%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO278+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 12:24:49 PM UTC 2026
% Result : Theorem 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 11 unt; 4 def)
% Number of atoms : 137 ( 31 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 176 ( 78 ~; 71 |; 20 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 53 ( 50 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [Vdthex] :
( ( rcircle(Vdthex)
& rcenter(vd1089,Vdthex)
& ron(vd1096,Vdthex) )
=> Vdthex = vd1102 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [Vdthex] :
( ( rcircle(Vdthex)
& rcenter(vd1089,Vdthex)
& ron(vd1096,Vdthex) )
=> Vdthex = vd1102 ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
( rcircle(vd1102)
& rcenter(vd1089,vd1102)
& ron(vd1096,vd1102) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
rpoint(vd1096),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [Vd837,Vd838,Vd842,Vd843,Vd844] :
( ( ? [Vd840] :
( rpoint(Vd840)
& Vd837 = Vd840 )
& ? [Vd841] :
( rpoint(Vd841)
& Vd838 = Vd841 )
& rcenter(Vd842,Vd843)
& rcenter(Vd842,Vd844)
& ron(Vd837,Vd843)
& ron(Vd838,Vd844)
& vf(Vd842,Vd837) = vf(Vd842,Vd838) )
=> Vd843 = Vd844 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f132,plain,
? [Vdthex] :
( Vdthex != vd1102
& rcircle(Vdthex)
& rcenter(vd1089,Vdthex)
& ron(vd1096,Vdthex) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f133,plain,
( sK0_skl != vd1102
& rcircle(sK0_skl)
& rcenter(vd1089,sK0_skl)
& ron(vd1096,sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Vdthex,sK0_skl)],[f132]) ).
fof(f134,plain,
ron(vd1096,sK0_skl),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f135,plain,
rcenter(vd1089,sK0_skl),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f137,plain,
sK0_skl != vd1102,
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f138,plain,
ron(vd1096,vd1102),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f139,plain,
rcenter(vd1089,vd1102),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f148,plain,
rpoint(vd1096),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f234,plain,
! [Vd837,Vd838,Vd842,Vd843,Vd844] :
( Vd843 = Vd844
| ! [Vd840] :
( ~ rpoint(Vd840)
| Vd837 != Vd840 )
| ! [Vd841] :
( ~ rpoint(Vd841)
| Vd838 != Vd841 )
| ~ rcenter(Vd842,Vd843)
| ~ rcenter(Vd842,Vd844)
| ~ ron(Vd837,Vd843)
| ~ ron(Vd838,Vd844)
| vf(Vd842,Vd837) != vf(Vd842,Vd838) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f235,plain,
! [Vd843,Vd844] :
( Vd843 = Vd844
| ! [Vd837] :
( ! [Vd840] :
( ~ rpoint(Vd840)
| Vd837 != Vd840 )
| ! [Vd838] :
( ! [Vd841] :
( ~ rpoint(Vd841)
| Vd838 != Vd841 )
| ! [Vd842] :
( ~ rcenter(Vd842,Vd843)
| ~ rcenter(Vd842,Vd844)
| ~ ron(Vd837,Vd843)
| ~ ron(Vd838,Vd844)
| vf(Vd842,Vd837) != vf(Vd842,Vd838) ) ) ) ),
inference(miniscoping,[status(thm)],[f234]) ).
fof(f236,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( X4 = X3
| ~ rpoint(X6)
| X1 != X6
| ~ rpoint(X5)
| X2 != X5
| ~ rcenter(X0,X4)
| ~ rcenter(X0,X3)
| ~ ron(X1,X4)
| ~ ron(X2,X3)
| vf(X0,X1) != vf(X0,X2) ),
inference(cnf_transformation,[status(thm)],[f235]) ).
fof(f729,plain,
! [X0,X1,X2,X3,X4] :
( X4 = X3
| ~ rpoint(X1)
| ~ rpoint(X2)
| ~ rcenter(X0,X4)
| ~ rcenter(X0,X3)
| ~ ron(X1,X4)
| ~ ron(X2,X3)
| vf(X0,X1) != vf(X0,X2) ),
inference(destructive_equality_resolution,[status(thm)],[f236]) ).
