%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM564+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 08:17:25 AM UTC 2026
% Result : Theorem 16.33s 2.83s
% Output : CNFRefutation 16.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 58 ( 28 unt; 0 def)
% Number of atoms : 149 ( 34 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 157 ( 66 ~; 60 |; 20 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 58 ( 4 sgn 27 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefEmp,axiom,
! [W0] :
( W0 = slcrc0
<=> ( ~ ? [W1] : aElementOf0(W1,W0)
& aSet0(W0) ) ),
file('theBenchmark.p',mDefEmp) ).
fof(mDefSub,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& aSet0(W1) ) ) ),
file('theBenchmark.p',mDefSub) ).
fof(mNATSet,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('theBenchmark.p',mNATSet) ).
fof(mDefSeg,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( W1 = slbdtrb0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ( sdtlseqdt0(szszuzczcdt0(W2),W0)
& aElementOf0(W2,szNzAzT0) ) )
& aSet0(W1) ) ) ),
file('theBenchmark.p',mDefSeg) ).
fof(mCardSeg,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> sbrdtbr0(slbdtrb0(W0)) = W0 ),
file('theBenchmark.p',mCardSeg) ).
fof(mDefSel,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aSet0(W0) )
=> ! [W2] :
( W2 = slbdtsldtrb0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) ) )
& aSet0(W2) ) ) ),
file('theBenchmark.p',mDefSel) ).
fof(m__3435,axiom,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
file('theBenchmark.p',m__3435) ).
fof(m__3453,axiom,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aFunction0(xc) ),
file('theBenchmark.p',m__3453) ).
fof(m__,conjecture,
aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_77,plain,
( ~ aElementOf0(B,A)
| slcrc0 != A ),
inference(clausify,[status(thm)],[mDefEmp]) ).
fof(nnf_9,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ( ( ! [X0] :
( aElementOf0(X0,W0)
| ~ aElementOf0(X0,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mDefSub]) ).
fof(sk_mDefSub_sk,plain,
! [W0] :
( ! [W1] :
( ( ( ~ aElementOf0(sK0(W0,W1),W0)
& aElementOf0(sK0(W0,W1),W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ( ( ! [X0] :
( aElementOf0(X0,W0)
| ~ aElementOf0(X0,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W2,sK0(W0,W1))],[nnf_9]) ).
fof(sk_mDefSub,plain,
( ! [VAR_0,VAR_1] :
( ~ aElementOf0(sK0(VAR_0,VAR_1),VAR_0)
| ~ aSet0(VAR_1)
| aSubsetOf0(VAR_1,VAR_0)
| ~ aSet0(VAR_0) )
& ! [VAR_0,VAR_1] :
( aElementOf0(sK0(VAR_0,VAR_1),VAR_1)
| ~ aSet0(VAR_1)
| aSubsetOf0(VAR_1,VAR_0)
| ~ aSet0(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( aElementOf0(VAR_2,VAR_0)
| ~ aElementOf0(VAR_2,VAR_1)
| ~ aSubsetOf0(VAR_1,VAR_0)
| ~ aSet0(VAR_0) )
& ! [VAR_0,VAR_1] :
( aSet0(VAR_1)
| ~ aSubsetOf0(VAR_1,VAR_0)
| ~ aSet0(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_mDefSub_sk]) ).
cnf(c_82,plain,
( aSet0(B)
| ~ aSubsetOf0(B,A)
| ~ aSet0(A) ),
inference(split_conjunct,[status(thm)],[sk_mDefSub]) ).
cnf(c_84,plain,
( aElementOf0(sK0(A,B),B)
| ~ aSet0(B)
| aSubsetOf0(B,A)
| ~ aSet0(A) ),
inference(split_conjunct,[status(thm)],[sk_mDefSub]) ).
cnf(c_114,plain,
aSet0(szNzAzT0),
inference(clausify,[status(thm)],[mNATSet]) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('theBenchmark.p',mZeroNum) ).
cnf(c_116,plain,
aElementOf0(sz00,szNzAzT0),
inference(clausify,[status(thm)],[mZeroNum]) ).
