%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : PRO004+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 23.06s 3.33s
% Output : CNFRefutation 23.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 17
% Syntax : Number of formulae : 132 ( 43 unt; 0 def)
% Number of atoms : 363 ( 31 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 382 ( 151 ~; 152 |; 62 &)
% ( 5 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 217 ( 197 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X8,X9,X10,X11] :
( ( ~ min_precedes(X10,X11,X8)
& arboreal(X10)
& leaf_occ(X11,X9)
& subactivity_occurrence(X10,X9)
& occurrence_of(X9,X8) )
=> X11 = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X12,X13] :
( occurrence_of(X13,X12)
=> ( activity_occurrence(X13)
& activity(X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X21,X22,X23] :
( min_precedes(X22,X23,X21)
=> ? [X24] :
( subactivity_occurrence(X23,X24)
& subactivity_occurrence(X22,X24)
& occurrence_of(X24,X21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X28,X29,X30] :
( ( occurrence_of(X28,X30)
& occurrence_of(X28,X29) )
=> X29 = X30 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X31,X32,X33] :
( ( leaf_occ(X32,X31)
& occurrence_of(X31,X33) )
=> ~ ? [X34] : min_precedes(X32,X34,X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X41] :
( activity_occurrence(X41)
=> ? [X42] :
( occurrence_of(X41,X42)
& activity(X42) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X43] :
( legal(X43)
=> arboreal(X43) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X51,X52] :
( occurrence_of(X51,X52)
=> ( arboreal(X51)
<=> atomic(X52) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X53,X54] :
( root(X53,X54)
=> legal(X53) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X58,X59] :
( root_occ(X58,X59)
<=> ? [X60] :
( root(X58,X60)
& subactivity_occurrence(X58,X59)
& occurrence_of(X59,X60) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [X78,X79,X80] :
( next_subocc(X78,X79,X80)
<=> ( ~ ? [X81] :
( min_precedes(X81,X79,X80)
& min_precedes(X78,X81,X80) )
& min_precedes(X78,X79,X80) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [X90,X91,X92,X93] :
( ( root_occ(X91,X92)
& root_occ(X90,X92)
& occurrence_of(X92,X93) )
=> X90 = X91 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [X101] :
( occurrence_of(X101,tptp0)
=> ? [X102,X103] :
( next_subocc(X102,X103,tptp0)
& leaf_occ(X103,X101)
& occurrence_of(X103,tptp3)
& root_occ(X102,X101)
& occurrence_of(X102,tptp4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,axiom,
atomic(tptp1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,axiom,
tptp1 != tptp3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [X108,X109] :
( ( ~ leaf_occ(X108,X109)
& arboreal(X108)
& subactivity_occurrence(X108,X109)
& occurrence_of(X109,tptp0) )
=> ? [X110] :
( next_subocc(X108,X110,tptp0)
& occurrence_of(X110,tptp1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,conjecture,
~ ? [X111] : occurrence_of(X111,tptp0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
~ ~ ? [X111] : occurrence_of(X111,tptp0),
inference(negated_conjecture,[status(cth)],[f49]) ).
fof(f58,plain,
! [X8,X9,X10,X11] :
( X11 = X10
| min_precedes(X10,X11,X8)
| ~ arboreal(X10)
| ~ leaf_occ(X11,X9)
| ~ subactivity_occurrence(X10,X9)
| ~ occurrence_of(X9,X8) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f59,plain,
! [X10,X11] :
( X11 = X10
| ! [X8] :
( min_precedes(X10,X11,X8)
| ~ arboreal(X10)
| ! [X9] :
( ~ leaf_occ(X11,X9)
| ~ subactivity_occurrence(X10,X9)
| ~ occurrence_of(X9,X8) ) ) ),
inference(miniscoping,[status(thm)],[f58]) ).
