%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG046+1 : 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 : n016.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 08:26:29 AM UTC 2026
% Result : Theorem 0.50s 0.58s
% Output : CNFRefutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 12 unt; 0 def)
% Number of atoms : 43 ( 23 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 31 ( 10 ~; 8 |; 10 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mNegSc,axiom,
! [W0] :
( aScalar0(W0)
=> aScalar0(smndt0(W0)) ),
file('theBenchmark.p',mNegSc) ).
fof(mScZero,axiom,
! [W0] :
( aScalar0(W0)
=> ( smndt0(sz0z00) = sz0z00
& smndt0(smndt0(W0)) = W0
& sdtpldt0(smndt0(W0),W0) = sz0z00
& sdtpldt0(W0,smndt0(W0)) = sz0z00
& sdtasdt0(sz0z00,W0) = sz0z00
& sdtasdt0(W0,sz0z00) = sz0z00
& sdtpldt0(sz0z00,W0) = W0
& sdtpldt0(W0,sz0z00) = W0 ) ),
file('theBenchmark.p',mScZero) ).
fof(mMNeg,axiom,
! [W0,W1] :
( ( aScalar0(W1)
& aScalar0(W0) )
=> ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1))
& sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) ) ),
file('theBenchmark.p',mMNeg) ).
fof(m__799,axiom,
( aScalar0(xy)
& aScalar0(xx) ),
file('theBenchmark.p',m__799) ).
fof(m__,conjecture,
sdtasdt0(smndt0(xx),smndt0(xy)) = sdtasdt0(xx,xy),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
sdtasdt0(smndt0(xx),smndt0(xy)) != sdtasdt0(xx,xy),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_18,negated_conjecture,
sdtasdt0(smndt0(xx),smndt0(xy)) != sdtasdt0(xx,xy),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_19,plain,
aScalar0(xy),
inference(clausify,[status(thm)],[m__799]) ).
cnf(c_20,plain,
aScalar0(xx),
inference(clausify,[status(thm)],[m__799]) ).
cnf(c_21,plain,
( smndt0(sdtasdt0(A,B)) = sdtasdt0(smndt0(A),B)
| ~ aScalar0(B)
| ~ aScalar0(A) ),
inference(clausify,[status(thm)],[mMNeg]) ).
cnf(c_22,plain,
( smndt0(sdtasdt0(A,B)) = sdtasdt0(A,smndt0(B))
| ~ aScalar0(B)
| ~ aScalar0(A) ),
inference(clausify,[status(thm)],[mMNeg]) ).
cnf(c_34,plain,
( smndt0(smndt0(A)) = A
| ~ aScalar0(A) ),
inference(clausify,[status(thm)],[mScZero]) ).
cnf(c_41,plain,
( aScalar0(smndt0(A))
| ~ aScalar0(A) ),
inference(clausify,[status(thm)],[mNegSc]) ).
cnf(c_87,plain,
( smndt0(sdtasdt0(xx,A)) = sdtasdt0(smndt0(xx),A)
| ~ aScalar0(A) ),
inference(resolve,[status(thm)],[c_21,c_20]) ).
cnf(c_91,plain,
( smndt0(sdtasdt0(xx,A)) = sdtasdt0(xx,smndt0(A))
| ~ aScalar0(A) ),
inference(resolve,[status(thm)],[c_22,c_20]) ).
cnf(c_185,plain,
smndt0(smndt0(xy)) = xy,
inference(resolve,[status(thm)],[c_34,c_19]) ).
cnf(c_199,plain,
aScalar0(smndt0(xy)),
inference(resolve,[status(thm)],[c_41,c_19]) ).
cnf(c_485,plain,
smndt0(sdtasdt0(xx,smndt0(xy))) = sdtasdt0(smndt0(xx),smndt0(xy)),
inference(resolve,[status(thm)],[c_199,c_87]) ).
cnf(c_814,plain,
smndt0(sdtasdt0(xx,smndt0(xy))) = sdtasdt0(xx,smndt0(smndt0(xy))),
inference(resolve,[status(thm)],[c_91,c_199]) ).
cnf(c_815,plain,
sdtasdt0(smndt0(xx),smndt0(xy)) = sdtasdt0(xx,smndt0(smndt0(xy))),
inference(paramod,[status(thm)],[c_485,c_814]) ).
cnf(c_816,plain,
sdtasdt0(smndt0(xx),smndt0(xy)) = sdtasdt0(xx,xy),
inference(paramod,[status(thm)],[c_185,c_815]) ).
cnf(c_813,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_18,c_816]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG046+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n016.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sat Sep 26 05:56:45 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 151979 was started by sandbox2 on n016,
% 0.17/0.43 % Sat Sep 26 05:56:45 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.50/0.58
% 0.50/0.58 % SZS status Theorem for theBenchmark
% 0.50/0.58
% 0.50/0.58 % Proof 1 at 0.11 (+ 0.02) seconds.
% 0.50/0.58 % Length of proof is 18.
% 0.50/0.58 % Level of proof is 4.
% 0.50/0.58 % Maximum clause weight is 31.000.
% 0.50/0.58 % Given clauses 76.
% 0.50/0.58
% 0.50/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------