fof(f933,plain,
! [X0,X1,X2,X3] :
( X2 = X1
| ~ rpoint(X0)
| ~ rpoint(X0)
| ~ rcenter(X3,X2)
| ~ rcenter(X3,X1)
| ~ ron(X0,X2)
| ~ ron(X0,X1) ),
inference(equality_resolution,[status(thm)],[f729]) ).
fof(f934,plain,
! [X0,X1,X2,X3] :
( X2 = X1
| ~ rpoint(X0)
| ~ rcenter(X3,X2)
| ~ rcenter(X3,X1)
| ~ ron(X0,X2)
| ~ ron(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f933]) ).
fof(f969,plain,
! [X0,X1] :
( sK0_skl = X0
| ~ rpoint(vd1096)
| ~ rcenter(X1,sK0_skl)
| ~ rcenter(X1,X0)
| ~ ron(vd1096,X0) ),
inference(resolution,[status(thm)],[f934,f134]) ).
fof(f987,definition,
( sQ20_spl
<=> rpoint(vd1096) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f989,plain,
( sQ20_spl
| ~ rpoint(vd1096) ),
inference(component_clause,[status(thm)],[f987]) ).
fof(f991,definition,
! [X0,X1] :
( sQ21_spl
<=> ( sK0_skl = X0
| ~ rcenter(X1,sK0_skl)
| ~ rcenter(X1,X0)
| ~ ron(vd1096,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f992,plain,
! [X0,X1] :
( ~ sQ21_spl
| sK0_skl = X0
| ~ rcenter(X1,sK0_skl)
| ~ rcenter(X1,X0)
| ~ ron(vd1096,X0) ),
inference(component_clause,[status(thm)],[f991]) ).
fof(f994,plain,
( ~ sQ20_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f969,f991,f987]) ).
fof(f995,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f989,f148]) ).
fof(f996,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f995]) ).
fof(f999,plain,
! [X0] :
( ~ sQ21_spl
| sK0_skl = vd1102
| ~ rcenter(X0,sK0_skl)
| ~ rcenter(X0,vd1102) ),
inference(resolution,[status(thm)],[f992,f138]) ).
fof(f1001,definition,
! [X0] :
( sQ22_spl
<=> ( ~ rcenter(X0,sK0_skl)
| ~ rcenter(X0,vd1102) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f1002,plain,
! [X0] :
( ~ sQ22_spl
| ~ rcenter(X0,sK0_skl)
| ~ rcenter(X0,vd1102) ),
inference(component_clause,[status(thm)],[f1001]) ).
fof(f1004,definition,
( sQ23_spl
<=> sK0_skl = vd1102 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f1005,plain,
( ~ sQ23_spl
| sK0_skl = vd1102 ),
inference(component_clause,[status(thm)],[f1004]) ).
fof(f1007,plain,
( ~ sQ21_spl
| sQ23_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f999,f1001,f1004,f991]) ).
fof(f1016,plain,
( ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1005,f137]) ).
fof(f1017,plain,
~ sQ23_spl,
inference(contradiction_clause,[status(thm)],[f1016]) ).
fof(f1024,plain,
( ~ sQ22_spl
| ~ rcenter(vd1089,sK0_skl) ),
inference(resolution,[status(thm)],[f1002,f139]) ).
fof(f1025,plain,
( ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1024,f135]) ).
fof(f1026,plain,
~ sQ22_spl,
inference(contradiction_clause,[status(thm)],[f1025]) ).
fof(f1027,plain,
$false,
inference(sat_refutation,[status(thm)],[f994,f996,f1007,f1017,f1026]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO278+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.40 % Computer : n007.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 20 15:02:35 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.18/0.44 % Drodi V4.1.1
% 0.18/0.47 % Refutation found
% 0.18/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.55 % Elapsed time: 0.142165 seconds
% 0.23/0.55 % CPU time: 0.169629 seconds
% 0.23/0.55 % Total memory used: 22.394 MB
% 0.23/0.55 % Net memory used: 22.332 MB
%------------------------------------------------------------------------------