%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM547+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 : 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 08:17:21 AM UTC 2026
% Result : Theorem 0.10s 0.41s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 9 ( 3 unt; 0 def)
% Number of atoms : 211 ( 36 equ)
% Maximal formula atoms : 67 ( 23 avg)
% Number of connectives : 284 ( 82 ~; 80 |; 106 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 11 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 59 ( 1 sgn 51 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
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__,conjecture,
? [W0] :
( aElementOf0(W0,slbdtsldtrb0(xS,xk))
| ( sbrdtbr0(W0) = xk
& ( aSubsetOf0(W0,xS)
| ( ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) ) ) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ? [W0] :
( aElementOf0(W0,slbdtsldtrb0(xS,xk))
| ( sbrdtbr0(W0) = xk
& ( aSubsetOf0(W0,xS)
| ( ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) ) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_61,negated_conjecture,
~ aElementOf0(A,slbdtsldtrb0(xS,xk)),
inference(clausify,[status(thm)],[m___neg]) ).
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(sK4(X7),xS)
& aElementOf0(sK4(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(sK3(X3),xT)
& aElementOf0(sK3(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(sK2(X0),xS)
& aElementOf0(sK2(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,[sK2,sK3,sK4,sK0]),skolemize(X2,sK2(X0)),skolemize(X5,sK3(X3)),skolemize(W1,sK4(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(sK4(VAR_0),xS)
| ~ aSet0(VAR_0) )
& ! [VAR_0] :
( aElementOf0(VAR_0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(VAR_0) != xk
| aElementOf0(sK4(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(sK3(VAR_0),xT)
| ~ aSet0(VAR_0) )
& ! [VAR_0] :
( aElementOf0(VAR_0,slbdtsldtrb0(xT,xk))
| sbrdtbr0(VAR_0) != xk
| aElementOf0(sK3(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(sK2(VAR_0),xS)
| ~ aSet0(VAR_0) )
& ! [VAR_0] :
( aElementOf0(VAR_0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(VAR_0) != xk
| aElementOf0(sK2(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_67,plain,
aElementOf0(sK0,slbdtsldtrb0(xS,xk)),
inference(split_conjunct,[status(thm)],[sk_m__2227]) ).
cnf(c_68,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_61,c_67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM547+3 : 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 03:14:28 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 2984404 was started by sandbox on n015,
% 0.10/0.38 % Sat Sep 26 03:14:28 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 0.10/0.41
% 0.10/0.41 % SZS status Theorem for theBenchmark
% 0.10/0.41
% 0.10/0.41 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.10/0.41 % Length of proof is 5.
% 0.10/0.41 % Level of proof is 2.
% 0.10/0.41 % Maximum clause weight is 5.000.
% 0.10/0.41 % Given clauses 0.
% 0.10/0.41
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------