%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM468+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 : n015.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 4.00s 1.05s
% Output : CNFRefutation 4.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 48 ( 16 unt; 0 def)
% Number of atoms : 126 ( 68 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 125 ( 47 ~; 63 |; 9 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 6 !; 0 ?)
% 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)
& doDivides0(xl,xm) ),
file('theBenchmark.p',m__1240_04) ).
fof(m__,conjecture,
( xl != sz00
=> sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( xl != sz00
=> 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_36,negated_conjecture,
xl != sz00,
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_37,plain,
doDivides0(xl,xn),
inference(clausify,[status(thm)],[m__1240_04]) ).
cnf(c_38,plain,
doDivides0(xl,xm),
inference(clausify,[status(thm)],[m__1240_04]) ).
cnf(c_39,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[m__1240]) ).
cnf(c_40,plain,
aNaturalNumber0(xm),
inference(clausify,[status(thm)],[m__1240]) ).
cnf(c_41,plain,
aNaturalNumber0(xl),
inference(clausify,[status(thm)],[m__1240]) ).
cnf(c_44,plain,
( sdtasdt0(A,C) = B
| sdtsldt0(B,A) != C
| ~ doDivides0(A,B)
| sz00 = A
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefQuot]) ).
cnf(c_45,plain,
( aNaturalNumber0(C)
| sdtsldt0(B,A) != C
| ~ doDivides0(A,B)
| sz00 = A
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefQuot]) ).
cnf(c_81,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_82,plain,
( sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C)) = sdtasdt0(A,sdtpldt0(B,C))
| ~ aNaturalNumber0(C)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(copy,[status(thm)],[c_81]) ).
cnf(c_2442,plain,
( sdtasdt0(xl,B) = A
| sdtsldt0(A,xl) != B
| ~ doDivides0(xl,A)
| sz00 = xl
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_44,c_41]) ).
cnf(c_2443,plain,
( sdtasdt0(xl,A) = xm
| sdtsldt0(xm,xl) != A
| ~ doDivides0(xl,xm)
| sz00 = xl ),
inference(resolve,[status(thm)],[c_2442,c_40]) ).
cnf(c_2444,plain,
( sdtasdt0(xl,A) = xm
| sdtsldt0(xm,xl) != A
| sz00 = xl ),
inference(resolve,[status(thm)],[c_2443,c_38]) ).
cnf(c_2445,plain,
( sdtasdt0(xl,sdtsldt0(xm,xl)) = xm
| sz00 = xl ),
inference(xxres,[status(thm)],[c_2444]) ).
cnf(c_2446,plain,
( sdtasdt0(xl,sdtsldt0(xm,xl)) = xm
| xl = sz00 ),
inference(copy,[status(thm)],[c_2445]) ).
cnf(c_180,negated_conjecture,
sdtasdt0(xl,sdtsldt0(xm,xl)) = xm,
inference(resolve,[status(thm)],[c_36,c_2446]) ).
cnf(c_2447,plain,
( sdtasdt0(xl,B) = A
| sdtsldt0(A,xl) != B
| ~ doDivides0(xl,A)
| sz00 = xl
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_44,c_41]) ).
cnf(c_2448,plain,
( sdtasdt0(xl,A) = xn
| sdtsldt0(xn,xl) != A
| ~ doDivides0(xl,xn)
| sz00 = xl ),
inference(resolve,[status(thm)],[c_2447,c_39]) ).
cnf(c_2449,plain,
( sdtasdt0(xl,A) = xn
| sdtsldt0(xn,xl) != A
| sz00 = xl ),
inference(resolve,[status(thm)],[c_2448,c_37]) ).
cnf(c_2450,plain,
( sdtasdt0(xl,sdtsldt0(xn,xl)) = xn
| sz00 = xl ),
inference(xxres,[status(thm)],[c_2449]) ).
cnf(c_2451,plain,
( sdtasdt0(xl,sdtsldt0(xn,xl)) = xn
| xl = sz00 ),
inference(copy,[status(thm)],[c_2450]) ).
