%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : PRO011+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 0.12s 0.39s
% Output : CNFRefutation 0.12s
% 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(f10,axiom,
! [X31,X32,X33] :
( ( leaf_occ(X32,X31)
& occurrence_of(X31,X33) )
=> ~ ? [X34] : min_precedes(X32,X34,X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [X101] :
( occurrence_of(X101,tptp0)
=> ? [X102,X103,X104] :
( leaf_occ(X104,X101)
& next_subocc(X103,X104,tptp0)
& ( occurrence_of(X104,tptp2)
| occurrence_of(X104,tptp1) )
& next_subocc(X102,X103,tptp0)
& occurrence_of(X103,tptp4)
& root_occ(X102,X101)
& occurrence_of(X102,tptp3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,conjecture,
! [X105] :
( occurrence_of(X105,tptp0)
=> ? [X106,X107] :
( ( occurrence_of(X107,tptp2)
=> ~ ? [X109] :
( min_precedes(X106,X109,tptp0)
& subactivity_occurrence(X109,X105)
& occurrence_of(X109,tptp1) ) )
& ( occurrence_of(X107,tptp1)
=> ~ ? [X108] :
( min_precedes(X106,X108,tptp0)
& subactivity_occurrence(X108,X105)
& occurrence_of(X108,tptp2) ) )
& leaf_occ(X107,X105) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
~ ! [X105] :
( occurrence_of(X105,tptp0)
=> ? [X106,X107] :
( ( occurrence_of(X107,tptp2)
=> ~ ? [X109] :
( min_precedes(X106,X109,tptp0)
& subactivity_occurrence(X109,X105)
& occurrence_of(X109,tptp1) ) )
& ( occurrence_of(X107,tptp1)
=> ~ ? [X108] :
( min_precedes(X106,X108,tptp0)
& subactivity_occurrence(X108,X105)
& occurrence_of(X108,tptp2) ) )
& leaf_occ(X107,X105) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f80,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(f81,plain,
! [X32,X33] :
( ! [X34] : ~ min_precedes(X32,X34,X33)
| ! [X31] :
( ~ leaf_occ(X32,X31)
| ~ occurrence_of(X31,X33) ) ),
inference(miniscoping,[status(thm)],[f80]) ).
fof(f82,plain,
! [X0,X1,X2,X3] :
( ~ min_precedes(X2,X3,X1)
| ~ leaf_occ(X2,X0)
| ~ occurrence_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f176,plain,
! [X101] :
( ? [X102,X103,X104] :
( leaf_occ(X104,X101)
& next_subocc(X103,X104,tptp0)
& ( occurrence_of(X104,tptp2)
| occurrence_of(X104,tptp1) )
& next_subocc(X102,X103,tptp0)
& occurrence_of(X103,tptp4)
& root_occ(X102,X101)
& occurrence_of(X102,tptp3) )
| ~ occurrence_of(X101,tptp0) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f177,plain,
! [X101] :
( ? [X104] :
( leaf_occ(X104,X101)
& ? [X103] :
( next_subocc(X103,X104,tptp0)
& ( occurrence_of(X104,tptp2)
| occurrence_of(X104,tptp1) )
& ? [X102] :
( next_subocc(X102,X103,tptp0)
& occurrence_of(X103,tptp4)
& root_occ(X102,X101)
& occurrence_of(X102,tptp3) ) ) )
| ~ occurrence_of(X101,tptp0) ),
inference(miniscoping,[status(thm)],[f176]) ).
