%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM468+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 : n013.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 0.15s 30.69s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 53 ( 28 unt; 0 def)
% Number of atoms : 137 ( 74 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 131 ( 47 ~; 47 |; 27 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 6 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
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(mDefQuot,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W0,W1)
& W0 != sz00 )
=> ! [W2] :
( W2 = sdtsldt0(W1,W0)
<=> ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) ) ) ),
file('theBenchmark.p',mDefQuot) ).
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,
( xl != sz00
=> ( ( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) )
=> ( ( xn = sdtasdt0(xl,sdtsldt0(xn,xl))
& aNaturalNumber0(sdtsldt0(xn,xl)) )
=> sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( xl != sz00
=> ( ( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) )
=> ( ( xn = sdtasdt0(xl,sdtsldt0(xn,xl))
& aNaturalNumber0(sdtsldt0(xn,xl)) )
=> sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_35,negated_conjecture,
sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) != sdtpldt0(xm,xn),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_40,negated_conjecture,
xl != sz00,
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_41,plain,
doDivides0(xl,xn),
inference(split_conjunct,[status(thm)],[sk_m__1240_04]) ).
cnf(c_42,plain,
sdtasdt0(xl,sK0) = xn,
inference(split_conjunct,[status(thm)],[sk_m__1240_04]) ).
cnf(c_43,plain,
xn = sdtasdt0(xl,sK0),
inference(copy,[status(thm)],[c_42]) ).
cnf(c_44,plain,
aNaturalNumber0(sK0),
inference(split_conjunct,[status(thm)],[sk_m__1240_04]) ).
cnf(c_45,plain,
doDivides0(xl,xm),
inference(split_conjunct,[status(thm)],[sk_m__1240_04]) ).
cnf(c_46,plain,
sdtasdt0(xl,sK1) = xm,
inference(split_conjunct,[status(thm)],[sk_m__1240_04]) ).
cnf(c_47,plain,
xm = sdtasdt0(xl,sK1),
inference(copy,[status(thm)],[c_46]) ).
cnf(c_48,plain,
aNaturalNumber0(sK1),
inference(split_conjunct,[status(thm)],[sk_m__1240_04]) ).
cnf(c_49,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[m__1240]) ).
cnf(c_50,plain,
aNaturalNumber0(sdtasdt0(xl,sK0)),
inference(paramod,[status(thm)],[c_43,c_49]) ).
cnf(c_51,plain,
aNaturalNumber0(xm),
inference(clausify,[status(thm)],[m__1240]) ).
cnf(c_52,plain,
aNaturalNumber0(sdtasdt0(xl,sK1)),
inference(paramod,[status(thm)],[c_47,c_51]) ).
cnf(c_53,plain,
aNaturalNumber0(xl),
inference(clausify,[status(thm)],[m__1240]) ).
cnf(c_55,plain,
( sdtasdt0(A,C) != B
| ~ aNaturalNumber0(C)
| sdtsldt0(B,A) = C
| ~ doDivides0(A,B)
| sz00 = A
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefQuot]) ).
cnf(c_93,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_94,plain,
( sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C)) = sdtasdt0(A,sdtpldt0(B,C))
| ~ aNaturalNumber0(C)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(copy,[status(thm)],[c_93]) ).
cnf(c_110,plain,
doDivides0(xl,sdtasdt0(xl,sK0)),
inference(paramod,[status(thm)],[c_43,c_41]) ).
cnf(c_2545,negated_conjecture,
sdtasdt0(xl,sdtpldt0(sdtsldt0(sdtasdt0(xl,sK1),xl),sdtsldt0(xn,xl))) != sdtpldt0(xm,xn),
inference(paramod,[status(thm)],[c_47,c_35]) ).
cnf(c_2546,negated_conjecture,
sdtasdt0(xl,sdtpldt0(sdtsldt0(sdtasdt0(xl,sK1),xl),sdtsldt0(sdtasdt0(xl,sK0),xl))) != sdtpldt0(xm,xn),
inference(paramod,[status(thm)],[c_43,c_2545]) ).