fof(f60,plain,
! [X0,X1,X2,X3] :
( X3 = X2
| min_precedes(X2,X3,X1)
| ~ arboreal(X2)
| ~ leaf_occ(X3,X0)
| ~ subactivity_occurrence(X2,X0)
| ~ occurrence_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
! [X12,X13] :
( ( activity_occurrence(X13)
& activity(X12) )
| ~ occurrence_of(X13,X12) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f63,plain,
! [X0,X1] :
( activity_occurrence(X0)
| ~ occurrence_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f71,plain,
! [X21,X22,X23] :
( ? [X24] :
( subactivity_occurrence(X23,X24)
& subactivity_occurrence(X22,X24)
& occurrence_of(X24,X21) )
| ~ min_precedes(X22,X23,X21) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f72,plain,
! [X21,X22,X23] :
( ( subactivity_occurrence(X23,sK2_skl(X23,X22,X21))
& subactivity_occurrence(X22,sK2_skl(X23,X22,X21))
& occurrence_of(sK2_skl(X23,X22,X21),X21) )
| ~ min_precedes(X22,X23,X21) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(X24,sK2_skl(X23,X22,X21))],[f71]) ).
fof(f73,plain,
! [X0,X1,X2] :
( occurrence_of(sK2_skl(X1,X0,X2),X2)
| ~ min_precedes(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f74,plain,
! [X0,X1,X2] :
( subactivity_occurrence(X0,sK2_skl(X1,X0,X2))
| ~ min_precedes(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f75,plain,
! [X0,X1,X2] :
( subactivity_occurrence(X1,sK2_skl(X1,X0,X2))
| ~ min_precedes(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f80,plain,
! [X28,X29,X30] :
( X29 = X30
| ~ occurrence_of(X28,X30)
| ~ occurrence_of(X28,X29) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f81,plain,
! [X29,X30] :
( X29 = X30
| ! [X28] :
( ~ occurrence_of(X28,X30)
| ~ occurrence_of(X28,X29) ) ),
inference(miniscoping,[status(thm)],[f80]) ).
fof(f82,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ occurrence_of(X0,X2)
| ~ occurrence_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f83,plain,
! [X31,X32,X33] :
( ! [X34] : ~ min_precedes(X32,X34,X33)
| ~ leaf_occ(X32,X31)
| ~ occurrence_of(X31,X33) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f84,plain,
! [X32,X33] :
( ! [X34] : ~ min_precedes(X32,X34,X33)
| ! [X31] :
( ~ leaf_occ(X32,X31)
| ~ occurrence_of(X31,X33) ) ),
inference(miniscoping,[status(thm)],[f83]) ).
fof(f85,plain,
! [X0,X1,X2,X3] :
( ~ min_precedes(X2,X3,X1)
| ~ leaf_occ(X2,X0)
| ~ occurrence_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f92,plain,
! [X41] :
( ? [X42] :
( occurrence_of(X41,X42)
& activity(X42) )
| ~ activity_occurrence(X41) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f93,plain,
! [X41] :
( ( occurrence_of(X41,sK4_skl(X41))
& activity(sK4_skl(X41)) )
| ~ activity_occurrence(X41) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(X42,sK4_skl(X41))],[f92]) ).
fof(f95,plain,
! [X0] :
( occurrence_of(X0,sK4_skl(X0))
| ~ activity_occurrence(X0) ),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f96,plain,
! [X43] :
( arboreal(X43)
| ~ legal(X43) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f97,plain,
! [X0] :
( arboreal(X0)
| ~ legal(X0) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f113,plain,
! [X51,X52] :
( ( arboreal(X51)
<=> atomic(X52) )
| ~ occurrence_of(X51,X52) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f114,plain,
! [X51,X52] :
( ( ( ~ atomic(X52)
| arboreal(X51) )
& ( atomic(X52)
| ~ arboreal(X51) ) )
| ~ occurrence_of(X51,X52) ),
inference(NNF_transformation,[status(thm)],[f113]) ).
fof(f116,plain,
! [X0,X1] :
( ~ atomic(X1)
| arboreal(X0)
| ~ occurrence_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f117,plain,
! [X53,X54] :
( legal(X53)
| ~ root(X53,X54) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f118,plain,
! [X53] :
( legal(X53)
| ! [X54] : ~ root(X53,X54) ),
inference(miniscoping,[status(thm)],[f117]) ).
