%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO126+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 12:24:08 PM UTC 2026
% Result : Theorem 0.19s 0.51s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 62 ( 17 unt; 2 def)
% Number of atoms : 221 ( 20 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 252 ( 93 ~; 90 |; 58 &)
% ( 9 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 3 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 127 ( 108 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [P,C] :
( end_point(P,C)
<=> ( ! [C1,C2] :
( ( incident_c(P,C2)
& incident_c(P,C1)
& part_of(C2,C)
& part_of(C1,C) )
=> ( part_of(C2,C1)
| part_of(C1,C2) ) )
& incident_c(P,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [P,C] :
( inner_point(P,C)
<=> ( ~ end_point(P,C)
& incident_c(P,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [C] :
( open(C)
<=> ? [P] : end_point(P,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [C] :
? [P] : inner_point(P,C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [P,O] :
( start_point(P,O)
<=> ( ! [Q] :
( ( incident_o(Q,O)
& P != Q )
=> ordered_by(O,P,Q) )
& incident_o(P,O) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [O] :
? [C] :
( ! [P] :
( incident_o(P,O)
<=> incident_c(P,C) )
& open(C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [O] :
? [P] : start_point(P,O),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,conjecture,
! [O] :
? [P,Q] :
( P != Q
& ordered_by(O,P,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ ! [O] :
? [P,Q] :
( P != Q
& ordered_by(O,P,Q) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f46,plain,
! [P,C] :
( end_point(P,C)
<=> ( ! [C1,C2] :
( part_of(C2,C1)
| part_of(C1,C2)
| ~ incident_c(P,C2)
| ~ incident_c(P,C1)
| ~ part_of(C2,C)
| ~ part_of(C1,C) )
& incident_c(P,C) ) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f47,plain,
! [P,C] :
( ( ? [C1,C2] :
( ~ part_of(C2,C1)
& ~ part_of(C1,C2)
& incident_c(P,C2)
& incident_c(P,C1)
& part_of(C2,C)
& part_of(C1,C) )
| ~ incident_c(P,C)
| end_point(P,C) )
& ( ( ! [C1,C2] :
( part_of(C2,C1)
| part_of(C1,C2)
| ~ incident_c(P,C2)
| ~ incident_c(P,C1)
| ~ part_of(C2,C)
| ~ part_of(C1,C) )
& incident_c(P,C) )
| ~ end_point(P,C) ) ),
inference(NNF_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
( ! [P,C] :
( ? [C1,C2] :
( ~ part_of(C2,C1)
& ~ part_of(C1,C2)
& incident_c(P,C2)
& incident_c(P,C1)
& part_of(C2,C)
& part_of(C1,C) )
| ~ incident_c(P,C)
| end_point(P,C) )
& ! [P,C] :
( ( ! [C1,C2] :
( part_of(C2,C1)
| part_of(C1,C2)
| ~ incident_c(P,C2)
| ~ incident_c(P,C1)
| ~ part_of(C2,C)
| ~ part_of(C1,C) )
& incident_c(P,C) )
| ~ end_point(P,C) ) ),
inference(miniscoping,[status(thm)],[f47]) ).
fof(f49,plain,
( ! [P,C] :
( ( ~ part_of(sK3_skl(C,P),sK2_skl(C,P))
& ~ part_of(sK2_skl(C,P),sK3_skl(C,P))
& incident_c(P,sK3_skl(C,P))
& incident_c(P,sK2_skl(C,P))
& part_of(sK3_skl(C,P),C)
& part_of(sK2_skl(C,P),C) )
| ~ incident_c(P,C)
| end_point(P,C) )
& ! [P,C] :
( ( ! [C1,C2] :
( part_of(C2,C1)
| part_of(C1,C2)
| ~ incident_c(P,C2)
| ~ incident_c(P,C1)
| ~ part_of(C2,C)
| ~ part_of(C1,C) )
& incident_c(P,C) )
| ~ end_point(P,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(C1,sK2_skl(C,P)),skolemize(C2,sK3_skl(C,P))],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( incident_c(X0,X1)
| ~ end_point(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f58,plain,
! [P,C] :
( ( end_point(P,C)
| ~ incident_c(P,C)
| inner_point(P,C) )
& ( ( ~ end_point(P,C)
& incident_c(P,C) )
| ~ inner_point(P,C) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f59,plain,
( ! [P,C] :
( end_point(P,C)
| ~ incident_c(P,C)
| inner_point(P,C) )
& ! [P,C] :
( ( ~ end_point(P,C)
& incident_c(P,C) )
| ~ inner_point(P,C) ) ),
inference(miniscoping,[status(thm)],[f58]) ).
