%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM545+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 08:17:21 AM UTC 2026
% Result : Theorem 0.10s 0.43s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 7 unt; 0 def)
% Number of atoms : 110 ( 12 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 122 ( 40 ~; 33 |; 36 &)
% ( 4 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-1 aty)
% Number of variables : 35 ( 1 sgn 24 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefEmp,axiom,
! [W0] :
( W0 = slcrc0
<=> ( ~ ? [W1] : aElementOf0(W1,W0)
& aSet0(W0) ) ),
file('theBenchmark.p',mDefEmp) ).
fof(mSuccNum,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( szszuzczcdt0(W0) != sz00
& aElementOf0(szszuzczcdt0(W0),szNzAzT0) ) ),
file('theBenchmark.p',mSuccNum) ).
fof(m__1986,axiom,
( isFinite0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [W0] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,szNzAzT0) )
& aSet0(xS) ),
file('theBenchmark.p',m__1986) ).
fof(m__2035,axiom,
( ~ ( xS = slcrc0
& ~ ? [W0] : aElementOf0(W0,xS) )
=> ( aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& ! [W0] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) )
& ! [W0] :
( aElementOf0(W0,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
<=> ( sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(szmzazxdt0(xS)))
& aElementOf0(W0,szNzAzT0) ) )
& aSet0(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& ! [W0] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(W0,szmzazxdt0(xS)) )
& aElementOf0(szmzazxdt0(xS),xS) ) ),
file('theBenchmark.p',m__2035) ).
fof(m__,conjecture,
? [W0] :
( ( ( ! [W1] :
( aElementOf0(W1,slbdtrb0(W0))
<=> ( sdtlseqdt0(szszuzczcdt0(W1),W0)
& aElementOf0(W1,szNzAzT0) ) )
& aSet0(slbdtrb0(W0)) )
=> ( aSubsetOf0(xS,slbdtrb0(W0))
| ! [W1] :
( aElementOf0(W1,xS)
=> aElementOf0(W1,slbdtrb0(W0)) ) ) )
& aElementOf0(W0,szNzAzT0) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ? [W0] :
( ( ( ! [W1] :
( aElementOf0(W1,slbdtrb0(W0))
<=> ( sdtlseqdt0(szszuzczcdt0(W1),W0)
& aElementOf0(W1,szNzAzT0) ) )
& aSet0(slbdtrb0(W0)) )
=> ( aSubsetOf0(xS,slbdtrb0(W0))
| ! [W1] :
( aElementOf0(W1,xS)
=> aElementOf0(W1,slbdtrb0(W0)) ) ) )
& aElementOf0(W0,szNzAzT0) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(nnf_54,plain,
! [W0] :
( ( ~ aSubsetOf0(xS,slbdtrb0(W0))
& ? [W1] :
( ~ aElementOf0(W1,slbdtrb0(W0))
& aElementOf0(W1,xS) )
& ! [X0] :
( ( ~ sdtlseqdt0(szszuzczcdt0(X0),W0)
| ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(X0,slbdtrb0(W0)) )
& ( ( sdtlseqdt0(szszuzczcdt0(X0),W0)
& aElementOf0(X0,szNzAzT0) )
| ~ aElementOf0(X0,slbdtrb0(W0)) ) )
& aSet0(slbdtrb0(W0)) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[m___neg]) ).
fof(sk_m___neg_sk,plain,
! [W0] :
( ( ~ aSubsetOf0(xS,slbdtrb0(W0))
& ~ aElementOf0(sK0(W0),slbdtrb0(W0))
& aElementOf0(sK0(W0),xS)
& ! [X0] :
( ( ~ sdtlseqdt0(szszuzczcdt0(X0),W0)
| ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(X0,slbdtrb0(W0)) )
& ( ( sdtlseqdt0(szszuzczcdt0(X0),W0)
& aElementOf0(X0,szNzAzT0) )
| ~ aElementOf0(X0,slbdtrb0(W0)) ) )
& aSet0(slbdtrb0(W0)) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W1,sK0(W0))],[nnf_54]) ).
