%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG105+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 : n006.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 35.21s 10.12s
% Output : CNFRefutation 35.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 50 ( 24 unt; 0 def)
% Number of atoms : 94 ( 20 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 81 ( 37 ~; 29 |; 10 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 7 !; 1 ?)
% 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(mDefPrIdeal,axiom,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( W1 = slsdtgt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) ) )
& aSet0(W1) ) ) ),
file('theBenchmark.p',mDefPrIdeal) ).
fof(m__1933,axiom,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& aElementOf0(xx,slsdtgt0(xc)) ),
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))
& aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
& aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_67,negated_conjecture,
( ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) ),
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_68,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_69,plain,
sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(clausify,[status(thm)],[m__2010]) ).
cnf(c_70,plain,
sdtasdt0(xc,xv) = xy,
inference(clausify,[status(thm)],[m__1979]) ).
cnf(c_71,plain,
xy = sdtasdt0(xc,xv),
inference(copy,[status(thm)],[c_70]) ).
cnf(c_72,plain,
aElement0(xv),
inference(clausify,[status(thm)],[m__1979]) ).
cnf(c_73,plain,
sdtasdt0(xc,xu) = xx,
inference(clausify,[status(thm)],[m__1956]) ).
cnf(c_74,plain,
xx = sdtasdt0(xc,xu),
inference(copy,[status(thm)],[c_73]) ).
cnf(c_75,plain,
aElement0(xu),
inference(clausify,[status(thm)],[m__1956]) ).
cnf(c_76,plain,
aElement0(xz),
inference(clausify,[status(thm)],[m__1933]) ).
fof(m__1905,axiom,
aElement0(xc),
file('theBenchmark.p',m__1905) ).
cnf(c_81,plain,
aElement0(xc),
inference(clausify,[status(thm)],[m__1905]) ).
cnf(c_86,plain,
( sdtasdt0(A,D) != C
| ~ aElement0(D)
| aElementOf0(C,B)
| slsdtgt0(A) != B
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mDefPrIdeal]) ).
cnf(c_157,plain,
( aElement0(sdtasdt0(A,B))
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mSortsB_02]) ).
cnf(c_158,plain,
( aElement0(sdtpldt0(A,B))
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mSortsB]) ).
cnf(c_19039,negated_conjecture,
( ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(sdtasdt0(xc,xu),xy),slsdtgt0(xc)) ),
inference(paramod,[status(thm)],[c_74,c_67]) ).
cnf(c_19040,negated_conjecture,
( ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(sdtasdt0(xc,xu),sdtasdt0(xc,xv)),slsdtgt0(xc)) ),
inference(paramod,[status(thm)],[c_71,c_19039]) ).
cnf(c_177,negated_conjecture,
( ~ aElementOf0(sdtasdt0(xz,sdtasdt0(xc,xu)),slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(sdtasdt0(xc,xu),sdtasdt0(xc,xv)),slsdtgt0(xc)) ),
inference(paramod,[status(thm)],[c_74,c_19040]) ).
cnf(c_19041,plain,
sdtpldt0(sdtasdt0(xc,xu),xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(paramod,[status(thm)],[c_74,c_69]) ).
cnf(c_178,plain,
sdtpldt0(sdtasdt0(xc,xu),sdtasdt0(xc,xv)) = sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(paramod,[status(thm)],[c_71,c_19041]) ).
cnf(c_179,plain,
sdtasdt0(xz,sdtasdt0(xc,xu)) = sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(paramod,[status(thm)],[c_74,c_68]) ).
cnf(c_19042,negated_conjecture,
( ~ aElementOf0(sdtasdt0(xz,sdtasdt0(xc,xu)),slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(xc,sdtpldt0(xu,xv)),slsdtgt0(xc)) ),
inference(paramod,[status(thm)],[c_178,c_177]) ).
cnf(c_246,negated_conjecture,
( ~ aElementOf0(sdtasdt0(xc,sdtasdt0(xu,xz)),slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(xc,sdtpldt0(xu,xv)),slsdtgt0(xc)) ),
inference(paramod,[status(thm)],[c_179,c_19042]) ).
cnf(c_412,plain,
( sdtasdt0(A,C) != B
| ~ aElement0(C)
| aElementOf0(B,slsdtgt0(A))
| ~ aElement0(A) ),
inference(xxres,[status(thm)],[c_86]) ).
cnf(c_804,plain,
( aElement0(sdtasdt0(xu,A))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_157,c_75]) ).
cnf(c_812,plain,
( aElement0(sdtpldt0(xu,A))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_158,c_75]) ).
