%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG047+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 : Sun Sep 27 08:26:29 AM UTC 2026
% Result : Theorem 0.22s 0.78s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 15 unt; 0 def)
% Number of atoms : 52 ( 30 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 41 ( 13 ~; 7 |; 10 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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 : 11 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSuccEqu,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( szszuzczcdt0(W0) = szszuzczcdt0(W1)
=> W0 = W1 ) ),
file('theBenchmark.p',mSuccEqu) ).
fof(mDimNat,axiom,
! [W0] :
( aVector0(W0)
=> aNaturalNumber0(aDimensionOf0(W0)) ),
file('theBenchmark.p',mDimNat) ).
fof(m__1329_01,axiom,
( aDimensionOf0(xt) != sz00
& aDimensionOf0(xs) = aDimensionOf0(xt) ),
file('theBenchmark.p',m__1329_01) ).
fof(m__,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('theBenchmark.p',m__) ).
fof(m___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(assume_negation,[status(cth)],[m__]) ).
cnf(c_34,negated_conjecture,
aDimensionOf0(sziznziztdt0(xt)) != aDimensionOf0(sziznziztdt0(xs)),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_36,negated_conjecture,
aDimensionOf0(xt) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_37,negated_conjecture,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt),
inference(copy,[status(thm)],[c_36]) ).
cnf(c_38,negated_conjecture,
aVector0(sziznziztdt0(xt)),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_40,negated_conjecture,
aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_41,negated_conjecture,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs),
inference(copy,[status(thm)],[c_40]) ).
cnf(c_42,negated_conjecture,
aVector0(sziznziztdt0(xs)),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_44,plain,
aDimensionOf0(xt) = aDimensionOf0(xs),
inference(clausify,[status(thm)],[m__1329_01]) ).
cnf(c_53,plain,
( aNaturalNumber0(aDimensionOf0(A))
| ~ aVector0(A) ),
inference(clausify,[status(thm)],[mDimNat]) ).
cnf(c_89,plain,
( B = A
| szszuzczcdt0(B) != szszuzczcdt0(A)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mSuccEqu]) ).
cnf(c_96,negated_conjecture,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xs),
inference(paramod,[status(thm)],[c_44,c_37]) ).
cnf(c_206,plain,
aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))),
inference(resolve,[status(thm)],[c_53,c_42]) ).
cnf(c_207,plain,
aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt))),
inference(resolve,[status(thm)],[c_53,c_38]) ).
cnf(c_365,plain,
( A = aDimensionOf0(sziznziztdt0(xs))
| szszuzczcdt0(A) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs)))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_89,c_206]) ).
cnf(c_366,plain,
( aDimensionOf0(sziznziztdt0(xt)) = aDimensionOf0(sziznziztdt0(xs))
| szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) ),
inference(resolve,[status(thm)],[c_365,c_207]) ).
cnf(c_367,negated_conjecture,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))),
inference(resolve,[status(thm)],[c_366,c_34]) ).
cnf(c_368,negated_conjecture,
aDimensionOf0(xs) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))),
inference(paramod,[status(thm)],[c_96,c_367]) ).
cnf(c_369,negated_conjecture,
aDimensionOf0(xs) != aDimensionOf0(xs),
inference(paramod,[status(thm)],[c_41,c_368]) ).
cnf(c_364,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_369]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG047+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.65 % Computer : n017.cluster.edu
% 0.19/0.65 % Model : x86_64 x86_64
% 0.19/0.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.65 % Memory : 8046.5625MB
% 0.19/0.65 % OS : Linux 6.8.0-71-generic
% 0.19/0.65 % CPULimit : 300
% 0.19/0.65 % WCLimit : 300
% 0.19/0.65 % DateTime : Sat Sep 26 05:47:19 UTC 2026
% 0.22/0.65 % CPUTime :
% 0.22/0.65 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.22/0.65 % Process 4182830 was started by sandbox on n017,
% 0.22/0.65 % Sat Sep 26 05:47:19 2026
% 0.22/0.65 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.22/0.67
% 0.22/0.67 % From the command line: assign(max_seconds, 300).
% 0.22/0.78
% 0.22/0.78 % SZS status Theorem for theBenchmark
% 0.22/0.78
% 0.22/0.78 % Proof 1 at 0.09 (+ 0.02) seconds.
% 0.22/0.78 % Length of proof is 18.
% 0.22/0.78 % Level of proof is 4.
% 0.22/0.78 % Maximum clause weight is 12.000.
% 0.22/0.78 % Given clauses 136.
% 0.22/0.78
% 0.22/0.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------