%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO308+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 12:24:53 PM UTC 2026
% Result : Theorem 0.14s 5.45s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 14
% Syntax : Number of formulae : 64 ( 37 unt; 0 def)
% Number of atoms : 354 ( 108 equ)
% Maximal formula atoms : 26 ( 5 avg)
% Number of connectives : 524 ( 234 ~; 234 |; 54 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 41 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-3 aty)
% Number of variables : 105 ( 92 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
vangle(vd1288,vd1287,vd1289) = vangle(vd1299,vd1287,vd1289),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
vangle(vd1288,vd1287,vd1289) != vangle(vd1299,vd1287,vd1289),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f5,axiom,
~ rR(vd1287,vd1288,vd1299),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
( ? [Vd1291] :
( rpoint(Vd1291)
& vd1287 = Vd1291 )
& ? [Vd1292] :
( rpoint(Vd1292)
& vd1288 = Vd1292 )
& ? [Vd1293] :
( rpoint(Vd1293)
& vd1289 = Vd1293 )
& vd1287 != vd1288
& vd1287 != vd1289
& vd1288 != vd1289
& vf(vd1287,vd1288) = vf(vd1287,vd1289) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [Vd908,Vd909,Vd910,Vd911,Vd912,Vd919,Vd920] :
( ( ? [Vd914] :
( rpoint(Vd914)
& Vd908 = Vd914 )
& ? [Vd915] :
( rpoint(Vd915)
& Vd909 = Vd915 )
& ? [Vd916] :
( rpoint(Vd916)
& Vd910 = Vd916 )
& ? [Vd917] :
( rpoint(Vd917)
& Vd911 = Vd917 )
& ? [Vd918] :
( rpoint(Vd918)
& Vd912 = Vd918 )
& ? [Vd922] :
( rline(Vd922)
& Vd919 = Vd922 )
& ? [Vd923] :
( rline(Vd923)
& Vd920 = Vd923 )
& ron(Vd908,Vd919)
& ron(Vd909,Vd919)
& ron(Vd911,Vd919)
& ron(Vd910,Vd920)
& ron(Vd912,Vd920)
& Vd909 != Vd908
& Vd910 != Vd908
& Vd911 != Vd908
& Vd912 != Vd908
& ~ rR(Vd908,Vd909,Vd911)
& ~ rR(Vd908,Vd910,Vd912) )
=> vangle(Vd909,Vd908,Vd910) = vangle(Vd911,Vd908,Vd912) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [Vd340,Vd341,Vd342] :
( ( ? [Vd344] :
( rpoint(Vd344)
& Vd340 = Vd344 )
& ? [Vd345] :
( rpoint(Vd345)
& Vd341 = Vd345 )
& ? [Vd346] :
( rpoint(Vd346)
& Vd342 = Vd346 )
& rR(Vd341,Vd340,Vd342) )
=> ( rR(Vd341,Vd342,Vd340)
& Vd340 != Vd341
& Vd340 != Vd342
& ~ rR(Vd340,Vd341,Vd342) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
vd1299 = vd1300,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
rpoint(vd1300),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
vd1299 != vd1287,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
ron(vd1299,vd1295),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
ron(vd1289,vd1297),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
rline(vd1297),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
ron(vd1288,vd1295),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
ron(vd1287,vd1295),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
rline(vd1295),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f149,plain,
vangle(vd1288,vd1287,vd1289) != vangle(vd1299,vd1287,vd1289),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f152,plain,
~ rR(vd1287,vd1288,vd1299),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f159,plain,
( rpoint(sK2_skl)
& vd1287 = sK2_skl
& rpoint(sK1_skl)
& vd1288 = sK1_skl
& rpoint(sK0_skl)
& vd1289 = sK0_skl
& vd1287 != vd1288
& vd1287 != vd1289
& vd1288 != vd1289
& vf(vd1287,vd1288) = vf(vd1287,vd1289) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(Vd1293,sK0_skl),skolemize(Vd1292,sK1_skl),skolemize(Vd1291,sK2_skl)],[f9]) ).
