%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO025-3 : TPTP v9.3.1. Released v1.0.0.
% 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 12:23:49 PM UTC 2026
% Result : Unsatisfiable 65.87s 8.78s
% Output : CNFRefutation 65.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 17
% Syntax : Number of formulae : 62 ( 20 unt; 6 def)
% Number of atoms : 140 ( 16 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 145 ( 67 ~; 72 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 71 ( 71 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X,Y,Z] :
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,X1,Y1,Z,Z1,V,V1] :
( equidistant(Z,V,Z1,V1)
| X = Y
| ~ between(X1,Y1,Z1)
| ~ between(X,Y,Z)
| ~ equidistant(Y,V,Y1,V1)
| ~ equidistant(X,V,X1,V1)
| ~ equidistant(Y,Z,Y1,Z1)
| ~ equidistant(X,Y,X1,Y1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [U,V,W,X] :
( equidistant(W,X,U,V)
| ~ equidistant(U,V,W,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [U,V,W,X] :
( equidistant(V,U,X,W)
| ~ equidistant(U,V,W,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [U,V,W,X] :
( equidistant(W,X,V,U)
| ~ equidistant(U,V,W,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [U,V] : equidistant(U,U,V,V),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,hypothesis,
equidistant(u,v,u1,v1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,hypothesis,
equidistant(v,w,v1,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,hypothesis,
between(u1,v1,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
~ equidistant(u,w,u1,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,plain,
! [X,Y] :
( X = Y
| ! [Z] : ~ equidistant(X,Y,Z,Z) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f46,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f49,plain,
! [Z,Z1,V,V1] :
( equidistant(Z,V,Z1,V1)
| ! [X,Y] :
( X = Y
| ! [X1,Y1] :
( ~ between(X1,Y1,Z1)
| ~ between(X,Y,Z)
| ~ equidistant(Y,V,Y1,V1)
| ~ equidistant(X,V,X1,V1)
| ~ equidistant(Y,Z,Y1,Z1)
| ~ equidistant(X,Y,X1,Y1) ) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f50,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ between(X4,X0,X7)
| ~ equidistant(X4,X0,X5,X2)
| equidistant(X7,X1,X6,X3)
| ~ equidistant(X0,X7,X2,X6)
| ~ equidistant(X4,X1,X5,X3)
| ~ between(X5,X2,X6)
| X0 = X4
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f66,plain,
! [X0,X1,X2,X3] :
( ~ equidistant(X2,X3,X0,X1)
| equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( equidistant(X1,X0,X3,X2)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f70,plain,
! [X0,X1,X2,X3] :
( ~ equidistant(X3,X2,X0,X1)
| equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f83,plain,
! [X0,X1] : equidistant(X0,X0,X1,X1),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f84,plain,
equidistant(u,v,u1,v1),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f85,plain,
equidistant(v,w,v1,w1),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f86,plain,
between(u,v,w),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f87,plain,
between(u1,v1,w1),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f88,plain,
~ equidistant(u,w,u1,w1),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f97,plain,
~ equidistant(w,u,w1,u1),
inference(resolution,[status(thm)],[f69,f88]) ).
fof(f119,plain,
! [X0,X1,X2] :
( ~ equidistant(X2,X2,X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f66,f46]) ).
fof(f126,plain,
equidistant(u1,v1,v,u),
inference(resolution,[status(thm)],[f84,f70]) ).
fof(f190,plain,
! [X0,X1,X2,X3,X4] :
( ~ equidistant(X3,X4,v1,w1)
| ~ between(X0,X3,X4)
| ~ equidistant(X3,X1,v1,X2)
| equidistant(X4,X1,w1,X2)
| ~ equidistant(X0,X3,u1,v1)
| X0 = X3
| ~ equidistant(X0,X1,u1,X2) ),
inference(resolution,[status(thm)],[f50,f87]) ).
fof(f317,plain,
equidistant(v,u,v1,u1),
inference(resolution,[status(thm)],[f126,f70]) ).
fof(f384,plain,
! [X0,X1] :
( ~ equidistant(X1,u,v1,u1)
| ~ equidistant(X0,u,u1,u1)
| ~ equidistant(X1,w,v1,w1)
| ~ equidistant(X0,X1,u1,v1)
| ~ between(X0,X1,w)
| X0 = X1 ),
inference(resolution,[status(thm)],[f190,f97]) ).
