%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO272+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 : n006.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 12:24:48 PM UTC 2026
% Result : Theorem 0.14s 5.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 11 unt; 2 def)
% Number of atoms : 124 ( 35 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 154 ( 65 ~; 60 |; 24 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 50 ( 47 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [Vdthex] :
( ( rcircle(Vdthex)
& rcenter(vd1057,Vdthex)
& ron(vd1055,Vdthex) )
=> Vdthex = vd1063 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [Vdthex] :
( ( rcircle(Vdthex)
& rcenter(vd1057,Vdthex)
& ron(vd1055,Vdthex) )
=> Vdthex = vd1063 ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
( rcircle(vd1063)
& rcenter(vd1057,vd1063)
& ron(vd1055,vd1063) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
( rpoint(vd1056)
& vd1055 = vd1056
& rpoint(vd1058)
& vd1055 != vd1057
& vd1057 = vd1058 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,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(f110,plain,
? [Vdthex] :
( Vdthex != vd1063
& rcircle(Vdthex)
& rcenter(vd1057,Vdthex)
& ron(vd1055,Vdthex) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f111,plain,
( sK0_skl != vd1063
& rcircle(sK0_skl)
& rcenter(vd1057,sK0_skl)
& ron(vd1055,sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Vdthex,sK0_skl)],[f110]) ).
fof(f112,plain,
ron(vd1055,sK0_skl),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f113,plain,
rcenter(vd1057,sK0_skl),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f115,plain,
sK0_skl != vd1063,
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f116,plain,
ron(vd1055,vd1063),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f117,plain,
rcenter(vd1057,vd1063),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f128,plain,
vd1055 = vd1056,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f129,plain,
rpoint(vd1056),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f140,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)],[f10]) ).
fof(f141,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)],[f140]) ).
fof(f142,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)],[f141]) ).
fof(f649,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)],[f142]) ).
fof(f885,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)],[f649]) ).
fof(f886,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)],[f885]) ).
fof(f887,plain,
rpoint(vd1055),
inference(forward_demodulation,[status(thm)],[f128,f129]) ).
fof(f905,plain,
! [X0,X1,X2] :
( X1 = X0
| ~ rcenter(X2,X1)
| ~ rcenter(X2,X0)
| ~ ron(vd1055,X1)
| ~ ron(vd1055,X0) ),
inference(resolution,[status(thm)],[f886,f887]) ).
fof(f926,plain,
! [X0,X1] :
( vd1063 = X0
| ~ rcenter(X1,vd1063)
| ~ rcenter(X1,X0)
| ~ ron(vd1055,X0) ),
inference(resolution,[status(thm)],[f905,f116]) ).
fof(f928,plain,
! [X0] :
( vd1063 = X0
| ~ rcenter(vd1057,X0)
| ~ ron(vd1055,X0) ),
inference(resolution,[status(thm)],[f926,f117]) ).
fof(f930,plain,
( vd1063 = sK0_skl
| ~ ron(vd1055,sK0_skl) ),
inference(resolution,[status(thm)],[f928,f113]) ).
fof(f938,definition,
( sQ15_spl
<=> ron(vd1055,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f940,plain,
( sQ15_spl
| ~ ron(vd1055,sK0_skl) ),
inference(component_clause,[status(thm)],[f938]) ).
fof(f941,definition,
( sQ16_spl
<=> vd1063 = sK0_skl ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f942,plain,
( ~ sQ16_spl
| vd1063 = sK0_skl ),
inference(component_clause,[status(thm)],[f941]) ).
fof(f944,plain,
( sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f930,f938,f941]) ).
fof(f945,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f940,f112]) ).
fof(f946,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f945]) ).
fof(f949,plain,
( ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f942,f115]) ).
fof(f950,plain,
~ sQ16_spl,
inference(contradiction_clause,[status(thm)],[f949]) ).
fof(f951,plain,
$false,
inference(sat_refutation,[status(thm)],[f944,f946,f950]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO272+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.36 % Computer : n006.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.36 % DateTime : Sun Sep 20 14:58:48 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.38 % Drodi V4.1.1
% 0.14/5.40 % Refutation found
% 0.14/5.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.43 % Elapsed time: 0.062439 seconds
% 0.14/5.43 % CPU time: 0.200226 seconds
% 0.14/5.43 % Total memory used: 117.735 MB
% 0.14/5.43 % Net memory used: 117.369 MB
%------------------------------------------------------------------------------