%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO033-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 162.69s 35.88s
% Output : CNFRefutation 162.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 17 unt; 0 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 105 ( 54 ~; 51 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 56 ( 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f37,axiom,
! [U,V,U1,V1,W,W1] :
( equidistant(U,W,U1,W1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f68,hypothesis,
equidistant(u,v,u1,v1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f69,hypothesis,
equidistant(v,w,v1,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f70,hypothesis,
equidistant(u,x,u1,x1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f71,hypothesis,
equidistant(w,x,w1,x1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f72,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f73,hypothesis,
between(u1,v1,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f74,negated_conjecture,
~ equidistant(v,x,v1,x1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f117,plain,
! [U,U1,W,W1] :
( equidistant(U,W,U1,W1)
| ! [V1] :
( ~ between(U1,V1,W1)
| ! [V] :
( ~ between(U,V,W)
| ~ equidistant(V,W,V1,W1)
| ~ equidistant(U,V,U1,V1) ) ) ),
inference(miniscoping,[status(thm)],[f37]) ).
fof(f118,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ between(X5,X3,X4)
| ~ equidistant(X0,X1,X5,X3)
| equidistant(X0,X2,X5,X4)
| ~ equidistant(X1,X2,X3,X4)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f161,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(f162,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ between(X0,X6,X4)
| ~ equidistant(X4,X1,X5,X3)
| ~ between(X2,X7,X5)
| ~ equidistant(X0,X6,X2,X7)
| equidistant(X6,X1,X7,X3)
| ~ equidistant(X0,X4,X2,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f161]) ).
fof(f165,plain,
equidistant(u,v,u1,v1),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f166,plain,
equidistant(v,w,v1,w1),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f167,plain,
equidistant(u,x,u1,x1),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f168,plain,
equidistant(w,x,w1,x1),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f169,plain,
between(u,v,w),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f170,plain,
between(u1,v1,w1),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f171,plain,
~ equidistant(v,x,v1,x1),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f242,plain,
! [X0,X1,X2] :
( ~ equidistant(X0,X2,u1,v1)
| ~ between(X0,X2,X1)
| ~ equidistant(X2,X1,v1,w1)
| equidistant(X0,X1,u1,w1) ),
inference(resolution,[status(thm)],[f170,f118]) ).
fof(f248,plain,
! [X0,X1,X2,X3,X4] :
( ~ equidistant(X0,X2,u1,w1)
| ~ equidistant(X0,X1,u1,v1)
| ~ equidistant(X0,X3,u1,X4)
| equidistant(X1,X3,v1,X4)
| ~ equidistant(X2,X3,w1,X4)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f170,f162]) ).
fof(f766,plain,
( ~ equidistant(u,v,u1,v1)
| ~ equidistant(v,w,v1,w1)
| equidistant(u,w,u1,w1) ),
inference(resolution,[status(thm)],[f242,f169]) ).
fof(f772,plain,
( ~ equidistant(u,v,u1,v1)
| equidistant(u,w,u1,w1) ),
inference(forward_subsumption_resolution,[status(thm)],[f766,f166]) ).
fof(f784,plain,
! [X0,X1] :
( ~ equidistant(u,w,u1,w1)
| ~ equidistant(u,v,u1,v1)
| ~ equidistant(u,X0,u1,X1)
| equidistant(v,X0,v1,X1)
| ~ equidistant(w,X0,w1,X1) ),
inference(resolution,[status(thm)],[f248,f169]) ).
fof(f791,plain,
! [X0,X1] :
( equidistant(v,X0,v1,X1)
| ~ equidistant(w,X0,w1,X1)
| ~ equidistant(u,X0,u1,X1)
| ~ equidistant(u,w,u1,w1) ),
inference(forward_subsumption_resolution,[status(thm)],[f784,f165]) ).
fof(f9495,plain,
equidistant(u,w,u1,w1),
inference(forward_subsumption_resolution,[status(thm)],[f772,f165]) ).
fof(f10058,plain,
! [X0,X1] :
( ~ equidistant(w,X0,w1,X1)
| ~ equidistant(u,X0,u1,X1)
| equidistant(v,X0,v1,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f791,f9495]) ).
fof(f10059,plain,
( ~ equidistant(u,x,u1,x1)
| equidistant(v,x,v1,x1) ),
inference(resolution,[status(thm)],[f10058,f168]) ).
fof(f10075,plain,
~ equidistant(u,x,u1,x1),
inference(forward_subsumption_resolution,[status(thm)],[f10059,f171]) ).
fof(f10088,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f10075,f167]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO033-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/15.32 % Computer : n012.cluster.edu
% 0.03/15.32 % Model : x86_64 x86_64
% 0.03/15.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/15.32 % Memory : 8046.5625MB
% 0.03/15.32 % OS : Linux 6.8.0-71-generic
% 0.03/15.32 % CPULimit : 300
% 0.03/15.33 % WCLimit : 300
% 0.03/15.33 % DateTime : Sun Sep 20 08:29:10 UTC 2026
% 0.03/15.33 % CPUTime :
% 0.03/15.33 % Drodi V4.1.1
% 162.69/35.88 % Refutation found
% 162.69/35.88 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 162.69/35.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 27.53/35.92 % Elapsed time: 20.578762 seconds
% 27.53/35.92 % CPU time: 163.622716 seconds
% 27.53/35.92 % Total memory used: 333.452 MB
% 27.53/35.92 % Net memory used: 277.826 MB
%------------------------------------------------------------------------------