%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM560+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 : n019.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 08:17:24 AM UTC 2026
% Result : Theorem 233.83s 31.19s
% Output : CNFRefutation 233.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 11 unt; 0 def)
% Number of atoms : 103 ( 6 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 120 ( 49 ~; 50 |; 14 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 23 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefSub,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& aSet0(W1) ) ) ),
file('theBenchmark.p',mDefSub) ).
fof(mDomSet,axiom,
! [W0] :
( aFunction0(W0)
=> aSet0(szDzozmdt0(W0)) ),
file('theBenchmark.p',mDomSet) ).
fof(mDefPtt,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aFunction0(W0) )
=> ! [W2] :
( W2 = sdtlbdtrb0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( sdtlpdtrp0(W0,W3) = W1
& aElementOf0(W3,szDzozmdt0(W0)) ) )
& aSet0(W2) ) ) ),
file('theBenchmark.p',mDefPtt) ).
fof(m__2693,axiom,
( aElement0(xy)
& aFunction0(xF) ),
file('theBenchmark.p',m__2693) ).
fof(m__,conjecture,
aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF)),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF)),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_67,plain,
aFunction0(xF),
inference(clausify,[status(thm)],[m__2693]) ).
cnf(c_72,plain,
( aElementOf0(D,szDzozmdt0(A))
| ~ aElementOf0(D,C)
| sdtlbdtrb0(A,B) != C
| ~ aElement0(B)
| ~ aFunction0(A) ),
inference(clausify,[status(thm)],[mDefPtt]) ).
cnf(c_73,plain,
( aSet0(C)
| sdtlbdtrb0(A,B) != C
| ~ aElement0(B)
| ~ aFunction0(A) ),
inference(clausify,[status(thm)],[mDefPtt]) ).
cnf(c_75,plain,
( aSet0(szDzozmdt0(A))
| ~ aFunction0(A) ),
inference(clausify,[status(thm)],[mDomSet]) ).
cnf(c_76,plain,
aSet0(szDzozmdt0(xF)),
inference(resolve,[status(thm)],[c_75,c_67]) ).
cnf(c_78,plain,
( aSet0(B)
| sdtlbdtrb0(xF,A) != B
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_73,c_67]) ).
cnf(c_79,plain,
( aElementOf0(C,szDzozmdt0(xF))
| ~ aElementOf0(C,B)
| sdtlbdtrb0(xF,A) != B
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_72,c_67]) ).
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_94,plain,
( aElementOf0(sK0(A,B),B)
| ~ aSet0(B)
| aSubsetOf0(B,A)
| ~ aSet0(A) ),
inference(split_conjunct,[status(thm)],[sk_mDefSub]) ).
cnf(c_95,plain,
( ~ aElementOf0(sK0(A,B),A)
| ~ aSet0(B)
| aSubsetOf0(B,A)
| ~ aSet0(A) ),
inference(split_conjunct,[status(thm)],[sk_mDefSub]) ).
cnf(c_196,plain,
aElement0(xy),
inference(clausify,[status(thm)],[m__2693]) ).
cnf(c_197,negated_conjecture,
~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF)),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_239,plain,
( aSet0(sdtlbdtrb0(xF,A))
| ~ aElement0(A) ),
inference(xxres,[status(thm)],[c_78]) ).
cnf(c_240,plain,
( aElementOf0(B,szDzozmdt0(xF))
| ~ aElementOf0(B,sdtlbdtrb0(xF,A))
| ~ aElement0(A) ),
inference(xxres,[status(thm)],[c_79]) ).
cnf(c_247,plain,
( aElementOf0(sK0(szDzozmdt0(xF),A),A)
| ~ aSet0(A)
| aSubsetOf0(A,szDzozmdt0(xF)) ),
inference(resolve,[status(thm)],[c_94,c_76]) ).
cnf(c_249,plain,
( ~ aElementOf0(sK0(szDzozmdt0(xF),A),szDzozmdt0(xF))
| ~ aSet0(A)
| aSubsetOf0(A,szDzozmdt0(xF)) ),
inference(resolve,[status(thm)],[c_95,c_76]) ).