fof(f119,plain,
! [X0,X1] :
( legal(X0)
| ~ root(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f127,plain,
! [X58,X59] :
( ( ! [X60] :
( ~ root(X58,X60)
| ~ subactivity_occurrence(X58,X59)
| ~ occurrence_of(X59,X60) )
| root_occ(X58,X59) )
& ( ? [X60] :
( root(X58,X60)
& subactivity_occurrence(X58,X59)
& occurrence_of(X59,X60) )
| ~ root_occ(X58,X59) ) ),
inference(NNF_transformation,[status(thm)],[f20]) ).
fof(f128,plain,
( ! [X58,X59] :
( ! [X60] :
( ~ root(X58,X60)
| ~ subactivity_occurrence(X58,X59)
| ~ occurrence_of(X59,X60) )
| root_occ(X58,X59) )
& ! [X58,X59] :
( ? [X60] :
( root(X58,X60)
& subactivity_occurrence(X58,X59)
& occurrence_of(X59,X60) )
| ~ root_occ(X58,X59) ) ),
inference(miniscoping,[status(thm)],[f127]) ).
fof(f129,plain,
( ! [X58,X59] :
( ! [X60] :
( ~ root(X58,X60)
| ~ subactivity_occurrence(X58,X59)
| ~ occurrence_of(X59,X60) )
| root_occ(X58,X59) )
& ! [X58,X59] :
( ( root(X58,sK9_skl(X59,X58))
& subactivity_occurrence(X58,X59)
& occurrence_of(X59,sK9_skl(X59,X58)) )
| ~ root_occ(X58,X59) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(X60,sK9_skl(X59,X58))],[f128]) ).
fof(f130,plain,
! [X0,X1] :
( occurrence_of(X1,sK9_skl(X1,X0))
| ~ root_occ(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f131,plain,
! [X0,X1] :
( subactivity_occurrence(X0,X1)
| ~ root_occ(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f132,plain,
! [X0,X1] :
( root(X0,sK9_skl(X1,X0))
| ~ root_occ(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f133,plain,
! [X0,X1,X2] :
( ~ root(X0,X2)
| ~ subactivity_occurrence(X0,X1)
| ~ occurrence_of(X1,X2)
| root_occ(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f156,plain,
! [X78,X79,X80] :
( next_subocc(X78,X79,X80)
<=> ( ! [X81] :
( ~ min_precedes(X81,X79,X80)
| ~ min_precedes(X78,X81,X80) )
& min_precedes(X78,X79,X80) ) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f157,plain,
! [X78,X79,X80] :
( ( ? [X81] :
( min_precedes(X81,X79,X80)
& min_precedes(X78,X81,X80) )
| ~ min_precedes(X78,X79,X80)
| next_subocc(X78,X79,X80) )
& ( ( ! [X81] :
( ~ min_precedes(X81,X79,X80)
| ~ min_precedes(X78,X81,X80) )
& min_precedes(X78,X79,X80) )
| ~ next_subocc(X78,X79,X80) ) ),
inference(NNF_transformation,[status(thm)],[f156]) ).
fof(f158,plain,
( ! [X78,X79,X80] :
( ? [X81] :
( min_precedes(X81,X79,X80)
& min_precedes(X78,X81,X80) )
| ~ min_precedes(X78,X79,X80)
| next_subocc(X78,X79,X80) )
& ! [X78,X79,X80] :
( ( ! [X81] :
( ~ min_precedes(X81,X79,X80)
| ~ min_precedes(X78,X81,X80) )
& min_precedes(X78,X79,X80) )
| ~ next_subocc(X78,X79,X80) ) ),
inference(miniscoping,[status(thm)],[f157]) ).
fof(f159,plain,
( ! [X78,X79,X80] :
( ( min_precedes(sK11_skl(X80,X79,X78),X79,X80)
& min_precedes(X78,sK11_skl(X80,X79,X78),X80) )
| ~ min_precedes(X78,X79,X80)
| next_subocc(X78,X79,X80) )
& ! [X78,X79,X80] :
( ( ! [X81] :
( ~ min_precedes(X81,X79,X80)
| ~ min_precedes(X78,X81,X80) )
& min_precedes(X78,X79,X80) )
| ~ next_subocc(X78,X79,X80) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl]),skolemize(X81,sK11_skl(X80,X79,X78))],[f158]) ).
