%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM538+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 08:17:19 AM UTC 2026
% Result : Theorem 1.44s 0.61s
% Output : CNFRefutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 13 unt; 0 def)
% Number of atoms : 83 ( 18 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 81 ( 32 ~; 27 |; 9 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mEOfElem,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('theBenchmark.p',mEOfElem) ).
fof(mConsDiff,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ),
file('theBenchmark.p',mConsDiff) ).
fof(mFDiffSet,axiom,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( ( isFinite0(W1)
& aSet0(W1) )
=> isFinite0(sdtmndt0(W1,W0)) ) ),
file('theBenchmark.p',mFDiffSet) ).
fof(mCardCons,axiom,
! [W0] :
( ( isFinite0(W0)
& aSet0(W0) )
=> ! [W1] :
( aElement0(W1)
=> ( ~ aElementOf0(W1,W0)
=> sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) ),
file('theBenchmark.p',mCardCons) ).
fof(m__1522_02,axiom,
( aElementOf0(xx,xS)
& isFinite0(xS) ),
file('theBenchmark.p',m__1522_02) ).
fof(m__,conjecture,
( ( ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(xS) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( ( ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(xS) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_44,negated_conjecture,
sbrdtbr0(xS) != szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_45,negated_conjecture,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS),
inference(copy,[status(thm)],[c_44]) ).
cnf(c_47,negated_conjecture,
( xx != A
| ~ aElementOf0(A,sdtmndt0(xS,xx)) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_50,negated_conjecture,
aSet0(sdtmndt0(xS,xx)),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_51,plain,
aElementOf0(xx,xS),
inference(clausify,[status(thm)],[m__1522_02]) ).
cnf(c_52,plain,
isFinite0(xS),
inference(clausify,[status(thm)],[m__1522_02]) ).
fof(m__1522,axiom,
aSet0(xS),
file('theBenchmark.p',m__1522) ).
cnf(c_53,plain,
aSet0(xS),
inference(clausify,[status(thm)],[m__1522]) ).
cnf(c_54,plain,
( sbrdtbr0(sdtpldt0(A,B)) = szszuzczcdt0(sbrdtbr0(A))
| aElementOf0(B,A)
| ~ aElement0(B)
| ~ isFinite0(A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mCardCons]) ).
cnf(c_78,plain,
( isFinite0(sdtmndt0(B,A))
| ~ isFinite0(B)
| ~ aSet0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mFDiffSet]) ).
cnf(c_83,plain,
( sdtpldt0(sdtmndt0(A,B),B) = A
| ~ aElementOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mConsDiff]) ).
cnf(c_116,plain,
( aElement0(B)
| ~ aElementOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mEOfElem]) ).
cnf(c_128,plain,
~ aElementOf0(xx,sdtmndt0(xS,xx)),
inference(xxres,[status(thm)],[c_47]) ).
cnf(c_130,plain,
( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),A)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx)))
| aElementOf0(A,sdtmndt0(xS,xx))
| ~ aElement0(A)
| ~ isFinite0(sdtmndt0(xS,xx)) ),
inference(resolve,[status(thm)],[c_54,c_50]) ).
cnf(c_715,plain,
( sdtpldt0(sdtmndt0(xS,xx),xx) = xS
| ~ aSet0(xS) ),
inference(resolve,[status(thm)],[c_83,c_51]) ).
cnf(c_179,plain,
sdtpldt0(sdtmndt0(xS,xx),xx) = xS,
inference(resolve,[status(thm)],[c_53,c_715]) ).
cnf(c_716,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(resolve,[status(thm)],[c_116,c_51]) ).
cnf(c_377,plain,
aElement0(xx),
inference(resolve,[status(thm)],[c_53,c_716]) ).
cnf(c_717,plain,
( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx)))
| aElementOf0(xx,sdtmndt0(xS,xx))
| ~ isFinite0(sdtmndt0(xS,xx)) ),
inference(resolve,[status(thm)],[c_377,c_130]) ).
cnf(c_718,plain,
( sbrdtbr0(xS) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx)))
| aElementOf0(xx,sdtmndt0(xS,xx))
| ~ isFinite0(sdtmndt0(xS,xx)) ),
inference(paramod,[status(thm)],[c_179,c_717]) ).
cnf(c_719,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(xS)
| aElementOf0(xx,sdtmndt0(xS,xx))
| ~ isFinite0(sdtmndt0(xS,xx)) ),
inference(copy,[status(thm)],[c_718]) ).
cnf(c_720,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(xS)
| ~ isFinite0(sdtmndt0(xS,xx)) ),
inference(resolve,[status(thm)],[c_128,c_719]) ).
cnf(c_469,negated_conjecture,
~ isFinite0(sdtmndt0(xS,xx)),
inference(resolve,[status(thm)],[c_45,c_720]) ).
cnf(c_721,plain,
( isFinite0(sdtmndt0(xS,A))
| ~ isFinite0(xS)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_78,c_53]) ).
cnf(c_722,plain,
( isFinite0(sdtmndt0(xS,A))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_721,c_52]) ).
cnf(c_723,plain,
~ aElement0(xx),
inference(resolve,[status(thm)],[c_722,c_469]) ).
cnf(c_714,plain,
$false,
inference(resolve,[status(thm)],[c_377,c_723]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM538+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n026.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 03:11:40 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 4155719 was started by sandbox2 on n026,
% 0.11/0.37 % Sat Sep 26 03:11:40 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % From the command line: assign(max_seconds, 300).
% 1.44/0.61
% 1.44/0.61 % SZS status Theorem for theBenchmark
% 1.44/0.61
% 1.44/0.61 % Proof 1 at 0.17 (+ 0.04) seconds.
% 1.44/0.61 % Length of proof is 23.
% 1.44/0.61 % Level of proof is 4.
% 1.44/0.61 % Maximum clause weight is 43.000.
% 1.44/0.61 % Given clauses 126.
% 1.44/0.61
% 1.44/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------