%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM548+3 : 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 : n001.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 08:17:22 AM UTC 2026
% Result : Theorem 0.09s 0.44s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 15 unt; 0 def)
% Number of atoms : 236 ( 42 equ)
% Maximal formula atoms : 67 ( 8 avg)
% Number of connectives : 299 ( 91 ~; 85 |; 106 &)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn 51 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mCardNum,axiom,
! [W0] :
( aSet0(W0)
=> ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
file('theBenchmark.p',mCardNum) ).
fof(m__2227,axiom,
( ~ ( ! [W0] :
( ( ( sbrdtbr0(W0) = xk
& ( aSubsetOf0(W0,xS)
| ( ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) ) ) )
=> aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) ) ) )
=> ( slbdtsldtrb0(xS,xk) = slcrc0
| ~ ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
& ! [W0] :
( ( ( sbrdtbr0(W0) = xk
& ( aSubsetOf0(W0,xT)
| ( ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) )
& aSet0(W0) ) ) )
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
& ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
=> ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xT)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) )
& aSet0(W0) ) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [W0] :
( ( ( sbrdtbr0(W0) = xk
& ( aSubsetOf0(W0,xS)
| ( ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) ) ) )
=> aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) ) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
file('theBenchmark.p',m__2227) ).
fof(m__2270,axiom,
( aElementOf0(xQ,slbdtsldtrb0(xS,xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,xS)
& ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xS) )
& aSet0(xQ) ),
file('theBenchmark.p',m__2270) ).
fof(m__,conjecture,
isFinite0(xQ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ isFinite0(xQ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_62,negated_conjecture,
~ isFinite0(xQ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_64,plain,
sbrdtbr0(xQ) = xk,
inference(clausify,[status(thm)],[m__2270]) ).
cnf(c_65,plain,
xk = sbrdtbr0(xQ),
inference(copy,[status(thm)],[c_64]) ).
cnf(c_68,plain,
aSet0(xQ),
inference(clausify,[status(thm)],[m__2270]) ).
fof(nnf_59,plain,
( slbdtsldtrb0(xS,xk) != slcrc0
& ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk))
& ! [X7] :
( ( aElementOf0(X7,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X7) != xk
| ( ~ aSubsetOf0(X7,xS)
& ( ? [W1] :
( ~ aElementOf0(W1,xS)
& aElementOf0(W1,X7) )
| ~ aSet0(X7) ) ) )
& ( ( sbrdtbr0(X7) = xk
& aSubsetOf0(X7,xS)
& ! [X8] :
( aElementOf0(X8,xS)
| ~ aElementOf0(X8,X7) )
& aSet0(X7) )
| ~ aElementOf0(X7,slbdtsldtrb0(xS,xk)) ) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [X6] :
( aElementOf0(X6,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X6,slbdtsldtrb0(xS,xk)) )
& ! [X3] :
( ( aElementOf0(X3,slbdtsldtrb0(xT,xk))
| sbrdtbr0(X3) != xk
| ( ~ aSubsetOf0(X3,xT)
& ( ? [X5] :
( ~ aElementOf0(X5,xT)
& aElementOf0(X5,X3) )
| ~ aSet0(X3) ) ) )
& ( ( sbrdtbr0(X3) = xk
& aSubsetOf0(X3,xT)
& ! [X4] :
( aElementOf0(X4,xT)
| ~ aElementOf0(X4,X3) )
& aSet0(X3) )
| ~ aElementOf0(X3,slbdtsldtrb0(xT,xk)) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X0] :
( ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X0) != xk
| ( ~ aSubsetOf0(X0,xS)
& ( ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,X0) )
| ~ aSet0(X0) ) ) )
& ( ( sbrdtbr0(X0) = xk
& aSubsetOf0(X0,xS)
& ! [X1] :
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,X0) )
& aSet0(X0) )
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
inference(fof_nnf,[status(thm)],[m__2227]) ).
