%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO040-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 0.15s 0.45s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 11 unt; 3 def)
% Number of atoms : 58 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 52 ( 25 ~; 24 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-5 aty)
% Number of variables : 29 ( 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
between(v,u,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
u != v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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,w),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f45,plain,
between(v,u,w),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f46,plain,
u != v,
inference(cnf_transformation,[status(thm)],[f21]) ).
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(f78,plain,
! [X0] :
( v = inner_pasch(X0,v,w,u,v)
| ~ between(X0,v,w) ),
inference(resolution,[status(thm)],[f75,f45]) ).
fof(f144,definition,
( sQ0_spl
<=> between(v,u,w) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( sQ0_spl
| ~ between(v,u,w) ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f160,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f146,f45]) ).
fof(f161,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f160]) ).
fof(f168,definition,
( sQ4_spl
<=> between(u,v,w) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( sQ4_spl
| ~ between(u,v,w) ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f184,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f170,f44]) ).
fof(f185,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f184]) ).
fof(f354,plain,
v = inner_pasch(u,v,w,u,v),
inference(resolution,[status(thm)],[f78,f44]) ).
fof(f356,plain,
( between(u,v,u)
| ~ between(v,u,w)
| ~ between(u,v,w) ),
inference(paramodulation,[status(thm)],[f354,f33]) ).
fof(f358,definition,
( sQ19_spl
<=> between(u,v,u) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f359,plain,
( ~ sQ19_spl
| between(u,v,u) ),
inference(component_clause,[status(thm)],[f358]) ).
fof(f361,plain,
( sQ19_spl
| ~ sQ0_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f356,f168,f144,f358]) ).
fof(f370,plain,
( ~ sQ19_spl
| u = v ),
inference(resolution,[status(thm)],[f359,f31]) ).
fof(f372,plain,
( ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f370,f46]) ).
fof(f373,plain,
~ sQ19_spl,
inference(contradiction_clause,[status(thm)],[f372]) ).
fof(f374,plain,
$false,
inference(sat_refutation,[status(thm)],[f161,f185,f361,f373]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO040-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 08:34:47 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.15/0.38 % Drodi V4.1.1
% 0.15/0.45 % Refutation found
% 0.15/0.45 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.46 % Elapsed time: 0.084901 seconds
% 0.15/0.46 % CPU time: 0.370307 seconds
% 0.15/0.46 % Total memory used: 84.550 MB
% 0.15/0.46 % Net memory used: 83.771 MB
%------------------------------------------------------------------------------