%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO299+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 : n015.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 12:24:52 PM UTC 2026
% Result : Theorem 0.12s 0.41s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 43 ( 21 unt; 3 def)
% Number of atoms : 150 ( 65 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 159 ( 52 ~; 38 |; 65 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 15 con; 0-3 aty)
% Number of variables : 39 ( 22 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
vf(vd1185,vd1187) = vplus(vf(vd1185,vd1201),vf(vd1201,vd1187)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
vf(vd1185,vd1187) != vplus(vf(vd1185,vd1201),vf(vd1201,vd1187)),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
rR(vd1201,vd1185,vd1187),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [Vd828,Vd829,Vd830] :
( ( ? [Vd832] :
( rpoint(Vd832)
& Vd828 = Vd832 )
& ? [Vd833] :
( rpoint(Vd833)
& Vd829 = Vd833 )
& ? [Vd834] :
( rpoint(Vd834)
& Vd830 = Vd834 )
& rR(Vd829,Vd828,Vd830) )
=> vplus(vf(Vd828,Vd829),vf(Vd829,Vd830)) = vf(Vd828,Vd830) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
? [Vd1205] :
( rpoint(Vd1205)
& vd1201 = Vd1205 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
( ? [Vd1182] :
( rpoint(Vd1182)
& vd1178 = Vd1182 )
& ? [Vd1183] :
( rpoint(Vd1183)
& vd1179 = Vd1183 )
& ? [Vd1184] :
( rpoint(Vd1184)
& vd1180 = Vd1184 )
& vd1178 != vd1179
& vd1178 != vd1180
& vd1179 != vd1180
& ? [Vd1189] :
( rpoint(Vd1189)
& vd1185 = Vd1189 )
& ? [Vd1190] :
( rpoint(Vd1190)
& vd1186 = Vd1190 )
& ? [Vd1191] :
( rpoint(Vd1191)
& vd1187 = Vd1191 )
& vf(vd1178,vd1179) = vf(vd1185,vd1186)
& vf(vd1178,vd1180) = vf(vd1185,vd1187)
& vangle(vd1179,vd1178,vd1180) = vangle(vd1186,vd1185,vd1187)
& ~ ? [Vd1195] :
( rline(Vd1195)
& ron(vd1185,Vd1195)
& ron(vd1186,Vd1195)
& ron(vd1187,Vd1195) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f82,axiom,
vf(vd1199,vd1201) = vf(vd1185,vd1187),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f162,plain,
vf(vd1185,vd1187) != vplus(vf(vd1185,vd1201),vf(vd1201,vd1187)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f163,plain,
rR(vd1201,vd1185,vd1187),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f168,plain,
! [Vd828,Vd829,Vd830] :
( vplus(vf(Vd828,Vd829),vf(Vd829,Vd830)) = vf(Vd828,Vd830)
| ! [Vd832] :
( ~ rpoint(Vd832)
| Vd828 != Vd832 )
| ! [Vd833] :
( ~ rpoint(Vd833)
| Vd829 != Vd833 )
| ! [Vd834] :
( ~ rpoint(Vd834)
| Vd830 != Vd834 )
| ~ rR(Vd829,Vd828,Vd830) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f169,plain,
! [X0,X1,X2,X3,X4,X5] :
( vplus(vf(X1,X0),vf(X0,X2)) = vf(X1,X2)
| ~ rpoint(X5)
| X1 != X5
| ~ rpoint(X4)
| X0 != X4
| ~ rpoint(X3)
| X2 != X3
| ~ rR(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f168]) ).
fof(f188,plain,
( rpoint(sK0_skl)
& vd1201 = sK0_skl ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Vd1205,sK0_skl)],[f22]) ).
fof(f189,plain,
vd1201 = sK0_skl,
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f190,plain,
rpoint(sK0_skl),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f196,plain,
( ? [Vd1182] :
( rpoint(Vd1182)
& vd1178 = Vd1182 )
& ? [Vd1183] :
( rpoint(Vd1183)
& vd1179 = Vd1183 )
& ? [Vd1184] :
( rpoint(Vd1184)
& vd1180 = Vd1184 )
& vd1178 != vd1179
& vd1178 != vd1180
& vd1179 != vd1180
& ? [Vd1189] :
( rpoint(Vd1189)
& vd1185 = Vd1189 )
& ? [Vd1190] :
( rpoint(Vd1190)
& vd1186 = Vd1190 )
& ? [Vd1191] :
( rpoint(Vd1191)
& vd1187 = Vd1191 )
& vf(vd1178,vd1179) = vf(vd1185,vd1186)
& vf(vd1178,vd1180) = vf(vd1185,vd1187)
& vangle(vd1179,vd1178,vd1180) = vangle(vd1186,vd1185,vd1187)
& ! [Vd1195] :
( ~ rline(Vd1195)
| ~ ron(vd1185,Vd1195)
| ~ ron(vd1186,Vd1195)
| ~ ron(vd1187,Vd1195) ) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f197,plain,
( rpoint(sK7_skl)
& vd1178 = sK7_skl
& rpoint(sK6_skl)
& vd1179 = sK6_skl
& rpoint(sK5_skl)
& vd1180 = sK5_skl
& vd1178 != vd1179
& vd1178 != vd1180
& vd1179 != vd1180
& rpoint(sK4_skl)
& vd1185 = sK4_skl
& rpoint(sK3_skl)
& vd1186 = sK3_skl
& rpoint(sK2_skl)
& vd1187 = sK2_skl
& vf(vd1178,vd1179) = vf(vd1185,vd1186)
& vf(vd1178,vd1180) = vf(vd1185,vd1187)
& vangle(vd1179,vd1178,vd1180) = vangle(vd1186,vd1185,vd1187)
& ! [Vd1195] :
( ~ rline(Vd1195)
| ~ ron(vd1185,Vd1195)
| ~ ron(vd1186,Vd1195)
| ~ ron(vd1187,Vd1195) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl,sK5_skl,sK6_skl,sK7_skl]),skolemize(Vd1191,sK2_skl),skolemize(Vd1190,sK3_skl),skolemize(Vd1189,sK4_skl),skolemize(Vd1184,sK5_skl),skolemize(Vd1183,sK6_skl),skolemize(Vd1182,sK7_skl)],[f196]) ).
