%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO042-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 12:23:52 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.41s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 59 ( 21 unt; 6 def)
% Number of atoms : 111 ( 15 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 98 ( 46 ~; 46 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-5 aty)
% Number of variables : 77 ( 77 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X,Y,Z] :
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,W,V] : between(X,Y,extension(X,Y,W,V)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Y,X,W,V] : equidistant(Y,extension(X,Y,W,V),W,V),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] :
( X = Y
| ~ between(X,Y,X) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
between(u,v,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
between(v,w,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
~ between(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,plain,
! [X,Y] :
( X = Y
| ! [Z] : ~ equidistant(X,Y,Z,Z) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f26,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [X0,X1,X2,X3] : between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f28,plain,
! [X0,X1,X2,X3] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f31,plain,
! [X0,X1] :
( X0 = X1
| ~ between(X0,X1,X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f32,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(f33,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(f44,plain,
between(u,v,x),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f45,plain,
between(v,w,x),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f46,plain,
~ between(u,v,w),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f48,plain,
! [X0,X1,X2] : X0 = extension(X1,X0,X2,X2),
inference(resolution,[status(thm)],[f28,f26]) ).
fof(f50,plain,
! [X0,X1] : between(X0,X1,X1),
inference(paramodulation,[status(thm)],[f48,f27]) ).
fof(f75,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)],[f32,f31]) ).
fof(f76,plain,
! [X0] :
( v = inner_pasch(X0,v,x,w,v)
| ~ between(X0,v,x) ),
inference(resolution,[status(thm)],[f75,f45]) ).
fof(f80,plain,
! [X0,X1,X2] :
( X1 = inner_pasch(X0,X1,X2,X2,X1)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f75,f50]) ).
fof(f85,plain,
! [X0,X1] : X0 = inner_pasch(X1,X0,X0,X0,X0),
inference(resolution,[status(thm)],[f80,f50]) ).
fof(f88,plain,
! [X0,X1,X2,X3] :
( X0 = inner_pasch(X0,X1,X2,X0,X3)
| ~ between(X3,X0,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f33,f31]) ).
fof(f106,plain,
! [X0,X1] :
( between(X1,X1,X0)
| ~ between(X1,X1,X1)
| ~ between(X0,X1,X1) ),
inference(paramodulation,[status(thm)],[f85,f33]) ).
fof(f108,plain,
! [X0,X1] :
( between(X0,X0,X1)
| ~ between(X0,X0,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f106,f50]) ).
fof(f109,plain,
! [X0,X1] : between(X0,X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f108,f50]) ).
fof(f131,plain,
! [X0,X1,X2] :
( X0 = inner_pasch(X0,X1,X2,X0,X0)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f88,f109]) ).
fof(f147,plain,
u = inner_pasch(u,v,x,u,u),
inference(resolution,[status(thm)],[f131,f44]) ).
fof(f183,plain,
v = inner_pasch(u,v,x,w,v),
inference(resolution,[status(thm)],[f76,f44]) ).
fof(f188,definition,
( sQ0_spl
<=> between(v,w,x) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f190,plain,
( sQ0_spl
| ~ between(v,w,x) ),
inference(component_clause,[status(thm)],[f188]) ).
fof(f204,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f190,f45]) ).
fof(f205,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f204]) ).
fof(f213,definition,
( sQ4_spl
<=> between(u,v,x) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f215,plain,
( sQ4_spl
| ~ between(u,v,x) ),
inference(component_clause,[status(thm)],[f213]) ).
fof(f229,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f215,f44]) ).
fof(f230,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f229]) ).
fof(f268,plain,
( between(v,u,u)
| ~ between(u,u,x)
| ~ between(u,v,x) ),
inference(paramodulation,[status(thm)],[f147,f32]) ).
fof(f269,definition,
( sQ13_spl
<=> between(u,u,x) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f271,plain,
( sQ13_spl
| ~ between(u,u,x) ),
inference(component_clause,[status(thm)],[f269]) ).
fof(f276,definition,
( sQ15_spl
<=> between(v,u,u) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f279,plain,
( sQ15_spl
| ~ sQ13_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f268,f213,f269,f276]) ).
fof(f280,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f271,f109]) ).
fof(f281,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f280]) ).
fof(f282,plain,
( between(w,v,u)
| ~ between(v,w,x)
| ~ between(u,v,x) ),
inference(paramodulation,[status(thm)],[f183,f33]) ).
fof(f284,definition,
( sQ16_spl
<=> between(w,v,u) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f285,plain,
( ~ sQ16_spl
| between(w,v,u) ),
inference(component_clause,[status(thm)],[f284]) ).
fof(f287,plain,
( sQ16_spl
| ~ sQ0_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f282,f213,f188,f284]) ).
fof(f292,plain,
( ~ sQ16_spl
| v = inner_pasch(w,v,u,u,v) ),
inference(resolution,[status(thm)],[f285,f80]) ).
fof(f411,plain,
( ~ sQ16_spl
| between(u,v,w)
| ~ between(v,u,u)
| ~ between(w,v,u) ),
inference(paramodulation,[status(thm)],[f292,f33]) ).
fof(f413,definition,
( sQ23_spl
<=> between(u,v,w) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f414,plain,
( ~ sQ23_spl
| between(u,v,w) ),
inference(component_clause,[status(thm)],[f413]) ).
fof(f416,plain,
( sQ23_spl
| ~ sQ15_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f411,f284,f276,f413]) ).
fof(f418,plain,
( ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f414,f46]) ).
fof(f419,plain,
~ sQ23_spl,
inference(contradiction_clause,[status(thm)],[f418]) ).
fof(f420,plain,
$false,
inference(sat_refutation,[status(thm)],[f205,f230,f279,f281,f287,f416,f419]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO042-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n007.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 08:33:34 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.41 % Refutation found
% 0.08/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.44 % Elapsed time: 0.071730 seconds
% 0.08/0.44 % CPU time: 0.237223 seconds
% 0.08/0.44 % Total memory used: 82.427 MB
% 0.08/0.44 % Net memory used: 81.919 MB
%------------------------------------------------------------------------------