%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO066-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 12:23:58 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.48s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 40 ( 16 unt; 3 def)
% Number of atoms : 71 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 61 ( 30 ~; 28 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 67 ( 67 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X,Y,Z] :
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,W,V] : between(X,Y,extension(X,Y,W,V)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Y,X,W,V] : equidistant(Y,extension(X,Y,W,V),W,V),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] :
( X = Y
| ~ between(X,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [U,V,W,Y,X] :
( between(V,inner_pasch(U,V,W,X,Y),Y)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [U,V,W,Y,X] :
( between(X,inner_pasch(U,V,W,X,Y),U)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [Z,X,Y] :
( colinear(X,Y,Z)
| ~ between(Z,X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,hypothesis,
between(v,u,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
~ colinear(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,plain,
! [X,Y] :
( X = Y
| ! [Z] : ~ equidistant(X,Y,Z,Z) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f29,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
! [X0,X1,X2,X3] : between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f31,plain,
! [X0,X1,X2,X3] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f34,plain,
! [X0,X1] :
( X0 = X1
| ~ between(X0,X1,X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f35,plain,
! [X0,X1,X2,X3,X4] :
( between(X1,inner_pasch(X0,X1,X2,X4,X3),X3)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f36,plain,
! [X0,X1,X2,X3,X4] :
( between(X4,inner_pasch(X0,X1,X2,X4,X3),X0)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f49,plain,
! [X0,X1,X2] :
( colinear(X1,X2,X0)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f51,plain,
between(v,u,w),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f52,plain,
~ colinear(u,v,w),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f55,plain,
~ between(w,u,v),
inference(resolution,[status(thm)],[f49,f52]) ).
fof(f61,plain,
! [X0,X1,X2] : X0 = extension(X1,X0,X2,X2),
inference(resolution,[status(thm)],[f31,f29]) ).
fof(f63,plain,
! [X0,X1] : between(X0,X1,X1),
inference(paramodulation,[status(thm)],[f61,f30]) ).
fof(f67,plain,
! [X0,X1,X2,X3] :
( X1 = inner_pasch(X0,X1,X2,X3,X1)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f35,f34]) ).
fof(f98,plain,
! [X0,X1,X2] :
( X1 = inner_pasch(X0,X1,X2,X2,X1)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f67,f63]) ).
fof(f99,plain,
u = inner_pasch(v,u,w,w,u),
inference(resolution,[status(thm)],[f98,f51]) ).
fof(f104,plain,
( between(w,u,v)
| ~ between(u,w,w)
| ~ between(v,u,w) ),
inference(paramodulation,[status(thm)],[f99,f36]) ).
fof(f106,definition,
( sQ0_spl
<=> between(v,u,w) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( sQ0_spl
| ~ between(v,u,w) ),
inference(component_clause,[status(thm)],[f106]) ).
fof(f109,definition,
( sQ1_spl
<=> between(u,w,w) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f111,plain,
( sQ1_spl
| ~ between(u,w,w) ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,definition,
( sQ2_spl
<=> between(w,u,v) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f113,plain,
( ~ sQ2_spl
| between(w,u,v) ),
inference(component_clause,[status(thm)],[f112]) ).
fof(f115,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f104,f106,f109,f112]) ).
fof(f120,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f111,f63]) ).
fof(f121,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f120]) ).
fof(f122,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f108,f51]) ).
fof(f123,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f122]) ).
fof(f124,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f113,f55]) ).
fof(f125,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f124]) ).
fof(f126,plain,
$false,
inference(sat_refutation,[status(thm)],[f115,f121,f123,f125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO066-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n008.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sun Sep 20 09:19:54 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.46 % Drodi V4.1.1
% 0.17/0.48 % Refutation found
% 0.17/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.17/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.51 % Elapsed time: 0.062153 seconds
% 0.17/0.51 % CPU time: 0.182851 seconds
% 0.17/0.51 % Total memory used: 40.884 MB
% 0.17/0.51 % Net memory used: 40.736 MB
%------------------------------------------------------------------------------