%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO117+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 : 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 12:24:07 PM UTC 2026
% Result : Theorem 0.11s 10.60s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 8 unt; 0 def)
% Number of atoms : 147 ( 7 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 189 ( 72 ~; 65 |; 47 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-5 aty)
% Number of variables : 132 ( 122 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
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(f17,axiom,
! [C,P,Q,R] :
( between_c(C,P,Q,R)
<=> ( ? [Cpp] :
( inner_point(Q,Cpp)
& end_point(R,Cpp)
& end_point(P,Cpp)
& part_of(Cpp,C) )
& P != R ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [O,P,Q,R] :
( between_o(O,P,Q,R)
<=> ( ( ordered_by(O,Q,P)
& ordered_by(O,R,Q) )
| ( ordered_by(O,Q,R)
& ordered_by(O,P,Q) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [P,Q,R,O] :
( between_o(O,P,Q,R)
<=> ? [C] :
( between_c(C,P,Q,R)
& ! [P] :
( incident_o(P,O)
<=> incident_c(P,C) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,conjecture,
! [O,P] : ~ ordered_by(O,P,P),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ ! [O,P] : ~ ordered_by(O,P,P),
inference(negated_conjecture,[status(cth)],[f28]) ).
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(f61,plain,
! [X0,X1] :
( ~ end_point(X0,X1)
| ~ inner_point(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f115,plain,
! [C,P,Q,R] :
( ( ! [Cpp] :
( ~ inner_point(Q,Cpp)
| ~ end_point(R,Cpp)
| ~ end_point(P,Cpp)
| ~ part_of(Cpp,C) )
| P = R
| between_c(C,P,Q,R) )
& ( ( ? [Cpp] :
( inner_point(Q,Cpp)
& end_point(R,Cpp)
& end_point(P,Cpp)
& part_of(Cpp,C) )
& P != R )
| ~ between_c(C,P,Q,R) ) ),
inference(NNF_transformation,[status(thm)],[f17]) ).
fof(f116,plain,
( ! [C,P,Q,R] :
( ! [Cpp] :
( ~ inner_point(Q,Cpp)
| ~ end_point(R,Cpp)
| ~ end_point(P,Cpp)
| ~ part_of(Cpp,C) )
| P = R
| between_c(C,P,Q,R) )
& ! [C,P,Q,R] :
( ( ? [Cpp] :
( inner_point(Q,Cpp)
& end_point(R,Cpp)
& end_point(P,Cpp)
& part_of(Cpp,C) )
& P != R )
| ~ between_c(C,P,Q,R) ) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f117,plain,
( ! [C,P,Q,R] :
( ! [Cpp] :
( ~ inner_point(Q,Cpp)
| ~ end_point(R,Cpp)
| ~ end_point(P,Cpp)
| ~ part_of(Cpp,C) )
| P = R
| between_c(C,P,Q,R) )
& ! [C,P,Q,R] :
( ( inner_point(Q,sK13_skl(R,Q,P,C))
& end_point(R,sK13_skl(R,Q,P,C))
& end_point(P,sK13_skl(R,Q,P,C))
& part_of(sK13_skl(R,Q,P,C),C)
& P != R )
| ~ between_c(C,P,Q,R) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl]),skolemize(Cpp,sK13_skl(R,Q,P,C))],[f116]) ).
fof(f120,plain,
! [X0,X1,X2,X3] :
( end_point(X1,sK13_skl(X3,X2,X1,X0))
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f122,plain,
! [X0,X1,X2,X3] :
( inner_point(X2,sK13_skl(X3,X2,X1,X0))
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f124,plain,
! [O,P,Q,R] :
( ( ( ( ~ ordered_by(O,Q,P)
| ~ ordered_by(O,R,Q) )
& ( ~ ordered_by(O,Q,R)
| ~ ordered_by(O,P,Q) ) )
| between_o(O,P,Q,R) )
& ( ( ordered_by(O,Q,P)
& ordered_by(O,R,Q) )
| ( ordered_by(O,Q,R)
& ordered_by(O,P,Q) )
| ~ between_o(O,P,Q,R) ) ),
inference(NNF_transformation,[status(thm)],[f18]) ).
fof(f125,plain,
( ! [O,P,Q,R] :
( ( ( ~ ordered_by(O,Q,P)
| ~ ordered_by(O,R,Q) )
& ( ~ ordered_by(O,Q,R)
| ~ ordered_by(O,P,Q) ) )
| between_o(O,P,Q,R) )
& ! [O,P,Q,R] :
( ( ordered_by(O,Q,P)
& ordered_by(O,R,Q) )
| ( ordered_by(O,Q,R)
& ordered_by(O,P,Q) )
| ~ between_o(O,P,Q,R) ) ),
inference(miniscoping,[status(thm)],[f124]) ).
