0)
| ~ subactivity_occurrence(X1,X0)
| ~ occurrence_of(X0,tptp0) ),
inference(resolution,[status(thm)],[f207,f67]) ).
fof(f668,plain,
( atomic(tptp0)
| ~ occurrence_of(sK17_skl,tptp0)
| root_occ(sK13_skl(sK17_skl,tptp0),sK17_skl)
| ~ occurrence_of(sK17_skl,tptp0) ),
inference(resolution,[status(thm)],[f440,f177]) ).
fof(f669,plain,
! [X0,X1] :
( ~ occurrence_of(sK8_skl(X0,sK13_skl(sK17_skl,tptp0),X1),tptp0)
| root_occ(sK13_skl(sK17_skl,tptp0),sK8_skl(X0,sK13_skl(sK17_skl,tptp0),X1))
| ~ min_precedes(sK13_skl(sK17_skl,tptp0),X0,X1) ),
inference(resolution,[status(thm)],[f440,f151]) ).
fof(f672,plain,
( atomic(tptp0)
| root_occ(sK13_skl(sK17_skl,tptp0),sK17_skl)
| ~ occurrence_of(sK17_skl,tptp0) ),
inference(duplicate_literals_removal,[status(thm)],[f668]) ).
fof(f673,plain,
( atomic(tptp0)
| root_occ(sK13_skl(sK17_skl,tptp0),sK17_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f672,f209]) ).
fof(f679,plain,
root_occ(sK13_skl(sK17_skl,tptp0),sK17_skl),
inference(forward_subsumption_resolution,[status(thm)],[f673,f188]) ).
fof(f680,plain,
! [X0] :
( ~ occurrence_of(sK17_skl,X0)
| sK14_skl(sK17_skl) = sK13_skl(sK17_skl,tptp0) ),
inference(resolution,[status(thm)],[f679,f295]) ).
fof(f700,plain,
sK14_skl(sK17_skl) = sK13_skl(sK17_skl,tptp0),
inference(resolution,[status(thm)],[f680,f209]) ).
fof(f751,plain,
! [X0,X1] :
( ~ arboreal(X0)
| tptp1 = sK6_skl(sK16_skl(X0))
| ~ subactivity_occurrence(X0,X1)
| ~ occurrence_of(X1,tptp0)
| leaf_occ(X0,X1) ),
inference(resolution,[status(thm)],[f206,f223]) ).
fof(f891,plain,
! [X0] :
( sK6_skl(sK16_skl(X0)) = tptp1
| leaf_occ(X0,sK8_skl(sK15_skl(sK17_skl),sK14_skl(sK17_skl),tptp0))
| ~ arboreal(X0)
| ~ subactivity_occurrence(X0,sK8_skl(sK15_skl(sK17_skl),sK14_skl(sK17_skl),tptp0)) ),
inference(resolution,[status(thm)],[f751,f335]) ).
fof(f1099,plain,
! [X0] :
( ~ arboreal(X0)
| ~ subactivity_occurrence(X0,sK17_skl)
| min_precedes(X0,sK16_skl(X0),tptp0)
| leaf_occ(X0,sK17_skl) ),
inference(resolution,[status(thm)],[f586,f209]) ).
fof(f1101,plain,
( ~ arboreal(sK14_skl(sK17_skl))
| min_precedes(sK14_skl(sK17_skl),sK16_skl(sK14_skl(sK17_skl)),tptp0)
| leaf_occ(sK14_skl(sK17_skl),sK17_skl) ),
inference(resolution,[status(thm)],[f1099,f238]) ).
fof(f1104,plain,
( leaf_occ(sK14_skl(sK17_skl),sK17_skl)
| min_precedes(sK14_skl(sK17_skl),sK16_skl(sK14_skl(sK17_skl)),tptp0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1101,f248]) ).
fof(f1116,plain,
( ~ occurrence_of(sK17_skl,tptp0)
| min_precedes(sK14_skl(sK17_skl),sK16_skl(sK14_skl(sK17_skl)),tptp0) ),
inference(resolution,[status(thm)],[f1104,f340]) ).
fof(f1126,plain,
min_precedes(sK14_skl(sK17_skl),sK16_skl(sK14_skl(sK17_skl)),tptp0),
inference(forward_subsumption_resolution,[status(thm)],[f1116,f209]) ).
fof(f1140,plain,
! [X0] :
( ~ root_occ(sK16_skl(sK14_skl(sK17_skl)),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(resolution,[status(thm)],[f1126,f137]) ).
fof(f1143,plain,
occurrence_of(sK8_skl(sK16_skl(sK14_skl(sK17_skl)),sK14_skl(sK17_skl),tptp0),tptp0),
inference(resolution,[status(thm)],[f1126,f150]) ).
