%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG105+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 : n014.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 08:26:39 AM UTC 2026
% Result : Theorem 34.86s 4.88s
% Output : CNFRefutation 34.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 52 ( 27 unt; 0 def)
% Number of atoms : 125 ( 53 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 127 ( 54 ~; 43 |; 28 &)
% ( 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 : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 4 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsB,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> aElement0(sdtpldt0(W0,W1)) ),
file('theBenchmark.p',mSortsB) ).
fof(mSortsB_02,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> aElement0(sdtasdt0(W0,W1)) ),
file('theBenchmark.p',mSortsB_02) ).
fof(m__1933,axiom,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& ? [W0] :
( sdtasdt0(xc,W0) = xy
& aElement0(W0) )
& aElementOf0(xx,slsdtgt0(xc))
& ? [W0] :
( sdtasdt0(xc,W0) = xx
& aElement0(W0) ) ),
file('theBenchmark.p',m__1933) ).
fof(m__1956,axiom,
( sdtasdt0(xc,xu) = xx
& aElement0(xu) ),
file('theBenchmark.p',m__1956) ).
fof(m__1979,axiom,
( sdtasdt0(xc,xv) = xy
& aElement0(xv) ),
file('theBenchmark.p',m__1979) ).
fof(m__,conjecture,
( ( aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
| ? [W0] :
( sdtasdt0(xc,W0) = sdtasdt0(xz,xx)
& aElement0(W0) ) )
& ( aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| ? [W0] :
( sdtasdt0(xc,W0) = sdtpldt0(xx,xy)
& aElement0(W0) ) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( ( aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
| ? [W0] :
( sdtasdt0(xc,W0) = sdtasdt0(xz,xx)
& aElement0(W0) ) )
& ( aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| ? [W0] :
( sdtasdt0(xc,W0) = sdtpldt0(xx,xy)
& aElement0(W0) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_70,negated_conjecture,
( sdtasdt0(xz,xx) != sdtasdt0(xc,B)
| ~ aElement0(B)
| sdtasdt0(xc,A) != sdtpldt0(xx,xy)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[m___neg]) ).
fof(m__2043,axiom,
sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
file('theBenchmark.p',m__2043) ).
cnf(c_71,plain,
sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(clausify,[status(thm)],[m__2043]) ).
fof(m__2010,axiom,
sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
file('theBenchmark.p',m__2010) ).
cnf(c_72,plain,
sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(clausify,[status(thm)],[m__2010]) ).
cnf(c_73,plain,
sdtasdt0(xc,xv) = xy,
inference(clausify,[status(thm)],[m__1979]) ).
cnf(c_74,plain,
xy = sdtasdt0(xc,xv),
inference(copy,[status(thm)],[c_73]) ).
cnf(c_75,plain,
aElement0(xv),
inference(clausify,[status(thm)],[m__1979]) ).
cnf(c_76,plain,
sdtasdt0(xc,xu) = xx,
inference(clausify,[status(thm)],[m__1956]) ).
cnf(c_77,plain,
xx = sdtasdt0(xc,xu),
inference(copy,[status(thm)],[c_76]) ).
cnf(c_78,plain,
aElement0(xu),
inference(clausify,[status(thm)],[m__1956]) ).
fof(nnf_35,plain,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& ? [W0] :
( sdtasdt0(xc,W0) = xy
& aElement0(W0) )
& aElementOf0(xx,slsdtgt0(xc))
& ? [X0] :
( sdtasdt0(xc,X0) = xx
& aElement0(X0) ) ),
inference(fof_nnf,[status(thm)],[m__1933]) ).
fof(sk_m__1933,plain,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& sdtasdt0(xc,sK0) = xy
& aElement0(sK0)
& aElementOf0(xx,slsdtgt0(xc))
& sdtasdt0(xc,sK1) = xx
& aElement0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(X0,sK1),skolemize(W0,sK0)],[nnf_35]) ).
cnf(c_79,plain,
aElement0(xz),
inference(split_conjunct,[status(thm)],[sk_m__1933]) ).
