%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO331+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 : n001.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 12:24:55 PM UTC 2026
% Result : Theorem 0.15s 10.42s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 22 unt; 0 def)
% Number of atoms : 252 ( 132 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 314 ( 117 ~; 169 |; 24 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-3 aty)
% Number of variables : 45 ( 36 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
vf(vd1352,vd1353) = vf(vd1352,vd1354),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
vf(vd1352,vd1353) != vf(vd1352,vd1354),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
vangle(vd1352,vd1353,vd1354) = vangle(vd1352,vd1354,vd1353),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
vd1353 != vd1354,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
vd1352 != vd1354,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
vd1352 != vd1353,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
? [Vd1359] :
( rpoint(Vd1359)
& vd1354 = Vd1359 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
? [Vd1358] :
( rpoint(Vd1358)
& vd1353 = Vd1358 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
? [Vd1357] :
( rpoint(Vd1357)
& vd1352 = Vd1357 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [Vd1361,Vd1362,Vd1363] :
( ( ? [Vd1366] :
( rpoint(Vd1366)
& Vd1361 = Vd1366 )
& ? [Vd1367] :
( rpoint(Vd1367)
& Vd1362 = Vd1367 )
& ? [Vd1368] :
( rpoint(Vd1368)
& Vd1363 = Vd1368 )
& Vd1361 != Vd1362
& Vd1361 != Vd1363
& Vd1362 != Vd1363
& vangle(Vd1361,Vd1362,Vd1363) = vangle(Vd1361,Vd1363,Vd1362) )
=> ( vf(Vd1361,Vd1362) != vf(Vd1361,Vd1363)
=> ( rless(vf(Vd1361,Vd1363),vf(Vd1361,Vd1362))
| rless(vf(Vd1361,Vd1362),vf(Vd1361,Vd1363)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [Vd1361,Vd1362,Vd1363] :
( ( ? [Vd1366] :
( rpoint(Vd1366)
& Vd1361 = Vd1366 )
& ? [Vd1367] :
( rpoint(Vd1367)
& Vd1362 = Vd1367 )
& ? [Vd1368] :
( rpoint(Vd1368)
& Vd1363 = Vd1368 )
& Vd1361 != Vd1362
& Vd1361 != Vd1363
& Vd1362 != Vd1363
& vangle(Vd1361,Vd1362,Vd1363) = vangle(Vd1361,Vd1363,Vd1362) )
=> ( vf(Vd1361,Vd1362) != vf(Vd1361,Vd1363)
=> ~ rless(vf(Vd1361,Vd1362),vf(Vd1361,Vd1363)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f128,plain,
vf(vd1352,vd1353) != vf(vd1352,vd1354),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f129,plain,
vangle(vd1352,vd1353,vd1354) = vangle(vd1352,vd1354,vd1353),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f130,plain,
vd1353 != vd1354,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f131,plain,
vd1352 != vd1354,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f132,plain,
vd1352 != vd1353,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f133,plain,
( rpoint(sK0_skl)
& vd1354 = sK0_skl ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Vd1359,sK0_skl)],[f7]) ).
fof(f134,plain,
vd1354 = sK0_skl,
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f135,plain,
rpoint(sK0_skl),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f136,plain,
( rpoint(sK1_skl)
& vd1353 = sK1_skl ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(Vd1358,sK1_skl)],[f8]) ).
fof(f137,plain,
vd1353 = sK1_skl,
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f138,plain,
rpoint(sK1_skl),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f139,plain,
( rpoint(sK2_skl)
& vd1352 = sK2_skl ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Vd1357,sK2_skl)],[f9]) ).
