%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : PRO010+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 : n004.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 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 56 ( 14 unt; 1 def)
% Number of atoms : 209 ( 6 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 223 ( 70 ~; 70 |; 71 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 127 ( 96 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X35,X36] :
( leaf_occ(X35,X36)
<=> ? [X37] :
( leaf(X35,X37)
& subactivity_occurrence(X35,X36)
& occurrence_of(X36,X37) ) ),
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(f24,axiom,
! [X67,X68] :
( ( ~ atomic(X68)
& leaf(X67,X68) )
=> ? [X69] :
( leaf_occ(X67,X69)
& occurrence_of(X69,X68) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [X95] :
( occurrence_of(X95,tptp0)
=> ? [X96,X97,X98] :
( leaf_occ(X98,X95)
& next_subocc(X97,X98,tptp0)
& ( occurrence_of(X98,tptp2)
| occurrence_of(X98,tptp1) )
& next_subocc(X96,X97,tptp0)
& occurrence_of(X97,tptp4)
& root_occ(X96,X95)
& occurrence_of(X96,tptp3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,axiom,
~ atomic(tptp0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,conjecture,
! [X99] :
( occurrence_of(X99,tptp0)
=> ? [X100,X101] :
( ( occurrence_of(X101,tptp2)
=> ~ ? [X103] :
( min_precedes(X100,X103,tptp0)
& occurrence_of(X103,tptp1) ) )
& ( occurrence_of(X101,tptp1)
=> ~ ? [X102] :
( min_precedes(X100,X102,tptp0)
& occurrence_of(X102,tptp2) ) )
& leaf_occ(X101,X99) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
~ ! [X99] :
( occurrence_of(X99,tptp0)
=> ? [X100,X101] :
( ( occurrence_of(X101,tptp2)
=> ~ ? [X103] :
( min_precedes(X100,X103,tptp0)
& occurrence_of(X103,tptp1) ) )
& ( occurrence_of(X101,tptp1)
=> ~ ? [X102] :
( min_precedes(X100,X102,tptp0)
& occurrence_of(X102,tptp2) ) )
& leaf_occ(X101,X99) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f92,plain,
! [X35,X36] :
( ( ! [X37] :
( ~ leaf(X35,X37)
| ~ subactivity_occurrence(X35,X36)
| ~ occurrence_of(X36,X37) )
| leaf_occ(X35,X36) )
& ( ? [X37] :
( leaf(X35,X37)
& subactivity_occurrence(X35,X36)
& occurrence_of(X36,X37) )
| ~ leaf_occ(X35,X36) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f93,plain,
( ! [X35,X36] :
( ! [X37] :
( ~ leaf(X35,X37)
| ~ subactivity_occurrence(X35,X36)
| ~ occurrence_of(X36,X37) )
| leaf_occ(X35,X36) )
& ! [X35,X36] :
( ? [X37] :
( leaf(X35,X37)
& subactivity_occurrence(X35,X36)
& occurrence_of(X36,X37) )
| ~ leaf_occ(X35,X36) ) ),
inference(miniscoping,[status(thm)],[f92]) ).
fof(f94,plain,
( ! [X35,X36] :
( ! [X37] :
( ~ leaf(X35,X37)
| ~ subactivity_occurrence(X35,X36)
| ~ occurrence_of(X36,X37) )
| leaf_occ(X35,X36) )
& ! [X35,X36] :
( ( leaf(X35,sK2_skl(X36,X35))
& subactivity_occurrence(X35,X36)
& occurrence_of(X36,sK2_skl(X36,X35)) )
| ~ leaf_occ(X35,X36) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(X37,sK2_skl(X36,X35))],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( occurrence_of(X1,sK2_skl(X1,X0))
| ~ leaf_occ(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f97,plain,
! [X0,X1] :
( leaf(X0,sK2_skl(X1,X0))
| ~ leaf_occ(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f135,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(f136,plain,
! [X61,X62] :
( ! [X63] : ~ min_precedes(X61,X63,X62)
| ! [X60] :
( ~ leaf_occ(X61,X60)
| ~ occurrence_of(X60,X62) ) ),
inference(miniscoping,[status(thm)],[f135]) ).