cnf(c_181,negated_conjecture,
sdtasdt0(xl,sdtsldt0(xn,xl)) = xn,
inference(resolve,[status(thm)],[c_36,c_2451]) ).
cnf(c_2452,plain,
( aNaturalNumber0(B)
| sdtsldt0(A,xl) != B
| ~ doDivides0(xl,A)
| sz00 = xl
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_45,c_41]) ).
cnf(c_2453,plain,
( aNaturalNumber0(A)
| sdtsldt0(xm,xl) != A
| ~ doDivides0(xl,xm)
| sz00 = xl ),
inference(resolve,[status(thm)],[c_2452,c_40]) ).
cnf(c_2454,plain,
( aNaturalNumber0(A)
| sdtsldt0(xm,xl) != A
| sz00 = xl ),
inference(resolve,[status(thm)],[c_2453,c_38]) ).
cnf(c_2455,plain,
( aNaturalNumber0(sdtsldt0(xm,xl))
| sz00 = xl ),
inference(xxres,[status(thm)],[c_2454]) ).
cnf(c_2456,plain,
( aNaturalNumber0(sdtsldt0(xm,xl))
| xl = sz00 ),
inference(copy,[status(thm)],[c_2455]) ).
cnf(c_184,negated_conjecture,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(resolve,[status(thm)],[c_36,c_2456]) ).
cnf(c_2457,plain,
( aNaturalNumber0(B)
| sdtsldt0(A,xl) != B
| ~ doDivides0(xl,A)
| sz00 = xl
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_45,c_41]) ).
cnf(c_2458,plain,
( aNaturalNumber0(A)
| sdtsldt0(xn,xl) != A
| ~ doDivides0(xl,xn)
| sz00 = xl ),
inference(resolve,[status(thm)],[c_2457,c_39]) ).
cnf(c_2459,plain,
( aNaturalNumber0(A)
| sdtsldt0(xn,xl) != A
| sz00 = xl ),
inference(resolve,[status(thm)],[c_2458,c_37]) ).
cnf(c_2460,plain,
( aNaturalNumber0(sdtsldt0(xn,xl))
| sz00 = xl ),
inference(xxres,[status(thm)],[c_2459]) ).
cnf(c_2461,plain,
( aNaturalNumber0(sdtsldt0(xn,xl))
| xl = sz00 ),
inference(copy,[status(thm)],[c_2460]) ).
cnf(c_185,negated_conjecture,
aNaturalNumber0(sdtsldt0(xn,xl)),
inference(resolve,[status(thm)],[c_36,c_2461]) ).
cnf(c_2462,plain,
( sdtpldt0(sdtasdt0(xl,A),sdtasdt0(xl,B)) = sdtasdt0(xl,sdtpldt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_82,c_41]) ).
cnf(c_2463,plain,
( sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,A)) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_2462,c_184]) ).
cnf(c_2464,plain,
sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtsldt0(xn,xl))) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))),
inference(resolve,[status(thm)],[c_2463,c_185]) ).
cnf(c_2465,plain,
sdtpldt0(xm,sdtasdt0(xl,sdtsldt0(xn,xl))) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))),
inference(paramod,[status(thm)],[c_180,c_2464]) ).
cnf(c_2466,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))),
inference(paramod,[status(thm)],[c_181,c_2465]) ).
cnf(c_2467,plain,
sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) = sdtpldt0(xm,xn),
inference(copy,[status(thm)],[c_2466]) ).
cnf(c_2441,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_35,c_2467]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM468+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 02:55:27 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 2956403 was started by sandbox on n015,
% 0.11/0.37 % Sat Sep 26 02:55:27 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).
% 4.00/1.05
% 4.00/1.05 % SZS status Theorem for theBenchmark
% 4.00/1.05
% 4.00/1.05 % Proof 1 at 0.55 (+ 0.09) seconds.
% 4.00/1.05 % Length of proof is 21.
% 4.00/1.05 % Level of proof is 3.
% 4.00/1.05 % Maximum clause weight is 34.000.
% 4.00/1.05 % Given clauses 228.
% 4.00/1.05
% 4.00/1.05 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------