fof(sk_m__2227_sk,plain,
( slbdtsldtrb0(xS,xk) != slcrc0
& aElementOf0(sK0,slbdtsldtrb0(xS,xk))
& ! [X7] :
( ( aElementOf0(X7,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X7) != xk
| ( ~ aSubsetOf0(X7,xS)
& ( ( ~ aElementOf0(sK3(X7),xS)
& aElementOf0(sK3(X7),X7) )
| ~ aSet0(X7) ) ) )
& ( ( sbrdtbr0(X7) = xk
& aSubsetOf0(X7,xS)
& ! [X8] :
( aElementOf0(X8,xS)
| ~ aElementOf0(X8,X7) )
& aSet0(X7) )
| ~ aElementOf0(X7,slbdtsldtrb0(xS,xk)) ) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [X6] :
( aElementOf0(X6,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X6,slbdtsldtrb0(xS,xk)) )
& ! [X3] :
( ( aElementOf0(X3,slbdtsldtrb0(xT,xk))
| sbrdtbr0(X3) != xk
| ( ~ aSubsetOf0(X3,xT)
& ( ( ~ aElementOf0(sK2(X3),xT)
& aElementOf0(sK2(X3),X3) )
| ~ aSet0(X3) ) ) )
& ( ( sbrdtbr0(X3) = xk
& aSubsetOf0(X3,xT)
& ! [X4] :
( aElementOf0(X4,xT)
| ~ aElementOf0(X4,X3) )
& aSet0(X3) )
| ~ aElementOf0(X3,slbdtsldtrb0(xT,xk)) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X0] :
( ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X0) != xk
| ( ~ aSubsetOf0(X0,xS)
& ( ( ~ aElementOf0(sK1(X0),xS)
& aElementOf0(sK1(X0),X0) )
| ~ aSet0(X0) ) ) )
& ( ( sbrdtbr0(X0) = xk
& aSubsetOf0(X0,xS)
& ! [X1] :
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,X0) )
& aSet0(X0) )
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK0]),skolemize(X2,sK1(X0)),skolemize(X5,sK2(X3)),skolemize(W1,sK3(X7)),skolemize(W0,sK0)],[nnf_59]) ).
fof(sk_m__2227,plain,
( slbdtsldtrb0(xS,xk) != slcrc0
& aElementOf0(sK0,slbdtsldtrb0(xS,xk))
& ! [VAR_0] :
( aElementOf0(VAR_0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(VAR_0) != xk
| ~ aSubsetOf0(VAR_0,xS) )
& ! [VAR_0] :
( aElementOf0(VAR_0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(VAR_0) != xk
| ~ aElementOf0(sK3(VAR_0),xS)
| ~ aSet0(VAR_0) )
& ! [VAR_0] :
( aElementOf0(VAR_0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(VAR_0) != xk
| aElementOf0(sK3(VAR_0),VAR_0)
| ~ aSet0(VAR_0) )
& ! [VAR_0] :
( sbrdtbr0(VAR_0) = xk
| ~ aElementOf0(VAR_0,slbdtsldtrb0(xS,xk)) )
& ! [VAR_0] :
( aSubsetOf0(VAR_0,xS)
| ~ aElementOf0(VAR_0,slbdtsldtrb0(xS,xk)) )
& ! [VAR_0,VAR_1] :
( aElementOf0(VAR_1,xS)
| ~ aElementOf0(VAR_1,VAR_0)
| ~ aElementOf0(VAR_0,slbdtsldtrb0(xS,xk)) )
& ! [VAR_0] :
( aSet0(VAR_0)
| ~ aElementOf0(VAR_0,slbdtsldtrb0(xS,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [VAR_0] :
( aElementOf0(VAR_0,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(VAR_0,slbdtsldtrb0(xS,xk)) )
& ! [VAR_0] :
( aElementOf0(VAR_0,slbdtsldtrb0(xT,xk))
| sbrdtbr0(VAR_0) != xk
| ~ aSubsetOf0(VAR_0,xT) )
& ! [VAR_0] :
( aElementOf0(VAR_0,slbdtsldtrb0(xT,xk))
| sbrdtbr0(VAR_0) != xk
| ~ aElementOf0(sK2(VAR_0),xT)
| ~ aSet0(VAR_0) )
& ! [VAR_0] :
( aElementOf0(VAR_0,slbdtsldtrb0(xT,xk))
| sbrdtbr0(VAR_0) != xk
| aElementOf0(sK2(VAR_0),VAR_0)
| ~ aSet0(VAR_0) )
& ! [VAR_0] :
( sbrdtbr0(VAR_0) = xk
| ~ aElementOf0(VAR_0,slbdtsldtrb0(xT,xk)) )
& ! [VAR_0] :
( aSubsetOf0(VAR_0,xT)
| ~ aElementOf0(VAR_0,slbdtsldtrb0(xT,xk)) )
& ! [VAR_0,VAR_1] :
( aElementOf0(VAR_1,xT)
| ~ aElementOf0(VAR_1,VAR_0)
| ~ aElementOf0(VAR_0,slbdtsldtrb0(xT,xk)) )
& ! [VAR_0] :
( aSet0(VAR_0)
| ~ aElementOf0(VAR_0,slbdtsldtrb0(xT,xk)) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [VAR_0] :
( aElementOf0(VAR_0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(VAR_0) != xk
| ~ aSubsetOf0(VAR_0,xS) )
& ! [VAR_0] :
( aElementOf0(VAR_0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(VAR_0) != xk
| ~ aElementOf0(sK1(VAR_0),xS)
| ~ aSet0(VAR_0) )
& ! [VAR_0] :
( aElementOf0(VAR_0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(VAR_0) != xk
| aElementOf0(sK1(VAR_0),VAR_0)
| ~ aSet0(VAR_0) )
& ! [VAR_0] :
( sbrdtbr0(VAR_0) = xk
| ~ aElementOf0(VAR_0,slbdtsldtrb0(xS,xk)) )
& ! [VAR_0] :
( aSubsetOf0(VAR_0,xS)
| ~ aElementOf0(VAR_0,slbdtsldtrb0(xS,xk)) )
& ! [VAR_0,VAR_1] :
( aElementOf0(VAR_1,xS)
| ~ aElementOf0(VAR_1,VAR_0)
| ~ aElementOf0(VAR_0,slbdtsldtrb0(xS,xk)) )
& ! [VAR_0] :
( aSet0(VAR_0)
| ~ aElementOf0(VAR_0,slbdtsldtrb0(xS,xk)) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
inference(cnf_transformation,[status(thm)],[sk_m__2227_sk]) ).