fof(f1147,plain,
legal(sK16_skl(sK14_skl(sK17_skl))),
inference(resolution,[status(thm)],[f1126,f212]) ).
fof(f1153,plain,
arboreal(sK16_skl(sK14_skl(sK17_skl))),
inference(resolution,[status(thm)],[f1147,f127]) ).
fof(f1156,plain,
! [X0] :
( leaf_occ(sK16_skl(sK14_skl(sK17_skl)),X0)
| ~ subactivity_occurrence(sK16_skl(sK14_skl(sK17_skl)),X0)
| ~ occurrence_of(X0,tptp0)
| root_occ(sK16_skl(sK14_skl(sK17_skl)),X0) ),
inference(resolution,[status(thm)],[f1153,f202]) ).
fof(f1171,plain,
occurrence_of(sK15_skl(sK8_skl(sK16_skl(sK14_skl(sK17_skl)),sK14_skl(sK17_skl),tptp0)),tptp3),
inference(resolution,[status(thm)],[f1143,f184]) ).
fof(f1173,plain,
! [X0,X1] :
( ~ leaf_occ(X1,sK8_skl(sK16_skl(sK14_skl(sK17_skl)),sK14_skl(sK17_skl),tptp0))
| ~ leaf_occ(X0,sK8_skl(sK16_skl(sK14_skl(sK17_skl)),sK14_skl(sK17_skl),tptp0))
| X0 = X1 ),
inference(resolution,[status(thm)],[f1143,f215]) ).
fof(f1211,plain,
tptp3 = sK6_skl(sK15_skl(sK8_skl(sK16_skl(sK14_skl(sK17_skl)),sK14_skl(sK17_skl),tptp0))),
inference(resolution,[status(thm)],[f1171,f223]) ).
fof(f2656,plain,
! [X0,X1] :
( ~ occurrence_of(sK8_skl(X0,sK13_skl(sK17_skl,tptp0),X1),tptp0)
| root_occ(sK13_skl(sK17_skl,tptp0),sK8_skl(X0,sK13_skl(sK17_skl,tptp0),X1))
| ~ min_precedes(sK14_skl(sK17_skl),X0,X1) ),
inference(forward_demodulation,[status(thm)],[f700,f669]) ).
fof(f2657,plain,
! [X0,X1] :
( ~ occurrence_of(sK8_skl(X0,sK13_skl(sK17_skl,tptp0),X1),tptp0)
| root_occ(sK14_skl(sK17_skl),sK8_skl(X0,sK13_skl(sK17_skl,tptp0),X1))
| ~ min_precedes(sK14_skl(sK17_skl),X0,X1) ),
inference(forward_demodulation,[status(thm)],[f700,f2656]) ).
fof(f2658,plain,
! [X0,X1] :
( ~ occurrence_of(sK8_skl(X0,sK13_skl(sK17_skl,tptp0),X1),tptp0)
| root_occ(sK14_skl(sK17_skl),sK8_skl(X0,sK14_skl(sK17_skl),X1))
| ~ min_precedes(sK14_skl(sK17_skl),X0,X1) ),
inference(forward_demodulation,[status(thm)],[f700,f2657]) ).
fof(f2659,plain,
! [X0,X1] :
( ~ min_precedes(sK14_skl(sK17_skl),X0,X1)
| ~ occurrence_of(sK8_skl(X0,sK14_skl(sK17_skl),X1),tptp0)
| root_occ(sK14_skl(sK17_skl),sK8_skl(X0,sK14_skl(sK17_skl),X1)) ),
inference(forward_demodulation,[status(thm)],[f700,f2658]) ).
fof(f2662,plain,
( ~ min_precedes(sK14_skl(sK17_skl),sK15_skl(sK17_skl),tptp0)
| root_occ(sK14_skl(sK17_skl),sK8_skl(sK15_skl(sK17_skl),sK14_skl(sK17_skl),tptp0)) ),
inference(resolution,[status(thm)],[f2659,f335]) ).
fof(f2663,plain,
root_occ(sK14_skl(sK17_skl),sK8_skl(sK15_skl(sK17_skl),sK14_skl(sK17_skl),tptp0)),
inference(forward_subsumption_resolution,[status(thm)],[f2662,f327]) ).
fof(f2669,plain,
subactivity_occurrence(sK14_skl(sK17_skl),sK8_skl(sK15_skl(sK17_skl),sK14_skl(sK17_skl),tptp0)),
inference(resolution,[status(thm)],[f2663,f92]) ).
fof(f2778,plain,
( sK6_skl(sK16_skl(sK14_skl(sK17_skl))) = tptp1
| leaf_occ(sK14_skl(sK17_skl),sK8_skl(sK15_skl(sK17_skl),sK14_skl(sK17_skl),tptp0))
| ~ arboreal(sK14_skl(sK17_skl)) ),
inference(resolution,[status(thm)],[f891,f2669]) ).