cnf(c_13471,plain,
aElement0(sdtasdt0(xu,xz)),
inference(resolve,[status(thm)],[c_804,c_76]) ).
cnf(c_16291,plain,
aElement0(sdtpldt0(xu,xv)),
inference(resolve,[status(thm)],[c_812,c_72]) ).
cnf(c_19043,plain,
sdtasdt0(xc,sdtasdt0(xu,xz)) = sdtasdt0(xz,sdtasdt0(xc,xu)),
inference(copy,[status(thm)],[c_179]) ).
cnf(c_19044,plain,
( ~ aElement0(sdtasdt0(xu,xz))
| aElementOf0(sdtasdt0(xz,sdtasdt0(xc,xu)),slsdtgt0(xc))
| ~ aElement0(xc) ),
inference(resolve,[status(thm)],[c_412,c_19043]) ).
cnf(c_19045,plain,
( ~ aElement0(sdtasdt0(xu,xz))
| aElementOf0(sdtasdt0(xc,sdtasdt0(xu,xz)),slsdtgt0(xc))
| ~ aElement0(xc) ),
inference(paramod,[status(thm)],[c_179,c_19044]) ).
cnf(c_19046,plain,
( ~ aElement0(sdtasdt0(xu,xz))
| aElementOf0(sdtasdt0(xc,sdtasdt0(xu,xz)),slsdtgt0(xc)) ),
inference(resolve,[status(thm)],[c_81,c_19045]) ).
cnf(c_19019,plain,
aElementOf0(sdtasdt0(xc,sdtasdt0(xu,xz)),slsdtgt0(xc)),
inference(resolve,[status(thm)],[c_13471,c_19046]) ).
cnf(c_19047,plain,
sdtasdt0(xc,sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xc,xu),sdtasdt0(xc,xv)),
inference(copy,[status(thm)],[c_178]) ).
cnf(c_19048,plain,
( ~ aElement0(sdtpldt0(xu,xv))
| aElementOf0(sdtpldt0(sdtasdt0(xc,xu),sdtasdt0(xc,xv)),slsdtgt0(xc))
| ~ aElement0(xc) ),
inference(resolve,[status(thm)],[c_412,c_19047]) ).
cnf(c_19049,plain,
( ~ aElement0(sdtpldt0(xu,xv))
| aElementOf0(sdtasdt0(xc,sdtpldt0(xu,xv)),slsdtgt0(xc))
| ~ aElement0(xc) ),
inference(paramod,[status(thm)],[c_178,c_19048]) ).
cnf(c_19050,plain,
( ~ aElement0(sdtpldt0(xu,xv))
| aElementOf0(sdtasdt0(xc,sdtpldt0(xu,xv)),slsdtgt0(xc)) ),
inference(resolve,[status(thm)],[c_81,c_19049]) ).
cnf(c_19020,plain,
aElementOf0(sdtasdt0(xc,sdtpldt0(xu,xv)),slsdtgt0(xc)),
inference(resolve,[status(thm)],[c_16291,c_19050]) ).
cnf(c_19051,negated_conjecture,
~ aElementOf0(sdtasdt0(xc,sdtasdt0(xu,xz)),slsdtgt0(xc)),
inference(resolve,[status(thm)],[c_19020,c_246]) ).
cnf(c_19038,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_19019,c_19051]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG105+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.59 % Computer : n006.cluster.edu
% 0.10/5.59 % Model : x86_64 x86_64
% 0.10/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.59 % Memory : 8046.5625MB
% 0.10/5.59 % OS : Linux 6.8.0-71-generic
% 0.10/5.59 % CPULimit : 300
% 0.10/5.59 % WCLimit : 300
% 0.10/5.59 % DateTime : Sat Sep 26 06:06:01 UTC 2026
% 0.10/5.59 % CPUTime :
% 0.10/5.59 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.59 % Process 524748 was started by sandbox2 on n006,
% 0.10/5.59 % Sat Sep 26 06:06:01 2026
% 0.10/5.59 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/5.61
% 0.15/5.61 % From the command line: assign(max_seconds, 300).
% 35.21/10.12
% 35.21/10.12 % given #500 (T,wt=15): 767 sdtpldt0(sz00,xz) = xz. [resolve(153,a,76,a)].
% 35.21/10.12
% 35.21/10.12 % SZS status Theorem for theBenchmark
% 35.21/10.12
% 35.21/10.12 % Proof 1 at 4.14 (+ 0.34) seconds.
% 35.21/10.12 % Length of proof is 33.
% 35.21/10.12 % Level of proof is 5.
% 35.21/10.12 % Maximum clause weight is 38.000.
% 35.21/10.12 % Given clauses 630.
% 35.21/10.12
% 35.21/10.12 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------