fof(f140,plain,
vd1352 = sK2_skl,
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f141,plain,
rpoint(sK2_skl),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f142,plain,
! [Vd1361,Vd1362,Vd1363] :
( rless(vf(Vd1361,Vd1363),vf(Vd1361,Vd1362))
| rless(vf(Vd1361,Vd1362),vf(Vd1361,Vd1363))
| vf(Vd1361,Vd1362) = vf(Vd1361,Vd1363)
| ! [Vd1366] :
( ~ rpoint(Vd1366)
| Vd1361 != Vd1366 )
| ! [Vd1367] :
( ~ rpoint(Vd1367)
| Vd1362 != Vd1367 )
| ! [Vd1368] :
( ~ rpoint(Vd1368)
| Vd1363 != Vd1368 )
| Vd1361 = Vd1362
| Vd1361 = Vd1363
| Vd1362 = Vd1363
| vangle(Vd1361,Vd1362,Vd1363) != vangle(Vd1361,Vd1363,Vd1362) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f143,plain,
! [X0,X1,X2,X3,X4,X5] :
( rless(vf(X0,X2),vf(X0,X1))
| rless(vf(X0,X1),vf(X0,X2))
| vf(X0,X1) = vf(X0,X2)
| ~ rpoint(X5)
| X0 != X5
| ~ rpoint(X4)
| X1 != X4
| ~ rpoint(X3)
| X2 != X3
| X0 = X1
| X0 = X2
| X1 = X2
| vangle(X0,X1,X2) != vangle(X0,X2,X1) ),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f144,plain,
! [Vd1361,Vd1362,Vd1363] :
( ~ rless(vf(Vd1361,Vd1362),vf(Vd1361,Vd1363))
| vf(Vd1361,Vd1362) = vf(Vd1361,Vd1363)
| ! [Vd1366] :
( ~ rpoint(Vd1366)
| Vd1361 != Vd1366 )
| ! [Vd1367] :
( ~ rpoint(Vd1367)
| Vd1362 != Vd1367 )
| ! [Vd1368] :
( ~ rpoint(Vd1368)
| Vd1363 != Vd1368 )
| Vd1361 = Vd1362
| Vd1361 = Vd1363
| Vd1362 = Vd1363
| vangle(Vd1361,Vd1362,Vd1363) != vangle(Vd1361,Vd1363,Vd1362) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f145,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ rless(vf(X0,X1),vf(X0,X2))
| vf(X0,X1) = vf(X0,X2)
| ~ rpoint(X5)
| X0 != X5
| ~ rpoint(X4)
| X1 != X4
| ~ rpoint(X3)
| X2 != X3
| X0 = X1
| X0 = X2
| X1 = X2
| vangle(X0,X1,X2) != vangle(X0,X2,X1) ),
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f674,plain,
! [X0,X1,X2] :
( rless(vf(X0,X2),vf(X0,X1))
| rless(vf(X0,X1),vf(X0,X2))
| vf(X0,X1) = vf(X0,X2)
| ~ rpoint(X0)
| ~ rpoint(X1)
| ~ rpoint(X2)
| X0 = X1
| X0 = X2
| X1 = X2
| vangle(X0,X1,X2) != vangle(X0,X2,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f143]) ).
fof(f675,plain,
! [X0,X1,X2] :
( ~ rless(vf(X0,X1),vf(X0,X2))
| vf(X0,X1) = vf(X0,X2)
| ~ rpoint(X0)
| ~ rpoint(X1)
| ~ rpoint(X2)
| X0 = X1
| X0 = X2
| X1 = X2
| vangle(X0,X1,X2) != vangle(X0,X2,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f145]) ).
fof(f914,plain,
rpoint(vd1354),
inference(forward_demodulation,[status(thm)],[f134,f135]) ).
fof(f915,plain,
rpoint(vd1353),
inference(forward_demodulation,[status(thm)],[f137,f138]) ).
fof(f916,plain,
rpoint(vd1352),
inference(forward_demodulation,[status(thm)],[f140,f141]) ).
fof(f918,plain,
( rless(vf(vd1352,vd1354),vf(vd1352,vd1353))
| rless(vf(vd1352,vd1353),vf(vd1352,vd1354))
| vf(vd1352,vd1353) = vf(vd1352,vd1354)
| ~ rpoint(vd1352)
| ~ rpoint(vd1353)
| ~ rpoint(vd1354)
| vd1352 = vd1353
| vd1352 = vd1354
| vd1353 = vd1354 ),
inference(resolution,[status(thm)],[f674,f129]) ).