cnf(c_82,plain,
sdtasdt0(xc,sK0) = xy,
inference(split_conjunct,[status(thm)],[sk_m__1933]) ).
cnf(c_12659,plain,
sdtasdt0(xc,sK0) = sdtasdt0(xc,xv),
inference(paramod,[status(thm)],[c_74,c_82]) ).
cnf(c_83,plain,
sdtasdt0(xc,xv) = sdtasdt0(xc,sK0),
inference(copy,[status(thm)],[c_12659]) ).
cnf(c_87,plain,
sdtasdt0(xc,sK1) = xx,
inference(split_conjunct,[status(thm)],[sk_m__1933]) ).
cnf(c_12660,plain,
sdtasdt0(xc,sK1) = sdtasdt0(xc,xu),
inference(paramod,[status(thm)],[c_77,c_87]) ).
cnf(c_88,plain,
sdtasdt0(xc,xu) = sdtasdt0(xc,sK1),
inference(copy,[status(thm)],[c_12660]) ).
cnf(c_166,plain,
( aElement0(sdtasdt0(A,B))
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mSortsB_02]) ).
cnf(c_167,plain,
( aElement0(sdtpldt0(A,B))
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mSortsB]) ).
cnf(c_12661,negated_conjecture,
( sdtasdt0(xz,xx) != sdtasdt0(xc,B)
| ~ aElement0(B)
| sdtasdt0(xc,A) != sdtpldt0(sdtasdt0(xc,xu),xy)
| ~ aElement0(A) ),
inference(paramod,[status(thm)],[c_77,c_70]) ).
cnf(c_12662,negated_conjecture,
( sdtasdt0(xz,xx) != sdtasdt0(xc,B)
| ~ aElement0(B)
| sdtasdt0(xc,A) != sdtpldt0(sdtasdt0(xc,sK1),xy)
| ~ aElement0(A) ),
inference(paramod,[status(thm)],[c_88,c_12661]) ).
cnf(c_12663,negated_conjecture,
( sdtasdt0(xz,xx) != sdtasdt0(xc,B)
| ~ aElement0(B)
| sdtasdt0(xc,A) != sdtpldt0(sdtasdt0(xc,sK1),sdtasdt0(xc,xv))
| ~ aElement0(A) ),
inference(paramod,[status(thm)],[c_74,c_12662]) ).
cnf(c_12664,negated_conjecture,
( sdtasdt0(xz,xx) != sdtasdt0(xc,B)
| ~ aElement0(B)
| sdtasdt0(xc,A) != sdtpldt0(sdtasdt0(xc,sK1),sdtasdt0(xc,sK0))
| ~ aElement0(A) ),
inference(paramod,[status(thm)],[c_83,c_12663]) ).
cnf(c_12665,negated_conjecture,
( sdtasdt0(xz,sdtasdt0(xc,xu)) != sdtasdt0(xc,B)
| ~ aElement0(B)
| sdtasdt0(xc,A) != sdtpldt0(sdtasdt0(xc,sK1),sdtasdt0(xc,sK0))
| ~ aElement0(A) ),
inference(paramod,[status(thm)],[c_77,c_12664]) ).
cnf(c_187,negated_conjecture,
( sdtasdt0(xz,sdtasdt0(xc,sK1)) != sdtasdt0(xc,B)
| ~ aElement0(B)
| sdtasdt0(xc,A) != sdtpldt0(sdtasdt0(xc,sK1),sdtasdt0(xc,sK0))
| ~ aElement0(A) ),
inference(paramod,[status(thm)],[c_88,c_12665]) ).
cnf(c_12666,plain,
sdtpldt0(sdtasdt0(xc,xu),xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(paramod,[status(thm)],[c_77,c_72]) ).
cnf(c_12667,plain,
sdtpldt0(sdtasdt0(xc,sK1),xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(paramod,[status(thm)],[c_88,c_12666]) ).
cnf(c_12668,plain,
sdtpldt0(sdtasdt0(xc,sK1),sdtasdt0(xc,xv)) = sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(paramod,[status(thm)],[c_74,c_12667]) ).
