%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM466+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 : n010.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 08:17:05 AM UTC 2026
% Result : Theorem 40.43s 6.20s
% Output : CNFRefutation 40.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 13 unt; 0 def)
% Number of atoms : 79 ( 27 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 75 ( 24 ~; 16 |; 31 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 7 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsB_02,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('theBenchmark.p',mSortsB_02) ).
fof(mMulAsso,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ),
file('theBenchmark.p',mMulAsso) ).
fof(m__1218,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('theBenchmark.p',m__1218) ).
fof(m__,conjecture,
( ( doDivides0(xm,xn)
& ? [W0] :
( xn = sdtasdt0(xm,W0)
& aNaturalNumber0(W0) )
& doDivides0(xl,xm)
& ? [W0] :
( xm = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ) )
=> ( doDivides0(xl,xn)
| ? [W0] :
( xn = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( ( doDivides0(xm,xn)
& ? [W0] :
( xn = sdtasdt0(xm,W0)
& aNaturalNumber0(W0) )
& doDivides0(xl,xm)
& ? [W0] :
( xm = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ) )
=> ( doDivides0(xl,xn)
| ? [W0] :
( xn = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(nnf_32,plain,
( ~ doDivides0(xl,xn)
& ! [W0] :
( sdtasdt0(xl,W0) != xn
| ~ aNaturalNumber0(W0) )
& doDivides0(xm,xn)
& ? [X1] :
( sdtasdt0(xm,X1) = xn
& aNaturalNumber0(X1) )
& doDivides0(xl,xm)
& ? [X0] :
( sdtasdt0(xl,X0) = xm
& aNaturalNumber0(X0) ) ),
inference(fof_nnf,[status(thm)],[m___neg]) ).
fof(sk_m___neg,plain,
( ~ doDivides0(xl,xn)
& ! [W0] :
( sdtasdt0(xl,W0) != xn
| ~ aNaturalNumber0(W0) )
& doDivides0(xm,xn)
& sdtasdt0(xm,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(X1,sK0)],[nnf_32]) ).
cnf(c_34,negated_conjecture,
( sdtasdt0(xl,A) != xn
| ~ aNaturalNumber0(A) ),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_36,negated_conjecture,
sdtasdt0(xm,sK0) = xn,
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_37,negated_conjecture,
xn = sdtasdt0(xm,sK0),
inference(copy,[status(thm)],[c_36]) ).
cnf(c_38,negated_conjecture,
aNaturalNumber0(sK0),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_40,negated_conjecture,
sdtasdt0(xl,sK1) = xm,
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_41,negated_conjecture,
aNaturalNumber0(sK1),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_45,plain,
aNaturalNumber0(xl),
inference(clausify,[status(thm)],[m__1218]) ).
cnf(c_90,plain,
( sdtasdt0(sdtasdt0(A,B),C) = sdtasdt0(A,sdtasdt0(B,C))
| ~ aNaturalNumber0(C)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mMulAsso]) ).
cnf(c_96,plain,
( aNaturalNumber0(sdtasdt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mSortsB_02]) ).
cnf(c_13462,negated_conjecture,
( sdtasdt0(xl,A) != sdtasdt0(xm,sK0)
| ~ aNaturalNumber0(A) ),
inference(paramod,[status(thm)],[c_37,c_34]) ).
cnf(c_102,negated_conjecture,
( sdtasdt0(xm,sK0) != sdtasdt0(xl,A)
| ~ aNaturalNumber0(A) ),
inference(copy,[status(thm)],[c_13462]) ).
cnf(c_13463,plain,
( sdtasdt0(sdtasdt0(xl,A),B) = sdtasdt0(xl,sdtasdt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_90,c_45]) ).
cnf(c_13464,negated_conjecture,
( sdtasdt0(sdtasdt0(xl,sK1),A) = sdtasdt0(xl,sdtasdt0(sK1,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_13463,c_41]) ).
cnf(c_13465,negated_conjecture,
sdtasdt0(sdtasdt0(xl,sK1),sK0) = sdtasdt0(xl,sdtasdt0(sK1,sK0)),
inference(resolve,[status(thm)],[c_13464,c_38]) ).
cnf(c_13466,negated_conjecture,
sdtasdt0(xm,sK0) = sdtasdt0(xl,sdtasdt0(sK1,sK0)),
inference(paramod,[status(thm)],[c_40,c_13465]) ).
cnf(c_809,negated_conjecture,
sdtasdt0(xl,sdtasdt0(sK1,sK0)) = sdtasdt0(xm,sK0),
inference(copy,[status(thm)],[c_13466]) ).
cnf(c_13467,negated_conjecture,
( aNaturalNumber0(sdtasdt0(sK1,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_96,c_41]) ).
cnf(c_1692,negated_conjecture,
aNaturalNumber0(sdtasdt0(sK1,sK0)),
inference(resolve,[status(thm)],[c_13467,c_38]) ).
cnf(c_13468,negated_conjecture,
sdtasdt0(xm,sK0) != sdtasdt0(xl,sdtasdt0(sK1,sK0)),
inference(resolve,[status(thm)],[c_1692,c_102]) ).
cnf(c_13469,negated_conjecture,
sdtasdt0(xm,sK0) != sdtasdt0(xm,sK0),
inference(paramod,[status(thm)],[c_809,c_13468]) ).
cnf(c_13461,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_13469]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM466+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n010.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 02:52:16 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 2318315 was started by sandbox on n010,
% 0.11/0.37 % Sat Sep 26 02:52:16 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 40.43/6.20
% 40.43/6.20 % SZS status Theorem for theBenchmark
% 40.43/6.20
% 40.43/6.20 % Proof 1 at 5.17 (+ 0.56) seconds.
% 40.43/6.20 % Length of proof is 17.
% 40.43/6.20 % Level of proof is 4.
% 40.43/6.20 % Maximum clause weight is 42.000.
% 40.43/6.20 % Given clauses 380.
% 40.43/6.20
% 40.43/6.20 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------