cnf(c_72,plain,
aElementOf0(sK0,slbdtsldtrb0(xS,xk)),
inference(split_conjunct,[status(thm)],[sk_m__2227]) ).
cnf(c_73,plain,
aElementOf0(sK0,slbdtsldtrb0(xS,sbrdtbr0(xQ))),
inference(paramod,[status(thm)],[c_65,c_72]) ).
cnf(c_80,plain,
( sbrdtbr0(A) = xk
| ~ aElementOf0(A,slbdtsldtrb0(xS,xk)) ),
inference(split_conjunct,[status(thm)],[sk_m__2227]) ).
cnf(c_413,plain,
( sbrdtbr0(A) = xk
| ~ aElementOf0(A,slbdtsldtrb0(xS,sbrdtbr0(xQ))) ),
inference(paramod,[status(thm)],[c_65,c_80]) ).
cnf(c_414,plain,
( sbrdtbr0(A) = sbrdtbr0(xQ)
| ~ aElementOf0(A,slbdtsldtrb0(xS,sbrdtbr0(xQ))) ),
inference(paramod,[status(thm)],[c_65,c_413]) ).
cnf(c_81,plain,
( sbrdtbr0(xQ) = sbrdtbr0(A)
| ~ aElementOf0(A,slbdtsldtrb0(xS,sbrdtbr0(xQ))) ),
inference(copy,[status(thm)],[c_414]) ).
fof(m__2202,axiom,
aElementOf0(xk,szNzAzT0),
file('theBenchmark.p',m__2202) ).
cnf(c_123,plain,
aElementOf0(xk,szNzAzT0),
inference(clausify,[status(thm)],[m__2202]) ).
cnf(c_124,plain,
aElementOf0(sbrdtbr0(xQ),szNzAzT0),
inference(paramod,[status(thm)],[c_65,c_123]) ).
cnf(c_182,plain,
( isFinite0(A)
| ~ aElementOf0(sbrdtbr0(A),szNzAzT0)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mCardNum]) ).
cnf(c_273,plain,
sbrdtbr0(xQ) = sbrdtbr0(sK0),
inference(resolve,[status(thm)],[c_81,c_73]) ).
cnf(c_278,plain,
aElementOf0(sbrdtbr0(sK0),szNzAzT0),
inference(paramod,[status(thm)],[c_273,c_124]) ).
cnf(c_415,plain,
( isFinite0(xQ)
| ~ aElementOf0(sbrdtbr0(sK0),szNzAzT0)
| ~ aSet0(xQ) ),
inference(paramod,[status(thm)],[c_273,c_182]) ).
cnf(c_416,plain,
( isFinite0(xQ)
| ~ aElementOf0(sbrdtbr0(sK0),szNzAzT0) ),
inference(resolve,[status(thm)],[c_68,c_415]) ).
cnf(c_417,plain,
isFinite0(xQ),
inference(resolve,[status(thm)],[c_278,c_416]) ).
cnf(c_412,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_62,c_417]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM548+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 03:16:41 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 775228 was started by sandbox on n001,
% 0.09/0.36 % Sat Sep 26 03:16:41 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.44
% 0.09/0.44 % SZS status Theorem for theBenchmark
% 0.09/0.44
% 0.09/0.44 % Proof 1 at 0.03 (+ 0.02) seconds.
% 0.09/0.44 % Length of proof is 18.
% 0.09/0.44 % Level of proof is 6.
% 0.09/0.44 % Maximum clause weight is 11.000.
% 0.09/0.44 % Given clauses 137.
% 0.09/0.44
% 0.09/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------