fof(f162,plain,
vd1287 != vd1289,
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f163,plain,
vd1287 != vd1288,
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f164,plain,
vd1289 = sK0_skl,
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f165,plain,
rpoint(sK0_skl),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f166,plain,
vd1288 = sK1_skl,
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f167,plain,
rpoint(sK1_skl),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f168,plain,
vd1287 = sK2_skl,
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f169,plain,
rpoint(sK2_skl),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f170,plain,
! [Vd908,Vd909,Vd910,Vd911,Vd912,Vd919,Vd920] :
( vangle(Vd909,Vd908,Vd910) = vangle(Vd911,Vd908,Vd912)
| ! [Vd914] :
( ~ rpoint(Vd914)
| Vd908 != Vd914 )
| ! [Vd915] :
( ~ rpoint(Vd915)
| Vd909 != Vd915 )
| ! [Vd916] :
( ~ rpoint(Vd916)
| Vd910 != Vd916 )
| ! [Vd917] :
( ~ rpoint(Vd917)
| Vd911 != Vd917 )
| ! [Vd918] :
( ~ rpoint(Vd918)
| Vd912 != Vd918 )
| ! [Vd922] :
( ~ rline(Vd922)
| Vd919 != Vd922 )
| ! [Vd923] :
( ~ rline(Vd923)
| Vd920 != Vd923 )
| ~ ron(Vd908,Vd919)
| ~ ron(Vd909,Vd919)
| ~ ron(Vd911,Vd919)
| ~ ron(Vd910,Vd920)
| ~ ron(Vd912,Vd920)
| Vd909 = Vd908
| Vd910 = Vd908
| Vd911 = Vd908
| Vd912 = Vd908
| rR(Vd908,Vd909,Vd911)
| rR(Vd908,Vd910,Vd912) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f171,plain,
! [Vd908,Vd909,Vd910,Vd911,Vd912] :
( vangle(Vd909,Vd908,Vd910) = vangle(Vd911,Vd908,Vd912)
| ! [Vd914] :
( ~ rpoint(Vd914)
| Vd908 != Vd914 )
| ! [Vd915] :
( ~ rpoint(Vd915)
| Vd909 != Vd915 )
| ! [Vd916] :
( ~ rpoint(Vd916)
| Vd910 != Vd916 )
| ! [Vd917] :
( ~ rpoint(Vd917)
| Vd911 != Vd917 )
| ! [Vd918] :
( ~ rpoint(Vd918)
| Vd912 != Vd918 )
| ! [Vd919] :
( ! [Vd922] :
( ~ rline(Vd922)
| Vd919 != Vd922 )
| ! [Vd920] :
( ! [Vd923] :
( ~ rline(Vd923)
| Vd920 != Vd923 )
| ~ ron(Vd908,Vd919)
| ~ ron(Vd909,Vd919)
| ~ ron(Vd911,Vd919)
| ~ ron(Vd910,Vd920)
| ~ ron(Vd912,Vd920)
| Vd909 = Vd908
| Vd910 = Vd908
| Vd911 = Vd908
| Vd912 = Vd908
| rR(Vd908,Vd909,Vd911)
| rR(Vd908,Vd910,Vd912) ) ) ),
inference(miniscoping,[status(thm)],[f170]) ).
fof(f172,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13] :
( vangle(X3,X0,X1) = vangle(X4,X0,X2)
| ~ rpoint(X13)
| X0 != X13
| ~ rpoint(X12)
| X3 != X12
| ~ rpoint(X11)
| X1 != X11
| ~ rpoint(X10)
| X4 != X10
| ~ rpoint(X9)
| X2 != X9
| ~ rline(X8)
| X6 != X8
| ~ rline(X7)
| X5 != X7
| ~ ron(X0,X6)
| ~ ron(X3,X6)
| ~ ron(X4,X6)
| ~ ron(X1,X5)
| ~ ron(X2,X5)
| X3 = X0
| X1 = X0
| X4 = X0
| X2 = X0
| rR(X0,X3,X4)
| rR(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f176,plain,
! [Vd340,Vd341,Vd342] :
( ( rR(Vd341,Vd342,Vd340)
& Vd340 != Vd341
& Vd340 != Vd342
& ~ rR(Vd340,Vd341,Vd342) )
| ! [Vd344] :
( ~ rpoint(Vd344)
| Vd340 != Vd344 )
| ! [Vd345] :
( ~ rpoint(Vd345)
| Vd341 != Vd345 )
| ! [Vd346] :
( ~ rpoint(Vd346)
| Vd342 != Vd346 )
| ~ rR(Vd341,Vd340,Vd342) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f178,plain,
! [X0,X1,X2,X3,X4,X5] :
( X1 != X2
| ~ rpoint(X5)
| X1 != X5
| ~ rpoint(X4)
| X0 != X4
| ~ rpoint(X3)
| X2 != X3
| ~ rR(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f182,plain,
vd1299 = vd1300,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f183,plain,
rpoint(vd1300),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f184,plain,
vd1299 != vd1287,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f194,plain,
ron(vd1299,vd1295),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f195,plain,
ron(vd1289,vd1297),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f197,plain,
rline(vd1297),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f198,plain,
ron(vd1288,vd1295),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f199,plain,
ron(vd1287,vd1295),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f200,plain,
rline(vd1295),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f716,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vangle(X3,X0,X1) = vangle(X4,X0,X2)
| ~ rpoint(X0)
| ~ rpoint(X3)
| ~ rpoint(X1)
| ~ rpoint(X4)
| ~ rpoint(X2)
| ~ rline(X6)
| ~ rline(X5)
| ~ ron(X0,X6)
| ~ ron(X3,X6)
| ~ ron(X4,X6)
| ~ ron(X1,X5)
| ~ ron(X2,X5)
| X3 = X0
| X1 = X0
| X4 = X0
| X2 = X0
| rR(X0,X3,X4)
| rR(X0,X1,X2) ),
inference(destructive_equality_resolution,[status(thm)],[f172]) ).