fof(f580,definition,
( sQ5_spl
<=> u = v ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f581,plain,
( ~ sQ5_spl
| u = v ),
inference(component_clause,[status(thm)],[f580]) ).
fof(f591,definition,
( sQ8_spl
<=> u1 = v1 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f592,plain,
( ~ sQ8_spl
| v1 = u1 ),
inference(component_clause,[status(thm)],[f591]) ).
fof(f593,plain,
( sQ8_spl
| u1 != v1 ),
inference(component_clause,[status(thm)],[f591]) ).
fof(f630,plain,
( ~ sQ8_spl
| equidistant(v,w,u1,w1) ),
inference(backward_demodulation,[status(thm)],[f592,f85]) ).
fof(f696,plain,
( ~ sQ5_spl
| equidistant(u,u,u1,v1) ),
inference(backward_demodulation,[status(thm)],[f581,f84]) ).
fof(f940,plain,
( ~ sQ5_spl
| u1 = v1 ),
inference(resolution,[status(thm)],[f696,f119]) ).
fof(f2404,definition,
( sQ96_spl
<=> equidistant(u,v,u1,v1) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f2406,plain,
( sQ96_spl
| ~ equidistant(u,v,u1,v1) ),
inference(component_clause,[status(thm)],[f2404]) ).
fof(f2407,definition,
( sQ97_spl
<=> equidistant(v,w,v1,w1) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f2409,plain,
( sQ97_spl
| ~ equidistant(v,w,v1,w1) ),
inference(component_clause,[status(thm)],[f2407]) ).
fof(f2552,plain,
( ~ sQ8_spl
| ~ sQ5_spl
| equidistant(u,w,u1,w1) ),
inference(backward_demodulation,[status(thm)],[f581,f630]) ).
fof(f2562,plain,
( ~ sQ8_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2552,f88]) ).
fof(f2563,plain,
( ~ sQ8_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f2562]) ).
fof(f2605,plain,
( ~ sQ5_spl
| sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f940,f593]) ).
fof(f2606,plain,
( ~ sQ5_spl
| sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f2605]) ).
fof(f2891,plain,
( sQ96_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2406,f84]) ).
fof(f2892,plain,
sQ96_spl,
inference(contradiction_clause,[status(thm)],[f2891]) ).
fof(f3564,plain,
( sQ97_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2409,f85]) ).
fof(f3565,plain,
sQ97_spl,
inference(contradiction_clause,[status(thm)],[f3564]) ).
fof(f3575,plain,
( ~ equidistant(v,u,v1,u1)
| ~ equidistant(u,u,u1,u1)
| ~ equidistant(v,w,v1,w1)
| ~ equidistant(u,v,u1,v1)
| u = v ),
inference(resolution,[status(thm)],[f384,f86]) ).
fof(f3581,definition,
( sQ162_spl
<=> equidistant(u,u,u1,u1) ),
introduced(definition,[new_symbols(definition,[sQ162_spl])],[split_symbol_definition]) ).
fof(f3583,plain,
( sQ162_spl
| ~ equidistant(u,u,u1,u1) ),
inference(component_clause,[status(thm)],[f3581]) ).
fof(f3584,definition,
( sQ163_spl
<=> equidistant(v,u,v1,u1) ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f3586,plain,
( sQ163_spl
| ~ equidistant(v,u,v1,u1) ),
inference(component_clause,[status(thm)],[f3584]) ).
fof(f3587,plain,
( ~ sQ163_spl
| ~ sQ162_spl
| ~ sQ97_spl
| ~ sQ96_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f3575,f580,f2404,f2407,f3581,f3584]) ).
fof(f3598,plain,
( sQ162_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3583,f83]) ).
fof(f3599,plain,
sQ162_spl,
inference(contradiction_clause,[status(thm)],[f3598]) ).
fof(f3600,plain,
( sQ163_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3586,f317]) ).
fof(f3601,plain,
sQ163_spl,
inference(contradiction_clause,[status(thm)],[f3600]) ).
fof(f3602,plain,
$false,
inference(sat_refutation,[status(thm)],[f2563,f2606,f2892,f3565,f3587,f3599,f3601]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO025-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 08:27:21 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 65.87/8.78 % Refutation found
% 65.87/8.78 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 65.87/8.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 65.87/8.80 % Elapsed time: 8.419623 seconds
% 65.87/8.80 % CPU time: 66.579552 seconds
% 65.87/8.80 % Total memory used: 208.511 MB
% 65.87/8.80 % Net memory used: 183.377 MB
%------------------------------------------------------------------------------