cnf(c_480,plain,
aSet0(sdtlbdtrb0(xF,xy)),
inference(resolve,[status(thm)],[c_239,c_196]) ).
cnf(c_524,plain,
( aElementOf0(A,szDzozmdt0(xF))
| ~ aElementOf0(A,sdtlbdtrb0(xF,xy)) ),
inference(resolve,[status(thm)],[c_240,c_196]) ).
cnf(c_16527,plain,
( aElementOf0(sK0(szDzozmdt0(xF),sdtlbdtrb0(xF,xy)),sdtlbdtrb0(xF,xy))
| aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF)) ),
inference(resolve,[status(thm)],[c_247,c_480]) ).
cnf(c_933,negated_conjecture,
aElementOf0(sK0(szDzozmdt0(xF),sdtlbdtrb0(xF,xy)),sdtlbdtrb0(xF,xy)),
inference(resolve,[status(thm)],[c_197,c_16527]) ).
cnf(c_16528,plain,
( ~ aElementOf0(sK0(szDzozmdt0(xF),sdtlbdtrb0(xF,xy)),szDzozmdt0(xF))
| aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF)) ),
inference(resolve,[status(thm)],[c_249,c_480]) ).
cnf(c_1053,negated_conjecture,
~ aElementOf0(sK0(szDzozmdt0(xF),sdtlbdtrb0(xF,xy)),szDzozmdt0(xF)),
inference(resolve,[status(thm)],[c_197,c_16528]) ).
cnf(c_16529,plain,
aElementOf0(sK0(szDzozmdt0(xF),sdtlbdtrb0(xF,xy)),szDzozmdt0(xF)),
inference(resolve,[status(thm)],[c_933,c_524]) ).
cnf(c_16526,plain,
$false,
inference(resolve,[status(thm)],[c_1053,c_16529]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM560+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n019.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 03:14:19 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 272889 was started by sandbox2 on n019,
% 0.19/0.45 % Sat Sep 26 03:14:19 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.48
% 0.19/0.48 % From the command line: assign(max_seconds, 300).
% 233.83/31.19
% 233.83/31.19 % given #500 (T,wt=11): 2449 szNzAzT0 != A | aElementOf0(sz00,A). [resolve(488,a,1275,a),rewrite([319(5)])].
% 233.83/31.19
% 233.83/31.19 % given #1000 (F,wt=22): 6331 sdtpldt0(szNzAzT0,slbdtrb0(sz00)) != slbdtrb0(sz00). [resolve(6147,a,226,a),flip(b),unit_del(a,6176)].
% 233.83/31.19
% 233.83/31.19 % given #1500 (T,wt=22): 7672 aSet0(sdtmndt0(sdtpldt0(szNzAzT0,sz00),szszuzczcdt0(sz00))). [resolve(1267,a,1121,a)].
% 233.83/31.19
% 233.83/31.19 % given #2000 (A,wt=26): 554 -aElement0(A) | sdtmndt0(slbdtrb0(sz00),A) != B | -aElementOf0(C,B). [resolve(366,a,111,a),unit_del(d,470)].
% 233.83/31.19
% 233.83/31.19 % given #2500 (T,wt=24): 842 -aElementOf0(A,szNzAzT0) | sdtlseqdt0(f9(sz00,szNzAzT0),A) | sdtlseqdt0(szszuzczcdt0(A),f9(sz00,szNzAzT0)). [resolve(447,a,141,a)].
% 233.83/31.19
% 233.83/31.19 % given #3000 (W,wt=22): 15711 sbrdtbr0(sdtmndt0(szNzAzT0,sz00)) != f1(szNzAzT0). [resolve(15704,b,1314,a),flip(b),unit_del(a,1313)].
% 233.83/31.19
% 233.83/31.19 % SZS status Theorem for theBenchmark
% 233.83/31.19
% 233.83/31.19 % Proof 1 at 4.36 (+ 2.02) seconds.
% 233.83/31.19 % Length of proof is 25.
% 233.83/31.19 % Level of proof is 6.
% 233.83/31.19 % Maximum clause weight is 28.000.
% 233.83/31.19 % Given clauses 3461.
% 233.83/31.19
% 233.83/31.19 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------