cnf(c_153,plain,
( aSet0(B)
| slbdtrb0(A) != B
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mDefSeg]) ).
fof(mSegZero,axiom,
slbdtrb0(sz00) = slcrc0,
file('theBenchmark.p',mSegZero) ).
cnf(c_161,plain,
slbdtrb0(sz00) = slcrc0,
inference(clausify,[status(thm)],[mSegZero]) ).
cnf(c_162,plain,
slcrc0 = slbdtrb0(sz00),
inference(copy,[status(thm)],[c_161]) ).
cnf(c_170,plain,
( sbrdtbr0(slbdtrb0(A)) = A
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mCardSeg]) ).
cnf(c_174,plain,
( sbrdtbr0(D) != B
| ~ aSubsetOf0(D,A)
| aElementOf0(D,C)
| slbdtsldtrb0(A,B) != C
| ~ aElementOf0(B,szNzAzT0)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefSel]) ).
cnf(c_220,plain,
aSubsetOf0(xS,szNzAzT0),
inference(clausify,[status(thm)],[m__3435]) ).
cnf(c_223,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(clausify,[status(thm)],[m__3453]) ).
cnf(c_224,plain,
slbdtsldtrb0(xS,xK) = szDzozmdt0(xc),
inference(copy,[status(thm)],[c_223]) ).
fof(m__3462,axiom,
xK = sz00,
file('theBenchmark.p',m__3462) ).
cnf(c_231,plain,
xK = sz00,
inference(clausify,[status(thm)],[m__3462]) ).
cnf(c_232,negated_conjecture,
~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_233,negated_conjecture,
~ aElementOf0(slbdtrb0(sz00),slbdtsldtrb0(xS,sz00)),
inference(paramod,[status(thm)],[c_162,c_232]) ).
cnf(c_263,plain,
( ~ aElementOf0(B,A)
| slbdtrb0(sz00) != A ),
inference(paramod,[status(thm)],[c_162,c_77]) ).
cnf(c_282,plain,
slbdtsldtrb0(xS,sz00) = szDzozmdt0(xc),
inference(paramod,[status(thm)],[c_231,c_224]) ).
cnf(c_283,negated_conjecture,
~ aElementOf0(slbdtrb0(sz00),szDzozmdt0(xc)),
inference(paramod,[status(thm)],[c_282,c_233]) ).
cnf(c_12979,plain,
( aSet0(B)
| B != slbdtrb0(A)
| ~ aElementOf0(A,szNzAzT0) ),
inference(copy,[status(thm)],[c_153]) ).
cnf(c_12980,plain,
( aSet0(slcrc0)
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(resolve,[status(thm)],[c_162,c_12979]) ).
cnf(c_12981,plain,
( aSet0(slbdtrb0(sz00))
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(paramod,[status(thm)],[c_162,c_12980]) ).
cnf(c_393,plain,
aSet0(slbdtrb0(sz00)),
inference(resolve,[status(thm)],[c_116,c_12981]) ).
cnf(c_403,plain,
sbrdtbr0(slbdtrb0(sz00)) = sz00,
inference(resolve,[status(thm)],[c_170,c_116]) ).
cnf(c_418,plain,
( sbrdtbr0(C) != sz00
| ~ aSubsetOf0(C,A)
| aElementOf0(C,B)
| slbdtsldtrb0(A,sz00) != B
| ~ aSet0(A) ),
inference(resolve,[status(thm)],[c_174,c_116]) ).
cnf(c_12982,plain,
( aSet0(xS)
| ~ aSet0(szNzAzT0) ),
inference(resolve,[status(thm)],[c_220,c_82]) ).
cnf(c_581,plain,
aSet0(xS),
inference(resolve,[status(thm)],[c_114,c_12982]) ).
cnf(c_12983,plain,
slbdtrb0(sz00) = slcrc0,
inference(copy,[status(thm)],[c_162]) ).