fof(f178,plain,
! [X101] :
( ( leaf_occ(sK12_skl(X101),X101)
& next_subocc(sK13_skl(X101),sK12_skl(X101),tptp0)
& ( occurrence_of(sK12_skl(X101),tptp2)
| occurrence_of(sK12_skl(X101),tptp1) )
& next_subocc(sK14_skl(X101),sK13_skl(X101),tptp0)
& occurrence_of(sK13_skl(X101),tptp4)
& root_occ(sK14_skl(X101),X101)
& occurrence_of(sK14_skl(X101),tptp3) )
| ~ occurrence_of(X101,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl,sK14_skl]),skolemize(X104,sK12_skl(X101)),skolemize(X103,sK13_skl(X101)),skolemize(X102,sK14_skl(X101))],[f177]) ).
fof(f185,plain,
! [X0] :
( leaf_occ(sK12_skl(X0),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[status(thm)],[f178]) ).
fof(f198,plain,
? [X105] :
( ! [X106,X107] :
( ( ? [X109] :
( min_precedes(X106,X109,tptp0)
& subactivity_occurrence(X109,X105)
& occurrence_of(X109,tptp1) )
& occurrence_of(X107,tptp2) )
| ( ? [X108] :
( min_precedes(X106,X108,tptp0)
& subactivity_occurrence(X108,X105)
& occurrence_of(X108,tptp2) )
& occurrence_of(X107,tptp1) )
| ~ leaf_occ(X107,X105) )
& occurrence_of(X105,tptp0) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f199,definition,
! [X105,X106,X107] :
( sP0_prd(X107,X106,X105)
<=> ( ? [X108] :
( min_precedes(X106,X108,tptp0)
& subactivity_occurrence(X108,X105)
& occurrence_of(X108,tptp2) )
& occurrence_of(X107,tptp1) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f200,plain,
? [X105] :
( ! [X106,X107] :
( ( ? [X109] :
( min_precedes(X106,X109,tptp0)
& subactivity_occurrence(X109,X105)
& occurrence_of(X109,tptp1) )
& occurrence_of(X107,tptp2) )
| sP0_prd(X107,X106,X105)
| ~ leaf_occ(X107,X105) )
& occurrence_of(X105,tptp0) ),
inference(formula_renaming,[status(thm)],[f198,f199]) ).
fof(f201,plain,
( ! [X106,X107] :
( ( min_precedes(X106,sK16_skl(X107,X106),tptp0)
& subactivity_occurrence(sK16_skl(X107,X106),sK15_skl)
& occurrence_of(sK16_skl(X107,X106),tptp1)
& occurrence_of(X107,tptp2) )
| sP0_prd(X107,X106,sK15_skl)
| ~ leaf_occ(X107,sK15_skl) )
& occurrence_of(sK15_skl,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl,sK16_skl]),skolemize(X105,sK15_skl),skolemize(X109,sK16_skl(X107,X106))],[f200]) ).
fof(f202,plain,
occurrence_of(sK15_skl,tptp0),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f206,plain,
! [X0,X1] :
( min_precedes(X1,sK16_skl(X0,X1),tptp0)
| sP0_prd(X0,X1,sK15_skl)
| ~ leaf_occ(X0,sK15_skl) ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f207,plain,
! [X105,X106,X107] :
( ( ! [X108] :
( ~ min_precedes(X106,X108,tptp0)
| ~ subactivity_occurrence(X108,X105)
| ~ occurrence_of(X108,tptp2) )
| ~ occurrence_of(X107,tptp1)
| sP0_prd(X107,X106,X105) )
& ( ( ? [X108] :
( min_precedes(X106,X108,tptp0)
& subactivity_occurrence(X108,X105)
& occurrence_of(X108,tptp2) )
& occurrence_of(X107,tptp1) )
| ~ sP0_prd(X107,X106,X105) ) ),
inference(NNF_transformation,[status(thm)],[f199]) ).