fof(f719,plain,
! [X4,X3] :
( ~ rpoint(X3)
| ~ rpoint(X4)
| ~ rpoint(X3)
| ~ rR(X4,X3,X3) ),
inference(destructive_equality_resolution,[status(thm)],[f178]) ).
fof(f720,plain,
! [X0,X1] :
( ~ rpoint(X0)
| ~ rpoint(X1)
| ~ rR(X0,X1,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f719]) ).
fof(f952,plain,
rpoint(vd1289),
inference(forward_demodulation,[status(thm)],[f164,f165]) ).
fof(f953,plain,
rpoint(vd1288),
inference(forward_demodulation,[status(thm)],[f166,f167]) ).
fof(f954,plain,
rpoint(vd1287),
inference(forward_demodulation,[status(thm)],[f168,f169]) ).
fof(f955,plain,
rpoint(vd1299),
inference(forward_demodulation,[status(thm)],[f182,f183]) ).
fof(f956,plain,
! [X0,X1] :
( ~ rpoint(vd1287)
| ~ rpoint(vd1288)
| ~ rpoint(vd1289)
| ~ rpoint(vd1299)
| ~ rpoint(vd1289)
| ~ rline(X1)
| ~ rline(X0)
| ~ ron(vd1287,X1)
| ~ ron(vd1288,X1)
| ~ ron(vd1299,X1)
| ~ ron(vd1289,X0)
| ~ ron(vd1289,X0)
| vd1288 = vd1287
| vd1289 = vd1287
| vd1299 = vd1287
| vd1289 = vd1287
| rR(vd1287,vd1288,vd1299)
| rR(vd1287,vd1289,vd1289) ),
inference(resolution,[status(thm)],[f716,f149]) ).
fof(f960,plain,
! [X0,X1] :
( ~ rpoint(vd1287)
| ~ rpoint(vd1288)
| ~ rpoint(vd1299)
| ~ rpoint(vd1289)
| ~ rline(X1)
| ~ rline(X0)
| ~ ron(vd1287,X1)
| ~ ron(vd1288,X1)
| ~ ron(vd1299,X1)
| ~ ron(vd1289,X0)
| vd1288 = vd1287
| vd1299 = vd1287
| vd1289 = vd1287
| rR(vd1287,vd1288,vd1299)
| rR(vd1287,vd1289,vd1289) ),
inference(duplicate_literals_removal,[status(thm)],[f956]) ).
fof(f961,plain,
! [X0,X1] :
( ~ rpoint(vd1287)
| ~ rpoint(vd1288)
| ~ rpoint(vd1299)
| ~ rpoint(vd1289)
| ~ rline(X1)
| ~ rline(X0)
| ~ ron(vd1287,X1)
| ~ ron(vd1288,X1)
| ~ ron(vd1299,X1)
| ~ ron(vd1289,X0)
| vd1288 = vd1287
| vd1299 = vd1287
| vd1289 = vd1287
| rR(vd1287,vd1289,vd1289) ),
inference(forward_subsumption_resolution,[status(thm)],[f960,f152]) ).
fof(f966,plain,
! [X0,X1] :
( ~ rpoint(vd1287)
| ~ rpoint(vd1288)
| ~ rpoint(vd1299)
| ~ rpoint(vd1289)
| ~ rline(X1)
| ~ rline(X0)
| ~ ron(vd1287,X1)
| ~ ron(vd1288,X1)
| ~ ron(vd1299,X1)
| ~ ron(vd1289,X0)
| vd1288 = vd1287
| vd1299 = vd1287
| rR(vd1287,vd1289,vd1289) ),
inference(forward_subsumption_resolution,[status(thm)],[f961,f162]) ).