fof(f137,plain,
! [X0,X1,X2,X3] :
( ~ min_precedes(X2,X3,X1)
| ~ leaf_occ(X2,X0)
| ~ occurrence_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f138,plain,
! [X64,X65,X66] :
( X65 = X66
| ~ occurrence_of(X64,X66)
| ~ occurrence_of(X64,X65) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f139,plain,
! [X65,X66] :
( X65 = X66
| ! [X64] :
( ~ occurrence_of(X64,X66)
| ~ occurrence_of(X64,X65) ) ),
inference(miniscoping,[status(thm)],[f138]) ).
fof(f140,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ occurrence_of(X0,X2)
| ~ occurrence_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f141,plain,
! [X67,X68] :
( ? [X69] :
( leaf_occ(X67,X69)
& occurrence_of(X69,X68) )
| atomic(X68)
| ~ leaf(X67,X68) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f142,plain,
! [X67,X68] :
( ( leaf_occ(X67,sK7_skl(X68,X67))
& occurrence_of(sK7_skl(X68,X67),X68) )
| atomic(X68)
| ~ leaf(X67,X68) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(X69,sK7_skl(X68,X67))],[f141]) ).
fof(f143,plain,
! [X0,X1] :
( occurrence_of(sK7_skl(X1,X0),X1)
| atomic(X1)
| ~ leaf(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f144,plain,
! [X0,X1] :
( leaf_occ(X0,sK7_skl(X1,X0))
| atomic(X1)
| ~ leaf(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f177,plain,
! [X95] :
( ? [X96,X97,X98] :
( leaf_occ(X98,X95)
& next_subocc(X97,X98,tptp0)
& ( occurrence_of(X98,tptp2)
| occurrence_of(X98,tptp1) )
& next_subocc(X96,X97,tptp0)
& occurrence_of(X97,tptp4)
& root_occ(X96,X95)
& occurrence_of(X96,tptp3) )
| ~ occurrence_of(X95,tptp0) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f178,plain,
! [X95] :
( ? [X98] :
( leaf_occ(X98,X95)
& ? [X97] :
( next_subocc(X97,X98,tptp0)
& ( occurrence_of(X98,tptp2)
| occurrence_of(X98,tptp1) )
& ? [X96] :
( next_subocc(X96,X97,tptp0)
& occurrence_of(X97,tptp4)
& root_occ(X96,X95)
& occurrence_of(X96,tptp3) ) ) )
| ~ occurrence_of(X95,tptp0) ),
inference(miniscoping,[status(thm)],[f177]) ).
fof(f179,plain,
! [X95] :
( ( leaf_occ(sK14_skl(X95),X95)
& next_subocc(sK15_skl(X95),sK14_skl(X95),tptp0)
& ( occurrence_of(sK14_skl(X95),tptp2)
| occurrence_of(sK14_skl(X95),tptp1) )
& next_subocc(sK16_skl(X95),sK15_skl(X95),tptp0)
& occurrence_of(sK15_skl(X95),tptp4)
& root_occ(sK16_skl(X95),X95)
& occurrence_of(sK16_skl(X95),tptp3) )
| ~ occurrence_of(X95,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl,sK16_skl]),skolemize(X98,sK14_skl(X95)),skolemize(X97,sK15_skl(X95)),skolemize(X96,sK16_skl(X95))],[f178]) ).
fof(f186,plain,
! [X0] :
( leaf_occ(sK14_skl(X0),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[status(thm)],[f179]) ).
