%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM549+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 : n003.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 0.13s 0.46s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 17 unt; 0 def)
% Number of atoms : 284 ( 71 equ)
% Maximal formula atoms : 67 ( 6 avg)
% Number of connectives : 354 ( 115 ~; 105 |; 115 &)
% ( 2 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 61 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mEOfElem,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('theBenchmark.p',mEOfElem) ).
fof(mDefEmp,axiom,
! [W0] :
( W0 = slcrc0
<=> ( ~ ? [W1] : aElementOf0(W1,W0)
& aSet0(W0) ) ),
file('theBenchmark.p',mDefEmp) ).
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,
? [W0] :
( aElementOf0(W0,xQ)
& aElement0(W0) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ? [W0] :
( aElementOf0(W0,xQ)
& aElement0(W0) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_63,negated_conjecture,
( ~ aElementOf0(A,xQ)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_64,plain,
sbrdtbr0(xQ) = xk,
inference(clausify,[status(thm)],[m__2291]) ).
cnf(c_65,plain,
xk = sbrdtbr0(xQ),
inference(copy,[status(thm)],[c_64]) ).
cnf(c_67,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(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_76,plain,
aElementOf0(sK0,slbdtsldtrb0(xS,xk)),
inference(split_conjunct,[status(thm)],[sk_m__2227]) ).
cnf(c_77,plain,
aElementOf0(sK0,slbdtsldtrb0(xS,sbrdtbr0(xQ))),
inference(paramod,[status(thm)],[c_65,c_76]) ).
cnf(c_84,plain,
( sbrdtbr0(A) = xk
| ~ aElementOf0(A,slbdtsldtrb0(xS,xk)) ),
inference(split_conjunct,[status(thm)],[sk_m__2227]) ).
cnf(c_723,plain,
( sbrdtbr0(A) = xk
| ~ aElementOf0(A,slbdtsldtrb0(xS,sbrdtbr0(xQ))) ),
inference(paramod,[status(thm)],[c_65,c_84]) ).
cnf(c_724,plain,
( sbrdtbr0(A) = sbrdtbr0(xQ)
| ~ aElementOf0(A,slbdtsldtrb0(xS,sbrdtbr0(xQ))) ),
inference(paramod,[status(thm)],[c_65,c_723]) ).
cnf(c_85,plain,
( sbrdtbr0(xQ) = sbrdtbr0(A)
| ~ aElementOf0(A,slbdtsldtrb0(xS,sbrdtbr0(xQ))) ),
inference(copy,[status(thm)],[c_724]) ).
cnf(c_123,plain,
xk != sz00,
inference(clausify,[status(thm)],[m__2202_02]) ).
cnf(c_124,plain,
sbrdtbr0(xQ) != sz00,
inference(paramod,[status(thm)],[c_65,c_123]) ).
fof(mSegZero,axiom,
slbdtrb0(sz00) = slcrc0,
file('theBenchmark.p',mSegZero) ).
cnf(c_147,plain,
slbdtrb0(sz00) = slcrc0,
inference(clausify,[status(thm)],[mSegZero]) ).
cnf(c_148,plain,
slcrc0 = slbdtrb0(sz00),
inference(copy,[status(thm)],[c_147]) ).
cnf(c_181,plain,
( slcrc0 != A
| sbrdtbr0(A) = sz00
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mCardEmpty]) ).
cnf(c_182,plain,
( slbdtrb0(sz00) != A
| sbrdtbr0(A) = sz00
| ~ aSet0(A) ),
inference(paramod,[status(thm)],[c_148,c_181]) ).
fof(nnf_5,plain,
! [W0] :
( ( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| slcrc0 = W0 )
& ( ( ! [X7] : ~ aElementOf0(X7,W0)
& aSet0(W0) )
| slcrc0 != W0 ) ),
inference(fof_nnf,[status(thm)],[mDefEmp]) ).
fof(sk_mDefEmp_sk,plain,
! [W0] :
( ( aElementOf0(sK1(W0),W0)
| ~ aSet0(W0)
| slcrc0 = W0 )
& ( ( ! [X7] : ~ aElementOf0(X7,W0)
& aSet0(W0) )
| slcrc0 != W0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(W1,sK1(W0))],[nnf_5]) ).
fof(sk_mDefEmp,plain,
( ! [VAR_0] :
( aElementOf0(sK1(VAR_0),VAR_0)
| ~ aSet0(VAR_0)
| slcrc0 = VAR_0 )
& ! [VAR_0,VAR_1] :
( ~ aElementOf0(VAR_1,VAR_0)
| slcrc0 != VAR_0 )
& ! [VAR_0] :
( aSet0(VAR_0)
| slcrc0 != VAR_0 ) ),
inference(cnf_transformation,[status(thm)],[sk_mDefEmp_sk]) ).
cnf(c_243,plain,
( aElementOf0(sK1(A),A)
| ~ aSet0(A)
| slcrc0 = A ),
inference(split_conjunct,[status(thm)],[sk_mDefEmp]) ).
cnf(c_244,plain,
( aElementOf0(sK1(A),A)
| ~ aSet0(A)
| slbdtrb0(sz00) = A ),
inference(paramod,[status(thm)],[c_148,c_243]) ).
cnf(c_249,plain,
( aElement0(B)
| ~ aElementOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mEOfElem]) ).
cnf(c_276,plain,
sbrdtbr0(xQ) = sbrdtbr0(sK0),
inference(resolve,[status(thm)],[c_85,c_77]) ).
cnf(c_281,plain,
sbrdtbr0(sK0) != sz00,
inference(paramod,[status(thm)],[c_276,c_124]) ).
cnf(c_725,plain,
( slbdtrb0(sz00) != xQ
| sbrdtbr0(xQ) = sz00 ),
inference(resolve,[status(thm)],[c_182,c_67]) ).
cnf(c_726,plain,
( slbdtrb0(sz00) != xQ
| sbrdtbr0(sK0) = sz00 ),
inference(paramod,[status(thm)],[c_276,c_725]) ).
cnf(c_315,plain,
slbdtrb0(sz00) != xQ,
inference(resolve,[status(thm)],[c_281,c_726]) ).
cnf(c_727,plain,
( aElementOf0(sK1(xQ),xQ)
| slbdtrb0(sz00) = xQ ),
inference(resolve,[status(thm)],[c_244,c_67]) ).
cnf(c_397,plain,
aElementOf0(sK1(xQ),xQ),
inference(resolve,[status(thm)],[c_315,c_727]) ).
cnf(c_728,plain,
( aElement0(sK1(xQ))
| ~ aSet0(xQ) ),
inference(resolve,[status(thm)],[c_397,c_249]) ).
cnf(c_709,plain,
aElement0(sK1(xQ)),
inference(resolve,[status(thm)],[c_67,c_728]) ).
cnf(c_729,negated_conjecture,
~ aElement0(sK1(xQ)),
inference(resolve,[status(thm)],[c_397,c_63]) ).
cnf(c_722,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_709,c_729]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM549+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 03:13:38 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1903178 was started by sandbox on n003,
% 0.09/0.36 % Sat Sep 26 03:13:38 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.46
% 0.13/0.46 % SZS status Theorem for theBenchmark
% 0.13/0.46
% 0.13/0.46 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.13/0.46 % Length of proof is 30.
% 0.13/0.46 % Level of proof is 9.
% 0.13/0.46 % Maximum clause weight is 11.000.
% 0.13/0.46 % Given clauses 183.
% 0.13/0.46
% 0.13/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
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