fof(f131,plain,
! [X0,X1,X2,X3] :
( ~ ordered_by(X0,X2,X1)
| ~ ordered_by(X0,X3,X2)
| between_o(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f159,plain,
! [P,Q,R,O] :
( ( ! [C] :
( ~ between_c(C,P,Q,R)
| ? [P] :
( ( incident_c(P,C)
| incident_o(P,O) )
& ( ~ incident_c(P,C)
| ~ incident_o(P,O) ) ) )
| between_o(O,P,Q,R) )
& ( ? [C] :
( between_c(C,P,Q,R)
& ! [P] :
( ( ~ incident_c(P,C)
| incident_o(P,O) )
& ( incident_c(P,C)
| ~ incident_o(P,O) ) ) )
| ~ between_o(O,P,Q,R) ) ),
inference(NNF_transformation,[status(thm)],[f23]) ).
fof(f160,plain,
( ! [P,Q,R,O] :
( ! [C] :
( ~ between_c(C,P,Q,R)
| ? [P] :
( ( incident_c(P,C)
| incident_o(P,O) )
& ( ~ incident_c(P,C)
| ~ incident_o(P,O) ) ) )
| between_o(O,P,Q,R) )
& ! [P,Q,R,O] :
( ? [C] :
( between_c(C,P,Q,R)
& ! [P] :
( ~ incident_c(P,C)
| incident_o(P,O) )
& ! [P] :
( incident_c(P,C)
| ~ incident_o(P,O) ) )
| ~ between_o(O,P,Q,R) ) ),
inference(miniscoping,[status(thm)],[f159]) ).
fof(f161,plain,
( ! [P,Q,R,O] :
( ! [C] :
( ~ between_c(C,P,Q,R)
| ( ( incident_c(sK18_skl(C,O,R,Q,P),C)
| incident_o(sK18_skl(C,O,R,Q,P),O) )
& ( ~ incident_c(sK18_skl(C,O,R,Q,P),C)
| ~ incident_o(sK18_skl(C,O,R,Q,P),O) ) ) )
| between_o(O,P,Q,R) )
& ! [P,Q,R,O] :
( ( between_c(sK17_skl(O,R,Q,P),P,Q,R)
& ! [P] :
( ~ incident_c(P,sK17_skl(O,R,Q,P))
| incident_o(P,O) )
& ! [P] :
( incident_c(P,sK17_skl(O,R,Q,P))
| ~ incident_o(P,O) ) )
| ~ between_o(O,P,Q,R) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl]),skolemize(C,sK17_skl(O,R,Q,P)),skolemize(P,sK18_skl(C,O,R,Q,P))],[f160]) ).
fof(f164,plain,
! [X0,X1,X2,X3] :
( between_c(sK17_skl(X0,X3,X2,X1),X1,X2,X3)
| ~ between_o(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f161]) ).
fof(f188,plain,
? [O,P] : ordered_by(O,P,P),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f189,plain,
ordered_by(sK24_skl,sK25_skl,sK25_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24_skl,sK25_skl]),skolemize(O,sK24_skl),skolemize(P,sK25_skl)],[f188]) ).
fof(f190,plain,
ordered_by(sK24_skl,sK25_skl,sK25_skl),
inference(cnf_transformation,[status(thm)],[f189]) ).
fof(f237,plain,
! [X0,X1,X2,X3] :
( ~ end_point(X2,sK13_skl(X3,X2,X1,X0))
| ~ between_c(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f122,f61]) ).
fof(f264,plain,
! [X0,X1,X2] :
( ~ between_c(X0,X1,X1,X2)
| ~ between_c(X0,X1,X1,X2) ),
inference(resolution,[status(thm)],[f237,f120]) ).
fof(f270,plain,
! [X0,X1,X2] : ~ between_c(X0,X1,X1,X2),
inference(duplicate_literals_removal,[status(thm)],[f264]) ).
fof(f413,plain,
! [X0,X1,X2] : ~ between_o(X0,X1,X1,X2),
inference(resolution,[status(thm)],[f164,f270]) ).
fof(f416,plain,
! [X0,X1,X2] :
( ~ ordered_by(X0,X2,X2)
| ~ ordered_by(X0,X1,X2) ),
inference(resolution,[status(thm)],[f413,f131]) ).
fof(f422,plain,
$false,
inference(resolution,[status(thm)],[f416,f190]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO117+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/10.55 % Computer : n016.cluster.edu
% 0.11/10.55 % Model : x86_64 x86_64
% 0.11/10.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.55 % Memory : 8046.5625MB
% 0.11/10.55 % OS : Linux 6.8.0-71-generic
% 0.11/10.55 % CPULimit : 300
% 0.11/10.55 % WCLimit : 300
% 0.11/10.55 % DateTime : Sun Sep 20 11:37:34 UTC 2026
% 0.11/10.55 % CPUTime :
% 0.11/10.56 % Drodi V4.1.1
% 0.11/10.60 % Refutation found
% 0.11/10.60 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/10.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/10.63 % Elapsed time: 0.067137 seconds
% 0.15/10.63 % CPU time: 0.274907 seconds
% 0.15/10.63 % Total memory used: 86.241 MB
% 0.15/10.63 % Net memory used: 85.870 MB
%------------------------------------------------------------------------------