%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG047+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 02:04:47 PM UTC 2026
% Result : Theorem 0.10s 0.56s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 10 unt; 0 def)
% Number of atoms : 70 ( 35 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 71 ( 25 ~; 19 |; 16 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( szszuzczcdt0(W0) = szszuzczcdt0(W1)
=> W0 = W1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [W0] :
( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,hypothesis,
( aDimensionOf0(xt) != sz00
& aDimensionOf0(xs) = aDimensionOf0(xt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,conjecture,
( ( ! [W0] :
( aNaturalNumber0(W0)
=> sdtlbdtrb0(sziznziztdt0(xs),W0) = sdtlbdtrb0(xs,W0) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& aVector0(sziznziztdt0(xs)) )
=> ( ( ! [W0] :
( aNaturalNumber0(W0)
=> sdtlbdtrb0(sziznziztdt0(xt),W0) = sdtlbdtrb0(xt,W0) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt)
& aVector0(sziznziztdt0(xt)) )
=> aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
~ ( ( ! [W0] :
( aNaturalNumber0(W0)
=> sdtlbdtrb0(sziznziztdt0(xs),W0) = sdtlbdtrb0(xs,W0) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& aVector0(sziznziztdt0(xs)) )
=> ( ( ! [W0] :
( aNaturalNumber0(W0)
=> sdtlbdtrb0(sziznziztdt0(xt),W0) = sdtlbdtrb0(xt,W0) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt)
& aVector0(sziznziztdt0(xt)) )
=> aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f48,plain,
! [W0,W1] :
( W0 = W1
| szszuzczcdt0(W0) != szszuzczcdt0(W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f49,plain,
! [X0,X1] :
( X0 = X1
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f112,plain,
! [W0] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f113,plain,
! [X0] :
( aNaturalNumber0(aDimensionOf0(X0))
| ~ aVector0(X0) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f127,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f129,plain,
( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt))
& ! [W0] :
( sdtlbdtrb0(sziznziztdt0(xt),W0) = sdtlbdtrb0(xt,W0)
| ~ aNaturalNumber0(W0) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt)
& aVector0(sziznziztdt0(xt))
& ! [W0] :
( sdtlbdtrb0(sziznziztdt0(xs),W0) = sdtlbdtrb0(xs,W0)
| ~ aNaturalNumber0(W0) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& aVector0(sziznziztdt0(xs)) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f130,plain,
aVector0(sziznziztdt0(xs)),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f131,plain,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f133,plain,
aVector0(sziznziztdt0(xt)),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f134,plain,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f136,plain,
aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f141,plain,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xt),
inference(backward_demodulation,[status(thm)],[f127,f131]) ).
fof(f152,plain,
! [X0] :
( X0 = aDimensionOf0(sziznziztdt0(xt))
| szszuzczcdt0(X0) != aDimensionOf0(xt)
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ~ aNaturalNumber0(X0) ),
inference(paramodulation,[status(thm)],[f134,f49]) ).
fof(f171,plain,
! [X0] :
( ~ aVector0(sziznziztdt0(xt))
| X0 = aDimensionOf0(sziznziztdt0(xt))
| szszuzczcdt0(X0) != aDimensionOf0(xt)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f152,f113]) ).
fof(f172,plain,
! [X0] :
( X0 = aDimensionOf0(sziznziztdt0(xt))
| szszuzczcdt0(X0) != aDimensionOf0(xt)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f171,f133]) ).
fof(f173,plain,
( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))) ),
inference(resolution,[status(thm)],[f172,f141]) ).
fof(f178,plain,
~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))),
inference(forward_subsumption_resolution,[status(thm)],[f173,f136]) ).
fof(f182,plain,
~ aVector0(sziznziztdt0(xs)),
inference(resolution,[status(thm)],[f178,f113]) ).
fof(f183,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f182,f130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG047+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.53 % Computer : n015.cluster.edu
% 0.10/0.53 % Model : x86_64 x86_64
% 0.10/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.53 % Memory : 8046.5625MB
% 0.10/0.53 % OS : Linux 6.8.0-71-generic
% 0.10/0.53 % CPULimit : 300
% 0.10/0.53 % WCLimit : 300
% 0.10/0.53 % DateTime : Mon Sep 21 04:18:21 UTC 2026
% 0.10/0.53 % CPUTime :
% 0.10/0.54 % Drodi V4.1.1
% 0.10/0.56 % Refutation found
% 0.10/0.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.59 % Elapsed time: 0.055520 seconds
% 0.17/0.59 % CPU time: 0.143867 seconds
% 0.17/0.59 % Total memory used: 90.582 MB
% 0.17/0.59 % Net memory used: 90.509 MB
%------------------------------------------------------------------------------