fof(sk_m___neg,plain,
( ! [VAR_0] :
( ~ aSubsetOf0(xS,slbdtrb0(VAR_0))
| ~ aElementOf0(VAR_0,szNzAzT0) )
& ! [VAR_0] :
( ~ aElementOf0(sK0(VAR_0),slbdtrb0(VAR_0))
| ~ aElementOf0(VAR_0,szNzAzT0) )
& ! [VAR_0] :
( aElementOf0(sK0(VAR_0),xS)
| ~ aElementOf0(VAR_0,szNzAzT0) )
& ! [VAR_0,VAR_1] :
( ~ sdtlseqdt0(szszuzczcdt0(VAR_1),VAR_0)
| ~ aElementOf0(VAR_1,szNzAzT0)
| aElementOf0(VAR_1,slbdtrb0(VAR_0))
| ~ aElementOf0(VAR_0,szNzAzT0) )
& ! [VAR_0,VAR_1] :
( sdtlseqdt0(szszuzczcdt0(VAR_1),VAR_0)
| ~ aElementOf0(VAR_1,slbdtrb0(VAR_0))
| ~ aElementOf0(VAR_0,szNzAzT0) )
& ! [VAR_0,VAR_1] :
( aElementOf0(VAR_1,szNzAzT0)
| ~ aElementOf0(VAR_1,slbdtrb0(VAR_0))
| ~ aElementOf0(VAR_0,szNzAzT0) )
& ! [VAR_0] :
( aSet0(slbdtrb0(VAR_0))
| ~ aElementOf0(VAR_0,szNzAzT0) ) ),
inference(cnf_transformation,[status(thm)],[sk_m___neg_sk]) ).
cnf(c_55,negated_conjecture,
( ~ aSubsetOf0(xS,slbdtrb0(A))
| ~ aElementOf0(A,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_57,negated_conjecture,
( aElementOf0(sK0(A),xS)
| ~ aElementOf0(A,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_62,plain,
( aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| xS = slcrc0 ),
inference(clausify,[status(thm)],[m__2035]) ).
cnf(c_63,plain,
( aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| slcrc0 = xS ),
inference(copy,[status(thm)],[c_62]) ).
cnf(c_76,plain,
( aElementOf0(szmzazxdt0(xS),xS)
| xS = slcrc0 ),
inference(clausify,[status(thm)],[m__2035]) ).
cnf(c_77,plain,
( aElementOf0(szmzazxdt0(xS),xS)
| slcrc0 = xS ),
inference(copy,[status(thm)],[c_76]) ).
cnf(c_88,plain,
( aElementOf0(A,szNzAzT0)
| ~ aElementOf0(A,xS) ),
inference(clausify,[status(thm)],[m__1986]) ).
cnf(c_139,plain,
( aElementOf0(szszuzczcdt0(A),szNzAzT0)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mSuccNum]) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('theBenchmark.p',mZeroNum) ).
cnf(c_140,plain,
aElementOf0(sz00,szNzAzT0),
inference(clausify,[status(thm)],[mZeroNum]) ).
cnf(c_179,plain,
( ~ aElementOf0(B,A)
| slcrc0 != A ),
inference(clausify,[status(thm)],[mDefEmp]) ).
cnf(c_202,plain,
( ~ aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0)
| slcrc0 = xS ),
inference(resolve,[status(thm)],[c_63,c_55]) ).
cnf(c_203,plain,
( slcrc0 = xS
| aElementOf0(szmzazxdt0(xS),szNzAzT0) ),
inference(resolve,[status(thm)],[c_88,c_77]) ).
cnf(c_246,plain,
aElementOf0(sK0(sz00),xS),
inference(resolve,[status(thm)],[c_140,c_57]) ).
cnf(c_320,plain,
( aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0)
| slcrc0 = xS ),
inference(resolve,[status(thm)],[c_203,c_139]) ).
cnf(c_544,plain,
slcrc0 != xS,
inference(resolve,[status(thm)],[c_246,c_179]) ).
cnf(c_599,plain,
aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0),
inference(resolve,[status(thm)],[c_544,c_320]) ).
cnf(c_644,plain,
~ aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0),
inference(resolve,[status(thm)],[c_544,c_202]) ).
cnf(c_643,plain,
$false,
inference(resolve,[status(thm)],[c_599,c_644]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM545+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 03:10:32 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 2016799 was started by sandbox2 on n014,
% 0.10/0.37 % Sat Sep 26 03:10:32 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 0.10/0.43
% 0.10/0.43 % SZS status Theorem for theBenchmark
% 0.10/0.43
% 0.10/0.43 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.10/0.43 % Length of proof is 22.
% 0.10/0.43 % Level of proof is 6.
% 0.10/0.43 % Maximum clause weight is 29.000.
% 0.10/0.43 % Given clauses 178.
% 0.10/0.43
% 0.10/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------