fof(f60,plain,
! [X0,X1] :
( incident_c(X0,X1)
| ~ inner_point(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
! [X0,X1] :
( ~ end_point(X0,X1)
| ~ inner_point(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f80,plain,
! [C] :
( ( ! [P] : ~ end_point(P,C)
| open(C) )
& ( ? [P] : end_point(P,C)
| ~ open(C) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f81,plain,
( ! [C] :
( ! [P] : ~ end_point(P,C)
| open(C) )
& ! [C] :
( ? [P] : end_point(P,C)
| ~ open(C) ) ),
inference(miniscoping,[status(thm)],[f80]) ).
fof(f82,plain,
( ! [C] :
( ! [P] : ~ end_point(P,C)
| open(C) )
& ! [C] :
( end_point(sK6_skl(C),C)
| ~ open(C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(P,sK6_skl(C))],[f81]) ).
fof(f83,plain,
! [X0] :
( end_point(sK6_skl(X0),X0)
| ~ open(X0) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f91,plain,
! [C] : inner_point(sK7_skl(C),C),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(P,sK7_skl(C))],[f10]) ).
fof(f92,plain,
! [X0] : inner_point(sK7_skl(X0),X0),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f132,plain,
! [P,O] :
( start_point(P,O)
<=> ( ! [Q] :
( ordered_by(O,P,Q)
| ~ incident_o(Q,O)
| P = Q )
& incident_o(P,O) ) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f133,plain,
! [P,O] :
( ( ? [Q] :
( ~ ordered_by(O,P,Q)
& incident_o(Q,O)
& P != Q )
| ~ incident_o(P,O)
| start_point(P,O) )
& ( ( ! [Q] :
( ordered_by(O,P,Q)
| ~ incident_o(Q,O)
| P = Q )
& incident_o(P,O) )
| ~ start_point(P,O) ) ),
inference(NNF_transformation,[status(thm)],[f132]) ).
fof(f134,plain,
( ! [P,O] :
( ? [Q] :
( ~ ordered_by(O,P,Q)
& incident_o(Q,O)
& P != Q )
| ~ incident_o(P,O)
| start_point(P,O) )
& ! [P,O] :
( ( ! [Q] :
( ordered_by(O,P,Q)
| ~ incident_o(Q,O)
| P = Q )
& incident_o(P,O) )
| ~ start_point(P,O) ) ),
inference(miniscoping,[status(thm)],[f133]) ).
fof(f135,plain,
( ! [P,O] :
( ( ~ ordered_by(O,P,sK14_skl(O,P))
& incident_o(sK14_skl(O,P),O)
& P != sK14_skl(O,P) )
| ~ incident_o(P,O)
| start_point(P,O) )
& ! [P,O] :
( ( ! [Q] :
( ordered_by(O,P,Q)
| ~ incident_o(Q,O)
| P = Q )
& incident_o(P,O) )
| ~ start_point(P,O) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl]),skolemize(Q,sK14_skl(O,P))],[f134]) ).
fof(f137,plain,
! [X0,X1,X2] :
( ordered_by(X1,X0,X2)
| ~ incident_o(X2,X1)
| X0 = X2
| ~ start_point(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f153,plain,
! [O] :
? [C] :
( ! [P] :
( ( ~ incident_c(P,C)
| incident_o(P,O) )
& ( incident_c(P,C)
| ~ incident_o(P,O) ) )
& open(C) ),
inference(NNF_transformation,[status(thm)],[f22]) ).
fof(f154,plain,
! [O] :
? [C] :
( ! [P] :
( ~ incident_c(P,C)
| incident_o(P,O) )
& ! [P] :
( incident_c(P,C)
| ~ incident_o(P,O) )
& open(C) ),
inference(miniscoping,[status(thm)],[f153]) ).
fof(f155,plain,
! [O] :
( ! [P] :
( ~ incident_c(P,sK16_skl(O))
| incident_o(P,O) )
& ! [P] :
( incident_c(P,sK16_skl(O))
| ~ incident_o(P,O) )
& open(sK16_skl(O)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl]),skolemize(C,sK16_skl(O))],[f154]) ).
fof(f156,plain,
! [X0] : open(sK16_skl(X0)),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f158,plain,
! [X0,X1] :
( ~ incident_c(X0,sK16_skl(X1))
| incident_o(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f167,plain,
! [O] : start_point(sK19_skl(O),O),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl]),skolemize(P,sK19_skl(O))],[f24]) ).
fof(f168,plain,
! [X0] : start_point(sK19_skl(X0),X0),
inference(cnf_transformation,[status(thm)],[f167]) ).
