%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG099+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 : n026.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 08:26:38 AM UTC 2026
% Result : Theorem 41.10s 5.73s
% Output : CNFRefutation 41.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 49 ( 23 unt; 0 def)
% Number of atoms : 127 ( 15 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 123 ( 45 ~; 41 |; 21 &)
% ( 3 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 18 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mEOfElem,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('theBenchmark.p',mEOfElem) ).
fof(mDefSSum,axiom,
! [W0,W1] :
( ( aSet0(W1)
& aSet0(W0) )
=> ! [W2] :
( W2 = sdtpldt1(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ? [W4,W5] :
( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) ) )
& aSet0(W2) ) ) ),
file('theBenchmark.p',mDefSSum) ).
fof(mDefIdeal,axiom,
! [W0] :
( aIdeal0(W0)
<=> ( ! [W1] :
( aElementOf0(W1,W0)
=> ( ! [W2] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) )
& ! [W2] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) ) ) )
& aSet0(W0) ) ),
file('theBenchmark.p',mDefIdeal) ).
fof(mIdeSum,axiom,
! [W0,W1] :
( ( aIdeal0(W1)
& aIdeal0(W0) )
=> aIdeal0(sdtpldt1(W0,W1)) ),
file('theBenchmark.p',mIdeSum) ).
fof(m__1205,axiom,
( aIdeal0(xJ)
& ! [W0] :
( aElementOf0(W0,xJ)
=> ( ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xJ) )
& ! [W1] :
( aElementOf0(W1,xJ)
=> aElementOf0(sdtpldt0(W0,W1),xJ) ) ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [W0] :
( aElementOf0(W0,xI)
=> ( ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) )
& ! [W1] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) ) ) )
& aSet0(xI) ),
file('theBenchmark.p',m__1205) ).
fof(m__1217,axiom,
( aElement0(xy)
& aElement0(xx) ),
file('theBenchmark.p',m__1217) ).
fof(m__1294,axiom,
( sdtpldt0(xa,xb) = sz10
& aElementOf0(xb,xJ)
& aElementOf0(xa,xI) ),
file('theBenchmark.p',m__1294) ).
fof(m__,conjecture,
? [W0] :
( ( sdteqdtlpzmzozddtrp0(W0,xy,xJ)
| aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ) )
& ( sdteqdtlpzmzozddtrp0(W0,xx,xI)
| aElementOf0(sdtpldt0(W0,smndt0(xx)),xI) )
& aElement0(W0) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ? [W0] :
( ( sdteqdtlpzmzozddtrp0(W0,xy,xJ)
| aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ) )
& ( sdteqdtlpzmzozddtrp0(W0,xx,xI)
| aElementOf0(sdtpldt0(W0,smndt0(xx)),xI) )
& aElement0(W0) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_56,plain,
( aElement0(B)
| ~ aElementOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mEOfElem]) ).
cnf(c_65,plain,
( sdtpldt0(E,F) != D
| ~ aElementOf0(F,B)
| ~ aElementOf0(E,A)
| aElementOf0(D,C)
| sdtpldt1(A,B) != C
| ~ aSet0(B)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefSSum]) ).
cnf(c_78,plain,
( aSet0(A)
| ~ aIdeal0(A) ),
inference(clausify,[status(thm)],[mDefIdeal]) ).
cnf(c_86,plain,
( aIdeal0(sdtpldt1(A,B))
| ~ aIdeal0(B)
| ~ aIdeal0(A) ),
inference(clausify,[status(thm)],[mIdeSum]) ).
cnf(c_90,plain,
aSet0(xI),
inference(clausify,[status(thm)],[m__1205]) ).
cnf(c_92,plain,
( aElementOf0(sdtasdt0(B,A),xI)
| ~ aElement0(B)
| ~ aElementOf0(A,xI) ),
inference(clausify,[status(thm)],[m__1205]) ).
cnf(c_93,plain,
aIdeal0(xI),
inference(clausify,[status(thm)],[m__1205]) ).
cnf(c_94,plain,
aSet0(xJ),
inference(clausify,[status(thm)],[m__1205]) ).
cnf(c_96,plain,
( aElementOf0(sdtasdt0(B,A),xJ)
| ~ aElement0(B)
| ~ aElementOf0(A,xJ) ),
inference(clausify,[status(thm)],[m__1205]) ).
cnf(c_97,plain,
aIdeal0(xJ),
inference(clausify,[status(thm)],[m__1205]) ).
cnf(c_102,plain,
aElement0(xx),
inference(clausify,[status(thm)],[m__1217]) ).
cnf(c_103,plain,
aElement0(xy),
inference(clausify,[status(thm)],[m__1217]) ).
cnf(c_104,plain,
aElementOf0(xa,xI),
inference(clausify,[status(thm)],[m__1294]) ).
cnf(c_105,plain,
aElementOf0(xb,xJ),
inference(clausify,[status(thm)],[m__1294]) ).
fof(m__1319,axiom,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
file('theBenchmark.p',m__1319) ).
cnf(c_108,plain,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
inference(clausify,[status(thm)],[m__1319]) ).