fof(f188,plain,
~ atomic(tptp0),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f199,plain,
? [X99] :
( ! [X100,X101] :
( ( ? [X103] :
( min_precedes(X100,X103,tptp0)
& occurrence_of(X103,tptp1) )
& occurrence_of(X101,tptp2) )
| ( ? [X102] :
( min_precedes(X100,X102,tptp0)
& occurrence_of(X102,tptp2) )
& occurrence_of(X101,tptp1) )
| ~ leaf_occ(X101,X99) )
& occurrence_of(X99,tptp0) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f200,definition,
! [X100,X101] :
( sP0_prd(X101,X100)
<=> ( ? [X102] :
( min_precedes(X100,X102,tptp0)
& occurrence_of(X102,tptp2) )
& occurrence_of(X101,tptp1) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f201,plain,
? [X99] :
( ! [X100,X101] :
( ( ? [X103] :
( min_precedes(X100,X103,tptp0)
& occurrence_of(X103,tptp1) )
& occurrence_of(X101,tptp2) )
| sP0_prd(X101,X100)
| ~ leaf_occ(X101,X99) )
& occurrence_of(X99,tptp0) ),
inference(formula_renaming,[status(thm)],[f199,f200]) ).
fof(f202,plain,
( ! [X100,X101] :
( ( min_precedes(X100,sK18_skl(X101,X100),tptp0)
& occurrence_of(sK18_skl(X101,X100),tptp1)
& occurrence_of(X101,tptp2) )
| sP0_prd(X101,X100)
| ~ leaf_occ(X101,sK17_skl) )
& occurrence_of(sK17_skl,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl]),skolemize(X99,sK17_skl),skolemize(X103,sK18_skl(X101,X100))],[f201]) ).
fof(f203,plain,
occurrence_of(sK17_skl,tptp0),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f206,plain,
! [X0,X1] :
( min_precedes(X1,sK18_skl(X0,X1),tptp0)
| sP0_prd(X0,X1)
| ~ leaf_occ(X0,sK17_skl) ),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f207,plain,
! [X100,X101] :
( ( ! [X102] :
( ~ min_precedes(X100,X102,tptp0)
| ~ occurrence_of(X102,tptp2) )
| ~ occurrence_of(X101,tptp1)
| sP0_prd(X101,X100) )
& ( ( ? [X102] :
( min_precedes(X100,X102,tptp0)
& occurrence_of(X102,tptp2) )
& occurrence_of(X101,tptp1) )
| ~ sP0_prd(X101,X100) ) ),
inference(NNF_transformation,[status(thm)],[f200]) ).
fof(f208,plain,
( ! [X100,X101] :
( ! [X102] :
( ~ min_precedes(X100,X102,tptp0)
| ~ occurrence_of(X102,tptp2) )
| ~ occurrence_of(X101,tptp1)
| sP0_prd(X101,X100) )
& ! [X100,X101] :
( ( ? [X102] :
( min_precedes(X100,X102,tptp0)
& occurrence_of(X102,tptp2) )
& occurrence_of(X101,tptp1) )
| ~ sP0_prd(X101,X100) ) ),
inference(miniscoping,[status(thm)],[f207]) ).
fof(f209,plain,
( ! [X100,X101] :
( ! [X102] :
( ~ min_precedes(X100,X102,tptp0)
| ~ occurrence_of(X102,tptp2) )
| ~ occurrence_of(X101,tptp1)
| sP0_prd(X101,X100) )
& ! [X100,X101] :
( ( min_precedes(X100,sK19_skl(X101,X100),tptp0)
& occurrence_of(sK19_skl(X101,X100),tptp2)
& occurrence_of(X101,tptp1) )
| ~ sP0_prd(X101,X100) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl]),skolemize(X102,sK19_skl(X101,X100))],[f208]) ).
fof(f212,plain,
! [X0,X1] :
( min_precedes(X1,sK19_skl(X0,X1),tptp0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f209]) ).
