%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : PRO010+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 01:59:16 PM UTC 2026
% Result : Theorem 0.09s 5.56s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 62 ( 13 unt; 5 def)
% Number of atoms : 204 ( 13 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 215 ( 73 ~; 69 |; 56 &)
% ( 7 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 5 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 111 ( 86 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X4,X5,X6] :
( ( occurrence_of(X4,X6)
& occurrence_of(X4,X5) )
=> X5 = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X16,X17] :
( occurrence_of(X16,X17)
=> ( arboreal(X16)
<=> atomic(X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [X148,X149,X150] :
( min_precedes(X148,X149,X150)
=> arboreal(X148) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [X161] :
( occurrence_of(X161,tptp0)
=> ? [X162,X163,X164] :
( leaf_occ(X164,X161)
& next_subocc(X163,X164,tptp0)
& ( occurrence_of(X164,tptp2)
| occurrence_of(X164,tptp1) )
& next_subocc(X162,X163,tptp0)
& occurrence_of(X163,tptp4)
& root_occ(X162,X161)
& occurrence_of(X162,tptp3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,axiom,
~ atomic(tptp0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f62,axiom,
tptp1 != tptp2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f63,conjecture,
! [X165] :
( occurrence_of(X165,tptp0)
=> ? [X166,X167] :
( ( occurrence_of(X167,tptp2)
=> ~ ? [X169] :
( min_precedes(X166,X169,tptp0)
& occurrence_of(X169,tptp1) ) )
& ( occurrence_of(X167,tptp1)
=> ~ ? [X168] :
( min_precedes(X166,X168,tptp0)
& occurrence_of(X168,tptp2) ) )
& leaf_occ(X167,X165) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f64,negated_conjecture,
~ ! [X165] :
( occurrence_of(X165,tptp0)
=> ? [X166,X167] :
( ( occurrence_of(X167,tptp2)
=> ~ ? [X169] :
( min_precedes(X166,X169,tptp0)
& occurrence_of(X169,tptp1) ) )
& ( occurrence_of(X167,tptp1)
=> ~ ? [X168] :
( min_precedes(X166,X168,tptp0)
& occurrence_of(X168,tptp2) ) )
& leaf_occ(X167,X165) ) ),
inference(negated_conjecture,[status(cth)],[f63]) ).
fof(f72,plain,
! [X4,X5,X6] :
( X5 = X6
| ~ occurrence_of(X4,X6)
| ~ occurrence_of(X4,X5) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f73,plain,
! [X5,X6] :
( X5 = X6
| ! [X4] :
( ~ occurrence_of(X4,X6)
| ~ occurrence_of(X4,X5) ) ),
inference(miniscoping,[status(thm)],[f72]) ).
fof(f74,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ occurrence_of(X0,X2)
| ~ occurrence_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f85,plain,
! [X16,X17] :
( ( arboreal(X16)
<=> atomic(X17) )
| ~ occurrence_of(X16,X17) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f86,plain,
! [X16,X17] :
( ( ( ~ atomic(X17)
| arboreal(X16) )
& ( atomic(X17)
| ~ arboreal(X16) ) )
| ~ occurrence_of(X16,X17) ),
inference(NNF_transformation,[status(thm)],[f85]) ).
fof(f87,plain,
! [X0,X1] :
( atomic(X1)
| ~ arboreal(X0)
| ~ occurrence_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f240,plain,
! [X148,X149,X150] :
( arboreal(X148)
| ~ min_precedes(X148,X149,X150) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f241,plain,
! [X148] :
( arboreal(X148)
| ! [X149,X150] : ~ min_precedes(X148,X149,X150) ),
inference(miniscoping,[status(thm)],[f240]) ).
fof(f242,plain,
! [X0,X1,X2] :
( arboreal(X0)
| ~ min_precedes(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f241]) ).