fof(f202,plain,
vd1187 = sK2_skl,
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f203,plain,
rpoint(sK2_skl),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f206,plain,
vd1185 = sK4_skl,
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f207,plain,
rpoint(sK4_skl),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f351,plain,
vf(vd1199,vd1201) = vf(vd1185,vd1187),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f807,plain,
! [X0,X1,X2] :
( vplus(vf(X1,X0),vf(X0,X2)) = vf(X1,X2)
| ~ rpoint(X1)
| ~ rpoint(X0)
| ~ rpoint(X2)
| ~ rR(X0,X1,X2) ),
inference(destructive_equality_resolution,[status(thm)],[f169]) ).
fof(f1028,plain,
vf(vd1199,vd1201) != vplus(vf(vd1185,vd1201),vf(vd1201,vd1187)),
inference(backward_demodulation,[status(thm)],[f351,f162]) ).
fof(f1041,plain,
rpoint(vd1201),
inference(forward_demodulation,[status(thm)],[f189,f190]) ).
fof(f1047,plain,
rpoint(vd1187),
inference(forward_demodulation,[status(thm)],[f202,f203]) ).
fof(f1048,plain,
! [X0,X1] :
( vplus(vf(X1,X0),vf(X0,vd1187)) = vf(X1,vd1187)
| ~ rpoint(X1)
| ~ rpoint(X0)
| ~ rR(X0,X1,vd1187) ),
inference(resolution,[status(thm)],[f1047,f807]) ).
fof(f1106,plain,
( vplus(vf(vd1185,vd1201),vf(vd1201,vd1187)) = vf(vd1185,vd1187)
| ~ rpoint(vd1185)
| ~ rpoint(vd1201) ),
inference(resolution,[status(thm)],[f1048,f163]) ).
fof(f1107,definition,
( sQ27_spl
<=> rpoint(vd1201) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f1109,plain,
( sQ27_spl
| ~ rpoint(vd1201) ),
inference(component_clause,[status(thm)],[f1107]) ).
fof(f1110,definition,
( sQ28_spl
<=> rpoint(vd1185) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f1112,plain,
( sQ28_spl
| ~ rpoint(vd1185) ),
inference(component_clause,[status(thm)],[f1110]) ).
fof(f1113,definition,
( sQ29_spl
<=> vplus(vf(vd1185,vd1201),vf(vd1201,vd1187)) = vf(vd1185,vd1187) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f1114,plain,
( ~ sQ29_spl
| vplus(vf(vd1185,vd1201),vf(vd1201,vd1187)) = vf(vd1185,vd1187) ),
inference(component_clause,[status(thm)],[f1113]) ).
fof(f1116,plain,
( sQ29_spl
| ~ sQ28_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f1106,f1107,f1110,f1113]) ).
fof(f1117,plain,
( ~ sQ29_spl
| vplus(vf(vd1185,vd1201),vf(vd1201,vd1187)) = vf(vd1199,vd1201) ),
inference(forward_demodulation,[status(thm)],[f351,f1114]) ).
fof(f1118,plain,
( ~ sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1117,f1028]) ).
fof(f1119,plain,
~ sQ29_spl,
inference(contradiction_clause,[status(thm)],[f1118]) ).
fof(f1120,plain,
( sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1109,f1041]) ).
fof(f1121,plain,
sQ27_spl,
inference(contradiction_clause,[status(thm)],[f1120]) ).
fof(f1128,plain,
rpoint(vd1185),
inference(forward_demodulation,[status(thm)],[f206,f207]) ).
fof(f1129,plain,
( sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1128,f1112]) ).
fof(f1130,plain,
sQ28_spl,
inference(contradiction_clause,[status(thm)],[f1129]) ).
fof(f1131,plain,
$false,
inference(sat_refutation,[status(thm)],[f1116,f1119,f1121,f1130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO299+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n015.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 15:19:20 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.38 % Drodi V4.1.1
% 0.12/0.41 % Refutation found
% 0.12/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.44 % Elapsed time: 0.083542 seconds
% 0.12/0.44 % CPU time: 0.304779 seconds
% 0.12/0.44 % Total memory used: 66.444 MB
% 0.12/0.44 % Net memory used: 66.033 MB
%------------------------------------------------------------------------------