%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : PRO011+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 : n003.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 01:59:17 PM UTC 2026
% Result : Theorem 0.11s 0.37s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 4 unt; 3 def)
% Number of atoms : 168 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 196 ( 64 ~; 54 |; 67 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 3 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 97 ( 71 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(f46,conjecture,
! [X99] :
( occurrence_of(X99,tptp0)
=> ? [X100,X101] :
( ( occurrence_of(X101,tptp2)
=> ~ ? [X103] :
( min_precedes(X100,X103,tptp0)
& subactivity_occurrence(X103,X99)
& occurrence_of(X103,tptp1) ) )
& ( occurrence_of(X101,tptp1)
=> ~ ? [X102] :
( min_precedes(X100,X102,tptp0)
& subactivity_occurrence(X102,X99)
& 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)
& subactivity_occurrence(X103,X99)
& occurrence_of(X103,tptp1) ) )
& ( occurrence_of(X101,tptp1)
=> ~ ? [X102] :
( min_precedes(X100,X102,tptp0)
& subactivity_occurrence(X102,X99)
& occurrence_of(X102,tptp2) ) )
& leaf_occ(X101,X99) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
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(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(f199,plain,
? [X99] :
( ! [X100,X101] :
( ( ? [X103] :
( min_precedes(X100,X103,tptp0)
& subactivity_occurrence(X103,X99)
& occurrence_of(X103,tptp1) )
& occurrence_of(X101,tptp2) )
| ( ? [X102] :
( min_precedes(X100,X102,tptp0)
& subactivity_occurrence(X102,X99)
& 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,
! [X99,X100,X101] :
( sP0_prd(X101,X100,X99)
<=> ( ? [X102] :
( min_precedes(X100,X102,tptp0)
& subactivity_occurrence(X102,X99)
& 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)
& subactivity_occurrence(X103,X99)
& occurrence_of(X103,tptp1) )
& occurrence_of(X101,tptp2) )
| sP0_prd(X101,X100,X99)
| ~ 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)
& subactivity_occurrence(sK18_skl(X101,X100),sK17_skl)
& occurrence_of(sK18_skl(X101,X100),tptp1)
& occurrence_of(X101,tptp2) )
| sP0_prd(X101,X100,sK17_skl)
| ~ 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(f207,plain,
! [X0,X1] :
( min_precedes(X1,sK18_skl(X0,X1),tptp0)
| sP0_prd(X0,X1,sK17_skl)
| ~ leaf_occ(X0,sK17_skl) ),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f208,plain,
! [X99,X100,X101] :
( ( ! [X102] :
( ~ min_precedes(X100,X102,tptp0)
| ~ subactivity_occurrence(X102,X99)
| ~ occurrence_of(X102,tptp2) )
| ~ occurrence_of(X101,tptp1)
| sP0_prd(X101,X100,X99) )
& ( ( ? [X102] :
( min_precedes(X100,X102,tptp0)
& subactivity_occurrence(X102,X99)
& occurrence_of(X102,tptp2) )
& occurrence_of(X101,tptp1) )
| ~ sP0_prd(X101,X100,X99) ) ),
inference(NNF_transformation,[status(thm)],[f200]) ).
fof(f209,plain,
( ! [X99,X100,X101] :
( ! [X102] :
( ~ min_precedes(X100,X102,tptp0)
| ~ subactivity_occurrence(X102,X99)
| ~ occurrence_of(X102,tptp2) )
| ~ occurrence_of(X101,tptp1)
| sP0_prd(X101,X100,X99) )
& ! [X99,X100,X101] :
( ( ? [X102] :
( min_precedes(X100,X102,tptp0)
& subactivity_occurrence(X102,X99)
& occurrence_of(X102,tptp2) )
& occurrence_of(X101,tptp1) )
| ~ sP0_prd(X101,X100,X99) ) ),
inference(miniscoping,[status(thm)],[f208]) ).
fof(f210,plain,
( ! [X99,X100,X101] :
( ! [X102] :
( ~ min_precedes(X100,X102,tptp0)
| ~ subactivity_occurrence(X102,X99)
| ~ occurrence_of(X102,tptp2) )
| ~ occurrence_of(X101,tptp1)
| sP0_prd(X101,X100,X99) )
& ! [X99,X100,X101] :
( ( min_precedes(X100,sK19_skl(X101,X100,X99),tptp0)
& subactivity_occurrence(sK19_skl(X101,X100,X99),X99)
& occurrence_of(sK19_skl(X101,X100,X99),tptp2)
& occurrence_of(X101,tptp1) )
| ~ sP0_prd(X101,X100,X99) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl]),skolemize(X102,sK19_skl(X101,X100,X99))],[f209]) ).
fof(f214,plain,
! [X0,X1,X2] :
( min_precedes(X1,sK19_skl(X0,X1,X2),tptp0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f221,plain,
! [X0,X1,X2,X3] :
( ~ sP0_prd(X2,X1,X3)
| ~ leaf_occ(X1,X0)
| ~ occurrence_of(X0,tptp0) ),
inference(resolution,[status(thm)],[f137,f214]) ).
fof(f223,definition,
! [X0,X1] :
( sQ0_spl
<=> ( ~ leaf_occ(X1,X0)
| ~ occurrence_of(X0,tptp0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f224,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ leaf_occ(X1,X0)
| ~ occurrence_of(X0,tptp0) ),
inference(component_clause,[status(thm)],[f223]) ).
fof(f265,definition,
! [X0] :
( sQ7_spl
<=> ~ leaf_occ(X0,sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f266,plain,
! [X0] :
( ~ sQ7_spl
| ~ leaf_occ(X0,sK17_skl) ),
inference(component_clause,[status(thm)],[f265]) ).
fof(f270,plain,
! [X0,X1,X2] :
( ~ leaf_occ(X1,X2)
| ~ occurrence_of(X2,tptp0)
| sP0_prd(X0,X1,sK17_skl)
| ~ leaf_occ(X0,sK17_skl) ),
inference(resolution,[status(thm)],[f207,f137]) ).
fof(f286,plain,
! [X0,X1,X2] :
( ~ leaf_occ(X2,X1)
| ~ occurrence_of(X1,tptp0)
| ~ leaf_occ(X0,sK17_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f270,f221]) ).
fof(f490,plain,
( sQ0_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f286,f265,f223]) ).
fof(f491,plain,
( ~ sQ7_spl
| ~ occurrence_of(sK17_skl,tptp0) ),
inference(resolution,[status(thm)],[f266,f186]) ).
fof(f492,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f491,f203]) ).
fof(f493,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f492]) ).
fof(f494,plain,
! [X0] :
( ~ sQ0_spl
| ~ occurrence_of(X0,tptp0) ),
inference(backward_subsumption_resolution,[status(thm)],[f186,f224]) ).
fof(f495,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f203,f494]) ).
fof(f496,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f495]) ).
fof(f497,plain,
$false,
inference(sat_refutation,[status(thm)],[f490,f493,f496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PRO011+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n003.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 21 03:44:16 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.11/0.36 % Drodi V4.1.1
% 0.11/0.37 % Refutation found
% 0.11/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.40 % Elapsed time: 0.051866 seconds
% 0.11/0.40 % CPU time: 0.169612 seconds
% 0.11/0.40 % Total memory used: 33.013 MB
% 0.11/0.40 % Net memory used: 32.903 MB
%------------------------------------------------------------------------------