cnf(c_2547,negated_conjecture,
sdtasdt0(xl,sdtpldt0(sdtsldt0(sdtasdt0(xl,sK1),xl),sdtsldt0(sdtasdt0(xl,sK0),xl))) != sdtpldt0(sdtasdt0(xl,sK1),xn),
inference(paramod,[status(thm)],[c_47,c_2546]) ).
cnf(c_113,negated_conjecture,
sdtasdt0(xl,sdtpldt0(sdtsldt0(sdtasdt0(xl,sK1),xl),sdtsldt0(sdtasdt0(xl,sK0),xl))) != sdtpldt0(sdtasdt0(xl,sK1),sdtasdt0(xl,sK0)),
inference(paramod,[status(thm)],[c_43,c_2547]) ).
cnf(c_114,plain,
doDivides0(xl,sdtasdt0(xl,sK1)),
inference(paramod,[status(thm)],[c_47,c_45]) ).
cnf(c_2548,plain,
( sdtpldt0(sdtasdt0(xl,A),sdtasdt0(xl,B)) = sdtasdt0(xl,sdtpldt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_94,c_53]) ).
cnf(c_2549,plain,
( sdtpldt0(sdtasdt0(xl,sK1),sdtasdt0(xl,A)) = sdtasdt0(xl,sdtpldt0(sK1,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_2548,c_48]) ).
cnf(c_619,plain,
sdtpldt0(sdtasdt0(xl,sK1),sdtasdt0(xl,sK0)) = sdtasdt0(xl,sdtpldt0(sK1,sK0)),
inference(resolve,[status(thm)],[c_2549,c_44]) ).
cnf(c_756,negated_conjecture,
sdtasdt0(xl,sdtpldt0(sdtsldt0(sdtasdt0(xl,sK1),xl),sdtsldt0(sdtasdt0(xl,sK0),xl))) != sdtasdt0(xl,sdtpldt0(sK1,sK0)),
inference(paramod,[status(thm)],[c_619,c_113]) ).
cnf(c_2550,plain,
( sdtasdt0(xl,B) != A
| ~ aNaturalNumber0(B)
| sdtsldt0(A,xl) = B
| ~ doDivides0(xl,A)
| sz00 = xl
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_55,c_53]) ).
cnf(c_2551,plain,
( sdtasdt0(xl,A) != sdtasdt0(xl,sK0)
| ~ aNaturalNumber0(A)
| sdtsldt0(sdtasdt0(xl,sK0),xl) = A
| ~ doDivides0(xl,sdtasdt0(xl,sK0))
| sz00 = xl ),
inference(resolve,[status(thm)],[c_2550,c_50]) ).
cnf(c_2552,plain,
( sdtasdt0(xl,A) != sdtasdt0(xl,sK0)
| ~ aNaturalNumber0(A)
| sdtsldt0(sdtasdt0(xl,sK0),xl) = A
| sz00 = xl ),
inference(resolve,[status(thm)],[c_2551,c_110]) ).
cnf(c_2553,plain,
( sdtasdt0(xl,sK0) != sdtasdt0(xl,sK0)
| sdtsldt0(sdtasdt0(xl,sK0),xl) = sK0
| sz00 = xl ),
inference(resolve,[status(thm)],[c_2552,c_44]) ).
cnf(c_2554,plain,
( sdtsldt0(sdtasdt0(xl,sK0),xl) = sK0
| sz00 = xl ),
inference(xxres,[status(thm)],[c_2553]) ).
cnf(c_2555,plain,
( sdtsldt0(sdtasdt0(xl,sK0),xl) = sK0
| xl = sz00 ),
inference(copy,[status(thm)],[c_2554]) ).