fof(f160,plain,
! [X0,X1,X2] :
( min_precedes(X0,X1,X2)
| ~ next_subocc(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f161,plain,
! [X0,X1,X2,X3] :
( ~ min_precedes(X3,X1,X2)
| ~ min_precedes(X0,X3,X2)
| ~ next_subocc(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f170,plain,
! [X90,X91,X92,X93] :
( X90 = X91
| ~ root_occ(X91,X92)
| ~ root_occ(X90,X92)
| ~ occurrence_of(X92,X93) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f171,plain,
! [X90,X91] :
( X90 = X91
| ! [X92] :
( ~ root_occ(X91,X92)
| ~ root_occ(X90,X92)
| ! [X93] : ~ occurrence_of(X92,X93) ) ),
inference(miniscoping,[status(thm)],[f170]) ).
fof(f172,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ root_occ(X3,X0)
| ~ root_occ(X2,X0)
| ~ occurrence_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f179,plain,
! [X101] :
( ? [X102,X103] :
( next_subocc(X102,X103,tptp0)
& leaf_occ(X103,X101)
& occurrence_of(X103,tptp3)
& root_occ(X102,X101)
& occurrence_of(X102,tptp4) )
| ~ occurrence_of(X101,tptp0) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f180,plain,
! [X101] :
( ( next_subocc(sK12_skl(X101),sK13_skl(X101),tptp0)
& leaf_occ(sK13_skl(X101),X101)
& occurrence_of(sK13_skl(X101),tptp3)
& root_occ(sK12_skl(X101),X101)
& occurrence_of(sK12_skl(X101),tptp4) )
| ~ occurrence_of(X101,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl]),skolemize(X102,sK12_skl(X101)),skolemize(X103,sK13_skl(X101))],[f179]) ).
fof(f182,plain,
! [X0] :
( root_occ(sK12_skl(X0),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[status(thm)],[f180]) ).
fof(f183,plain,
! [X0] :
( occurrence_of(sK13_skl(X0),tptp3)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[status(thm)],[f180]) ).
fof(f184,plain,
! [X0] :
( leaf_occ(sK13_skl(X0),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[status(thm)],[f180]) ).
fof(f185,plain,
! [X0] :
( next_subocc(sK12_skl(X0),sK13_skl(X0),tptp0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[status(thm)],[f180]) ).
fof(f191,plain,
atomic(tptp1),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f195,plain,
tptp1 != tptp3,
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f202,plain,
! [X108,X109] :
( ? [X110] :
( next_subocc(X108,X110,tptp0)
& occurrence_of(X110,tptp1) )
| leaf_occ(X108,X109)
| ~ arboreal(X108)
| ~ subactivity_occurrence(X108,X109)
| ~ occurrence_of(X109,tptp0) ),
inference(pre_NNF_transformation,[status(thm)],[f48]) ).
fof(f203,plain,
! [X108] :
( ? [X110] :
( next_subocc(X108,X110,tptp0)
& occurrence_of(X110,tptp1) )
| ! [X109] :
( leaf_occ(X108,X109)
| ~ arboreal(X108)
| ~ subactivity_occurrence(X108,X109)
| ~ occurrence_of(X109,tptp0) ) ),
inference(miniscoping,[status(thm)],[f202]) ).
fof(f204,plain,
! [X108] :
( ( next_subocc(X108,sK14_skl(X108),tptp0)
& occurrence_of(sK14_skl(X108),tptp1) )
| ! [X109] :
( leaf_occ(X108,X109)
| ~ arboreal(X108)
| ~ subactivity_occurrence(X108,X109)
| ~ occurrence_of(X109,tptp0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl]),skolemize(X110,sK14_skl(X108))],[f203]) ).
fof(f205,plain,
! [X0,X1] :
( occurrence_of(sK14_skl(X1),tptp1)
| leaf_occ(X1,X0)
| ~ arboreal(X1)
| ~ subactivity_occurrence(X1,X0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f206,plain,
! [X0,X1] :
( next_subocc(X1,sK14_skl(X1),tptp0)
| leaf_occ(X1,X0)
| ~ arboreal(X1)
| ~ subactivity_occurrence(X1,X0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f207,plain,
occurrence_of(sK15_skl,tptp0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl]),skolemize(X111,sK15_skl)],[f50]) ).