fof(f188,plain,
? [O] :
! [P,Q] :
( P = Q
| ~ ordered_by(O,P,Q) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f189,plain,
! [P,Q] :
( P = Q
| ~ ordered_by(sK24_skl,P,Q) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24_skl]),skolemize(O,sK24_skl)],[f188]) ).
fof(f190,plain,
! [X0,X1] :
( X0 = X1
| ~ ordered_by(sK24_skl,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f189]) ).
fof(f198,plain,
! [X0] : incident_c(sK7_skl(X0),X0),
inference(resolution,[status(thm)],[f60,f92]) ).
fof(f199,plain,
! [X0] : ~ end_point(sK7_skl(X0),X0),
inference(resolution,[status(thm)],[f61,f92]) ).
fof(f207,plain,
! [X0] :
( incident_c(sK6_skl(X0),X0)
| ~ open(X0) ),
inference(resolution,[status(thm)],[f83,f50]) ).
fof(f213,plain,
! [X0] :
( ~ open(sK16_skl(X0))
| incident_o(sK6_skl(sK16_skl(X0)),X0) ),
inference(resolution,[status(thm)],[f158,f207]) ).
fof(f216,plain,
! [X0] : incident_o(sK7_skl(sK16_skl(X0)),X0),
inference(resolution,[status(thm)],[f158,f198]) ).
fof(f218,plain,
! [X0] : incident_o(sK6_skl(sK16_skl(X0)),X0),
inference(forward_subsumption_resolution,[status(thm)],[f213,f156]) ).
fof(f314,plain,
! [X0,X1] :
( X0 = X1
| ~ incident_o(X1,sK24_skl)
| X0 = X1
| ~ start_point(X0,sK24_skl) ),
inference(resolution,[status(thm)],[f137,f190]) ).
fof(f317,plain,
! [X0,X1] :
( ~ incident_o(X1,sK24_skl)
| X0 = X1
| ~ start_point(X0,sK24_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f314]) ).
fof(f318,plain,
! [X0] :
( ~ incident_o(X0,sK24_skl)
| sK19_skl(sK24_skl) = X0 ),
inference(resolution,[status(thm)],[f317,f168]) ).
fof(f322,plain,
sK19_skl(sK24_skl) = sK7_skl(sK16_skl(sK24_skl)),
inference(resolution,[status(thm)],[f318,f216]) ).
fof(f324,plain,
sK19_skl(sK24_skl) = sK6_skl(sK16_skl(sK24_skl)),
inference(resolution,[status(thm)],[f318,f218]) ).
fof(f352,plain,
~ end_point(sK19_skl(sK24_skl),sK16_skl(sK24_skl)),
inference(paramodulation,[status(thm)],[f322,f199]) ).
fof(f357,plain,
( end_point(sK19_skl(sK24_skl),sK16_skl(sK24_skl))
| ~ open(sK16_skl(sK24_skl)) ),
inference(paramodulation,[status(thm)],[f324,f83]) ).
fof(f358,definition,
( sQ6_spl
<=> open(sK16_skl(sK24_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f360,plain,
( sQ6_spl
| ~ open(sK16_skl(sK24_skl)) ),
inference(component_clause,[status(thm)],[f358]) ).
fof(f365,definition,
( sQ8_spl
<=> end_point(sK19_skl(sK24_skl),sK16_skl(sK24_skl)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f366,plain,
( ~ sQ8_spl
| end_point(sK19_skl(sK24_skl),sK16_skl(sK24_skl)) ),
inference(component_clause,[status(thm)],[f365]) ).
fof(f368,plain,
( sQ8_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f357,f358,f365]) ).
fof(f369,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f360,f156]) ).
fof(f370,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f369]) ).
fof(f427,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f366,f352]) ).
fof(f428,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f427]) ).
fof(f429,plain,
$false,
inference(sat_refutation,[status(thm)],[f368,f370,f428]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO126+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 % Computer : n009.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.47 % CPULimit : 300
% 0.19/0.47 % WCLimit : 300
% 0.19/0.47 % DateTime : Sun Sep 20 11:56:57 UTC 2026
% 0.19/0.47 % CPUTime :
% 0.19/0.49 % Drodi V4.1.1
% 0.19/0.51 % Refutation found
% 0.19/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.56 % Elapsed time: 0.077762 seconds
% 0.22/0.56 % CPU time: 0.171890 seconds
% 0.22/0.56 % Total memory used: 24.347 MB
% 0.22/0.56 % Net memory used: 24.263 MB
%------------------------------------------------------------------------------