%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO045-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 12:23:53 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.43s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 12 unt; 2 def)
% Number of atoms : 51 ( 6 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 46 ( 23 ~; 21 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 19 ( 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f46,axiom,
! [U,V,W] :
( between(W,V,U)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,axiom,
! [U,V,W,X] :
( V = W
| between(U,W,X)
| ~ between(V,W,X)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,hypothesis,
between(v,w,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,hypothesis,
v != w,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,negated_conjecture,
~ between(u,v,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f114,plain,
! [X0,X1,X2] :
( between(X2,X1,X0)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f128,plain,
! [V,W] :
( V = W
| ! [U,X] :
( between(U,W,X)
| ~ between(V,W,X)
| ~ between(U,V,W) ) ),
inference(miniscoping,[status(thm)],[f54]) ).
fof(f129,plain,
! [X0,X1,X2,X3] :
( X1 = X2
| between(X0,X2,X3)
| ~ between(X1,X2,X3)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,plain,
between(u,v,w),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f131,plain,
between(v,w,x),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f132,plain,
v != w,
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f133,plain,
~ between(u,v,x),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f140,plain,
~ between(x,v,u),
inference(resolution,[status(thm)],[f114,f133]) ).
fof(f192,plain,
! [X0] :
( X0 = v
| ~ between(X0,v,u)
| ~ between(x,X0,v) ),
inference(resolution,[status(thm)],[f140,f129]) ).
fof(f226,definition,
( sQ13_spl
<=> between(x,w,v) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f228,plain,
( sQ13_spl
| ~ between(x,w,v) ),
inference(component_clause,[status(thm)],[f226]) ).
fof(f230,plain,
( ~ between(w,v,u)
| ~ between(x,w,v) ),
inference(resolution,[status(thm)],[f192,f132]) ).
fof(f231,definition,
( sQ14_spl
<=> between(w,v,u) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f233,plain,
( sQ14_spl
| ~ between(w,v,u) ),
inference(component_clause,[status(thm)],[f231]) ).
fof(f234,plain,
( ~ sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f230,f226,f231]) ).
fof(f266,plain,
( sQ13_spl
| ~ between(v,w,x) ),
inference(resolution,[status(thm)],[f228,f114]) ).
fof(f269,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f266,f131]) ).
fof(f270,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f269]) ).
fof(f289,plain,
( sQ14_spl
| ~ between(u,v,w) ),
inference(resolution,[status(thm)],[f233,f114]) ).
fof(f292,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f289,f130]) ).
fof(f293,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f292]) ).
fof(f294,plain,
$false,
inference(sat_refutation,[status(thm)],[f234,f270,f293]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO045-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 08:37:40 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 0.10/0.43 % Refutation found
% 0.10/0.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.47 % Elapsed time: 0.077228 seconds
% 0.10/0.47 % CPU time: 0.275127 seconds
% 0.10/0.47 % Total memory used: 104.180 MB
% 0.10/0.47 % Net memory used: 103.992 MB
%------------------------------------------------------------------------------