fof(f208,plain,
occurrence_of(sK15_skl,tptp0),
inference(cnf_transformation,[status(thm)],[f207]) ).
fof(f209,plain,
! [X0] :
( tptp0 = X0
| ~ occurrence_of(sK15_skl,X0) ),
inference(resolution,[status(thm)],[f82,f208]) ).
fof(f302,plain,
root_occ(sK12_skl(sK15_skl),sK15_skl),
inference(resolution,[status(thm)],[f182,f208]) ).
fof(f303,plain,
root(sK12_skl(sK15_skl),sK9_skl(sK15_skl,sK12_skl(sK15_skl))),
inference(resolution,[status(thm)],[f302,f132]) ).
fof(f304,plain,
occurrence_of(sK15_skl,sK9_skl(sK15_skl,sK12_skl(sK15_skl))),
inference(resolution,[status(thm)],[f302,f130]) ).
fof(f305,plain,
subactivity_occurrence(sK12_skl(sK15_skl),sK15_skl),
inference(resolution,[status(thm)],[f302,f131]) ).
fof(f313,plain,
legal(sK12_skl(sK15_skl)),
inference(resolution,[status(thm)],[f303,f119]) ).
fof(f314,plain,
tptp0 = sK9_skl(sK15_skl,sK12_skl(sK15_skl)),
inference(resolution,[status(thm)],[f304,f209]) ).
fof(f328,plain,
arboreal(sK12_skl(sK15_skl)),
inference(resolution,[status(thm)],[f313,f97]) ).
fof(f330,plain,
root(sK12_skl(sK15_skl),tptp0),
inference(backward_demodulation,[status(thm)],[f314,f303]) ).
fof(f362,plain,
! [X0,X1] :
( ~ min_precedes(X0,X1,tptp0)
| ~ leaf_occ(X0,sK15_skl) ),
inference(resolution,[status(thm)],[f85,f208]) ).
fof(f521,plain,
next_subocc(sK12_skl(sK15_skl),sK13_skl(sK15_skl),tptp0),
inference(resolution,[status(thm)],[f185,f208]) ).
fof(f523,plain,
min_precedes(sK12_skl(sK15_skl),sK13_skl(sK15_skl),tptp0),
inference(resolution,[status(thm)],[f521,f160]) ).
fof(f528,plain,
~ leaf_occ(sK12_skl(sK15_skl),sK15_skl),
inference(resolution,[status(thm)],[f523,f362]) ).
fof(f801,plain,
! [X0] :
( occurrence_of(sK14_skl(X0),tptp1)
| leaf_occ(X0,sK15_skl)
| ~ arboreal(X0)
| ~ subactivity_occurrence(X0,sK15_skl) ),
inference(resolution,[status(thm)],[f205,f208]) ).
fof(f804,plain,
! [X0] :
( next_subocc(X0,sK14_skl(X0),tptp0)
| leaf_occ(X0,sK15_skl)
| ~ arboreal(X0)
| ~ subactivity_occurrence(X0,sK15_skl) ),
inference(resolution,[status(thm)],[f206,f208]) ).
fof(f806,plain,
( occurrence_of(sK14_skl(sK12_skl(sK15_skl)),tptp1)
| leaf_occ(sK12_skl(sK15_skl),sK15_skl)
| ~ arboreal(sK12_skl(sK15_skl)) ),
inference(resolution,[status(thm)],[f801,f305]) ).
fof(f807,plain,
( occurrence_of(sK14_skl(sK12_skl(sK15_skl)),tptp1)
| leaf_occ(sK12_skl(sK15_skl),sK15_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f806,f328]) ).
fof(f808,plain,
occurrence_of(sK14_skl(sK12_skl(sK15_skl)),tptp1),
inference(forward_subsumption_resolution,[status(thm)],[f807,f528]) ).
fof(f815,plain,
( ~ atomic(tptp1)
| arboreal(sK14_skl(sK12_skl(sK15_skl))) ),
inference(resolution,[status(thm)],[f808,f116]) ).