fof(f923,plain,
( rless(vf(vd1352,vd1354),vf(vd1352,vd1353))
| rless(vf(vd1352,vd1353),vf(vd1352,vd1354))
| vf(vd1352,vd1353) = vf(vd1352,vd1354)
| ~ rpoint(vd1352)
| ~ rpoint(vd1353)
| ~ rpoint(vd1354)
| vd1352 = vd1353
| vd1352 = vd1354 ),
inference(forward_subsumption_resolution,[status(thm)],[f918,f130]) ).
fof(f930,plain,
( ~ rless(vf(vd1352,vd1353),vf(vd1352,vd1354))
| vf(vd1352,vd1353) = vf(vd1352,vd1354)
| ~ rpoint(vd1352)
| ~ rpoint(vd1353)
| ~ rpoint(vd1354)
| vd1352 = vd1353
| vd1352 = vd1354
| vd1353 = vd1354 ),
inference(resolution,[status(thm)],[f675,f129]) ).
fof(f931,plain,
( ~ rless(vf(vd1352,vd1354),vf(vd1352,vd1353))
| vf(vd1352,vd1354) = vf(vd1352,vd1353)
| ~ rpoint(vd1352)
| ~ rpoint(vd1354)
| ~ rpoint(vd1353)
| vd1352 = vd1354
| vd1352 = vd1353
| vd1354 = vd1353 ),
inference(resolution,[status(thm)],[f675,f129]) ).
fof(f936,plain,
( ~ rless(vf(vd1352,vd1353),vf(vd1352,vd1354))
| vf(vd1352,vd1353) = vf(vd1352,vd1354)
| ~ rpoint(vd1352)
| ~ rpoint(vd1353)
| ~ rpoint(vd1354)
| vd1352 = vd1353
| vd1352 = vd1354 ),
inference(forward_subsumption_resolution,[status(thm)],[f930,f130]) ).
fof(f937,plain,
( ~ rless(vf(vd1352,vd1354),vf(vd1352,vd1353))
| vf(vd1352,vd1354) = vf(vd1352,vd1353)
| ~ rpoint(vd1352)
| ~ rpoint(vd1354)
| ~ rpoint(vd1353)
| vd1352 = vd1354
| vd1352 = vd1353 ),
inference(forward_subsumption_resolution,[status(thm)],[f931,f130]) ).
fof(f942,plain,
( ~ rless(vf(vd1352,vd1353),vf(vd1352,vd1354))
| vf(vd1352,vd1353) = vf(vd1352,vd1354)
| ~ rpoint(vd1352)
| ~ rpoint(vd1353)
| ~ rpoint(vd1354)
| vd1352 = vd1353 ),
inference(forward_subsumption_resolution,[status(thm)],[f936,f131]) ).
fof(f943,plain,
( ~ rless(vf(vd1352,vd1354),vf(vd1352,vd1353))
| vf(vd1352,vd1354) = vf(vd1352,vd1353)
| ~ rpoint(vd1352)
| ~ rpoint(vd1354)
| ~ rpoint(vd1353)
| vd1352 = vd1354 ),
inference(forward_subsumption_resolution,[status(thm)],[f937,f132]) ).
fof(f944,plain,
( rless(vf(vd1352,vd1354),vf(vd1352,vd1353))
| rless(vf(vd1352,vd1353),vf(vd1352,vd1354))
| vf(vd1352,vd1353) = vf(vd1352,vd1354)
| ~ rpoint(vd1352)
| ~ rpoint(vd1353)
| ~ rpoint(vd1354)
| vd1352 = vd1353 ),
inference(forward_subsumption_resolution,[status(thm)],[f923,f131]) ).
fof(f945,plain,
( vf(vd1352,vd1354) = vf(vd1352,vd1353)
| ~ rpoint(vd1352)
| ~ rpoint(vd1354)
| ~ rpoint(vd1353)
| vd1352 = vd1354
| rless(vf(vd1352,vd1353),vf(vd1352,vd1354))
| vf(vd1352,vd1353) = vf(vd1352,vd1354)
| ~ rpoint(vd1352)
| ~ rpoint(vd1353)
| ~ rpoint(vd1354)
| vd1352 = vd1353 ),
inference(resolution,[status(thm)],[f944,f943]) ).
