%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM613+1 : 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 : n020.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 08:17:34 AM UTC 2026
% Result : Theorem 3.64s 0.92s
% Output : CNFRefutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 15 unt; 0 def)
% Number of atoms : 37 ( 27 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 26 ( 12 ~; 8 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 5 ( 0 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSuccEquSucc,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( szszuzczcdt0(W0) = szszuzczcdt0(W1)
=> W0 = W1 ) ),
file('theBenchmark.p',mSuccEquSucc) ).
fof(m__3533,axiom,
( szszuzczcdt0(xk) = xK
& aElementOf0(xk,szNzAzT0) ),
file('theBenchmark.p',m__3533) ).
fof(m__5255,axiom,
( aElementOf0(sbrdtbr0(xP),szNzAzT0)
& szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ)
& sbrdtbr0(xQ) = szszuzczcdt0(xk) ),
file('theBenchmark.p',m__5255) ).
fof(m__,conjecture,
sbrdtbr0(xP) = xk,
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
sbrdtbr0(xP) != xk,
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_139,plain,
( B = A
| szszuzczcdt0(B) != szszuzczcdt0(A)
| ~ aElementOf0(B,szNzAzT0)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mSuccEquSucc]) ).
cnf(c_249,plain,
aElementOf0(xk,szNzAzT0),
inference(clausify,[status(thm)],[m__3533]) ).
cnf(c_250,plain,
szszuzczcdt0(xk) = xK,
inference(clausify,[status(thm)],[m__3533]) ).
cnf(c_305,plain,
sbrdtbr0(xQ) = szszuzczcdt0(xk),
inference(clausify,[status(thm)],[m__5255]) ).
cnf(c_306,plain,
szszuzczcdt0(xk) = sbrdtbr0(xQ),
inference(copy,[status(thm)],[c_305]) ).
cnf(c_307,plain,
sbrdtbr0(xQ) = szszuzczcdt0(sbrdtbr0(xP)),
inference(clausify,[status(thm)],[m__5255]) ).
cnf(c_308,plain,
szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ),
inference(copy,[status(thm)],[c_307]) ).
cnf(c_309,plain,
aElementOf0(sbrdtbr0(xP),szNzAzT0),
inference(clausify,[status(thm)],[m__5255]) ).
cnf(c_310,negated_conjecture,
sbrdtbr0(xP) != xk,
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_557,plain,
( xk = A
| szszuzczcdt0(xk) != szszuzczcdt0(A)
| ~ aElementOf0(A,szNzAzT0) ),
inference(resolve,[status(thm)],[c_249,c_139]) ).
cnf(c_948,plain,
sbrdtbr0(xQ) = xK,
inference(paramod,[status(thm)],[c_306,c_250]) ).
cnf(c_3142,plain,
szszuzczcdt0(sbrdtbr0(xP)) = xK,
inference(paramod,[status(thm)],[c_948,c_308]) ).
cnf(c_9146,plain,
( xk = sbrdtbr0(xP)
| szszuzczcdt0(xk) != szszuzczcdt0(sbrdtbr0(xP)) ),
inference(resolve,[status(thm)],[c_557,c_309]) ).
cnf(c_9147,plain,
( xk = sbrdtbr0(xP)
| szszuzczcdt0(sbrdtbr0(xP)) != szszuzczcdt0(xk) ),
inference(copy,[status(thm)],[c_9146]) ).
cnf(c_9148,plain,
( sbrdtbr0(xP) = xk
| szszuzczcdt0(sbrdtbr0(xP)) != szszuzczcdt0(xk) ),
inference(copy,[status(thm)],[c_9147]) ).
cnf(c_9144,negated_conjecture,
szszuzczcdt0(sbrdtbr0(xP)) != szszuzczcdt0(xk),
inference(resolve,[status(thm)],[c_310,c_9148]) ).
cnf(c_9149,plain,
szszuzczcdt0(sbrdtbr0(xP)) != xK,
inference(paramod,[status(thm)],[c_250,c_9144]) ).
cnf(c_9145,plain,
$false,
inference(resolve,[status(thm)],[c_3142,c_9149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM613+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 03:27:34 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.03/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.35 % Process 497029 was started by sandbox on n020,
% 0.03/0.35 % Sat Sep 26 03:27:34 2026
% 0.03/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/0.38
% 0.03/0.38 % From the command line: assign(max_seconds, 300).
% 3.64/0.92
% 3.64/0.92 % given #500 (F,wt=19): 2456 -aSet0(sdtlpdtrp0(xN,xK)) | sdtlpdtrp0(xN,xK) != slcrc0. [resolve(616,a,101,b),flip(b)].
% 3.64/0.92
% 3.64/0.92 % given #1000 (W,wt=15): 5884 -isFinite0(szDzozmdt0(xN)) | isFinite0(szNzAzT0). [resolve(5856,a,106,c),unit_del(a,584)].
% 3.64/0.92
% 3.64/0.92 % SZS status Theorem for theBenchmark
% 3.64/0.92
% 3.64/0.92 % Proof 1 at 0.40 (+ 0.11) seconds.
% 3.64/0.92 % Length of proof is 18.
% 3.64/0.92 % Level of proof is 5.
% 3.64/0.92 % Maximum clause weight is 24.000.
% 3.64/0.92 % Given clauses 1135.
% 3.64/0.92
% 3.64/0.92 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------