%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM538+1 : 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 : n010.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 17.83s 2.74s
% Output : CNFRefutation 17.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 15 unt; 0 def)
% Number of atoms : 100 ( 28 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 103 ( 44 ~; 40 |; 7 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 39 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mEOfElem,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('theBenchmark.p',mEOfElem) ).
fof(mDefDiff,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aSet0(W0) )
=> ! [W2] :
( W2 = sdtmndt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) ) )
& aSet0(W2) ) ) ),
file('theBenchmark.p',mDefDiff) ).
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,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(xS),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
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_46,plain,
aElementOf0(xx,xS),
inference(clausify,[status(thm)],[m__1522_02]) ).
cnf(c_47,plain,
isFinite0(xS),
inference(clausify,[status(thm)],[m__1522_02]) ).
fof(m__1522,axiom,
aSet0(xS),
file('theBenchmark.p',m__1522) ).
cnf(c_48,plain,
aSet0(xS),
inference(clausify,[status(thm)],[m__1522]) ).
cnf(c_49,plain,
( sbrdtbr0(sdtpldt0(A,B)) = szszuzczcdt0(sbrdtbr0(A))
| aElementOf0(B,A)
| ~ aElement0(B)
| ~ isFinite0(A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mCardCons]) ).
cnf(c_73,plain,
( isFinite0(sdtmndt0(B,A))
| ~ isFinite0(B)
| ~ aSet0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mFDiffSet]) ).
cnf(c_78,plain,
( sdtpldt0(sdtmndt0(A,B),B) = A
| ~ aElementOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mConsDiff]) ).
cnf(c_84,plain,
( D != B
| ~ aElementOf0(D,C)
| sdtmndt0(A,B) != C
| ~ aElement0(B)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefDiff]) ).
cnf(c_87,plain,
( aSet0(C)
| sdtmndt0(A,B) != C
| ~ aElement0(B)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefDiff]) ).
cnf(c_111,plain,
( aElement0(B)
| ~ aElementOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mEOfElem]) ).
cnf(c_6744,plain,
( sdtpldt0(sdtmndt0(xS,xx),xx) = xS
| ~ aSet0(xS) ),
inference(resolve,[status(thm)],[c_78,c_46]) ).
cnf(c_143,plain,
sdtpldt0(sdtmndt0(xS,xx),xx) = xS,
inference(resolve,[status(thm)],[c_48,c_6744]) ).
cnf(c_6745,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(resolve,[status(thm)],[c_111,c_46]) ).
cnf(c_189,plain,
aElement0(xx),
inference(resolve,[status(thm)],[c_48,c_6745]) ).
cnf(c_6746,plain,
( aSet0(B)
| sdtmndt0(xS,A) != B
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_87,c_48]) ).
cnf(c_6747,plain,
( aSet0(A)
| sdtmndt0(xS,xx) != A ),
inference(resolve,[status(thm)],[c_6746,c_189]) ).
cnf(c_327,plain,
aSet0(sdtmndt0(xS,xx)),
inference(xxres,[status(thm)],[c_6747]) ).
cnf(c_6748,plain,
( isFinite0(sdtmndt0(A,xx))
| ~ isFinite0(A)
| ~ aSet0(A) ),
inference(resolve,[status(thm)],[c_73,c_189]) ).
cnf(c_6749,plain,
( isFinite0(sdtmndt0(xS,xx))
| ~ isFinite0(xS) ),
inference(resolve,[status(thm)],[c_6748,c_48]) ).
cnf(c_348,plain,
isFinite0(sdtmndt0(xS,xx)),
inference(resolve,[status(thm)],[c_6749,c_47]) ).
cnf(c_6750,plain,
( C != A
| ~ aElementOf0(C,B)
| sdtmndt0(xS,A) != B
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_84,c_48]) ).
cnf(c_6751,plain,
( B != xx
| ~ aElementOf0(B,A)
| sdtmndt0(xS,xx) != A ),
inference(resolve,[status(thm)],[c_6750,c_189]) ).
cnf(c_6752,plain,
( A != xx
| ~ aElementOf0(A,sdtmndt0(xS,xx)) ),
inference(xxres,[status(thm)],[c_6751]) ).
cnf(c_353,plain,
~ aElementOf0(xx,sdtmndt0(xS,xx)),
inference(xxres,[status(thm)],[c_6752]) ).
cnf(c_6753,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_49,c_327]) ).
cnf(c_6754,plain,
( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),A)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx)))
| aElementOf0(A,sdtmndt0(xS,xx))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_6753,c_348]) ).
cnf(c_6755,plain,
( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx)))
| aElementOf0(xx,sdtmndt0(xS,xx)) ),
inference(resolve,[status(thm)],[c_6754,c_189]) ).
cnf(c_6756,plain,
( sbrdtbr0(xS) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx)))
| aElementOf0(xx,sdtmndt0(xS,xx)) ),
inference(paramod,[status(thm)],[c_143,c_6755]) ).
cnf(c_6757,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(xS)
| aElementOf0(xx,sdtmndt0(xS,xx)) ),
inference(copy,[status(thm)],[c_6756]) ).
cnf(c_6758,plain,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(xS),
inference(resolve,[status(thm)],[c_353,c_6757]) ).
cnf(c_6743,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_45,c_6758]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM538+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.43 % Computer : n010.cluster.edu
% 0.19/0.43 % Model : x86_64 x86_64
% 0.19/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.43 % Memory : 8046.5625MB
% 0.19/0.43 % OS : Linux 6.8.0-71-generic
% 0.19/0.43 % CPULimit : 300
% 0.19/0.43 % WCLimit : 300
% 0.19/0.43 % DateTime : Sat Sep 26 03:09:14 UTC 2026
% 0.19/0.43 % CPUTime :
% 0.19/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.44 % Process 2347459 was started by sandbox2 on n010,
% 0.19/0.44 % Sat Sep 26 03:09:14 2026
% 0.19/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 17.83/2.74
% 17.83/2.74 % SZS status Theorem for theBenchmark
% 17.83/2.74
% 17.83/2.74 % Proof 1 at 1.97 (+ 0.29) seconds.
% 17.83/2.74 % Length of proof is 24.
% 17.83/2.74 % Level of proof is 4.
% 17.83/2.74 % Maximum clause weight is 32.000.
% 17.83/2.74 % Given clauses 153.
% 17.83/2.74
% 17.83/2.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------