cnf(c_2528,negated_conjecture,
sdtsldt0(sdtasdt0(xl,sK0),xl) = sK0,
inference(resolve,[status(thm)],[c_40,c_2555]) ).
cnf(c_2532,negated_conjecture,
sdtasdt0(xl,sdtpldt0(sdtsldt0(sdtasdt0(xl,sK1),xl),sK0)) != sdtasdt0(xl,sdtpldt0(sK1,sK0)),
inference(paramod,[status(thm)],[c_2528,c_756]) ).
cnf(c_2556,plain,
( sdtasdt0(xl,B) != A
| ~ aNaturalNumber0(B)
| sdtsldt0(A,xl) = B
| ~ doDivides0(xl,A)
| sz00 = xl
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_55,c_53]) ).
cnf(c_2557,plain,
( sdtasdt0(xl,A) != sdtasdt0(xl,sK1)
| ~ aNaturalNumber0(A)
| sdtsldt0(sdtasdt0(xl,sK1),xl) = A
| ~ doDivides0(xl,sdtasdt0(xl,sK1))
| sz00 = xl ),
inference(resolve,[status(thm)],[c_2556,c_52]) ).
cnf(c_2558,plain,
( sdtasdt0(xl,A) != sdtasdt0(xl,sK1)
| ~ aNaturalNumber0(A)
| sdtsldt0(sdtasdt0(xl,sK1),xl) = A
| sz00 = xl ),
inference(resolve,[status(thm)],[c_2557,c_114]) ).
cnf(c_2559,plain,
( sdtasdt0(xl,sK1) != sdtasdt0(xl,sK1)
| sdtsldt0(sdtasdt0(xl,sK1),xl) = sK1
| sz00 = xl ),
inference(resolve,[status(thm)],[c_2558,c_48]) ).
cnf(c_2560,plain,
( sdtsldt0(sdtasdt0(xl,sK1),xl) = sK1
| sz00 = xl ),
inference(xxres,[status(thm)],[c_2559]) ).
cnf(c_2561,plain,
( sdtsldt0(sdtasdt0(xl,sK1),xl) = sK1
| xl = sz00 ),
inference(copy,[status(thm)],[c_2560]) ).
cnf(c_2540,negated_conjecture,
sdtsldt0(sdtasdt0(xl,sK1),xl) = sK1,
inference(resolve,[status(thm)],[c_40,c_2561]) ).
cnf(c_2562,negated_conjecture,
sdtasdt0(xl,sdtpldt0(sK1,sK0)) != sdtasdt0(xl,sdtpldt0(sK1,sK0)),
inference(paramod,[status(thm)],[c_2540,c_2532]) ).
cnf(c_2544,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_2562]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM468+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/30.41 % Computer : n013.cluster.edu
% 0.11/30.41 % Model : x86_64 x86_64
% 0.11/30.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/30.41 % Memory : 8046.5625MB
% 0.11/30.41 % OS : Linux 6.8.0-71-generic
% 0.11/30.41 % CPULimit : 300
% 0.11/30.41 % WCLimit : 300
% 0.11/30.41 % DateTime : Sat Sep 26 02:52:21 UTC 2026
% 0.11/30.41 % CPUTime :
% 0.11/30.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/30.41 % Process 1788693 was started by sandbox2 on n013,
% 0.11/30.41 % Sat Sep 26 02:52:21 2026
% 0.11/30.41 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/30.43
% 0.11/30.43 % From the command line: assign(max_seconds, 300).
% 0.15/30.69
% 0.15/30.69 % SZS status Theorem for theBenchmark
% 0.15/30.69
% 0.15/30.69 % Proof 1 at 0.19 (+ 0.05) seconds.
% 0.15/30.69 % Length of proof is 32.
% 0.15/30.69 % Level of proof is 6.
% 0.15/30.69 % Maximum clause weight is 46.000.
% 0.15/30.69 % Given clauses 58.
% 0.15/30.69
% 0.15/30.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------