cnf(c_12984,plain,
~ aElementOf0(A,slcrc0),
inference(resolve,[status(thm)],[c_263,c_12983]) ).
cnf(c_693,plain,
~ aElementOf0(A,slbdtrb0(sz00)),
inference(paramod,[status(thm)],[c_162,c_12984]) ).
cnf(c_12985,plain,
( aElementOf0(sK0(A,slbdtrb0(sz00)),slbdtrb0(sz00))
| aSubsetOf0(slbdtrb0(sz00),A)
| ~ aSet0(A) ),
inference(resolve,[status(thm)],[c_393,c_84]) ).
cnf(c_1000,plain,
( aSubsetOf0(slbdtrb0(sz00),A)
| ~ aSet0(A) ),
inference(resolve,[status(thm)],[c_693,c_12985]) ).
cnf(c_2761,plain,
aSubsetOf0(slbdtrb0(sz00),xS),
inference(resolve,[status(thm)],[c_1000,c_581]) ).
cnf(c_12986,plain,
( sbrdtbr0(slbdtrb0(sz00)) != sz00
| aElementOf0(slbdtrb0(sz00),A)
| slbdtsldtrb0(xS,sz00) != A
| ~ aSet0(xS) ),
inference(resolve,[status(thm)],[c_418,c_2761]) ).
cnf(c_12987,plain,
( sbrdtbr0(slbdtrb0(sz00)) != sz00
| aElementOf0(slbdtrb0(sz00),A)
| szDzozmdt0(xc) != A
| ~ aSet0(xS) ),
inference(paramod,[status(thm)],[c_282,c_12986]) ).
cnf(c_12988,plain,
( sz00 != sz00
| aElementOf0(slbdtrb0(sz00),A)
| szDzozmdt0(xc) != A
| ~ aSet0(xS) ),
inference(paramod,[status(thm)],[c_403,c_12987]) ).
cnf(c_12989,plain,
( aElementOf0(slbdtrb0(sz00),A)
| szDzozmdt0(xc) != A
| ~ aSet0(xS) ),
inference(copy,[status(thm)],[c_12988]) ).
cnf(c_12970,plain,
( aElementOf0(slbdtrb0(sz00),A)
| szDzozmdt0(xc) != A ),
inference(resolve,[status(thm)],[c_581,c_12989]) ).
cnf(c_12990,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,sz00),
inference(copy,[status(thm)],[c_282]) ).
cnf(c_12991,plain,
aElementOf0(slbdtrb0(sz00),slbdtsldtrb0(xS,sz00)),
inference(resolve,[status(thm)],[c_12970,c_12990]) ).
cnf(c_12992,plain,
aElementOf0(slbdtrb0(sz00),szDzozmdt0(xc)),
inference(paramod,[status(thm)],[c_282,c_12991]) ).
cnf(c_12978,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_283,c_12992]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM564+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 03:18:13 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2989138 was started by sandbox on n015,
% 0.10/0.37 % Sat Sep 26 03:18:13 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.40
% 0.10/0.40 % From the command line: assign(max_seconds, 300).
% 16.33/2.83
% 16.33/2.83 % given #500 (T,wt=17): 3768 sz00 != A | sdtlseqdt0(A,f1(szNzAzT0)). [back_rewrite(1509),rewrite([3754(2)])].
% 16.33/2.83
% 16.33/2.83 % given #1000 (A,wt=26): 399 -aElementOf0(A,szNzAzT0) | aElementOf0(A,slbdtrb0(szszuzczcdt0(sz00))) | sz00 != A. [resolve(165,b,116,a)].
% 16.33/2.83
% 16.33/2.83 % SZS status Theorem for theBenchmark
% 16.33/2.83
% 16.33/2.83 % Proof 1 at 1.61 (+ 0.58) seconds.
% 16.33/2.83 % Length of proof is 37.
% 16.33/2.83 % Level of proof is 7.
% 16.33/2.83 % Maximum clause weight is 30.000.
% 16.33/2.83 % Given clauses 1170.
% 16.33/2.83
% 16.33/2.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------