%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM550+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 : n013.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 0.10s 0.49s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 13 unt; 0 def)
% Number of atoms : 240 ( 61 equ)
% Maximal formula atoms : 67 ( 8 avg)
% Number of connectives : 309 ( 99 ~; 86 |; 108 &)
% ( 1 <=>; 15 =>; 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 : 63 ( 0 sgn 50 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mCardEmpty,axiom,
! [W0] :
( aSet0(W0)
=> ( sbrdtbr0(W0) = sz00
<=> W0 = slcrc0 ) ),
file('theBenchmark.p',mCardEmpty) ).
fof(m__2202_02,axiom,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('theBenchmark.p',m__2202_02) ).
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__2291,axiom,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ),
file('theBenchmark.p',m__2291) ).
fof(m__,conjecture,
~ ( xQ = slcrc0
& ~ ? [W0] : aElementOf0(W0,xQ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ~ ( xQ = slcrc0
& ~ ? [W0] : aElementOf0(W0,xQ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_63,negated_conjecture,
xQ = slcrc0,
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_64,negated_conjecture,
slcrc0 = xQ,
inference(copy,[status(thm)],[c_63]) ).
cnf(c_66,plain,
sbrdtbr0(xQ) = xk,
inference(clausify,[status(thm)],[m__2291]) ).
cnf(c_67,plain,
xk = sbrdtbr0(xQ),
inference(copy,[status(thm)],[c_66]) ).
cnf(c_69,plain,
aSet0(xQ),
inference(clausify,[status(thm)],[m__2291]) ).
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_77,plain,
aElementOf0(sK0,slbdtsldtrb0(xS,xk)),
inference(split_conjunct,[status(thm)],[sk_m__2227]) ).
cnf(c_78,plain,
aElementOf0(sK0,slbdtsldtrb0(xS,sbrdtbr0(xQ))),
inference(paramod,[status(thm)],[c_67,c_77]) ).
cnf(c_85,plain,
( sbrdtbr0(A) = xk
| ~ aElementOf0(A,slbdtsldtrb0(xS,xk)) ),
inference(split_conjunct,[status(thm)],[sk_m__2227]) ).
cnf(c_402,plain,
( sbrdtbr0(A) = xk
| ~ aElementOf0(A,slbdtsldtrb0(xS,sbrdtbr0(xQ))) ),
inference(paramod,[status(thm)],[c_67,c_85]) ).
cnf(c_403,plain,
( sbrdtbr0(A) = sbrdtbr0(xQ)
| ~ aElementOf0(A,slbdtsldtrb0(xS,sbrdtbr0(xQ))) ),
inference(paramod,[status(thm)],[c_67,c_402]) ).
cnf(c_86,plain,
( sbrdtbr0(xQ) = sbrdtbr0(A)
| ~ aElementOf0(A,slbdtsldtrb0(xS,sbrdtbr0(xQ))) ),
inference(copy,[status(thm)],[c_403]) ).
cnf(c_124,plain,
xk != sz00,
inference(clausify,[status(thm)],[m__2202_02]) ).
cnf(c_125,plain,
sbrdtbr0(xQ) != sz00,
inference(paramod,[status(thm)],[c_67,c_124]) ).
cnf(c_183,plain,
( slcrc0 != A
| sbrdtbr0(A) = sz00
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mCardEmpty]) ).
cnf(c_184,plain,
( xQ != A
| sbrdtbr0(A) = sz00
| ~ aSet0(A) ),
inference(paramod,[status(thm)],[c_64,c_183]) ).
cnf(c_275,plain,
sbrdtbr0(xQ) = sbrdtbr0(sK0),
inference(resolve,[status(thm)],[c_86,c_78]) ).
cnf(c_279,plain,
sbrdtbr0(sK0) != sz00,
inference(paramod,[status(thm)],[c_275,c_125]) ).
cnf(c_404,plain,
( xQ != xQ
| sbrdtbr0(xQ) = sz00 ),
inference(resolve,[status(thm)],[c_184,c_69]) ).
cnf(c_405,plain,
( xQ != xQ
| sbrdtbr0(sK0) = sz00 ),
inference(paramod,[status(thm)],[c_275,c_404]) ).
cnf(c_406,plain,
sbrdtbr0(sK0) = sz00,
inference(copy,[status(thm)],[c_405]) ).
cnf(c_401,plain,
$false,
inference(resolve,[status(thm)],[c_279,c_406]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM550+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n013.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 03:11:21 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1815847 was started by sandbox on n013,
% 0.10/0.37 % Sat Sep 26 03:11:21 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 0.10/0.42 --- backtrace (16 frames) ---
% 0.10/0.42 [0x41fd9f]
% 0.10/0.42 [0x484fd0]
% 0.10/0.42 [0x467349]
% 0.10/0.42 [0x46b3ab]
% 0.10/0.42 [0x416b10]
% 0.10/0.42 [0x41887f]
% 0.10/0.42 [0x466dba]
% 0.10/0.42 [0x466eb1]
% 0.10/0.42 [0x41b799]
% 0.10/0.42 [0x4039a8]
% 0.10/0.42 [0x403f27]
% 0.10/0.42 [0x4049d4]
% 0.10/0.42 [0x402997]
% 0.10/0.42 [0x482698]
% 0.10/0.42 [0x484860]
% 0.10/0.42 [0x402a35]
% 0.10/0.42 --- end backtrace ---
% 0.10/0.45 --- backtrace (16 frames) ---
% 0.10/0.45 [0x41fd9f]
% 0.10/0.45 [0x484fd0]
% 0.10/0.45 [0x467349]
% 0.10/0.45 [0x46b3ab]
% 0.10/0.45 [0x416b10]
% 0.10/0.45 [0x41887f]
% 0.10/0.45 [0x466dba]
% 0.10/0.45 [0x466eb1]
% 0.10/0.45 [0x41b799]
% 0.10/0.45 [0x4039a8]
% 0.10/0.45 [0x40412f]
% 0.10/0.45 [0x4049d4]
% 0.10/0.45 [0x402997]
% 0.10/0.45 [0x482698]
% 0.10/0.45 [0x484860]
% 0.10/0.45 [0x402a35]
% 0.10/0.45 --- end backtrace ---
% 0.10/0.45 --- backtrace (16 frames) ---
% 0.10/0.45 [0x41fd9f]
% 0.10/0.45 [0x484fd0]
% 0.10/0.45 [0x467349]
% 0.10/0.45 [0x46b3ab]
% 0.10/0.45 [0x416b10]
% 0.10/0.45 [0x41887f]
% 0.10/0.45 [0x466dba]
% 0.10/0.45 [0x466eb1]
% 0.10/0.45 [0x41b799]
% 0.10/0.45 [0x4039a8]
% 0.10/0.45 [0x403f27]
% 0.10/0.45 [0x4049d4]
% 0.10/0.45 [0x402997]
% 0.10/0.45 [0x482698]
% 0.10/0.45 [0x484860]
% 0.10/0.45 [0x402a35]
% 0.10/0.45 --- end backtrace ---
% 0.10/0.49
% 0.10/0.49 % SZS status Theorem for theBenchmark
% 0.10/0.49
% 0.10/0.49 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.10/0.49 % Length of proof is 21.
% 0.10/0.49 % Level of proof is 6.
% 0.10/0.49 % Maximum clause weight is 26.000.
% 0.10/0.49 % Given clauses 58.
% 0.10/0.49
% 0.10/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------