cnf(c_191,plain,
sdtpldt0(sdtasdt0(xc,sK1),sdtasdt0(xc,sK0)) = sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(paramod,[status(thm)],[c_83,c_12668]) ).
cnf(c_12669,plain,
sdtasdt0(xz,sdtasdt0(xc,xu)) = sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(paramod,[status(thm)],[c_77,c_71]) ).
cnf(c_192,plain,
sdtasdt0(xz,sdtasdt0(xc,sK1)) = sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(paramod,[status(thm)],[c_88,c_12669]) ).
cnf(c_12670,negated_conjecture,
( sdtasdt0(xz,sdtasdt0(xc,sK1)) != sdtasdt0(xc,B)
| ~ aElement0(B)
| sdtasdt0(xc,A) != sdtasdt0(xc,sdtpldt0(xu,xv))
| ~ aElement0(A) ),
inference(paramod,[status(thm)],[c_191,c_187]) ).
cnf(c_12671,negated_conjecture,
( sdtasdt0(xc,sdtasdt0(xu,xz)) != sdtasdt0(xc,B)
| ~ aElement0(B)
| sdtasdt0(xc,A) != sdtasdt0(xc,sdtpldt0(xu,xv))
| ~ aElement0(A) ),
inference(paramod,[status(thm)],[c_192,c_12670]) ).
cnf(c_267,negated_conjecture,
( sdtasdt0(xc,sdtasdt0(xu,xz)) != sdtasdt0(xc,B)
| ~ aElement0(B)
| sdtasdt0(xc,sdtpldt0(xu,xv)) != sdtasdt0(xc,A)
| ~ aElement0(A) ),
inference(copy,[status(thm)],[c_12671]) ).
cnf(c_883,plain,
( aElement0(sdtasdt0(xu,A))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_166,c_78]) ).
cnf(c_1474,plain,
( ~ aElement0(sdtasdt0(xu,xz))
| sdtasdt0(xc,sdtpldt0(xu,xv)) != sdtasdt0(xc,A)
| ~ aElement0(A) ),
inference(xxres,[status(thm)],[c_267]) ).
cnf(c_1556,plain,
( ~ aElement0(sdtasdt0(xu,xz))
| ~ aElement0(sdtpldt0(xu,xv)) ),
inference(xxres,[status(thm)],[c_1474]) ).
cnf(c_12585,plain,
aElement0(sdtasdt0(xu,xz)),
inference(resolve,[status(thm)],[c_883,c_79]) ).
cnf(c_12639,plain,
~ aElement0(sdtpldt0(xu,xv)),
inference(resolve,[status(thm)],[c_12585,c_1556]) ).
cnf(c_12672,plain,
( aElement0(sdtpldt0(A,xv))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_167,c_75]) ).
cnf(c_12673,plain,
~ aElement0(xu),
inference(resolve,[status(thm)],[c_12672,c_12639]) ).
cnf(c_12658,plain,
$false,
inference(resolve,[status(thm)],[c_78,c_12673]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG105+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n014.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 06:06:16 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2352671 was started by sandbox2 on n014,
% 0.09/0.37 % Sat Sep 26 06:06:16 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.39
% 0.14/0.39 % From the command line: assign(max_seconds, 300).
% 34.86/4.88
% 34.86/4.88 % given #500 (T,wt=8): 8150 doDivides0(c1,sz10) | sz10 != c1. [para(766(a,1),202(d,1)),flip(d),unit_del(a,89),unit_del(b,169)].
% 34.86/4.88
% 34.86/4.88 % SZS status Theorem for theBenchmark
% 34.86/4.88
% 34.86/4.88 % Proof 1 at 4.17 (+ 0.24) seconds.
% 34.86/4.88 % Length of proof is 32.
% 34.86/4.88 % Level of proof is 9.
% 34.86/4.88 % Maximum clause weight is 32.000.
% 34.86/4.88 % Given clauses 803.
% 34.86/4.88
% 34.86/4.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------