%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM540+1 : 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 08:17:20 AM UTC 2026
% Result : Theorem 0.82s 0.58s
% Output : CNFRefutation 0.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 11 unt; 0 def)
% Number of atoms : 122 ( 24 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 150 ( 56 ~; 68 |; 21 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 2 sgn 28 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefEmp,axiom,
! [W0] :
( W0 = slcrc0
<=> ( ~ ? [W1] : aElementOf0(W1,W0)
& aSet0(W0) ) ),
file('theBenchmark.p',mDefEmp) ).
fof(mNoScLessZr,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ~ sdtlseqdt0(szszuzczcdt0(W0),sz00) ),
file('theBenchmark.p',mNoScLessZr) ).
fof(mDefSeg,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( W1 = slbdtrb0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ( sdtlseqdt0(szszuzczcdt0(W2),W0)
& aElementOf0(W2,szNzAzT0) ) )
& aSet0(W1) ) ) ),
file('theBenchmark.p',mDefSeg) ).
fof(m__,conjecture,
slbdtrb0(sz00) = slcrc0,
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
slbdtrb0(sz00) != slcrc0,
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_51,negated_conjecture,
slbdtrb0(sz00) != slcrc0,
inference(clausify,[status(thm)],[m___neg]) ).
fof(nnf_48,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ( ~ sdtlseqdt0(szszuzczcdt0(W2),W0)
| ~ aElementOf0(W2,szNzAzT0)
| ~ aElementOf0(W2,W1) )
& ( ( sdtlseqdt0(szszuzczcdt0(W2),W0)
& aElementOf0(W2,szNzAzT0) )
| aElementOf0(W2,W1) ) )
| ~ aSet0(W1)
| slbdtrb0(W0) = W1 )
& ( ( ! [X0] :
( ( ~ sdtlseqdt0(szszuzczcdt0(X0),W0)
| ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(X0,W1) )
& ( ( sdtlseqdt0(szszuzczcdt0(X0),W0)
& aElementOf0(X0,szNzAzT0) )
| ~ aElementOf0(X0,W1) ) )
& aSet0(W1) )
| slbdtrb0(W0) != W1 ) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mDefSeg]) ).
fof(sk_mDefSeg_sk,plain,
! [W0] :
( ! [W1] :
( ( ( ( ~ sdtlseqdt0(szszuzczcdt0(sK0(W0,W1)),W0)
| ~ aElementOf0(sK0(W0,W1),szNzAzT0)
| ~ aElementOf0(sK0(W0,W1),W1) )
& ( ( sdtlseqdt0(szszuzczcdt0(sK0(W0,W1)),W0)
& aElementOf0(sK0(W0,W1),szNzAzT0) )
| aElementOf0(sK0(W0,W1),W1) ) )
| ~ aSet0(W1)
| slbdtrb0(W0) = W1 )
& ( ( ! [X0] :
( ( ~ sdtlseqdt0(szszuzczcdt0(X0),W0)
| ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(X0,W1) )
& ( ( sdtlseqdt0(szszuzczcdt0(X0),W0)
& aElementOf0(X0,szNzAzT0) )
| ~ aElementOf0(X0,W1) ) )
& aSet0(W1) )
| slbdtrb0(W0) != W1 ) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W2,sK0(W0,W1))],[nnf_48]) ).
fof(sk_mDefSeg,plain,
( ! [VAR_0,VAR_1] :
( ~ sdtlseqdt0(szszuzczcdt0(sK0(VAR_0,VAR_1)),VAR_0)
| ~ aElementOf0(sK0(VAR_0,VAR_1),szNzAzT0)
| ~ aElementOf0(sK0(VAR_0,VAR_1),VAR_1)
| ~ aSet0(VAR_1)
| slbdtrb0(VAR_0) = VAR_1
| ~ aElementOf0(VAR_0,szNzAzT0) )
& ! [VAR_0,VAR_1] :
( sdtlseqdt0(szszuzczcdt0(sK0(VAR_0,VAR_1)),VAR_0)
| aElementOf0(sK0(VAR_0,VAR_1),VAR_1)
| ~ aSet0(VAR_1)
| slbdtrb0(VAR_0) = VAR_1
| ~ aElementOf0(VAR_0,szNzAzT0) )
& ! [VAR_0,VAR_1] :
( aElementOf0(sK0(VAR_0,VAR_1),szNzAzT0)
| aElementOf0(sK0(VAR_0,VAR_1),VAR_1)
| ~ aSet0(VAR_1)
| slbdtrb0(VAR_0) = VAR_1
| ~ aElementOf0(VAR_0,szNzAzT0) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ sdtlseqdt0(szszuzczcdt0(VAR_2),VAR_0)
| ~ aElementOf0(VAR_2,szNzAzT0)
| aElementOf0(VAR_2,VAR_1)
| slbdtrb0(VAR_0) != VAR_1
| ~ aElementOf0(VAR_0,szNzAzT0) )
& ! [VAR_0,VAR_1,VAR_2] :
( sdtlseqdt0(szszuzczcdt0(VAR_2),VAR_0)
| ~ aElementOf0(VAR_2,VAR_1)
| slbdtrb0(VAR_0) != VAR_1
| ~ aElementOf0(VAR_0,szNzAzT0) )
& ! [VAR_0,VAR_1,VAR_2] :
( aElementOf0(VAR_2,szNzAzT0)
| ~ aElementOf0(VAR_2,VAR_1)
| slbdtrb0(VAR_0) != VAR_1
| ~ aElementOf0(VAR_0,szNzAzT0) )
& ! [VAR_0,VAR_1] :
( aSet0(VAR_1)
| slbdtrb0(VAR_0) != VAR_1
| ~ aElementOf0(VAR_0,szNzAzT0) ) ),
inference(cnf_transformation,[status(thm)],[sk_mDefSeg_sk]) ).
