%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG047+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 0.09s 0.41s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 14 unt; 1 def)
% Number of atoms : 127 ( 74 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 131 ( 47 ~; 57 |; 19 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 37 ( 35 !; 2 ?)
% 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(f32,definition,
! [W0] :
( aVector0(W0)
=> ( aDimensionOf0(W0) != sz00
=> ! [W1] :
( W1 = sziznziztdt0(W0)
<=> ( ! [W2] :
( aNaturalNumber0(W2)
=> sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2) )
& szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0)
& aVector0(W1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,hypothesis,
( aVector0(xt)
& aVector0(xs) ),
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,
aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
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(f116,plain,
! [W0] :
( ! [W1] :
( W1 = sziznziztdt0(W0)
<=> ( ! [W2] :
( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2)
| ~ aNaturalNumber0(W2) )
& szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0)
& aVector0(W1) ) )
| aDimensionOf0(W0) = sz00
| ~ aVector0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f117,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( sdtlbdtrb0(W1,W2) != sdtlbdtrb0(W0,W2)
& aNaturalNumber0(W2) )
| szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0)
| ~ aVector0(W1)
| W1 = sziznziztdt0(W0) )
& ( ( ! [W2] :
( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2)
| ~ aNaturalNumber0(W2) )
& szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0)
& aVector0(W1) )
| W1 != sziznziztdt0(W0) ) )
| aDimensionOf0(W0) = sz00
| ~ aVector0(W0) ),
inference(NNF_transformation,[status(thm)],[f116]) ).
fof(f118,plain,
! [W0] :
( ( ! [W1] :
( ? [W2] :
( sdtlbdtrb0(W1,W2) != sdtlbdtrb0(W0,W2)
& aNaturalNumber0(W2) )
| szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0)
| ~ aVector0(W1)
| W1 = sziznziztdt0(W0) )
& ! [W1] :
( ( ! [W2] :
( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2)
| ~ aNaturalNumber0(W2) )
& szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0)
& aVector0(W1) )
| W1 != sziznziztdt0(W0) ) )
| aDimensionOf0(W0) = sz00
| ~ aVector0(W0) ),
inference(miniscoping,[status(thm)],[f117]) ).
fof(f119,plain,
! [W0] :
( ( ! [W1] :
( ( sdtlbdtrb0(W1,sK1_skl(W1,W0)) != sdtlbdtrb0(W0,sK1_skl(W1,W0))
& aNaturalNumber0(sK1_skl(W1,W0)) )
| szszuzczcdt0(aDimensionOf0(W1)) != aDimensionOf0(W0)
| ~ aVector0(W1)
| W1 = sziznziztdt0(W0) )
& ! [W1] :
( ( ! [W2] :
( sdtlbdtrb0(W1,W2) = sdtlbdtrb0(W0,W2)
| ~ aNaturalNumber0(W2) )
& szszuzczcdt0(aDimensionOf0(W1)) = aDimensionOf0(W0)
& aVector0(W1) )
| W1 != sziznziztdt0(W0) ) )
| aDimensionOf0(W0) = sz00
| ~ aVector0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W2,sK1_skl(W1,W0))],[f118]) ).
fof(f120,plain,
! [X0,X1] :
( aVector0(X1)
| X1 != sziznziztdt0(X0)
| aDimensionOf0(X0) = sz00
| ~ aVector0(X0) ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f121,plain,
! [X0,X1] :
( szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X0)
| X1 != sziznziztdt0(X0)
| aDimensionOf0(X0) = sz00
| ~ aVector0(X0) ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f125,plain,
aVector0(xs),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f126,plain,
aVector0(xt),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f127,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f128,plain,
aDimensionOf0(xt) != sz00,
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f129,plain,
aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f130,plain,
! [X0] :
( aVector0(sziznziztdt0(X0))
| aDimensionOf0(X0) = sz00
| ~ aVector0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f120]) ).
fof(f131,plain,
! [X0] :
( szszuzczcdt0(aDimensionOf0(sziznziztdt0(X0))) = aDimensionOf0(X0)
| aDimensionOf0(X0) = sz00
| ~ aVector0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f121]) ).
fof(f133,plain,
aDimensionOf0(xs) != sz00,
inference(backward_demodulation,[status(thm)],[f127,f128]) ).
fof(f134,plain,
( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt)
| aDimensionOf0(xt) = sz00 ),
inference(resolution,[status(thm)],[f131,f126]) ).
fof(f136,plain,
( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
| aDimensionOf0(xs) = sz00 ),
inference(resolution,[status(thm)],[f131,f125]) ).
fof(f137,plain,
( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt)
| aDimensionOf0(xs) = sz00 ),
inference(forward_demodulation,[status(thm)],[f127,f134]) ).
fof(f138,plain,
( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xs)
| aDimensionOf0(xs) = sz00 ),
inference(forward_demodulation,[status(thm)],[f127,f137]) ).
fof(f139,plain,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xs),
inference(forward_subsumption_resolution,[status(thm)],[f138,f133]) ).
fof(f140,plain,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs),
inference(forward_subsumption_resolution,[status(thm)],[f136,f133]) ).
fof(f168,plain,
! [X0] :
( aDimensionOf0(X0) = sz00
| ~ aVector0(X0)
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(X0))) ),
inference(resolution,[status(thm)],[f113,f130]) ).
fof(f184,plain,
( aDimensionOf0(xt) = sz00
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt))) ),
inference(resolution,[status(thm)],[f168,f126]) ).
fof(f186,plain,
( aDimensionOf0(xs) = sz00
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))) ),
inference(resolution,[status(thm)],[f168,f125]) ).
fof(f187,plain,
( aDimensionOf0(xs) = sz00
| aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt))) ),
inference(forward_demodulation,[status(thm)],[f127,f184]) ).
fof(f188,plain,
aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt))),
inference(forward_subsumption_resolution,[status(thm)],[f187,f133]) ).
fof(f189,plain,
aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))),
inference(forward_subsumption_resolution,[status(thm)],[f186,f133]) ).
fof(f191,plain,
! [X0] :
( X0 = aDimensionOf0(sziznziztdt0(xt))
| szszuzczcdt0(X0) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt)))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[f188,f49]) ).
fof(f195,plain,
! [X0] :
( X0 = aDimensionOf0(sziznziztdt0(xt))
| szszuzczcdt0(X0) != aDimensionOf0(xs)
| ~ aNaturalNumber0(X0) ),
inference(forward_demodulation,[status(thm)],[f139,f191]) ).
fof(f245,plain,
( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt))
| szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) != aDimensionOf0(xs) ),
inference(resolution,[status(thm)],[f195,f189]) ).
fof(f251,plain,
( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt))
| aDimensionOf0(xs) != aDimensionOf0(xs) ),
inference(forward_demodulation,[status(thm)],[f140,f245]) ).
fof(f252,plain,
aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)),
inference(trivial_equality_resolution,[status(thm)],[f251]) ).
fof(f253,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f252,f129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG047+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 04:19:53 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.41 % Refutation found
% 0.09/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.44 % Elapsed time: 0.056399 seconds
% 0.09/0.44 % CPU time: 0.166471 seconds
% 0.09/0.44 % Total memory used: 103.786 MB
% 0.09/0.44 % Net memory used: 103.693 MB
%------------------------------------------------------------------------------