%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO030-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 41.87s 10.77s
% Output : CNFRefutation 41.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 15
% Syntax : Number of formulae : 50 ( 17 unt; 6 def)
% Number of atoms : 128 ( 15 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 148 ( 70 ~; 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 : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 65 ( 65 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X,Y,Z] :
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [U,V] : equidistant(U,V,U,V),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [U,V,W,X] :
( equidistant(W,X,V,U)
| ~ equidistant(U,V,W,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f66,hypothesis,
equidistant(u,w,u,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f67,hypothesis,
equidistant(v,w,v,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f68,hypothesis,
u != v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f69,negated_conjecture,
w != w1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f73,plain,
! [X,Y] :
( X = Y
| ! [Z] : ~ equidistant(X,Y,Z,Z) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ~ equidistant(X1,X0,X2,X2)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f77,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(f78,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ equidistant(X0,X5,X2,X6)
| equidistant(X4,X5,X7,X6)
| ~ between(X2,X3,X7)
| X0 = X1
| ~ equidistant(X1,X4,X3,X7)
| ~ equidistant(X1,X5,X3,X6)
| ~ between(X0,X1,X4)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f93,plain,
! [X0,X1] : equidistant(X0,X1,X0,X1),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f98,plain,
! [X0,X1,X2,X3] :
( ~ equidistant(X3,X2,X0,X1)
| equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f154,plain,
between(u,v,w),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f155,plain,
equidistant(u,w,u,w1),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f156,plain,
equidistant(v,w,v,w1),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f157,plain,
u != v,
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f158,plain,
w1 != w,
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f170,plain,
! [X0,X1,X2,X3,X4] :
( ~ equidistant(X0,X1,u,v)
| ~ equidistant(X0,X3,u,X4)
| equidistant(X2,X3,w,X4)
| ~ equidistant(X1,X2,v,w)
| X1 = X0
| ~ equidistant(X1,X3,v,X4)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f78,f154]) ).
fof(f180,plain,
! [X0,X1,X2] :
( ~ equidistant(v,X0,v,w)
| ~ equidistant(v,X1,v,X2)
| u = v
| ~ equidistant(u,X1,u,X2)
| ~ between(u,v,X0)
| equidistant(X0,X1,w,X2) ),
inference(resolution,[status(thm)],[f170,f93]) ).
fof(f184,definition,
( sQ1_spl
<=> v = u ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( ~ sQ1_spl
| v = u ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f188,definition,
! [X0,X1,X2] :
( sQ2_spl
<=> ( ~ equidistant(v,X0,v,w)
| ~ equidistant(v,X1,v,X2)
| ~ equidistant(u,X1,u,X2)
| ~ between(u,v,X0)
| equidistant(X0,X1,w,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f189,plain,
! [X0,X1,X2] :
( ~ sQ2_spl
| ~ equidistant(u,X0,u,X1)
| ~ between(u,v,X2)
| ~ equidistant(v,X2,v,w)
| equidistant(X2,X0,w,X1)
| ~ equidistant(v,X0,v,X1) ),
inference(component_clause,[status(thm)],[f188]) ).
fof(f191,plain,
( sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f180,f188,f184]) ).
fof(f192,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f185,f157]) ).
fof(f193,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f192]) ).
fof(f204,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ equidistant(u,X0,u,X1)
| equidistant(w,X0,w,X1)
| ~ equidistant(v,X0,v,X1)
| ~ between(u,v,w) ),
inference(resolution,[status(thm)],[f189,f93]) ).
fof(f205,definition,
( sQ3_spl
<=> between(u,v,w) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f207,plain,
( sQ3_spl
| ~ between(u,v,w) ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,definition,
! [X0,X1] :
( sQ4_spl
<=> ( ~ equidistant(u,X0,u,X1)
| equidistant(w,X0,w,X1)
| ~ equidistant(v,X0,v,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f209,plain,
! [X0,X1] :
( ~ sQ4_spl
| equidistant(w,X0,w,X1)
| ~ equidistant(v,X0,v,X1)
| ~ equidistant(u,X0,u,X1) ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f211,plain,
( ~ sQ2_spl
| sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f204,f205,f208,f188]) ).
fof(f212,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f207,f154]) ).
fof(f213,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f212]) ).
fof(f222,plain,
( ~ sQ4_spl
| equidistant(w,w,w,w1)
| ~ equidistant(v,w,v,w1) ),
inference(resolution,[status(thm)],[f209,f155]) ).
fof(f227,definition,
( sQ5_spl
<=> equidistant(v,w,v,w1) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f229,plain,
( sQ5_spl
| ~ equidistant(v,w,v,w1) ),
inference(component_clause,[status(thm)],[f227]) ).
fof(f230,definition,
( sQ6_spl
<=> equidistant(w,w,w,w1) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f231,plain,
( ~ sQ6_spl
| equidistant(w,w,w,w1) ),
inference(component_clause,[status(thm)],[f230]) ).
fof(f233,plain,
( ~ sQ4_spl
| sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f222,f227,f230,f208]) ).
fof(f242,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f229,f156]) ).
fof(f243,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f242]) ).
fof(f341,plain,
( ~ sQ6_spl
| equidistant(w,w1,w,w) ),
inference(resolution,[status(thm)],[f231,f98]) ).
fof(f349,plain,
( ~ sQ6_spl
| w1 = w ),
inference(resolution,[status(thm)],[f341,f74]) ).
fof(f350,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f349,f158]) ).
fof(f351,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f350]) ).
fof(f352,plain,
$false,
inference(sat_refutation,[status(thm)],[f191,f193,f211,f213,f233,f243,f351]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO030-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n010.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sun Sep 20 08:23:30 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.15/5.40 % Drodi V4.1.1
% 41.87/10.77 % Refutation found
% 41.87/10.77 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 41.87/10.77 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 24.36/10.81 % Elapsed time: 5.407130 seconds
% 24.36/10.81 % CPU time: 42.665189 seconds
% 24.36/10.81 % Total memory used: 233.987 MB
% 24.36/10.81 % Net memory used: 204.049 MB
%------------------------------------------------------------------------------