fof(f820,plain,
activity_occurrence(sK14_skl(sK12_skl(sK15_skl))),
inference(resolution,[status(thm)],[f808,f63]) ).
fof(f824,plain,
! [X0] :
( tptp1 = X0
| ~ occurrence_of(sK14_skl(sK12_skl(sK15_skl)),X0) ),
inference(resolution,[status(thm)],[f808,f82]) ).
fof(f825,plain,
arboreal(sK14_skl(sK12_skl(sK15_skl))),
inference(forward_subsumption_resolution,[status(thm)],[f815,f191]) ).
fof(f826,plain,
occurrence_of(sK14_skl(sK12_skl(sK15_skl)),sK4_skl(sK14_skl(sK12_skl(sK15_skl)))),
inference(resolution,[status(thm)],[f820,f95]) ).
fof(f830,plain,
( next_subocc(sK12_skl(sK15_skl),sK14_skl(sK12_skl(sK15_skl)),tptp0)
| leaf_occ(sK12_skl(sK15_skl),sK15_skl)
| ~ arboreal(sK12_skl(sK15_skl)) ),
inference(resolution,[status(thm)],[f804,f305]) ).
fof(f831,plain,
( next_subocc(sK12_skl(sK15_skl),sK14_skl(sK12_skl(sK15_skl)),tptp0)
| leaf_occ(sK12_skl(sK15_skl),sK15_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f830,f328]) ).
fof(f832,plain,
tptp1 = sK4_skl(sK14_skl(sK12_skl(sK15_skl))),
inference(resolution,[status(thm)],[f826,f824]) ).
fof(f994,plain,
next_subocc(sK12_skl(sK15_skl),sK14_skl(sK12_skl(sK15_skl)),tptp0),
inference(forward_subsumption_resolution,[status(thm)],[f831,f528]) ).
fof(f996,plain,
min_precedes(sK12_skl(sK15_skl),sK14_skl(sK12_skl(sK15_skl)),tptp0),
inference(resolution,[status(thm)],[f994,f160]) ).
fof(f1013,plain,
subactivity_occurrence(sK14_skl(sK12_skl(sK15_skl)),sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0)),
inference(resolution,[status(thm)],[f996,f75]) ).
fof(f1014,plain,
subactivity_occurrence(sK12_skl(sK15_skl),sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0)),
inference(resolution,[status(thm)],[f996,f74]) ).
fof(f1015,plain,
occurrence_of(sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0),tptp0),
inference(resolution,[status(thm)],[f996,f73]) ).
fof(f1035,plain,
next_subocc(sK12_skl(sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0)),sK13_skl(sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0)),tptp0),
inference(resolution,[status(thm)],[f1015,f185]) ).
fof(f1036,plain,
occurrence_of(sK13_skl(sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0)),tptp3),
inference(resolution,[status(thm)],[f1015,f183]) ).
fof(f1038,plain,
leaf_occ(sK13_skl(sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0)),sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0)),
inference(resolution,[status(thm)],[f1015,f184]) ).
fof(f1039,plain,
root_occ(sK12_skl(sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0)),sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0)),
inference(resolution,[status(thm)],[f1015,f182]) ).
fof(f1041,plain,
! [X0] :
( ~ root(X0,tptp0)
| ~ subactivity_occurrence(X0,sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0))
| root_occ(X0,sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0)) ),
inference(resolution,[status(thm)],[f1015,f133]) ).
fof(f1043,plain,
! [X0,X1] :
( X0 = X1
| ~ root_occ(X1,sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0))
| ~ root_occ(X0,sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0)) ),
inference(resolution,[status(thm)],[f1015,f172]) ).
fof(f1049,plain,
! [X0,X1] :
( X1 = X0
| min_precedes(X0,X1,tptp0)
| ~ arboreal(X0)
| ~ leaf_occ(X1,sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0))
| ~ subactivity_occurrence(X0,sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0)) ),
inference(resolution,[status(thm)],[f1015,f60]) ).
fof(f1112,plain,
activity_occurrence(sK13_skl(sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0))),
inference(resolution,[status(thm)],[f1036,f63]) ).
