%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG047+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 : Fri Sep 25 02:37:35 PM UTC 2026
% Result : Theorem 62.99s 9.53s
% Output : Proof 62.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 12 unt; 0 def)
% Number of atoms : 83 ( 45 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 81 ( 27 ~; 19 |; 24 &)
% ( 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 : 20 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f33,hypothesis,
( aDimensionOf0(xt) != sz00
& aDimensionOf0(xs) = aDimensionOf0(xt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1329_01) ).
fof(f33_nnf,plain,
( aDimensionOf0(xt) != sz00
& aDimensionOf0(xs) = aDimensionOf0(xt) ),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
( aDimensionOf0(xt) != sz00
& aDimensionOf0(xs) = aDimensionOf0(xt) ),
inference(skolemisation,[status(esa)],[f33_nnf]) ).
cnf(c53,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
fof(f34,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/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f34_neg,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)],[f34]) ).
fof(f34_nnf,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(nnf_transformation,[status(thm)],[f34_neg]) ).
fof(f34_sk,plain,
! [W0] :
( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt))
& ( sdtlbdtrb0(sziznziztdt0(xt),W0) = sdtlbdtrb0(xt,W0)
| ~ aNaturalNumber0(W0) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt)
& aVector0(sziznziztdt0(xt))
& ( sdtlbdtrb0(sziznziztdt0(xs),W0) = sdtlbdtrb0(xs,W0)
| ~ aNaturalNumber0(W0) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& aVector0(sziznziztdt0(xs)) ),
inference(skolemisation,[status(esa)],[f34_nnf]) ).
cnf(c59,plain,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p1232,plain,
aDimensionOf0(xt) = aDimensionOf0(xs),
inference(superposition,[status(thm)],[c53,c59]) ).
cnf(p1233,plain,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xs),
inference(demodulation,[status(thm)],[p1232,c59]) ).
fof(f29,axiom,
! [W0] :
( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDimNat) ).
fof(f29_nnf,plain,
! [W0] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [W0] :
( aNaturalNumber0(aDimensionOf0(W0))
| ~ aVector0(W0) ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c44,plain,
( aNaturalNumber0(aDimensionOf0(X0))
| ~ aVector0(X0) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(c58,plain,
aVector0(sziznziztdt0(xt)),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p100,plain,
aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt))),
inference(resolution,[status(thm)],[c44,c58]) ).
fof(f4,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( szszuzczcdt0(W0) = szszuzczcdt0(W1)
=> W0 = W1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccEqu) ).
fof(f4_nnf,plain,
! [W0,W1] :
( W0 = W1
| szszuzczcdt0(W0) != szszuzczcdt0(W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [W0,W1] :
( W0 = W1
| szszuzczcdt0(W0) != szszuzczcdt0(W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c6,plain,
( X0 = X1
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p114,plain,
( aDimensionOf0(sziznziztdt0(xt)) = X0
| szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != szszuzczcdt0(X0)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[p100,c6]) ).
cnf(c55,plain,
aVector0(sziznziztdt0(xs)),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p99,plain,
aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))),
inference(resolution,[status(thm)],[c44,c55]) ).
cnf(p270,plain,
( aDimensionOf0(sziznziztdt0(xt)) = aDimensionOf0(sziznziztdt0(xs))
| szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != aDimensionOf0(xs) ),
inference(resolution,[status(thm)],[p114,p99]) ).
cnf(p1531,plain,
aDimensionOf0(sziznziztdt0(xt)) = aDimensionOf0(sziznziztdt0(xs)),
inference(resolution,[status(thm)],[p1233,p270]) ).
cnf(c61,plain,
aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p1532,plain,
aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xs)),
inference(demodulation,[status(thm)],[p1531,c61]) ).
cnf(p2214,plain,
$false,
inference(equality_resolution,[status(thm)],[p1532]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG047+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.38 % Computer : n005.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Thu Sep 24 07:57:03 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 62.99/9.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 62.99/9.53 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------