fof(f995,plain,
! [X0,X1] :
( ~ rpoint(vd1287)
| ~ rpoint(vd1288)
| ~ rpoint(vd1299)
| ~ rpoint(vd1289)
| ~ rline(X1)
| ~ rline(X0)
| ~ ron(vd1287,X1)
| ~ ron(vd1288,X1)
| ~ ron(vd1299,X1)
| ~ ron(vd1289,X0)
| vd1288 = vd1287
| vd1299 = vd1287 ),
inference(backward_subsumption_resolution,[status(thm)],[f966,f720]) ).
fof(f997,plain,
! [X0,X1] :
( ~ rpoint(vd1287)
| ~ rpoint(vd1288)
| ~ rpoint(vd1299)
| ~ rpoint(vd1289)
| ~ rline(X1)
| ~ rline(X0)
| ~ ron(vd1287,X1)
| ~ ron(vd1288,X1)
| ~ ron(vd1299,X1)
| ~ ron(vd1289,X0)
| vd1288 = vd1287 ),
inference(forward_subsumption_resolution,[status(thm)],[f995,f184]) ).
fof(f999,plain,
! [X0,X1] :
( ~ rpoint(vd1287)
| ~ rpoint(vd1288)
| ~ rpoint(vd1299)
| ~ rpoint(vd1289)
| ~ rline(X1)
| ~ rline(X0)
| ~ ron(vd1287,X1)
| ~ ron(vd1288,X1)
| ~ ron(vd1299,X1)
| ~ ron(vd1289,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f997,f163]) ).
fof(f1000,plain,
! [X0] :
( ~ rpoint(vd1287)
| ~ rpoint(vd1288)
| ~ rpoint(vd1299)
| ~ rpoint(vd1289)
| ~ rline(vd1295)
| ~ rline(X0)
| ~ ron(vd1287,vd1295)
| ~ ron(vd1288,vd1295)
| ~ ron(vd1289,X0) ),
inference(resolution,[status(thm)],[f999,f194]) ).
fof(f1001,plain,
! [X0] :
( ~ rpoint(vd1287)
| ~ rpoint(vd1288)
| ~ rpoint(vd1299)
| ~ rpoint(vd1289)
| ~ rline(vd1295)
| ~ rline(X0)
| ~ ron(vd1287,vd1295)
| ~ ron(vd1289,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1000,f198]) ).
fof(f1002,plain,
! [X0] :
( ~ rpoint(vd1287)
| ~ rpoint(vd1288)
| ~ rpoint(vd1299)
| ~ rpoint(vd1289)
| ~ rline(vd1295)
| ~ rline(X0)
| ~ ron(vd1289,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1001,f199]) ).
fof(f1003,plain,
( ~ rpoint(vd1287)
| ~ rpoint(vd1288)
| ~ rpoint(vd1299)
| ~ rpoint(vd1289)
| ~ rline(vd1295)
| ~ rline(vd1297) ),
inference(resolution,[status(thm)],[f1002,f195]) ).
fof(f1004,plain,
( ~ rpoint(vd1287)
| ~ rpoint(vd1288)
| ~ rpoint(vd1299)
| ~ rpoint(vd1289)
| ~ rline(vd1295) ),
inference(forward_subsumption_resolution,[status(thm)],[f1003,f197]) ).
fof(f1005,plain,
( ~ rpoint(vd1287)
| ~ rpoint(vd1288)
| ~ rpoint(vd1299)
| ~ rpoint(vd1289) ),
inference(forward_subsumption_resolution,[status(thm)],[f1004,f200]) ).
fof(f1006,plain,
( ~ rpoint(vd1287)
| ~ rpoint(vd1288)
| ~ rpoint(vd1289) ),
inference(resolution,[status(thm)],[f1005,f955]) ).
fof(f1007,plain,
( ~ rpoint(vd1287)
| ~ rpoint(vd1288) ),
inference(forward_subsumption_resolution,[status(thm)],[f1006,f952]) ).
fof(f1009,plain,
~ rpoint(vd1287),
inference(forward_subsumption_resolution,[status(thm)],[f1007,f953]) ).
fof(f1010,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f954,f1009]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO308+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n006.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sun Sep 20 15:18:04 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.14/5.41 % Drodi V4.1.1
% 0.14/5.45 % Refutation found
% 0.14/5.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/5.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.48 % Elapsed time: 0.086804 seconds
% 0.14/5.48 % CPU time: 0.287499 seconds
% 0.14/5.48 % Total memory used: 123.323 MB
% 0.14/5.48 % Net memory used: 122.671 MB
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