fof(f1116,plain,
! [X0] :
( tptp3 = X0
| ~ occurrence_of(sK13_skl(sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0)),X0) ),
inference(resolution,[status(thm)],[f1036,f82]) ).
fof(f1118,plain,
occurrence_of(sK13_skl(sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0)),sK4_skl(sK13_skl(sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0)))),
inference(resolution,[status(thm)],[f1112,f95]) ).
fof(f3637,plain,
! [X0] :
( sK12_skl(sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0)) = X0
| ~ root_occ(X0,sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0)) ),
inference(resolution,[status(thm)],[f1043,f1039]) ).
fof(f3639,plain,
tptp3 = sK4_skl(sK13_skl(sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0))),
inference(resolution,[status(thm)],[f1118,f1116]) ).
fof(f4157,plain,
( ~ root(sK12_skl(sK15_skl),tptp0)
| root_occ(sK12_skl(sK15_skl),sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0)) ),
inference(resolution,[status(thm)],[f1041,f1014]) ).
fof(f4160,plain,
root_occ(sK12_skl(sK15_skl),sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0)),
inference(forward_subsumption_resolution,[status(thm)],[f4157,f330]) ).
fof(f4161,plain,
sK12_skl(sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0)) = sK12_skl(sK15_skl),
inference(resolution,[status(thm)],[f4160,f3637]) ).
fof(f4177,plain,
next_subocc(sK12_skl(sK15_skl),sK13_skl(sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0)),tptp0),
inference(backward_demodulation,[status(thm)],[f4161,f1035]) ).
fof(f4224,plain,
! [X0] :
( ~ min_precedes(X0,sK13_skl(sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0)),tptp0)
| ~ min_precedes(sK12_skl(sK15_skl),X0,tptp0) ),
inference(resolution,[status(thm)],[f4177,f161]) ).
fof(f9568,plain,
! [X0] :
( X0 = sK14_skl(sK12_skl(sK15_skl))
| min_precedes(sK14_skl(sK12_skl(sK15_skl)),X0,tptp0)
| ~ arboreal(sK14_skl(sK12_skl(sK15_skl)))
| ~ leaf_occ(X0,sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0)) ),
inference(resolution,[status(thm)],[f1049,f1013]) ).
fof(f9571,plain,
! [X0] :
( X0 = sK14_skl(sK12_skl(sK15_skl))
| min_precedes(sK14_skl(sK12_skl(sK15_skl)),X0,tptp0)
| ~ leaf_occ(X0,sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f9568,f825]) ).
fof(f9580,plain,
( sK13_skl(sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0)) = sK14_skl(sK12_skl(sK15_skl))
| min_precedes(sK14_skl(sK12_skl(sK15_skl)),sK13_skl(sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0)),tptp0) ),
inference(resolution,[status(thm)],[f9571,f1038]) ).
fof(f10605,plain,
( ~ min_precedes(sK12_skl(sK15_skl),sK14_skl(sK12_skl(sK15_skl)),tptp0)
| sK13_skl(sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0)) = sK14_skl(sK12_skl(sK15_skl)) ),
inference(resolution,[status(thm)],[f9580,f4224]) ).
fof(f10622,plain,
sK13_skl(sK2_skl(sK14_skl(sK12_skl(sK15_skl)),sK12_skl(sK15_skl),tptp0)) = sK14_skl(sK12_skl(sK15_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f10605,f996]) ).
fof(f10777,plain,
tptp3 = sK4_skl(sK14_skl(sK12_skl(sK15_skl))),
inference(backward_demodulation,[status(thm)],[f10622,f3639]) ).
fof(f10840,plain,
tptp3 = tptp1,
inference(forward_demodulation,[status(thm)],[f832,f10777]) ).
fof(f10841,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f10840,f195]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PRO004+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n007.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 03:38:51 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 23.06/3.33 % Refutation found
% 23.06/3.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 23.06/3.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 23.06/3.38 % Elapsed time: 3.023536 seconds
% 23.06/3.38 % CPU time: 23.625826 seconds
% 23.06/3.38 % Total memory used: 278.559 MB
% 23.06/3.38 % Net memory used: 262.597 MB
%------------------------------------------------------------------------------