fof(f208,plain,
( ! [X105,X106,X107] :
( ! [X108] :
( ~ min_precedes(X106,X108,tptp0)
| ~ subactivity_occurrence(X108,X105)
| ~ occurrence_of(X108,tptp2) )
| ~ occurrence_of(X107,tptp1)
| sP0_prd(X107,X106,X105) )
& ! [X105,X106,X107] :
( ( ? [X108] :
( min_precedes(X106,X108,tptp0)
& subactivity_occurrence(X108,X105)
& occurrence_of(X108,tptp2) )
& occurrence_of(X107,tptp1) )
| ~ sP0_prd(X107,X106,X105) ) ),
inference(miniscoping,[status(thm)],[f207]) ).
fof(f209,plain,
( ! [X105,X106,X107] :
( ! [X108] :
( ~ min_precedes(X106,X108,tptp0)
| ~ subactivity_occurrence(X108,X105)
| ~ occurrence_of(X108,tptp2) )
| ~ occurrence_of(X107,tptp1)
| sP0_prd(X107,X106,X105) )
& ! [X105,X106,X107] :
( ( min_precedes(X106,sK17_skl(X107,X106,X105),tptp0)
& subactivity_occurrence(sK17_skl(X107,X106,X105),X105)
& occurrence_of(sK17_skl(X107,X106,X105),tptp2)
& occurrence_of(X107,tptp1) )
| ~ sP0_prd(X107,X106,X105) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl]),skolemize(X108,sK17_skl(X107,X106,X105))],[f208]) ).
fof(f213,plain,
! [X0,X1,X2] :
( min_precedes(X1,sK17_skl(X0,X1,X2),tptp0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f209]) ).
fof(f220,plain,
! [X0,X1,X2,X3] :
( ~ sP0_prd(X2,X1,X3)
| ~ leaf_occ(X1,X0)
| ~ occurrence_of(X0,tptp0) ),
inference(resolution,[status(thm)],[f82,f213]) ).
fof(f222,definition,
! [X0,X1] :
( sQ0_spl
<=> ( ~ leaf_occ(X1,X0)
| ~ occurrence_of(X0,tptp0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f223,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ leaf_occ(X1,X0)
| ~ occurrence_of(X0,tptp0) ),
inference(component_clause,[status(thm)],[f222]) ).
fof(f239,plain,
! [X0,X1,X2] :
( ~ leaf_occ(X1,X2)
| ~ occurrence_of(X2,tptp0)
| sP0_prd(X0,X1,sK15_skl)
| ~ leaf_occ(X0,sK15_skl) ),
inference(resolution,[status(thm)],[f206,f82]) ).
fof(f277,definition,
! [X0] :
( sQ9_spl
<=> ~ leaf_occ(X0,sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f278,plain,
! [X0] :
( ~ sQ9_spl
| ~ leaf_occ(X0,sK15_skl) ),
inference(component_clause,[status(thm)],[f277]) ).
fof(f290,plain,
! [X0,X1,X2] :
( ~ leaf_occ(X2,X1)
| ~ occurrence_of(X1,tptp0)
| ~ leaf_occ(X0,sK15_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f239,f220]) ).
fof(f504,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f202,f505]) ).
fof(f505,plain,
! [X0] :
( ~ sQ0_spl
| ~ occurrence_of(X0,tptp0) ),
inference(forward_subsumption_resolution,[status(thm)],[f185,f223]) ).
fof(f507,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f504]) ).
fof(f659,plain,
( ~ sQ9_spl
| ~ occurrence_of(sK15_skl,tptp0) ),
inference(resolution,[status(thm)],[f185,f278]) ).
fof(f662,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f659,f202]) ).
fof(f663,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f662]) ).
fof(f682,plain,
( sQ0_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f290,f277,f222]) ).
fof(f683,plain,
$false,
inference(sat_refutation,[status(thm)],[f507,f663,f682]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PRO011+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n016.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 03:47:23 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.43 % Elapsed time: 0.065831 seconds
% 0.12/0.43 % CPU time: 0.191801 seconds
% 0.12/0.43 % Total memory used: 84.803 MB
% 0.12/0.43 % Net memory used: 84.644 MB
%------------------------------------------------------------------------------