cnf(c_54,plain,
( sdtlseqdt0(szszuzczcdt0(sK0(A,B)),A)
| aElementOf0(sK0(A,B),B)
| ~ aSet0(B)
| slbdtrb0(A) = B
| ~ aElementOf0(A,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[sk_mDefSeg]) ).
cnf(c_55,plain,
( aElementOf0(sK0(A,B),szNzAzT0)
| aElementOf0(sK0(A,B),B)
| ~ aSet0(B)
| slbdtrb0(A) = B
| ~ aElementOf0(A,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[sk_mDefSeg]) ).
cnf(c_87,plain,
( ~ sdtlseqdt0(szszuzczcdt0(A),sz00)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mNoScLessZr]) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('theBenchmark.p',mZeroNum) ).
cnf(c_95,plain,
aElementOf0(sz00,szNzAzT0),
inference(clausify,[status(thm)],[mZeroNum]) ).
cnf(c_134,plain,
( ~ aElementOf0(B,A)
| slcrc0 != A ),
inference(clausify,[status(thm)],[mDefEmp]) ).
cnf(c_135,plain,
( aSet0(A)
| slcrc0 != A ),
inference(clausify,[status(thm)],[mDefEmp]) ).
cnf(c_163,plain,
( aElementOf0(sK0(sz00,A),szNzAzT0)
| aElementOf0(sK0(sz00,A),A)
| ~ aSet0(A)
| slbdtrb0(sz00) = A ),
inference(resolve,[status(thm)],[c_95,c_55]) ).
cnf(c_164,plain,
( sdtlseqdt0(szszuzczcdt0(sK0(sz00,A)),sz00)
| aElementOf0(sK0(sz00,A),A)
| ~ aSet0(A)
| slbdtrb0(sz00) = A ),
inference(resolve,[status(thm)],[c_95,c_54]) ).
cnf(c_193,plain,
~ aElementOf0(A,slcrc0),
inference(xxres,[status(thm)],[c_134]) ).
cnf(c_195,plain,
aSet0(slcrc0),
inference(xxres,[status(thm)],[c_135]) ).
cnf(c_691,plain,
( aElementOf0(sK0(sz00,slcrc0),szNzAzT0)
| aElementOf0(sK0(sz00,slcrc0),slcrc0)
| slbdtrb0(sz00) = slcrc0 ),
inference(resolve,[status(thm)],[c_163,c_195]) ).
cnf(c_692,negated_conjecture,
( aElementOf0(sK0(sz00,slcrc0),szNzAzT0)
| aElementOf0(sK0(sz00,slcrc0),slcrc0) ),
inference(resolve,[status(thm)],[c_51,c_691]) ).
cnf(c_478,negated_conjecture,
aElementOf0(sK0(sz00,slcrc0),szNzAzT0),
inference(resolve,[status(thm)],[c_193,c_692]) ).
cnf(c_693,plain,
( sdtlseqdt0(szszuzczcdt0(sK0(sz00,slcrc0)),sz00)
| aElementOf0(sK0(sz00,slcrc0),slcrc0)
| slbdtrb0(sz00) = slcrc0 ),
inference(resolve,[status(thm)],[c_164,c_195]) ).
cnf(c_694,negated_conjecture,
( sdtlseqdt0(szszuzczcdt0(sK0(sz00,slcrc0)),sz00)
| aElementOf0(sK0(sz00,slcrc0),slcrc0) ),
inference(resolve,[status(thm)],[c_51,c_693]) ).
cnf(c_479,negated_conjecture,
sdtlseqdt0(szszuzczcdt0(sK0(sz00,slcrc0)),sz00),
inference(resolve,[status(thm)],[c_193,c_694]) ).
cnf(c_695,plain,
~ sdtlseqdt0(szszuzczcdt0(sK0(sz00,slcrc0)),sz00),
inference(resolve,[status(thm)],[c_87,c_478]) ).
cnf(c_690,plain,
$false,
inference(resolve,[status(thm)],[c_479,c_695]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM540+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % 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 03:11:08 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 1894494 was started by sandbox on n003,
% 0.09/0.35 % Sat Sep 26 03:11:08 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 0.82/0.58
% 0.82/0.58 % SZS status Theorem for theBenchmark
% 0.82/0.58
% 0.82/0.58 % Proof 1 at 0.18 (+ 0.02) seconds.
% 0.82/0.58 % Length of proof is 18.
% 0.82/0.58 % Level of proof is 4.
% 0.82/0.58 % Maximum clause weight is 35.000.
% 0.82/0.58 % Given clauses 173.
% 0.82/0.58
% 0.82/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------