fof(f214,plain,
! [X0] :
( tptp0 = X0
| ~ occurrence_of(sK17_skl,X0) ),
inference(resolution,[status(thm)],[f140,f203]) ).
fof(f216,plain,
! [X0,X1] :
( ~ min_precedes(X0,X1,tptp0)
| ~ leaf_occ(X0,sK17_skl) ),
inference(resolution,[status(thm)],[f137,f203]) ).
fof(f300,plain,
leaf_occ(sK14_skl(sK17_skl),sK17_skl),
inference(resolution,[status(thm)],[f186,f203]) ).
fof(f302,plain,
! [X0] :
( min_precedes(X0,sK18_skl(sK14_skl(sK17_skl),X0),tptp0)
| sP0_prd(sK14_skl(sK17_skl),X0) ),
inference(resolution,[status(thm)],[f300,f206]) ).
fof(f305,plain,
leaf(sK14_skl(sK17_skl),sK2_skl(sK17_skl,sK14_skl(sK17_skl))),
inference(resolution,[status(thm)],[f300,f97]) ).
fof(f306,plain,
occurrence_of(sK17_skl,sK2_skl(sK17_skl,sK14_skl(sK17_skl))),
inference(resolution,[status(thm)],[f300,f95]) ).
fof(f370,plain,
! [X0] :
( ~ leaf_occ(X0,sK17_skl)
| sP0_prd(sK14_skl(sK17_skl),X0) ),
inference(resolution,[status(thm)],[f302,f216]) ).
fof(f383,plain,
tptp0 = sK2_skl(sK17_skl,sK14_skl(sK17_skl)),
inference(resolution,[status(thm)],[f306,f214]) ).
fof(f450,plain,
sP0_prd(sK14_skl(sK17_skl),sK14_skl(sK17_skl)),
inference(resolution,[status(thm)],[f370,f300]) ).
fof(f451,plain,
min_precedes(sK14_skl(sK17_skl),sK19_skl(sK14_skl(sK17_skl),sK14_skl(sK17_skl)),tptp0),
inference(resolution,[status(thm)],[f450,f212]) ).
fof(f486,plain,
leaf(sK14_skl(sK17_skl),tptp0),
inference(forward_demodulation,[status(thm)],[f383,f305]) ).
fof(f488,plain,
( leaf_occ(sK14_skl(sK17_skl),sK7_skl(tptp0,sK14_skl(sK17_skl)))
| atomic(tptp0) ),
inference(resolution,[status(thm)],[f486,f144]) ).
fof(f489,plain,
( occurrence_of(sK7_skl(tptp0,sK14_skl(sK17_skl)),tptp0)
| atomic(tptp0) ),
inference(resolution,[status(thm)],[f486,f143]) ).
fof(f491,plain,
leaf_occ(sK14_skl(sK17_skl),sK7_skl(tptp0,sK14_skl(sK17_skl))),
inference(forward_subsumption_resolution,[status(thm)],[f488,f188]) ).
fof(f492,plain,
occurrence_of(sK7_skl(tptp0,sK14_skl(sK17_skl)),tptp0),
inference(forward_subsumption_resolution,[status(thm)],[f489,f188]) ).
fof(f506,plain,
! [X0,X1] :
( ~ min_precedes(X0,X1,tptp0)
| ~ leaf_occ(X0,sK7_skl(tptp0,sK14_skl(sK17_skl))) ),
inference(resolution,[status(thm)],[f492,f137]) ).
fof(f1109,plain,
! [X0] : ~ min_precedes(sK14_skl(sK17_skl),X0,tptp0),
inference(resolution,[status(thm)],[f506,f491]) ).
fof(f1132,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f451,f1109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PRO010+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n004.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 03:42:20 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.071226 seconds
% 0.13/0.43 % CPU time: 0.270392 seconds
% 0.13/0.43 % Total memory used: 85.703 MB
% 0.13/0.43 % Net memory used: 85.493 MB
%------------------------------------------------------------------------------