fof(f2785,plain,
( leaf_occ(sK14_skl(sK17_skl),sK8_skl(sK15_skl(sK17_skl),sK14_skl(sK17_skl),tptp0))
| sK6_skl(sK16_skl(sK14_skl(sK17_skl))) = tptp1 ),
inference(forward_subsumption_resolution,[status(thm)],[f2778,f248]) ).
fof(f2787,plain,
( ~ occurrence_of(sK8_skl(sK15_skl(sK17_skl),sK14_skl(sK17_skl),tptp0),tptp0)
| sK6_skl(sK16_skl(sK14_skl(sK17_skl))) = tptp1 ),
inference(resolution,[status(thm)],[f2785,f340]) ).
fof(f2803,plain,
sK6_skl(sK16_skl(sK14_skl(sK17_skl))) = tptp1,
inference(forward_subsumption_resolution,[status(thm)],[f2787,f335]) ).
fof(f3964,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| leaf_occ(sK16_skl(sK14_skl(sK17_skl)),X0)
| ~ subactivity_occurrence(sK16_skl(sK14_skl(sK17_skl)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1156,f1140]) ).
fof(f3966,plain,
! [X0,X1] :
( ~ occurrence_of(sK8_skl(sK16_skl(sK14_skl(sK17_skl)),X0,X1),tptp0)
| leaf_occ(sK16_skl(sK14_skl(sK17_skl)),sK8_skl(sK16_skl(sK14_skl(sK17_skl)),X0,X1))
| ~ min_precedes(X0,sK16_skl(sK14_skl(sK17_skl)),X1) ),
inference(resolution,[status(thm)],[f3964,f152]) ).
fof(f5333,plain,
! [X0] :
( ~ occurrence_of(sK8_skl(sK16_skl(sK14_skl(sK17_skl)),sK14_skl(sK17_skl),tptp0),tptp0)
| ~ leaf_occ(X0,sK8_skl(sK16_skl(sK14_skl(sK17_skl)),sK14_skl(sK17_skl),tptp0))
| X0 = sK15_skl(sK8_skl(sK16_skl(sK14_skl(sK17_skl)),sK14_skl(sK17_skl),tptp0)) ),
inference(resolution,[status(thm)],[f1173,f185]) ).
fof(f5334,plain,
! [X0] :
( ~ leaf_occ(X0,sK8_skl(sK16_skl(sK14_skl(sK17_skl)),sK14_skl(sK17_skl),tptp0))
| sK15_skl(sK8_skl(sK16_skl(sK14_skl(sK17_skl)),sK14_skl(sK17_skl),tptp0)) = X0 ),
inference(forward_subsumption_resolution,[status(thm)],[f5333,f1143]) ).
fof(f11681,plain,
( leaf_occ(sK16_skl(sK14_skl(sK17_skl)),sK8_skl(sK16_skl(sK14_skl(sK17_skl)),sK14_skl(sK17_skl),tptp0))
| ~ min_precedes(sK14_skl(sK17_skl),sK16_skl(sK14_skl(sK17_skl)),tptp0) ),
inference(resolution,[status(thm)],[f3966,f1143]) ).
fof(f11682,plain,
leaf_occ(sK16_skl(sK14_skl(sK17_skl)),sK8_skl(sK16_skl(sK14_skl(sK17_skl)),sK14_skl(sK17_skl),tptp0)),
inference(forward_subsumption_resolution,[status(thm)],[f11681,f1126]) ).
fof(f11694,plain,
sK15_skl(sK8_skl(sK16_skl(sK14_skl(sK17_skl)),sK14_skl(sK17_skl),tptp0)) = sK16_skl(sK14_skl(sK17_skl)),
inference(resolution,[status(thm)],[f11682,f5334]) ).
fof(f12100,plain,
tptp3 = sK6_skl(sK16_skl(sK14_skl(sK17_skl))),
inference(backward_demodulation,[status(thm)],[f11694,f1211]) ).
fof(f12117,plain,
tptp3 = tptp1,
inference(forward_demodulation,[status(thm)],[f2803,f12100]) ).
fof(f12118,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f12117,f196]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PRO004+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 03:40:50 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 64.92/8.62 % Refutation found
% 64.92/8.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 64.92/8.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 38.05/8.71 % Elapsed time: 8.330137 seconds
% 38.05/8.71 % CPU time: 65.664600 seconds
% 38.05/8.71 % Total memory used: 362.387 MB
% 38.05/8.71 % Net memory used: 340.114 MB
%------------------------------------------------------------------------------