%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM469+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 08:17:06 AM UTC 2026
% Result : Theorem 10.06s 1.79s
% Output : CNFRefutation 10.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 11 unt; 0 def)
% Number of atoms : 74 ( 24 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 68 ( 24 ~; 19 |; 23 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 5 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsB,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('theBenchmark.p',mSortsB) ).
fof(mAMDistr,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) ) ),
file('theBenchmark.p',mAMDistr) ).
fof(m__1240,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('theBenchmark.p',m__1240) ).
fof(m__1240_04,axiom,
( doDivides0(xl,xn)
& ? [W0] :
( xn = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) )
& doDivides0(xl,xm)
& ? [W0] :
( xm = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ) ),
file('theBenchmark.p',m__1240_04) ).
fof(m__,conjecture,
( doDivides0(xl,sdtpldt0(xm,xn))
| ? [W0] :
( sdtpldt0(xm,xn) = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ? [W0] :
( sdtpldt0(xm,xn) = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_37,negated_conjecture,
( sdtasdt0(xl,A) != sdtpldt0(xm,xn)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[m___neg]) ).
fof(nnf_33,plain,
( doDivides0(xl,xn)
& ? [W0] :
( sdtasdt0(xl,W0) = xn
& aNaturalNumber0(W0) )
& doDivides0(xl,xm)
& ? [X0] :
( sdtasdt0(xl,X0) = xm
& aNaturalNumber0(X0) ) ),
inference(fof_nnf,[status(thm)],[m__1240_04]) ).
fof(sk_m__1240_04,plain,
( doDivides0(xl,xn)
& sdtasdt0(xl,sK0) = xn
& aNaturalNumber0(sK0)
& doDivides0(xl,xm)
& sdtasdt0(xl,sK1) = xm
& aNaturalNumber0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(X0,sK1),skolemize(W0,sK0)],[nnf_33]) ).
cnf(c_44,plain,
sdtasdt0(xl,sK0) = xn,
inference(split_conjunct,[status(thm)],[sk_m__1240_04]) ).
cnf(c_45,plain,
xn = sdtasdt0(xl,sK0),
inference(copy,[status(thm)],[c_44]) ).
cnf(c_46,plain,
aNaturalNumber0(sK0),
inference(split_conjunct,[status(thm)],[sk_m__1240_04]) ).
cnf(c_48,plain,
sdtasdt0(xl,sK1) = xm,
inference(split_conjunct,[status(thm)],[sk_m__1240_04]) ).
cnf(c_49,plain,
xm = sdtasdt0(xl,sK1),
inference(copy,[status(thm)],[c_48]) ).
cnf(c_50,plain,
aNaturalNumber0(sK1),
inference(split_conjunct,[status(thm)],[sk_m__1240_04]) ).
cnf(c_55,plain,
aNaturalNumber0(xl),
inference(clausify,[status(thm)],[m__1240]) ).
cnf(c_95,plain,
( sdtasdt0(A,sdtpldt0(B,C)) = sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C))
| ~ aNaturalNumber0(C)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mAMDistr]) ).
cnf(c_96,plain,
( sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C)) = sdtasdt0(A,sdtpldt0(B,C))
| ~ aNaturalNumber0(C)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(copy,[status(thm)],[c_95]) ).
cnf(c_108,plain,
( aNaturalNumber0(sdtpldt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mSortsB]) ).
cnf(c_5158,negated_conjecture,
( sdtasdt0(xl,A) != sdtpldt0(sdtasdt0(xl,sK1),xn)
| ~ aNaturalNumber0(A) ),
inference(paramod,[status(thm)],[c_49,c_37]) ).
cnf(c_116,negated_conjecture,
( sdtasdt0(xl,A) != sdtpldt0(sdtasdt0(xl,sK1),sdtasdt0(xl,sK0))
| ~ aNaturalNumber0(A) ),
inference(paramod,[status(thm)],[c_45,c_5158]) ).
cnf(c_5159,plain,
( sdtpldt0(sdtasdt0(xl,A),sdtasdt0(xl,B)) = sdtasdt0(xl,sdtpldt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_96,c_55]) ).
cnf(c_5160,plain,
( sdtpldt0(sdtasdt0(xl,sK1),sdtasdt0(xl,A)) = sdtasdt0(xl,sdtpldt0(sK1,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_5159,c_50]) ).
cnf(c_616,plain,
sdtpldt0(sdtasdt0(xl,sK1),sdtasdt0(xl,sK0)) = sdtasdt0(xl,sdtpldt0(sK1,sK0)),
inference(resolve,[status(thm)],[c_5160,c_46]) ).
cnf(c_5161,negated_conjecture,
( sdtasdt0(xl,A) != sdtasdt0(xl,sdtpldt0(sK1,sK0))
| ~ aNaturalNumber0(A) ),
inference(paramod,[status(thm)],[c_616,c_116]) ).
cnf(c_754,negated_conjecture,
( sdtasdt0(xl,sdtpldt0(sK1,sK0)) != sdtasdt0(xl,A)
| ~ aNaturalNumber0(A) ),
inference(copy,[status(thm)],[c_5161]) ).
cnf(c_5162,plain,
( aNaturalNumber0(sdtpldt0(sK1,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_108,c_50]) ).
cnf(c_1830,plain,
aNaturalNumber0(sdtpldt0(sK1,sK0)),
inference(resolve,[status(thm)],[c_5162,c_46]) ).
cnf(c_5163,plain,
~ aNaturalNumber0(sdtpldt0(sK1,sK0)),
inference(xxres,[status(thm)],[c_754]) ).
cnf(c_5157,plain,
$false,
inference(resolve,[status(thm)],[c_1830,c_5163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM469+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n019.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 02:52:34 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 243790 was started by sandbox2 on n019,
% 0.09/0.36 % Sat Sep 26 02:52:34 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 10.06/1.79
% 10.06/1.79 % SZS status Theorem for theBenchmark
% 10.06/1.79
% 10.06/1.79 % Proof 1 at 1.02 (+ 0.17) seconds.
% 10.06/1.79 % Length of proof is 21.
% 10.06/1.79 % Level of proof is 5.
% 10.06/1.79 % Maximum clause weight is 34.000.
% 10.06/1.79 % Given clauses 172.
% 10.06/1.79
% 10.06/1.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------