fof(f249,plain,
! [X161] :
( ? [X162,X163,X164] :
( leaf_occ(X164,X161)
& next_subocc(X163,X164,tptp0)
& ( occurrence_of(X164,tptp2)
| occurrence_of(X164,tptp1) )
& next_subocc(X162,X163,tptp0)
& occurrence_of(X163,tptp4)
& root_occ(X162,X161)
& occurrence_of(X162,tptp3) )
| ~ occurrence_of(X161,tptp0) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f250,plain,
! [X161] :
( ? [X164] :
( leaf_occ(X164,X161)
& ? [X163] :
( next_subocc(X163,X164,tptp0)
& ( occurrence_of(X164,tptp2)
| occurrence_of(X164,tptp1) )
& ? [X162] :
( next_subocc(X162,X163,tptp0)
& occurrence_of(X163,tptp4)
& root_occ(X162,X161)
& occurrence_of(X162,tptp3) ) ) )
| ~ occurrence_of(X161,tptp0) ),
inference(miniscoping,[status(thm)],[f249]) ).
fof(f251,plain,
! [X161] :
( ( leaf_occ(sK16_skl(X161),X161)
& next_subocc(sK17_skl(X161),sK16_skl(X161),tptp0)
& ( occurrence_of(sK16_skl(X161),tptp2)
| occurrence_of(sK16_skl(X161),tptp1) )
& next_subocc(sK18_skl(X161),sK17_skl(X161),tptp0)
& occurrence_of(sK17_skl(X161),tptp4)
& root_occ(sK18_skl(X161),X161)
& occurrence_of(sK18_skl(X161),tptp3) )
| ~ occurrence_of(X161,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl,sK17_skl,sK18_skl]),skolemize(X164,sK16_skl(X161)),skolemize(X163,sK17_skl(X161)),skolemize(X162,sK18_skl(X161))],[f250]) ).
fof(f258,plain,
! [X0] :
( leaf_occ(sK16_skl(X0),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[status(thm)],[f251]) ).
fof(f260,plain,
~ atomic(tptp0),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f270,plain,
tptp1 != tptp2,
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f271,plain,
? [X165] :
( ! [X166,X167] :
( ( ? [X169] :
( min_precedes(X166,X169,tptp0)
& occurrence_of(X169,tptp1) )
& occurrence_of(X167,tptp2) )
| ( ? [X168] :
( min_precedes(X166,X168,tptp0)
& occurrence_of(X168,tptp2) )
& occurrence_of(X167,tptp1) )
| ~ leaf_occ(X167,X165) )
& occurrence_of(X165,tptp0) ),
inference(pre_NNF_transformation,[status(thm)],[f64]) ).
fof(f272,definition,
! [X166,X167] :
( sP0_prd(X167,X166)
<=> ( ? [X168] :
( min_precedes(X166,X168,tptp0)
& occurrence_of(X168,tptp2) )
& occurrence_of(X167,tptp1) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f273,plain,
? [X165] :
( ! [X166,X167] :
( ( ? [X169] :
( min_precedes(X166,X169,tptp0)
& occurrence_of(X169,tptp1) )
& occurrence_of(X167,tptp2) )
| sP0_prd(X167,X166)
| ~ leaf_occ(X167,X165) )
& occurrence_of(X165,tptp0) ),
inference(formula_renaming,[status(thm)],[f271,f272]) ).
fof(f274,plain,
( ! [X166,X167] :
( ( min_precedes(X166,sK20_skl(X167,X166),tptp0)
& occurrence_of(sK20_skl(X167,X166),tptp1)
& occurrence_of(X167,tptp2) )
| sP0_prd(X167,X166)
| ~ leaf_occ(X167,sK19_skl) )
& occurrence_of(sK19_skl,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl,sK20_skl]),skolemize(X165,sK19_skl),skolemize(X169,sK20_skl(X167,X166))],[f273]) ).
fof(f275,plain,
occurrence_of(sK19_skl,tptp0),
inference(cnf_transformation,[status(thm)],[f274]) ).
