%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO275+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 16 unt; 4 def)
% Number of atoms : 150 ( 37 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 180 ( 78 ~; 71 |; 24 &)
% ( 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 : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 55 ( 50 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [Vdthex] :
( ( rcircle(Vdthex)
& rcenter(vd1080,Vdthex)
& ron(vd1081,Vdthex) )
=> Vdthex = vd1095 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [Vdthex] :
( ( rcircle(Vdthex)
& rcenter(vd1080,Vdthex)
& ron(vd1081,Vdthex) )
=> Vdthex = vd1095 ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
( rcircle(vd1095)
& rcenter(vd1080,vd1095)
& ron(vd1081,vd1095) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
? [Vd1084] :
( rpoint(Vd1084)
& vd1081 = Vd1084 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
? [Vd1083] :
( rpoint(Vd1083)
& vd1080 = Vd1083 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f107,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/sandbox/benchmark/theBenchmark.p') ).
fof(f122,plain,
? [Vdthex] :
( Vdthex != vd1095
& rcircle(Vdthex)
& rcenter(vd1080,Vdthex)
& ron(vd1081,Vdthex) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f123,plain,
( sK0_skl != vd1095
& rcircle(sK0_skl)
& rcenter(vd1080,sK0_skl)
& ron(vd1081,sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Vdthex,sK0_skl)],[f122]) ).
fof(f124,plain,
ron(vd1081,sK0_skl),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f125,plain,
rcenter(vd1080,sK0_skl),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f127,plain,
sK0_skl != vd1095,
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f128,plain,
ron(vd1081,vd1095),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f129,plain,
rcenter(vd1080,vd1095),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f138,plain,
( rpoint(sK1_skl)
& vd1081 = sK1_skl ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(Vd1084,sK1_skl)],[f8]) ).
fof(f139,plain,
vd1081 = sK1_skl,
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f140,plain,
rpoint(sK1_skl),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f141,plain,
( rpoint(sK2_skl)
& vd1080 = sK2_skl ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Vd1083,sK2_skl)],[f9]) ).
fof(f142,plain,
vd1080 = sK2_skl,
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f558,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)],[f107]) ).
fof(f559,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)],[f558]) ).
fof(f560,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)],[f559]) ).
fof(f858,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)],[f560]) ).
fof(f923,plain,
ron(sK1_skl,vd1095),
inference(backward_demodulation,[status(thm)],[f139,f128]) ).
fof(f924,plain,
ron(sK1_skl,sK0_skl),
inference(backward_demodulation,[status(thm)],[f139,f124]) ).
fof(f929,plain,
rcenter(sK2_skl,vd1095),
inference(backward_demodulation,[status(thm)],[f142,f129]) ).
fof(f930,plain,
rcenter(sK2_skl,sK0_skl),
inference(backward_demodulation,[status(thm)],[f142,f125]) ).
fof(f950,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)],[f858]) ).
fof(f953,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)],[f950]) ).
fof(f973,plain,
! [X0,X1] :
( sK0_skl = X0
| ~ rpoint(sK1_skl)
| ~ rcenter(X1,sK0_skl)
| ~ rcenter(X1,X0)
| ~ ron(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f953,f924]) ).
fof(f979,definition,
( sQ18_spl
<=> rpoint(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f981,plain,
( sQ18_spl
| ~ rpoint(sK1_skl) ),
inference(component_clause,[status(thm)],[f979]) ).
fof(f983,definition,
! [X0,X1] :
( sQ19_spl
<=> ( sK0_skl = X0
| ~ rcenter(X1,sK0_skl)
| ~ rcenter(X1,X0)
| ~ ron(sK1_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f984,plain,
! [X0,X1] :
( ~ sQ19_spl
| sK0_skl = X0
| ~ rcenter(X1,sK0_skl)
| ~ rcenter(X1,X0)
| ~ ron(sK1_skl,X0) ),
inference(component_clause,[status(thm)],[f983]) ).
fof(f986,plain,
( ~ sQ18_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f973,f983,f979]) ).
fof(f1001,plain,
( sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f981,f140]) ).
fof(f1002,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f1001]) ).
fof(f1101,plain,
! [X0] :
( ~ sQ19_spl
| sK0_skl = vd1095
| ~ rcenter(X0,sK0_skl)
| ~ rcenter(X0,vd1095) ),
inference(resolution,[status(thm)],[f984,f923]) ).
fof(f1104,definition,
! [X0] :
( sQ40_spl
<=> ( ~ rcenter(X0,sK0_skl)
| ~ rcenter(X0,vd1095) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f1105,plain,
! [X0] :
( ~ sQ40_spl
| ~ rcenter(X0,sK0_skl)
| ~ rcenter(X0,vd1095) ),
inference(component_clause,[status(thm)],[f1104]) ).
fof(f1107,definition,
( sQ41_spl
<=> sK0_skl = vd1095 ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f1108,plain,
( ~ sQ41_spl
| sK0_skl = vd1095 ),
inference(component_clause,[status(thm)],[f1107]) ).
fof(f1110,plain,
( ~ sQ19_spl
| sQ41_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f1101,f1104,f1107,f983]) ).
fof(f1126,plain,
( ~ sQ40_spl
| ~ rcenter(sK2_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f1105,f929]) ).
fof(f1127,plain,
( ~ sQ40_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1126,f930]) ).
fof(f1128,plain,
~ sQ40_spl,
inference(contradiction_clause,[status(thm)],[f1127]) ).
fof(f1129,plain,
( ~ sQ41_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1108,f127]) ).
fof(f1130,plain,
~ sQ41_spl,
inference(contradiction_clause,[status(thm)],[f1129]) ).
fof(f1131,plain,
$false,
inference(sat_refutation,[status(thm)],[f986,f1002,f1110,f1128,f1130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO275+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n013.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sun Sep 20 15:00:35 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.38 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.46 % Elapsed time: 0.100682 seconds
% 0.13/0.46 % CPU time: 0.144692 seconds
% 0.13/0.46 % Total memory used: 18.895 MB
% 0.13/0.46 % Net memory used: 18.788 MB
%------------------------------------------------------------------------------