%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO032-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 12:23:50 PM UTC 2026
% Result : Unsatisfiable 157.23s 20.29s
% Output : CNFRefutation 157.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 12
% Syntax : Number of formulae : 38 ( 17 unt; 5 def)
% Number of atoms : 87 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 93 ( 44 ~; 44 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 6 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 34 ( 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f36,axiom,
! [U,V] : equidistant(U,U,V,V),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,axiom,
! [U,V,U1,V1,W,W1,X,X1] :
( equidistant(V,X,V1,X1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f67,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f68,hypothesis,
between(u1,v1,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f69,hypothesis,
equidistant(u,v,u1,v1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f70,hypothesis,
equidistant(u,w,u1,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f71,negated_conjecture,
~ equidistant(v,w,v1,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f113,plain,
! [X0,X1] : equidistant(X0,X0,X1,X1),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f158,plain,
! [V,V1,X,X1] :
( equidistant(V,X,V1,X1)
| ! [U1,W1] :
( ~ between(U1,V1,W1)
| ! [U,W] :
( ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) ) ) ),
inference(miniscoping,[status(thm)],[f66]) ).
fof(f159,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( equidistant(X1,X6,X3,X7)
| ~ between(X2,X3,X5)
| ~ between(X0,X1,X4)
| ~ equidistant(X4,X6,X5,X7)
| ~ equidistant(X0,X6,X2,X7)
| ~ equidistant(X0,X4,X2,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f158]) ).
fof(f160,plain,
between(u,v,w),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f161,plain,
between(u1,v1,w1),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f162,plain,
equidistant(u,v,u1,v1),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f163,plain,
equidistant(u,w,u1,w1),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f164,plain,
~ equidistant(v,w,v1,w1),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f302,definition,
( sQ18_spl
<=> equidistant(w,w,w1,w1) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f304,plain,
( sQ18_spl
| ~ equidistant(w,w,w1,w1) ),
inference(component_clause,[status(thm)],[f302]) ).
fof(f1234,plain,
! [X0,X1] :
( equidistant(X0,w,X1,w1)
| ~ between(u1,X1,w1)
| ~ between(u,X0,w)
| ~ equidistant(w,w,w1,w1)
| ~ equidistant(u,X0,u1,X1) ),
inference(resolution,[status(thm)],[f159,f163]) ).
fof(f1437,definition,
! [X0,X1] :
( sQ57_spl
<=> ( equidistant(X0,w,X1,w1)
| ~ between(u1,X1,w1)
| ~ between(u,X0,w)
| ~ equidistant(u,X0,u1,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f1438,plain,
! [X0,X1] :
( ~ sQ57_spl
| equidistant(X0,w,X1,w1)
| ~ between(u1,X1,w1)
| ~ between(u,X0,w)
| ~ equidistant(u,X0,u1,X1) ),
inference(component_clause,[status(thm)],[f1437]) ).
fof(f1440,plain,
( ~ sQ18_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f1234,f1437,f302]) ).
fof(f1561,plain,
( sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f304,f113]) ).
fof(f1562,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f1561]) ).
fof(f3221,definition,
( sQ108_spl
<=> equidistant(v,w,v1,w1) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f3222,plain,
( ~ sQ108_spl
| equidistant(v,w,v1,w1) ),
inference(component_clause,[status(thm)],[f3221]) ).
fof(f3258,plain,
( ~ sQ108_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3222,f164]) ).
fof(f3259,plain,
~ sQ108_spl,
inference(contradiction_clause,[status(thm)],[f3258]) ).
fof(f16038,plain,
( ~ sQ57_spl
| equidistant(v,w,v1,w1)
| ~ between(u1,v1,w1)
| ~ between(u,v,w) ),
inference(resolution,[status(thm)],[f1438,f162]) ).
fof(f16073,definition,
( sQ595_spl
<=> between(u,v,w) ),
introduced(definition,[new_symbols(definition,[sQ595_spl])],[split_symbol_definition]) ).
fof(f16075,plain,
( sQ595_spl
| ~ between(u,v,w) ),
inference(component_clause,[status(thm)],[f16073]) ).
fof(f16076,definition,
( sQ596_spl
<=> between(u1,v1,w1) ),
introduced(definition,[new_symbols(definition,[sQ596_spl])],[split_symbol_definition]) ).
fof(f16078,plain,
( sQ596_spl
| ~ between(u1,v1,w1) ),
inference(component_clause,[status(thm)],[f16076]) ).
fof(f16079,plain,
( ~ sQ57_spl
| sQ108_spl
| ~ sQ596_spl
| ~ sQ595_spl ),
inference(split_clause,[status(thm)],[f16038,f16073,f16076,f3221,f1437]) ).
fof(f16101,plain,
( sQ595_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f16075,f160]) ).
fof(f16102,plain,
sQ595_spl,
inference(contradiction_clause,[status(thm)],[f16101]) ).
fof(f16103,plain,
( sQ596_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f16078,f161]) ).
fof(f16104,plain,
sQ596_spl,
inference(contradiction_clause,[status(thm)],[f16103]) ).
fof(f16105,plain,
$false,
inference(sat_refutation,[status(thm)],[f1440,f1562,f3259,f16079,f16102,f16104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO032-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.36 % Computer : n016.cluster.edu
% 0.02/0.36 % Model : x86_64 x86_64
% 0.02/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.36 % Memory : 8046.5625MB
% 0.02/0.36 % OS : Linux 6.8.0-71-generic
% 0.02/0.36 % CPULimit : 300
% 0.02/0.36 % WCLimit : 300
% 0.02/0.36 % DateTime : Sun Sep 20 08:29:07 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.37 % Drodi V4.1.1
% 157.23/20.29 % Refutation found
% 157.23/20.29 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 157.23/20.29 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.06/20.31 % Elapsed time: 19.932825 seconds
% 9.06/20.31 % CPU time: 158.004554 seconds
% 9.06/20.31 % Total memory used: 263.726 MB
% 9.06/20.31 % Net memory used: 223.770 MB
%------------------------------------------------------------------------------