fof(f276,plain,
! [X0,X1] :
( occurrence_of(X0,tptp2)
| sP0_prd(X0,X1)
| ~ leaf_occ(X0,sK19_skl) ),
inference(cnf_transformation,[status(thm)],[f274]) ).
fof(f278,plain,
! [X0,X1] :
( min_precedes(X1,sK20_skl(X0,X1),tptp0)
| sP0_prd(X0,X1)
| ~ leaf_occ(X0,sK19_skl) ),
inference(cnf_transformation,[status(thm)],[f274]) ).
fof(f279,plain,
! [X166,X167] :
( ( ! [X168] :
( ~ min_precedes(X166,X168,tptp0)
| ~ occurrence_of(X168,tptp2) )
| ~ occurrence_of(X167,tptp1)
| sP0_prd(X167,X166) )
& ( ( ? [X168] :
( min_precedes(X166,X168,tptp0)
& occurrence_of(X168,tptp2) )
& occurrence_of(X167,tptp1) )
| ~ sP0_prd(X167,X166) ) ),
inference(NNF_transformation,[status(thm)],[f272]) ).
fof(f280,plain,
( ! [X166,X167] :
( ! [X168] :
( ~ min_precedes(X166,X168,tptp0)
| ~ occurrence_of(X168,tptp2) )
| ~ occurrence_of(X167,tptp1)
| sP0_prd(X167,X166) )
& ! [X166,X167] :
( ( ? [X168] :
( min_precedes(X166,X168,tptp0)
& occurrence_of(X168,tptp2) )
& occurrence_of(X167,tptp1) )
| ~ sP0_prd(X167,X166) ) ),
inference(miniscoping,[status(thm)],[f279]) ).
fof(f281,plain,
( ! [X166,X167] :
( ! [X168] :
( ~ min_precedes(X166,X168,tptp0)
| ~ occurrence_of(X168,tptp2) )
| ~ occurrence_of(X167,tptp1)
| sP0_prd(X167,X166) )
& ! [X166,X167] :
( ( min_precedes(X166,sK21_skl(X167,X166),tptp0)
& occurrence_of(sK21_skl(X167,X166),tptp2)
& occurrence_of(X167,tptp1) )
| ~ sP0_prd(X167,X166) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21_skl]),skolemize(X168,sK21_skl(X167,X166))],[f280]) ).
fof(f282,plain,
! [X0,X1] :
( occurrence_of(X0,tptp1)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f281]) ).
fof(f284,plain,
! [X0,X1] :
( min_precedes(X1,sK21_skl(X0,X1),tptp0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f281]) ).
fof(f288,plain,
! [X0,X1,X2] :
( sP0_prd(X0,X2)
| ~ leaf_occ(X0,sK19_skl)
| X1 = tptp2
| ~ occurrence_of(X0,X1) ),
inference(resolution,[status(thm)],[f74,f276]) ).
fof(f387,plain,
! [X0] :
( ~ arboreal(X0)
| ~ occurrence_of(X0,tptp0) ),
inference(resolution,[status(thm)],[f87,f260]) ).
fof(f388,plain,
~ arboreal(sK19_skl),
inference(resolution,[status(thm)],[f387,f275]) ).
fof(f389,plain,
! [X0,X1] : ~ min_precedes(sK19_skl,X0,X1),
inference(resolution,[status(thm)],[f388,f242]) ).
fof(f397,plain,
! [X0] : ~ sP0_prd(X0,sK19_skl),
inference(resolution,[status(thm)],[f389,f284]) ).
fof(f421,plain,
leaf_occ(sK16_skl(sK19_skl),sK19_skl),
inference(resolution,[status(thm)],[f258,f275]) ).
fof(f422,plain,
! [X0,X1] :
( sP0_prd(sK16_skl(sK19_skl),X1)
| X0 = tptp2
| ~ occurrence_of(sK16_skl(sK19_skl),X0) ),
inference(resolution,[status(thm)],[f421,f288]) ).