cnf(c_109,plain,
sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)) = xw,
inference(copy,[status(thm)],[c_108]) ).
fof(m__1332,axiom,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
file('theBenchmark.p',m__1332) ).
cnf(c_110,plain,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(clausify,[status(thm)],[m__1332]) ).
fof(m__1409,axiom,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
file('theBenchmark.p',m__1409) ).
cnf(c_111,plain,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
inference(clausify,[status(thm)],[m__1409]) ).
cnf(c_112,negated_conjecture,
( ~ aElementOf0(sdtpldt0(A,smndt0(xy)),xJ)
| ~ aElementOf0(sdtpldt0(A,smndt0(xx)),xI)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_269,plain,
( sdtpldt0(D,E) != C
| ~ aElementOf0(E,A)
| ~ aElementOf0(D,xI)
| aElementOf0(C,B)
| sdtpldt1(xI,A) != B
| ~ aSet0(A) ),
inference(resolve,[status(thm)],[c_90,c_65]) ).
cnf(c_308,plain,
( aIdeal0(sdtpldt1(xI,A))
| ~ aIdeal0(A) ),
inference(resolve,[status(thm)],[c_93,c_86]) ).
cnf(c_478,plain,
( aElementOf0(sdtasdt0(A,xa),xI)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_104,c_92]) ).
cnf(c_501,plain,
( aElementOf0(sdtasdt0(A,xb),xJ)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_105,c_96]) ).
cnf(c_10676,negated_conjecture,
( ~ aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ)
| ~ aElement0(xw) ),
inference(resolve,[status(thm)],[c_112,c_110]) ).
cnf(c_559,negated_conjecture,
~ aElement0(xw),
inference(resolve,[status(thm)],[c_111,c_10676]) ).
cnf(c_4544,plain,
aIdeal0(sdtpldt1(xI,xJ)),
inference(resolve,[status(thm)],[c_308,c_97]) ).
cnf(c_4577,plain,
aSet0(sdtpldt1(xI,xJ)),
inference(resolve,[status(thm)],[c_4544,c_78]) ).
cnf(c_10677,plain,
( aElement0(A)
| ~ aElementOf0(A,sdtpldt1(xI,xJ)) ),
inference(resolve,[status(thm)],[c_56,c_4577]) ).
cnf(c_4643,plain,
~ aElementOf0(xw,sdtpldt1(xI,xJ)),
inference(resolve,[status(thm)],[c_10677,c_559]) ).
cnf(c_10205,plain,
aElementOf0(sdtasdt0(xy,xa),xI),
inference(resolve,[status(thm)],[c_478,c_103]) ).
cnf(c_10678,plain,
( sdtpldt0(C,D) != B
| ~ aElementOf0(D,xJ)
| ~ aElementOf0(C,xI)
| aElementOf0(B,A)
| sdtpldt1(xI,xJ) != A ),
inference(resolve,[status(thm)],[c_269,c_94]) ).
cnf(c_10679,plain,
( sdtpldt0(B,C) != A
| ~ aElementOf0(C,xJ)
| ~ aElementOf0(B,xI)
| aElementOf0(A,sdtpldt1(xI,xJ)) ),
inference(xxres,[status(thm)],[c_10678]) ).
cnf(c_10680,plain,
( sdtpldt0(A,B) != xw
| ~ aElementOf0(B,xJ)
| ~ aElementOf0(A,xI) ),
inference(resolve,[status(thm)],[c_10679,c_4643]) ).
cnf(c_10681,plain,
( sdtpldt0(sdtasdt0(xy,xa),A) != xw
| ~ aElementOf0(A,xJ) ),
inference(resolve,[status(thm)],[c_10680,c_10205]) ).
cnf(c_10515,plain,
~ aElementOf0(sdtasdt0(xx,xb),xJ),
inference(resolve,[status(thm)],[c_10681,c_109]) ).
cnf(c_10682,plain,
aElementOf0(sdtasdt0(xx,xb),xJ),
inference(resolve,[status(thm)],[c_501,c_102]) ).
cnf(c_10675,plain,
$false,
inference(resolve,[status(thm)],[c_10515,c_10682]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG099+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n026.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 06:07:56 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.03/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.37 % Process 266640 was started by sandbox2 on n026,
% 0.03/0.37 % Sat Sep 26 06:07:56 2026
% 0.03/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/0.39
% 0.03/0.39 % From the command line: assign(max_seconds, 300).
% 41.10/5.73
% 41.10/5.73 % given #500 (A,wt=13): 261 -aSet0(A) | sdtasasdt0(xI,A) != B | aSet0(B). [resolve(90,a,71,a)].
% 41.10/5.73
% 41.10/5.73 % SZS status Theorem for theBenchmark
% 41.10/5.73
% 41.10/5.73 % Proof 1 at 4.80 (+ 0.26) seconds.
% 41.10/5.73 % Length of proof is 38.
% 41.10/5.73 % Level of proof is 7.
% 41.10/5.73 % Maximum clause weight is 27.000.
% 41.10/5.73 % Given clauses 552.
% 41.10/5.73
% 41.10/5.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------