fof(f946,plain,
( vd1352 = vd1354
| rless(vf(vd1352,vd1353),vf(vd1352,vd1354))
| vf(vd1352,vd1353) = vf(vd1352,vd1354)
| ~ rpoint(vd1352)
| ~ rpoint(vd1353)
| ~ rpoint(vd1354)
| vd1352 = vd1353 ),
inference(duplicate_literals_removal,[status(thm)],[f945]) ).
fof(f947,plain,
( vd1352 = vd1354
| rless(vf(vd1352,vd1353),vf(vd1352,vd1354))
| vf(vd1352,vd1353) = vf(vd1352,vd1354)
| ~ rpoint(vd1352)
| ~ rpoint(vd1353)
| ~ rpoint(vd1354) ),
inference(forward_subsumption_resolution,[status(thm)],[f946,f132]) ).
fof(f948,plain,
( vd1352 = vd1354
| rless(vf(vd1352,vd1353),vf(vd1352,vd1354))
| vf(vd1352,vd1353) = vf(vd1352,vd1354)
| ~ rpoint(vd1352)
| ~ rpoint(vd1353) ),
inference(forward_subsumption_resolution,[status(thm)],[f947,f914]) ).
fof(f949,plain,
( vf(vd1352,vd1353) = vf(vd1352,vd1354)
| ~ rpoint(vd1352)
| ~ rpoint(vd1353)
| ~ rpoint(vd1354)
| vd1352 = vd1353
| vd1352 = vd1354
| vf(vd1352,vd1353) = vf(vd1352,vd1354)
| ~ rpoint(vd1352)
| ~ rpoint(vd1353) ),
inference(resolution,[status(thm)],[f948,f942]) ).
fof(f950,plain,
( ~ rpoint(vd1354)
| vd1352 = vd1353
| vd1352 = vd1354
| vf(vd1352,vd1353) = vf(vd1352,vd1354)
| ~ rpoint(vd1352)
| ~ rpoint(vd1353) ),
inference(duplicate_literals_removal,[status(thm)],[f949]) ).
fof(f951,plain,
( ~ rpoint(vd1354)
| vd1352 = vd1353
| vd1352 = vd1354
| vf(vd1352,vd1353) = vf(vd1352,vd1354)
| ~ rpoint(vd1352) ),
inference(forward_subsumption_resolution,[status(thm)],[f950,f915]) ).
fof(f952,plain,
( ~ rpoint(vd1354)
| vd1352 = vd1353
| vd1352 = vd1354
| vf(vd1352,vd1353) = vf(vd1352,vd1354) ),
inference(forward_subsumption_resolution,[status(thm)],[f951,f916]) ).
fof(f953,plain,
( ~ rpoint(vd1354)
| vd1352 = vd1353
| vd1352 = vd1354 ),
inference(resolution,[status(thm)],[f952,f128]) ).
fof(f954,plain,
( ~ rpoint(vd1354)
| vd1352 = vd1353 ),
inference(forward_subsumption_resolution,[status(thm)],[f953,f131]) ).
fof(f956,plain,
~ rpoint(vd1354),
inference(forward_subsumption_resolution,[status(thm)],[f954,f132]) ).
fof(f957,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f914,f956]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO331+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/10.37 % Computer : n001.cluster.edu
% 0.10/10.37 % Model : x86_64 x86_64
% 0.10/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.37 % Memory : 8046.5625MB
% 0.10/10.37 % OS : Linux 6.8.0-71-generic
% 0.10/10.37 % CPULimit : 300
% 0.10/10.37 % WCLimit : 300
% 0.10/10.37 % DateTime : Sun Sep 20 15:30:39 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.10/10.39 % Drodi V4.1.1
% 0.15/10.42 % Refutation found
% 0.15/10.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/10.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/10.46 % Elapsed time: 0.065409 seconds
% 0.15/10.46 % CPU time: 0.232133 seconds
% 0.15/10.46 % Total memory used: 122.017 MB
% 0.15/10.46 % Net memory used: 121.577 MB
%------------------------------------------------------------------------------