fof(f424,plain,
! [X0] :
( min_precedes(X0,sK20_skl(sK16_skl(sK19_skl),X0),tptp0)
| sP0_prd(sK16_skl(sK19_skl),X0) ),
inference(resolution,[status(thm)],[f421,f278]) ).
fof(f430,definition,
! [X0] :
( sQ14_spl
<=> ( X0 = tptp2
| ~ occurrence_of(sK16_skl(sK19_skl),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f431,plain,
! [X0] :
( ~ sQ14_spl
| X0 = tptp2
| ~ occurrence_of(sK16_skl(sK19_skl),X0) ),
inference(component_clause,[status(thm)],[f430]) ).
fof(f433,definition,
! [X1] :
( sQ15_spl
<=> sP0_prd(sK16_skl(sK19_skl),X1) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f434,plain,
! [X0] :
( ~ sQ15_spl
| sP0_prd(sK16_skl(sK19_skl),X0) ),
inference(component_clause,[status(thm)],[f433]) ).
fof(f436,plain,
( sQ15_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f422,f430,f433]) ).
fof(f445,plain,
( ~ sQ15_spl
| $false ),
inference(resolution,[status(thm)],[f434,f397]) ).
fof(f452,plain,
~ sQ15_spl,
inference(contradiction_clause,[status(thm)],[f445]) ).
fof(f491,plain,
! [X0] :
( ~ sQ14_spl
| ~ sP0_prd(sK16_skl(sK19_skl),X0)
| tptp1 = tptp2 ),
inference(resolution,[status(thm)],[f431,f282]) ).
fof(f497,definition,
( sQ23_spl
<=> tptp1 = tptp2 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f498,plain,
( ~ sQ23_spl
| tptp1 = tptp2 ),
inference(component_clause,[status(thm)],[f497]) ).
fof(f500,definition,
! [X0] :
( sQ24_spl
<=> ~ sP0_prd(sK16_skl(sK19_skl),X0) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f501,plain,
! [X0] :
( ~ sQ24_spl
| ~ sP0_prd(sK16_skl(sK19_skl),X0) ),
inference(component_clause,[status(thm)],[f500]) ).
fof(f503,plain,
( ~ sQ14_spl
| sQ24_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f491,f497,f500,f430]) ).
fof(f504,plain,
( ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f498,f270]) ).
fof(f505,plain,
~ sQ23_spl,
inference(contradiction_clause,[status(thm)],[f504]) ).
fof(f586,plain,
! [X0] :
( ~ sQ24_spl
| min_precedes(X0,sK20_skl(sK16_skl(sK19_skl),X0),tptp0) ),
inference(forward_subsumption_resolution,[status(thm)],[f424,f501]) ).
fof(f587,plain,
( ~ sQ24_spl
| $false ),
inference(resolution,[status(thm)],[f586,f389]) ).
fof(f593,plain,
~ sQ24_spl,
inference(contradiction_clause,[status(thm)],[f587]) ).
fof(f594,plain,
$false,
inference(sat_refutation,[status(thm)],[f436,f452,f503,f505,f593]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PRO010+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.51 % Computer : n002.cluster.edu
% 0.09/5.51 % Model : x86_64 x86_64
% 0.09/5.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.51 % Memory : 8046.5625MB
% 0.09/5.51 % OS : Linux 6.8.0-71-generic
% 0.09/5.51 % CPULimit : 300
% 0.09/5.51 % WCLimit : 300
% 0.09/5.51 % DateTime : Mon Sep 21 03:44:54 UTC 2026
% 0.09/5.52 % CPUTime :
% 0.09/5.53 % Drodi V4.1.1
% 0.09/5.56 % Refutation found
% 0.09/5.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/5.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/5.60 % Elapsed time: 0.064587 seconds
% 0.09/5.60 % CPU time: 0.171455 seconds
% 0.09/5.60 % Total memory used: 84.857 MB
% 0.09/5.60 % Net memory used: 84.722 MB
%------------------------------------------------------------------------------